some refactoring in tests

closes #38, again

.gitignore

@@ -5,3 +5,5 @@ result
 *~
 quox
 quox-tests
+golden-tests/tests/*/output
+golden-tests/tests/*/*.ss

CREDITS.md

@@ -0,0 +1,4 @@
+the "logo" is an edit of [an emoji] made by [khr].
+
+[an emoji]: https://github.com/chr-1x/dragn-emoji
+[khr]: https://dragon.monster

examples/all.quox

@@ -5,3 +5,6 @@ load "maybe.quox"
 load "nat.quox"
 load "pair.quox"
 load "list.quox"
+load "eta.quox"
+load "fail.quox"
+load "qty.quox"

examples/bool.quox

@@ -4,24 +4,35 @@ namespace bool {
 
 def0 Bool : ★ = {true, false};
 
-def boolω : 1.Bool → [ω.Bool] =
-  λ b ⇒ case1 b return [ω.Bool] of { 'true ⇒ ['true]; 'false ⇒ ['false] };
+def if-dep : 0.(P : Bool → ★) → (b : Bool) → ω.(P 'true) → ω.(P 'false) → P b =
+  λ P b t f ⇒ case b return b' ⇒ P b' of { 'true ⇒ t; 'false ⇒ f };
 
-def if : 0.(A : ★) → 1.Bool → ω.A → ω.A → A =
-  λ A b t f ⇒ case1 b return A of { 'true ⇒ t; 'false ⇒ f };
+def if : 0.(A : ★) → (b : Bool) → ω.A → ω.A → A =
+  λ A ⇒ if-dep (λ _ ⇒ A);
 
-def0 If : 1.Bool → 0.★ → 0.★ → ★ =
-  λ b T F ⇒ case1 b return ★ of { 'true ⇒ T; 'false ⇒ F };
+def0 if-same : (A : ★) → (b : Bool) → (x : A) → if A b x x ≡ x : A =
+  λ A b x ⇒ if-dep (λ b' ⇒ if A b' x x ≡ x : A) b (δ _ ⇒ x) (δ _ ⇒ x);
 
-def0 T : ω.Bool → ★ = λ b ⇒ If b True False;
+def if2 : 0.(A B : ★) → (b : Bool) → ω.A → ω.B → if¹ ★ b A B =
+  λ A B ⇒ if-dep (λ b ⇒ if-dep¹ (λ _ ⇒ ★) b A B);
+
+def0 T : Bool → ★ = λ b ⇒ if¹ ★ b True False;
+
+def dup! : (b : Bool) → [ω. Sing Bool b] =
+  λ b ⇒ if-dep (λ b ⇒ [ω. Sing Bool b]) b
+    [('true,  [δ _ ⇒ 'true])]
+    [('false, [δ _ ⇒ 'false])];
+
+def dup : Bool → [ω. Bool] =
+  λ b ⇒ appω (Sing Bool b) Bool (sing.val Bool b) (dup! b);
 
 def true-not-false : Not ('true ≡ 'false : Bool) =
-  λ eq ⇒ coe (i ⇒ T (eq @i)) 'true;
+  λ eq ⇒ coe (𝑖 ⇒ T (eq @𝑖)) 'true;
 
 
 -- [todo] infix
-def and : 1.Bool → ω.Bool → Bool = λ a b ⇒ if Bool a b 'false;
-def or  : 1.Bool → ω.Bool → Bool = λ a b ⇒ if Bool a 'true b;
+def and : Bool → ω.Bool → Bool = λ a b ⇒ if Bool a b 'false;
+def or  : Bool → ω.Bool → Bool = λ a b ⇒ if Bool a 'true b;
 
 }
 

examples/either.quox

@@ -5,35 +5,35 @@ namespace either {
 
 def0 Tag : ★ = {left, right};
 
-def0 Payload : 0.★ → 0.★ → 1.Tag → ★ =
-  λ A B tag ⇒ case1 tag return ★ of { 'left ⇒ A; 'right ⇒ B };
+def0 Payload : ★ → ★ → Tag → ★ =
+  λ A B tag ⇒ case tag return ★ of { 'left ⇒ A; 'right ⇒ B };
 
-def0 Either : 0.★ → 0.★ → ★ =
+def0 Either : ★ → ★ → ★ =
   λ A B ⇒ (tag : Tag) × Payload A B tag;
 
-def Left : 0.(A B : ★) → 1.A → Either A B =
+def Left : 0.(A B : ★) → A → Either A B =
   λ A B x ⇒ ('left, x);
 
-def Right : 0.(A B : ★) → 1.B → Either A B =
+def Right : 0.(A B : ★) → B → Either A B =
   λ A B x ⇒ ('right, x);
 
 def elim' :
     0.(A B : ★) → 0.(P : 0.(Either A B) → ★) →
-    ω.(1.(x : A) → P (Left  A B x)) →
-    ω.(1.(x : B) → P (Right A B x)) →
-    1.(t : Tag) → 1.(a : Payload A B t) → P (t, a) =
+    ω.((x : A) → P (Left  A B x)) →
+    ω.((x : B) → P (Right A B x)) →
+    (t : Tag) → (a : Payload A B t) → P (t, a) =
   λ A B P f g t ⇒
-    case1 t
-    return t' ⇒ 1.(a : Payload A B t') → P (t', a)
+    case t
+    return t' ⇒ (a : Payload A B t') → P (t', a)
     of { 'left ⇒ f; 'right ⇒ g };
 
 def elim :
     0.(A B : ★) → 0.(P : 0.(Either A B) → ★) →
-    ω.(1.(x : A) → P (Left  A B x)) →
-    ω.(1.(x : B) → P (Right A B x)) →
-    1.(x : Either A B) → P x =
+    ω.((x : A) → P (Left  A B x)) →
+    ω.((x : B) → P (Right A B x)) →
+    (x : Either A B) → P x =
   λ A B P f g e ⇒
-    case1 e return e' ⇒ P e' of { (t, a) ⇒ elim' A B P f g t a };
+    case e return e' ⇒ P e' of { (t, a) ⇒ elim' A B P f g t a };
 
 
 }
@@ -45,25 +45,25 @@ def  Right  = either.Right;
 
 namespace dec {
 
-def0 Dec : 0.★ → ★ = λ A ⇒ Either [0.A] [0.Not A];
+def0 Dec : ★ → ★ = λ A ⇒ Either [0.A] [0.Not A];
 
 def Yes : 0.(A : ★) → 0.A       → Dec A = λ A y ⇒ Left  [0.A] [0.Not A] [y];
 def No  : 0.(A : ★) → 0.(Not A) → Dec A = λ A n ⇒ Right [0.A] [0.Not A] [n];
 
-def0 DecEq : 0.★ → ★ =
+def0 DecEq : ★ → ★ =
   λ A ⇒ ω.(x : A) → ω.(y : A) → Dec (x ≡ y : A);
 
 def elim :
     0.(A : ★) → 0.(P : 0.(Dec A) → ★) →
     ω.(0.(y : A)     → P (Yes A y)) →
     ω.(0.(n : Not A) → P (No  A n)) →
-    1.(x : Dec A) → P x =
+    (x : Dec A) → P x =
   λ A P f g ⇒
     either.elim [0.A] [0.Not A] P
       (λ y ⇒ case0 y return y' ⇒ P (Left  [0.A] [0.Not A] y') of {[y'] ⇒ f y'})
       (λ n ⇒ case0 n return n' ⇒ P (Right [0.A] [0.Not A] n') of {[n'] ⇒ g n'});
 
-def bool : 0.(A : ★) → 1.(Dec A) → Bool =
+def bool : 0.(A : ★) → Dec A → Bool =
   λ A ⇒ elim A (λ _ ⇒ Bool) (λ _ ⇒ 'true) (λ _ ⇒ 'false);
 
 }

examples/eta.quox

@@ -0,0 +1,25 @@
+load "misc.quox"
+
+namespace eta {
+
+def0 Π : (A : ★) → (A → ★) → ★ = λ A B ⇒ (x : A) → B x
+def0 Σ : (A : ★) → (A → ★) → ★ = λ A B ⇒ (x : A) × B x
+
+def0 function : (A : ★) → (B : A → Type) → (P : Π A B → ★) → (f : Π A B) →
+                P (λ x ⇒ f x) → P f =
+  λ A B P f p ⇒ p
+
+def0 box : (A : ★) → (P : [ω.A] → ★) → (e : [ω.A]) →
+           P [case1 e return A of {[x] ⇒ x}] → P e =
+  λ A P e p ⇒ p
+
+def0 pair : (A : ★) → (B : A → ★) → (P : Σ A B → ★) → (e : Σ A B) →
+            P (fst e, snd e) → P e =
+  λ A B P e p ⇒ p
+
+-- not exactly η, but kinda related
+def0 from-false : (A : ★) → (P : (0.False → A) → ★) → (f : 0.False → A) →
+                  P (void A) → P f =
+  λ A P f p ⇒ p
+
+}

examples/fail.quox

@@ -0,0 +1,16 @@
+#[fail "but cases for"]
+def missing-b : {a, b} → {a} =
+  λ x ⇒ case x return {a} of { 'a ⇒ 'a }
+
+#[fail "duplicate arms"]
+def repeat-enum-case : {a} → {a} =
+  λ x ⇒ case x return {a} of { 'a ⇒ 'a; 'a ⇒ 'a }
+
+#[fail "duplicate tags"]
+def repeat-enum-type : {a, a} = 'a
+
+#[fail "double-def.X has already been defined"]
+namespace double-def {
+  def0 X : ★ = {a}
+  def0 X : ★ = {a}
+}

examples/hello.quox

@@ -0,0 +1,26 @@
+def0 Unit : ★ = {tt}
+
+def drop-unit : 0.(A : ★) → Unit → A → A =
+  λ A u x ⇒ case u return A of {'tt ⇒ x}
+
+def0 IO : ★ → ★ = λ A ⇒ IOState → A × IOState
+
+def bind : 0.(A B : ★) → IO A → (A → IO B) → IO B =
+  λ A B m k s0 ⇒
+  case m s0 return B × IOState of { (x, s1) ⇒ k x s1 }
+
+def seq : IO Unit → IO Unit → IO Unit =
+  λ a b ⇒ bind Unit Unit a (λ u ⇒ drop-unit (IO Unit) u b)
+
+#[compile-scheme "(lambda (n) (builtin-io (printf \"~d~n\" n) 'tt))"]
+postulate print-ℕ : ℕ → IO Unit
+
+#[compile-scheme "(lambda (s) (builtin-io (printf \"~s~n\" s) 'tt))"]
+postulate print : String → IO Unit
+
+load "nat.quox"
+
+#[main]
+def main : IO Unit =
+  let1 sixty-nine = nat.plus 60 9 in
+  seq (print-ℕ sixty-nine) (print "(nice)")

examples/io.quox

@@ -0,0 +1,31 @@
+load "misc.quox"
+
+namespace io {
+
+def0 IORes : ★ → ★ = λ A ⇒ A × IOState
+
+def0 IO : ★ → ★ = λ A ⇒ IOState → IORes A
+
+def pure : 0.(A : ★) → A → IO A = λ A x s ⇒ (x, s)
+
+def bind : 0.(A B : ★) → IO A → (A → IO B) → IO B =
+  λ A B m k s0 ⇒
+  case m s0 return IORes B of { (x, s1) ⇒ k x s1 }
+
+def seq : 0.(B : ★) → IO True → IO B → IO B =
+  λ B x y ⇒ bind True B x (λ u ⇒ case u return IO B of { 'true ⇒ y })
+
+def seq' : IO True → IO True → IO True = seq True
+
+#[compile-scheme "(lambda (str) (builtin-io (display str) 'true))"]
+postulate print : String → IO True
+
+def newline = print "\n"
+
+def println : String → IO True =
+  λ str ⇒ seq' (print str) newline
+
+#[compile-scheme "(builtin-io (get-line (current-input-port)))"]
+postulate readln : IO String
+
+}

examples/list.quox

@@ -1,41 +1,91 @@
 load "nat.quox";
 
-namespace list {
+namespace vec {
 
-def0 Vec : 0.ℕ → 0.★ → ★ =
+def0 Vec : ℕ → ★ → ★ =
   λ n A ⇒
   caseω n return ★ of {
     zero           ⇒ {nil};
     succ _, 0.Tail ⇒ A × Tail
   };
 
-def0 List : 0.★ → ★ =
-  λ A ⇒ (len : ℕ) × Vec len A;
+def elim : 0.(A : ★) → 0.(P : (n : ℕ) → Vec n A → ★) →
+           P 0 'nil →
+           ω.((x : A) → 0.(n : ℕ) → 0.(xs : Vec n A) →
+                P n xs → P (succ n) (x, xs)) →
+           (n : ℕ) → (xs : Vec n A) → P n xs =
+  λ A P pn pc n ⇒
+    case n return n' ⇒ (xs' : Vec n' A) → P n' xs' of {
+      zero ⇒ λ n ⇒
+        case n return n' ⇒ P 0 n' of { 'nil ⇒ pn };
+      succ n, ih ⇒ λ c ⇒
+        case c return c' ⇒ P (succ n) c' of {
+          (first, rest) ⇒ pc first n rest (ih rest)
+        }
+    };
 
-def nil : 0.(A : ★) → List A =
-  λ A ⇒ (0, 'nil);
-
-def cons : 0.(A : ★) → 1.A → 1.(List A) → List A =
-  λ A x xs ⇒ case1 xs return List A of { (len, elems) ⇒ (succ len, x, elems) };
-
-def foldr' : 0.(A B : ★) →
-             1.B → ω.(1.A → 1.B → B) → 1.(n : ℕ) → 1.(Vec n A) → B =
-  λ A B z c n ⇒
-  case1 n return n' ⇒ 1.(Vec n' A) → B of {
-    zero ⇒
-      λ nil ⇒ case1 nil return B of { 'nil ⇒ z };
-    succ n, 1.ih ⇒
-      λ cons ⇒ case1 cons return B of { (first, rest) ⇒ c first (ih rest) }
-  };
-
-def foldr : 0.(A B : ★) → 1.B → ω.(1.A → 1.B → B) → 1.(List A) → B =
-  λ A B z c xs ⇒
-  case1 xs return B of { (len, elems) ⇒ foldr' A B z c len elems };
-
-def sum : 1.(List ℕ) → ℕ = foldr ℕ ℕ 0 nat.plus;
-
-def numbers : List ℕ = (5, (0, 1, 2, 3, 4, 'nil));
-
-def number-sum : sum numbers ≡ 10 : ℕ = δ _ ⇒ 10;
+#[compile-scheme "(lambda% (n xs) xs)"]
+def up : 0.(A : ★) → (n : ℕ) → Vec n A → Vec¹ n A =
+  λ A n ⇒
+    case n return n' ⇒ Vec n' A → Vec¹ n' A of {
+      zero ⇒ λ xs ⇒
+        case xs return Vec¹ 0 A of { 'nil ⇒ 'nil };
+      succ n', f' ⇒ λ xs ⇒
+        case xs return Vec¹ (succ n') A of {
+          (first, rest) ⇒ (first, f' rest)
+        }
+    }
 
 }
+
+def0 Vec = vec.Vec;
+
+
+namespace list {
+
+def0 List : ★ → ★ =
+  λ A ⇒ (len : ℕ) × Vec len A;
+
+def Nil : 0.(A : ★) → List A =
+  λ A ⇒ (0, 'nil);
+
+def Cons : 0.(A : ★) → A → List A → List A =
+  λ A x xs ⇒ case xs return List A of { (len, elems) ⇒ (succ len, x, elems) };
+
+def elim : 0.(A : ★) → 0.(P : List A → ★) →
+           P (Nil A) →
+           ω.((x : A) → 0.(xs : List A) → P xs → P (Cons A x xs)) →
+           (xs : List A) → P xs =
+  λ A P pn pc xs ⇒
+    case xs return xs' ⇒ P xs' of { (len, elems) ⇒
+      vec.elim A (λ n xs ⇒ P (n, xs))
+        pn (λ x n xs ih ⇒ pc x (n, xs) ih)
+        len elems
+    };
+
+-- [fixme] List A <: List¹ A should be automatic, imo
+#[compile-scheme "(lambda (xs) xs)"]
+def up : 0.(A : ★) → List A → List¹ A =
+  λ A xs ⇒
+  case xs return List¹ A of { (len, elems) ⇒
+    case nat.dup! len return List¹ A of { [p] ⇒
+      caseω p return List¹ A of { (lenω, eq0) ⇒
+        case eq0 return List¹ A of { [eq] ⇒
+          (lenω, vec.up A lenω (coe (𝑖 ⇒ Vec (eq @𝑖) A) @1 @0 elems))
+        }
+      }
+    }
+  };
+
+def foldr : 0.(A B : ★) → B → ω.(A → B → B) → List A → B =
+  λ A B z f xs ⇒ elim A (λ _ ⇒ B) z (λ x _ y ⇒ f x y) xs;
+
+def map : 0.(A B : ★) → ω.(A → B) → List A → List B =
+  λ A B f ⇒ foldr A (List B) (Nil B) (λ x ys ⇒ Cons B (f x) ys);
+
+def0 All : (A : ★) → (P : A → ★) → List A → ★ =
+  λ A P xs ⇒ foldr¹ A ★ True (λ x ps ⇒ P x × ps) (up A xs);
+
+}
+
+def0 List = list.List;

examples/maybe.quox

@@ -5,10 +5,10 @@ namespace maybe {
 
 def0 Tag : ★ = {nothing, just}
 
-def0 Payload : ω.Tag → ω.★ → ★ =
-  λ tag A ⇒ caseω tag return ★ of { 'nothing ⇒ True; 'just ⇒ A }
+def0 Payload : Tag → ★ → ★ =
+  λ tag A ⇒ case tag return ★ of { 'nothing ⇒ True; 'just ⇒ A }
 
-def0 Maybe : ω.★ → ★ =
+def0 Maybe : ★ → ★ =
   λ A ⇒ (t : Tag) × Payload t A
 
 def tag : 0.(A : ★) → ω.(Maybe A) → Tag =
@@ -17,13 +17,13 @@ def tag : 0.(A : ★) → ω.(Maybe A) → Tag =
 def Nothing : 0.(A : ★) → Maybe A =
   λ _ ⇒ ('nothing, 'true)
 
-def Just : 0.(A : ★) → 1.A → Maybe A =
+def Just : 0.(A : ★) → A → Maybe A =
   λ _ x ⇒ ('just, x)
 
-def0 IsJustTag : ω.Tag → ★ =
-  λ t ⇒ caseω t return ★ of { 'just ⇒ True; 'nothing ⇒ False }
+def0 IsJustTag : Tag → ★ =
+  λ t ⇒ case t return ★ of { 'just ⇒ True; 'nothing ⇒ False }
 
-def0 IsJust : 0.(A : ★) → ω.(Maybe A) → ★ =
+def0 IsJust : (A : ★) → Maybe A → ★ =
   λ A x ⇒ IsJustTag (tag A x)
 
 def is-just? : 0.(A : ★) → ω.(x : Maybe A) → Dec (IsJust A x) =
@@ -34,32 +34,31 @@ def is-just? : 0.(A : ★) → ω.(x : Maybe A) → Dec (IsJust A x) =
   }
 
 def0 nothing-unique :
-    0.(A : ★) → ω.(x : True) → ('nothing, x) ≡ Nothing A : Maybe A =
+    (A : ★) → (x : True) → ('nothing, x) ≡ Nothing A : Maybe A =
   λ A x ⇒
-  caseω x return x' ⇒ ('nothing, x') ≡ Nothing A : Maybe A of {
+  case x return x' ⇒ ('nothing, x') ≡ Nothing A : Maybe A of {
     'true ⇒ δ _ ⇒ ('nothing, 'true)
   }
 
 def elim :
     0.(A : ★) →
-    0.(P : 0.(Maybe A) → ★) →
+    0.(P : Maybe A → ★) →
     ω.(P (Nothing A)) →
-    ω.(ω.(x : A) → P (Just A x)) →
-    1.(x : Maybe A) → P x =
+    ω.((x : A) → P (Just A x)) →
+    (x : Maybe A) → P x =
   λ A P n j x ⇒
-  caseω x return x' ⇒ P x' of {
-    (tag, payload) ⇒
-      (caseω tag
-       return t ⇒
-         0.(eq : tag ≡ t : Tag) → P (t, coe (i ⇒ Payload (eq @i) A) payload)
-       of {
-         'nothing ⇒
-            λ eq ⇒
-            caseω coe (i ⇒ Payload (eq @i) A) payload
-            return p ⇒ P ('nothing, p)
-            of { 'true ⇒ n };
-         'just ⇒ λ eq ⇒ j (coe (i ⇒ Payload (eq @i) A) payload)
-       }) (δ _ ⇒ tag)
+  case x return x' ⇒ P x' of { (tag, payload) ⇒
+    (case tag
+     return t ⇒
+       0.(eq : tag ≡ t : Tag) → P (t, coe (i ⇒ Payload (eq @i) A) payload)
+     of {
+       'nothing ⇒
+          λ eq ⇒
+          case coe (i ⇒ Payload (eq @i) A) payload
+          return p ⇒ P ('nothing, p)
+          of { 'true ⇒ n };
+       'just ⇒ λ eq ⇒ j (coe (i ⇒ Payload (eq @i) A) payload)
+     }) (δ _ ⇒ tag)
   }
 
 }

examples/misc.quox

@@ -1,36 +1,83 @@
-def0 True : ★ = {true};
+def0 True : ★ = {true}
 
-def0 False : ★ = {};
-def0 Not : 0.★ → ★ = λ A ⇒ ω.A → False;
+def0 False : ★ = {}
+def0 Not : ★ → ★ = λ A ⇒ ω.A → False
 
 def void : 0.(A : ★) → 0.False → A =
-  λ A v ⇒ case0 v return A of { };
+  λ A v ⇒ case0 v return A of { }
 
-def0 Pred : 0.★ → ★¹ = λ A ⇒ 0.A → ★;
+def0 All : (A : ★) → (0.A → ★) → ★ =
+  λ A P ⇒ (x : A) → P x
 
-def0 All : 0.(A : ★) → 0.(Pred A) → ★¹ =
-  λ A P ⇒ 1.(x : A) → P x;
+def0 cong :
+    (A : ★) → (P : 0.A → ★) → (p : All A P) →
+    (x y : A) → (xy : x ≡ y : A) → Eq (𝑖 ⇒ P (xy @𝑖)) (p x) (p y) =
+  λ A P p x y xy ⇒ δ 𝑖 ⇒ p (xy @𝑖)
+
+def0 cong' :
+    (A B : ★) → (f : A → B) →
+    (x y : A) → (xy : x ≡ y : A) → f x ≡ f y : B =
+  λ A B ⇒ cong A (λ _ ⇒ B)
+
+def0 coherence :
+    (A B : ★) → (AB : A ≡ B : ★) → (x : A) →
+    Eq (𝑖 ⇒ AB @𝑖) x (coe (𝑖 ⇒ AB @𝑖) x) =
+  λ A B AB x ⇒
+    δ 𝑗 ⇒ coe (𝑖 ⇒ AB @𝑖) @0 @𝑗 x
 
-def cong :
-    0.(A : ★) → 0.(P : Pred A) → 1.(p : All A P) →
-    0.(x y : A) → 1.(xy : x ≡ y : A) → Eq (𝑖 ⇒ P (xy @𝑖)) (p x) (p y) =
-  λ A P p x y xy ⇒ δ 𝑖 ⇒ p (xy @𝑖);
 
 def0 eq-f :
-    0.(A : ★) → 0.(P : Pred A) →
+    0.(A : ★) → 0.(P : 0.A → ★) →
     0.(p : All A P) → 0.(q : All A P) →
     0.A → ★ =
-  λ A P p q x ⇒ p x ≡ q x : P x;
+  λ A P p q x ⇒ p x ≡ q x : P x
 
 def funext :
-    0.(A : ★) → 0.(P : Pred A) → 0.(p q : All A P) →
-    1.(All A (eq-f A P p q)) → p ≡ q : All A P =
-  λ A P p q eq ⇒ δ 𝑖 ⇒ λ x ⇒ eq x @𝑖;
+    0.(A : ★) → 0.(P : 0.A → ★) → 0.(p q : All A P) →
+    (All A (eq-f A P p q)) → p ≡ q : All A P =
+  λ A P p q eq ⇒ δ 𝑖 ⇒ λ x ⇒ eq x @𝑖
 
-def sym : 0.(A : ★) → 0.(x y : A) → 1.(x ≡ y : A) → y ≡ x : A =
-  λ A x y eq ⇒ δ 𝑖 ⇒ comp A (eq @0) @𝑖 { 0 𝑗 ⇒ eq @𝑗; 1 _ ⇒ eq @0 };
+def refl : 0.(A : ★) → (x : A) → x ≡ x : A = λ A x ⇒ δ _ ⇒ x
+
+def sym : 0.(A : ★) → 0.(x y : A) → (x ≡ y : A) → y ≡ x : A =
+  λ A x y eq ⇒ δ 𝑖 ⇒ comp A (eq @0) @𝑖 { 0 𝑗 ⇒ eq @𝑗; 1 _ ⇒ eq @0 }
 
 def trans : 0.(A : ★) → 0.(x y z : A) →
             ω.(x ≡ y : A) → ω.(y ≡ z : A) → x ≡ z : A =
   λ A x y z eq1 eq2 ⇒ δ 𝑖 ⇒
-    comp A (eq1 @𝑖) @𝑖 { 0 _ ⇒ eq1 @0; 1 𝑗 ⇒ eq2 @𝑗 };
+    comp A (eq1 @𝑖) @𝑖 { 0 _ ⇒ eq1 @0; 1 𝑗 ⇒ eq2 @𝑗 }
+
+def appω : 0.(A B : ★) → ω.(f : A → B) → [ω.A] → [ω.B] =
+  λ A B f x ⇒
+  case x return [ω.B] of { [x'] ⇒ [f x'] }
+
+def0 HEq : (A B : ★) → A → B → ★¹ =
+  λ A B x y ⇒ (AB : A ≡ B : ★) × Eq (𝑖 ⇒ AB @𝑖) x y
+
+
+def0 Sing : (A : ★) → A → ★ =
+  λ A x ⇒ (val : A) × [0. val ≡ x : A]
+
+def sing : 0.(A : ★) → (x : A) → Sing A x =
+  λ A x ⇒ (x, [δ _ ⇒ x])
+
+namespace sing {
+
+def val : 0.(A : ★) → 0.(x : A) → Sing A x → A =
+  λ A _ sg ⇒
+  case sg return A of { (x, eq) ⇒ case eq return A of { [_] ⇒ x } }
+
+def0 proof : (A : ★) → (x : A) → (sg : Sing A x) → val A x sg ≡ x : A =
+  λ A x sg ⇒
+  case sg return sg' ⇒ val A x sg' ≡ x : A of { (x', eq) ⇒
+    case eq return eq' ⇒ val A x (x', eq') ≡ x : A of { [eq'] ⇒ eq' }
+  }
+
+def app : 0.(A B : ★) → 0.(x : A) →
+          (f : A → B) → Sing A x → Sing B (f x) =
+  λ A B x f sg ⇒
+  case sg return Sing B (f x) of { (x_, eq) ⇒
+    case eq return Sing B (f x) of { [eq] ⇒ (f x_, [δ 𝑖 ⇒ f (eq @𝑖)]) }
+  }
+
+}

examples/nat.quox

@@ -4,41 +4,72 @@ load "either.quox";
 
 namespace nat {
 
-def dup : 1.ℕ → [ω.ℕ] =
+def elim-0-1 :
+    0.(P : ℕ → ★) →
+    ω.(P 0) → ω.(P 1) →
+    ω.(0.(n : ℕ) → P n → P (succ n)) →
+    (n : ℕ) → P n =
+  λ P p0 p1 ps n ⇒
+  case n return n' ⇒ P n' of {
+    zero    ⇒ p0;
+    succ n' ⇒
+      case n' return n'' ⇒ P (succ n'') of {
+        zero         ⇒ p1;
+        succ n'', IH ⇒ ps (succ n'') IH
+      }
+  }
+
+#[compile-scheme "(lambda (n) (cons n 'erased))"]
+def dup! : (n : ℕ) → [ω. Sing ℕ n] =
   λ n ⇒
-  case1 n return [ω.ℕ] of {
-    zero        ⇒ [zero];
-    succ _, 1.d ⇒ case1 d return [ω.ℕ] of { [d] ⇒ [succ d] }
+  case n return n' ⇒ [ω. Sing ℕ n'] of {
+    zero ⇒ [(zero, [δ _ ⇒ zero])];
+    succ n, d ⇒
+      appω (Sing ℕ n) (Sing ℕ (succ n))
+        (sing.app ℕ ℕ n (λ n ⇒ succ n)) d
   };
 
-def plus : 1.ℕ → 1.ℕ → ℕ =
+def dup : ℕ → [ω.ℕ] =
+  λ n ⇒ appω (Sing ℕ n) ℕ (sing.val ℕ n) (dup! n);
+
+#[compile-scheme "(lambda% (m n) (+ m n))"]
+def plus : ℕ → ℕ → ℕ =
   λ m n ⇒
-  case1 m return ℕ of {
-    zero        ⇒ n;
-    succ _, 1.p ⇒ succ p
+  case m return ℕ of {
+    zero      ⇒ n;
+    succ _, p ⇒ succ p
   };
 
-def timesω : 1.ℕ → ω.ℕ → ℕ =
+#[compile-scheme "(lambda% (m n) (* m n))"]
+def timesω : ℕ → ω.ℕ → ℕ =
   λ m n ⇒
-  case1 m return ℕ of {
-    zero        ⇒ zero;
-    succ _, 1.t ⇒ plus n t
+  case m return ℕ of {
+    zero      ⇒ zero;
+    succ _, t ⇒ plus n t
   };
 
-def times : 1.ℕ → 1.ℕ → ℕ =
-  λ m n ⇒ case1 dup n return ℕ of { [n] ⇒ timesω m n };
+def times : ℕ → ℕ → ℕ =
+  λ m n ⇒ case dup n return ℕ of { [n] ⇒ timesω m n };
 
-def pred : 1.ℕ → ℕ = λ n ⇒ case1 n return ℕ of { zero ⇒ zero; succ n ⇒ n };
+def pred : ℕ → ℕ = λ n ⇒ case n return ℕ of { zero ⇒ zero; succ n ⇒ n };
 
 def pred-succ : ω.(n : ℕ) → pred (succ n) ≡ n : ℕ =
   λ n ⇒ δ 𝑖 ⇒ n;
 
-def0 succ-inj : 0.(m n : ℕ) → 0.(succ m ≡ succ n : ℕ) → m ≡ n : ℕ =
+def0 succ-inj : (m n : ℕ) → succ m ≡ succ n : ℕ → m ≡ n : ℕ =
   λ m n eq ⇒ δ 𝑖 ⇒ pred (eq @𝑖);
 
+#[compile-scheme "(lambda% (m n) (max 0 (- m n)))"]
+def minus : ℕ → ℕ → ℕ =
+  λ m n ⇒
+  (case n return ℕ → ℕ of {
+    zero      ⇒ λ m ⇒ m;
+    succ _, f ⇒ λ m ⇒ f (pred m)
+  }) m;
 
-def0 IsSucc : 0.ℕ → ★ =
-  λ n ⇒ caseω n return ★ of { zero ⇒ False; succ _ ⇒ True };
+
+def0 IsSucc : ℕ → ★ =
+  λ n ⇒ case n return ★ of { zero ⇒ False; succ _ ⇒ True };
 
 def isSucc? : ω.(n : ℕ) → Dec (IsSucc n) =
   λ n ⇒
@@ -54,14 +85,15 @@ def succ-not-zero : 0.(m : ℕ) → Not (succ m ≡ zero : ℕ) =
   λ m eq ⇒ coe (𝑖 ⇒ IsSucc (eq @𝑖)) 'true;
 
 
-def0 not-succ-self : 0.(m : ℕ) → Not (m ≡ succ m : ℕ) =
+def0 not-succ-self : (m : ℕ) → Not (m ≡ succ m : ℕ) =
   λ m ⇒
-  caseω m return m' ⇒ Not (m' ≡ succ m' : ℕ) of {
+  case m return m' ⇒ Not (m' ≡ succ m' : ℕ) of {
     zero         ⇒ zero-not-succ 0;
     succ n, ω.ih ⇒ λ eq ⇒ ih (succ-inj n (succ n) eq)
   }
 
 
+#[compile-scheme "(lambda% (m n) (if (= m n) Yes No))"]
 def eq? : DecEq ℕ =
   λ m ⇒
   caseω m
@@ -86,28 +118,48 @@ def eq? : DecEq ℕ =
 def eqb : ω.ℕ → ω.ℕ → Bool = λ m n ⇒ dec.bool (m ≡ n : ℕ) (eq? m n);
 
 
-def0 plus-zero : 0.(m : ℕ) → m ≡ plus m 0 : ℕ =
+def0 plus-zero : (m : ℕ) → m ≡ plus m 0 : ℕ =
   λ m ⇒
-  caseω m return m' ⇒ m' ≡ plus m' 0 : ℕ of {
-    zero         ⇒ δ _ ⇒ zero;
-    succ _, ω.ih ⇒ δ 𝑖 ⇒ succ (ih @𝑖)
+  case m return m' ⇒ m' ≡ plus m' 0 : ℕ of {
+    zero        ⇒ δ _ ⇒ 0;
+    succ m', ih ⇒ δ 𝑖 ⇒ succ (ih @𝑖)
   };
 
-def0 plus-succ : 0.(m n : ℕ) → succ (plus m n) ≡ plus m (succ n) : ℕ =
+def0 plus-succ : (m n : ℕ) → succ (plus m n) ≡ plus m (succ n) : ℕ =
   λ m n ⇒
-  caseω m return m' ⇒ succ (plus m' n) ≡ plus m' (succ n) : ℕ of {
-    zero         ⇒ δ _ ⇒ succ n;
-    succ _, ω.ih ⇒ δ 𝑖 ⇒ succ (ih @𝑖)
+  case m return m' ⇒ succ (plus m' n) ≡ plus m' (succ n) : ℕ of {
+    zero       ⇒ δ _ ⇒ succ n;
+    succ _, ih ⇒ δ 𝑖 ⇒ succ (ih @𝑖)
   };
 
-def0 plus-comm : 0.(m n : ℕ) → plus m n ≡ plus n m : ℕ =
+def0 plus-comm : (m n : ℕ) → plus m n ≡ plus n m : ℕ =
   λ m n ⇒
-  caseω m return m' ⇒ plus m' n ≡ plus n m' : ℕ of {
+  case m return m' ⇒ plus m' n ≡ plus n m' : ℕ of {
     zero ⇒ plus-zero n;
-    succ m', ω.ih ⇒
+    succ m', ih ⇒
       trans ℕ (succ (plus m' n)) (succ (plus n m')) (plus n (succ m'))
         (δ 𝑖 ⇒ succ (ih @𝑖))
         (plus-succ n m')
   };
 
+def0 times-zero : (m : ℕ) → 0 ≡ timesω m 0 : ℕ =
+  λ m ⇒
+  case m return m' ⇒ 0 ≡ timesω m' 0 : ℕ of {
+    zero        ⇒ δ _ ⇒ zero;
+    succ m', ih ⇒ ih
+  };
+
+{-
+-- unfinished
+def0 times-succ : (m n : ℕ) → plus m (timesω m n) ≡ timesω m (succ n) : ℕ =
+  λ m n ⇒
+  case m
+  return m' ⇒ plus m' (timesω m' n) ≡ timesω m' (succ n) : ℕ
+  of {
+    zero ⇒ δ _ ⇒ 0;
+    succ m', ih ⇒
+      δ 𝑖 ⇒ plus (succ n) (ih @𝑖)
+  };
+-}
+
 }

examples/pair.quox

@@ -1,55 +1,74 @@
 namespace pair {
 
-def0 Σ : 0.(A : ★) → 0.(0.A → ★) → ★ = λ A B ⇒ (x : A) × B x;
+def0 Σ : (A : ★) → (A → ★) → ★ = λ A B ⇒ (x : A) × B x;
 
-def fst : 0.(A : ★) → 0.(B : 0.A → ★) → ω.(Σ A B) → A =
+{-
+-- now builtins
+def fst : 0.(A : ★) → 0.(B : A → ★) → ω.(Σ A B) → A =
   λ A B p ⇒ caseω p return A of { (x, _) ⇒ x };
 
-def snd : 0.(A : ★) → 0.(B : 0.A → ★) → ω.(p : Σ A B) → B (fst A B p) =
+def snd : 0.(A : ★) → 0.(B : A → ★) → ω.(p : Σ A B) → B (fst A B p) =
   λ A B p ⇒ caseω p return p' ⇒ B (fst A B p') of { (_, y) ⇒ y };
+-}
 
 def uncurry :
-    0.(A : ★) → 0.(B : 0.A → ★) → 0.(C : 0.(x : A) → 0.(B x) → ★) →
-    1.(f : 1.(x : A) → 1.(y : B x) → C x y) →
-    1.(p : Σ A B) → C (fst A B p) (snd A B p) =
+    0.(A : ★) → 0.(B : A → ★) → 0.(C : (x : A) → (B x) → ★) →
+    (f : (x : A) → (y : B x) → C x y) →
+    (p : Σ A B) → C (fst p) (snd p) =
   λ A B C f p ⇒
-    case1 p return p' ⇒ C (fst A B p') (snd A B p') of { (x, y) ⇒ f x y };
+    case p return p' ⇒ C (fst p') (snd p') of { (x, y) ⇒ f x y };
 
 def uncurry' :
-    0.(A B C : ★) → 1.(1.A → 1.B → C) → 1.(A × B) → C =
+    0.(A B C : ★) → (A → B → C) → (A × B) → C =
   λ A B C ⇒ uncurry A (λ _ ⇒ B) (λ _ _ ⇒ C);
 
 def curry :
-    0.(A : ★) → 0.(B : 0.A → ★) → 0.(C : 0.(Σ A B) → ★) →
-    1.(f : 1.(p : Σ A B) → C p) → 1.(x : A) → 1.(y : B x) → C (x, y) =
+    0.(A : ★) → 0.(B : A → ★) → 0.(C : (Σ A B) → ★) →
+    (f : (p : Σ A B) → C p) → (x : A) → (y : B x) → C (x, y) =
   λ A B C f x y ⇒ f (x, y);
 
 def curry' :
-    0.(A B C : ★) → 1.(1.(A × B) → C) → 1.A → 1.B → C =
+    0.(A B C : ★) → (A × B → C) → A → B → C =
   λ A B C ⇒ curry A (λ _ ⇒ B) (λ _ ⇒ C);
 
 def0 fst-snd :
-    0.(A : ★) → 0.(B : 0.A → ★) →
-    1.(p : Σ A B) → p ≡ (fst A B p, snd A B p) : Σ A B =
+    (A : ★) → (B : A → ★) →
+    (p : Σ A B) → p ≡ (fst p, snd p) : Σ A B =
   λ A B p ⇒
-    case1 p
-    return p' ⇒ p' ≡ (fst A B p', snd A B p') : Σ A B
+    case p
+    return p' ⇒ p' ≡ (fst p', snd p') : Σ A B
     of { (x, y) ⇒ δ 𝑖 ⇒ (x, y) };
 
+def0 fst-eq :
+    (A : ★) → (B : A → ★) →
+    (p q : Σ A B) → p ≡ q : Σ A B → fst p ≡ fst q : A =
+  λ A B p q eq ⇒ δ 𝑖 ⇒ fst (eq @𝑖);
+
+def0 snd-eq :
+    (A : ★) → (B : A → ★) →
+    (p q : Σ A B) → (eq : p ≡ q : Σ A B) →
+    Eq (𝑖 ⇒ B (fst-eq A B p q eq @𝑖)) (snd p) (snd q) =
+  λ A B p q eq ⇒ δ 𝑖 ⇒ snd (eq @𝑖);
+
 def map :
     0.(A A' : ★) →
-    0.(B : 0.A → ★) → 0.(B' : 0.A' → ★) →
-    1.(f : 1.A → A') → 1.(g : 0.(x : A) → 1.(B x) → B' (f x)) →
-    1.(Σ A B) → Σ A' B' =
+    0.(B : A → ★) → 0.(B' : A' → ★) →
+    (f : A → A') → (g : 0.(x : A) → (B x) → B' (f x)) →
+    Σ A B → Σ A' B' =
   λ A A' B B' f g p ⇒
-    case1 p return Σ A' B' of { (x, y) ⇒ (f x, g x y) };
+    case p return Σ A' B' of { (x, y) ⇒ (f x, g x y) };
 
-def map' : 0.(A A' B B' : ★) →
-           1.(1.A → A') → 1.(1.B → B') → 1.(A × B) → A' × B' =
+def map' : 0.(A A' B B' : ★) → (A → A') → (B → B') → (A × B) → A' × B' =
   λ A A' B B' f g ⇒ map A A' (λ _ ⇒ B) (λ _ ⇒ B') f (λ _ ⇒ g);
 
+def map-fst : 0.(A A' B : ★) → (A → A') → A × B → A' × B =
+  λ A A' B f ⇒ map' A A' B B f (λ x ⇒ x);
+
+def map-snd : 0.(A B B' : ★) → (B → B') → A × B → A × B' =
+  λ A B B' f ⇒ map' A A B B' (λ x ⇒ x) f;
+
 }
 
 def0 Σ   = pair.Σ;
-def  fst = pair.fst;
-def  snd = pair.snd;
+-- def  fst = pair.fst;
+-- def  snd = pair.snd;

examples/qty.quox

@@ -0,0 +1,77 @@
+def0 Qty : ★ = {"zero", one, any}
+
+def dup : Qty → [ω.Qty] =
+  λ π ⇒ case π return [ω.Qty] of {
+    'zero ⇒ ['zero];
+    'one  ⇒ ['one];
+    'any  ⇒ ['any];
+  }
+
+def drop : 0.(A : ★) → Qty → A → A =
+  λ A π x ⇒ case π return A of {
+    'zero ⇒ x;
+    'one  ⇒ x;
+    'any  ⇒ x;
+  }
+
+def if-zero : 0.(A : ★) → Qty → ω.A → ω.A → A =
+  λ A π z nz ⇒
+  case π return A of { 'zero ⇒ z; 'one ⇒ nz; 'any ⇒ nz }
+
+def plus : Qty → Qty → Qty =
+  λ π ρ ⇒
+  case π return Qty of {
+    'zero ⇒ ρ;
+    'one  ⇒ if-zero Qty ρ 'one 'any;
+    'any  ⇒ drop Qty ρ 'any;
+  }
+
+def times : Qty → Qty → Qty =
+  λ π ρ ⇒
+  case π return Qty of {
+    'zero ⇒ drop Qty ρ 'zero;
+    'one  ⇒ ρ;
+    'any  ⇒ if-zero Qty ρ 'zero 'any;
+  }
+
+def0 FUN : Qty → (A : ★) → (A → ★) → ★ =
+  λ π A B ⇒
+  case π return ★ of {
+    'zero ⇒ 0.(x : A) → B x;
+    'one  ⇒ 1.(x : A) → B x;
+    'any  ⇒ ω.(x : A) → B x;
+  }
+
+def0 Fun : Qty → ★ → ★ → ★ =
+  λ π A B ⇒ FUN π A (λ _ ⇒ B)
+
+def0 Box : Qty → ★ → ★ =
+  λ π A ⇒
+  case π return ★ of {
+    'zero ⇒ [0.A];
+    'one  ⇒ [1.A];
+    'any  ⇒ [ω.A];
+  }
+
+def0 unbox : (π : Qty) → (A : ★) → Box π A → A =
+  λ π A ⇒
+  case π return π' ⇒ Box π' A → A of {
+    'zero ⇒ λ x ⇒ case x return A of { [x] ⇒ x };
+    'one  ⇒ λ x ⇒ case x return A of { [x] ⇒ x };
+    'any  ⇒ λ x ⇒ case x return A of { [x] ⇒ x };
+  }
+
+def0 unbox0 = unbox 'zero
+def0 unbox1 = unbox 'one
+def0 unboxω = unbox 'any
+
+def apply : (π : Qty) → 0.(A : ★) → 0.(B : A → ★) →
+            FUN π A B → (x : Box π A) → B (unbox π A x) =
+  λ π A B ⇒
+  case π
+  return π' ⇒ FUN π' A B → (x : Box π' A) → B (unbox π' A x)
+  of {
+    'zero ⇒ λ f x ⇒ case x return x' ⇒ B (unbox0 A x') of { [x] ⇒ f x };
+    'one  ⇒ λ f x ⇒ case x return x' ⇒ B (unbox1 A x') of { [x] ⇒ f x };
+    'any  ⇒ λ f x ⇒ case x return x' ⇒ B (unboxω A x') of { [x] ⇒ f x };
+  }

exe/CompileMonad.idr

@@ -0,0 +1,164 @@
+module CompileMonad
+
+import Quox.Syntax as Q
+import Quox.Definition as Q
+import Quox.Untyped.Syntax as U
+import Quox.Parser
+import Quox.Untyped.Erase
+import Quox.Untyped.Scheme
+import Quox.Pretty
+import Quox.Log
+import Options
+import Output
+import Error
+
+import System.File
+import Data.IORef
+import Data.Maybe
+import Control.Eff
+
+%default total
+
+%hide Doc.(>>=)
+%hide Core.(>>=)
+
+%hide FromParser.Error
+%hide Erase.Error
+%hide Lexer.Error
+%hide Parser.Error
+
+
+
+public export
+record State where
+  constructor MkState
+  seen : IORef SeenSet
+  defs : IORef Q.Definitions
+  ns   : IORef Mods
+  suf  : IORef NameSuf
+%name CompileMonad.State state
+
+export %inline
+newState : HasIO io => io State
+newState = pure $ MkState {
+  seen = !(newIORef empty),
+  defs = !(newIORef empty),
+  ns   = !(newIORef [<]),
+  suf  = !(newIORef 0)
+}
+
+
+public export
+data CompileTag = OPTS | STATE
+
+public export
+Compile : List (Type -> Type)
+Compile =
+  [Except Error,
+   ReaderL STATE State, ReaderL OPTS Options, Log,
+   LoadFile, IO]
+
+
+export %inline
+handleLog : IORef LevelStack -> OpenFile -> LogL x a -> IOErr Error a
+handleLog ref f l = case f of
+  OConsole ch => handleLogIO (const $ pure ()) ref (consoleHandle ch) l
+  OFile _ h   => handleLogIO (const $ pure ()) ref h l
+  ONone       => do
+    lvls   <- readIORef ref
+    lenRef <- newIORef (length lvls)
+    res    <- handleLogDiscardIO lenRef l
+    writeIORef ref $ fixupDiscardedLog !(readIORef lenRef) lvls
+    pure res
+
+private %inline
+withLogFile : Options ->
+              (IORef LevelStack -> OpenFile -> IO (Either Error a)) ->
+              IO (Either Error a)
+withLogFile opts act = do
+  lvlStack <- newIORef $ singleton opts.logLevels
+  withOutFile CErr opts.logFile fromError $ act lvlStack
+where
+  fromError : String -> FileError -> IO (Either Error a)
+  fromError file err = pure $ Left $ WriteError file err
+
+export covering %inline
+runCompile : Options -> State -> Eff Compile a -> IO (Either Error a)
+runCompile opts state act = do
+  withLogFile opts $ \lvls, logFile =>
+    fromIOErr $ runEff act $ with Union.(::)
+      [handleExcept (\e => ioLeft e),
+       handleReaderConst state,
+       handleReaderConst opts,
+       handleLog lvls logFile,
+       handleLoadFileIOE loadError ParseError state.seen opts.include,
+       liftIO]
+
+private %inline
+rethrowFileC : String -> Either FileError a -> Eff Compile a
+rethrowFileC f = rethrow . mapFst (WriteError f)
+
+
+export %inline
+outputStr : OpenFile -> Lazy String -> Eff Compile ()
+outputStr ONone           _   = pure ()
+outputStr (OConsole COut) str = putStr str
+outputStr (OConsole CErr) str = fPutStr stderr str >>= rethrowFileC "<stderr>"
+outputStr (OFile f h)     str = fPutStr h str >>= rethrowFileC f
+
+export %inline
+outputDocs : OpenFile ->
+             ({opts : LayoutOpts} -> Eff Pretty (List (Doc opts))) ->
+             Eff Compile ()
+outputDocs file docs = do
+  opts <- askAt OPTS
+  for_ (runPretty opts (toOutFile file) docs) $ \x =>
+    outputStr file $ render (Opts opts.width) x
+
+export %inline
+outputDoc : OpenFile ->
+            ({opts : LayoutOpts} -> Eff Pretty (Doc opts)) -> Eff Compile ()
+outputDoc file doc = outputDocs file $ singleton <$> doc
+
+
+public export
+data StopTag = STOP
+
+public export
+CompileStop : List (Type -> Type)
+CompileStop = FailL STOP :: Compile
+
+export %inline
+withEarlyStop : Eff CompileStop () -> Eff Compile ()
+withEarlyStop = ignore . runFailAt STOP
+
+export %inline
+stopHere : Has (FailL STOP) fs => Eff fs ()
+stopHere = failAt STOP
+
+
+export %inline
+liftFromParser : Eff FromParserIO a -> Eff Compile a
+liftFromParser act =
+  runEff act $ with Union.(::)
+    [handleExcept $ \err => throw $ FromParserError err,
+     handleStateIORef !(asksAt STATE defs),
+     handleStateIORef !(asksAt STATE ns),
+     handleStateIORef !(asksAt STATE suf),
+     \g => send g,
+     \g => send g]
+
+export %inline
+liftErase : Q.Definitions -> Eff Erase a -> Eff Compile a
+liftErase defs act =
+  runEff act
+    [handleExcept $ \err => throw $ EraseError err,
+     handleStateIORef !(asksAt STATE suf),
+     \g => send g]
+
+export %inline
+liftScheme : Eff Scheme a -> Eff Compile (a, List Id)
+liftScheme act = do
+  runEff [|MkPair act (getAt MAIN)|]
+    [handleStateIORef !(newIORef empty),
+     handleStateIORef !(newIORef [])]

exe/Error.idr

@@ -0,0 +1,49 @@
+module Error
+
+import Quox.Pretty
+import Quox.Parser
+import Quox.Untyped.Erase
+import Quox.Untyped.Scheme
+import Options
+import Output
+
+import System.File
+
+
+public export
+data Error =
+  ParseError String Parser.Error
+| FromParserError FromParser.Error
+| EraseError Erase.Error
+| WriteError FilePath FileError
+| NoMain
+| MultipleMains (List Scheme.Id)
+
+%hide FromParser.Error
+%hide Erase.Error
+%hide Lexer.Error
+%hide Parser.Error
+
+
+export
+loadError : Loc -> FilePath -> FileError -> Error
+loadError loc file err = FromParserError $ LoadError loc file err
+
+export
+prettyError : {opts : LayoutOpts} -> Error -> Eff Pretty (Doc opts)
+prettyError (ParseError file e) = prettyParseError file e
+prettyError (FromParserError e) = FromParser.prettyError True e
+prettyError (EraseError      e) = Erase.prettyError True e
+prettyError NoMain              = pure "no #[main] function given"
+prettyError (MultipleMains xs)  =
+  pure $ sep ["multiple #[main] functions given:",
+              separateLoose "," !(traverse prettyId xs)]
+prettyError (WriteError file e) = pure $
+  hangSingle 2 (text "couldn't write file \{file}:") (pshow e)
+
+export
+dieError : Options -> Error -> IO a
+dieError opts e =
+  die (Opts opts.width) $
+  runPretty ({outFile := Console} opts) Console $
+  prettyError e

exe/Main.idr

@@ -1,46 +1,118 @@
 module Main
 
-import Quox.Syntax
+import Quox.Syntax as Q
+import Quox.Definition as Q
+import Quox.Untyped.Syntax as U
 import Quox.Parser
-import Quox.Definition
+import Quox.Untyped.Erase
+import Quox.Untyped.Scheme
 import Quox.Pretty
+import Quox.Log
+import Options
+import Output
+import Error
+import CompileMonad
 
 import System
+import System.File
 import Data.IORef
-import Data.SortedSet
 import Control.Eff
 
-private
-Opts : LayoutOpts
-Opts = Opts 80
+%default total
+
+%hide Doc.(>>=)
+%hide Core.(>>=)
+
+%hide FromParser.Error
+%hide Erase.Error
+%hide Lexer.Error
+%hide Parser.Error
+
 
 private
-putDoc : Doc Opts -> IO ()
-putDoc = putStr . render Opts
+Step : Type -> Type -> Type
+Step a b = OpenFile -> a -> Eff Compile b
 
 private
-die : Doc Opts -> IO a
-die err = do putDoc err; exitFailure
+step : ConsoleChannel -> Phase -> OutFile -> Step a b -> a -> Eff CompileStop b
+step console phase file act x = do
+  opts <- askAt OPTS
+  res  <- withOutFile console file fromError $ \h => lift $ act h x
+  when (opts.until == Just phase) stopHere
+  pure res
+where
+  fromError : String -> FileError -> Eff CompileStop c
+  fromError file err = throw $ WriteError file err
 
-private
-prettySig : {opts : _} -> Name -> Definition -> Eff Pretty (Doc opts)
-prettySig name def = do
-  qty  <- prettyQty def.qty.fst
-  name <- prettyFree name
-  type <- prettyTerm [<] [<] def.type
-  hangDSingle (hsep [hcat [qty, !dotD, name], !colonD]) type
 
-export
+private covering
+parse : Step String PFile
+parse h file = do
+  Just ast <- loadFile noLoc file
+    | Nothing => pure []
+  outputStr h $ show ast
+  pure ast
+
+private covering
+check : Step PFile (List Q.NDefinition)
+check h decls =
+  map concat $ for decls $ \decl => do
+    defs <- liftFromParser $ fromPTopLevel decl
+    outputDocs h $ traverse (\(x, d) => prettyDef x d) defs
+    pure defs
+
+private covering
+erase : Step (List Q.NDefinition) (List U.NDefinition)
+erase h defList =
+  for defList $ \(x, def) => do
+    def <- liftErase defs $ eraseDef defs x def
+    outputDoc h $ U.prettyDef x def
+    pure (x, def)
+where defs = SortedMap.fromList defList
+
+private covering
+scheme : Step (List U.NDefinition) (List Sexp, List Id)
+scheme h defs = do
+  sexps' <- for defs $ \(x, d) => do
+    (msexp, mains) <- liftScheme $ defToScheme x d
+    outputDoc h $ case msexp of
+      Just s  => prettySexp s
+      Nothing => pure $ hsep [";;", prettyName x, "erased"]
+    pure (msexp, mains)
+  pure $ bimap catMaybes concat $ unzip sexps'
+
+private covering
+output : Step (List Sexp, List Id) ()
+output h (sexps, mains) = do
+  main <- case mains of
+    [m] => pure m
+    []  => throw NoMain
+    _   => throw $ MultipleMains mains
+  lift $ outputDocs h $ do
+    res    <- traverse prettySexp sexps
+    runner <- makeRunMain main
+    pure $ text Scheme.prelude :: res ++ [runner]
+
+private covering
+processFile : String -> Eff Compile ()
+processFile file = withEarlyStop $ pipeline !(askAt OPTS) file where
+  pipeline : Options -> String -> Eff CompileStop ()
+  pipeline opts =
+    step CErr Parse  opts.dump.parse  Main.parse  >=>
+    step CErr Check  opts.dump.check  Main.check  >=>
+    step CErr Erase  opts.dump.erase  Main.erase  >=>
+    step CErr Scheme opts.dump.scheme Main.scheme >=>
+    step COut End    opts.outFile     Main.output
+
+
+export covering
 main : IO ()
 main = do
-  seen <- newIORef SortedSet.empty
-  defs <- newIORef SortedMap.empty
-  suf  <- newIORef $ the Nat 0
-  for_ (drop 1 !getArgs) $ \file => do
-    putStrLn "checking \{file}"
-    Right res <- fromParserIO ["."] seen suf defs $ loadProcessFile noLoc file
-      | Left err => die $ runPrettyColor $ prettyError True err
-    for_ res $ \(name, def) => putDoc $ runPrettyColor $ prettySig name def
+  (_, opts, files) <- options
+  case !(runCompile opts !newState $ traverse_ processFile files) of
+    Right () => pure ()
+    Left  e  => dieError opts e
+
 
 -----------------------------------
 {-
@@ -55,6 +127,13 @@ text _ =
    #" /_/"#,
    ""]
 
+--   ["",
+--    #" __ _ _  _ _____ __"#,
+--    #"/ _` | || / _ \ \ /"#,
+--    #"\__, |\_,_\___/_\_\"#,
+--    #"   |_|"#,
+--    ""]
+
 private
 qtuwu : PrettyOpts -> List String
 qtuwu opts =

exe/Options.idr

@@ -0,0 +1,258 @@
+module Options
+
+import Quox.Pretty
+import Quox.Log
+import Data.DPair
+import Data.SortedMap
+import System
+import System.Console.GetOpt
+import System.File
+import System.Term
+import Derive.Prelude
+
+%default total
+%language ElabReflection
+
+public export
+data OutFile = File String | Console | NoOut
+%name OutFile f
+%runElab derive "OutFile" [Eq, Show]
+
+public export
+data Phase = Parse | Check | Erase | Scheme | End
+%name Phase p
+%runElab derive "Phase" [Eq, Show]
+
+||| a list of all intermediate `Phase`s (excluding `End`)
+public export %inline
+allPhases : List Phase
+allPhases = %runElab do
+  cs <- getCons $ fst !(lookupName "Phase")
+  traverse (check . var) $ fromMaybe [] $ init' cs
+
+||| `Guess` is `Term` for a terminal and `NoHL` for a file
+public export
+data HLType = Guess | NoHL | Term | Html
+%runElab derive "HLType" [Eq, Show]
+
+public export
+record Dump where
+  constructor MkDump
+  parse, check, erase, scheme : OutFile
+%name Dump dump
+%runElab derive "Dump" [Show]
+
+public export
+record Options where
+  constructor MkOpts
+  include   : List String
+  dump      : Dump
+  outFile   : OutFile
+  until     : Maybe Phase
+  hlType    : HLType
+  flavor    : Pretty.Flavor
+  width     : Nat
+  logLevels : LogLevels
+  logFile   : OutFile
+%name Options opts
+%runElab derive "Options" [Show]
+
+export
+defaultWidth : IO Nat
+defaultWidth = do
+  w <- cast {to = Nat} <$> getTermCols
+  pure $ if w == 0 then 80 else w
+
+export
+defaultOpts : IO Options
+defaultOpts = pure $ MkOpts {
+  include   = ["."],
+  dump      = MkDump NoOut NoOut NoOut NoOut,
+  outFile   = Console,
+  until     = Nothing,
+  hlType    = Guess,
+  flavor    = Unicode,
+  width     = !defaultWidth,
+  logLevels = defaultLogLevels,
+  logFile   = Console
+}
+
+private
+data HelpType = Common | All
+
+private
+data OptAction = ShowHelp HelpType | Err String | Ok (Options -> Options)
+%name OptAction act
+
+private
+toOutFile : String -> OutFile
+toOutFile ""  = NoOut
+toOutFile "-" = Console
+toOutFile f   = File f
+
+private
+toPhase : String -> OptAction
+toPhase str =
+  let lstr = toLower str in
+  case find (\p => toLower (show p) == lstr) allPhases of
+    Just p  => Ok $ setPhase p
+    Nothing => Err "unknown phase name \{show str}\nphases: \{phaseNames}"
+where
+  phaseNames = joinBy ", " $ map (toLower . show) allPhases
+
+  defConsole : OutFile -> OutFile
+  defConsole NoOut = Console
+  defConsole f     = f
+
+  setPhase : Phase -> Options -> Options
+  setPhase Parse  = {until := Just Parse,  dump.parse  $= defConsole}
+  setPhase Check  = {until := Just Check,  dump.check  $= defConsole}
+  setPhase Erase  = {until := Just Erase,  dump.erase  $= defConsole}
+  setPhase Scheme = {until := Just Scheme, dump.scheme $= defConsole}
+  setPhase End    = id
+
+private
+toWidth : String -> OptAction
+toWidth s = case parsePositive s of
+  Just n  => Ok {width := n}
+  Nothing => Err "invalid width: \{show s}"
+
+private
+toHLType : String -> OptAction
+toHLType str = case toLower str of
+  "none" => Ok {hlType := NoHL}
+  "term" => Ok {hlType := Term}
+  "html" => Ok {hlType := Html}
+  _      => Err "unknown highlighting type \{show str}\ntypes: term, html, none"
+
+||| like ghc, `-i ""` clears the search path;
+||| `-i a:b:c` adds `a`, `b`, `c` to the end
+private
+dirListFlag : String -> List String -> List String
+dirListFlag ""   val = []
+dirListFlag dirs val = val ++ toList (split (== ':') dirs)
+
+private
+splitLogFlag : String -> Either String (List (Maybe LogCategory, LogLevel))
+splitLogFlag = traverse flag1 . toList . split (== ':') where
+  parseLogCategory : String -> Either String LogCategory
+  parseLogCategory cat = do
+    let Just cat = toLogCategory cat
+      | _ => let catList = joinBy ", " logCategories in
+             Left "unknown log category. categories are:\n\{catList}"
+    pure cat
+
+  parseLogLevel : String -> Either String LogLevel
+  parseLogLevel lvl = do
+    let Just lvl = parsePositive lvl
+      | _ => Left "log level \{lvl} not a number"
+    let Just lvl = toLogLevel lvl
+      | _ => Left "log level \{show lvl} out of range 0–\{show maxLogLevel}"
+    pure lvl
+
+  flag1 : String -> Either String (Maybe LogCategory, LogLevel)
+  flag1 str = do
+    let (first, second) = break (== '=') str
+    case strM second of
+      StrCons '=' lvl => do
+        cat <- parseLogCategory first
+        lvl <- parseLogLevel lvl
+        pure (Just cat, lvl)
+      StrNil => (Nothing,) <$> parseLogLevel first
+      _      => Left "invalid log flag \{str}"
+
+private
+setLogFlag : LogLevels -> (Maybe LogCategory, LogLevel) -> LogLevels
+setLogFlag lvls (Nothing,   lvl) = {defLevel := lvl} lvls
+setLogFlag lvls (Just name, lvl) = {levels $= ((name, lvl) ::)} lvls
+
+private
+logFlag : String -> OptAction
+logFlag str = case splitLogFlag str of
+  Left  err   => Err err
+  Right flags => Ok $ \o => {logLevels := foldl setLogFlag o.logLevels flags} o
+
+private
+commonOptDescrs' : List (OptDescr OptAction)
+commonOptDescrs' = [
+  MkOpt ['i'] ["include"]
+    (ReqArg (\is => Ok {include $= dirListFlag is}) "<dir>:<dir>...")
+    "add directories to look for source files",
+  MkOpt ['o'] ["output"] (ReqArg (\s => Ok {outFile := toOutFile s}) "<file>")
+    "output file (\"-\" for stdout, \"\" for no output)",
+  MkOpt ['P'] ["phase"] (ReqArg toPhase "<phase>")
+    "stop after the given phase",
+  MkOpt ['l'] ["log"] (ReqArg logFlag "[<cat>=]<n>:...")
+    "set log level",
+  MkOpt ['L'] ["log-file"] (ReqArg (\s => Ok {logFile := toOutFile s}) "<file>")
+    "set log output file"
+]
+
+private
+extraOptDescrs : List (OptDescr OptAction)
+extraOptDescrs = [
+  MkOpt [] ["unicode"] (NoArg $ Ok {flavor := Unicode})
+    "use unicode syntax when printing (default)",
+  MkOpt [] ["ascii"] (NoArg $ Ok {flavor := Ascii})
+    "use ascii syntax when printing",
+  MkOpt [] ["width"] (ReqArg toWidth "<width>")
+    "max output width (defaults to terminal width)",
+  MkOpt [] ["color", "colour"] (ReqArg toHLType "<type>")
+    "select highlighting type",
+
+  MkOpt [] ["dump-parse"]
+    (ReqArg (\s => Ok {dump.parse := toOutFile s}) "<file>")
+    "dump AST",
+  MkOpt [] ["dump-check"]
+    (ReqArg (\s => Ok {dump.check := toOutFile s}) "<file>")
+    "dump typechecker output",
+  MkOpt [] ["dump-erase"]
+    (ReqArg (\s => Ok {dump.erase := toOutFile s}) "<file>")
+    "dump erasure output",
+  MkOpt [] ["dump-scheme"]
+    (ReqArg (\s => Ok {dump.scheme := toOutFile s}) "<file>")
+    "dump scheme output (without prelude)"
+]
+
+private
+helpOptDescrs : List (OptDescr OptAction)
+helpOptDescrs = [
+  MkOpt ['h'] ["help"]     (NoArg $ ShowHelp Common) "show common options",
+  MkOpt []    ["help-all"] (NoArg $ ShowHelp All)    "show all options"
+]
+
+commonOptDescrs = commonOptDescrs' ++ helpOptDescrs
+allOptDescrs    = commonOptDescrs' ++ extraOptDescrs ++ helpOptDescrs
+
+export
+usageHeader : String
+usageHeader = trim """
+quox [options] [file.quox ...]
+rawr
+"""
+
+export
+usage : List (OptDescr _) -> IO a
+usage ds = do
+  ignore $ fPutStr stderr $ usageInfo usageHeader ds
+  exitSuccess
+
+private
+applyAction : Options -> OptAction -> IO Options
+applyAction opts (ShowHelp Common) = usage commonOptDescrs
+applyAction opts (ShowHelp All)    = usage allOptDescrs
+applyAction opts (Err err)         = die err
+applyAction opts (Ok f)            = pure $ f opts
+
+export
+options : IO (String, Options, List String)
+options = do
+  app :: args <- getArgs
+    | [] => die "couldn't get command line arguments"
+  let res = getOpt Permute allOptDescrs args
+  unless (null res.errors) $
+    die $ trim $ concat res.errors
+  unless (null res.unrecognized) $
+    die "unrecognised options: \{joinBy ", " res.unrecognized}"
+  opts <- foldlM applyAction !defaultOpts res.options
+  pure (app, opts, res.nonOptions)

exe/Output.idr

@@ -0,0 +1,59 @@
+module Output
+
+import Quox.Pretty
+import Options
+
+import System.File
+import System
+
+public export
+data ConsoleChannel = COut | CErr
+
+export
+consoleHandle : ConsoleChannel -> File
+consoleHandle COut = stdout
+consoleHandle CErr = stderr
+
+public export
+data OpenFile = OConsole ConsoleChannel | OFile String File | ONone
+
+export
+toOutFile : OpenFile -> OutFile
+toOutFile (OConsole _) = Console
+toOutFile (OFile f _)  = File f
+toOutFile ONone        = NoOut
+
+export
+withFile : HasIO m => String -> (String -> FileError -> m a) ->
+           (OpenFile -> m a) -> m a
+withFile f catch act = Prelude.do
+  res <- withFile f WriteTruncate pure (Prelude.map Right . act . OFile f)
+  either (catch f) pure res
+
+export
+withOutFile : HasIO m => ConsoleChannel -> OutFile ->
+              (String -> FileError -> m a) -> (OpenFile -> m a) -> m a
+withOutFile _  (File f) catch act = withFile f catch act
+withOutFile ch Console  catch act = act $ OConsole ch
+withOutFile _  NoOut    catch act = act ONone
+
+
+
+private
+hlFor : HLType -> OutFile -> HL -> Highlight
+hlFor Guess Console = highlightSGR
+hlFor Guess _       = noHighlight
+hlFor NoHL  _       = noHighlight
+hlFor Term  _       = highlightSGR
+hlFor Html  _       = highlightHtml
+
+export
+runPretty : Options -> OutFile -> Eff Pretty a -> a
+runPretty opts file act =
+  runPrettyWith Outer opts.flavor (hlFor opts.hlType file) 2 act
+
+export
+die : HasIO io => (opts : LayoutOpts) -> Doc opts -> io a
+die opts err = do
+  ignore $ fPutStr stderr $ render opts err
+  exitFailure

exe/quox.ipkg

@@ -1,7 +1,7 @@
 package quox
 version = 0
 
-depends = base, contrib, elab-util, sop, quox-lib
+depends = base, contrib, elab-util, pretty-show, quox-lib
 
 executable = quox
 main = Main

golden-tests/Tests.idr

@@ -0,0 +1,15 @@
+module Tests
+
+import Test.Golden
+import Language.Reflection
+import System
+import System.Path
+
+%language ElabReflection
+
+projDir = %runElab idrisDir ProjectDir
+testDir = projDir </> "tests"
+
+tests = testsInDir { poolName = "quox golden tests", dirName = testDir }
+
+main = runner [!tests]

golden-tests/quox-golden-tests.ipkg

@@ -0,0 +1,4 @@
+package quox-golden-tests
+depends = quox, contrib, test
+executable = quox-golden-tests
+main = Tests

golden-tests/run-tests.sh

@@ -0,0 +1,10 @@
+#!/bin/bash
+
+set -e
+
+quox="$PWD/../exe/build/exec/quox"
+run_tests="$PWD/build/exec/quox-golden-tests"
+test -f "$quox"      || pack build quox
+test -f "$run_tests" || pack build quox-golden-tests
+
+"$run_tests" "$quox" "$@"

golden-tests/tests/empty/run

@@ -0,0 +1,2 @@
+. ../lib.sh
+scheme "$1" empty.quox

golden-tests/tests/eta-singleton/eta-sing.quox

@@ -0,0 +1,33 @@
+-- inspired by https://github.com/agda/agda/issues/2556
+
+postulate0 A : ★
+
+def0 ZZ : ★ = 0 ≡ 0 : ℕ
+
+def reflZ : ZZ = δ _ ⇒ 0
+
+
+namespace erased {
+  def0 ZZA : ★ = 0.ZZ → A
+
+  def propeq : (x : ZZA) → x ≡ (λ _ ⇒ x reflZ) : ZZA =
+    λ x ⇒ δ _ ⇒ x
+
+  def defeq : 0.(P : ZZA → ★) → 0.(x : ZZA) → P (λ _ ⇒ x reflZ) → P x =
+    λ P x p ⇒ p
+}
+
+namespace unrestricted {
+  def0 ZZA : ★ = ω.ZZ → A
+
+  def defeq : 0.(P : ZZA → ★) → 0.(x : ZZA) → P (λ _ ⇒ x reflZ) → P x =
+    λ P x p ⇒ p
+}
+
+namespace linear {
+  def0 ZZA : ★ = 1.ZZ → A
+
+  #[fail "λ _ ⇒ x reflZ is not equal to x"]
+  def defeq : 0.(P : ZZA → ★) → 0.(x : ZZA) → P (λ _ ⇒ x reflZ) → P x =
+    λ P x p ⇒ p
+}

golden-tests/tests/eta-singleton/expected

@@ -0,0 +1,9 @@
+0.A : ★
+0.ZZ : ★
+ω.reflZ : ZZ
+0.erased.ZZA : ★
+ω.erased.propeq : 1.(x : erased.ZZA) → x ≡ (λ _ ⇒ x reflZ) : erased.ZZA
+ω.erased.defeq : 0.(P : 1.erased.ZZA → ★) → 0.(x : erased.ZZA) → 1.(P (λ _ ⇒ (x reflZ))) → P x
+0.unrestricted.ZZA : ★
+ω.unrestricted.defeq : 0.(P : 1.unrestricted.ZZA → ★) → 0.(x : unrestricted.ZZA) → 1.(P (λ _ ⇒ (x reflZ))) → P x
+0.linear.ZZA : ★

golden-tests/tests/eta-singleton/run

@@ -0,0 +1,2 @@
+. ../lib.sh
+check "$1" eta-sing.quox

golden-tests/tests/file-not-found/expected

@@ -0,0 +1,3 @@
+no location:
+couldn't load file nonexistent.quox
+File Not Found

golden-tests/tests/file-not-found/run

@@ -0,0 +1,2 @@
+. ../lib.sh
+check "$1" nonexistent.quox

golden-tests/tests/hello/expected

@@ -0,0 +1,12 @@
+0.IO : 1.★ → ★
+ω.print : 1.String → IO {ok}
+ω.main : IO {ok}
+IO = □
+print = scheme:(lambda (str) (builtin-io (display str) (newline)))
+#[main] main = print "hello 🐉"
+;; IO erased
+(define print
+   (lambda (str) (builtin-io (display str) (newline))))
+(define main
+   (print "hello \x1f409;"))
+hello 🐉

golden-tests/tests/hello/hello.quox

@@ -0,0 +1,7 @@
+def0 IO : ★ → ★ = λ A ⇒ IOState → A × IOState
+
+#[compile-scheme "(lambda (str) (builtin-io (display str) (newline)))"]
+postulate print : String → IO {ok}
+
+#[main]
+def main = print "hello 🐉"

golden-tests/tests/hello/run

@@ -0,0 +1,2 @@
+. ../lib.sh
+compile_run "$1" hello.quox hello.ss

golden-tests/tests/ill-typed-main/expected

@@ -0,0 +1,3 @@
+ill-typed-main.quox:1:11-1:12:
+    when checking a function declared as #[main] has type 1.IOState → {𝑎} × IOState
+    expected a function type, but got ℕ

golden-tests/tests/ill-typed-main/ill-typed-main.quox

@@ -0,0 +1,2 @@
+#[main]
+def main : ℕ = 5

golden-tests/tests/ill-typed-main/run

@@ -0,0 +1,2 @@
+. ../lib.sh
+check "$1" ill-typed-main.quox

golden-tests/tests/isprop-subsing/expected

@@ -0,0 +1,2 @@
+0.IsProp : 1.★ → ★
+0.feq : 1.(A : ★) → 1.(f : IsProp A) → 1.(g : IsProp A) → f ≡ g : IsProp A

golden-tests/tests/isprop-subsing/isprop-subsing.quox

@@ -0,0 +1,4 @@
+def0 IsProp : ★ → ★ = λ A ⇒ (x y : A) → x ≡ y : A
+
+def0 feq : (A : ★) → (f g : IsProp A) → f ≡ g : IsProp A =
+  λ A f g ⇒ δ _ ⇒ f

golden-tests/tests/isprop-subsing/run

@@ -0,0 +1,2 @@
+. ../lib.sh
+check "$1" isprop-subsing.quox

golden-tests/tests/it-5/expected

@@ -0,0 +1,4 @@
+ω.five : ℕ
+five = 5
+(define five
+   5)

golden-tests/tests/it-5/five.quox

@@ -0,0 +1 @@
+def five : ℕ = 5

golden-tests/tests/it-5/run

@@ -0,0 +1,2 @@
+. ../lib.sh
+scheme "$1" five.quox

golden-tests/tests/lib.sh

@@ -0,0 +1,18 @@
+FLAGS="--dump-check - --dump-erase - --dump-scheme - --color=none --width=100000"
+
+check() {
+  $1 $FLAGS "$2" -P check 2>&1
+}
+
+erase() {
+  $1 $FLAGS "$2" -P erase 2>&1
+}
+
+scheme() {
+  $1 $FLAGS "$2" -P scheme 2>&1
+}
+
+compile_run() {
+  $1 $FLAGS "$2" -o "$3" 2>&1
+  chezscheme --program "$3"
+}

golden-tests/tests/load/expected

@@ -0,0 +1,16 @@
+0.lib.IO : 1.★ → ★
+ω.lib.print : 1.String → lib.IO {ok}
+ω.lib.main : lib.IO {ok}
+ω.main : lib.IO {ok}
+lib.IO = □
+lib.print = scheme:(lambda (str) (builtin-io (display str) (newline)))
+lib.main = lib.print "hello 🐉"
+#[main] main = lib.main
+;; lib.IO erased
+(define lib.print
+   (lambda (str) (builtin-io (display str) (newline))))
+(define lib.main
+   (lib.print "hello \x1f409;"))
+(define main
+   lib.main)
+hello 🐉

golden-tests/tests/load/lib.quox

@@ -0,0 +1,8 @@
+namespace lib {
+def0 IO : ★ → ★ = λ A ⇒ IOState → A × IOState
+
+#[compile-scheme "(lambda (str) (builtin-io (display str) (newline)))"]
+postulate print : String → IO {ok}
+
+def main = print "hello 🐉"
+}

golden-tests/tests/load/main.quox

@@ -0,0 +1,4 @@
+load "lib.quox"
+
+#[main]
+def main = lib.main

golden-tests/tests/load/run

@@ -0,0 +1,2 @@
+. ../lib.sh
+compile_run "$1" main.quox load.ss

golden-tests/tests/regularity/expected

@@ -0,0 +1 @@
+0.reggie : 1.(A : ★) → 1.(AA : A ≡ A : ★) → 1.(s : A) → 1.(P : 1.A → ★) → 1.(P (coe (𝑖 ⇒ AA @𝑖) @0 @1 s)) → P s

golden-tests/tests/regularity/regularity.quox

@@ -0,0 +1,12 @@
+-- this definition depends on coercion regularity in xtt. which is this
+-- (adapted to quox):
+--
+--           Ψ | Γ ⊢ 0 · A‹0/𝑖› = A‹1/𝑖› ⇐ ★
+-- ---------------------------------------------------------
+--  Ψ | Γ ⊢ π · coe (𝑖 ⇒ A) @p @q s ⇝ (s ∷ A‹1/𝑖›) ⇒ A‹1/𝑖›
+--
+-- otherwise, the types P (coe ⋯ s) and P s are incompatible
+
+def0 reggie : (A : ★) → (AA : A ≡ A : ★) → (s : A) →
+              (P : A → ★) → P (coe (𝑖 ⇒ AA @𝑖) s) → P s =
+  λ A AA s P p ⇒ p

golden-tests/tests/regularity/run

@@ -0,0 +1,2 @@
+. ../lib.sh
+check "$1" regularity.quox

golden-tests/tests/useless-coe/coe.quox

@@ -0,0 +1,9 @@
+-- non-dependent coe should reduce to its body
+
+def five  : ℕ = 5
+def five? : ℕ = coe ℕ 5
+
+def eq : five ≡ five? : ℕ = δ _ ⇒ 5
+
+def subst1 : 0.(P : ℕ → ★) → P five  → P five? = λ P p ⇒ p
+def subst2 : 0.(P : ℕ → ★) → P five? → P five  = λ P p ⇒ p

golden-tests/tests/useless-coe/expected

@@ -0,0 +1,5 @@
+ω.five : ℕ
+ω.five? : ℕ
+ω.eq : five ≡ five? : ℕ
+ω.subst1 : 0.(P : 1.ℕ → ★) → 1.(P five) → P five?
+ω.subst2 : 0.(P : 1.ℕ → ★) → 1.(P five?) → P five

golden-tests/tests/useless-coe/run

@@ -0,0 +1,2 @@
+. ../lib.sh
+check "$1" coe.quox

lib/Control/Monad/ST/Extra.idr

@@ -0,0 +1,82 @@
+module Control.Monad.ST.Extra
+
+import public Control.Monad.ST
+import Data.IORef
+import Control.MonadRec
+
+%default total
+
+export %inline
+MonadRec (ST s) where
+  tailRecM seed (Access rec) st f = MkST $ do
+    let MkST io = f seed st
+    case !io of
+      Done res           => pure res
+      Cont seed2 prf vst =>
+        let MkST io = tailRecM seed2 (rec seed2 prf) vst f in io
+
+
+public export
+interface HasST (0 m : Type -> Type -> Type) where
+  liftST : ST s a -> m s a
+
+export %inline HasST ST where liftST = id
+
+
+public export
+record STErr e s a where
+  constructor STE
+  fromSTErr : ST s (Either e a)
+
+export
+Functor (STErr e s) where
+  map f (STE e) = STE $ map f <$> e
+
+export
+Applicative (STErr e s) where
+  pure x = STE $ pure $ pure x
+  STE f <*> STE x = STE [|f <*> x|]
+
+export
+Monad (STErr e s) where
+  STE m >>= k = STE $ do
+    case !m of
+      Left  err => pure $ Left err
+      Right x   => fromSTErr $ k x
+
+export
+MonadRec (STErr e s) where
+  tailRecM s (Access r) x k = STE $ do
+    let STE m = k s x
+    case !m of
+      Left  err           => pure $ Left err
+      Right (Cont s' p y) => fromSTErr $ tailRecM s' (r s' p) y k
+      Right (Done y)      => pure $ Right y
+
+export
+runSTErr : (forall s. STErr e s a) -> Either e a
+runSTErr ste = runST $ fromSTErr ste
+
+export %inline HasST (STErr e) where liftST = STE . map Right
+
+export
+stLeft : e -> STErr e s a
+stLeft e = STE $ pure $ Left e
+
+
+parameters {auto _ : HasST m}
+  export %inline
+  newSTRef' : a -> m s (STRef s a)
+  newSTRef' x = liftST $ newSTRef x
+
+  export %inline
+  readSTRef' : STRef s a -> m s a
+  readSTRef' r = liftST $ readSTRef r
+
+  export %inline
+  writeSTRef' : STRef s a -> a -> m s ()
+  writeSTRef' r x = liftST $ writeSTRef r x
+
+  export %inline
+  modifySTRef' : STRef s a -> (a -> a) -> m s ()
+  modifySTRef' r f = liftST $ modifySTRef r f

lib/Quox/BoolExtra.idr

@@ -3,8 +3,8 @@ module Quox.BoolExtra
 import public Data.Bool
 
 
-infixr 5 `andM`
-infixr 4 `orM`
+export infixr 5 `andM`
+export infixr 4 `orM`
 
 public export
 andM, orM : Monad m => m Bool -> m Bool -> m Bool

lib/Quox/CharExtra.idr

@@ -166,3 +166,10 @@ isWhitespace ch = ch == '\t' || ch == '\r' || ch == '\n' || isSeparator ch
 export
 %foreign "scheme:string-normalize-nfc"
 normalizeNfc : String -> String
+
+
+export
+isCodepoint : Int -> Bool
+isCodepoint n =
+  n <= 0x10FFFF &&
+  not (n >= 0xD800 && n <= 0xDBFF || n >= 0xDC00 && n <= 0xDFFF)

lib/Quox/CheckBuiltin.idr

@@ -0,0 +1,33 @@
+||| check that special functions (e.g. `main`) have the expected type
+module Quox.CheckBuiltin
+
+import Quox.Syntax
+import Quox.Typing
+import Quox.Whnf
+
+%default total
+
+
+export covering
+expectSingleEnum : Definitions -> TyContext d n -> SQty -> Loc ->
+                   Term d n -> Eff Whnf ()
+expectSingleEnum defs ctx sg loc s = do
+  let err = delay $ ExpectedSingleEnum loc ctx.names s
+  cases <- wrapErr (const err) $ expectEnum defs ctx sg loc s
+  unless (length (SortedSet.toList cases) == 1) $ throw err
+
+||| `main` should have a type `1.IOState → {𝑎} × IOState`,
+||| for some (single) tag `𝑎`
+export covering
+expectMainType : Definitions -> Term 0 0 -> Eff Whnf ()
+expectMainType defs ty =
+  wrapErr (WrongBuiltinType Main) $ do
+    let ctx = TyContext.empty
+    (qty, arg, res) <- expectPi defs ctx SZero ty.loc ty
+    expectEqualQ ty.loc qty One
+    expectIOState defs ctx SZero arg.loc arg
+    let ctx = extendTy qty res.name arg ctx
+    (ret, st) <- expectSig defs ctx SZero res.loc res.term
+    expectSingleEnum defs ctx SZero ret.loc ret
+    let ctx = extendTy qty st.name ret ctx
+    expectIOState defs ctx SZero st.loc st.term

lib/Quox/Context.idr

@@ -6,16 +6,13 @@ import Quox.Name
 
 import Data.DPair
 import Data.Nat
-import Data.Fin
 import Data.Singleton
 import Data.SnocList
 import Data.SnocVect
 import Data.Vect
 import Control.Monad.Identity
-import Derive.Prelude
 
 %default total
-%language ElabReflection
 
 
 ||| a sequence of bindings under an existing context. each successive element
@@ -61,6 +58,7 @@ public export
 tail : Context tm (S n) -> Context tm n
 tail = fst . unsnoc
 
+
 parameters {0 tm : Nat -> Type} (f : forall n. tm n -> a)
   export
   toSnocListWith : Telescope tm _ _ -> SnocList a
@@ -87,13 +85,6 @@ export %inline
 toSnocList' : Telescope' a _ _ -> SnocList a
 toSnocList' = toSnocListWith id
 
-export %inline
-toSnocListRelevant : {n1 : Nat} -> Telescope tm n1 n2 -> SnocList (n ** tm n)
-toSnocListRelevant tel = toSnocList' $ snd $ go tel where
-  go : Telescope tm n1 n2' -> (Singleton n2', Telescope' (n ** tm n) n1 n2')
-  go [<]        = (Val n1, [<])
-  go (tel :< x) = let (Val n, tel) = go tel in (Val (S n), tel :< (n ** x))
-
 export %inline
 toList : Telescope tm _ _ -> List (Exists tm)
 toList = toListWith (Evidence _)
@@ -118,10 +109,17 @@ fromSnocVect [<]       = [<]
 fromSnocVect (sx :< x) = fromSnocVect sx :< x
 
 
+public export
+tabulateLT : (n : Nat) -> ((i : Nat) -> (0 p : i `LT` n) => tm i) ->
+             Context tm n
+tabulateLT 0     f = [<]
+tabulateLT (S k) f =
+  tabulateLT k (\i => f i @{lteSuccRight %search}) :< f k @{reflexive}
+
 public export
 tabulate : ((n : Nat) -> tm n) -> (n : Nat) -> Context tm n
-tabulate f 0     = [<]
-tabulate f (S k) = tabulate f k :< f k
+tabulate f n = tabulateLT n (\i => f i)
+-- [todo] fixup argument order lol
 
 public export
 replicate : (n : Nat) -> a -> Context' a n
@@ -147,34 +145,34 @@ tel ++ (sx :< x) = (tel ++ sx) :< x
 
 public export
 getShiftWith : (forall from, to. tm from -> Shift from to -> tm to) ->
-               Shift len out -> Context tm len -> Fin len -> tm out
-getShiftWith shft by (ctx :< t) FZ     = t `shft` ssDown by
-getShiftWith shft by (ctx :< t) (FS i) = getShiftWith shft (ssDown by) ctx i
+               Shift len out -> Context tm len -> Var len -> tm out
+getShiftWith shft by (ctx :< t) VZ     = t `shft` ssDown by
+getShiftWith shft by (ctx :< t) (VS i) = getShiftWith shft (ssDown by) ctx i
 
 public export %inline
-getShift : CanShift tm => Shift len out -> Context tm len -> Fin len -> tm out
+getShift : CanShift tm => Shift len out -> Context tm len -> Var len -> tm out
 getShift = getShiftWith (//)
 
 public export %inline
 getWith : (forall from, to. tm from -> Shift from to -> tm to) ->
-          Context tm len -> Fin len -> tm len
+          Context tm len -> Var len -> tm len
 getWith shft = getShiftWith shft SZ
 
-infixl 8 !!
+export infixl 8 !!
 public export %inline
-(!!) : CanShift tm => Context tm len -> Fin len -> tm len
+(!!) : CanShift tm => Context tm len -> Var len -> tm len
 (!!) = getWith (//)
 
-infixl 8 !!!
+export infixl 8 !!!
 public export %inline
-(!!!) : Context' tm len -> Fin len -> tm
+(!!!) : Context' tm len -> Var len -> tm
 (!!!) = getWith const
 
 public export
 find : Alternative f =>
-       (forall n. tm n -> Bool) -> Context tm len -> f (Fin len)
+       (forall n. tm n -> Bool) -> Context tm len -> f (Var len)
 find p [<]        = empty
-find p (ctx :< x) = (guard (p x) $> FZ) <|> (FS <$> find p ctx)
+find p (ctx :< x) = (guard (p x) $> VZ) <|> (VS <$> find p ctx)
 
 
 export
@@ -191,6 +189,12 @@ export %hint
 succGT = LTESucc reflexive
 
 
+public export
+drop : (m : Nat) -> Context term (m + n) -> Context term n
+drop 0     ctx        = ctx
+drop (S m) (ctx :< _) = drop m ctx
+
+
 parameters {auto _ : Applicative f}
   export
   traverse : (forall n. tm1 n -> f (tm2 n)) ->
@@ -202,7 +206,7 @@ parameters {auto _ : Applicative f}
   traverse' : (a -> f b) -> Telescope' a from to -> f (Telescope' b from to)
   traverse' f = traverse f
 
-  infixl 3 `app`
+  export infixl 3 `app`
   ||| like `(<*>)` but with effects
   export
   app : Telescope (\n => tm1 n -> f (tm2 n)) from to ->
@@ -269,16 +273,17 @@ unzip3 (tel :< (x, y, z)) =
 
 
 public export
-lengthPrf : Telescope _ from to -> (len ** len + from = to)
-lengthPrf [<]        = (0 ** Refl)
+lengthPrf : Telescope _ from to -> Subset Nat (\len => len + from = to)
+lengthPrf [<]        = Element 0 Refl
 lengthPrf (tel :< _) =
-  let len = lengthPrf tel in (S len.fst ** cong S len.snd)
+  let len = lengthPrf tel in Element (S len.fst) (cong S len.snd)
 
 export
-lengthPrf0 : Context _ to -> (len ** len = to)
+lengthPrf0 : Context _ to -> Singleton to
 lengthPrf0 ctx =
-  let len = lengthPrf ctx in
-  (len.fst ** rewrite sym $ plusZeroRightNeutral len.fst in len.snd)
+  let Element len prf = lengthPrf ctx in
+  rewrite sym prf `trans` plusZeroRightNeutral len in
+  [|len|]
 
 public export %inline
 length : Telescope {} -> Nat
@@ -297,6 +302,10 @@ foldl : {0 acc : Nat -> Type} ->
 foldl f z [<]        = z
 foldl f z (tel :< t) = f (foldl f z tel) (rewrite (lengthPrf tel).snd in t)
 
+export %inline
+foldl_ : (acc -> tm -> acc) -> acc -> Telescope' tm from to -> acc
+foldl_ f z tel = foldl f z tel
+
 export %inline
 foldMap : Monoid a => (forall n. tm n -> a) -> Telescope tm from to -> a
 foldMap f = foldl (\acc, tm => acc <+> f tm) neutral
@@ -331,14 +340,6 @@ export %inline
     where Show (Exists tm) where showPrec d t = showPrec d t.snd
 
 
-export
-implementation [ShowTelRelevant]
-  {n1 : Nat} -> ({n : Nat} -> Show (f n)) => Show (Telescope f n1 n2)
-where
-  showPrec d = showPrec d . toSnocListRelevant
-    where Show (n : Nat ** f n) where showPrec d (_ ** t) = showPrec d t
-
-
 parameters {opts : LayoutOpts} {0 tm : Nat -> Type}
            (nameHL : HL)
            (pterm : forall n. BContext n -> tm n -> Eff Pretty (Doc opts))
@@ -364,4 +365,4 @@ parameters {opts : LayoutOpts} {0 tm : Nat -> Type}
 namespace BContext
   export
   toNames : BContext n -> SnocList BaseName
-  toNames = foldl (\xs, x => xs :< x.name) [<]
+  toNames = foldl (\xs, x => xs :< x.val) [<]

lib/Quox/Definition.idr

@@ -2,9 +2,12 @@ module Quox.Definition
 
 import public Quox.No
 import public Quox.Syntax
+import Quox.Displace
 import public Data.SortedMap
 import public Quox.Loc
+import Quox.Pretty
 import Control.Eff
+import Data.Singleton
 import Decidable.Decidable
 
 
@@ -23,18 +26,24 @@ namespace DefBody
 public export
 record Definition where
   constructor MkDef
-  qty   : GQty
-  type0 : Term 0 0
-  body0 : DefBody
-  loc_  : Loc
+  qty    : GQty
+  type0  : Term 0 0
+  body0  : DefBody
+  scheme : Maybe String
+  isMain : Bool
+  loc_   : Loc
 
 public export %inline
-mkPostulate : GQty -> (type0 : Term 0 0) -> Loc -> Definition
-mkPostulate qty type0 loc_ = MkDef {qty, type0, body0 = Postulate, loc_}
+mkPostulate : GQty -> (type0 : Term 0 0) -> Maybe String -> Bool -> Loc ->
+              Definition
+mkPostulate qty type0 scheme isMain loc_ =
+  MkDef {qty, type0, body0 = Postulate, scheme, isMain, loc_}
 
 public export %inline
-mkDef : GQty -> (type0, term0 : Term 0 0) -> Loc -> Definition
-mkDef qty type0 term0 loc_ = MkDef {qty, type0, body0 = Concrete term0, loc_}
+mkDef : GQty -> (type0, term0 : Term 0 0) -> Maybe String -> Bool -> Loc ->
+        Definition
+mkDef qty type0 term0 scheme isMain loc_ =
+  MkDef {qty, type0, body0 = Concrete term0, scheme, isMain, loc_}
 
 export Located Definition where def.loc = def.loc_
 export Relocatable Definition where setLoc loc = {loc_ := loc}
@@ -45,27 +54,51 @@ parameters {d, n : Nat}
   (.type) : Definition -> Term d n
   g.type = g.type0 // shift0 d // shift0 n
 
+  public export %inline
+  (.typeAt) : Definition -> Universe -> Term d n
+  g.typeAt u = displace u g.type
+
   public export %inline
   (.term) : Definition -> Maybe (Term d n)
   g.term = g.body0.term0 <&> \t => t // shift0 d // shift0 n
 
   public export %inline
-  toElim : Definition -> Maybe $ Elim d n
-  toElim def = pure $ Ann !def.term def.type def.loc
+  (.termAt) : Definition -> Universe -> Maybe (Term d n)
+  g.termAt u = displace u <$> g.term
+
+  public export %inline
+  toElim : Definition -> Universe -> Maybe $ Elim d n
+  toElim def u = pure $ Ann !(def.termAt u) (def.typeAt u) def.loc
+
+public export
+(.typeWith) : Definition -> Singleton d -> Singleton n -> Term d n
+g.typeWith (Val d) (Val n) = g.type
+
+public export
+(.typeWithAt) : Definition -> Singleton d -> Singleton n -> Universe -> Term d n
+g.typeWithAt d n u = displace u $ g.typeWith d n
+
+public export
+(.termWith) : Definition -> Singleton d -> Singleton n -> Maybe (Term d n)
+g.termWith (Val d) (Val n) = g.term
 
 
 public export %inline
 isZero : Definition -> Bool
-isZero g = g.qty.fst == Zero
+isZero g = g.qty == GZero
 
 
 public export
-data DefEnvTag = DEFS
+NDefinition : Type
+NDefinition = (Name, Definition)
 
 public export
 Definitions : Type
 Definitions = SortedMap Name Definition
 
+public export
+data DefEnvTag = DEFS
+
 public export
 DefsReader : Type -> Type
 DefsReader = ReaderL DEFS Definitions
@@ -74,7 +107,21 @@ public export
 DefsState : Type -> Type
 DefsState = StateL DEFS Definitions
 
+public export %inline
+lookupElim : {d, n : Nat} -> Name -> Universe -> Definitions -> Maybe (Elim d n)
+lookupElim x u defs = toElim !(lookup x defs) u
 
 public export %inline
-lookupElim : {d, n : Nat} -> Name -> Definitions -> Maybe (Elim d n)
-lookupElim x defs = toElim !(lookup x defs)
+lookupElim0 : Name -> Universe -> Definitions -> Maybe (Elim 0 0)
+lookupElim0 = lookupElim
+
+
+export
+prettyDef : {opts : LayoutOpts} -> Name -> Definition -> Eff Pretty (Doc opts)
+prettyDef name def = withPrec Outer $ do
+  qty   <- prettyQty def.qty.qty
+  dot   <- dotD
+  name  <- prettyFree name
+  colon <- colonD
+  type  <- prettyTerm [<] [<] def.type
+  hangDSingle (hsep [hcat [qty, dot, name], colon]) type

lib/Quox/Displace.idr

@@ -2,6 +2,8 @@ module Quox.Displace
 
 import Quox.Syntax
 
+%default total
+
 
 parameters (k : Universe)
   namespace Term
@@ -14,6 +16,7 @@ parameters (k : Universe)
 
   namespace Term
     doDisplace (TYPE l loc) = TYPE (k + l) loc
+    doDisplace (IOState loc) = IOState loc
     doDisplace (Pi qty arg res loc) =
       Pi qty (doDisplace arg) (doDisplaceS res) loc
     doDisplace (Lam body loc) = Lam (doDisplaceS body) loc
@@ -24,14 +27,18 @@ parameters (k : Universe)
     doDisplace (Eq ty l r loc) =
       Eq (doDisplaceDS ty) (doDisplace l) (doDisplace r) loc
     doDisplace (DLam body loc) = DLam (doDisplaceDS body) loc
-    doDisplace (Nat loc) = Nat loc
-    doDisplace (Zero loc) = Zero loc
+    doDisplace (NAT loc) = NAT loc
+    doDisplace (Nat n loc) = Nat n loc
     doDisplace (Succ p loc) = Succ (doDisplace p) loc
+    doDisplace (STRING loc) = STRING loc
+    doDisplace (Str s loc) = Str s loc
     doDisplace (BOX qty ty loc) = BOX qty (doDisplace ty) loc
     doDisplace (Box val loc) = Box (doDisplace val) loc
+    doDisplace (Let qty rhs body loc) =
+      Let qty (doDisplace rhs) (doDisplaceS body) loc
     doDisplace (E e) = E (doDisplace e)
     doDisplace (CloT (Sub t th)) =
-      CloT (Sub (doDisplace t) (map doDisplace th))
+      CloT (Sub (doDisplace t) (assert_total $ map doDisplace th))
     doDisplace (DCloT (Sub t th)) =
       DCloT (Sub (doDisplace t) th)
 
@@ -47,8 +54,11 @@ parameters (k : Universe)
     doDisplace (App fun arg loc) = App (doDisplace fun) (doDisplace arg) loc
     doDisplace (CasePair qty pair ret body loc) =
       CasePair qty (doDisplace pair) (doDisplaceS ret) (doDisplaceS body) loc
+    doDisplace (Fst pair loc) = Fst (doDisplace pair) loc
+    doDisplace (Snd pair loc) = Snd (doDisplace pair) loc
     doDisplace (CaseEnum qty tag ret arms loc) =
-      CaseEnum qty (doDisplace tag) (doDisplaceS ret) (map doDisplace arms) loc
+      CaseEnum qty (doDisplace tag) (doDisplaceS ret)
+               (assert_total $ map doDisplace arms) loc
     doDisplace (CaseNat qty qtyIH nat ret zero succ loc) =
       CaseNat qty qtyIH (doDisplace nat) (doDisplaceS ret)
               (doDisplace zero) (doDisplaceS succ) loc
@@ -65,9 +75,9 @@ parameters (k : Universe)
            (doDisplaceDS zero) (doDisplaceDS one) loc
     doDisplace (TypeCase ty ret arms def loc) =
       TypeCase (doDisplace ty) (doDisplace ret)
-               (map doDisplaceS arms) (doDisplace def) loc
+               (assert_total $ map doDisplaceS arms) (doDisplace def) loc
     doDisplace (CloE (Sub e th)) =
-      CloE (Sub (doDisplace e) (map doDisplace th))
+      CloE (Sub (doDisplace e) (assert_total $ map doDisplace th))
     doDisplace (DCloE (Sub e th)) =
       DCloE (Sub (doDisplace e) th)
 

lib/Quox/EffExtra.idr

@@ -2,6 +2,7 @@ module Quox.EffExtra
 
 import public Control.Eff
 
+import Control.Monad.ST.Extra
 import Data.IORef
 
 
@@ -26,48 +27,40 @@ local_ : Has (State s) fs => s -> Eff fs a -> Eff fs a
 local_ = localAt_ ()
 
 
-export
-hasDrop : (0 neq : Not (a = b)) ->
-          (ha : Has a fs) => (hb : Has b fs) =>
-          Has a (drop fs hb)
-hasDrop neq {ha = Z}    {hb = Z}    = void $ neq Refl
-hasDrop neq {ha = S ha} {hb = Z}    = ha
-hasDrop neq {ha = Z}    {hb = S hb} = Z
-hasDrop neq {ha = S ha} {hb = S hb} = S $ hasDrop neq {ha, hb}
+export %inline
+getsAt : (0 lbl : tag) -> Has (StateL lbl s) fs => (s -> a) -> Eff fs a
+getsAt lbl f = f <$> getAt lbl
+
+export %inline
+gets : Has (State s) fs => (s -> a) -> Eff fs a
+gets = getsAt ()
+
+
+export %inline
+stateAt : (0 lbl : tag) -> Has (StateL lbl s) fs => (s -> (a, s)) -> Eff fs a
+stateAt lbl f = do (res, x) <- getsAt lbl f; putAt lbl x $> res
+
+export %inline
+state : Has (State s) fs => (s -> (a, s)) -> Eff fs a
+state = stateAt ()
 
-private
-0 ioNotState : Not (IO = StateL _ _)
-ioNotState Refl impossible
 
 export
-runStateIORefAt : (0 lbl : tag) -> (Has IO fs, Has (StateL lbl s) fs) =>
-                  IORef s -> Eff fs a -> Eff (fs - StateL lbl s) a
-runStateIORefAt lbl ref act = do
-  let hh : Has IO (fs - StateL lbl s) := hasDrop ioNotState
-  (val, st) <- runStateAt lbl !(readIORef ref) act
-  writeIORef ref st $> val
-
-export %inline
-runStateIORef : (Has IO fs, Has (State s) fs) =>
-                IORef s -> Eff fs a -> Eff (fs - State s) a
-runStateIORef = runStateIORefAt ()
-
-
-export %inline
-evalStateAt : (0 lbl : tag) -> Has (StateL lbl s) fs =>
-              s -> Eff fs a -> Eff (fs - StateL lbl s) a
-evalStateAt lbl s act = map fst $ runStateAt lbl s act
-
-export %inline
-evalState : Has (State s) fs => s -> Eff fs a -> Eff (fs - State s) a
-evalState = evalStateAt ()
+handleStateIORef : HasIO m => IORef st -> StateL lbl st a -> m a
+handleStateIORef r Get     = readIORef r
+handleStateIORef r (Put s) = writeIORef r s
 
+export
+handleStateSTRef : HasST m => STRef s st -> StateL lbl st a -> m s a
+handleStateSTRef r Get     = liftST $ readSTRef r
+handleStateSTRef r (Put s) = liftST $ writeSTRef r s
 
 
 public export
 data Length : List a -> Type where
   Z : Length []
   S : Length xs -> Length (x :: xs)
+%builtin Natural Length
 
 export
 subsetWith : Length xs => (forall z. Has z xs -> Has z ys) ->
@@ -80,23 +73,77 @@ subsetSelf : Length xs => Subset xs xs
 subsetSelf = subsetWith id
 
 export
-subsetTail : Length xs => Subset xs (x :: xs)
-subsetTail = subsetWith S
+subsetTail : Length xs => (0 x : a) -> Subset xs (x :: xs)
+subsetTail _ = subsetWith S
+
 
 
--- [fixme] allow the error to be anywhere in the effect list
 export
-wrapErrAt : Length fs => (0 lbl : tag) -> (e -> e) ->
-            Eff (ExceptL lbl e :: fs) a -> Eff (ExceptL lbl e :: fs) a
-wrapErrAt lbl f act =
-  rethrowAt lbl . mapFst f =<< lift @{subsetTail} (runExceptAt lbl act)
+rethrowAtWith : (0 lbl : tag) -> Has (ExceptL lbl e') fs =>
+                (e -> e') -> Either e a -> Eff fs a
+rethrowAtWith lbl f = rethrowAt lbl . mapFst f
+
+export
+rethrowWith : Has (Except e') fs => (e -> e') -> Either e a -> Eff fs a
+rethrowWith = rethrowAtWith ()
+
+export
+wrapErr : Length fs => (e -> e') ->
+          Eff (ExceptL lbl e  :: fs) a ->
+          Eff (ExceptL lbl e' :: fs) a
+wrapErr f act =
+  catchAt lbl (throwAt lbl . f) @{S Z} $
+  lift @{subsetTail _} act
+
+
+export
+handleExcept : Functor m => (forall c. e -> m c) -> ExceptL lbl e a -> m a
+handleExcept thr (Err e) = thr e
+
+
+export
+handleReaderConst : Applicative m => r -> ReaderL lbl r a -> m a
+handleReaderConst x Ask = pure x
+
+export
+handleWriterSTRef : HasST m => STRef s (SnocList w) -> WriterL lbl w a -> m s a
+handleWriterSTRef ref (Tell w) = liftST $ modifySTRef ref (:< w)
+
+
+public export
+record IOErr e a where
+  constructor IOE
+  fromIOErr : IO (Either e a)
+
+export
+Functor (IOErr e) where
+  map f (IOE e) = IOE $ map f <$> e
+
+export
+Applicative (IOErr e) where
+  pure x = IOE $ pure $ pure x
+  IOE f <*> IOE x = IOE [|f <*> x|]
+
+export
+Monad (IOErr e) where
+  IOE m >>= k = IOE $ do
+    case !m of
+      Left  err => pure $ Left err
+      Right x   => fromIOErr $ k x
+
+export
+MonadRec (IOErr e) where
+  tailRecM s (Access r) x k = IOE $ do
+    let IOE m = k s x
+    case !m of
+      Left  err           => pure $ Left err
+      Right (Cont s' p y) => fromIOErr $ tailRecM s' (r s' p) y k
+      Right (Done y)      => pure $ Right y
+
+export
+HasIO (IOErr e) where
+  liftIO = IOE . map Right
 
 export %inline
-wrapErr : Length fs => (e -> e) ->
-          Eff (Except e :: fs) a -> Eff (Except e :: fs) a
-wrapErr = wrapErrAt ()
-
-
-export %inline
-runIO : (MonadRec io, HasIO io) => Eff [IO] a -> io a
-runIO act = runEff act [liftIO]
+ioLeft : e -> IOErr e a
+ioLeft = IOE . pure . Left

lib/Quox/FinExtra.idr

@@ -1,44 +0,0 @@
-module Quox.FinExtra
-
-import public Data.Fin
-import Quox.Decidable
-
-public export
-data LT : Rel (Fin n) where
-  LTZ : FZ `LT` FS i
-  LTS : i `LT` j -> FS i `LT` FS j
-%builtin Natural FinExtra.LT
-%name FinExtra.LT lt
-
-public export %inline
-GT : Rel (Fin n)
-GT = flip LT
-
-export
-Transitive (Fin n) LT where
-  transitive LTZ     (LTS _) = LTZ
-  transitive (LTS p) (LTS q) = LTS $ transitive p q
-
-export Uninhabited (i `FinExtra.LT` i) where uninhabited (LTS p) = uninhabited p
-export Uninhabited (FS i `LT` FZ) where uninhabited _ impossible
-
-
-public export
-data Compare : Rel (Fin n) where
-  IsLT : (lt : i `LT` j) -> Compare i j
-  IsEQ :                    Compare i i
-  IsGT : (gt : i `GT` j) -> Compare i j
-%name Compare cmp
-
-export
-compareS : Compare i j -> Compare (FS i) (FS j)
-compareS (IsLT lt) = IsLT (LTS lt)
-compareS IsEQ      = IsEQ
-compareS (IsGT gt) = IsGT (LTS gt)
-
-export
-compareP : (i, j : Fin n) -> Compare i j
-compareP FZ     FZ     = IsEQ
-compareP FZ     (FS j) = IsLT LTZ
-compareP (FS i) FZ     = IsGT LTZ
-compareP (FS i) (FS j) = compareS $ compareP i j

lib/Quox/FreeVars.idr

@@ -0,0 +1,310 @@
+module Quox.FreeVars
+
+import Quox.Syntax.Term.Base
+import Data.Maybe
+import Data.Nat
+import Data.Singleton
+import Data.SortedSet
+import Derive.Prelude
+
+%language ElabReflection
+
+
+public export
+FreeVars' : Nat -> Type
+FreeVars' n = Context' Bool n
+
+public export
+record FreeVars n where
+  constructor FV
+  vars : FreeVars' n
+%name FreeVars xs
+
+%runElab deriveIndexed "FreeVars" [Eq, Ord, Show]
+
+
+export %inline
+(||) : FreeVars n -> FreeVars n -> FreeVars n
+FV s || FV t = FV $ zipWith (\x, y => x || y) s t
+
+export %inline
+(&&) : FreeVars n -> FreeVars n -> FreeVars n
+FV s && FV t = FV $ zipWith (\x, y => x && y) s t
+
+export %inline Semigroup (FreeVars n) where (<+>) = (||)
+
+export %inline [AndS] Semigroup (FreeVars n) where (<+>) = (&&)
+
+export
+only : {n : Nat} -> Var n -> FreeVars n
+only i = FV $ only' i where
+  only' : {n' : Nat} -> Var n' -> FreeVars' n'
+  only' VZ     = replicate (pred n') False :< True
+  only' (VS i) = only' i :< False
+
+export %inline
+all : {n : Nat} -> FreeVars n
+all = FV $ replicate n True
+
+export %inline
+none : {n : Nat} -> FreeVars n
+none = FV $ replicate n False
+
+
+export %inline
+uncons : FreeVars (S n) -> (FreeVars n, Bool)
+uncons (FV (xs :< x)) = (FV xs, x)
+
+
+export %inline {n : Nat} -> Monoid (FreeVars n) where neutral = none
+export %inline [AndM] {n : Nat} -> Monoid (FreeVars n) where neutral = all
+
+
+private
+self : {n : Nat} -> Context' (FreeVars n) n
+self = tabulate (\i => FV $ tabulate (== i) n) n
+
+export
+shift : forall from, to. Shift from to -> FreeVars from -> FreeVars to
+shift by (FV xs) = FV $ shift' by xs where
+  shift' : Shift from' to' -> FreeVars' from' -> FreeVars' to'
+  shift' SZ      ctx = ctx
+  shift' (SS by) ctx = shift' by ctx :< False
+
+
+export
+fromSet : {n : Nat} -> SortedSet (Var n) -> FreeVars n
+fromSet vs = FV $ tabulateLT n $ \i => contains (V i) vs
+
+export
+toSet : {n : Nat} -> FreeVars n -> SortedSet (Var n)
+toSet (FV vs) =
+  foldl_ (\s, i => maybe s (\i => insert i s) i) empty $
+  zipWith (\i, b => guard b $> i) (tabulateLT n V) vs
+
+
+public export
+interface HasFreeVars (0 tm : Nat -> Type) where
+  constructor HFV
+  fv : {n : Nat} -> tm n -> FreeVars n
+
+public export
+interface HasFreeDVars (0 tm : TermLike) where
+  constructor HFDV
+  fdv : {d, n : Nat} -> tm d n -> FreeVars d
+
+public export %inline
+fvWith : HasFreeVars tm => Singleton n -> tm n -> FreeVars n
+fvWith (Val n) = fv
+
+public export %inline
+fdvWith : HasFreeDVars tm => Singleton d -> Singleton n -> tm d n -> FreeVars d
+fdvWith (Val d) (Val n) = fdv
+
+export
+Fdv : (0 tm : TermLike) -> {n : Nat} ->
+      HasFreeDVars tm => HasFreeVars (\d => tm d n)
+Fdv tm @{HFDV fdv} = HFV fdv
+
+
+export
+fvEach : {n1, n2 : Nat} -> HasFreeVars env =>
+         Subst env n1 n2 -> Context' (Lazy (FreeVars n2)) n1
+fvEach (Shift by) = map (delay . shift by) self
+fvEach (t ::: th) = fvEach th :< fv t
+
+export
+fdvEach : {d, n1, n2 : Nat} -> HasFreeDVars env =>
+          Subst (env d) n1 n2 -> Context' (Lazy (FreeVars d)) n1
+fdvEach (Shift by) = replicate n1 none
+fdvEach (t ::: th) = fdvEach th :< fdv t
+
+
+export
+HasFreeVars Dim where
+  fv (K _ _) = none
+  fv (B i _) = only i
+
+
+export
+{s : Nat} -> HasFreeVars tm => HasFreeVars (Scoped s tm) where
+  fv (S _ (Y body)) = FV $ drop s (fv body).vars
+  fv (S _ (N body)) = fv body
+
+export
+implementation [DScope]
+  {s : Nat} -> HasFreeDVars tm =>
+  HasFreeDVars (\d, n => Scoped s (\d' => tm d' n) d)
+where
+  fdv (S _ (Y body)) = FV $ drop s (fdv body).vars
+  fdv (S _ (N body)) = fdv body
+
+export
+fvD : {0 tm : TermLike} -> {n : Nat} -> (forall d. HasFreeVars (tm d)) =>
+      Scoped s (\d => tm d n) d -> FreeVars n
+fvD (S _ (Y body)) = fv body
+fvD (S _ (N body)) = fv body
+
+export
+fdvT : HasFreeDVars tm => {s, d, n : Nat} -> Scoped s (tm d) n -> FreeVars d
+fdvT (S _ (Y body)) = fdv body
+fdvT (S _ (N body)) = fdv body
+
+
+private
+guardM : Monoid a => Bool -> Lazy a -> a
+guardM b x = if b then x else neutral
+
+export
+implementation
+  (HasFreeVars tm, HasFreeVars env) =>
+  HasFreeVars (WithSubst tm env)
+where
+  fv (Sub term subst) =
+    let Val from = getFrom subst in
+    foldMap (uncurry guardM) $ zipWith (,) (fv term).vars (fvEach subst)
+
+export
+implementation [WithSubst]
+  ((forall d. HasFreeVars (tm d)), HasFreeDVars tm, HasFreeDVars env) =>
+  HasFreeDVars (\d => WithSubst (tm d) (env d))
+where
+  fdv (Sub term subst) =
+    let Val from = getFrom subst in
+    fdv term <+>
+    foldMap (uncurry guardM) (zipWith (,) (fv term).vars (fdvEach subst))
+
+
+export HasFreeVars (Term d)
+export HasFreeVars (Elim d)
+
+export
+HasFreeVars (Term d) where
+  fv (TYPE    {})             = none
+  fv (IOState {})             = none
+  fv (Pi      {arg, res, _})  = fv arg <+> fv res
+  fv (Lam     {body, _})      = fv body
+  fv (Sig     {fst, snd, _})  = fv fst <+> fv snd
+  fv (Pair    {fst, snd, _})  = fv fst <+> fv snd
+  fv (Enum    {})             = none
+  fv (Tag     {})             = none
+  fv (Eq      {ty, l, r, _})  = fvD ty <+> fv l <+> fv r
+  fv (DLam    {body, _})      = fvD body
+  fv (NAT     {})             = none
+  fv (Nat     {})             = none
+  fv (Succ    {p, _})         = fv p
+  fv (STRING  {})             = none
+  fv (Str     {})             = none
+  fv (BOX     {ty, _})        = fv ty
+  fv (Box     {val, _})       = fv val
+  fv (Let     {rhs, body, _}) = fv rhs <+> fv body
+  fv (E       e)              = fv e
+  fv (CloT    s)              = fv s
+  fv (DCloT   s)              = fv s.term
+
+export
+HasFreeVars (Elim d) where
+  fv (F {}) = none
+  fv (B i _) = only i
+  fv (App {fun, arg, _}) = fv fun <+> fv arg
+  fv (CasePair {pair, ret, body, _}) = fv pair <+> fv ret <+> fv body
+  fv (Fst pair _) = fv pair
+  fv (Snd pair _) = fv pair
+  fv (CaseEnum {tag, ret, arms, _}) =
+    fv tag <+> fv ret <+> foldMap fv (values arms)
+  fv (CaseNat {nat, ret, zero, succ, _}) =
+    fv nat <+> fv ret <+> fv zero <+> fv succ
+  fv (CaseBox {box, ret, body, _}) =
+    fv box <+> fv ret <+> fv body
+  fv (DApp {fun, _}) = fv fun
+  fv (Ann {tm, ty, _}) = fv tm <+> fv ty
+  fv (Coe {ty, val, _}) = fvD ty <+> fv val
+  fv (Comp {ty, val, zero, one, _}) =
+    fv ty <+> fv val <+> fvD zero <+> fvD one
+  fv (TypeCase {ty, ret, arms, def, _}) =
+    fv ty <+> fv ret <+> fv def <+> foldMap (\x => fv x.snd) (toList arms)
+  fv (CloE s) = fv s
+  fv (DCloE s) = fv s.term
+
+
+
+private
+expandDShift : {d1 : Nat} -> Shift d1 d2 -> Loc -> Context' (Dim d2) d1
+expandDShift by loc = tabulateLT d1 (\i => BV i loc // by)
+
+private
+expandDSubst : {d1 : Nat} -> DSubst d1 d2 -> Loc -> Context' (Dim d2) d1
+expandDSubst (Shift by) loc = expandDShift by loc
+expandDSubst (t ::: th) loc = expandDSubst th loc :< t
+
+
+private
+fdvSubst' : {d1, d2, n : Nat} -> (Located2 tm, HasFreeDVars tm) =>
+            tm d1 n -> DSubst d1 d2 -> FreeVars d2
+fdvSubst' t th =
+  fold $ zipWith maybeOnly (fdv t).vars (expandDSubst th t.loc)
+where
+  maybeOnly : {d : Nat} -> Bool -> Dim d -> FreeVars d
+  maybeOnly True (B i _) = only i
+  maybeOnly _    _       = none
+
+private
+fdvSubst : {d, n : Nat} -> (Located2 tm, HasFreeDVars tm) =>
+           WithSubst (\d => tm d n) Dim d -> FreeVars d
+fdvSubst (Sub t th) = let Val from = getFrom th in fdvSubst' t th
+
+
+export HasFreeDVars Term
+export HasFreeDVars Elim
+
+export
+HasFreeDVars Term where
+  fdv (TYPE    {})             = none
+  fdv (IOState {})             = none
+  fdv (Pi      {arg, res, _})  = fdv arg <+> fdvT res
+  fdv (Lam     {body, _})      = fdvT body
+  fdv (Sig     {fst, snd, _})  = fdv fst <+> fdvT snd
+  fdv (Pair    {fst, snd, _})  = fdv fst <+> fdv snd
+  fdv (Enum    {})             = none
+  fdv (Tag     {})             = none
+  fdv (Eq      {ty, l, r, _})  = fdv @{DScope} ty <+> fdv l <+> fdv r
+  fdv (DLam    {body, _})      = fdv @{DScope} body
+  fdv (NAT     {})             = none
+  fdv (Nat     {})             = none
+  fdv (Succ    {p, _})         = fdv p
+  fdv (STRING  {})             = none
+  fdv (Str     {})             = none
+  fdv (BOX     {ty, _})        = fdv ty
+  fdv (Box     {val, _})       = fdv val
+  fdv (Let     {rhs, body, _}) = fdv rhs <+> fdvT body
+  fdv (E       e)              = fdv e
+  fdv (CloT    s)              = fdv s @{WithSubst}
+  fdv (DCloT   s)              = fdvSubst s
+
+export
+HasFreeDVars Elim where
+  fdv (F {}) = none
+  fdv (B {}) = none
+  fdv (App {fun, arg, _}) = fdv fun <+> fdv arg
+  fdv (CasePair {pair, ret, body, _}) = fdv pair <+> fdvT ret <+> fdvT body
+  fdv (Fst pair _) = fdv pair
+  fdv (Snd pair _) = fdv pair
+  fdv (CaseEnum {tag, ret, arms, _}) =
+    fdv tag <+> fdvT ret <+> foldMap fdv (values arms)
+  fdv (CaseNat {nat, ret, zero, succ, _}) =
+    fdv nat <+> fdvT ret <+> fdv zero <+> fdvT succ
+  fdv (CaseBox {box, ret, body, _}) =
+    fdv box <+> fdvT ret <+> fdvT body
+  fdv (DApp {fun, arg, _}) =
+    fdv fun <+> fv arg
+  fdv (Ann {tm, ty, _}) =
+    fdv tm <+> fdv ty
+  fdv (Coe {ty, p, q, val, _}) =
+    fdv @{DScope} ty <+> fv p <+> fv q <+> fdv val
+  fdv (Comp {ty, p, q, val, r, zero, one, _}) =
+    fdv ty <+> fv p <+> fv q <+> fdv val <+>
+    fv r <+> fdv @{DScope} zero <+> fdv @{DScope} one
+  fdv (TypeCase {ty, ret, arms, def, _}) =
+    fdv ty <+> fdv ret <+> fdv def <+> foldMap (\x => fdvT x.snd) (toList arms)
+  fdv (CloE s) = fdv s @{WithSubst}
+  fdv (DCloE s) = fdvSubst s

lib/Quox/Loc.idr

@@ -1,6 +1,7 @@
 ||| file locations
 module Quox.Loc
 
+import Quox.PrettyValExtra
 import public Text.Bounded
 import Data.SortedMap
 import Derive.Prelude
@@ -12,12 +13,12 @@ public export
 FileName : Type
 FileName = String
 
-%runElab derive "Bounds" [Ord]
+%runElab derive "Bounds" [Ord, PrettyVal]
 
 public export
 data Loc_ = NoLoc | YesLoc FileName Bounds
 %name Loc_ loc
-%runElab derive "Loc_" [Eq, Ord, Show]
+%runElab derive "Loc_" [Eq, Ord, Show, PrettyVal]
 
 
 ||| a wrapper for locations which are always considered equal
@@ -39,6 +40,18 @@ public export %inline
 makeLoc : FileName -> Bounds -> Loc
 makeLoc = L .: YesLoc
 
+public export %inline
+loc : FileName -> (sl, sc, el, ec : Int) -> Loc
+loc file sl sc el ec = makeLoc file $ MkBounds sl sc el ec
+
+export
+PrettyVal Loc where
+  prettyVal (L NoLoc) = Con "noLoc" []
+  prettyVal (L (YesLoc file (MkBounds sl sc el ec))) =
+    Con "loc" [prettyVal file,
+               prettyVal sl, prettyVal sc,
+               prettyVal el, prettyVal ec]
+
 
 export
 onlyStart_ : Loc_ -> Loc_
@@ -95,7 +108,7 @@ extendL : Loc -> Loc -> Loc
 extendL l1 l2 = l1 `extend'` l2.bounds
 
 
-infixr 1 `or_`, `or`
+export infixr 1 `or_`, `or`
 export %inline
 or_ : Loc_ -> Loc_ -> Loc_
 or_ l1@(YesLoc {}) _  = l1
@@ -105,6 +118,11 @@ export %inline
 or : Loc -> Loc -> Loc
 or (L l1) (L l2) = L $ l1 `or_` l2
 
+export %inline
+extendOr : Loc -> Loc -> Loc
+extendOr l1 l2 = (l1 `extendL` l2) `or` l2
+
+
 
 public export
 interface Located a where (.loc) : a -> Loc
@@ -113,9 +131,22 @@ public export
 0 Located1 : (a -> Type) -> Type
 Located1 f = forall x. Located (f x)
 
+public export
+0 Located2 : (a -> b -> Type) -> Type
+Located2 f = forall x, y. Located (f x y)
+
 public export
 interface Located a => Relocatable a where setLoc : Loc -> a -> a
 
 public export
 0 Relocatable1 : (a -> Type) -> Type
 Relocatable1 f = forall x. Relocatable (f x)
+
+public export
+0 Relocatable2 : (a -> b -> Type) -> Type
+Relocatable2 f = forall x, y. Relocatable (f x y)
+
+
+export
+locs : Located a => Foldable t => t a -> Loc
+locs = foldl (\loc, y => loc `extendOr` y.loc) noLoc

lib/Quox/Log.idr

@@ -0,0 +1,317 @@
+module Quox.Log
+
+import Quox.Loc
+import Quox.Pretty
+import Quox.PrettyValExtra
+
+import Data.So
+import Data.DPair
+import Data.Maybe
+import Data.List1
+import Control.Eff
+import Control.Monad.ST.Extra
+import Data.IORef
+import System.File
+import Derive.Prelude
+
+%default total
+%language ElabReflection
+
+
+public export %inline
+maxLogLevel : Nat
+maxLogLevel = 100
+
+public export %inline
+logCategories : List String
+logCategories = ["whnf", "equal", "check"]
+
+public export %inline
+isLogLevel : Nat -> Bool
+isLogLevel l = l <= maxLogLevel
+
+public export
+IsLogLevel : Nat -> Type
+IsLogLevel l = So $ isLogLevel l
+
+public export %inline
+isLogCategory : String -> Bool
+isLogCategory cat = cat `elem` logCategories
+
+public export
+IsLogCategory : String -> Type
+IsLogCategory cat = So $ isLogCategory cat
+
+-- Q: why are you using `So` instead of `LT` and `Elem`
+-- A: ① proof search gives up before finding a proof of e.g. ``99 `LT` 100``
+--      (i.e. `LTESucc⁹⁹ LTEZero`)
+--    ② the proofs aren't looked at in any way, i just wanted to make sure the
+--      list of categories was consistent everywhere
+
+
+||| a verbosity level from 0–100. higher is noisier. each log entry has a
+||| verbosity level above which it will be printed, chosen, uh, based on vibes.
+public export
+LogLevel : Type
+LogLevel = Subset Nat IsLogLevel
+
+||| a logging category, like "check" (type checking), "whnf", or whatever.
+public export
+LogCategory : Type
+LogCategory = Subset String IsLogCategory
+
+
+public export %inline
+toLogLevel : Nat -> Maybe LogLevel
+toLogLevel l =
+  case choose $ isLogLevel l of
+    Left  y => Just $ Element l y
+    Right _ => Nothing
+
+public export %inline
+toLogCategory : String -> Maybe LogCategory
+toLogCategory c =
+  case choose $ isLogCategory c of
+    Left  y => Just $ Element c y
+    Right _ => Nothing
+
+
+||| verbosity levels for each category, if they differ from the default
+public export
+LevelMap : Type
+LevelMap = List (LogCategory, LogLevel)
+
+-- Q: why `List` instead of `SortedMap`
+-- A: oof ouch my constant factors (maybe this one was more obvious)
+
+
+public export
+record LogLevels where
+  constructor MkLogLevels
+  defLevel : LogLevel
+  levels   : LevelMap
+%name LogLevels lvls
+%runElab derive "LogLevels" [Eq, Show, PrettyVal]
+
+public export
+LevelStack : Type
+LevelStack = List LogLevels
+
+public export %inline
+defaultLevel : LogLevel
+defaultLevel = Element 0 Oh
+
+export %inline
+defaultLogLevels : LogLevels
+defaultLogLevels = MkLogLevels defaultLevel []
+
+export %inline
+initStack : LevelStack
+initStack = []
+
+export %inline
+getLevel1 : LogCategory -> LogLevels -> LogLevel
+getLevel1 cat (MkLogLevels def lvls) = fromMaybe def $ lookup cat lvls
+
+export %inline
+getLevel : LogCategory -> LevelStack -> LogLevel
+getLevel cat (lvls :: _) = getLevel1 cat lvls
+getLevel cat []          = defaultLevel
+
+export %inline
+getCurLevels : LevelStack -> LogLevels
+getCurLevels (lvls :: _) = lvls
+getCurLevels []          = defaultLogLevels
+
+
+public export
+LogDoc : Type
+LogDoc = Doc (Opts {lineLength = 80})
+
+
+private %inline
+replace : Eq a => a -> b -> List (a, b) -> List (a, b)
+replace k v kvs = (k, v) :: filter (\y => fst y /= k) kvs
+
+private %inline
+mergeLeft : Eq a => List (a, b) -> List (a, b) -> List (a, b)
+mergeLeft l r = foldl (\lst, (k, v) => replace k v lst) r l
+
+
+public export
+data PushArg =
+    SetDefault LogLevel
+  | SetCat     LogCategory LogLevel
+  | SetAll     LogLevel
+%runElab derive "PushArg" [Eq, Ord, Show, PrettyVal]
+%name PushArg push
+
+export %inline
+applyPush : LogLevels -> PushArg -> LogLevels
+applyPush lvls (SetDefault def)     = {defLevel := def} lvls
+applyPush lvls (SetCat     cat lvl) = {levels   $= replace cat lvl} lvls
+applyPush lvls (SetAll     lvl)     = MkLogLevels lvl []
+
+export %inline
+fromPush : PushArg -> LogLevels
+fromPush = applyPush defaultLogLevels
+
+
+public export
+record LogMsg where
+  constructor (:>)
+  level : Nat
+  {auto 0 levelOk : IsLogLevel level}
+  message : Lazy LogDoc
+export infix 0 :>
+%name Log.LogMsg msg
+
+public export
+data LogL : (lbl : tag) -> Type -> Type where
+  ||| print some log messages
+  SayMany : (cat : LogCategory) -> (loc : Loc) ->
+            (msgs : List LogMsg) -> LogL lbl ()
+  ||| set some verbosity levels
+  Push : (push : List PushArg) -> LogL lbl ()
+  ||| restore the previous verbosity levels.
+  ||| returns False if the stack was already empty
+  Pop : LogL lbl Bool
+  ||| returns the current verbosity levels
+  CurLevels : LogL lbl LogLevels
+
+public export
+Log : Type -> Type
+Log = LogL ()
+
+parameters (0 lbl : tag) {auto _ : Has (LogL lbl) fs}
+  public export %inline
+  sayManyAt : (cat : String) -> (0 catOk : IsLogCategory cat) =>
+              Loc -> List LogMsg -> Eff fs ()
+  sayManyAt cat loc msgs {catOk} =
+    send $ SayMany {lbl} (Element cat catOk) loc msgs
+
+  public export %inline
+  sayAt : (cat : String) -> (0 catOk : IsLogCategory cat) =>
+          (lvl : Nat)    -> (0 lvlOk : IsLogLevel lvl) =>
+          Loc -> Lazy LogDoc -> Eff fs ()
+  sayAt cat lvl loc msg = sayManyAt cat loc [lvl :> msg]
+
+  public export %inline
+  pushAt : List PushArg -> Eff fs ()
+  pushAt lvls = send $ Push {lbl} lvls
+
+  public export %inline
+  push1At : PushArg -> Eff fs ()
+  push1At lvl = pushAt [lvl]
+
+  public export %inline
+  popAt : Eff fs Bool
+  popAt = send $ Pop {lbl}
+
+  public export %inline
+  curLevelsAt : Eff fs LogLevels
+  curLevelsAt = send $ CurLevels {lbl}
+
+parameters {auto _ : Has Log fs}
+  public export %inline
+  sayMany : (cat : String) -> (0 catOk : IsLogCategory cat) =>
+            Loc -> List LogMsg -> Eff fs ()
+  sayMany = sayManyAt ()
+
+  public export %inline
+  say : (cat : String) -> (0 _ : IsLogCategory cat) =>
+        (lvl : Nat)    -> (0 _ : IsLogLevel lvl) =>
+        Loc -> Lazy LogDoc -> Eff fs ()
+  say = sayAt ()
+
+  public export %inline
+  push : List PushArg -> Eff fs ()
+  push = pushAt ()
+
+  public export %inline
+  push1 : PushArg -> Eff fs ()
+  push1 = push1At ()
+
+  public export %inline
+  pop : Eff fs Bool
+  pop = popAt ()
+
+  public export %inline
+  curLevels : Eff fs LogLevels
+  curLevels = curLevelsAt ()
+
+
+||| handles a `Log` effect with an existing `State` and `Writer`
+export %inline
+handleLogSW : (0 s : ts) -> (0 w : tw) ->
+              Has (StateL s LevelStack) fs => Has (WriterL w LogDoc) fs =>
+              LogL tag a -> Eff fs a
+handleLogSW s w = \case
+  Push push => modifyAt s $ \lst =>
+    foldl applyPush (fromMaybe defaultLogLevels (head' lst)) push :: lst
+  Pop => stateAt s $ maybe (False, []) (True,) . tail'
+  SayMany cat loc msgs => do
+    catLvl <- getsAt s $ fst . getLevel cat
+    let loc = runPretty $ prettyLoc loc
+    for_ msgs $ \(lvl :> msg) => when (lvl <= catLvl) $ tellAt w $
+      hcat [loc, text cat.fst, "@", pshow lvl, ":"] <++> msg
+  CurLevels =>
+    getsAt s getCurLevels
+
+export %inline
+handleLogSW_ : LogL tag a -> Eff [State LevelStack, Writer LogDoc] a
+handleLogSW_ = handleLogSW () ()
+
+export %inline
+handleLogIO : HasIO m => MonadRec m =>
+              (FileError -> m ()) -> IORef LevelStack -> File ->
+              LogL tag a -> m a
+handleLogIO th lvls h act =
+  runEff (handleLogSW_ act) [handleStateIORef lvls, handleWriter {m} printMsg]
+where printMsg : LogDoc -> m ()
+      printMsg msg = fPutStr h (render _ msg) >>= either th pure
+
+export %inline
+handleLogST : HasST m => MonadRec (m s) =>
+              STRef s (SnocList LogDoc) -> STRef s LevelStack ->
+              LogL tag a -> m s a
+handleLogST docs lvls act =
+  runEff (handleLogSW_ act) [handleStateSTRef lvls, handleWriterSTRef docs]
+
+export %inline
+handleLogDiscard : (0 s : ts) -> Has (StateL s Nat) fs =>
+                   LogL tag a -> Eff fs a
+handleLogDiscard s = \case
+  Push _     => modifyAt s S
+  Pop        => stateAt s $ \k => (k > 0, pred k)
+  SayMany {} => pure ()
+  CurLevels  => pure defaultLogLevels
+
+export %inline
+handleLogDiscard_ : LogL tag a -> Eff [State Nat] a
+handleLogDiscard_ = handleLogDiscard ()
+
+export %inline
+handleLogDiscardST : HasST m => MonadRec (m s) => STRef s Nat ->
+                     LogL tag a -> m s a
+handleLogDiscardST ref act =
+  runEff (handleLogDiscard_ act) [handleStateSTRef ref]
+
+export %inline
+handleLogDiscardIO : HasIO m => MonadRec m => IORef Nat ->
+                     LogL tag a -> m a
+handleLogDiscardIO ref act =
+  runEff (handleLogDiscard_ act) [handleStateIORef ref]
+
+
+||| approximate the push/pop effects in a discarded log by trimming a stack or
+||| repeating its most recent element
+export %inline
+fixupDiscardedLog : Nat -> LevelStack -> LevelStack
+fixupDiscardedLog want lvls =
+  let len = length lvls in
+  case compare len want of
+    EQ => lvls
+    GT => drop (len `minus` want) lvls
+    LT => let new = fromMaybe defaultLogLevels $ head' lvls in
+          replicate (want `minus` len) new ++ lvls

lib/Quox/Name.idr

@@ -2,6 +2,7 @@ module Quox.Name
 
 import Quox.Loc
 import Quox.CharExtra
+import Quox.PrettyValExtra
 import public Data.SnocList
 import Data.List
 import Control.Eff
@@ -23,7 +24,7 @@ data BaseName
 = UN String         -- user-given name
 | MN String NameSuf -- machine-generated name
 | Unused            -- "_"
-%runElab derive "BaseName" [Eq, Ord]
+%runElab derive "BaseName" [Eq, Ord, PrettyVal]
 
 export
 baseStr : BaseName -> String
@@ -42,14 +43,14 @@ Mods = SnocList String
 
 public export
 record Name where
-  constructor MakeName
+  constructor MkName
   mods : Mods
   base : BaseName
 %runElab derive "Name" [Eq, Ord]
 
 public export %inline
 unq : BaseName -> Name
-unq = MakeName [<]
+unq = MkName [<]
 
 ||| add some namespaces to the beginning of a name
 public export %inline
@@ -63,31 +64,31 @@ PBaseName = String
 
 public export
 record PName where
-  constructor MakePName
+  constructor MkPName
   mods : Mods
   base : PBaseName
-%runElab derive "PName" [Eq, Ord]
+%runElab derive "PName" [Eq, Ord, PrettyVal]
 
 export %inline
 fromPName : PName -> Name
-fromPName p = MakeName p.mods $ UN p.base
+fromPName p = MkName p.mods $ UN p.base
 
 export %inline
 toPName : Name -> PName
-toPName p = MakePName p.mods $ baseStr p.base
+toPName p = MkPName p.mods $ baseStr p.base
 
 export %inline
 fromPBaseName : PBaseName -> Name
-fromPBaseName = MakeName [<] . UN
+fromPBaseName = MkName [<] . UN
 
 export
 Show PName where
-  show (MakePName mods base) =
+  show (MkPName mods base) =
     show $ concat $ intersperse "." $ toList $ mods :< base
 
 export Show Name where show = show . toPName
 
-export FromString PName where fromString = MakePName [<]
+export FromString PName where fromString = MkPName [<]
 
 export FromString Name where fromString = fromPBaseName
 
@@ -95,9 +96,9 @@ export FromString Name where fromString = fromPBaseName
 public export
 record BindName where
   constructor BN
-  name : BaseName
+  val  : BaseName
   loc_ : Loc
-%runElab derive "BindName" [Eq, Ord, Show]
+%runElab derive "BindName" [Eq, Ord, Show, PrettyVal]
 
 export Located BindName where n.loc = n.loc_
 export Relocatable BindName where setLoc loc (BN x _) = BN x loc
@@ -115,7 +116,7 @@ export
 fromListP : List1 String -> PName
 fromListP (x ::: xs) = go [<] x xs where
   go : SnocList String -> String -> List String -> PName
-  go mods x []        = MakePName mods x
+  go mods x []        = MkPName mods x
   go mods x (y :: ys) = go (mods :< x) y ys
 
 export %inline
@@ -169,14 +170,6 @@ public export
 NameGen : Type -> Type
 NameGen = StateL GEN NameSuf
 
-export
-runNameGenWith : Has NameGen fs =>
-                 NameSuf -> Eff fs a -> Eff (fs - NameGen) (a, NameSuf)
-runNameGenWith = runStateAt GEN
-
-export
-runNameGen : Has NameGen fs => Eff fs a -> Eff (fs - NameGen) a
-runNameGen = map fst . runNameGenWith 0
 
 ||| generate a fresh name with the given base
 export
@@ -186,15 +179,13 @@ mn base = do
   modifyAt GEN S
   pure $ MN base i
 
-||| generate a fresh binding name with the given base and
-||| (optionally) location `loc`
+||| generate a fresh binding name with the given base and location `loc`
 export
-mnb : Has NameGen fs =>
-      PBaseName -> {default noLoc loc : Loc} -> Eff fs BindName
-mnb base = pure $ BN !(mn base) loc
+mnb : Has NameGen fs => PBaseName -> Loc -> Eff fs BindName
+mnb base loc = pure $ BN !(mn base) loc
 
 export
 fresh : Has NameGen fs => BindName -> Eff fs BindName
-fresh (BN (UN str)   loc) = mnb str {loc}
-fresh (BN (MN str k) loc) = mnb str {loc}
-fresh (BN Unused     loc) = mnb "x" {loc}
+fresh (BN (UN str)   loc) = mnb str loc
+fresh (BN (MN str k) loc) = mnb str loc
+fresh (BN Unused     loc) = mnb "x" loc

lib/Quox/NatExtra.idr

@@ -1,19 +1,13 @@
 module Quox.NatExtra
 
 import public Data.Nat
-import public Data.Nat.Views
 import Data.Nat.Division
 import Data.SnocList
 import Data.Vect
-import Syntax.PreorderReasoning
+import Data.String
 
 %default total
 
-infixl 8 `shiftL`, `shiftR`
-infixl 7 .&.
-infixl 6 `xor`
-infixl 5 .|.
-
 
 public export
 data LTE' : Nat -> Nat -> Type where
@@ -59,151 +53,42 @@ parameters {base : Nat} {auto 0 _ : base `GTE` 2} (chars : Vect base Char)
   showAtBase : Nat -> String
   showAtBase = pack . showAtBase' []
 
-export
-showHex : Nat -> String
-showHex = showAtBase $ fromList $ unpack "0123456789ABCDEF"
+namespace Nat
+  export
+  showHex : Nat -> String
+  showHex = showAtBase $ fromList $ unpack "0123456789abcdef"
+
+namespace Int
+  export
+  showHex : Int -> String
+  showHex x =
+    if x < 0 then "-" ++ Nat.showHex (cast (-x)) else Nat.showHex (cast x)
 
 
-export
-0 notEvenOdd : (a, b : Nat) -> Not (a + a = S (b + b))
-notEvenOdd 0     b prf = absurd prf
-notEvenOdd (S a) b prf =
-  notEvenOdd b a $ Calc $
-    |~ b + b
-    ~~ a + S a   ..<(inj S prf)
-    ~~ S (a + a) ..<(plusSuccRightSucc {})
+namespace Int
+  export
+  fromHexit : Char -> Maybe Int
+  fromHexit c =
+    if      c >= '0' && c <= '9' then Just $ ord c - ord '0'
+    else if c >= 'a' && c <= 'f' then Just $ ord c - ord 'a' + 10
+    else if c >= 'A' && c <= 'F' then Just $ ord c - ord 'A' + 10
+    else Nothing
 
-export
-0 doubleInj : (m, n : Nat) -> m + m = n + n -> m = n
-doubleInj 0     0     _   = Refl
-doubleInj (S m) (S n) prf =
-  cong S $ doubleInj m n $
-  inj S $ Calc $
-    |~ S (m + m)
-    ~~ m + S m   ...(plusSuccRightSucc {})
-    ~~ n + S n   ...(inj S prf)
-    ~~ S (n + n) ..<(plusSuccRightSucc {})
+  private
+  fromHex' : Int -> String -> Maybe Int
+  fromHex' acc str = case strM str of
+    StrNil       => Just acc
+    StrCons c cs => fromHex' (16 * acc + !(fromHexit c)) (assert_smaller str cs)
 
-export
-0 halfDouble : (n : Nat) -> half (n + n) = HalfEven n
-halfDouble n with (half (n + n)) | (n + n) proof nn
-  _ | HalfOdd  k | S (k + k) = void $ notEvenOdd n k nn
-  _ | HalfEven k | k + k     = rewrite doubleInj n k nn in Refl
+  export %inline
+  fromHex : String -> Maybe Int
+  fromHex str = do guard $ str /= ""; fromHex' 0 str
 
-export
-floorHalf : Nat -> Nat
-floorHalf k = case half k of
-  HalfOdd  n => n
-  HalfEven n => n
+namespace Nat
+  export
+  fromHexit : Char -> Maybe Nat
+  fromHexit = map cast . Int.fromHexit
 
-
-||| like in intercal ☺
-|||
-||| take all the bits of `subj` that are set in `mask`, and squish them down
-||| towards the lsb
-public export
-select : (mask, subj : Nat) -> Nat
-select mask subj = go 1 (halfRec mask) subj 0 where
-  go : forall mask. Nat -> HalfRec mask -> Nat -> Nat -> Nat
-  go bit HalfRecZ            subj res = res
-  go bit (HalfRecEven _ rec) subj res = go bit rec (floorHalf subj) res
-  go bit (HalfRecOdd  _ rec) subj res = case half subj of
-    HalfOdd  subj => go (bit + bit) rec subj (res + bit)
-    HalfEven subj => go (bit + bit) rec subj res
-
-||| take the i least significant bits of subj (where i = popCount mask),
-||| and place them where mask's set bits are
-|||
-||| left inverse of select if mask .|. subj = mask
-public export
-spread : (mask, subj : Nat) -> Nat
-spread mask subj = go 1 (halfRec mask) subj 0 where
-  go : forall mask. Nat -> HalfRec mask -> Nat -> Nat -> Nat
-  go bit HalfRecZ            subj res = res
-  go bit (HalfRecEven _ rec) subj res = go (bit + bit) rec subj res
-  go bit (HalfRecOdd  _ rec) subj res = case half subj of
-    HalfOdd  subj => go (bit + bit) rec subj (res + bit)
-    HalfEven subj => go (bit + bit) rec subj res
-
-
-
-public export
-data BitwiseRec : Nat -> Nat -> Type where
-  BwDone : BitwiseRec 0 0
-  Bw00   : (m, n : Nat) -> Lazy (BitwiseRec m n) ->
-           BitwiseRec (m + m) (n + n)
-  Bw01   : (m, n : Nat) -> Lazy (BitwiseRec m n) ->
-           BitwiseRec (m + m) (S (n + n))
-  Bw10   : (m, n : Nat) -> Lazy (BitwiseRec m n) ->
-           BitwiseRec (S (m + m)) (n + n)
-  Bw11   : (m, n : Nat) -> Lazy (BitwiseRec m n) ->
-           BitwiseRec (S (m + m)) (S (n + n))
-
-export
-bitwiseRec : (m, n : Nat) -> BitwiseRec m n
-bitwiseRec m n = go (halfRec m) (halfRec n) where
-  go : forall m, n. HalfRec m -> HalfRec n -> BitwiseRec m n
-  go HalfRecZ           HalfRecZ           = BwDone
-  go HalfRecZ           (HalfRecEven n nr) = Bw00 0 n $ go HalfRecZ nr
-  go HalfRecZ           (HalfRecOdd  n nr) = Bw01 0 n $ go HalfRecZ nr
-  go (HalfRecEven m mr) HalfRecZ           = Bw00 m 0 $ go mr HalfRecZ
-  go (HalfRecEven m mr) (HalfRecEven n nr) = Bw00 m n $ go mr nr
-  go (HalfRecEven m mr) (HalfRecOdd  n nr) = Bw01 m n $ go mr nr
-  go (HalfRecOdd  m mr) HalfRecZ           = Bw10 m 0 $ go mr HalfRecZ
-  go (HalfRecOdd  m mr) (HalfRecEven n nr) = Bw10 m n $ go mr nr
-  go (HalfRecOdd  m mr) (HalfRecOdd  n nr) = Bw11 m n $ go mr nr
-
-public export
-bitwise : (Bool -> Bool -> Bool) -> Nat -> Nat -> Nat
-bitwise f m n = go 1 (bitwiseRec m n) 0 where
-  one : Bool -> Bool -> Nat -> Nat -> Nat
-  one p q bit res = if f p q then bit + res else res
-  go : forall m, n. Nat -> BitwiseRec m n -> Nat -> Nat
-  go bit BwDone         res = res
-  go bit (Bw00 m n rec) res = go (bit + bit) rec $ one False False bit res
-  go bit (Bw01 m n rec) res = go (bit + bit) rec $ one False True  bit res
-  go bit (Bw10 m n rec) res = go (bit + bit) rec $ one True  False bit res
-  go bit (Bw11 m n rec) res = go (bit + bit) rec $ one True  True  bit res
-
-public export
-(.&.) : Nat -> Nat -> Nat
-(.&.) = bitwise $ \p, q => p && q
-
-private %foreign "scheme:blodwen-and"
-primAnd : Nat -> Nat -> Nat
-%transform "NatExtra.(.&.)" NatExtra.(.&.) m n = primAnd m n
-
-public export
-(.|.) : Nat -> Nat -> Nat
-(.|.) = bitwise $ \p, q => p || q
-
-private %foreign "scheme:blodwen-or"
-primOr : Nat -> Nat -> Nat
-%transform "NatExtra.(.|.)" NatExtra.(.|.) m n = primOr m n
-
-public export
-xor : Nat -> Nat -> Nat
-xor = bitwise (/=)
-
-private %foreign "scheme:blodwen-xor"
-primXor : Nat -> Nat -> Nat
-%transform "NatExtra.xor" NatExtra.xor m n = primXor m n
-
-
-public export
-shiftL : Nat -> Nat -> Nat
-shiftL n 0     = n
-shiftL n (S i) = shiftL (n + n) i
-
-private %foreign "scheme:blodwen-shl"
-primShiftL : Nat -> Nat -> Nat
-%transform "NatExtra.shiftL" NatExtra.shiftL n i = primShiftL n i
-
-public export
-shiftR : Nat -> Nat -> Nat
-shiftR n 0     = n
-shiftR n (S i) = shiftL (floorHalf n) i
-
-private %foreign "scheme:blodwen-shr"
-primShiftR : Nat -> Nat -> Nat
-%transform "NatExtra.shiftR" NatExtra.shiftR n i = primShiftR n i
+  export %inline
+  fromHex : String -> Maybe Nat
+  fromHex = map cast . Int.fromHex

lib/Quox/No.idr

@@ -43,7 +43,7 @@ parameters {0 a, b : Bool}
   noOr2 = snd . noOr
 
 
-infixr 1 `orNo`
+export infixr 1 `orNo`
 export %inline
 orNo : No a -> No b -> No (a || b)
 orNo Ah Ah = Ah
@@ -52,3 +52,8 @@ export %inline
 nchoose : (b : Bool) -> Either (So b) (No b)
 nchoose True  = Left  Oh
 nchoose False = Right Ah
+
+export
+0 notYesNo : {f : Dec p} -> Not p -> No (isYes f)
+notYesNo {f = Yes y} g = absurd $ g y
+notYesNo {f = No  n} g = Ah

lib/Quox/OPE.idr

@@ -1,76 +0,0 @@
-||| "order preserving embeddings", for recording a correspondence between
-||| a smaller scope and part of a larger one.
-module Quox.OPE
-
-import Quox.NatExtra
-import Data.Nat
-
-%default total
-
-
-public export
-data OPE : Nat -> Nat -> Type where
-  Id   : OPE n n
-  Drop : OPE m n -> OPE m     (S n)
-  Keep : OPE m n -> OPE (S m) (S n)
-%name OPE p, q
-
-public export %inline Injective Drop where injective Refl = Refl
-public export %inline Injective Keep where injective Refl = Refl
-
-public export
-opeZero : {n : Nat} -> OPE 0 n
-opeZero {n = 0}   = Id
-opeZero {n = S n} = Drop opeZero
-
-public export
-(.) : OPE m n -> OPE n p -> OPE m p
-p      . Id     = p
-Id     . q      = q
-p      . Drop q = Drop $ p . q
-Drop p . Keep q = Drop $ p . q
-Keep p . Keep q = Keep $ p . q
-
-public export
-toLTE : {m : Nat} -> OPE m n -> m `LTE` n
-toLTE Id       = reflexive
-toLTE (Drop p) = lteSuccRight $ toLTE p
-toLTE (Keep p) = LTESucc      $ toLTE p
-
-
-public export
-keepN : (n : Nat) -> OPE a b -> OPE (n + a) (n + b)
-keepN 0     p = p
-keepN (S n) p = Keep $ keepN n p
-
-public export
-dropInner' : LTE' m n -> OPE m n
-dropInner' LTERefl      = Id
-dropInner' (LTESuccR p) = Drop $ dropInner' $ force p
-
-public export
-dropInner : {n : Nat} -> LTE m n -> OPE m n
-dropInner = dropInner' . fromLte
-
-public export
-dropInnerN : (m : Nat) -> OPE n (m + n)
-dropInnerN 0     = Id
-dropInnerN (S m) = Drop $ dropInnerN m
-
-
-public export
-interface Tighten t where
-  tighten : OPE m n -> t n -> Maybe (t m)
-
-parameters {auto _ : Tighten t}
-  export %inline
-  tightenInner : {n : Nat} -> m `LTE` n -> t n -> Maybe (t m)
-  tightenInner = tighten . dropInner
-
-  export %inline
-  tightenN : (m : Nat) -> t (m + n) -> Maybe (t n)
-  tightenN m = tighten $ dropInnerN m
-
-  export %inline
-  tighten1 : t (S n) -> Maybe (t n)
-  tighten1 = tightenN 1

lib/Quox/Parser/FromParser.idr

@@ -1,39 +1,31 @@
 ||| take freshly-parsed input, scope check, type check, add to env
 module Quox.Parser.FromParser
 
+import public Quox.Parser.FromParser.Error as Quox.Parser.FromParser
+
+import Quox.Pretty
 import Quox.Parser.Syntax
 import Quox.Parser.Parser
+import public Quox.Parser.LoadFile
 import Quox.Typechecker
+import Quox.CheckBuiltin
 
 import Data.List
 import Data.Maybe
 import Data.SnocVect
 import Quox.EffExtra
+import Control.Monad.ST.Extra
 
 import System.File
 import System.Path
 import Data.IORef
 
-import public Quox.Parser.FromParser.Error as Quox.Parser.FromParser
-
-%default total
 
 %hide Typing.Error
 %hide Lexer.Error
 %hide Parser.Error
 
-
-public export
-NDefinition : Type
-NDefinition = (Name, Definition)
-
-public export
-IncludePath : Type
-IncludePath = List String
-
-public export
-SeenFiles : Type
-SeenFiles = SortedSet String
+%default total
 
 
 public export
@@ -41,27 +33,50 @@ data StateTag = NS | SEEN
 
 public export
 FromParserPure : List (Type -> Type)
-FromParserPure =
-  [Except Error, DefsState, StateL NS Mods, NameGen]
-
-public export
-LoadFile' : List (Type -> Type)
-LoadFile' = [IO, StateL SEEN SeenFiles, Reader IncludePath]
-
-public export
-LoadFile : List (Type -> Type)
-LoadFile = LoadFile' ++ [Except Error]
+FromParserPure = [Except Error, DefsState, StateL NS Mods, NameGen, Log]
 
 public export
 FromParserIO : List (Type -> Type)
-FromParserIO = FromParserPure ++ LoadFile'
+FromParserIO = FromParserPure ++ [LoadFile]
+
+
+public export
+record PureParserResult a where
+  constructor MkPureParserResult
+  val       : a
+  suf       : NameSuf
+  defs      : Definitions
+  log       : SnocList LogDoc
+  logLevels : LevelStack
+
+export
+fromParserPure : Mods -> NameSuf -> Definitions -> LevelStack ->
+                 Eff FromParserPure a -> Either Error (PureParserResult a)
+fromParserPure ns suf defs lvls act = runSTErr $ do
+  suf  <- newSTRef' suf
+  defs <- newSTRef' defs
+  log  <- newSTRef' [<]
+  lvls <- newSTRef' lvls
+  res  <- runEff act $ with Union.(::)
+    [handleExcept $ \e => stLeft e,
+     handleStateSTRef defs,
+     handleStateSTRef !(newSTRef' ns),
+     handleStateSTRef suf,
+     handleLogST log lvls]
+  pure $ MkPureParserResult {
+    val       = res,
+    suf       = !(readSTRef' suf),
+    defs      = !(readSTRef' defs),
+    log       = !(readSTRef' log),
+    logLevels = !(readSTRef' lvls)
+  }
 
 
 parameters {auto _ : Functor m} (b : Var n -> m a) (f : PName -> m a)
            (xs : Context' PatVar n)
   private
   fromBaseName : PBaseName -> m a
-  fromBaseName x = maybe (f $ MakePName [<] x) b $
+  fromBaseName x = maybe (f $ MkPName [<] x) b $
                    Context.find (\y => y.name == Just x) xs
 
   private
@@ -113,11 +128,10 @@ fromV : Context' PatVar d -> Context' PatVar n ->
         PName -> Maybe Universe -> Loc -> Eff FromParserPure (Term d n)
 fromV ds ns x u loc = fromName bound free ns x where
   bound : Var n -> Eff FromParserPure (Term d n)
-  bound i = do whenJust u $ \u => throw $ DisplacedBoundVar loc x
-               pure $ E $ B i loc
+  bound i = unless (isNothing u) (throw $ DisplacedBoundVar loc x) $> BT i loc
+
   free : PName -> Eff FromParserPure (Term d n)
-  free x = do x <- avoidDim ds loc x
-              resolveName !(getAt NS) loc x u
+  free x = resolveName !(getAt NS) loc !(avoidDim ds loc x) u
 
 mutual
   export
@@ -127,6 +141,9 @@ mutual
     TYPE k loc =>
       pure $ TYPE k loc
 
+    IOState loc =>
+      pure $ IOState loc
+
     Pi pi x s t loc =>
       Pi (fromPQty pi)
         <$> fromPTermWith ds ns s
@@ -157,17 +174,26 @@ mutual
         <*> fromPTermTScope ds ns [< x, y] body
         <*> pure loc
 
+    Fst pair loc =>
+      map E $ Fst <$> fromPTermElim ds ns pair <*> pure loc
+
+    Snd pair loc =>
+      map E $ Snd <$> fromPTermElim ds ns pair <*> pure loc
+
     Case pi tag (r, ret) (CaseEnum arms _) loc =>
       map E $ CaseEnum (fromPQty pi)
         <$> fromPTermElim ds ns tag
         <*> fromPTermTScope ds ns [< r] ret
-        <*> assert_total fromPTermEnumArms ds ns arms
+        <*> assert_total fromPTermEnumArms loc ds ns arms
         <*> pure loc
 
-    Nat loc => pure $ Nat loc
-    Zero loc => pure $ Zero loc
+    NAT loc => pure $ NAT loc
+    Nat n loc => pure $ Nat n loc
     Succ n loc => [|Succ (fromPTermWith ds ns n) (pure loc)|]
 
+    STRING loc => pure $ STRING loc
+    Str str loc => pure $ Str str loc
+
     Case pi nat (r, ret) (CaseNat zer (s, pi', ih, suc) _) loc =>
       map E $ CaseNat (fromPQty pi) (fromPQty pi')
         <$> fromPTermElim ds ns nat
@@ -176,12 +202,11 @@ mutual
         <*> fromPTermTScope ds ns [< s, ih] suc
         <*> pure loc
 
-    Enum strs loc =>
-      let set = SortedSet.fromList strs in
-      if length strs == length (SortedSet.toList set) then
-        pure $ Enum set loc
-      else
-        throw $ DuplicatesInEnum loc strs
+    Enum strs loc => do
+      let set = SortedSet.fromList strs
+      unless (length strs == length (SortedSet.toList set)) $
+        throw $ DuplicatesInEnumType loc strs
+      pure $ Enum set loc
 
     Tag str loc => pure $ Tag str loc
 
@@ -238,13 +263,22 @@ mutual
         <*> fromPTermDScope ds ns [< j1] val1
         <*> pure loc
 
+    Let (qty, x, rhs) body loc =>
+      Let (fromPQty qty)
+        <$> fromPTermElim ds ns rhs
+        <*> fromPTermTScope ds ns [< x] body
+        <*> pure loc
+
   private
-  fromPTermEnumArms : Context' PatVar d -> Context' PatVar n ->
+  fromPTermEnumArms : Loc -> Context' PatVar d -> Context' PatVar n ->
                       List (PTagVal, PTerm) ->
                       Eff FromParserPure (CaseEnumArms d n)
-  fromPTermEnumArms ds ns =
-    map SortedMap.fromList .
-    traverse (bitraverse (pure . fromPTagVal) (fromPTermWith ds ns))
+  fromPTermEnumArms loc ds ns arms = do
+    res <- SortedMap.fromList <$>
+           traverse (bitraverse (pure . fromPTagVal) (fromPTermWith ds ns)) arms
+    unless (length (keys res) == length arms) $
+      throw $ DuplicatesInEnumCase loc (map (fromPTagVal . fst) arms)
+    pure res
 
   private
   fromPTermElim : Context' PatVar d -> Context' PatVar n ->
@@ -263,7 +297,7 @@ mutual
     if all isUnused xs then
       SN <$> fromPTermWith ds ns t
     else
-      ST (fromSnocVect $ map fromPatVar xs) <$> fromPTermWith ds (ns ++ xs) t
+      SY (fromSnocVect $ map fromPatVar xs) <$> fromPTermWith ds (ns ++ xs) t
 
   private
   fromPTermDScope : {s : Nat} -> Context' PatVar d -> Context' PatVar n ->
@@ -271,9 +305,9 @@ mutual
                     Eff FromParserPure (DScopeTermN s d n)
   fromPTermDScope ds ns xs t =
     if all isUnused xs then
-      SN <$> fromPTermWith ds ns t
+      SN {f = \d => Term d n} <$> fromPTermWith ds ns t
     else
-      DST (fromSnocVect $ map fromPatVar xs) <$> fromPTermWith (ds ++ xs) ns t
+      SY (fromSnocVect $ map fromPatVar xs) <$> fromPTermWith (ds ++ xs) ns t
 
 
 export %inline
@@ -282,72 +316,110 @@ fromPTerm = fromPTermWith [<] [<]
 
 
 export
-globalPQty : Loc -> (q : Qty) -> Eff [Except Error] (So $ isGlobal q)
-globalPQty loc pi = case choose $ isGlobal pi of
-  Left  y => pure y
-  Right _ => throw $ QtyNotGlobal loc pi
-
+globalPQty : Has (Except Error) fs => PQty -> Eff fs GQty
+globalPQty (PQ pi loc) = case toGlobal pi of
+  Just g  => pure g
+  Nothing => throw $ QtyNotGlobal loc pi
 
 export
-fromPBaseNameNS : PBaseName -> Eff [StateL NS Mods] Name
+fromPBaseNameNS : Has (StateL NS Mods) fs => PBaseName -> Eff fs Name
 fromPBaseNameNS name = pure $ addMods !(getAt NS) $ fromPBaseName name
 
+
 private
-liftTC : TC a -> Eff FromParserPure a
-liftTC act = do
-  res <- lift $ runExcept $ runReaderAt DEFS !(getAt DEFS) act
-  rethrow $ mapFst WrapTypeError res
+liftTC : Eff TC a -> Eff FromParserPure a
+liftTC tc = runEff tc $ with Union.(::)
+  [handleExcept $ \e => throw $ WrapTypeError e,
+   handleReaderConst !(getAt DEFS),
+   \g => send g,
+   \g => send g]
+
+private
+liftWhnf : Eff Whnf a -> Eff FromParserPure a
+liftWhnf tc = runEff tc $ with Union.(::)
+  [handleExcept $ \e => throw $ WrapTypeError e,
+   \g => send g,
+   \g => send g]
+
+private
+addDef : Has DefsState fs => Name -> Definition -> Eff fs NDefinition
+addDef name def = do
+  modifyAt DEFS $ insert name def
+  pure (name, def)
+
 
 export covering
 fromPDef : PDefinition -> Eff FromParserPure NDefinition
-fromPDef (MkPDef qty pname ptype pterm defLoc) = do
-  name <- lift $ fromPBaseNameNS pname
-  qtyGlobal <- lift $ globalPQty qty.loc qty.val
-  let gqty = Element qty.val qtyGlobal
-      sqty = globalToSubj gqty
-  type <- lift $ traverse fromPTerm ptype
-  term <- lift $ fromPTerm pterm
-  case type of
-    Just type => do
-      liftTC $ checkTypeC empty type Nothing
-      liftTC $ ignore $ checkC empty sqty term type
-      let def = mkDef gqty type term defLoc
-      modifyAt DEFS $ insert name def
-      pure (name, def)
-    Nothing => do
-      let E elim = term | _ => throw $ AnnotationNeeded term.loc empty term
-      res <- liftTC $ inferC empty sqty elim
-      let def = mkDef gqty res.type term defLoc
-      modifyAt DEFS $ insert name def
-      pure (name, def)
+fromPDef def = do
+  name <- fromPBaseNameNS def.name
+  defs <- getAt DEFS
+  when (isJust $ lookup name defs) $ do
+    throw $ AlreadyExists def.loc name
+  gqty <- globalPQty def.qty
+  let sqty = globalToSubj gqty
+  case def.body of
+    PConcrete ptype pterm => do
+      type <- traverse fromPTerm ptype
+      term <- fromPTerm pterm
+      type <- case type of
+        Just type => do
+          ignore $ liftTC $ do
+            checkTypeC empty type Nothing
+            checkC empty sqty term type
+          pure type
+        Nothing => do
+          let E elim = term
+            | _ => throw $ AnnotationNeeded term.loc empty term
+          res <- liftTC $ inferC empty sqty elim
+          pure res.type
+      when def.main $ liftWhnf $ expectMainType defs type
+      addDef name $ mkDef gqty type term def.scheme def.main def.loc
+    PPostulate ptype => do
+      type <- fromPTerm ptype
+      addDef name $ mkPostulate gqty type def.scheme def.main def.loc
+
+
+public export
+data HasFail = NoFail | AnyFail | FailWith String
+
+export covering
+expectFail : Loc -> Eff FromParserPure a -> Eff FromParserPure Error
+expectFail loc act = do
+  gen <- getAt GEN; defs <- getAt DEFS; ns <- getAt NS; lvl <- curLevels
+  case fromParserPure ns gen defs (singleton lvl) act of
+    Left  err => pure err
+    Right _   => throw $ ExpectedFail loc
+
+export covering
+maybeFail : Monoid a =>
+            PFail -> Loc -> Eff FromParserPure a -> Eff FromParserPure a
+maybeFail PSucceed         _   act = act
+maybeFail PFailAny         loc act = expectFail loc act $> neutral
+maybeFail (PFailMatch str) loc act = do
+    err <- expectFail loc act
+    let msg = runPretty $ prettyError False err {opts = Opts 10_000} -- w/e
+    if str `isInfixOf` renderInfinite msg
+       then pure neutral
+       else throw $ WrongFail str err loc
 
 export covering
 fromPDecl : PDecl -> Eff FromParserPure (List NDefinition)
-fromPDecl (PDef def) = singleton <$> fromPDef def
+fromPDecl (PDef def) =
+  maybeFail def.fail def.loc $ singleton <$> fromPDef def
 fromPDecl (PNs  ns)  =
+  maybeFail ns.fail ns.loc $
   localAt NS (<+> ns.name) $ concat <$> traverse fromPDecl ns.decls
-
-
-export covering
-loadFile : Loc -> String -> Eff LoadFile (Maybe String)
-loadFile loc file =
-  if contains file !(getAt SEEN) then
-    pure Nothing
-  else do
-    Just ifile <- firstExists (map (</> file) !ask)
-      | Nothing => throw $ LoadError loc file FileNotFound
-    case !(readFile ifile) of
-      Right res => modifyAt SEEN (insert file) $> Just res
-      Left  err => throw $ LoadError loc ifile err
+fromPDecl (PPrag prag) =
+  case prag of
+    PLogPush p _ => Log.push p $> []
+    PLogPop    _ => Log.pop    $> []
 
 mutual
   export covering
   loadProcessFile : Loc -> String -> Eff FromParserIO (List NDefinition)
   loadProcessFile loc file =
-    case !(lift $ loadFile loc file) of
-      Just inp => do
-        tl <- either (throw . WrapParseError file) pure $ lexParseInput file inp
-        concat <$> traverse fromPTopLevel tl
+    case !(loadFile loc file) of
+      Just tl => concat <$> traverse fromPTopLevel tl
       Nothing => pure []
 
   ||| populates the `defs` field of the state
@@ -355,28 +427,3 @@ mutual
   fromPTopLevel : PTopLevel -> Eff FromParserIO (List NDefinition)
   fromPTopLevel (PD    decl)     = lift $ fromPDecl decl
   fromPTopLevel (PLoad file loc) = loadProcessFile loc file
-
-export
-fromParserPure : NameSuf -> Definitions ->
-                 Eff FromParserPure a ->
-                 (Either Error (a, Definitions), NameSuf)
-fromParserPure suf defs act =
-  extract $
-  runStateAt GEN suf $
-  runExcept $
-  evalStateAt NS [<] $
-  runStateAt DEFS defs act
-
-export
-fromParserIO : (MonadRec io, HasIO io) =>
-               IncludePath ->
-               IORef SeenFiles -> IORef NameSuf -> IORef Definitions ->
-               Eff FromParserIO a -> io (Either Error a)
-fromParserIO inc seen suf defs act =
-  runIO $
-  runStateIORefAt GEN suf $
-  runExcept $
-  evalStateAt NS [<] $
-  runStateIORefAt SEEN seen $
-  runStateIORefAt DEFS defs $
-  runReader inc act

lib/Quox/Parser/FromParser/Error.idr

@@ -1,11 +1,14 @@
 module Quox.Parser.FromParser.Error
 
 import Quox.Parser.Parser
+import Quox.Parser.LoadFile
 import Quox.Typing
 import System.File
 
 import Quox.Pretty
 
+%default total
+
 %hide Text.PrettyPrint.Prettyprinter.Doc.infixr.(<++>)
 
 
@@ -21,26 +24,34 @@ ParseError = Parser.Error
 public export
 data Error =
     AnnotationNeeded Loc (NameContexts d n) (Term d n)
-  | DuplicatesInEnum Loc (List TagVal)
+  | DuplicatesInEnumType Loc (List TagVal)
+  | DuplicatesInEnumCase Loc (List TagVal)
   | TermNotInScope Loc Name
   | DimNotInScope Loc PBaseName
   | QtyNotGlobal Loc Qty
   | DimNameInTerm Loc PBaseName
   | DisplacedBoundVar Loc PName
   | WrapTypeError TypeError
-  | LoadError Loc String FileError
+  | AlreadyExists Loc Name
+  | LoadError Loc FilePath FileError
+  | ExpectedFail Loc
+  | SchemeOnNamespace Loc Mods
+  | MainOnNamespace Loc Mods
+  | WrongFail String Error Loc
   | WrapParseError String ParseError
 
 
 export
 prettyLexError : {opts : _} -> String -> LexError -> Eff Pretty (Doc opts)
 prettyLexError file (Err reason line col char) = do
-  let loc = makeLoc file (MkBounds line col line col)
   reason <- case reason of
-    EndInput    => pure "unexpected end of input"
-    NoRuleApply => pure $ text "unrecognised character: \{show char}"
+    Other msg => pure $ text msg
+    NoRuleApply => case char of
+      Just char => pure $ text "unrecognised character: \{show char}"
+      Nothing   => pure $ text "unexpected end of input"
     ComposeNotClosing (sl, sc) (el, ec) => pure $
       hsep ["unterminated token at", !(prettyBounds (MkBounds sl sc el ec))]
+  let loc = makeLoc file (MkBounds line col line col)
   pure $ vappend !(prettyLoc loc) reason
 
 export
@@ -61,19 +72,23 @@ prettyParseError file (ParseError errs) =
     traverse (map ("-" <++>) . prettyParseError1 file) (toList errs)
 
 
-parameters (showContext : Bool)
+parameters {opts : LayoutOpts} (showContext : Bool)
   export
-  prettyError : {opts : _} -> Error -> Eff Pretty (Doc opts)
+  prettyError : Error -> Eff Pretty (Doc opts)
   prettyError (AnnotationNeeded loc ctx tm) =
     [|vappend (prettyLoc loc)
         (hangD "type annotation needed on"
                !(prettyTerm ctx.dnames ctx.tnames tm))|]
     -- [todo] print the original PTerm instead
 
-  prettyError (DuplicatesInEnum loc tags) =
+  prettyError (DuplicatesInEnumType loc tags) =
     [|vappend (prettyLoc loc)
         (hangD "duplicate tags in enum type" !(prettyEnum tags))|]
 
+  prettyError (DuplicatesInEnumCase loc tags) =
+    [|vappend (prettyLoc loc)
+        (hangD "duplicate arms in enum case" !(prettyEnum tags))|]
+
   prettyError (DimNotInScope loc i) =
     [|vappend (prettyLoc loc)
         (pure $ hsep ["dimension", !(hl DVar $ text i), "not in scope"])|]
@@ -100,10 +115,32 @@ parameters (showContext : Bool)
   prettyError (WrapTypeError err) =
     Typing.prettyError showContext $ trimContext 2 err
 
-  prettyError (LoadError loc str err) = pure $
+  prettyError (AlreadyExists loc name) = pure $
     vsep [!(prettyLoc loc),
-          "couldn't load file" <++> text str,
+          sep [!(prettyFree name), "has already been defined"]]
+
+  prettyError (LoadError loc file err) = pure $
+    vsep [!(prettyLoc loc),
+          "couldn't load file" <++> text file,
           text $ show err]
 
+  prettyError (ExpectedFail loc) = pure $
+    vsep [!(prettyLoc loc), "expected error"]
+
+  prettyError (SchemeOnNamespace loc ns) = pure $
+    vsep [!(prettyLoc loc),
+          hsep ["namespace", !(hl Free $ text $ joinBy "." $ toList ns),
+                "cannot have #[compile-scheme] attached"]]
+
+  prettyError (MainOnNamespace loc ns) = pure $
+    vsep [!(prettyLoc loc),
+          hsep ["namespace", !(hl Free $ text $ joinBy "." $ toList ns),
+                "cannot have #[main] attached"]]
+
+  prettyError (WrongFail str err loc) = pure $
+    vsep [!(prettyLoc loc),
+          "wrong error, expected to match", !(hl Constant $ text "\"\{str}\""),
+          "but got", !(prettyError err)]
+
   prettyError (WrapParseError file err) =
     prettyParseError file err

lib/Quox/Parser/Lexer.idr

@@ -1,6 +1,7 @@
 module Quox.Parser.Lexer
 
 import Quox.CharExtra
+import Quox.NatExtra
 import Quox.Name
 import Data.String.Extra
 import Data.SortedMap
@@ -19,7 +20,7 @@ import Derive.Prelude
 ||| @ Reserved reserved token
 ||| @ Name name, possibly qualified
 ||| @ Nat nat literal
-||| @ String string literal
+||| @ Str string literal
 ||| @ Tag tag literal
 ||| @ TYPE "Type" or "★" with ascii nat directly after
 ||| @ Sup superscript or ^ number (displacement, or universe for ★)
@@ -34,16 +35,27 @@ data Token =
   | Sup Nat
 %runElab derive "Token" [Eq, Ord, Show]
 
--- token or whitespace
+||| token or whitespace
+||| @ Skip whitespace, comments, etc
+||| @ Invalid a token which failed a post-lexer check
+|||           (e.g. a qualified name containing a keyword)
+||| @ T a well formed token
 public export
-0 TokenW : Type
-TokenW = Maybe Token
+data ExtToken = Skip | Invalid String String | T Token
+%runElab derive "ExtToken" [Eq, Ord, Show]
 
 
+public export
+data ErrorReason =
+    NoRuleApply
+  | ComposeNotClosing (Int, Int) (Int, Int)
+  | Other String
+%runElab derive "ErrorReason" [Eq, Ord, Show]
+
 public export
 record Error where
   constructor Err
-  reason    : StopReason
+  reason    : ErrorReason
   line, col : Int
   ||| `Nothing` if the error is at the end of the input
   char      : Maybe Char
@@ -52,77 +64,118 @@ record Error where
 
 
 private
-skip : Lexer -> Tokenizer TokenW
-skip t = match t $ const Nothing
+skip : Lexer -> Tokenizer ExtToken
+skip t = match t $ const Skip
 
 private
-match : Lexer -> (String -> Token) -> Tokenizer TokenW
-match t f = Tokenizer.match t (Just . f)
-%hide Tokenizer.match
+tmatch : Lexer -> (String -> Token) -> Tokenizer ExtToken
+tmatch t f = match t (T . f)
 
 
-private
-name : Tokenizer TokenW
-name = match name $ Name . fromListP . split (== '.') . normalizeNfc
-
-||| [todo] escapes other than `\"` and (accidentally) `\\`
 export
-fromStringLit : String -> String
-fromStringLit = pack . go . unpack . drop 1 . dropLast 1 where
-  go : List Char -> List Char
-  go []                = []
-  go ['\\']            = ['\\'] -- i guess???
-  go ('\\' :: c :: cs) = c :: go cs
-  go (c :: cs)         = c :: go cs
+fromStringLit : (String -> Token) -> String -> ExtToken
+fromStringLit f str =
+  case go $ unpack $ drop 1 $ dropLast 1 str of
+    Left  err => Invalid err str
+    Right ok  => T $ f $ pack ok
+where
+  Interpolation Char where interpolate = singleton
+
+  go, hexEscape : List Char -> Either String (List Char)
+
+  go []                   = Right []
+  go ['\\']               = Left "string ends with \\"
+  go ('\\' :: 'n'  :: cs) = ('\n' ::) <$> go cs
+  go ('\\' :: 't'  :: cs) = ('\t' ::) <$> go cs
+  go ('\\' :: 'x'  :: cs) = hexEscape cs
+  go ('\\' :: 'X'  :: cs) = hexEscape cs
+  go ('\\' :: '\\' :: cs) = ('\\' ::) <$> go cs
+  go ('\\' :: '"'  :: cs) = ('"'  ::) <$> go cs
+  -- [todo] others
+  go ('\\' :: c :: _)     = Left "unknown escape '\{c}'"
+  go (c :: cs)            = (c ::) <$> go cs
+
+  hexEscape cs =
+    case break (== ';') cs of
+      (hs, ';' :: rest) => do
+        let hs = pack hs
+        let Just c = Int.fromHex hs
+          | Nothing => Left #"invalid hex string "\#{hs}" in escape"#
+        if isCodepoint c
+           then (chr c ::) <$> go (assert_smaller cs rest)
+           else Left "codepoint \{hs} out of range"
+      _ => Left "unterminated hex escape"
 
 private
-string : Tokenizer TokenW
-string = match stringLit (Str . fromStringLit)
+string : Tokenizer ExtToken
+string = match stringLit $ fromStringLit Str
+
+
+%hide binLit
+%hide octLit
+%hide hexLit
 
 private
-nat : Tokenizer TokenW
-nat = match (some (range '0' '9')) (Nat . cast)
+nat : Tokenizer ExtToken
+nat = match  hexLit fromHexLit
+  <|> tmatch decLit fromDecLit
+where
+  withUnderscores : Lexer -> Lexer
+  withUnderscores l = l <+> many (opt (is '_') <+> l)
+
+  withoutUnderscores : String -> String
+  withoutUnderscores = pack . go . unpack where
+    go : List Char -> List Char
+    go []          = []
+    go ('_' :: cs) =      go cs
+    go (c   :: cs) = c :: go cs
+
+  decLit =
+    withUnderscores (range '0' '9') <+> reject idContEnd
+
+  hexLit =
+    approx "0x" <+>
+    withUnderscores (range '0' '9' <|> range 'a' 'f' <|> range 'A' 'F') <+>
+    reject idContEnd
+
+  fromDecLit : String -> Token
+  fromDecLit = Nat . cast . withoutUnderscores
+
+  fromHexLit : String -> ExtToken
+  fromHexLit str =
+    maybe (Invalid "invalid hex sequence" str) (T . Nat) $
+    fromHex $ withoutUnderscores $ drop 2 str
+
 
 private
-tag : Tokenizer TokenW
-tag = match (is '\'' <+> name)      (Tag . drop 1)
-  <|> match (is '\'' <+> stringLit) (Tag . fromStringLit . drop 1)
+tag : Tokenizer ExtToken
+tag = tmatch (is '\'' <+> name)      (Tag . drop 1)
+  <|>  match (is '\'' <+> stringLit) (fromStringLit Tag . drop 1)
 
 
-
-private %inline
-fromSub : Char -> Char
-fromSub c = case c of
-  '₀' => '0'; '₁' => '1'; '₂' => '2'; '₃' => '3'; '₄' => '4'
-  '₅' => '5'; '₆' => '6'; '₇' => '7'; '₈' => '8'; '₉' => '9'; _ => c
-
 private %inline
 fromSup : Char -> Char
 fromSup c = case c of
   '⁰' => '0'; '¹' => '1'; '²' => '2'; '³' => '3'; '⁴' => '4'
   '⁵' => '5'; '⁶' => '6'; '⁷' => '7'; '⁸' => '8'; '⁹' => '9'; _ => c
 
-private %inline
-subToNat : String -> Nat
-subToNat = cast . pack . map fromSub . unpack
-
 private %inline
 supToNat : String -> Nat
 supToNat = cast . pack . map fromSup . unpack
 
--- ★0, Type0. base ★/Type is a Reserved
+-- ★0, Type0. base ★/Type is a Reserved and ★¹/Type¹ are sequences of two tokens
 private
-universe : Tokenizer TokenW
+universe : Tokenizer ExtToken
 universe = universeWith "★" <|> universeWith "Type" where
-  universeWith : String -> Tokenizer TokenW
+  universeWith : String -> Tokenizer ExtToken
   universeWith pfx =
     let len = length pfx in
-    match (exact pfx <+> digits) (TYPE . cast . drop len)
+    tmatch (exact pfx <+> digits) (TYPE . cast . drop len)
 
 private
-sup : Tokenizer TokenW
-sup = match (some $ pred isSupDigit) (Sup . supToNat)
-  <|> match (is '^' <+> digits)      (Sup . cast . drop 1)
+sup : Tokenizer ExtToken
+sup = tmatch (some $ pred isSupDigit) (Sup . supToNat)
+  <|> tmatch (is '^' <+> digits)      (Sup . cast . drop 1)
 
 
 private %inline
@@ -134,9 +187,11 @@ namespace Reserved
   ||| description of a reserved symbol
   ||| @ Word a reserved word (must not be followed by letters, digits, etc)
   ||| @ Sym a reserved symbol (must not be followed by symbolic chars)
-  ||| @ Punc a character that doesn't show up in names (brackets, etc)
+  ||| @ Punc a character that doesn't show up in names (brackets, etc);
+  |||        also a sequence ending in one of those, like `#[`, since the
+  |||        difference relates to lookahead
   public export
-  data Reserved1 = Word String | Sym String | Punc Char
+  data Reserved1 = Word String | Sym String | Punc String
   %runElab derive "Reserved1" [Eq, Ord, Show]
 
   ||| description of a token that might have unicode & ascii-only aliases
@@ -145,17 +200,14 @@ namespace Reserved
   %runElab derive "Reserved" [Eq, Ord, Show]
 
   public export
-  Sym1, Word1 : String -> Reserved
-  Sym1 = Only . Sym
+  Sym1, Word1, Punc1 : String -> Reserved
+  Sym1  = Only . Sym
   Word1 = Only . Word
-
-  public export
-  Punc1 : Char -> Reserved
   Punc1 = Only . Punc
 
 public export
 resString1 : Reserved1 -> String
-resString1 (Punc x) = singleton x
+resString1 (Punc x) = x
 resString1 (Word w) = w
 resString1 (Sym  s) = s
 
@@ -166,17 +218,23 @@ resString : Reserved -> String
 resString (Only r)   = resString1 r
 resString (r `Or` _) = resString1 r
 
+||| return both representative strings for a token description
+public export
+resString2 : Reserved -> List String
+resString2 (Only r)   = [resString1 r]
+resString2 (r `Or` s) = [resString1 r, resString1 s]
+
 private
-resTokenizer1 : Reserved1 -> String -> Tokenizer TokenW
+resTokenizer1 : Reserved1 -> String -> Tokenizer ExtToken
 resTokenizer1 r str =
   let res : String -> Token := const $ Reserved str in
-  case r of Word w => match (exact w <+> reject idContEnd) res
-            Sym s  => match (exact s <+> reject symCont)   res
-            Punc x => match (is x)                         res
+  case r of Word w => tmatch (exact w <+> reject idContEnd) res
+            Sym  s => tmatch (exact s <+> reject symCont)   res
+            Punc x => tmatch (exact x)                      res
 
 ||| match a reserved token
 export
-resTokenizer : Reserved -> Tokenizer TokenW
+resTokenizer : Reserved -> Tokenizer ExtToken
 resTokenizer (Only r)   = resTokenizer1 r (resString1 r)
 resTokenizer (r `Or` s) =
   resTokenizer1 r (resString1 r) <|> resTokenizer1 s (resString1 r)
@@ -188,8 +246,8 @@ resTokenizer (r `Or` s) =
 public export
 reserved : List Reserved
 reserved =
-  [Punc1 '(', Punc1 ')', Punc1 '[', Punc1 ']', Punc1 '{', Punc1 '}',
-   Punc1 ',', Punc1 ';',
+  [Punc1 "(", Punc1 ")", Punc1 "[", Punc1 "]", Punc1 "{", Punc1 "}",
+   Punc1 ",", Punc1 ";", Punc1 "#[", Punc1 "#![",
    Sym1 "@",
    Sym1 ":",
    Sym "⇒" `Or` Sym "=>",
@@ -197,12 +255,16 @@ reserved =
    Sym "×" `Or` Sym "**",
    Sym "≡" `Or` Sym "==",
    Sym "∷" `Or` Sym "::",
-   Punc1 '.',
+   Punc1 ".",
    Word1 "case",
    Word1 "case0", Word1 "case1",
    Word "caseω" `Or` Word "case#",
    Word1 "return",
    Word1 "of",
+   Word1 "let", Word1 "in",
+   Word1 "let0", Word1 "let1",
+   Word "letω" `Or` Word "let#",
+   Word1 "fst", Word1 "snd",
    Word1 "_",
    Word1 "Eq",
    Word "λ" `Or` Word "fun",
@@ -210,35 +272,71 @@ reserved =
    Word "ω" `Or` Sym "#",
    Sym "★" `Or` Word "Type",
    Word "ℕ" `Or` Word "Nat",
+   Word1 "IOState",
+   Word1 "String",
    Word1 "zero", Word1 "succ",
    Word1 "coe", Word1 "comp",
    Word1 "def",
    Word1 "def0",
    Word "defω" `Or` Word "def#",
+   Word1 "postulate",
+   Word1 "postulate0",
+   Word "postulateω" `Or` Word "postulate#",
    Sym1 "=",
    Word1 "load",
    Word1 "namespace"]
 
+public export
+reservedStrings : List String
+reservedStrings = map resString reserved
+
+public export
+allReservedStrings : List String
+allReservedStrings = foldMap resString2 reserved
+
 ||| `IsReserved str` is true if `Reserved str` might actually show up in
 ||| the token stream
 public export
 IsReserved : String -> Type
-IsReserved str = str `Elem` map resString reserved
+IsReserved str = So (str `elem` reservedStrings)
+
+private
+name : Tokenizer ExtToken
+name =
+  match name $ \str =>
+    let parts = split (== '.') $ normalizeNfc str in
+    case find (`elem` allReservedStrings) (toList parts) of
+      Nothing => T $ Name $ fromListP parts
+      Just w  => Invalid "reserved word '\{w}' inside name \{str}" str
 
 export
-tokens : Tokenizer TokenW
+tokens : Tokenizer ExtToken
 tokens = choice $
   map skip [pred isWhitespace,
             lineComment (exact "--" <+> reject symCont),
             blockComment (exact "{-") (exact "-}")] <+>
-  [universe] <+>  -- ★ᵢ takes precedence over bare ★
+  [universe] <+>  -- Type<i> takes precedence over bare Type
   map resTokenizer reserved <+>
   [sup, nat, string, tag, name]
 
+export
+check : Alternative f =>
+        WithBounds ExtToken -> Either Error (f (WithBounds Token))
+check (MkBounded val irr bounds@(MkBounds line col _ _)) = case val of
+  Skip            => Right empty
+  T tok           => Right $ pure $ MkBounded tok irr bounds
+  Invalid msg tok => Left  $ Err (Other msg) line col (index 0 tok)
+
+export
+toErrorReason : StopReason -> Maybe ErrorReason
+toErrorReason EndInput                = Nothing
+toErrorReason NoRuleApply             = Just NoRuleApply
+toErrorReason (ComposeNotClosing s e) = Just $ ComposeNotClosing s e
+
 export
 lex : String -> Either Error (List (WithBounds Token))
 lex str =
   let (res, reason, line, col, str) = lex tokens str in
-  case reason of
-    EndInput => Right $ mapMaybe sequence res
-    _        => Left  $ Err {reason, line, col, char = index 0 str}
+  case toErrorReason reason of
+    Nothing => concatMap check res @{MonoidApplicative}
+    Just e  => Left $ Err {reason = e, line, col, char = index 0 str}

lib/Quox/Parser/LoadFile.idr

@@ -0,0 +1,100 @@
+module Quox.Parser.LoadFile
+
+import public Quox.Parser.Syntax
+import Quox.Parser.Parser
+import Quox.Loc
+import Quox.EffExtra
+import Data.IORef
+import Data.SortedSet
+import System.File
+import System.Path
+
+
+%default total
+
+public export
+FilePath : Type
+FilePath = String
+
+
+public export
+data LoadFileL : (lbl : k) -> Type -> Type where
+  [search lbl]
+  Seen    : FilePath -> LoadFileL lbl Bool
+  SetSeen : FilePath -> LoadFileL lbl ()
+  DoLoad  : Loc -> FilePath -> LoadFileL lbl PFile
+
+public export
+LoadFile : Type -> Type
+LoadFile = LoadFileL ()
+
+
+export
+seenAt : (0 lbl : k) -> Has (LoadFileL lbl) fs => FilePath -> Eff fs Bool
+seenAt lbl file = send $ Seen {lbl} file
+
+export %inline
+seen : Has LoadFile fs => FilePath -> Eff fs Bool
+seen = seenAt ()
+
+
+export
+setSeenAt : (0 lbl : k) -> Has (LoadFileL lbl) fs => FilePath -> Eff fs ()
+setSeenAt lbl file = send $ SetSeen {lbl} file
+
+export %inline
+setSeen : Has LoadFile fs => FilePath -> Eff fs ()
+setSeen = setSeenAt ()
+
+
+export
+doLoadAt : (0 lbl : k) -> Has (LoadFileL lbl) fs =>
+           Loc -> FilePath -> Eff fs PFile
+doLoadAt lbl loc file = send $ DoLoad {lbl} loc file
+
+export %inline
+doLoad : Has LoadFile fs => Loc -> FilePath -> Eff fs PFile
+doLoad = doLoadAt ()
+
+
+public export
+SeenSet : Type
+SeenSet = SortedSet FilePath
+
+public export
+IncludePath : Type
+IncludePath = List String
+
+export covering
+readFileFrom : HasIO io => IncludePath -> FilePath ->
+               io (Either FileError String)
+readFileFrom inc f =
+  case !(firstExists $ map (</> f) inc) of
+    Just path => readFile path
+    Nothing   => pure $ Left $ FileNotFound
+
+export covering
+handleLoadFileIOE : (Loc -> FilePath -> FileError -> e) ->
+                    (FilePath -> Parser.Error -> e) ->
+                    IORef SeenSet -> IncludePath ->
+                    LoadFileL lbl a -> IOErr e a
+handleLoadFileIOE injf injp seen inc = \case
+  Seen    f   => contains f <$> readIORef seen
+  SetSeen f   => modifyIORef seen $ insert f
+  DoLoad  l f =>
+    case !(readFileFrom inc f) of
+      Left  err => ioLeft $ injf l f err
+      Right str => either (ioLeft . injp f) pure $ lexParseInput f str
+
+
+export
+loadFileAt : (0 lbl : k) -> Has (LoadFileL lbl) fs =>
+             Loc -> FilePath -> Eff fs (Maybe PFile)
+loadFileAt lbl loc file =
+  if !(seenAt lbl file)
+     then pure Nothing
+     else Just <$> doLoadAt lbl loc file <* setSeenAt lbl file
+
+export
+loadFile : Has LoadFile fs => Loc -> FilePath -> Eff fs (Maybe PFile)
+loadFile = loadFileAt ()

lib/Quox/Parser/Parser.idr

@@ -124,7 +124,7 @@ qname = terminalMatch "name" `(Name n) `(n)
 ||| unqualified name
 export
 baseName : Grammar True PBaseName
-baseName = terminalMatch "unqualified name" `(Name (MakePName [<] b)) `(b)
+baseName = terminalMatch "unqualified name" `(Name (MkPName [<] b)) `(b)
 
 ||| dimension constant (0 or 1)
 export
@@ -149,6 +149,12 @@ export
 qty : FileName -> Grammar True PQty
 qty fname = withLoc fname [|PQ qtyVal|]
 
+export
+exactName : String -> Grammar True ()
+exactName name = terminal "expected '\{name}'" $ \case
+  Name (MkPName [<] x) => guard $ x == name
+  _                    => Nothing
+
 
 ||| pattern var (unqualified name or _)
 export
@@ -198,18 +204,21 @@ export
 enumType : Grammar True (List TagVal)
 enumType = delimSep "{" "}" "," bareTag
 
-||| e.g. `case` or `case 1.`
+||| e.g. `case1` or `case 1.`
 export
 caseIntro : FileName -> Grammar True PQty
 caseIntro fname =
       withLoc fname (PQ Zero <$ res "case0")
   <|> withLoc fname (PQ One  <$ res "case1")
   <|> withLoc fname (PQ Any  <$ res "caseω")
-  <|> delim "case" "." (qty fname)
+  <|> do resC "case"
+         qty fname <* needRes "." <|> defLoc fname (PQ One)
 
 export
 qtyPatVar : FileName -> Grammar True (PQty, PatVar)
-qtyPatVar fname = [|(,) (qty fname) (needRes "." *> patVar fname)|]
+qtyPatVar fname =
+      [|(,) (qty fname) (needRes "." *> patVar fname)|]
+  <|> [|(,) (defLoc fname $ PQ One) (patVar fname)|]
 
 
 export
@@ -277,19 +286,81 @@ export
 universe1 : Grammar True Universe
 universe1 = universeTok <|> res "★" *> option 0 super
 
-||| argument/atomic term: single-token terms, or those with delimiters e.g.
-||| `[t]`
+
+public export
+PCaseArm : Type
+PCaseArm = (PCasePat, PTerm)
+
+export
+caseArm : FileName -> Grammar True PCaseArm
+caseArm fname =
+  [|(,) (casePat fname) (needRes "⇒" *> assert_total term fname)|]
+
+export
+checkCaseArms : Loc -> List PCaseArm -> Grammar False PCaseBody
+checkCaseArms loc [] = pure $ CaseEnum [] loc
+checkCaseArms loc ((PPair x y _, rhs) :: rest) =
+  if null rest then pure $ CasePair (x, y) rhs loc
+  else fatalError "unexpected pattern after pair"
+checkCaseArms loc ((PTag tag _, rhs1) :: rest) = do
+  let rest = for rest $ \case
+        (PTag tag _, rhs) => Just (tag, rhs)
+        _                 => Nothing
+  maybe (fatalError "expected all patterns to be tags")
+        (\rest => pure $ CaseEnum ((tag, rhs1) :: rest) loc) rest
+checkCaseArms loc ((PZero _, rhs1) :: rest) = do
+  let [(PSucc p q ih _, rhs2)] = rest
+    | _ => fatalError "expected succ pattern after zero"
+  pure $ CaseNat rhs1 (p, q, ih, rhs2) loc
+checkCaseArms loc ((PSucc p q ih _, rhs1) :: rest) = do
+  let [(PZero _, rhs2)] = rest
+    | _ => fatalError "expected zero pattern after succ"
+  pure $ CaseNat rhs2 (p, q, ih, rhs1) loc
+checkCaseArms loc ((PBox x _, rhs) :: rest) =
+  if null rest then pure $ CaseBox x rhs loc
+  else fatalError "unexpected pattern after box"
+
+export
+caseBody : FileName -> Grammar True PCaseBody
+caseBody fname = do
+  body <- bounds $ delimSep "{" "}" ";" $ caseArm fname
+  let loc = makeLoc fname body.bounds
+  checkCaseArms loc body.val
+
+export
+caseReturn : FileName -> Grammar True (PatVar, PTerm)
+caseReturn fname = do
+  x   <- patVar fname <* resC "⇒" <|> unused fname
+  ret <- assert_total term fname
+  pure (x, ret)
+
+export
+caseTerm : FileName -> Grammar True PTerm
+caseTerm fname = withLoc fname $ do
+  qty <- caseIntro fname;                     commit
+  head <- mustWork $ assert_total term fname; needRes "return"
+  ret  <- mustWork $ caseReturn fname;        needRes "of"
+  body <- mustWork $ caseBody fname
+  pure $ Case qty head ret body
+
+
+||| argument/atomic term: single-token terms, or those with delimiters
+||| e.g. `[t]`. includes `case` because the end delimiter is the `}`.
 export
 termArg : FileName -> Grammar True PTerm
 termArg fname = withLoc fname $
       [|TYPE universe1|]
+  <|> IOState <$ res "IOState"
   <|> [|Enum enumType|]
   <|> [|Tag tag|]
   <|> const <$> boxTerm fname
-  <|> Nat  <$ res "ℕ"
-  <|> Zero <$ res "zero"
-  <|> [|fromNat nat|]
+  <|> NAT    <$ res "ℕ"
+  <|> Nat 0  <$ res "zero"
+  <|> [|Nat nat|]
+  <|> STRING <$ res "String"
+  <|> [|Str strLit|]
   <|> [|V qname displacement|]
+  <|> const <$> caseTerm fname
   <|> const <$> tupleTerm fname
 
 export
@@ -369,10 +440,10 @@ eqTerm : FileName -> Grammar True PTerm
 eqTerm fname = withLoc fname $
   resC "Eq" *> mustWork [|Eq (typeLine fname) (termArg fname) (termArg fname)|]
 
-export
-succTerm : FileName -> Grammar True PTerm
-succTerm fname = withLoc fname $
-  resC "succ" *> mustWork [|Succ (termArg fname)|]
+private
+appArg : Loc -> PTerm -> Either PDim PTerm -> PTerm
+appArg loc f (Left  p) = DApp f p loc
+appArg loc f (Right s) = App  f s loc
 
 ||| a dimension argument with an `@` prefix, or
 ||| a term argument with no prefix
@@ -380,15 +451,32 @@ export
 anyArg : FileName -> Grammar True (Either PDim PTerm)
 anyArg fname = dimArg fname <||> termArg fname
 
+export
+resAppTerm : FileName -> (word : String) -> (0 _ : IsReserved word) =>
+             (PTerm -> Loc -> PTerm) -> Grammar True PTerm
+resAppTerm fname word f = withLoc fname $ do
+  head <- withLoc fname $ resC word *> mustWork [|f (termArg fname)|]
+  args <- many $ anyArg fname
+  pure $ \loc => foldl (appArg loc) head args
+
+export
+succTerm : FileName -> Grammar True PTerm
+succTerm fname = resAppTerm fname "succ" Succ
+
+export
+fstTerm : FileName -> Grammar True PTerm
+fstTerm fname = resAppTerm fname "fst" Fst
+
+export
+sndTerm : FileName -> Grammar True PTerm
+sndTerm fname = resAppTerm fname "snd" Snd
+
 export
 normalAppTerm : FileName -> Grammar True PTerm
 normalAppTerm fname = withLoc fname $ do
   head <- termArg fname
   args <- many $ anyArg fname
-  pure $ \loc => foldl (ap loc) head args
-where ap : Loc -> PTerm -> Either PDim PTerm -> PTerm
-      ap loc f (Left  p) = DApp f p loc
-      ap loc f (Right s) = App  f s loc
+  pure $ \loc => foldl (appArg loc) head args
 
 ||| application term `f x @y z`, or other terms that look like application
 ||| like `succ` or `coe`.
@@ -400,6 +488,8 @@ appTerm fname =
   <|> splitUniverseTerm fname
   <|> eqTerm fname
   <|> succTerm fname
+  <|> fstTerm fname
+  <|> sndTerm fname
   <|> normalAppTerm fname
 
 export
@@ -438,18 +528,6 @@ properBinders fname = assert_total $ do
   t  <- term fname;          needRes ")"
   pure (xs, t)
 
-export
-piTerm : FileName -> Grammar True PTerm
-piTerm fname = withLoc fname $ do
-  q   <- qty fname;               resC "."
-  dom <- piBinder;                needRes "→"
-  cod <- assert_total term fname; commit
-  pure $ \loc => foldr (\x, t => Pi q x (snd dom) t loc) cod (fst dom)
-where
-  piBinder : Grammar True (List1 PatVar, PTerm)
-  piBinder = properBinders fname
-         <|> [|(,) [|singleton $ unused fname|] (termArg fname)|]
-
 export
 sigmaTerm : FileName -> Grammar True PTerm
 sigmaTerm fname =
@@ -470,105 +548,320 @@ where
     rest <- optional $ resC "×" *> sepBy1 (res "×") (annTerm fname)
     pure $ foldr1 cross $ fst ::: maybe [] toList rest
 
-public export
-PCaseArm : Type
-PCaseArm = (PCasePat, PTerm)
+export
+piTerm : FileName -> Grammar True PTerm
+piTerm fname = withLoc fname $ do
+  q   <- [|GivenQ $ qty fname <* resC "."|] <|> defLoc fname DefaultQ
+  dom <- [|Dep $ properBinders fname|] <|> [|Nondep $ ndDom q fname|]
+  cod <- optional $ do resC "→"; assert_total term fname <* commit
+  when (needCod q dom && isNothing cod) $ fail "missing function type result"
+  pure $ maybe (const $ toTerm dom) (makePi q dom) cod
+where
+  data PiQty = GivenQ PQty | DefaultQ Loc
+  data PiDom = Dep (List1 PatVar, PTerm) | Nondep PTerm
+
+  ndDom : PiQty -> FileName -> Grammar True PTerm
+  ndDom (GivenQ   _) = termArg   -- ｢1.(List A)｣, not ｢1.List A｣
+  ndDom (DefaultQ _) = sigmaTerm
+
+  needCod : PiQty -> PiDom -> Bool
+  needCod (DefaultQ _) (Nondep _) = False
+  needCod _            _          = True
+
+  toTerm : PiDom -> PTerm
+  toTerm (Dep (_, s)) = s
+  toTerm (Nondep s)   = s
+
+  toQty : PiQty -> PQty
+  toQty (GivenQ   qty) = qty
+  toQty (DefaultQ loc) = PQ One loc
+
+  toDoms : PQty -> PiDom -> List1 (PQty, PatVar, PTerm)
+  toDoms qty (Dep (xs, s)) = [(qty, x, s) | x <- xs]
+  toDoms qty (Nondep s)    = singleton (qty, Unused s.loc, s)
+
+  makePi : PiQty -> PiDom -> PTerm -> Loc -> PTerm
+  makePi q doms cod loc =
+    foldr (\(q, x, s), t => Pi q x s t loc) cod $ toDoms (toQty q) doms
+
 
 export
-caseArm : FileName -> Grammar True PCaseArm
-caseArm fname =
-  [|(,) (casePat fname) (needRes "⇒" *> assert_total term fname)|]
+letIntro : FileName -> Grammar True (Maybe PQty)
+letIntro fname =
+      withLoc fname (Just . PQ Zero <$ res "let0")
+  <|> withLoc fname (Just . PQ One  <$ res "let1")
+  <|> withLoc fname (Just . PQ Any  <$ res "letω")
+  <|> Nothing <$ resC "let"
+
+private
+letBinder : FileName -> Maybe PQty -> Grammar True (PQty, PatVar, PTerm)
+letBinder fname mq = do
+  qty  <- letQty fname mq
+  x    <- patVar fname
+  type <- optional $ resC ":" *> term fname
+  rhs  <- resC "=" *> term fname
+  pure (qty, x, makeLetRhs rhs type)
+where
+  letQty : FileName -> Maybe PQty -> Grammar False PQty
+  letQty fname Nothing  = qty fname <* mustWork (resC ".") <|> defLoc fname (PQ One)
+  letQty fname (Just q) = pure q
+
+  makeLetRhs : PTerm -> Maybe PTerm -> PTerm
+  makeLetRhs tm ty = maybe tm (\t => Ann tm t (extendL tm.loc t.loc)) ty
 
 export
-checkCaseArms : Loc -> List PCaseArm -> Grammar False PCaseBody
-checkCaseArms loc [] = pure $ CaseEnum [] loc
-checkCaseArms loc ((PPair x y _, rhs) :: rest) =
-  if null rest then pure $ CasePair (x, y) rhs loc
-  else fatalError "unexpected pattern after pair"
-checkCaseArms loc ((PTag tag _, rhs1) :: rest) = do
-  let rest = for rest $ \case
-        (PTag tag _, rhs) => Just (tag, rhs)
-        _                 => Nothing
-  maybe (fatalError "expected all patterns to be tags")
-        (\rest => pure $ CaseEnum ((tag, rhs1) :: rest) loc) rest
-checkCaseArms loc ((PZero _, rhs1) :: rest) = do
-  let [(PSucc p q ih _, rhs2)] = rest
-    | _ => fatalError "expected succ pattern after zero"
-  pure $ CaseNat rhs1 (p, q, ih, rhs2) loc
-checkCaseArms loc ((PSucc p q ih _, rhs1) :: rest) = do
-  let [(PZero _, rhs2)] = rest
-    | _ => fatalError "expected zero pattern after succ"
-  pure $ CaseNat rhs2 (p, q, ih, rhs1) loc
-checkCaseArms loc ((PBox x _, rhs) :: rest) =
-  if null rest then pure $ CaseBox x rhs loc
-  else fatalError "unexpected pattern after box"
+letTerm : FileName -> Grammar True PTerm
+letTerm fname = withLoc fname $ do
+  qty   <- letIntro fname
+  binds <- sepEndBy1 (res ";") $ assert_total letBinder fname qty
+  mustWork $ resC "in"
+  body  <- assert_total term fname
+  pure $ \loc => foldr (\b, s => Let b s loc) body binds
 
-export
-caseBody : FileName -> Grammar True PCaseBody
-caseBody fname = do
-  body <- bounds $ delimSep "{" "}" ";" $ caseArm fname
-  let loc = makeLoc fname body.bounds
-  checkCaseArms loc body.val
-
-export
-caseReturn : FileName -> Grammar True (PatVar, PTerm)
-caseReturn fname = do
-  x   <- patVar fname <* resC "⇒" <|> unused fname
-  ret <- assert_total term fname
-  pure (x, ret)
-
-export
-caseTerm : FileName -> Grammar True PTerm
-caseTerm fname = withLoc fname $ do
-  qty <- caseIntro fname;                     commit
-  head <- mustWork $ assert_total term fname; needRes "return"
-  ret  <- mustWork $ caseReturn fname;        needRes "of"
-  body <- mustWork $ caseBody fname
-  pure $ Case qty head ret body
-
--- export
 -- term : FileName -> Grammar True PTerm
 term fname = lamTerm fname
-         <|> caseTerm fname
          <|> piTerm fname
          <|> sigmaTerm fname
+         <|> letTerm fname
 
 
 export
-decl : FileName -> Grammar True PDecl
+attr' : FileName -> (o : String) -> (0 _ : IsReserved o) =>
+        Grammar True PAttr
+attr' fname o = withLoc fname $ do
+  resC o
+  name <- baseName
+  args <- many $ termArg fname
+  mustWork $ resC "]"
+  pure $ PA name args
+
+export %inline
+attr : FileName -> Grammar True PAttr
+attr fname = attr' fname "#["
 
-||| `def` alone means `defω`
 export
-defIntro : FileName -> Grammar True PQty
-defIntro fname =
-      withLoc fname (PQ Zero <$ resC "def0")
-  <|> withLoc fname (PQ Any  <$ resC "defω")
-  <|> do pos <- bounds $ resC "def"
+findDups : List PAttr -> List String
+findDups attrs =
+  SortedSet.toList $ snd $ foldl check (empty, empty) attrs
+where
+  Seen = SortedSet String; Dups = SortedSet String
+  check : (Seen, Dups) -> PAttr -> (Seen, Dups)
+  check (seen, dups) (PA a _ _) =
+    (insert a seen, if contains a seen then insert a dups else dups)
+
+export
+noDups : List PAttr -> Grammar False ()
+noDups attrs = do
+  let dups = findDups attrs
+  when (not $ null dups) $
+    fatalError "duplicate attribute names: \{joinBy "," dups}"
+
+export
+attrList : FileName -> Grammar False (List PAttr)
+attrList fname = do
+  res <- many $ attr fname
+  noDups res $> res
+
+public export
+data AttrMatch a =
+    Matched a
+  | NoMatch String (List String)
+  | Malformed String String
+
+export
+Functor AttrMatch where
+  map f (Matched x)     = Matched $ f x
+  map f (NoMatch s w)   = NoMatch s w
+  map f (Malformed a e) = Malformed a e
+
+export
+(<|>) : AttrMatch a -> AttrMatch a -> AttrMatch a
+Matched x     <|> _ = Matched x
+NoMatch {}    <|> y = y
+Malformed a e <|> _ = Malformed a e
+
+export
+isFail : PAttr -> List String -> AttrMatch PFail
+isFail (PA "fail" []        _) _ = Matched PFailAny
+isFail (PA "fail" [Str s _] _) _ = Matched $ PFailMatch s
+isFail (PA "fail" _ _) _ = Malformed "fail" "be absent or a string literal"
+isFail a w = NoMatch a.name w
+
+export
+isMain : PAttr -> List String -> AttrMatch ()
+isMain (PA "main" [] _) _ = Matched ()
+isMain (PA "main" _  _) _ = Malformed "main" "have no arguments"
+isMain a w = NoMatch a.name w
+
+export
+isScheme : PAttr -> List String -> AttrMatch String
+isScheme (PA "compile-scheme" [Str s _] _) _ = Matched s
+isScheme (PA "compile-scheme" _ _) _ =
+  Malformed "compile-scheme" "be a string literal"
+isScheme a w = NoMatch a.name w
+
+export
+matchAttr : String -> AttrMatch a -> Either String a
+matchAttr _ (Matched x) = Right x
+matchAttr d (NoMatch a w) = Left $ unlines
+  ["unrecognised \{d} attribute \{a}", "expected one of: \{show w}"]
+matchAttr _ (Malformed a s) = Left $ unlines
+  ["invalid \{a} attribute", "(should \{s})"]
+
+export
+mkPDef : List PAttr -> PQty -> PBaseName -> PBody ->
+         Either String (Loc -> PDefinition)
+mkPDef attrs qty name body = do
+  let start = MkPDef qty name body PSucceed False Nothing noLoc
+  res <- foldlM addAttr start attrs
+  pure $ \l => {loc_ := l} (the PDefinition res)
+where
+  data PDefAttr = DefFail PFail | DefMain | DefScheme String
+
+  isDefAttr : PAttr -> Either String PDefAttr
+  isDefAttr attr =
+    let defAttrs = ["fail", "main", "compile-scheme"] in
+    matchAttr "definition" $
+        DefFail   <$> isFail attr defAttrs
+    <|> DefMain   <$  isMain attr defAttrs
+    <|> DefScheme <$> isScheme attr defAttrs
+
+  addAttr : PDefinition -> PAttr -> Either String PDefinition
+  addAttr def attr =
+    case !(isDefAttr attr) of
+      DefFail   f   => pure $ {fail := f} def
+      DefMain       => pure $ {main := True} def
+      DefScheme str => pure $ {scheme := Just str} def
+
+export
+mkPNamespace : List PAttr -> Mods -> List PDecl ->
+               Either String (Loc -> PNamespace)
+mkPNamespace attrs name decls = do
+  let start = MkPNamespace name decls PSucceed noLoc
+  res <- foldlM addAttr start attrs
+  pure $ \l => {loc_ := l} (the PNamespace res)
+where
+  isNsAttr a = matchAttr "namespace" $ isFail a ["fail"]
+
+  addAttr : PNamespace -> PAttr -> Either String PNamespace
+  addAttr ns attr = pure $ {fail := !(isNsAttr attr)} ns
+
+||| `def` alone means `defω`; same for `postulate`
+export
+defIntro' : (bare, zero, omega : String) ->
+            (0 _ : IsReserved bare) =>
+            (0 _ : IsReserved zero) =>
+            (0 _ : IsReserved omega) =>
+            FileName -> Grammar True PQty
+defIntro' bare zero omega fname =
+      withLoc fname (PQ Zero <$ resC zero)
+  <|> withLoc fname (PQ Any  <$ resC omega)
+  <|> do pos <- bounds $ resC bare
          let any = PQ Any $ makeLoc fname pos.bounds
          option any $ qty fname <* needRes "."
 
 export
-definition : FileName -> Grammar True PDefinition
-definition fname = withLoc fname $ do
+defIntro : FileName -> Grammar True PQty
+defIntro = defIntro' "def" "def0" "defω"
+
+export
+postulateIntro : FileName -> Grammar True PQty
+postulateIntro = defIntro' "postulate" "postulate0" "postulateω"
+
+export
+postulate : FileName -> List PAttr -> Grammar True PDefinition
+postulate fname attrs = withLoc fname $ do
+  qty  <- postulateIntro fname
+  name <- baseName
+  type <- resC ":" *> mustWork (term fname)
+  optRes ";"
+  either fatalError pure $ mkPDef attrs qty name $ PPostulate type
+
+export
+concrete : FileName -> List PAttr -> Grammar True PDefinition
+concrete fname attrs = withLoc fname $ do
   qty  <- defIntro fname
   name <- baseName
   type <- optional $ resC ":" *> mustWork (term fname)
   term <- needRes "=" *> mustWork (term fname)
   optRes ";"
-  pure $ MkPDef qty name type term
+  either fatalError pure $ mkPDef attrs qty name $ PConcrete type term
 
 export
-namespace_ : FileName -> Grammar True PNamespace
-namespace_ fname = withLoc fname $ do
-  ns    <- resC "namespace" *> qname; needRes "{"
-  decls <- nsInner; optRes ";"
-  pure $ MkPNamespace (ns.mods :< ns.base) decls
+definition : FileName -> List PAttr -> Grammar True PDefinition
+definition fname attrs =
+  try (postulate fname attrs) <|> concrete fname attrs
+
+export
+nsname : Grammar True Mods
+nsname = do ns <- qname; pure $ ns.mods :< ns.base
+
+export
+pragma : FileName -> Grammar True PPragma
+pragma fname = do
+  a <- attr' fname "#!["
+  either fatalError pure $ case a.name of
+    "log" => logArgs a.args a.loc
+    _     => Left $
+      #"unrecognised pragma "\#{a.name}"\n"# ++
+      #"known pragmas: ["log"]"#
+where
+  levelOOB : Nat -> Either String a
+  levelOOB n = Left $
+    "log level \{show n} out of bounds\n" ++
+    "expected number in range 0–\{show maxLogLevel} inclusive"
+
+  toLevel : Nat -> Either String LogLevel
+  toLevel lvl = maybe (levelOOB lvl) Right $ toLogLevel lvl
+
+  unknownCat : String -> Either String a
+  unknownCat cat = Left $
+    "unknown log category \{show cat}\n" ++
+    "known categories: \{show $ ["all", "default"] ++ logCategories}"
+
+  toCat : String -> Either String LogCategory
+  toCat cat = maybe (unknownCat cat) Right $ toLogCategory cat
+
+  fromPair : PTerm -> Either String (String, Nat)
+  fromPair (Pair (V (MkPName [<] x) Nothing _) (Nat n _) _) = Right (x, n)
+  fromPair _ = Left "invalid argument to log pragma"
+
+  logCatArg : (String, Nat) -> Either String Log.PushArg
+  logCatArg ("default", lvl) = [|SetDefault $ toLevel lvl|]
+  logCatArg ("all",     lvl) = [|SetAll $ toLevel lvl|]
+  logCatArg (cat,       lvl) = [|SetCat (toCat cat) (toLevel lvl)|]
+
+  logArgs : List PTerm -> Loc -> Either String PPragma
+  logArgs [] _ = Left "missing arguments to log pragma"
+  logArgs [V "pop" Nothing _] loc = Right $ PLogPop loc
+  logArgs other loc = do
+    args <- traverse (logCatArg <=< fromPair) other
+    pure $ PLogPush args loc
+
+
+export
+decl : FileName -> Grammar True PDecl
+
+export
+namespace_ : FileName -> List PAttr -> Grammar True PNamespace
+namespace_ fname attrs = withLoc fname $ do
+  ns    <- resC "namespace" *> nsname; needRes "{"
+  decls <- nsInner
+  either fatalError pure $ mkPNamespace attrs ns decls
 where
   nsInner : Grammar True (List PDecl)
   nsInner = [] <$ resC "}"
         <|> [|(assert_total decl fname <* commit) :: assert_total nsInner|]
 
-decl fname = [|PDef $ definition fname|] <|> [|PNs $ namespace_ fname|]
+export
+declBody : FileName -> List PAttr -> Grammar True PDecl
+declBody fname attrs =
+  [|PDef $ definition fname attrs|] <|> [|PNs $ namespace_ fname attrs|]
+
+-- decl : FileName -> Grammar True PDecl
+decl fname =
+      (attrList fname >>= declBody fname)
+  <|> PPrag <$> pragma fname
 
 export
 load : FileName -> Grammar True PTopLevel
@@ -580,7 +873,7 @@ topLevel : FileName -> Grammar True PTopLevel
 topLevel fname = load fname <|> [|PD $ decl fname|]
 
 export
-input : FileName -> Grammar False (List PTopLevel)
+input : FileName -> Grammar False PFile
 input fname = [] <$ eof
           <|> [|(topLevel fname <* commit) :: assert_total input fname|]
 
@@ -589,5 +882,5 @@ lexParseTerm : FileName -> String -> Either Error PTerm
 lexParseTerm = lexParseWith . term
 
 export
-lexParseInput : FileName -> String -> Either Error (List PTopLevel)
+lexParseInput : FileName -> String -> Either Error PFile
 lexParseInput = lexParseWith . input

lib/Quox/Parser/Syntax.idr

@@ -3,6 +3,8 @@ module Quox.Parser.Syntax
 import public Quox.Loc
 import public Quox.Syntax
 import public Quox.Definition
+import Quox.PrettyValExtra
+import public Quox.Log
 
 import Derive.Prelude
 %hide TT.Name
@@ -14,9 +16,9 @@ import Derive.Prelude
 public export
 data PatVar = Unused Loc | PV PBaseName Loc
 %name PatVar v
-%runElab derive "PatVar" [Eq, Ord, Show]
+%runElab derive "PatVar" [Eq, Ord, Show, PrettyVal]
 
-export
+export %inline
 Located PatVar where
   (Unused loc).loc = loc
   (PV _   loc).loc = loc
@@ -38,17 +40,17 @@ record PQty where
   val  : Qty
   loc_ : Loc
 %name PQty qty
-%runElab derive "PQty" [Eq, Ord, Show]
+%runElab derive "PQty" [Eq, Ord, Show, PrettyVal]
 
-export Located PQty where q.loc = q.loc_
+export %inline Located PQty where q.loc = q.loc_
 
 namespace PDim
   public export
   data PDim = K DimConst Loc | V PBaseName Loc
   %name PDim p, q
-  %runElab derive "PDim" [Eq, Ord, Show]
+  %runElab derive "PDim" [Eq, Ord, Show, PrettyVal]
 
-export
+export %inline
 Located PDim where
   (K _ loc).loc = loc
   (V _ loc).loc = loc
@@ -56,7 +58,7 @@ Located PDim where
 public export
 data PTagVal = PT TagVal Loc
 %name PTagVal tag
-%runElab derive "PTagVal" [Eq, Ord, Show]
+%runElab derive "PTagVal" [Eq, Ord, Show, PrettyVal]
 
 
 namespace PTerm
@@ -66,6 +68,8 @@ namespace PTerm
     data PTerm =
         TYPE Universe Loc
 
+      | IOState Loc
+
       | Pi PQty PatVar PTerm PTerm Loc
       | Lam PatVar PTerm Loc
       | App PTerm PTerm Loc
@@ -73,6 +77,7 @@ namespace PTerm
       | Sig PatVar PTerm PTerm Loc
       | Pair PTerm PTerm Loc
       | Case PQty PTerm (PatVar, PTerm) PCaseBody Loc
+      | Fst PTerm Loc | Snd PTerm Loc
 
       | Enum (List TagVal) Loc
       | Tag TagVal Loc
@@ -81,8 +86,11 @@ namespace PTerm
       | DLam PatVar PTerm Loc
       | DApp PTerm PDim Loc
 
-      | Nat Loc
-      | Zero Loc | Succ PTerm Loc
+      | NAT Loc
+      | Nat Nat Loc | Succ PTerm Loc
+
+      | STRING Loc  -- "String" is a reserved word in idris
+      | Str String Loc
 
       | BOX PQty PTerm Loc
       | Box PTerm Loc
@@ -93,6 +101,8 @@ namespace PTerm
       | Coe (PatVar, PTerm) PDim PDim PTerm Loc
       | Comp (PatVar, PTerm) PDim PDim PTerm PDim
              (PatVar, PTerm) (PatVar, PTerm) Loc
+
+      | Let (PQty, PatVar, PTerm) PTerm Loc
     %name PTerm s, t
 
     public export
@@ -103,33 +113,43 @@ namespace PTerm
       | CaseBox PatVar PTerm Loc
     %name PCaseBody body
 
-%runElab deriveMutual ["PTerm", "PCaseBody"] [Eq, Ord, Show]
+  public export %inline
+  Zero : Loc -> PTerm
+  Zero = Nat 0
 
-export
+%runElab deriveMutual ["PTerm", "PCaseBody"] [Eq, Ord, Show, PrettyVal]
+
+export %inline
 Located PTerm where
-  (TYPE _             loc).loc = loc
-  (Pi   _ _ _ _       loc).loc = loc
-  (Lam  _ _           loc).loc = loc
-  (App  _ _           loc).loc = loc
-  (Sig  _ _ _         loc).loc = loc
-  (Pair _ _           loc).loc = loc
-  (Case _ _ _ _       loc).loc = loc
-  (Enum _             loc).loc = loc
-  (Tag  _             loc).loc = loc
-  (Eq   _ _ _         loc).loc = loc
-  (DLam _ _           loc).loc = loc
-  (DApp _ _           loc).loc = loc
-  (Nat                loc).loc = loc
-  (Zero               loc).loc = loc
-  (Succ _             loc).loc = loc
-  (BOX  _ _           loc).loc = loc
-  (Box  _             loc).loc = loc
-  (V    _ _           loc).loc = loc
-  (Ann  _ _           loc).loc = loc
-  (Coe  _ _ _ _       loc).loc = loc
-  (Comp _ _ _ _ _ _ _ loc).loc = loc
+  (TYPE    _             loc).loc = loc
+  (IOState               loc).loc = loc
+  (Pi      _ _ _ _       loc).loc = loc
+  (Lam     _ _           loc).loc = loc
+  (App     _ _           loc).loc = loc
+  (Sig     _ _ _         loc).loc = loc
+  (Pair    _ _           loc).loc = loc
+  (Fst     _             loc).loc = loc
+  (Snd     _             loc).loc = loc
+  (Case    _ _ _ _       loc).loc = loc
+  (Enum    _             loc).loc = loc
+  (Tag     _             loc).loc = loc
+  (Eq      _ _ _         loc).loc = loc
+  (DLam    _ _           loc).loc = loc
+  (DApp    _ _           loc).loc = loc
+  (NAT                   loc).loc = loc
+  (Nat     _             loc).loc = loc
+  (Succ    _             loc).loc = loc
+  (STRING                loc).loc = loc
+  (Str     _             loc).loc = loc
+  (BOX     _ _           loc).loc = loc
+  (Box     _             loc).loc = loc
+  (V       _ _           loc).loc = loc
+  (Ann     _ _           loc).loc = loc
+  (Coe     _ _ _ _       loc).loc = loc
+  (Comp    _ _ _ _ _ _ _ loc).loc = loc
+  (Let     _ _           loc).loc = loc
 
-export
+export %inline
 Located PCaseBody where
   (CasePair _ _ loc).loc = loc
   (CaseEnum _   loc).loc = loc
@@ -137,18 +157,45 @@ Located PCaseBody where
   (CaseBox  _ _ loc).loc = loc
 
 
+public export
+data PBody = PConcrete (Maybe PTerm) PTerm | PPostulate PTerm
+%name PBody body
+%runElab derive "PBody" [Eq, Ord, Show, PrettyVal]
+
+
+public export
+data PFail =
+  PSucceed
+| PFailAny
+| PFailMatch String
+%runElab derive "PFail" [Eq, Ord, Show, PrettyVal]
+
 public export
 record PDefinition where
   constructor MkPDef
-  qty  : PQty
-  name : PBaseName
-  type : Maybe PTerm
-  term : PTerm
-  loc_ : Loc
+  qty    : PQty
+  name   : PBaseName
+  body   : PBody
+  fail   : PFail
+  main   : Bool
+  scheme : Maybe String
+  loc_   : Loc
 %name PDefinition def
-%runElab derive "PDefinition" [Eq, Ord, Show]
+%runElab derive "PDefinition" [Eq, Ord, Show, PrettyVal]
 
-export Located PDefinition where def.loc = def.loc_
+export %inline Located PDefinition where def.loc = def.loc_
+
+public export
+data PPragma =
+    PLogPush (List Log.PushArg) Loc
+  | PLogPop  Loc
+%name PPragma prag
+%runElab derive "PPragma" [Eq, Ord, Show, PrettyVal]
+
+export %inline
+Located PPragma where
+  (PLogPush _ loc).loc = loc
+  (PLogPop    loc).loc = loc
 
 mutual
   public export
@@ -156,35 +203,49 @@ mutual
     constructor MkPNamespace
     name  : Mods
     decls : List PDecl
+    fail  : PFail
     loc_  : Loc
   %name PNamespace ns
 
   public export
   data PDecl =
-      PDef PDefinition
-    | PNs  PNamespace
+      PDef  PDefinition
+    | PNs   PNamespace
+    | PPrag PPragma
   %name PDecl decl
-%runElab deriveMutual ["PNamespace", "PDecl"] [Eq, Ord, Show]
+%runElab deriveMutual ["PNamespace", "PDecl"] [Eq, Ord, Show, PrettyVal]
 
-export Located PNamespace where ns.loc = ns.loc_
+export %inline Located PNamespace where ns.loc = ns.loc_
 
-export
+export %inline
 Located PDecl where
-  (PDef def).loc = def.loc
-  (PNs  ns).loc  = ns.loc
+  (PDef  d).loc    = d.loc
+  (PNs   ns).loc   = ns.loc
+  (PPrag prag).loc = prag.loc
 
 public export
 data PTopLevel = PD PDecl | PLoad String Loc
 %name PTopLevel t
-%runElab derive "PTopLevel" [Eq, Ord, Show]
+%runElab derive "PTopLevel" [Eq, Ord, Show, PrettyVal]
 
-export
+export %inline
 Located PTopLevel where
   (PD    decl).loc  = decl.loc
   (PLoad _ loc).loc = loc
 
 
 public export
-fromNat : Nat -> Loc -> PTerm
-fromNat 0     loc = Zero loc
-fromNat (S k) loc = Succ (fromNat k loc) loc
+record PAttr where
+  constructor PA
+  name : PBaseName
+  args : List PTerm
+  loc_ : Loc
+%name PAttr attr
+%runElab derive "PAttr" [Eq, Ord, Show, PrettyVal]
+
+export %inline Located PAttr where attr.loc = attr.loc_
+
+
+public export
+PFile : Type
+PFile = List PTopLevel

lib/Quox/Pretty.idr

@@ -3,6 +3,7 @@ module Quox.Pretty
 import Quox.Loc
 import Quox.Name
 
+import Control.Monad.ST.Extra
 import public Text.PrettyPrint.Bernardy
 import public Text.PrettyPrint.Bernardy.Core.Decorate
 import public Quox.EffExtra
@@ -40,7 +41,7 @@ data HL
 | Dim  | DVar | DVarErr
 | Qty  | Universe
 | Syntax
-| Tag
+| Constant
 %runElab derive "HL" [Eq, Ord, Show]
 
 
@@ -65,11 +66,12 @@ export %inline
 runPrettyWith : PPrec -> Flavor -> (HL -> Highlight) -> Nat ->
                 Eff Pretty a -> a
 runPrettyWith prec flavor highlight indent act =
-  extract $
-  evalStateAt PREC prec $
-  runReaderAt FLAVOR flavor $
-  runReaderAt HIGHLIGHT highlight $
-  runReaderAt INDENT indent act
+  runST $ do
+    runEff act $ with Union.(::)
+      [handleStateSTRef !(newSTRef prec),
+       handleReaderConst flavor,
+       handleReaderConst highlight,
+       handleReaderConst indent]
 
 
 export %inline
@@ -84,43 +86,65 @@ toSGR DVarErr  = [SetForeground BrightGreen, SetStyle SingleUnderline]
 toSGR Qty      = [SetForeground BrightMagenta]
 toSGR Universe = [SetForeground BrightRed]
 toSGR Syntax   = [SetForeground BrightCyan]
-toSGR Tag      = [SetForeground BrightRed]
+toSGR Constant = [SetForeground BrightRed]
 
 export %inline
 highlightSGR : HL -> Highlight
 highlightSGR h = MkHighlight (escapeSGR $ toSGR h) (escapeSGR [Reset])
 
+export %inline
+toClass : HL -> String
+toClass Delim    = "dl"
+toClass Free     = "fr"
+toClass TVar     = "tv"
+toClass TVarErr  = "tv err"
+toClass Dim      = "dc"
+toClass DVar     = "dv"
+toClass DVarErr  = "dv err"
+toClass Qty      = "qt"
+toClass Universe = "un"
+toClass Syntax   = "sy"
+toClass Constant = "co"
+
+export %inline
+highlightHtml : HL -> Highlight
+highlightHtml h = MkHighlight #"<span class="\#{toClass h}">"# "</span>"
+
+
+export %inline
+runPrettyHL : (HL -> Highlight) -> Eff Pretty a -> a
+runPrettyHL f = runPrettyWith Outer Unicode f 2
 
 export %inline
 runPretty : Eff Pretty a -> a
-runPretty = runPrettyWith Outer Unicode noHighlight 2
-
-export %inline
-runPrettyColor : Eff Pretty a -> a
-runPrettyColor = runPrettyWith Outer Unicode highlightSGR 2
+runPretty = runPrettyHL noHighlight
 
 
 export %inline
-hl : {opts : _} -> HL -> Doc opts -> Eff Pretty (Doc opts)
+hl : {opts : LayoutOpts} -> HL -> Doc opts -> Eff Pretty (Doc opts)
 hl h doc = asksAt HIGHLIGHT $ \f => decorate (f h) doc
 
 
 export %inline
-indentD : {opts : _} -> Doc opts -> Eff Pretty (Doc opts)
+indentD : {opts : LayoutOpts} -> Doc opts -> Eff Pretty (Doc opts)
 indentD doc = pure $ indent !(askAt INDENT) doc
 
 export %inline
-hangD : {opts : _} -> Doc opts -> Doc opts -> Eff Pretty (Doc opts)
+hangD : {opts : LayoutOpts} -> Doc opts -> Doc opts -> Eff Pretty (Doc opts)
 hangD d1 d2 = pure $ hangSep !(askAt INDENT) d1 d2
 
 export %inline
-hangDSingle : {opts : _} -> Doc opts -> Doc opts -> Eff Pretty (Doc opts)
-hangDSingle d1 d2 =
-  pure $ ifMultiline (d1 <++> d2) (vappend d1 !(indentD d2))
+hangSingle : {opts : LayoutOpts} -> Nat -> Doc opts -> Doc opts -> Doc opts
+hangSingle n d1 d2 = ifMultiline (d1 <++> d2) (vappend d1 (indent n d2))
+
+export %inline
+hangDSingle : {opts : LayoutOpts} -> Doc opts -> Doc opts ->
+              Eff Pretty (Doc opts)
+hangDSingle d1 d2 = pure $ hangSingle !(askAt INDENT) d1 d2
 
 
 export
-tightDelims : {opts : _} -> (l, r : String) -> (inner : Doc opts) ->
+tightDelims : {opts : LayoutOpts} -> (l, r : String) -> (inner : Doc opts) ->
               Eff Pretty (Doc opts)
 tightDelims l r inner = do
   l <- hl Delim $ text l
@@ -128,7 +152,7 @@ tightDelims l r inner = do
   pure $ hcat [l, inner, r]
 
 export
-looseDelims : {opts : _} -> (l, r : String) -> (inner : Doc opts) ->
+looseDelims : {opts : LayoutOpts} -> (l, r : String) -> (inner : Doc opts) ->
               Eff Pretty (Doc opts)
 looseDelims l r inner = do
   l <- hl Delim $ text l
@@ -138,39 +162,39 @@ looseDelims l r inner = do
   pure $ ifMultiline short long
 
 export %inline
-parens : {opts : _} -> Doc opts -> Eff Pretty (Doc opts)
+parens : {opts : LayoutOpts} -> Doc opts -> Eff Pretty (Doc opts)
 parens = tightDelims "(" ")"
 
 export %inline
-bracks : {opts : _} -> Doc opts -> Eff Pretty (Doc opts)
+bracks : {opts : LayoutOpts} -> Doc opts -> Eff Pretty (Doc opts)
 bracks = tightDelims "[" "]"
 
 export %inline
-braces : {opts : _} -> Doc opts -> Eff Pretty (Doc opts)
+braces : {opts : LayoutOpts} -> Doc opts -> Eff Pretty (Doc opts)
 braces = looseDelims "{" "}"
 
 export %inline
-tightBraces : {opts : _} -> Doc opts -> Eff Pretty (Doc opts)
+tightBraces : {opts : LayoutOpts} -> Doc opts -> Eff Pretty (Doc opts)
 tightBraces = tightDelims "{" "}"
 
 export %inline
-parensIf : {opts : _} -> Bool -> Doc opts -> Eff Pretty (Doc opts)
+parensIf : {opts : LayoutOpts} -> Bool -> Doc opts -> Eff Pretty (Doc opts)
 parensIf True  = parens
 parensIf False = pure
 
 
 ||| uses hsep only if the whole list fits on one line
 export
-sepSingle : {opts : _} -> List (Doc opts) -> Doc opts
+sepSingle : {opts : LayoutOpts} -> List (Doc opts) -> Doc opts
 sepSingle xs = ifMultiline (hsep xs) (vsep xs)
 
 export
-fillSep : {opts : _} -> List (Doc opts) -> Doc opts
+fillSep : {opts : LayoutOpts} -> List (Doc opts) -> Doc opts
 fillSep []        = empty
 fillSep (x :: xs) = foldl (\x, y => sep [x, y]) x xs
 
 export
-exceptLast : {opts : _} -> (Doc opts -> Doc opts) ->
+exceptLast : {opts : LayoutOpts} -> (Doc opts -> Doc opts) ->
              List (Doc opts) -> List (Doc opts)
 exceptLast f []        = []
 exceptLast f [x]       = [x]
@@ -185,11 +209,24 @@ parameters {opts : LayoutOpts} {auto _ : Foldable t}
   separateTight : Doc opts -> t (Doc opts) -> Doc opts
   separateTight d = sep . exceptLast (<+> d) . toList
 
+  export
+  hseparateTight : Doc opts -> t (Doc opts) -> Doc opts
+  hseparateTight d = hsep . exceptLast (<+> d) . toList
+
+  export
+  vseparateTight : Doc opts -> t (Doc opts) -> Doc opts
+  vseparateTight d = vsep . exceptLast (<+> d) . toList
+
   export
   fillSeparateTight : Doc opts -> t (Doc opts) -> Doc opts
   fillSeparateTight d = fillSep . exceptLast (<+> d) . toList
 
 
+export %inline
+pshow : {opts : LayoutOpts} -> Show a => a -> Doc opts
+pshow = text . show
+
+
 export %inline
 ifUnicode : (uni, asc : Lazy a) -> Eff Pretty a
 ifUnicode uni asc =
@@ -198,7 +235,7 @@ ifUnicode uni asc =
     Ascii   => asc
 
 export %inline
-parensIfM : {opts : _} -> PPrec -> Doc opts -> Eff Pretty (Doc opts)
+parensIfM : {opts : LayoutOpts} -> PPrec -> Doc opts -> Eff Pretty (Doc opts)
 parensIfM d doc = parensIf (!(getAt PREC) > d) doc
 
 export %inline
@@ -211,64 +248,73 @@ prettyName : Name -> Doc opts
 prettyName = text . toDots
 
 export
-prettyFree : {opts : _} -> Name -> Eff Pretty (Doc opts)
+prettyFree : {opts : LayoutOpts} -> Name -> Eff Pretty (Doc opts)
 prettyFree = hl Free . prettyName
 
 export
 prettyBind' : BindName -> Doc opts
-prettyBind' = text . baseStr . name
+prettyBind' = text . baseStr . val
 
 export
-prettyTBind : {opts : _} -> BindName -> Eff Pretty (Doc opts)
+prettyTBind : {opts : LayoutOpts} -> BindName -> Eff Pretty (Doc opts)
 prettyTBind = hl TVar . prettyBind'
 
 export
-prettyDBind : {opts : _} -> BindName -> Eff Pretty (Doc opts)
+prettyDBind : {opts : LayoutOpts} -> BindName -> Eff Pretty (Doc opts)
 prettyDBind = hl DVar . prettyBind'
 
 
 
 export %inline
-typeD, arrowD, darrowD, timesD, lamD, eqndD, dlamD, annD, natD,
-eqD, colonD, commaD, semiD, caseD, typecaseD, returnD,
-ofD, dotD, zeroD, succD, coeD, compD, undD, cstD, pipeD :
-  {opts : _} -> Eff Pretty (Doc opts)
+typeD, ioStateD, arrowD, darrowD, timesD, lamD, eqndD, dlamD, annD, natD,
+stringD, eqD, colonD, commaD, semiD, atD, caseD, typecaseD, returnD, ofD, dotD,
+zeroD, succD, coeD, compD, undD, cstD, pipeD, fstD, sndD, letD, inD :
+  {opts : LayoutOpts} -> Eff Pretty (Doc opts)
 typeD     = hl Syntax . text =<< ifUnicode "★" "Type"
-arrowD    = hl Delim  . text =<< ifUnicode "→" "->"
-darrowD   = hl Delim  . text =<< ifUnicode "⇒" "=>"
-timesD    = hl Delim  . text =<< ifUnicode "×" "**"
+ioStateD  = hl Syntax $ text "IOState"
+arrowD    = hl Syntax . text =<< ifUnicode "→" "->"
+darrowD   = hl Syntax . text =<< ifUnicode "⇒" "=>"
+timesD    = hl Syntax . text =<< ifUnicode "×" "**"
 lamD      = hl Syntax . text =<< ifUnicode "λ" "fun"
-eqndD     = hl Delim  . text =<< ifUnicode "≡" "=="
+eqndD     = hl Syntax . text =<< ifUnicode "≡" "=="
 dlamD     = hl Syntax . text =<< ifUnicode "δ" "dfun"
-annD      = hl Delim  . text =<< ifUnicode "∷" "::"
+annD      = hl Syntax . text =<< ifUnicode "∷" "::"
 natD      = hl Syntax . text =<< ifUnicode "ℕ" "Nat"
-eqD       = hl Syntax $ text "Eq"
-colonD    = hl Delim  $ text ":"
-commaD    = hl Delim  $ text ","
-semiD     = hl Delim  $ text ";"
-caseD     = hl Syntax $ text "case"
-typecaseD = hl Syntax $ text "type-case"
-ofD       = hl Syntax $ text "of"
-returnD   = hl Syntax $ text "return"
-dotD      = hl Delim  $ text "."
-zeroD     = hl Syntax $ text "zero"
-succD     = hl Syntax $ text "succ"
-coeD      = hl Syntax $ text "coe"
-compD     = hl Syntax $ text "comp"
-undD      = hl Syntax $ text "_"
-cstD      = hl Syntax $ text "="
-pipeD     = hl Syntax $ text "|"
+stringD   = hl Syntax   $ text "String"
+eqD       = hl Syntax   $ text "Eq"
+colonD    = hl Syntax   $ text ":"
+commaD    = hl Syntax   $ text ","
+semiD     = hl Delim    $ text ";"
+atD       = hl Delim    $ text "@"
+caseD     = hl Syntax   $ text "case"
+typecaseD = hl Syntax   $ text "type-case"
+ofD       = hl Syntax   $ text "of"
+returnD   = hl Syntax   $ text "return"
+dotD      = hl Delim    $ text "."
+zeroD     = hl Constant $ text "zero"
+succD     = hl Constant $ text "succ"
+coeD      = hl Syntax   $ text "coe"
+compD     = hl Syntax   $ text "comp"
+undD      = hl Syntax   $ text "_"
+cstD      = hl Syntax   $ text "="
+pipeD     = hl Delim    $ text "|"
+fstD      = hl Syntax   $ text "fst"
+sndD      = hl Syntax   $ text "snd"
+letD      = hl Syntax   $ text "let"
+inD       = hl Syntax   $ text "in"
 
 
 export
-prettyApp : {opts : _} -> Nat -> Doc opts -> List (Doc opts) -> Doc opts
+prettyApp : {opts : LayoutOpts} -> Nat -> Doc opts ->
+            List (Doc opts) -> Doc opts
 prettyApp ind f args =
-      hsep (f :: args)
-  <|> hsep [f, vsep args]
-  <|> vsep (f :: map (indent ind) args)
+  ifMultiline
+    (hsep (f :: args))
+    (f <++> vsep args <|> vsep (f :: map (indent ind) args))
 
 export
-prettyAppD : {opts : _} -> Doc opts -> List (Doc opts) -> Eff Pretty (Doc opts)
+prettyAppD : {opts : LayoutOpts} -> Doc opts -> List (Doc opts) ->
+             Eff Pretty (Doc opts)
 prettyAppD f args = pure $ prettyApp !(askAt INDENT) f args
 
 
@@ -288,7 +334,7 @@ quoteTag tag =
   "\"" ++ escapeString tag ++ "\""
 
 export
-prettyBounds : {opts : _} -> Bounds -> Eff Pretty (Doc opts)
+prettyBounds : {opts : LayoutOpts} -> Bounds -> Eff Pretty (Doc opts)
 prettyBounds (MkBounds l1 c1 l2 c2) =
   hcat <$> sequence
     [hl TVar $ text $ show l1, colonD,
@@ -297,8 +343,22 @@ prettyBounds (MkBounds l1 c1 l2 c2) =
      hl DVar $ text $ show c2, colonD]
 
 export
-prettyLoc : {opts : _} -> Loc -> Eff Pretty (Doc opts)
+prettyLoc : {opts : LayoutOpts} -> Loc -> Eff Pretty (Doc opts)
 prettyLoc (L NoLoc) =
   hcat <$> sequence [hl TVarErr "no location", colonD]
 prettyLoc (L (YesLoc file b)) =
   hcat <$> sequence [hl Free $ text file, colonD, prettyBounds b]
+
+export
+prettyTag : {opts : _} -> String -> Eff Pretty (Doc opts)
+prettyTag tag = hl Constant $ text $ "'" ++ quoteTag tag
+
+export
+prettyStrLit : {opts : _} -> String -> Eff Pretty (Doc opts)
+prettyStrLit s =
+  let s = concatMap esc1 $ unpack s in
+  hl Constant $ hcat ["\"", text s, "\""]
+where
+  esc1 : Char -> String
+  esc1 '"' = "\""; esc1 '\\' = "\\"
+  esc1 c   = singleton c

lib/Quox/PrettyValExtra.idr

@@ -0,0 +1,20 @@
+module Quox.PrettyValExtra
+
+import Data.DPair
+import Derive.Prelude
+import public Text.Show.Value
+import public Text.Show.PrettyVal
+import public Text.Show.PrettyVal.Derive
+
+%language ElabReflection
+
+%runElab derive "SnocList" [PrettyVal]
+
+
+export %inline
+PrettyVal a => PrettyVal (Subset a p) where
+  prettyVal (Element x _) = Con "Element" [prettyVal x, Con "_" []]
+
+export %inline
+(forall x. PrettyVal (p x)) => PrettyVal (Exists p) where
+  prettyVal (Evidence _ p) = Con "Evidence" [Con "_" [], prettyVal p]

lib/Quox/Reduce.idr

@@ -1,751 +0,0 @@
-module Quox.Reduce
-
-import Quox.No
-import Quox.Syntax
-import Quox.Definition
-import Quox.Displace
-import Quox.Typing.Context
-import Quox.Typing.Error
-import Data.SnocVect
-import Data.Maybe
-import Data.List
-import Control.Eff
-
-%default total
-
-
-public export
-Whnf : List (Type -> Type)
-Whnf = [NameGen, Except Error]
-
-export
-runWhnfWith : NameSuf -> Eff Whnf a -> (Either Error a, NameSuf)
-runWhnfWith suf act = extract $ runStateAt GEN suf $ runExcept act
-
-export
-runWhnf : Eff Whnf a -> Either Error a
-runWhnf = fst . runWhnfWith 0
-
-
-public export
-0 RedexTest : TermLike -> Type
-RedexTest tm = {d, n : Nat} -> Definitions -> tm d n -> Bool
-
-public export
-interface CanWhnf (0 tm : TermLike) (0 isRedex : RedexTest tm) | tm
-where
-  whnf : {d, n : Nat} -> (defs : Definitions) ->
-         (ctx : WhnfContext d n) ->
-         tm d n -> Eff Whnf (Subset (tm d n) (No . isRedex defs))
-
-public export %inline
-whnf0 : {d, n : Nat} -> {0 isRedex : RedexTest tm} -> CanWhnf tm isRedex =>
-        (defs : Definitions) -> WhnfContext d n -> tm d n -> Eff Whnf (tm d n)
-whnf0 defs ctx t = fst <$> whnf defs ctx t
-
-public export
-0 IsRedex, NotRedex : {isRedex : RedexTest tm} -> CanWhnf tm isRedex =>
-                      Definitions -> Pred (tm d n)
-IsRedex  defs = So . isRedex defs
-NotRedex defs = No . isRedex defs
-
-public export
-0 NonRedex : (tm : TermLike) -> {isRedex : RedexTest tm} ->
-             CanWhnf tm isRedex => (d, n : Nat) -> (defs : Definitions) -> Type
-NonRedex tm d n defs = Subset (tm d n) (NotRedex defs)
-
-public export %inline
-nred : {0 isRedex : RedexTest tm} -> (0 _ : CanWhnf tm isRedex) =>
-       (t : tm d n) -> (0 nr : NotRedex defs t) => NonRedex tm d n defs
-nred t = Element t nr
-
-
-public export %inline
-isLamHead : Elim {} -> Bool
-isLamHead (Ann (Lam {}) (Pi {}) _) = True
-isLamHead (Coe {})                 = True
-isLamHead _                        = False
-
-public export %inline
-isDLamHead : Elim {} -> Bool
-isDLamHead (Ann (DLam {}) (Eq {}) _) = True
-isDLamHead (Coe {})                  = True
-isDLamHead _                         = False
-
-public export %inline
-isPairHead : Elim {} -> Bool
-isPairHead (Ann (Pair {}) (Sig {}) _) = True
-isPairHead (Coe {})                   = True
-isPairHead _                          = False
-
-public export %inline
-isTagHead : Elim {} -> Bool
-isTagHead (Ann (Tag {}) (Enum {}) _) = True
-isTagHead (Coe {})                   = True
-isTagHead _                          = False
-
-public export %inline
-isNatHead : Elim {} -> Bool
-isNatHead (Ann (Zero {}) (Nat {}) _) = True
-isNatHead (Ann (Succ {}) (Nat {}) _) = True
-isNatHead (Coe {})                   = True
-isNatHead _                          = False
-
-public export %inline
-isBoxHead : Elim {} -> Bool
-isBoxHead (Ann (Box {}) (BOX {}) _) = True
-isBoxHead (Coe {})                  = True
-isBoxHead _                         = False
-
-public export %inline
-isE : Term {} -> Bool
-isE (E {}) = True
-isE _      = False
-
-public export %inline
-isAnn : Elim {} -> Bool
-isAnn (Ann {}) = True
-isAnn _        = False
-
-||| true if a term is syntactically a type.
-public export %inline
-isTyCon : Term {} -> Bool
-isTyCon (TYPE  {}) = True
-isTyCon (Pi    {}) = True
-isTyCon (Lam   {}) = False
-isTyCon (Sig   {}) = True
-isTyCon (Pair  {}) = False
-isTyCon (Enum  {}) = True
-isTyCon (Tag   {}) = False
-isTyCon (Eq    {}) = True
-isTyCon (DLam  {}) = False
-isTyCon (Nat   {}) = True
-isTyCon (Zero  {}) = False
-isTyCon (Succ  {}) = False
-isTyCon (BOX   {}) = True
-isTyCon (Box   {}) = False
-isTyCon (E     {}) = False
-isTyCon (CloT  {}) = False
-isTyCon (DCloT {}) = False
-
-||| true if a term is syntactically a type, or a neutral.
-public export %inline
-isTyConE : Term {} -> Bool
-isTyConE s = isTyCon s || isE s
-
-||| true if a term is syntactically a type.
-public export %inline
-isAnnTyCon : Elim {} -> Bool
-isAnnTyCon (Ann ty (TYPE {}) _) = isTyCon ty
-isAnnTyCon _                    = False
-
-public export %inline
-isK : Dim d -> Bool
-isK (K {}) = True
-isK _      = False
-
-
-mutual
-  public export
-  isRedexE : RedexTest Elim
-  isRedexE defs (F {x, _}) {d, n} =
-    isJust $ lookupElim x defs {d, n}
-  isRedexE _ (B {}) = False
-  isRedexE defs (App {fun, _}) =
-    isRedexE defs fun || isLamHead fun
-  isRedexE defs (CasePair {pair, _}) =
-    isRedexE defs pair || isPairHead pair
-  isRedexE defs (CaseEnum {tag, _}) =
-    isRedexE defs tag || isTagHead tag
-  isRedexE defs (CaseNat {nat, _}) =
-    isRedexE defs nat || isNatHead nat
-  isRedexE defs (CaseBox {box, _}) =
-    isRedexE defs box || isBoxHead box
-  isRedexE defs (DApp {fun, arg, _}) =
-    isRedexE defs fun || isDLamHead fun || isK arg
-  isRedexE defs (Ann {tm, ty, _}) =
-    isE tm || isRedexT defs tm || isRedexT defs ty
-  isRedexE defs (Coe {val, _}) =
-    isRedexT defs val || not (isE val)
-  isRedexE defs (Comp {ty, r, _}) =
-    isRedexT defs ty || isK r
-  isRedexE defs (TypeCase {ty, ret, _}) =
-    isRedexE defs ty || isRedexT defs ret || isAnnTyCon ty
-  isRedexE _ (CloE  {}) = True
-  isRedexE _ (DCloE {}) = True
-
-  public export
-  isRedexT : RedexTest Term
-  isRedexT _    (CloT  {}) = True
-  isRedexT _    (DCloT {}) = True
-  isRedexT defs (E {e, _}) = isAnn e || isRedexE defs e
-  isRedexT _    _          = False
-
-
-public export
-tycaseRhs : (k : TyConKind) -> TypeCaseArms d n ->
-            Maybe (ScopeTermN (arity k) d n)
-tycaseRhs k arms = lookupPrecise k arms
-
-public export
-tycaseRhsDef : Term d n -> (k : TyConKind) -> TypeCaseArms d n ->
-               ScopeTermN (arity k) d n
-tycaseRhsDef def k arms = fromMaybe (SN def) $ tycaseRhs k arms
-
-public export
-tycaseRhs0 : (k : TyConKind) -> TypeCaseArms d n ->
-             (0 eq : arity k = 0) => Maybe (Term d n)
-tycaseRhs0 k arms {eq} with (tycaseRhs k arms) | (arity k)
-  tycaseRhs0 k arms {eq = Refl} | res | 0 = map (.term) res
-
-public export
-tycaseRhsDef0 : Term d n -> (k : TyConKind) -> TypeCaseArms d n ->
-                (0 eq : arity k = 0) => Term d n
-tycaseRhsDef0 def k arms = fromMaybe def $ tycaseRhs0 k arms
-
-
-
-private
-weakDS : (by : Nat) -> DScopeTerm d n -> DScopeTerm d (by + n)
-weakDS by (S names (Y body)) = S names $ Y $ weakT by body
-weakDS by (S names (N body)) = S names $ N $ weakT by body
-
-private
-dweakS : (by : Nat) -> ScopeTerm d n -> ScopeTerm (by + d) n
-dweakS by (S names (Y body)) = S names $ Y $ dweakT by body
-dweakS by (S names (N body)) = S names $ N $ dweakT by body
-
-private
-coeScoped : {s : Nat} -> DScopeTerm d n -> Dim d -> Dim d -> Loc ->
-            ScopeTermN s d n -> ScopeTermN s d n
-coeScoped ty p q loc (S names (Y body)) =
-  S names $ Y $ E $ Coe (weakDS s ty) p q body loc
-coeScoped ty p q loc (S names (N body)) =
-  S names $ N $ E $ Coe ty p q body loc
-
-
-export covering
-CanWhnf Term Reduce.isRedexT
-
-export covering
-CanWhnf Elim Reduce.isRedexE
-
-parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
-  ||| performs the minimum work required to recompute the type of an elim.
-  |||
-  ||| ⚠ **assumes the elim is already typechecked.** ⚠
-  export covering
-  computeElimType : (e : Elim d n) -> (0 ne : No (isRedexE defs e)) =>
-                    Eff Whnf (Term d n)
-  computeElimType (F {x, u, loc}) = do
-    let Just def = lookup x defs | Nothing => throw $ NotInScope loc x
-    pure $ displace u def.type
-  computeElimType (B {i, _}) = pure $ ctx.tctx !! i
-  computeElimType (App {fun = f, arg = s, loc}) {ne} = do
-    Pi {arg, res, _} <- whnf0 defs ctx =<< computeElimType f {ne = noOr1 ne}
-      | t => throw $ ExpectedPi loc ctx.names t
-    pure $ sub1 res $ Ann s arg loc
-  computeElimType (CasePair {pair, ret, _}) = pure $ sub1 ret pair
-  computeElimType (CaseEnum {tag, ret, _}) = pure $ sub1 ret tag
-  computeElimType (CaseNat {nat, ret, _}) = pure $ sub1 ret nat
-  computeElimType (CaseBox {box, ret, _}) = pure $ sub1 ret box
-  computeElimType (DApp {fun = f, arg = p, loc}) {ne} = do
-    Eq {ty, _} <- whnf0 defs ctx =<< computeElimType f {ne = noOr1 ne}
-      | t => throw $ ExpectedEq loc ctx.names t
-    pure $ dsub1 ty p
-  computeElimType (Ann {ty, _}) = pure ty
-  computeElimType (Coe {ty, q, _}) = pure $ dsub1 ty q
-  computeElimType (Comp {ty, _}) = pure ty
-  computeElimType (TypeCase {ret, _}) = pure ret
-
-parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext (S d) n)
-  ||| for π.(x : A) → B, returns (A, B);
-  ||| for an elim returns a pair of type-cases that will reduce to that;
-  ||| for other intro forms error
-  private covering
-  tycasePi : (t : Term (S d) n) -> (0 tnf : No (isRedexT defs t)) =>
-             Eff Whnf (Term (S d) n, ScopeTerm (S d) n)
-  tycasePi (Pi {arg, res, _}) = pure (arg, res)
-  tycasePi (E e) {tnf} = do
-    ty <- computeElimType defs ctx e @{noOr2 tnf}
-    let loc  = e.loc
-        narg = mnb "Arg"; nret = mnb "Ret"
-        arg  = E $ typeCase1Y e ty KPi [< !narg, !nret] (BVT 1 loc) loc
-        res' = typeCase1Y e (Arr Zero arg ty loc) KPi [< !narg, !nret]
-                 (BVT 0 loc) loc
-        res  = SY [< !narg] $ E $ App (weakE 1 res') (BVT 0 loc) loc
-    pure (arg, res)
-  tycasePi t = throw $ ExpectedPi t.loc ctx.names t
-
-  ||| for (x : A) × B, returns (A, B);
-  ||| for an elim returns a pair of type-cases that will reduce to that;
-  ||| for other intro forms error
-  private covering
-  tycaseSig : (t : Term (S d) n) -> (0 tnf : No (isRedexT defs t)) =>
-              Eff Whnf (Term (S d) n, ScopeTerm (S d) n)
-  tycaseSig (Sig {fst, snd, _}) = pure (fst, snd)
-  tycaseSig (E e) {tnf} = do
-    ty <- computeElimType defs ctx e @{noOr2 tnf}
-    let loc  = e.loc
-        nfst = mnb "Fst"; nsnd = mnb "Snd"
-        fst  = E $ typeCase1Y e ty KSig [< !nfst, !nsnd] (BVT 1 loc) loc
-        snd' = typeCase1Y e (Arr Zero fst ty loc) KSig [< !nfst, !nsnd]
-                 (BVT 0 loc) loc
-        snd  = SY [< !nfst] $ E $ App (weakE 1 snd') (BVT 0 loc) loc
-    pure (fst, snd)
-  tycaseSig t = throw $ ExpectedSig t.loc ctx.names t
-
-  ||| for [π. A], returns A;
-  ||| for an elim returns a type-case that will reduce to that;
-  ||| for other intro forms error
-  private covering
-  tycaseBOX : (t : Term (S d) n) -> (0 tnf : No (isRedexT defs t)) =>
-              Eff Whnf (Term (S d) n)
-  tycaseBOX (BOX {ty, _}) = pure ty
-  tycaseBOX (E e) {tnf} = do
-    ty <- computeElimType defs ctx e @{noOr2 tnf}
-    pure $ E $ typeCase1Y e ty KBOX [< !(mnb "Ty")] (BVT 0 e.loc) e.loc
-  tycaseBOX t = throw $ ExpectedBOX t.loc ctx.names t
-
-  ||| for Eq [i ⇒ A] l r, returns (A‹0/i›, A‹1/i›, A, l, r);
-  ||| for an elim returns five type-cases that will reduce to that;
-  ||| for other intro forms error
-  private covering
-  tycaseEq : (t : Term (S d) n) -> (0 tnf : No (isRedexT defs t)) =>
-             Eff Whnf (Term (S d) n, Term (S d) n, DScopeTerm (S d) n,
-                       Term (S d) n, Term (S d) n)
-  tycaseEq (Eq {ty, l, r, _}) = pure (ty.zero, ty.one, ty, l, r)
-  tycaseEq (E e) {tnf} = do
-    ty <- computeElimType defs ctx e @{noOr2 tnf}
-    let loc   = e.loc
-        names = traverse' (\x => mnb x) [< "A0", "A1", "A", "L", "R"]
-        a0    = E $ typeCase1Y e ty KEq !names (BVT 4 loc) loc
-        a1    = E $ typeCase1Y e ty KEq !names (BVT 3 loc) loc
-        a'    = typeCase1Y e (Eq0 ty a0 a1 loc) KEq !names (BVT 2 loc) loc
-        a     = SY [< !(mnb "i")] $ E $ DApp (dweakE 1 a') (B VZ loc) loc
-        l     = E $ typeCase1Y e a0 KEq !names (BVT 1 loc) loc
-        r     = E $ typeCase1Y e a1 KEq !names (BVT 0 loc) loc
-    pure (a0, a1, a, l, r)
-  tycaseEq t = throw $ ExpectedEq t.loc ctx.names t
-
--- new block because the functions below might pass a different ctx
--- into the ones above
-parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
-  ||| reduce a function application `App (Coe ty p q val) s loc`
-  private covering
-  piCoe : (ty : DScopeTerm d n) -> (p, q : Dim d) ->
-          (val, s : Term d n) -> Loc ->
-          Eff Whnf (Subset (Elim d n) (No . isRedexE defs))
-  piCoe sty@(S [< i] ty) p q val s loc = do
-    -- (coe [i ⇒ π.(x : A) → B] @p @q t) s ⇝
-    -- coe [i ⇒ B[𝒔‹i›/x] @p @q ((t ∷ (π.(x : A) → B)‹p/i›) 𝒔‹p›)
-    --   where 𝒔‹j› ≔ coe [i ⇒ A] @q @j s
-    --
-    -- type-case is used to expose A,B if the type is neutral
-    let ctx1 = extendDim i ctx
-    Element ty tynf <- whnf defs ctx1 ty.term
-    (arg, res) <- tycasePi defs ctx1 ty
-    let s0   = CoeT i arg q p s s.loc
-        body = E $ App (Ann val (ty // one p) val.loc) (E s0) loc
-        s1   = CoeT i (arg // (BV 0 i.loc ::: shift 2)) (weakD 1 q) (BV 0 i.loc)
-                    (s // shift 1) s.loc
-    whnf defs ctx $ CoeT i (sub1 res s1) p q body loc
-
-  ||| reduce a pair elimination `CasePair pi (Coe ty p q val) ret body loc`
-  private covering
-  sigCoe : (qty : Qty) ->
-           (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
-           (ret : ScopeTerm d n) -> (body : ScopeTermN 2 d n) -> Loc ->
-           Eff Whnf (Subset (Elim d n) (No . isRedexE defs))
-  sigCoe qty sty@(S [< i] ty) p q val ret body loc = do
-    -- caseπ (coe [i ⇒ (x : A) × B] @p @q s) return z ⇒ C of { (a, b) ⇒ e }
-    -- ⇝
-    -- caseπ s ∷ ((x : A) × B)‹p/i› return z ⇒ C
-    -- of { (a, b) ⇒
-    --   e[(coe [i ⇒ A] @p @q a)/a,
-    --     (coe [i ⇒ B[(coe [j ⇒ A‹j/i›] @p @i a)/x]] @p @q b)/b] }
-    --
-    -- type-case is used to expose A,B if the type is neutral
-    let ctx1 = extendDim i ctx
-    Element ty tynf <- whnf defs ctx1 ty.term
-    (tfst, tsnd) <- tycaseSig defs ctx1 ty
-    let [< x, y] = body.names
-        a' = CoeT i (weakT 2 tfst) p q (BVT 1 noLoc) x.loc
-        tsnd' = tsnd.term //
-          (CoeT i (weakT 2 $ tfst // (B VZ noLoc ::: shift 2))
-            (weakD 1 p) (B VZ noLoc) (BVT 1 noLoc) y.loc ::: shift 2)
-        b' = CoeT i tsnd' p q (BVT 0 noLoc) y.loc
-    whnf defs ctx $ CasePair qty (Ann val (ty // one p) val.loc) ret
-      (ST body.names $ body.term // (a' ::: b' ::: shift 2)) loc
-
-  ||| reduce a dimension application `DApp (Coe ty p q val) r loc`
-  private covering
-  eqCoe : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
-          (r : Dim d) -> Loc ->
-          Eff Whnf (Subset (Elim d n) (No . isRedexE defs))
-  eqCoe sty@(S [< j] ty) p q val r loc = do
-    -- (coe [j ⇒ Eq [i ⇒ A] L R] @p @q eq) @r
-    -- ⇝
-    -- comp [j ⇒ A‹r/i›] @p @q (eq ∷ (Eq [i ⇒ A] L R)‹p/j›)
-    --   @r { 0 j ⇒ L; 1 j ⇒ R }
-    let ctx1 = extendDim j ctx
-    Element ty tynf <- whnf defs ctx1 ty.term
-    (a0, a1, a, s, t) <- tycaseEq defs ctx1 ty
-    let a'   = dsub1 a (weakD 1 r)
-        val' = E $ DApp (Ann val (ty // one p) val.loc) r loc
-    whnf defs ctx $ CompH j a' p q val' r j s j t loc
-
-  ||| reduce a pair elimination `CaseBox pi (Coe ty p q val) ret body`
-  private covering
-  boxCoe : (qty : Qty) ->
-           (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
-           (ret : ScopeTerm d n) -> (body : ScopeTerm d n) -> Loc ->
-           Eff Whnf (Subset (Elim d n) (No . isRedexE defs))
-  boxCoe qty sty@(S [< i] ty) p q val ret body loc = do
-    -- caseπ (coe [i ⇒ [ρ. A]] @p @q s) return z ⇒ C of { [a] ⇒ e }
-    -- ⇝
-    -- caseπ s ∷ [ρ. A]‹p/i› return z ⇒ C
-    -- of { [a] ⇒ e[(coe [i ⇒ A] p q a)/a] }
-    let ctx1 = extendDim i ctx
-    Element ty tynf <- whnf defs ctx1 ty.term
-    ta <- tycaseBOX defs ctx1 ty
-    let a' = CoeT i (weakT 1 ta) p q (BVT 0 noLoc) body.name.loc
-    whnf defs ctx $ CaseBox qty (Ann val (ty // one p) val.loc) ret
-      (ST body.names $ body.term // (a' ::: shift 1)) loc
-
-
-||| reduce a type-case applied to a type constructor
-private covering
-reduceTypeCase : {d, n : Nat} -> (defs : Definitions) -> WhnfContext d n ->
-                 (ty : Term d n) -> (u : Universe) -> (ret : Term d n) ->
-                 (arms : TypeCaseArms d n) -> (def : Term d n) ->
-                 (0 _ : So (isTyCon ty)) => Loc ->
-                 Eff Whnf (Subset (Elim d n) (No . isRedexE defs))
-reduceTypeCase defs ctx ty u ret arms def loc = case ty of
-  -- (type-case ★ᵢ ∷ _ return Q of { ★ ⇒ s; ⋯ }) ⇝ s ∷ Q
-  TYPE {} =>
-    whnf defs ctx $ Ann (tycaseRhsDef0 def KTYPE arms) ret loc
-
-  -- (type-case π.(x : A) → B ∷ ★ᵢ return Q of { (a → b) ⇒ s; ⋯ }) ⇝
-  -- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ Q
-  Pi {arg, res, loc = piLoc, _} =>
-    let arg' = Ann arg (TYPE u noLoc) arg.loc
-        res' = Ann (Lam res res.loc)
-                   (Arr Zero arg (TYPE u noLoc) arg.loc) res.loc
-    in
-    whnf defs ctx $
-      Ann (subN (tycaseRhsDef def KPi arms) [< arg', res']) ret loc
-
-  -- (type-case (x : A) × B ∷ ★ᵢ return Q of { (a × b) ⇒ s; ⋯ }) ⇝
-  -- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ Q
-  Sig {fst, snd, loc = sigLoc, _} =>
-    let fst' = Ann fst (TYPE u noLoc) fst.loc
-        snd' = Ann (Lam snd snd.loc)
-                   (Arr Zero fst (TYPE u noLoc) fst.loc) snd.loc
-    in
-    whnf defs ctx $
-      Ann (subN (tycaseRhsDef def KSig arms) [< fst', snd']) ret loc
-
-  -- (type-case {⋯} ∷ _ return Q of { {} ⇒ s; ⋯ }) ⇝ s ∷ Q
-  Enum {} =>
-    whnf defs ctx $ Ann (tycaseRhsDef0 def KEnum arms) ret loc
-
-  -- (type-case Eq [i ⇒ A] L R ∷ ★ᵢ return Q
-  --  of { Eq a₀ a₁ a l r ⇒ s; ⋯ }) ⇝
-  -- s[(A‹0/i› ∷ ★ᵢ)/a₀, (A‹1/i› ∷ ★ᵢ)/a₁,
-  --   ((δ i ⇒ A) ∷ Eq [★ᵢ] A‹0/i› A‹1/i›)/a,
-  --   (L ∷ A‹0/i›)/l, (R ∷ A‹1/i›)/r] ∷ Q
-  Eq {ty = a, l, r, loc = eqLoc, _} =>
-    let a0 = a.zero; a1 = a.one in
-    whnf defs ctx $ Ann
-      (subN (tycaseRhsDef def KEq arms)
-         [< Ann a0 (TYPE u noLoc) a.loc, Ann a1 (TYPE u noLoc) a.loc,
-            Ann (DLam a a.loc) (Eq0 (TYPE u noLoc) a0 a1 a.loc) a.loc,
-            Ann l a0 l.loc, Ann r a1 r.loc])
-      ret loc
-
-  -- (type-case ℕ ∷ _ return Q of { ℕ ⇒ s; ⋯ }) ⇝ s ∷ Q
-  Nat {} =>
-    whnf defs ctx $ Ann (tycaseRhsDef0 def KNat arms) ret loc
-
-  -- (type-case [π.A] ∷ ★ᵢ return Q of { [a] ⇒ s; ⋯ }) ⇝ s[(A ∷ ★ᵢ)/a] ∷ Q
-  BOX {ty = a, loc = boxLoc, _} =>
-    whnf defs ctx $ Ann
-      (sub1 (tycaseRhsDef def KBOX arms) (Ann a (TYPE u noLoc) a.loc))
-      ret loc
-
-
-||| pushes a coercion inside a whnf-ed term
-private covering
-pushCoe : {d, n : Nat} -> (defs : Definitions) -> WhnfContext d n ->
-          BindName ->
-          (ty : Term (S d) n) -> (0 tynf : No (isRedexT defs ty)) =>
-          Dim d -> Dim d ->
-          (s : Term d n) -> (0 snf : No (isRedexT defs s)) => Loc ->
-          Eff Whnf (NonRedex Elim d n defs)
-pushCoe defs ctx i ty p q s loc =
-  if p == q then whnf defs ctx $ Ann s (ty // one q) loc else
-  case s of
-    -- (coe [_ ⇒ ★ᵢ] @_ @_ ty) ⇝ (ty ∷ ★ᵢ)
-    TYPE {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
-    Pi   {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
-    Sig  {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
-    Enum {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
-    Eq   {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
-    Nat  {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
-    BOX  {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
-
-    -- just η expand it. then whnf for App will handle it later
-    -- this is how @xtt does it
-    --
-    -- (coe [i ⇒ A] @p @q (λ x ⇒ s)) ⇝
-    -- (λ y ⇒ (coe [i ⇒ A] @p @q (λ x ⇒ s)) y) ∷ A‹q/i› ⇝ ⋯
-    lam@(Lam {body, _}) => do
-      let lam'  = CoeT i ty p q lam loc
-          term' = LamY !(fresh body.name)
-                    (E $ App (weakE 1 lam') (BVT 0 noLoc) loc) loc
-          type' = ty // one q
-      whnf defs ctx $ Ann term' type' loc
-
-    -- (coe [i ⇒ (x : A) × B] @p @q (s, t)) ⇝
-    -- (coe [i ⇒ A] @p @q s,
-    --  coe [i ⇒ B[(coe [j ⇒ A‹j/i›] @p @i s)/x]] @p @q t)
-    --   ∷ (x : A‹q/i›) × B‹q/i›
-    --
-    -- can't use η here because... it doesn't exist
-    Pair {fst, snd, loc = pairLoc} => do
-      let Sig {fst = tfst, snd = tsnd, loc = sigLoc} = ty
-        | _ => throw $ ExpectedSig ty.loc (extendDim i ctx.names) ty
-      let fst'  = E $ CoeT i tfst p q fst fst.loc
-          tfst' = tfst // (B VZ noLoc ::: shift 2)
-          tsnd' = sub1 tsnd $
-                  CoeT !(fresh i) tfst' (weakD 1 p) (B VZ noLoc)
-                    (dweakT 1 fst) fst.loc
-          snd'  = E $ CoeT i tsnd' p q snd snd.loc
-      pure $
-        Element (Ann (Pair fst' snd' pairLoc)
-                     (Sig (tfst // one q) (tsnd // one q) sigLoc) loc) Ah
-
-    -- η expand, like for Lam
-    --
-    -- (coe [i ⇒ A] @p @q (δ j ⇒ s)) ⇝
-    -- (δ k ⇒ (coe [i ⇒ A] @p @q (δ j ⇒ s)) @k) ∷ A‹q/i› ⇝ ⋯
-    dlam@(DLam {body, _}) => do
-      let dlam' = CoeT i ty p q dlam loc
-          term' = DLamY !(mnb "j")
-                    (E $ DApp (dweakE 1 dlam') (B VZ noLoc) loc) loc
-          type' = ty // one q
-      whnf defs ctx $ Ann term' type' loc
-
-    -- (coe [_ ⇒ {⋯}] @_ @_ t) ⇝ (t ∷ {⋯})
-    Tag {tag, loc = tagLoc} => do
-      let Enum {cases, loc = enumLoc} = ty
-        | _ => throw $ ExpectedEnum ty.loc (extendDim i ctx.names) ty
-      pure $ Element (Ann (Tag tag tagLoc) (Enum cases enumLoc) loc) Ah
-
-    -- (coe [_ ⇒ ℕ] @_ @_ n) ⇝ (n ∷ ℕ)
-    Zero {loc = zeroLoc} => do
-      pure $ Element (Ann (Zero zeroLoc) (Nat ty.loc) loc) Ah
-    Succ {p = pred, loc = succLoc} => do
-      pure $ Element (Ann (Succ pred succLoc) (Nat ty.loc) loc) Ah
-
-    -- (coe [i ⇒ [π.A]] @p @q [s]) ⇝
-    -- [coe [i ⇒ A] @p @q s] ∷ [π. A‹q/i›]
-    Box {val, loc = boxLoc} => do
-      let BOX {qty, ty = a, loc = tyLoc} = ty
-        | _ => throw $ ExpectedBOX ty.loc (extendDim i ctx.names) ty
-      pure $ Element
-        (Ann (Box (E $ CoeT i a p q val val.loc) boxLoc)
-             (BOX qty (a // one q) tyLoc) loc)
-        Ah
-
-    E e => pure $ Element (CoeT i ty p q (E e) e.loc) (snf `orNo` Ah)
-where
-  unwrapTYPE : Term (S d) n -> Eff Whnf Universe
-  unwrapTYPE (TYPE {l, _}) = pure l
-  unwrapTYPE ty = throw $ ExpectedTYPE ty.loc (extendDim i ctx.names) ty
-
-
-export covering
-CanWhnf Elim Reduce.isRedexE where
-  whnf defs ctx (F x u loc) with (lookupElim x defs) proof eq
-    _ | Just y  = whnf defs ctx $ setLoc loc $ displace u y
-    _ | Nothing = pure $ Element (F x u loc) $ rewrite eq in Ah
-
-  whnf _ _ (B i loc) = pure $ nred $ B i loc
-
-  -- ((λ x ⇒ t) ∷ (π.x : A) → B) s ⇝ t[s∷A/x] ∷ B[s∷A/x]
-  whnf defs ctx (App f s appLoc) = do
-    Element f fnf <- whnf defs ctx f
-    case nchoose $ isLamHead f of
-      Left _ => case f of
-        Ann (Lam {body, _}) (Pi {arg, res, _}) floc =>
-          let s = Ann s arg s.loc in
-          whnf defs ctx $ Ann (sub1 body s) (sub1 res s) appLoc
-        Coe ty p q val _ => piCoe defs ctx ty p q val s appLoc
-      Right nlh => pure $ Element (App f s appLoc) $ fnf `orNo` nlh
-
-  -- case (s, t) ∷ (x : A) × B return p ⇒ C of { (a, b) ⇒ u } ⇝
-  -- u[s∷A/a, t∷B[s∷A/x]] ∷ C[(s, t)∷((x : A) × B)/p]
-  whnf defs ctx (CasePair pi pair ret body caseLoc) = do
-    Element pair pairnf <- whnf defs ctx pair
-    case nchoose $ isPairHead pair of
-      Left _ => case pair of
-        Ann (Pair {fst, snd, _}) (Sig {fst = tfst, snd = tsnd, _}) pairLoc =>
-          let fst = Ann fst tfst fst.loc
-              snd = Ann snd (sub1 tsnd fst) snd.loc
-          in
-          whnf defs ctx $ Ann (subN body [< fst, snd]) (sub1 ret pair) caseLoc
-        Coe ty p q val _ => do
-          sigCoe defs ctx pi ty p q val ret body caseLoc
-      Right np =>
-        pure $ Element (CasePair pi pair ret body caseLoc) $ pairnf `orNo` np
-
-  -- case 'a ∷ {a,…} return p ⇒ C of { 'a ⇒ u } ⇝
-  -- u ∷ C['a∷{a,…}/p]
-  whnf defs ctx (CaseEnum pi tag ret arms caseLoc) = do
-    Element tag tagnf <- whnf defs ctx tag
-    case nchoose $ isTagHead tag of
-      Left _ => case tag of
-        Ann (Tag t _) (Enum ts _) _ =>
-          let ty = sub1 ret tag in
-          case lookup t arms of
-            Just arm => whnf defs ctx $ Ann arm ty arm.loc
-            Nothing  => throw $ MissingEnumArm caseLoc t (keys arms)
-        Coe ty p q val _ =>
-          -- there is nowhere an equality can be hiding inside an enum type
-          whnf defs ctx $
-            CaseEnum pi (Ann val (dsub1 ty q) val.loc) ret arms caseLoc
-      Right nt =>
-        pure $ Element (CaseEnum pi tag ret arms caseLoc) $ tagnf `orNo` nt
-
-  -- case zero ∷ ℕ return p ⇒ C of { zero ⇒ u; … } ⇝
-  --   u ∷ C[zero∷ℕ/p]
-  --
-  -- case succ n ∷ ℕ return p ⇒ C of { succ n', π.ih ⇒ u; … } ⇝
-  --   u[n∷ℕ/n', (case n ∷ ℕ ⋯)/ih] ∷ C[succ n ∷ ℕ/p]
-  whnf defs ctx (CaseNat pi piIH nat ret zer suc caseLoc) = do
-    Element nat natnf <- whnf defs ctx nat
-    case nchoose $ isNatHead nat of
-      Left _ =>
-        let ty = sub1 ret nat in
-        case nat of
-          Ann (Zero _) (Nat _) _ =>
-            whnf defs ctx $ Ann zer ty zer.loc
-          Ann (Succ n succLoc) (Nat natLoc) _ =>
-            let nn = Ann n (Nat natLoc) succLoc
-                tm = subN suc [< nn, CaseNat pi piIH nn ret zer suc caseLoc]
-            in
-            whnf defs ctx $ Ann tm ty caseLoc
-          Coe ty p q val _ =>
-            -- same deal as Enum
-            whnf defs ctx $
-              CaseNat pi piIH (Ann val (dsub1 ty q) val.loc) ret zer suc caseLoc
-      Right nn => pure $
-        Element (CaseNat pi piIH nat ret zer suc caseLoc) $ natnf `orNo` nn
-
-  -- case [t] ∷ [π.A] return p ⇒ C of { [x] ⇒ u } ⇝
-  --   u[t∷A/x] ∷ C[[t] ∷ [π.A]/p]
-  whnf defs ctx (CaseBox pi box ret body caseLoc) = do
-    Element box boxnf <- whnf defs ctx box
-    case nchoose $ isBoxHead box of
-      Left _ => case box of
-        Ann (Box val boxLoc) (BOX q bty tyLoc) _ =>
-          let ty = sub1 ret box in
-          whnf defs ctx $ Ann (sub1 body (Ann val bty val.loc)) ty caseLoc
-        Coe ty p q val _ =>
-          boxCoe defs ctx pi ty p q val ret body caseLoc
-      Right nb =>
-        pure $ Element (CaseBox pi box ret body caseLoc) $ boxnf `orNo` nb
-
-  -- e : Eq (𝑗 ⇒ A) t u ⊢ e @0 ⇝ t ∷ A‹0/𝑗›
-  -- e : Eq (𝑗 ⇒ A) t u ⊢ e @1 ⇝ u ∷ A‹1/𝑗›
-  --
-  -- ((δ 𝑖 ⇒ s) ∷ Eq (𝑗 ⇒ A) t u) @𝑘 ⇝ s‹𝑘/𝑖› ∷ A‹𝑘/𝑗›
-  whnf defs ctx (DApp f p appLoc) = do
-    Element f fnf <- whnf defs ctx f
-    case nchoose $ isDLamHead f of
-      Left _ => case f of
-        Ann (DLam {body, _}) (Eq {ty, l, r, _}) _ =>
-          whnf defs ctx $
-            Ann (endsOr (setLoc appLoc l) (setLoc appLoc r) (dsub1 body p) p)
-                (dsub1 ty p) appLoc
-        Coe ty p' q' val _ =>
-          eqCoe defs ctx ty p' q' val p appLoc
-      Right ndlh => case p of
-        K e _ => do
-          Eq {l, r, ty, _} <- whnf0 defs ctx =<< computeElimType defs ctx f
-            | ty => throw $ ExpectedEq ty.loc ctx.names ty
-          whnf defs ctx $
-            ends (Ann (setLoc appLoc l) ty.zero appLoc)
-                 (Ann (setLoc appLoc r) ty.one  appLoc) e
-        B {} => pure $ Element (DApp f p appLoc) $ fnf `orNo` ndlh `orNo` Ah
-
-  -- e ∷ A ⇝ e
-  whnf defs ctx (Ann s a annLoc) = do
-    Element s snf <- whnf defs ctx s
-    case nchoose $ isE s of
-      Left  _  => let E e = s in pure $ Element e $ noOr2 snf
-      Right ne => do
-        Element a anf <- whnf defs ctx a
-        pure $ Element (Ann s a annLoc) $ ne `orNo` snf `orNo` anf
-
-  whnf defs ctx (Coe (S _ (N ty)) _ _ val coeLoc) =
-    whnf defs ctx $ Ann val ty coeLoc
-  whnf defs ctx (Coe (S [< i] ty) p q val coeLoc) = do
-    Element ty  tynf  <- whnf defs (extendDim i ctx) ty.term
-    Element val valnf <- whnf defs ctx val
-    pushCoe defs ctx i ty p q val coeLoc
-
-  whnf defs ctx (Comp ty p q val r zero one compLoc) =
-    -- comp [A] @p @p s { ⋯ } ⇝ s ∷ A
-    if p == q then whnf defs ctx $ Ann val ty compLoc else
-    case nchoose (isK r) of
-      -- comp [A] @p @q s @0 { 0 j ⇒ t; ⋯ } ⇝ t‹q/j› ∷ A
-      -- comp [A] @p @q s @1 { 1 j ⇒ t; ⋯ } ⇝ t‹q/j› ∷ A
-      Left y => case r of
-        K Zero _ => whnf defs ctx $ Ann (dsub1 zero q) ty compLoc
-        K One  _ => whnf defs ctx $ Ann (dsub1 one  q) ty compLoc
-      Right nk => do
-        Element ty tynf <- whnf defs ctx ty
-        pure $ Element (Comp ty p q val r zero one compLoc) $ tynf `orNo` nk
-
-  whnf defs ctx (TypeCase ty ret arms def tcLoc) = do
-    Element ty  tynf  <- whnf defs ctx ty
-    Element ret retnf <- whnf defs ctx ret
-    case nchoose $ isAnnTyCon ty of
-      Left  y  =>
-        let Ann ty (TYPE u _) _ = ty in
-        reduceTypeCase defs ctx ty u ret arms def tcLoc
-      Right nt => pure $
-        Element (TypeCase ty ret arms def tcLoc) (tynf `orNo` retnf `orNo` nt)
-
-  whnf defs ctx (CloE  (Sub el th)) = whnf defs ctx $ pushSubstsWith' id th el
-  whnf defs ctx (DCloE (Sub el th)) = whnf defs ctx $ pushSubstsWith' th id el
-
-export covering
-CanWhnf Term Reduce.isRedexT where
-  whnf _ _ t@(TYPE {}) = pure $ nred t
-  whnf _ _ t@(Pi   {}) = pure $ nred t
-  whnf _ _ t@(Lam  {}) = pure $ nred t
-  whnf _ _ t@(Sig  {}) = pure $ nred t
-  whnf _ _ t@(Pair {}) = pure $ nred t
-  whnf _ _ t@(Enum {}) = pure $ nred t
-  whnf _ _ t@(Tag  {}) = pure $ nred t
-  whnf _ _ t@(Eq   {}) = pure $ nred t
-  whnf _ _ t@(DLam {}) = pure $ nred t
-  whnf _ _ t@(Nat  {}) = pure $ nred t
-  whnf _ _ t@(Zero {}) = pure $ nred t
-  whnf _ _ t@(Succ {}) = pure $ nred t
-  whnf _ _ t@(BOX  {}) = pure $ nred t
-  whnf _ _ t@(Box  {}) = pure $ nred t
-
-  -- s ∷ A ⇝ s   (in term context)
-  whnf defs ctx (E e) = do
-    Element e enf <- whnf defs ctx e
-    case nchoose $ isAnn e of
-      Left  _  => let Ann {tm, _} = e in pure $ Element tm $ noOr1 $ noOr2 enf
-      Right na => pure $ Element (E e) $ na `orNo` enf
-
-  whnf defs ctx (CloT  (Sub tm th)) = whnf defs ctx $ pushSubstsWith' id th tm
-  whnf defs ctx (DCloT (Sub tm th)) = whnf defs ctx $ pushSubstsWith' th id tm

lib/Quox/Scoped.idr

@@ -0,0 +1,59 @@
+module Quox.Scoped
+
+import public Quox.Var
+import public Quox.Context
+
+import Derive.Prelude
+
+%language ElabReflection
+%default total
+
+
+public export
+data ScopedBody : Nat -> (Nat -> Type) -> Nat -> Type where
+  Y : (body : f (s + n)) -> ScopedBody s f n
+  N : (body : f n)       -> ScopedBody s f n
+%name ScopedBody body
+
+export %inline %hint
+EqScopedBody : (forall n. Eq (f n)) => Eq (ScopedBody s f n)
+EqScopedBody = deriveEq
+
+export %inline %hint
+ShowScopedBody : (forall n. Show (f n)) => Show (ScopedBody s f n)
+ShowScopedBody = deriveShow
+
+||| a scoped term with names
+public export
+record Scoped (s : Nat) (f : Nat -> Type) (n : Nat) where
+  constructor S
+  names : BContext s
+  body  : ScopedBody s f n
+%name Scoped body
+
+export %inline
+(forall n. Eq (f n)) => Eq (Scoped s f n) where
+  s == t = s.body == t.body
+
+export %inline %hint
+ShowScoped : (forall n. Show (f n)) => Show (Scoped s f n)
+ShowScoped = deriveShow
+
+
+||| scope which ignores all its binders
+public export %inline
+SN : Located1 f => {s : Nat} -> f n -> Scoped s f n
+SN body = S (replicate s $ BN Unused body.loc) $ N body
+
+||| scope which uses its binders
+public export %inline
+SY : BContext s -> f (s + n) -> Scoped s f n
+SY ns = S ns . Y
+
+public export %inline
+name : Scoped 1 f n -> BindName
+name (S [< x] _) = x
+
+public export %inline
+(.name) : Scoped 1 f n -> BindName
+s.name = name s

lib/Quox/Syntax.idr

@@ -6,4 +6,5 @@ import public Quox.Syntax.Qty
 import public Quox.Syntax.Shift
 import public Quox.Syntax.Subst
 import public Quox.Syntax.Term
-import public Quox.Syntax.Var
+import public Quox.Syntax.Builtin
+import public Quox.Var

lib/Quox/Syntax/Builtin.idr

@@ -0,0 +1,27 @@
+module Quox.Syntax.Builtin
+
+import Derive.Prelude
+import Quox.PrettyValExtra
+import Quox.Pretty
+import Quox.Syntax.Term
+
+
+%default total
+%language ElabReflection
+
+public export
+data Builtin
+= Main
+%runElab derive "Builtin" [Eq, Ord, Show, PrettyVal]
+
+public export
+builtinDesc : Builtin -> String
+builtinDesc Main = "a function declared as #[main]"
+
+public export
+builtinTypeDoc : {opts : LayoutOpts} -> Builtin -> Eff Pretty (Doc opts)
+builtinTypeDoc Main =
+  prettyTerm [<] [<] $
+    Pi One (IOState noLoc)
+      (SN $ Sig (Enum (fromList [!(ifUnicode "𝑎" "a")]) noLoc)
+                (SN (IOState noLoc)) noLoc) noLoc

lib/Quox/Syntax/Dim.idr

@@ -1,18 +1,16 @@
 module Quox.Syntax.Dim
 
-import Quox.Thin
-import Quox.Syntax.Var
+import Quox.Loc
+import Quox.Name
+import Quox.Var
 import Quox.Syntax.Subst
 import Quox.Pretty
-import Quox.Name
-import Quox.Loc
 import Quox.Context
+import Quox.PrettyValExtra
 
 import Decidable.Equality
 import Control.Function
 import Derive.Prelude
-import Data.DPair
-import Data.SnocVect
 
 %default total
 %language ElabReflection
@@ -21,7 +19,7 @@ import Data.SnocVect
 public export
 data DimConst = Zero | One
 %name DimConst e
-%runElab derive "DimConst" [Eq, Ord, Show]
+%runElab derive "DimConst" [Eq, Ord, Show, PrettyVal]
 
 ||| `ends l r e` returns `l` if `e` is `Zero`, or `r` if it is `One`.
 public export
@@ -42,48 +40,38 @@ DecEq DimConst where
 
 public export
 data Dim : Nat -> Type where
-  K : DimConst -> Loc -> Dim 0
-  B : Loc -> Dim 1
+  K : DimConst -> Loc -> Dim d
+  B : Var d -> Loc -> Dim d
 %name Dim.Dim p, q
 %runElab deriveIndexed "Dim" [Eq, Ord, Show]
 
 
-public export
-DimT : Nat -> Type
-DimT = Thinned Dim
-
-public export %inline
-KT : DimConst -> Loc -> DimT d
-KT e loc = Th zero $ K e loc
-
-
 ||| `endsOr l r x p` returns `ends l r ε` if `p` is a constant ε, and
 ||| `x` otherwise.
 public export
 endsOr : Lazy a -> Lazy a -> Lazy a -> Dim n -> a
 endsOr l r x (K e _) = ends l r e
-endsOr l r x (B _)   = x
+endsOr l r x (B _ _) = x
 
 
 export
 Located (Dim d) where
   (K _ loc).loc = loc
-  (B loc).loc   = loc
+  (B _ loc).loc = loc
 
 export
 Relocatable (Dim d) where
   setLoc loc (K e _) = K e loc
-  setLoc loc (B _)   = B loc
+  setLoc loc (B i _) = B i loc
 
-parameters {opts : LayoutOpts}
-  export
-  prettyDimConst : DimConst -> Eff Pretty (Doc opts)
-  prettyDimConst = hl Dim . text . ends "0" "1"
+export
+prettyDimConst : {opts : _} -> DimConst -> Eff Pretty (Doc opts)
+prettyDimConst = hl Dim . text . ends "0" "1"
 
-  export
-  prettyDim : {d : Nat} -> BContext d -> DimT d -> Eff Pretty (Doc opts)
-  prettyDim names (Th _ (K e _)) = prettyDimConst e
-  prettyDim names (Th i (B _)) = prettyDBind $ names !!! i.fin
+export
+prettyDim : {opts : _} -> BContext d -> Dim d -> Eff Pretty (Doc opts)
+prettyDim names (K e _) = prettyDimConst e
+prettyDim names (B i _) = prettyDBind $ names !!! i
 
 
 public export %inline
@@ -96,54 +84,57 @@ DSubst : Nat -> Nat -> Type
 DSubst = Subst Dim
 
 
--- public export FromVar Dim where fromVarLoc = B
+public export FromVar Dim where fromVarLoc = B
 
 
--- export
--- CanShift Dim where
---   K e loc // _  = K e loc
---   B i loc // by = B (i // by) loc
+export
+CanShift Dim where
+  K e loc // _  = K e loc
+  B i loc // by = B (i // by) loc
 
-export %inline FromVar Dim where var = B
-
-export %inline
+export
 CanSubstSelf Dim where
-  Th _ (K e loc) // _  = KT e loc
-  Th i (B loc)   // th = get th i.fin
+  K e loc // _  = K e loc
+  B i loc // th = getLoc th i loc
 
 
-export Uninhabited (B loc1   = K e loc2) where uninhabited _ impossible
-export Uninhabited (K e loc1 = B loc2)   where uninhabited _ impossible
+export Uninhabited (B i loc1 = K e loc2) where uninhabited _ impossible
+export Uninhabited (K e loc1 = B i loc2) where uninhabited _ impossible
 
--- public export
--- data Eqv : Dim d1 -> Dim d2 -> Type where
---   EK : K e _ `Eqv` K e _
---   EB : i `Eqv` j -> B i _ `Eqv` B j _
+public export
+data Eqv : Dim d1 -> Dim d2 -> Type where
+  EK : K e _ `Eqv` K e _
+  EB : i `Eqv` j -> B i _ `Eqv` B j _
 
--- export Uninhabited (K e l1 `Eqv` B i l2) where uninhabited _ impossible
--- export Uninhabited (B i l1 `Eqv` K e l2) where uninhabited _ impossible
+export Uninhabited (K e l1 `Eqv` B i l2) where uninhabited _ impossible
+export Uninhabited (B i l1 `Eqv` K e l2) where uninhabited _ impossible
 
--- export
--- injectiveB : B i loc1 `Eqv` B j loc2 -> i `Eqv` j
--- injectiveB (EB e) = e
+export
+injectiveB : B i loc1 `Eqv` B j loc2 -> i `Eqv` j
+injectiveB (EB e) = e
 
--- export
--- injectiveK : K e loc1 `Eqv` K f loc2 -> e = f
--- injectiveK EK = Refl
+export
+injectiveK : K e loc1 `Eqv` K f loc2 -> e = f
+injectiveK EK = Refl
 
--- public export
--- decEqv : Dec2 Dim.Eqv
--- decEqv (K e _) (K f _) = case decEq e f of
---   Yes Refl => Yes EK
---   No  n    => No $ n . injectiveK
--- decEqv (B i _) (B j _) = case decEqv i j of
---   Yes y => Yes $ EB y
---   No  n => No  $ \(EB y) => n y
--- decEqv (B _ _) (K _ _) = No absurd
--- decEqv (K _ _) (B _ _) = No absurd
+public export
+decEqv : Dec2 Dim.Eqv
+decEqv (K e _) (K f _) = case decEq e f of
+  Yes Refl => Yes EK
+  No  n    => No $ n . injectiveK
+decEqv (B i _) (B j _) = case decEqv i j of
+  Yes y => Yes $ EB y
+  No  n => No  $ \(EB y) => n y
+decEqv (B _ _) (K _ _) = No absurd
+decEqv (K _ _) (B _ _) = No absurd
 
 ||| abbreviation for a bound variable like `BV 4` instead of
 ||| `B (VS (VS (VS (VS VZ))))`
 public export %inline
-BV : (i : Fin d) -> (loc : Loc) -> DimT d
-BV i loc = Th (one' i) $ B loc
+BV : (i : Nat) -> (0 _ : LT i d) => (loc : Loc) -> Dim d
+BV i loc = B (V i) loc
+
+
+export
+weakD : (by : Nat) -> Dim d -> Dim (by + d)
+weakD by p = p // shift by

lib/Quox/Syntax/DimEq.idr

@@ -1,19 +1,17 @@
 module Quox.Syntax.DimEq
 
-import public Quox.Syntax.Var
+import public Quox.Var
 import public Quox.Syntax.Dim
 import public Quox.Syntax.Subst
 import public Quox.Context
 import Quox.Pretty
 import Quox.Name
-import Quox.Thin
-import Quox.FinExtra
+import Quox.FreeVars
 
 import Data.Maybe
 import Data.Nat
 import Data.DPair
 import Data.Fun.Graph
-import Data.SnocVect
 import Decidable.Decidable
 import Decidable.Equality
 import Derive.Prelude
@@ -24,7 +22,7 @@ import Derive.Prelude
 
 public export
 DimEq' : Nat -> Type
-DimEq' = Context (Maybe . DimT)
+DimEq' = Context (Maybe . Dim)
 
 
 public export
@@ -32,12 +30,7 @@ data DimEq : Nat -> Type where
   ZeroIsOne : DimEq d
   C         : (eqs : DimEq' d) -> DimEq d
 %name DimEq eqs
-%runElab deriveIndexed "DimEq" [Eq]
-
-export
-Show (DimEq d) where
-  showPrec d ZeroIsOne = "ZeroIsOne"
-  showPrec d (C eq')   = showCon d "C" $ showArg eq' @{ShowTelRelevant}
+%runElab deriveIndexed "DimEq" [Eq, Ord, Show]
 
 
 public export
@@ -66,10 +59,15 @@ Traversable (IfConsistent eqs) where
   traverse f Nothing  = pure Nothing
   traverse f (Just x) = Just <$> f x
 
+public export
+ifConsistentElse : Applicative f => (eqs : DimEq d) ->
+                   f a -> f () -> f (IfConsistent eqs a)
+ifConsistentElse ZeroIsOne yes no = Nothing <$  no
+ifConsistentElse (C _)     yes no = Just    <$> yes
+
 public export
 ifConsistent : Applicative f => (eqs : DimEq d) -> f a -> f (IfConsistent eqs a)
-ifConsistent ZeroIsOne act = pure Nothing
-ifConsistent (C _)     act = Just <$> act
+ifConsistent eqs act = ifConsistentElse eqs act (pure ())
 
 public export
 toMaybe : IfConsistent eqs a -> Maybe a
@@ -78,13 +76,13 @@ toMaybe (Just x) = Just x
 
 
 export
-fromGround' : Context' DimConst d -> DimEq' d
-fromGround' [<]        = [<]
-fromGround' (ctx :< e) = fromGround' ctx :< Just (KT e noLoc)
+fromGround' : BContext d -> Context' DimConst d -> DimEq' d
+fromGround' [<]       [<]        = [<]
+fromGround' (xs :< x) (ctx :< e) = fromGround' xs ctx :< Just (K e x.loc)
 
 export
-fromGround : Context' DimConst d -> DimEq d
-fromGround = C . fromGround'
+fromGround : BContext d -> Context' DimConst d -> DimEq d
+fromGround = C .: fromGround'
 
 
 public export %inline
@@ -102,40 +100,39 @@ new = C new'
 
 
 public export %inline
-get' : DimEq' d -> Fin d -> Maybe (DimT d)
+get' : DimEq' d -> Var d -> Maybe (Dim d)
 get' = getWith $ \p, by => map (// by) p
 
 public export %inline
-getShift' : Shift len out -> DimEq' len -> Fin len -> Maybe (DimT out)
+getVar : DimEq' d -> Var d -> Loc -> Dim d
+getVar eqs i loc = fromMaybe (B i loc) $ get' eqs i
+
+public export %inline
+getShift' : Shift len out -> DimEq' len -> Var len -> Maybe (Dim out)
 getShift' = getShiftWith $ \p, by => map (// by) p
 
 public export %inline
-get : {d : Nat} -> DimEq' d -> DimT d -> DimT d
-get eqs p@(Th _ (K {})) = p
-get eqs p@(Th i (B _))  = fromMaybe p $ get' eqs i.fin
+get : DimEq' d -> Dim d -> Dim d
+get _   (K e loc) = K e loc
+get eqs (B i loc) = getVar eqs i loc
 
 
 public export %inline
-equal : {d : Nat} -> DimEq d -> (p, q : DimT d) -> Bool
+equal : DimEq d -> (p, q : Dim d) -> Bool
 equal ZeroIsOne p q = True
 equal (C eqs)   p q = get eqs p == get eqs q
 
 
-infixl 7 :<?
+export infixl 7 :<?
 export %inline
-(:<?) : {d : Nat} -> DimEq d -> Maybe (DimT d) -> DimEq (S d)
+(:<?) : DimEq d -> Maybe (Dim d) -> DimEq (S d)
 ZeroIsOne :<? d = ZeroIsOne
 C eqs     :<? d = C $ eqs :< map (get eqs) d
 
 
 private %inline
-isVar : {d : Nat} -> Fin d -> DimT d -> Bool
-isVar i (Th j (B _))  = i == j.fin
-isVar i (Th _ (K {})) = False
-
-private %inline
-ifVar : {d : Nat} -> Fin d -> DimT d -> Maybe (DimT d) -> Maybe (DimT d)
-ifVar i p = map $ \q => if isVar i q then p else q
+ifVar : Var d -> Dim d -> Maybe (Dim d) -> Maybe (Dim d)
+ifVar i p = map $ \q => if q == B i noLoc then p else q
 
 -- (using decEq instead of (==) because of the proofs below)
 private %inline
@@ -144,45 +141,43 @@ checkConst e f eqs = if isYes $ e `decEq` f then C eqs else ZeroIsOne
 
 
 export
-setConst : {d : Nat} -> Fin d -> DimConst -> Loc -> DimEq' d -> DimEq d
-setConst FZ e loc (eqs :< Nothing) =
-  C $ eqs :< Just (KT e loc)
-setConst FZ e _ (eqs :< Just (Th _ (K f loc))) =
-  checkConst e f $ eqs :< Just (KT f loc)
-setConst FZ e loc (eqs :< Just (Th j (B _))) =
-  setConst j.fin e loc eqs :<? Just (KT e loc)
-setConst (FS i) e loc (eqs :< p) =
-  setConst i e loc eqs :<? ifVar i (KT e loc) p
+setConst : Var d -> DimConst -> Loc -> DimEq' d -> DimEq d
+setConst VZ e loc (eqs :< Nothing) =
+  C $ eqs :< Just (K e loc)
+setConst VZ e _ (eqs :< Just (K f loc)) =
+  checkConst e f $ eqs :< Just (K f loc)
+setConst VZ e loc (eqs :< Just (B i _)) =
+  setConst i e loc eqs :<? Just (K e loc)
+setConst (VS i) e loc (eqs :< p) =
+  setConst i e loc eqs :<? ifVar i (K e loc) p
 
 mutual
   private
-  setVar' : {d : Nat} ->
-            (i, j : Fin d) -> (0 _ : i `LT` j) -> Loc -> DimEq' d -> DimEq d
-  setVar' FZ (FS i) LTZ loc (eqs :< Nothing) =
-    C eqs :<? Just (BV i loc)
-  setVar' FZ (FS i) LTZ loc (eqs :< Just (Th _ (K e eloc))) =
-    setConst i e loc eqs :<? Just (KT e eloc)
-  setVar' FZ (FS i) LTZ loc (eqs :< Just (Th j (B jloc))) =
-    let j = j.fin in
-    setVar i j loc jloc eqs :<? Just (if j > i then BV j jloc else BV i loc)
-  setVar' (FS i) (FS j) (LTS lt) loc (eqs :< p) =
-    setVar' i j lt loc eqs :<? ifVar i (BV j loc) p
+  setVar' : (i, j : Var d) -> (0 _ : i `LT` j) -> Loc -> DimEq' d -> DimEq d
+  setVar' VZ (VS i) LTZ loc (eqs :< Nothing) =
+    C eqs :<? Just (B i loc)
+  setVar' VZ (VS i) LTZ loc (eqs :< Just (K e eloc)) =
+    setConst i e loc eqs :<? Just (K e eloc)
+  setVar' VZ (VS i) LTZ loc (eqs :< Just (B j jloc)) =
+    setVar i j loc jloc eqs :<? Just (if j > i then B j jloc else B i loc)
+  setVar' (VS i) (VS j) (LTS lt) loc (eqs :< p) =
+    setVar' i j lt loc eqs :<? ifVar i (B j loc) p
 
   export %inline
-  setVar : {d : Nat} -> (i, j : Fin d) -> Loc -> Loc -> DimEq' d -> DimEq d
-  setVar i j li lj eqs with (compareP i j)
-    setVar i j li lj eqs | IsLT lt = setVar' i j lt lj eqs
-    setVar i i li lj eqs | IsEQ    = C eqs
-    setVar i j li lj eqs | IsGT gt = setVar' j i gt li eqs
+  setVar : (i, j : Var d) -> Loc -> Loc -> DimEq' d -> DimEq d
+  setVar i j li lj eqs with (compareP i j) | (compare i.nat j.nat)
+    setVar i j li lj eqs | IsLT lt | LT = setVar' i j lt lj eqs
+    setVar i i li lj eqs | IsEQ    | EQ = C eqs
+    setVar i j li lj eqs | IsGT gt | GT = setVar' j i gt li eqs
 
 
 export %inline
-set : {d : Nat} -> (p, q : DimT d) -> DimEq d -> DimEq d
+set : (p, q : Dim d) -> DimEq d -> DimEq d
 set _ _ ZeroIsOne = ZeroIsOne
-set (Th _ (K e _))  (Th _ (K f _))  (C eqs) = checkConst e f eqs
-set (Th _ (K e el)) (Th j (B _))    (C eqs) = setConst j.fin e el eqs
-set (Th i (B _))    (Th _ (K e el)) (C eqs) = setConst i.fin e el eqs
-set (Th i (B il))   (Th j (B jl))   (C eqs) = setVar i.fin j.fin il jl eqs
+set (K e eloc) (K f floc) (C eqs) = checkConst e f eqs
+set (K e eloc) (B i iloc) (C eqs) = setConst i e eloc eqs
+set (B i iloc) (K e eloc) (C eqs) = setConst i e eloc eqs
+set (B i iloc) (B j jloc) (C eqs) = setVar   i j iloc jloc eqs
 
 
 public export %inline
@@ -190,99 +185,116 @@ Split : Nat -> Type
 Split d = (DimEq' d, DSubst (S d) d)
 
 export %inline
-split1 : {d : Nat} -> DimConst -> Loc -> DimEq' (S d) -> Maybe (Split d)
-split1 e loc eqs = case setConst 0 e loc eqs of
+split1 : DimConst -> Loc -> DimEq' (S d) -> Maybe (Split d)
+split1 e loc eqs = case setConst VZ e loc eqs of
   ZeroIsOne    => Nothing
-  C (eqs :< _) => Just (eqs, id (B loc) :< KT e loc)
+  C (eqs :< _) => Just (eqs, K e loc ::: id)
 
 export %inline
-split : {d : Nat} -> Loc -> DimEq' (S d) -> List (Split d)
-split loc eqs = toList (split1 Zero loc eqs) <+> toList (split1 One loc eqs)
+split1' : DimConst -> Loc -> DimEq' (S d) -> List (Split d)
+split1' e loc eqs = toList $ split1 e loc eqs
+
+export %inline
+split : Loc -> DimEq' (S d) -> Bool -> List (Split d)
+split loc eqs False = split1' Zero loc eqs
+split loc eqs True  = split1' Zero loc eqs <+> split1' One loc eqs
 
 export
-splits' : {d : Nat} -> Loc -> DimEq' d -> List (DSubst d 0)
-splits' _   [<]          = [[<]]
-splits' loc eqs@(_ :< _) =
-  [th . ph | (eqs', th) <- split loc eqs, ph <- splits' loc eqs']
+splits' : Loc -> DimEq' d -> FreeVars d -> List (DSubst d 0)
+splits' _   [<]          _  = [id]
+splits' loc eqs@(_ :< _) us = do
+  let (us, u) = uncons us
+  (eqs', th) <- split loc eqs u
+  ph         <- splits' loc eqs' us
+  pure $ th . ph
 
 ||| the Loc is put into each of the DimConsts
 export %inline
-splits : {d : Nat} -> Loc -> DimEq d -> List (DSubst d 0)
-splits _   ZeroIsOne = []
-splits loc (C eqs)   = splits' loc eqs
+splits : Loc -> DimEq d -> FreeVars d -> List (DSubst d 0)
+splits _   ZeroIsOne _   = []
+splits loc (C eqs)   fvs = splits' loc eqs fvs
 
 
--- private
--- 0 newGetShift : (d : Nat) -> (i : Fin d) -> (by : Shift d d') ->
---                 getShift' by (new' {d}) i = Nothing
--- newGetShift (S d) FZ     by = Refl
--- newGetShift (S d) (FS i) by = newGetShift d i (ssDown by)
+private
+0 newGetShift : (d : Nat) -> (i : Var d) -> (by : Shift d d') ->
+                getShift' by (new' {d}) i = Nothing
+newGetShift (S d) VZ     by = Refl
+newGetShift (S d) (VS i) by = newGetShift d i (ssDown by)
 
--- export
--- 0 newGet' : (d : Nat) -> (i : Fin d) -> get' (new' {d}) i = Nothing
--- newGet' d i = newGetShift d i SZ
+export
+0 newGet' : (d : Nat) -> (i : Var d) -> get' (new' {d}) i = Nothing
+newGet' d i = newGetShift d i SZ
 
--- export
--- 0 newGet : (d : Nat) -> (p : Dim d) -> get (new' {d}) p = p
--- newGet d (K e _) = Refl
--- newGet d (B i _) = rewrite newGet' d i in Refl
+export
+0 newGet : (d : Nat) -> (p : Dim d) -> get (new' {d}) p = p
+newGet d (K e _) = Refl
+newGet d (B i _) = rewrite newGet' d i in Refl
 
 
--- export
--- 0 setSelf : (p : Dim d) -> (eqs : DimEq d) -> set p p eqs = eqs
--- setSelf p ZeroIsOne = Refl
--- setSelf (K Zero _) (C eqs) = Refl
--- setSelf (K One _)  (C eqs) = Refl
--- setSelf (B i _)    (C eqs) with (compareP i i) | (compare i.nat i.nat)
---   _ | IsLT lt | LT = absurd lt
---   _ | IsEQ    | EQ = Refl
---   _ | IsGT gt | GT = absurd gt
+export
+0 setSelf : (p : Dim d) -> (eqs : DimEq d) -> set p p eqs = eqs
+setSelf p ZeroIsOne = Refl
+setSelf (K Zero _) (C eqs) = Refl
+setSelf (K One _)  (C eqs) = Refl
+setSelf (B i _)    (C eqs) with (compareP i i) | (compare i.nat i.nat)
+  _ | IsLT lt | LT = absurd lt
+  _ | IsEQ    | EQ = Refl
+  _ | IsGT gt | GT = absurd gt
 
 
-parameters {opts : LayoutOpts}
-  private
-  prettyDVars : {d : Nat} -> BContext d -> Eff Pretty (SnocList (Doc opts))
-  prettyDVars = traverse prettyDBind . toSnocList'
+private %inline
+dimEqPrec : BContext d -> Maybe (DimEq' d) -> PPrec
+dimEqPrec vars eqs =
+  if length vars <= 1 && maybe True null eqs then Arg else Outer
 
-  private
-  prettyCst : {d : Nat} -> BContext d -> DimT d -> DimT d -> Eff Pretty (Doc opts)
-  prettyCst dnames p q =
-    hsep <$> sequence [prettyDim dnames p, cstD, prettyDim dnames q]
+private
+prettyDVars' : {opts : _} -> BContext d -> Eff Pretty (SnocList (Doc opts))
+prettyDVars' = traverse prettyDBind . toSnocList'
 
-  private
-  prettyCsts : {d : Nat} -> BContext d -> DimEq' d ->
-               Eff Pretty (SnocList (Doc opts))
-  prettyCsts [<] [<] = pure [<]
-  prettyCsts dnames (eqs :< Nothing) = prettyCsts (tail dnames) eqs
-  prettyCsts dnames (eqs :< Just q)  =
-    [|prettyCsts (tail dnames) eqs :<
-      prettyCst dnames (BV 0 noLoc) (weak 1 q)|]
+export
+prettyDVars : {opts : _} -> BContext d -> Eff Pretty (Doc opts)
+prettyDVars vars =
+  parensIfM (dimEqPrec vars Nothing) $
+  fillSeparateTight !commaD $ !(prettyDVars' vars)
 
-  export
-  prettyDimEq' : {d : Nat} -> BContext d -> DimEq' d -> Eff Pretty (Doc opts)
-  prettyDimEq' dnames eqs = do
-    vars <- prettyDVars dnames
-    eqs  <- prettyCsts dnames eqs
-    let prec = if length vars <= 1 && null eqs then Arg else Outer
-    parensIfM prec $ fillSeparateTight !commaD $ toList vars ++ toList eqs
+private
+prettyCst : {opts : _} -> BContext d -> Dim d -> Dim d -> Eff Pretty (Doc opts)
+prettyCst dnames p q =
+  hsep <$> sequence [prettyDim dnames p, cstD, prettyDim dnames q]
 
-  export
-  prettyDimEq : {d : Nat} -> BContext d -> DimEq d -> Eff Pretty (Doc opts)
-  prettyDimEq dnames ZeroIsOne = do
-    vars <- prettyDVars dnames
-    cst  <- prettyCst [<] (KT Zero noLoc) (KT One noLoc)
-    pure $ separateTight !commaD $ vars :< cst
-  prettyDimEq dnames (C eqs) = prettyDimEq' dnames eqs
+private
+prettyCsts : {opts : _} -> BContext d -> DimEq' d ->
+             Eff Pretty (SnocList (Doc opts))
+prettyCsts [<] [<] = pure [<]
+prettyCsts dnames (eqs :< Nothing) = prettyCsts (tail dnames) eqs
+prettyCsts dnames (eqs :< Just q)  =
+  [|prettyCsts (tail dnames) eqs :< prettyCst dnames (BV 0 noLoc) (weakD 1 q)|]
+
+export
+prettyDimEq' : {opts : _} -> BContext d -> DimEq' d -> Eff Pretty (Doc opts)
+prettyDimEq' vars eqs = do
+  vars' <- prettyDVars' vars
+  eqs'  <- prettyCsts vars eqs
+  parensIfM (dimEqPrec vars (Just eqs)) $
+    fillSeparateTight !commaD $ vars' ++ eqs'
+
+export
+prettyDimEq : {opts : _} -> BContext d -> DimEq d -> Eff Pretty (Doc opts)
+prettyDimEq dnames ZeroIsOne = do
+  vars <- prettyDVars' dnames
+  cst  <- prettyCst [<] (K Zero noLoc) (K One noLoc)
+  pure $ separateTight !commaD $ vars :< cst
+prettyDimEq dnames (C eqs) = prettyDimEq' dnames eqs
 
 
 public export
-wf' : {d : Nat} -> DimEq' d -> Bool
-wf' [<]                         = True
-wf' (eqs :< Nothing)            = wf' eqs
-wf' (eqs :< Just (Th _ (K {}))) = wf' eqs
-wf' (eqs :< Just (Th i (B _)))  = isNothing (get' eqs i.fin) && wf' eqs
+wf' : DimEq' d -> Bool
+wf' [<]                   = True
+wf' (eqs :< Nothing)      = wf' eqs
+wf' (eqs :< Just (K e _)) = wf' eqs
+wf' (eqs :< Just (B i _)) = isNothing (get' eqs i) && wf' eqs
 
 public export
-wf : {d : Nat} -> DimEq d -> Bool
+wf : DimEq d -> Bool
 wf ZeroIsOne = True
 wf (C eqs)   = wf' eqs

lib/Quox/Syntax/Qty.idr

@@ -6,6 +6,7 @@ module Quox.Syntax.Qty
 
 import Quox.Pretty
 import Quox.Decidable
+import Quox.PrettyValExtra
 import Data.DPair
 import Derive.Prelude
 
@@ -20,7 +21,7 @@ import Derive.Prelude
 ||| - ω (or #): don't care. an ω variable *can* also be used 0/1 time
 public export
 data Qty = Zero | One | Any
-%runElab derive "Qty" [Eq, Ord, Show]
+%runElab derive "Qty" [Eq, Ord, Show, PrettyVal]
 %name Qty.Qty pi, rh
 
 
@@ -78,26 +79,16 @@ lub p q = if p == q then p else Any
 ||| to maintain subject reduction, only 0 or 1 can occur
 ||| for the subject of a typing judgment. see @qtt, §2.3 for more detail
 public export
-isSubj : Qty -> Bool
-isSubj Zero = True
-isSubj One  = True
-isSubj Any  = False
-
-public export
-SQty : Type
-SQty = Subset Qty $ So . isSubj
-
-public export %inline
-szero, sone : SQty
-szero = Element Zero Oh
-sone  = Element One  Oh
+data SQty = SZero | SOne
+%runElab derive "SQty" [Eq, Ord, Show, PrettyVal]
+%name Qty.SQty sg
 
 ||| "σ ⨴ π"
 |||
-||| σ ⨭ π is 0 if either of σ or π are, otherwise it is σ.
+||| σ ⨴ π is 0 if either of σ or π are, otherwise it is σ.
 public export
 subjMult : SQty -> Qty -> SQty
-subjMult _  Zero = szero
+subjMult _  Zero = SZero
 subjMult sg _    = sg
 
 
@@ -105,23 +96,59 @@ subjMult sg _    = sg
 ||| quantity of 1, so the only distinction is whether it is present
 ||| at runtime at all or not
 public export
-isGlobal : Qty -> Bool
-isGlobal Zero = True
-isGlobal One  = False
-isGlobal Any  = True
+data GQty = GZero | GAny
+%runElab derive "GQty" [Eq, Ord, Show, PrettyVal]
+%name GQty rh
 
 public export
-GQty : Type
-GQty = Subset Qty $ So . isGlobal
-
-public export
-gzero, gany : GQty
-gzero = Element Zero Oh
-gany  = Element Any  Oh
+toGlobal : Qty -> Maybe GQty
+toGlobal Zero = Just GZero
+toGlobal Any  = Just GAny
+toGlobal One  = Nothing
 
 ||| when checking a definition, a 0 definition is checked at 0,
 ||| but an ω definition is checked at 1 since ω isn't a subject quantity
 public export %inline
 globalToSubj : GQty -> SQty
-globalToSubj (Element Zero _) = szero
-globalToSubj (Element Any  _) = sone
+globalToSubj GZero = SZero
+globalToSubj GAny  = SOne
+
+
+public export
+DecEq Qty where
+  decEq Zero Zero = Yes Refl
+  decEq Zero One  = No $ \case _ impossible
+  decEq Zero Any  = No $ \case _ impossible
+  decEq One  Zero = No $ \case _ impossible
+  decEq One  One  = Yes Refl
+  decEq One  Any  = No $ \case _ impossible
+  decEq Any  Zero = No $ \case _ impossible
+  decEq Any  One  = No $ \case _ impossible
+  decEq Any  Any  = Yes Refl
+
+public export
+DecEq SQty where
+  decEq SZero SZero = Yes Refl
+  decEq SZero SOne  = No $ \case _ impossible
+  decEq SOne  SZero = No $ \case _ impossible
+  decEq SOne  SOne  = Yes Refl
+
+public export
+DecEq GQty where
+  decEq GZero GZero = Yes Refl
+  decEq GZero GAny  = No $ \case _ impossible
+  decEq GAny  GZero = No $ \case _ impossible
+  decEq GAny  GAny  = Yes Refl
+
+
+namespace SQty
+  public export %inline
+  (.qty) : SQty -> Qty
+  (SZero).qty = Zero
+  (SOne).qty  = One
+
+namespace GQty
+  public export %inline
+  (.qty) : GQty -> Qty
+  (GZero).qty = Zero
+  (GAny).qty  = Any

lib/Quox/Syntax/Shift.idr

@@ -1,11 +1,11 @@
 module Quox.Syntax.Shift
 
-import public Quox.Syntax.Var
-import public Quox.Thin
+import public Quox.Var
 
 import Data.Nat
 import Data.So
-import Data.DPair
+import Data.Singleton
+import Syntax.PreorderReasoning
 
 %default total
 
@@ -148,6 +148,25 @@ weakViaNat s by =
 %transform "Shift.weak" Shift.weak = weakViaNat
 
 
+export
+getFrom : {to : Nat} -> Shift from to -> Singleton from
+getFrom SZ      = Val to
+getFrom (SS by) = getFrom by
+
+private
+0 getFromViaNatProof : (by : Shift from to) -> from = to `minus` by.nat
+getFromViaNatProof by = Calc $
+  |~ from
+  ~~ minus (by.nat + from) by.nat ..<(minusPlus {})
+  ~~ minus to by.nat              ..<(cong (flip minus by.nat) (shiftDiff by))
+
+private
+getFromViaNat : {to : Nat} -> Shift from to -> Singleton from
+getFromViaNat by = rewrite getFromViaNatProof by in Val _
+
+%transform "Shift.getFrom" Shift.getFrom = getFromViaNat
+
+
 public export
 shift : Shift from to -> Var from -> Var to
 shift SZ      i = i
@@ -180,11 +199,12 @@ by . SS bz = SS $ by . bz
 private
 0 compNatProof : (by : Shift from mid) -> (bz : Shift mid to) ->
                  to = by.nat + bz.nat + from
-compNatProof by bz =
-  trans (shiftDiff bz) $
-  trans (cong (bz.nat +) (shiftDiff by)) $
-  trans (plusAssociative bz.nat by.nat from) $
-  cong (+ from) (plusCommutative bz.nat by.nat)
+compNatProof by bz = Calc $
+  |~ to
+  ~~ bz.nat + mid             ...(shiftDiff {})
+  ~~ bz.nat + (by.nat + from) ...(cong (bz.nat +) (shiftDiff {}))
+  ~~ bz.nat + by.nat + from   ...(plusAssociative {})
+  ~~ by.nat + bz.nat + from   ...(cong (+ from) (plusCommutative {}))
 
 private %inline
 compViaNat' : (by : Shift from mid) -> (bz : Shift mid to) ->
@@ -207,7 +227,7 @@ compViaNatCorrect by (SS bz) =
 %transform "Shift.(.)" Shift.(.) = compViaNat
 
 
-infixl 8 //
+export infixl 8 //
 public export
 interface CanShift f where
   (//) : f from -> Shift from to -> f to
@@ -222,15 +242,3 @@ namespace CanShift
 
   public export %inline
   [Const] CanShift (\_ => a) where x // _ = x
-
-
-export
-shiftOPE : {mask : Nat} -> (0 ope : OPE m n mask) ->
-           Shift n n' -> Subset Nat (OPE m n')
-shiftOPE ope SZ      = Element _ ope
-shiftOPE ope (SS by) =
-  let Element _ ope = shiftOPE ope by in Element _ $ drop ope
-
-export
-CanShift (Thinned f) where
-  Th ope tm // by = Th (shiftOPE ope by).snd tm

lib/Quox/Syntax/Subst.idr

@@ -1,11 +1,13 @@
 module Quox.Syntax.Subst
 
-import Quox.Thin
-import Quox.Loc
+import public Quox.Syntax.Shift
+import Quox.Var
+import Quox.Name
 
-import Data.DPair
+import Data.Nat
 import Data.List
 import Data.SnocVect
+import Data.Singleton
 import Derive.Prelude
 
 %default total
@@ -13,159 +15,155 @@ import Derive.Prelude
 
 
 public export
-Subst : (Nat -> Type) -> Nat -> Nat -> Type
-Subst env from to = SnocVect from (Lazy (Thinned env to))
+data Subst : (Nat -> Type) -> Nat -> Nat -> Type where
+  Shift : Shift from to -> Subst env from to
+  (:::) : (t : Lazy (env to)) -> Subst env from to -> Subst env (S from) to
+%name Subst th, ph, ps
 
+export infixr 7 !:::
+||| in case the automatic laziness insertion gets confused
 public export
-Subst2 : (Nat -> Nat -> Type) -> Nat -> Nat -> Nat -> Type
-Subst2 env d from to = SnocVect from (Lazy (Thinned2 env d to))
+(!:::) : env to -> Subst env from to -> Subst env (S from) to
+t !::: ts = t ::: ts
+
+
+private
+Repr : (Nat -> Type) -> Nat -> Type
+Repr f to = (List (f to), Nat)
+
+private
+repr : Subst f from to -> Repr f to
+repr (Shift by) = ([], by.nat)
+repr (t ::: th) = let (ts, i) = repr th in (t::ts, i)
+
+
+export Eq   (f to) => Eq   (Subst f from to) where (==) = (==) `on` repr
+export Ord  (f to) => Ord  (Subst f from to) where compare = compare `on` repr
+export Show (f to) => Show (Subst f from to) where show = show . repr
+
+
+export infixl 8 //
+public export
+interface FromVar term => CanSubstSelf term where
+  (//) : term from -> Lazy (Subst term from to) -> term to
 
 
 public export
-get : Subst env f t -> Fin f -> Thinned env t
-get (sx :< x) FZ     = x
-get (sx :< x) (FS i) = get sx i
+getLoc : FromVar term => Subst term from to -> Var from -> Loc -> term to
+getLoc (Shift by) i      loc = fromVarLoc (shift by i) loc
+getLoc (t ::: th) VZ     _   = t
+getLoc (t ::: th) (VS i) loc = getLoc th i loc
 
 
 public export
-interface FromVar (0 term : Nat -> Type) where
-  var : Loc -> term 1
-
-public export
-0 FromVar2 : (Nat -> Nat -> Type) -> Type
-FromVar2 t = FromVar (t 0)
-
-public export
-varT : FromVar term => Fin n -> Loc -> Thinned term n
-varT i loc = Th (one' i) (var loc)
-
-public export
-varT2 : FromVar2 term => Fin n -> Loc -> Thinned2 term d n
-varT2 i loc = Th2 zero (one' i) (var loc)
-
-infixl 8 //
-namespace CanSubstSelf
-  public export
-  interface FromVar term => CanSubstSelf term where
-    (//) : {f : Nat} -> Thinned term f -> Subst term f t -> Thinned term t
-
-namespace CanSubstSelf2
-  public export
-  interface FromVar2 term => CanSubstSelf2 term where
-    (//) : {f : Nat} -> Thinned2 term d f ->
-           Subst2 term d f t -> Thinned2 term d t
-
-public export
-(.) : {mid : Nat} -> CanSubstSelf f =>
-      Subst f from mid -> Subst f mid to -> Subst f from to
-th . ph = map (\(Delay x) => x // ph) th
-
-infixr 9 .%
-
-public export
-(.%) : {mid : Nat} -> CanSubstSelf2 f =>
-       Subst2 f d from mid -> Subst2 f d mid to -> Subst2 f d from to
-th .% ph = map (\(Delay x) => x // ph) th
-
-
-public export
-tabulate : (n : Nat) -> SnocVect n (Fin n)
-tabulate n = go n id where
-  go : (n : Nat) -> (Fin n -> Fin n') -> SnocVect n (Fin n')
-  go 0     f = [<]
-  go (S n) f = go n (f . FS) :< f FZ
-
-public export
-id : FromVar term => {n : Nat} -> (under : Nat) -> Loc ->
-     Subst term n (n + under)
-id under loc =
-  map (\i => delay $ varT (weakenN under i) loc) (tabulate n)
-
-public export
-id2 : FromVar2 term => {n : Nat} -> Loc -> Subst2 term d n n
-id2 loc = map (\i => delay $ varT2 i loc) $ tabulate n
-
-export
-select : {n, mask : Nat} -> (0 ope : OPE m n mask) ->
-         SnocVect n a -> SnocVect m a
-select ope sx with %syntactic (view ope)
-  select _ [<]       | StopV       = [<]
-  select _ (sx :< x) | DropV _ ope = select ope sx
-  select _ (sx :< x) | KeepV _ ope = select ope sx :< x
-
-export
-opeToFins : {n, mask : Nat} ->
-            (0 ope : OPE m n mask) -> SnocVect m (Fin n)
-opeToFins ope = select ope $ tabulate n
-
-export
-shift : FromVar term => {from : Nat} ->
-        (n : Nat) -> Loc -> Subst term from (n + from)
-shift n loc = map (\i => delay $ varT (shift n i) loc) $ tabulate from
-
-public export
-pushN : CanSubstSelf term => {to : Nat} -> (by : Nat) ->
-        Subst term from to -> Loc -> Subst term (by + from) (by + to)
-pushN by th loc =
-  rewrite plusCommutative by from in
-  (th . shift by loc) ++ id to loc
-
-public export %inline
-push : CanSubstSelf f => {to : Nat} ->
-       Subst f from to -> Loc -> Subst f (S from) (S to)
-push = pushN 1
+CanSubstSelf Var where
+  i    // Shift by   = shift by i
+  VZ   // (t ::: th) = t
+  VS i // (t ::: th) = i // th
 
 
 public export %inline
-one : Thinned f n -> Subst f 1 n
-one x = [< x]
+shift : (by : Nat) -> Subst env from (by + from)
+shift by = Shift $ fromNat by
+
+public export %inline
+shift0 : (by : Nat) -> Subst env 0 by
+shift0 by = rewrite sym $ plusZeroRightNeutral by in Shift $ fromNat by
+
+
+public export
+(.) : CanSubstSelf f => Subst f from mid -> Subst f mid to -> Subst f from to
+Shift by      . Shift bz   = Shift $ by . bz
+Shift SZ      . ph         = ph
+Shift (SS by) . (t ::: th) = Shift by . th
+(t ::: th)    . ph         = (t // ph) ::: (th . ph)
+
+public export %inline
+id : Subst f n n
+id = shift 0
+
+public export
+traverse : Applicative m =>
+           (f to -> m (g to)) -> Subst f from to -> m (Subst g from to)
+traverse f (Shift by) = pure $ Shift by
+traverse f (t ::: th) = [|f t !::: traverse f th|]
+
+-- not in terms of traverse because this map can maintain laziness better
+public export
+map : (f to -> g to) -> Subst f from to -> Subst g from to
+map f (Shift by) = Shift by
+map f (t ::: th) = f t ::: map f th
+
+
+public export %inline
+push : CanSubstSelf f => Loc -> Subst f from to -> Subst f (S from) (S to)
+push loc th = fromVarLoc VZ loc ::: (th . shift 1)
+
+-- [fixme] a better way to do this?
+public export
+pushN : CanSubstSelf f => (s : Nat) -> Loc ->
+        Subst f from to -> Subst f (s + from) (s + to)
+pushN 0     _   th = th
+pushN (S s) loc th =
+  rewrite plusSuccRightSucc s from in
+  rewrite plusSuccRightSucc s to in
+  pushN s loc $ fromVarLoc VZ loc ::: (th . shift 1)
+
+public export
+drop1 : Subst f (S from) to -> Subst f from to
+drop1 (Shift by) = Shift $ ssDown by
+drop1 (t ::: th) = th
+
+
+public export
+fromSnocVect : SnocVect s (f n) -> Subst f (s + n) n
+fromSnocVect [<]       = id
+fromSnocVect (xs :< x) = x ::: fromSnocVect xs
+
+public export %inline
+one : f n -> Subst f (S n) n
+one x = fromSnocVect [< x]
 
 
-||| whether two substitutions with the same codomain have the same domain
 export
-cmpShape : SnocVect m a -> SnocVect n a -> Either Ordering (m = n)
-cmpShape [<]       [<]       = Right Refl
-cmpShape [<]       (sx :< _) = Left LT
-cmpShape (sx :< _) [<]       = Left GT
-cmpShape (sx :< _) (sy :< _) = cong S <$> cmpShape sx sy
+getFrom : {to : Nat} -> Subst _ from to -> Singleton from
+getFrom (Shift by) = getFrom by
+getFrom (t ::: th) = [|S $ getFrom th|]
+
+
+||| whether two substitutions with the same codomain have the same shape
+||| (the same number of terms and the same shift at the end). if so, they
+||| also have the same domain
+export
+cmpShape : Subst env from1 to -> Subst env from2 to ->
+           Either Ordering (from1 = from2)
+cmpShape (Shift by) (Shift bz) = cmpLen by bz
+cmpShape (Shift _)  (_ ::: _)  = Left LT
+cmpShape (_ ::: _)  (Shift _)  = Left GT
+cmpShape (_ ::: th) (_ ::: ph) = map (\x => cong S x) $ cmpShape th ph
 
 
 public export
 record WithSubst tm env n where
   constructor Sub
   term  : tm from
-  subst : Subst env from n
+  subst : Lazy (Subst env from n)
 
-{-
 export
-(forall n. Eq (env n), forall n. Eq (tm n)) =>
-Eq (WithSubst tm env n) where
+(Eq (env n), forall n. Eq (tm n)) => Eq (WithSubst tm env n) where
   Sub t1 s1 == Sub t2 s2 =
     case cmpShape s1 s2 of
       Left  _    => False
-      Right Refl =>
-        t1 == t2 && concat @{All} (zipWith ((==) `on` force) s1 s2)
+      Right Refl => t1 == t2 && s1 == s2
 
 export
-(forall n. Ord (env n), forall n. Ord (tm n)) =>
-Ord (WithSubst tm env n) where
+(Ord (env n), forall n. Ord (tm n)) => Ord (WithSubst tm env n) where
   Sub t1 s1 `compare` Sub t2 s2 =
     case cmpShape s1 s2 of
       Left  o    => o
-      Right Refl =>
-        compare t1 t2 <+> concat (zipWith (compare `on` force) s1 s2)
+      Right Refl => compare (t1, s1) (t2, s2)
 
 export %hint
-ShowWithSubst : {n : Nat} ->
-                (forall n. Show (env n), forall n. Show (tm n)) =>
+ShowWithSubst : (Show (env n), forall n. Show (tm n)) =>
                 Show (WithSubst tm env n)
-ShowWithSubst = deriveShow where
-  Show (Lazy (Thinned env n)) where showPrec d = showPrec d . force
--}
-
-
-public export
-record WithSubst2 tm env d n where
-  constructor Sub2
-  term  : tm d from
-  subst : Subst2 env d from n
+ShowWithSubst = deriveShow

lib/Quox/Syntax/Term.idr

@@ -3,4 +3,3 @@ module Quox.Syntax.Term
 import public Quox.Syntax.Term.Base
 import public Quox.Syntax.Term.Subst
 import public Quox.Syntax.Term.Pretty
-import public Quox.Syntax.Term.Tighten

lib/Quox/Syntax/Term/Base.idr

@@ -1,7 +1,7 @@
 module Quox.Syntax.Term.Base
 
-import public Quox.Thin
-import public Quox.Syntax.Var
+import public Quox.Var
+import public Quox.Scoped
 import public Quox.Syntax.Shift
 import public Quox.Syntax.Subst
 import public Quox.Syntax.Qty
@@ -19,6 +19,9 @@ import Data.Maybe
 import Data.Nat
 import public Data.So
 import Data.String
+import public Data.SortedMap
+import public Data.SortedMap.Dependent
+import public Data.SortedSet
 import Derive.Prelude
 
 %default total
@@ -44,344 +47,406 @@ TagVal : Type
 TagVal = String
 
 
-||| type-checkable terms, which consists of types and constructor forms.
-|||
-||| first argument `d` is dimension scope size; second `n` is term scope size
-public export
-data Term : (d, n : Nat) -> Type
-%name Term s, t, r
+mutual
+  public export
+  TSubst : TSubstLike
+  TSubst d = Subst $ \n => Elim d n
 
-||| inferrable terms, which consists of elimination forms like application and
-||| `case` (as well as other terms with an annotation)
-|||
-||| first argument `d` is dimension scope size; second `n` is term scope size
-public export
-data Elim : (d, n : Nat) -> Type
-%name Elim e, f
+  ||| first argument `d` is dimension scope size;
+  ||| second `n` is term scope size
+  public export
+  data Term : (d, n : Nat) -> Type where
+    ||| type of types
+    TYPE : (l : Universe) -> (loc : Loc) -> Term d n
+
+    ||| IO state token. this is a builtin because otherwise #[main] being a
+    ||| builtin makes no sense
+    IOState : (loc : Loc) -> Term d n
+
+    ||| function type
+    Pi  : (qty : Qty) -> (arg : Term d n) ->
+          (res : ScopeTerm d n) -> (loc : Loc) -> Term d n
+    ||| function term
+    Lam : (body : ScopeTerm d n) -> (loc : Loc) -> Term d n
+
+    ||| pair type
+    Sig : (fst : Term d n) -> (snd : ScopeTerm d n) -> (loc : Loc) -> Term d n
+    ||| pair value
+    Pair : (fst, snd : Term d n) -> (loc : Loc) -> Term d n
+
+    ||| enumeration type
+    Enum : (cases : SortedSet TagVal) -> (loc : Loc) -> Term d n
+    ||| enumeration value
+    Tag : (tag : TagVal) -> (loc : Loc) -> Term d n
+
+    ||| equality type
+    Eq : (ty : DScopeTerm d n) -> (l, r : Term d n) -> (loc : Loc) -> Term d n
+    ||| equality term
+    DLam : (body : DScopeTerm d n) -> (loc : Loc) -> Term d n
+
+    ||| natural numbers (temporary until 𝐖 gets added)
+    NAT : (loc : Loc) -> Term d n
+    Nat : (val : Nat) -> (loc : Loc) -> Term d n
+    Succ : (p : Term d n) -> (loc : Loc) -> Term d n
+
+    ||| strings
+    STRING : (loc : Loc) -> Term d n
+    Str    : (str : String) -> (loc : Loc) -> Term d n
+
+    ||| "box" (package a value up with a certain quantity)
+    BOX : (qty : Qty) -> (ty : Term d n) -> (loc : Loc) -> Term d n
+    Box : (val : Term d n) -> (loc : Loc) -> Term d n
+
+    Let : (qty : Qty) -> (rhs : Elim d n) ->
+          (body : ScopeTerm d n) -> (loc : Loc) -> Term d n
+
+    ||| elimination
+    E : (e : Elim d n) -> Term d n
+
+    ||| term closure/suspended substitution
+    CloT  : WithSubst (Term d) (Elim d) n -> Term d n
+    ||| dimension closure/suspended substitution
+    DCloT : WithSubst (\d => Term d n) Dim d -> Term d n
+  %name Term s, t, r
+
+  ||| first argument `d` is dimension scope size, second `n` is term scope size
+  public export
+  data Elim : (d, n : Nat) -> Type where
+    ||| free variable, possibly with a displacement (see @crude, or @mugen for a
+    ||| more abstract and formalised take)
+    |||
+    ||| e.g. if f : ★₀ → ★₁, then f¹ : ★₁ → ★₂
+    F : (x : Name) -> (u : Universe) -> (loc : Loc) -> Elim d n
+    ||| bound variable
+    B : (i : Var n) -> (loc : Loc) -> Elim d n
+
+    ||| term application
+    App : (fun : Elim d n) -> (arg : Term d n) -> (loc : Loc) -> Elim d n
+
+    ||| pair destruction
+    |||
+    ||| `CasePair 𝜋 𝑒 ([𝑟], 𝐴) ([𝑥, 𝑦], 𝑡)` is
+    ||| `𝐜𝐚𝐬𝐞 𝜋 · 𝑒 𝐫𝐞𝐭𝐮𝐫𝐧 𝑟 ⇒ 𝐴 𝐨𝐟 { (𝑥, 𝑦) ⇒ 𝑡 }`
+    CasePair : (qty : Qty) -> (pair : Elim d n) ->
+               (ret : ScopeTerm d n) ->
+               (body : ScopeTermN 2 d n) ->
+               (loc : Loc) ->
+               Elim d n
+
+    ||| first element of a pair. only works in non-linear contexts.
+    Fst : (pair : Elim d n) -> (loc : Loc) -> Elim d n
+
+    ||| second element of a pair. only works in non-linear contexts.
+    Snd : (pair : Elim d n) -> (loc : Loc) -> Elim d n
+
+    ||| enum matching
+    CaseEnum : (qty : Qty) -> (tag : Elim d n) ->
+               (ret : ScopeTerm d n) ->
+               (arms : CaseEnumArms d n) ->
+               (loc : Loc) ->
+               Elim d n
+
+    ||| nat matching
+    CaseNat : (qty, qtyIH : Qty) -> (nat : Elim d n) ->
+              (ret : ScopeTerm d n) ->
+              (zero : Term d n) ->
+              (succ : ScopeTermN 2 d n) ->
+              (loc : Loc) ->
+              Elim d n
+
+    ||| unboxing
+    CaseBox : (qty : Qty) -> (box : Elim d n) ->
+              (ret : ScopeTerm d n) ->
+              (body : ScopeTerm d n) ->
+              (loc : Loc) ->
+              Elim d n
+
+    ||| dim application
+    DApp : (fun : Elim d n) -> (arg : Dim d) -> (loc : Loc) -> Elim d n
+
+    ||| type-annotated term
+    Ann : (tm, ty : Term d n) -> (loc : Loc) -> Elim d n
+
+    ||| coerce a value along a type equality, or show its coherence
+    ||| [@xtt; §2.1.1]
+    Coe : (ty : DScopeTerm d n) -> (p, q : Dim d) ->
+          (val : Term d n) -> (loc : Loc) -> Elim d n
+
+    ||| "generalised composition" [@xtt; §2.1.2]
+    Comp : (ty : Term d n) -> (p, q : Dim d) ->
+           (val : Term d n) -> (r : Dim d) ->
+           (zero, one : DScopeTerm d n) -> (loc : Loc) -> Elim d n
+
+    ||| match on types. needed for b.s. of coercions [@xtt; §2.2]
+    TypeCase : (ty : Elim d n) -> (ret : Term d n) ->
+               (arms : TypeCaseArms d n) -> (def : Term d n) ->
+               (loc : Loc) ->
+               Elim d n
+
+    ||| term closure/suspended substitution
+    CloE  : WithSubst (Elim d) (Elim d) n -> Elim d n
+    ||| dimension closure/suspended substitution
+    DCloE : WithSubst (\d => Elim d n) Dim d -> Elim d n
+  %name Elim e, f
+
+  public export
+  CaseEnumArms : TermLike
+  CaseEnumArms d n = SortedMap TagVal (Term d n)
+
+  public export
+  TypeCaseArms : TermLike
+  TypeCaseArms d n = SortedDMap TyConKind (\k => TypeCaseArmBody k d n)
+
+  public export
+  TypeCaseArm : TermLike
+  TypeCaseArm d n = (k ** TypeCaseArmBody k d n)
+
+  public export
+  TypeCaseArmBody : TyConKind -> TermLike
+  TypeCaseArmBody k = ScopeTermN (arity k)
 
 
-public export
-ScopeTermN : Nat -> TermLike
-ScopeTermN s d n = ScopedN s (\n => Term d n) n
+  public export
+  ScopeTermN, DScopeTermN : Nat -> TermLike
+  ScopeTermN  s d n = Scoped s (Term d) n
+  DScopeTermN s d n = Scoped s (\d => Term d n) d
 
-public export
-DScopeTermN : Nat -> TermLike
-DScopeTermN s d n = ScopedN s (\d => Term d n) d
+  public export
+  ScopeTerm, DScopeTerm : TermLike
+  ScopeTerm  = ScopeTermN 1
+  DScopeTerm = DScopeTermN 1
 
-public export
-ScopeTerm : TermLike
-ScopeTerm = ScopeTermN 1
+mutual
+  export %hint
+  EqTerm : Eq (Term d n)
+  EqTerm = assert_total {a = Eq (Term d n)} deriveEq
 
-public export
-DScopeTerm : TermLike
-DScopeTerm = DScopeTermN 1
+  export %hint
+  EqElim : Eq (Elim d n)
+  EqElim = assert_total {a = Eq (Elim d n)} deriveEq
 
+mutual
+  export %hint
+  ShowTerm : Show (Term d n)
+  ShowTerm = assert_total {a = Show (Term d n)} deriveShow
 
-public export
-TermT : TermLike
-TermT = Thinned2 (\d, n => Term d n)
-
-public export
-ElimT : TermLike
-ElimT = Thinned2 (\d, n => Elim d n)
-
-
-public export
-DimArg : TermLike
-DimArg d n = Dim d
-
-
-data Term where
-  ||| type of types
-  TYPE : (l : Universe) -> (loc : Loc) -> Term 0 0
-
-  ||| function type
-  Pi : Qty -> Subterms [Term, ScopeTerm] d n -> Loc -> Term d n
-  ||| function value
-  Lam : ScopeTerm d n -> Loc -> Term d n
-
-  ||| pair type
-  Sig : Subterms [Term, ScopeTerm] d n -> Loc -> Term d n
-  ||| pair value
-  Pair : Subterms [Term, Term] d n -> Loc -> Term d n
-
-  ||| enum type
-  Enum : List TagVal -> Loc -> Term 0 0
-  ||| enum value
-  Tag : TagVal -> Loc -> Term 0 0
-
-  ||| equality type
-  Eq : Subterms [DScopeTerm, Term, Term] d n -> Loc -> Term d n
-  ||| equality value
-  DLam : DScopeTerm d n -> Loc -> Term d n
-
-  ||| natural numbers (temporary until 𝐖 gets added)
-  Nat  : Loc -> Term 0 0
-  Zero : Loc -> Term 0 0
-  Succ : Term d n -> Loc -> Term 0 0
-
-  ||| package a value with a quantity
-  ||| e.g. a value of [ω. A], when unpacked, can be used ω times,
-  ||| even if the box itself is linear
-  BOX : Qty -> Term d n -> Loc -> Term d n
-  Box : Term d n -> Loc -> Term d n
-
-  E : Elim d n -> Term d n
-
-  ||| term closure/suspended substitution
-  CloT  : WithSubst2 Term Elim d n -> Term d n
-  ||| dimension closure/suspended substitution
-  DCloT : WithSubst (\d => Term d n) Dim d -> Term d n
-
-public export
-data Elim where
-  ||| free variable, possibly with a displacement (see @crude, or @mugen for a
-  ||| more abstract and formalised take)
-  |||
-  ||| e.g. if f : ★₀ → ★₁, then f¹ : ★₁ → ★₂
-  F : Name -> Universe -> Loc -> Elim 0 0
-  ||| bound variable
-  B : Loc -> Elim 0 1
-
-  ||| term application
-  App : Subterms [Elim, Term] d n -> Loc -> Elim d n
-
-  ||| pair match
-  ||| - the subterms are, in order: [head, return type, body]
-  ||| - the quantity is that of the head, and since pairs only have one
-  |||   constructor, can be 0
-  CasePair : Qty -> Subterms [Elim, ScopeTerm, ScopeTermN 2] d n ->
-             Loc -> Elim d n
-
-  ||| enum match
-  CaseEnum : Qty -> (arms : List TagVal) ->
-             Subterms (Elim :: ScopeTerm :: (Term <$ arms)) d n ->
-             Loc -> Elim d n
-
-  ||| nat match
-  CaseNat : Qty -> Qty ->
-            Subterms [Elim, ScopeTerm, Term, ScopeTermN 2] d n ->
-            Loc -> Elim d n
-
-  ||| box match
-  CaseBox : Qty -> Subterms [Elim, ScopeTerm, ScopeTerm] d n -> Loc -> Elim d n
-
-  ||| dim application
-  DApp : Subterms [Elim, DimArg] d n -> Loc -> Elim d n
-
-  ||| type-annotated term
-  Ann : Subterms [Term, Term] d n -> Loc -> Elim d n
-
-  ||| coerce a value along a type equality, or show its coherence
-  ||| [@xtt; §2.1.1]
-  Coe : Subterms [DScopeTerm, DimArg, DimArg, Term] d n ->
-        Loc -> Elim d n
-
-  ||| "generalised composition" [@xtt; §2.1.2]
-  Comp : Subterms [Term, DimArg, DimArg, Term,
-                   DimArg, DScopeTerm, DScopeTerm] d n ->
-         Loc -> Elim d n
-
-  ||| match on types. needed for b.s. of coercions [@xtt; §2.2]
-  TypeCase : Subterms [Elim, Term,   -- head, type
-                       Term,         -- ★
-                       ScopeTermN 2, -- pi
-                       ScopeTermN 2, -- sig
-                       Term,         -- enum
-                       ScopeTermN 5, -- eq
-                       Term,         -- nat
-                       ScopeTerm     -- box
-                      ] d n -> Loc -> Elim d n
-
-  ||| term closure/suspended substitution
-  CloE  : WithSubst2 Elim Elim d n -> Elim d n
-  ||| dimension closure/suspended substitution
-  DCloE : WithSubst (\d => Elim d n) Dim d -> Elim d n
-
-
--- this kills the idris ☹
--- export %hint
--- EqTerm : Eq (Term d n)
-
--- export %hint
--- EqElim : Eq (Elim d n)
-
--- EqTerm = deriveEq
--- EqElim = deriveEq
-
-
--- mutual
---   export %hint
---   ShowTerm : Show (Term d n)
---   ShowTerm = assert_total {a = Show (Term d n)} deriveShow
-
---   export %hint
---   ShowElim : Show (Elim d n)
---   ShowElim = assert_total {a = Show (Elim d n)} deriveShow
-
--- ||| scope which ignores all its binders
--- public export %inline
--- SN : {s : Nat} -> f n -> Scoped s f n
--- SN = S (replicate s $ BN Unused noLoc) . N
-
--- ||| scope which uses its binders
--- public export %inline
--- SY : BContext s -> f (s + n) -> Scoped s f n
--- SY ns = S ns . Y
-
--- public export %inline
--- name : Scoped 1 f n -> BindName
--- name (S [< x] _) = x
-
--- public export %inline
--- (.name) : Scoped 1 f n -> BindName
--- s.name = name s
-
--- ||| more convenient Pi
--- public export %inline
--- PiY : (qty : Qty) -> (x : BindName) ->
---       (arg : Term d n) -> (res : Term d (S n)) -> (loc : Loc) -> Term d n
--- PiY {qty, x, arg, res, loc} = Pi {qty, arg, res = SY [< x] res, loc}
-
--- ||| more convenient Lam
--- public export %inline
--- LamY : (x : BindName) -> (body : Term d (S n)) -> (loc : Loc) -> Term d n
--- LamY {x, body, loc} = Lam {body = SY [< x] body, loc}
-
--- public export %inline
--- LamN : (body : Term d n) -> (loc : Loc) -> Term d n
--- LamN {body, loc} = Lam {body = SN body, loc}
-
--- ||| non dependent function type
--- public export %inline
--- Arr : (qty : Qty) -> (arg, res : Term d n) -> (loc : Loc) -> Term d n
--- Arr {qty, arg, res, loc} = Pi {qty, arg, res = SN res, loc}
-
--- ||| more convenient Sig
--- public export %inline
--- SigY : (x : BindName) -> (fst : Term d n) ->
---        (snd : Term d (S n)) -> (loc : Loc) -> Term d n
--- SigY {x, fst, snd, loc} = Sig {fst, snd = SY [< x] snd, loc}
-
--- ||| non dependent pair type
--- public export %inline
--- And : (fst, snd : Term d n) -> (loc : Loc) -> Term d n
--- And {fst, snd, loc} = Sig {fst, snd = SN snd, loc}
-
--- ||| more convenient Eq
--- public export %inline
--- EqY : (i : BindName) -> (ty : Term (S d) n) ->
---       (l, r : Term d n) -> (loc : Loc) -> Term d n
--- EqY {i, ty, l, r, loc} = Eq {ty = SY [< i] ty, l, r, loc}
-
--- ||| more convenient DLam
--- public export %inline
--- DLamY : (i : BindName) -> (body : Term (S d) n) -> (loc : Loc) -> Term d n
--- DLamY {i, body, loc} = DLam {body = SY [< i] body, loc}
-
--- public export %inline
--- DLamN : (body : Term d n) -> (loc : Loc) -> Term d n
--- DLamN {body, loc} = DLam {body = SN body, loc}
-
--- ||| non dependent equality type
--- public export %inline
--- Eq0 : (ty, l, r : Term d n) -> (loc : Loc) -> Term d n
--- Eq0 {ty, l, r, loc} = Eq {ty = SN ty, l, r, loc}
-
-
-||| same as `F` but as a term
-public export %inline
-FT : Name -> Universe -> Loc -> Term 0 0
-FT x u loc = E $ F x u loc
-
-||| abbreviation for a bound variable like `BV 4` instead of
-||| `B (VS (VS (VS (VS VZ))))`
-public export %inline
-BV : (i : Fin n) -> (loc : Loc) -> ElimT d n
-BV i loc = Th2 zero (one' i) $ B loc
-
-||| same as `BV` but as a term
-public export %inline
-BVT : (i : Fin n) -> (loc : Loc) -> TermT d n
-BVT i loc = Th2 zero (one' i) $ E $ B loc
-
-public export
-makeNat : Nat -> Loc -> Term 0 0
-makeNat 0     loc = Zero loc
-makeNat (S k) loc = Succ (makeNat k loc) loc
+  export %hint
+  ShowElim : Show (Elim d n)
+  ShowElim = assert_total {a = Show (Elim d n)} deriveShow
 
 
 export
 Located (Elim d n) where
-  (F _ _ loc).loc          = loc
-  (B loc).loc              = loc
-  (App _ loc).loc          = loc
-  (CasePair _ _ loc).loc   = loc
-  (CaseEnum _ _ _ loc).loc = loc
-  (CaseNat _ _ _ loc).loc  = loc
-  (CaseBox _ _ loc).loc    = loc
-  (DApp _ loc).loc         = loc
-  (Ann _ loc).loc          = loc
-  (Coe _ loc).loc          = loc
-  (Comp _ loc).loc         = loc
-  (TypeCase _ loc).loc     = loc
-  (CloE (Sub2 e _)).loc    = e.loc
-  (DCloE (Sub e _)).loc    = e.loc
+  (F _ _ loc).loc               = loc
+  (B _ loc).loc                 = loc
+  (App _ _ loc).loc             = loc
+  (CasePair _ _ _ _ loc).loc    = loc
+  (Fst _ loc).loc               = loc
+  (Snd _ loc).loc               = loc
+  (CaseEnum _ _ _ _ loc).loc    = loc
+  (CaseNat _ _ _ _ _ _ loc).loc = loc
+  (CaseBox _ _ _ _ loc).loc     = loc
+  (DApp _ _ loc).loc            = loc
+  (Ann _ _ loc).loc             = loc
+  (Coe _ _ _ _ loc).loc         = loc
+  (Comp _ _ _ _ _ _ _ loc).loc  = loc
+  (TypeCase _ _ _ _ loc).loc    = loc
+  (CloE (Sub e _)).loc          = e.loc
+  (DCloE (Sub e _)).loc         = e.loc
 
 export
 Located (Term d n) where
   (TYPE _ loc).loc      = loc
-  (Pi _ _ loc).loc      = loc
+  (IOState loc).loc     = loc
+  (Pi _ _ _ loc).loc    = loc
   (Lam _ loc).loc       = loc
-  (Sig _ loc).loc       = loc
-  (Pair _ loc).loc      = loc
+  (Sig _ _ loc).loc     = loc
+  (Pair _ _ loc).loc    = loc
   (Enum _ loc).loc      = loc
   (Tag _ loc).loc       = loc
-  (Eq _ loc).loc        = loc
+  (Eq _ _ _ loc).loc    = loc
   (DLam _ loc).loc      = loc
-  (Nat loc).loc         = loc
-  (Zero loc).loc        = loc
+  (NAT loc).loc         = loc
+  (Nat _ loc).loc       = loc
+  (STRING loc).loc      = loc
+  (Str _ loc).loc       = loc
   (Succ _ loc).loc      = loc
   (BOX _ _ loc).loc     = loc
   (Box _ loc).loc       = loc
+  (Let _ _ _ loc).loc   = loc
   (E e).loc             = e.loc
-  (CloT (Sub2 t _)).loc = t.loc
+  (CloT (Sub t _)).loc  = t.loc
   (DCloT (Sub t _)).loc = t.loc
 
+export
+Located1 f => Located (ScopedBody s f n) where
+  (Y t).loc = t.loc
+  (N t).loc = t.loc
+
+export
+Located1 f => Located (Scoped s f n) where
+  t.loc = t.body.loc
+
 
 export
 Relocatable (Elim d n) where
-  setLoc loc (F x u _)                = F x u loc
-  setLoc loc (B _)                    = B loc
-  setLoc loc (App ts _)               = App ts loc
-  setLoc loc (CasePair qty ts _)      = CasePair qty ts loc
-  setLoc loc (CaseEnum qty arms ts _) = CaseEnum qty arms ts loc
-  setLoc loc (CaseNat qty qtyIH ts _) = CaseNat qty qtyIH ts loc
-  setLoc loc (CaseBox qty ts _)       = CaseBox qty ts loc
-  setLoc loc (DApp ts _)              = DApp ts loc
-  setLoc loc (Ann ts _)               = Ann ts loc
-  setLoc loc (Coe ts _)               = Coe ts loc
-  setLoc loc (Comp ts _)              = Comp ts loc
-  setLoc loc (TypeCase ts _)          = TypeCase ts loc
-  setLoc loc (CloE (Sub2 term subst)) = CloE $ Sub2 (setLoc loc term) subst
-  setLoc loc (DCloE (Sub term subst)) = DCloE $ Sub (setLoc loc term) subst
+  setLoc loc (F x u _) = F x u loc
+  setLoc loc (B i _) = B i loc
+  setLoc loc (App fun arg _) = App fun arg loc
+  setLoc loc (CasePair qty pair ret body _) =
+    CasePair qty pair ret body loc
+  setLoc loc (Fst pair _) = Fst pair loc
+  setLoc loc (Snd pair _) = Fst pair loc
+  setLoc loc (CaseEnum qty tag ret arms _) =
+    CaseEnum qty tag ret arms loc
+  setLoc loc (CaseNat qty qtyIH nat ret zero succ _) =
+    CaseNat qty qtyIH nat ret zero succ loc
+  setLoc loc (CaseBox qty box ret body _) =
+    CaseBox qty box ret body loc
+  setLoc loc (DApp fun arg _) =
+    DApp fun arg loc
+  setLoc loc (Ann tm ty _) =
+    Ann tm ty loc
+  setLoc loc (Coe ty p q val _) =
+    Coe ty p q val loc
+  setLoc loc (Comp ty p q val r zero one _) =
+    Comp ty p q val r zero one loc
+  setLoc loc (TypeCase ty ret arms def _) =
+    TypeCase ty ret arms def loc
+  setLoc loc (CloE (Sub term subst)) =
+    CloE $ Sub (setLoc loc term) subst
+  setLoc loc (DCloE (Sub term subst)) =
+    DCloE $ Sub (setLoc loc term) subst
 
 export
 Relocatable (Term d n) where
-  setLoc loc (TYPE l _)               = TYPE l loc
-  setLoc loc (Pi qty ts _)            = Pi qty ts loc
-  setLoc loc (Lam body _)             = Lam body loc
-  setLoc loc (Sig ts _)               = Sig ts loc
-  setLoc loc (Pair ts _)              = Pair ts loc
-  setLoc loc (Enum cases _)           = Enum cases loc
-  setLoc loc (Tag tag _)              = Tag tag loc
-  setLoc loc (Eq ts _)                = Eq ts loc
-  setLoc loc (DLam body _)            = DLam body loc
-  setLoc loc (Nat _)                  = Nat loc
-  setLoc loc (Zero _)                 = Zero loc
-  setLoc loc (Succ p _)               = Succ p loc
-  setLoc loc (BOX qty ty _)           = BOX qty ty loc
-  setLoc loc (Box val _)              = Box val loc
-  setLoc loc (E e)                    = E $ setLoc loc e
-  setLoc loc (CloT (Sub2 term subst)) = CloT $ Sub2 (setLoc loc term) subst
+  setLoc loc (TYPE l _) = TYPE l loc
+  setLoc loc (IOState _) = IOState loc
+  setLoc loc (Pi qty arg res _) = Pi qty arg res loc
+  setLoc loc (Lam body _) = Lam body loc
+  setLoc loc (Sig fst snd _) = Sig fst snd loc
+  setLoc loc (Pair fst snd _) = Pair fst snd loc
+  setLoc loc (Enum cases _) = Enum cases loc
+  setLoc loc (Tag tag _) = Tag tag loc
+  setLoc loc (Eq ty l r _) = Eq ty l r loc
+  setLoc loc (DLam body _) = DLam body loc
+  setLoc loc (NAT _) = NAT loc
+  setLoc loc (Nat n _) = Nat n loc
+  setLoc loc (Succ p _) = Succ p loc
+  setLoc loc (STRING _) = STRING loc
+  setLoc loc (Str s _) = Str s loc
+  setLoc loc (BOX qty ty _) = BOX qty ty loc
+  setLoc loc (Box val _) = Box val loc
+  setLoc loc (Let qty rhs body _) = Let qty rhs body loc
+  setLoc loc (E e) = E $ setLoc loc e
+  setLoc loc (CloT (Sub term subst)) = CloT $ Sub (setLoc loc term) subst
   setLoc loc (DCloT (Sub term subst)) = DCloT $ Sub (setLoc loc term) subst
+
+export
+Relocatable1 f => Relocatable (ScopedBody s f n) where
+  setLoc loc (Y body) = Y $ setLoc loc body
+  setLoc loc (N body) = N $ setLoc loc body
+
+export
+Relocatable1 f => Relocatable (Scoped s f n) where
+  setLoc loc (S names body) = S (setLoc loc <$> names) (setLoc loc body)
+
+
+||| more convenient Pi
+public export %inline
+PiY : (qty : Qty) -> (x : BindName) ->
+      (arg : Term d n) -> (res : Term d (S n)) -> (loc : Loc) -> Term d n
+PiY {qty, x, arg, res, loc} = Pi {qty, arg, res = SY [< x] res, loc}
+
+||| more convenient Lam
+public export %inline
+LamY : (x : BindName) -> (body : Term d (S n)) -> (loc : Loc) -> Term d n
+LamY {x, body, loc} = Lam {body = SY [< x] body, loc}
+
+public export %inline
+LamN : (body : Term d n) -> (loc : Loc) -> Term d n
+LamN {body, loc} = Lam {body = SN body, loc}
+
+||| non dependent function type
+public export %inline
+Arr : (qty : Qty) -> (arg, res : Term d n) -> (loc : Loc) -> Term d n
+Arr {qty, arg, res, loc} = Pi {qty, arg, res = SN res, loc}
+
+||| more convenient Sig
+public export %inline
+SigY : (x : BindName) -> (fst : Term d n) ->
+       (snd : Term d (S n)) -> (loc : Loc) -> Term d n
+SigY {x, fst, snd, loc} = Sig {fst, snd = SY [< x] snd, loc}
+
+||| non dependent pair type
+public export %inline
+And : (fst, snd : Term d n) -> (loc : Loc) -> Term d n
+And {fst, snd, loc} = Sig {fst, snd = SN snd, loc}
+
+||| more convenient Eq
+public export %inline
+EqY : (i : BindName) -> (ty : Term (S d) n) ->
+      (l, r : Term d n) -> (loc : Loc) -> Term d n
+EqY {i, ty, l, r, loc} = Eq {ty = SY [< i] ty, l, r, loc}
+
+||| more convenient DLam
+public export %inline
+DLamY : (i : BindName) -> (body : Term (S d) n) -> (loc : Loc) -> Term d n
+DLamY {i, body, loc} = DLam {body = SY [< i] body, loc}
+
+public export %inline
+DLamN : (body : Term d n) -> (loc : Loc) -> Term d n
+DLamN {body, loc} = DLam {body = SN body, loc}
+
+||| more convenient Coe
+public export %inline
+CoeY : (i : BindName) -> (ty : Term (S d) n) ->
+       (p, q : Dim d) -> (val : Term d n) -> (loc : Loc) -> Elim d n
+CoeY {i, ty, p, q, val, loc} = Coe {ty = SY [< i] ty, p, q, val, loc}
+
+||| non dependent equality type
+public export %inline
+Eq0 : (ty, l, r : Term d n) -> (loc : Loc) -> Term d n
+Eq0 {ty, l, r, loc} = Eq {ty = SN ty, l, r, loc}
+
+||| same as `F` but as a term
+public export %inline
+FT : Name -> Universe -> Loc -> Term d n
+FT x u loc = E $ F x u loc
+
+||| same as `B` but as a term
+public export %inline
+BT : Var n -> (loc : Loc) -> Term d n
+BT i loc = E $ B i loc
+
+||| abbreviation for a bound variable like `BV 4` instead of
+||| `B (VS (VS (VS (VS VZ))))`
+public export %inline
+BV : (i : Nat) -> (0 _ : LT i n) => (loc : Loc) -> Elim d n
+BV i loc = B (V i) loc
+
+||| same as `BV` but as a term
+public export %inline
+BVT : (i : Nat) -> (0 _ : LT i n) => (loc : Loc) -> Term d n
+BVT i loc = E $ BV i loc
+
+public export %inline
+Zero : Loc -> Term d n
+Zero = Nat 0
+
+public export %inline
+enum : List TagVal -> Loc -> Term d n
+enum ts loc = Enum (SortedSet.fromList ts) loc
+
+public export %inline
+typeCase : Elim d n -> Term d n ->
+           List (TypeCaseArm d n) -> Term d n -> Loc -> Elim d n
+typeCase ty ret arms def loc = TypeCase ty ret (fromList arms) def loc
+
+public export %inline
+typeCase1Y : Elim d n -> Term d n ->
+             (k : TyConKind) -> BContext (arity k) -> Term d (arity k + n) ->
+             (loc : Loc) ->
+             {default (NAT loc) def : Term d n} ->
+             Elim d n
+typeCase1Y ty ret k ns body loc = typeCase ty ret [(k ** SY ns body)] def loc

lib/Quox/Syntax/Term/Pretty.idr

@@ -18,11 +18,11 @@ prettyUniverse = hl Universe . text . show
 
 
 export
-prettyTerm : {opts : _} -> BContext d -> BContext n -> TermT d n ->
+prettyTerm : {opts : _} -> BContext d -> BContext n -> Term d n ->
              Eff Pretty (Doc opts)
 
 export
-prettyElim : {opts : _} -> BContext d -> BContext n -> ElimT d n ->
+prettyElim : {opts : _} -> BContext d -> BContext n -> Elim d n ->
              Eff Pretty (Doc opts)
 
 private
@@ -30,14 +30,6 @@ BTelescope : Nat -> Nat -> Type
 BTelescope = Telescope' BindName
 
 
-private
-subscript : String -> String
-subscript = pack . map sub . unpack where
-  sub : Char -> Char
-  sub c = case c of
-    '0' => '₀'; '1' => '₁'; '2' => '₂'; '3' => '₃'; '4' => '₄'
-    '5' => '₅'; '6' => '₆'; '7' => '₇'; '8' => '₈'; '9' => '₉'; _ => c
-
 private
 superscript : String -> String
 superscript = pack . map sup . unpack where
@@ -209,8 +201,7 @@ prettyTArg dnames tnames s =
 
 private
 prettyDArg : {opts : _} -> BContext d -> Dim d -> Eff Pretty (Doc opts)
-prettyDArg dnames p =
-  map (text "@" <+>) $ withPrec Arg $ prettyDim dnames p
+prettyDArg dnames p = [|atD <+> withPrec Arg (prettyDim dnames p)|]
 
 private
 splitApps : Elim d n -> (Elim d n, List (Either (Dim d) (Term d n)))
@@ -238,7 +229,6 @@ prettyDTApps dnames tnames f xs = do
 private
 record CaseArm opts d n where
   constructor MkCaseArm
-  {0 dinner, ninner : Nat}
   pat    : Doc opts
   dbinds : BTelescope d dinner -- 🍴
   tbinds : BTelescope n ninner
@@ -251,12 +241,11 @@ parameters {opts : LayoutOpts} (dnames : BContext d) (tnames : BContext n)
     body <- withPrec Outer $ assert_total
             prettyTerm (dnames . dbinds) (tnames . tbinds) body
     header <- (pat <++>) <$> darrowD
-    pure $ hsep [header, body] <|> vsep [header, !(indentD body)]
+    pure $ ifMultiline (header <++> body) (vsep [header, !(indentD body)])
 
   private
-  prettyCaseBody : List (CaseArm opts d n) -> Eff Pretty (Doc opts)
-  prettyCaseBody xs =
-    braces . separateTight !semiD =<< traverse prettyCaseArm xs
+  prettyCaseBody : List (CaseArm opts d n) -> Eff Pretty (List (Doc opts))
+  prettyCaseBody xs = traverse prettyCaseArm xs
 
 private
 prettyCompPat : {opts : _} -> DimConst -> BindName -> Eff Pretty (Doc opts)
@@ -283,16 +272,12 @@ layoutComp typq val r arms = do
       [typq, [val, r <++> lb], map (indent ind) arms, [rb]])
 
 
-export
-prettyTag : {opts : _} -> String -> Eff Pretty (Doc opts)
-prettyTag tag = hl Tag $ text $ "'" ++ quoteTag tag
-
 export
 prettyEnum : {opts : _} -> List String -> Eff Pretty (Doc opts)
 prettyEnum cases =
   tightBraces =<<
   fillSeparateTight !commaD <$>
-  traverse (hl Tag . Doc.text . quoteTag) cases
+  traverse (hl Constant . Doc.text . quoteTag) cases
 
 private
 prettyCaseRet : {opts : _} ->
@@ -303,7 +288,7 @@ prettyCaseRet dnames tnames body = withPrec Outer $ case body of
   S [< x] (Y tm) => do
     header <- [|prettyTBind x <++> darrowD|]
     body   <- assert_total prettyTerm dnames (tnames :< x) tm
-    pure $ hsep [header, body] <|> vsep [header, !(indentD body)]
+    hangDSingle header body
 
 private
 prettyCase_ : {opts : _} ->
@@ -311,10 +296,16 @@ prettyCase_ : {opts : _} ->
               Doc opts -> Elim d n -> ScopeTerm d n -> List (CaseArm opts d n) ->
               Eff Pretty (Doc opts)
 prettyCase_ dnames tnames intro head ret body = do
-  head <- assert_total prettyElim dnames tnames head
-  ret  <- prettyCaseRet dnames tnames ret
-  body <- prettyCaseBody dnames tnames body
-  parensIfM Outer $ sep [intro <++> head, !returnD <++> ret, !ofD <++> body]
+  head   <- withPrec Outer $ assert_total prettyElim dnames tnames head
+  ret    <- prettyCaseRet dnames tnames ret
+  bodys  <- prettyCaseBody dnames tnames body
+  return <- returnD; of_ <- ofD
+  lb     <- hl Delim "{"; rb <- hl Delim "}"; semi <- semiD
+  ind    <- askAt INDENT
+  parensIfM Outer $ ifMultiline
+    (hsep [intro, head, return, ret, of_, lb, hseparateTight semi bodys, rb])
+    (vsep [intro <++> head, return <++> ret, of_ <++> lb,
+           indent ind $ vseparateTight semi bodys, rb])
 
 private
 prettyCase : {opts : _} ->
@@ -325,6 +316,62 @@ prettyCase dnames tnames qty head ret body =
   prettyCase_ dnames tnames ![|caseD <+> prettyQty qty|] head ret body
 
 
+private
+LetBinder : Nat -> Nat -> Type
+LetBinder d n = (Qty, BindName, Elim d n)
+
+private
+LetExpr : Nat -> Nat -> Nat -> Type
+LetExpr d n n' = (Telescope (LetBinder d) n n', Term d n')
+
+-- [todo] factor out this and the untyped version somehow
+export
+splitLet : Telescope (LetBinder d) n n' -> Term d n' -> Exists (LetExpr d n)
+splitLet ys t@(Let qty rhs body _) =
+  splitLet (ys :< (qty, body.name, rhs)) (assert_smaller t body.term)
+splitLet ys t =
+  Evidence _ (ys, t)
+
+private covering
+prettyLets : {opts : LayoutOpts} ->
+             BContext d -> BContext a -> Telescope (LetBinder d) a b ->
+             Eff Pretty (SnocList (Doc opts))
+prettyLets dnames xs lets = snd <$> go lets where
+  peelAnn : forall d, n. Elim d n -> Maybe (Term d n, Term d n)
+  peelAnn (Ann tm ty _) = Just (tm, ty)
+  peelAnn e             = Nothing
+
+  letHeader : Qty -> BindName -> Eff Pretty (Doc opts)
+  letHeader qty x = do
+    lett <- [|letD <+> prettyQty qty|]
+    x    <- prettyTBind x
+    pure $ lett <++> x
+
+  letBody : forall n. BContext n ->
+            Doc opts -> Elim d n -> Eff Pretty (Doc opts)
+  letBody tnames hdr e = case peelAnn e of
+    Just (tm, ty) => do
+      ty <- withPrec Outer $ assert_total prettyTerm dnames tnames ty
+      tm <- withPrec Outer $ assert_total prettyTerm dnames tnames tm
+      colon <- colonD; eq <- cstD; d <- askAt INDENT
+      pure $ hangSingle d (hangSingle d hdr (colon <++> ty)) (eq <++> tm)
+    Nothing => do
+      e <- withPrec Outer $ assert_total prettyElim dnames tnames e
+      eq <- cstD; d <- askAt INDENT
+      inn <- inD
+      pure $ ifMultiline
+        (hsep [hdr, eq, e, inn])
+        (vsep [hdr, indent d $ hsep [eq, e, inn]])
+
+  go : forall b. Telescope (LetBinder d) a b ->
+       Eff Pretty (BContext b, SnocList (Doc opts))
+  go [<] = pure (xs, [<])
+  go (lets :< (qty, x, rhs)) = do
+    (ys, docs) <- go lets
+    doc        <- letBody ys !(letHeader qty x) rhs
+    pure (ys :< x, docs :< doc)
+
+
 private
 isDefaultDir : Dim d -> Dim d -> Bool
 isDefaultDir (K Zero _) (K One _) = True
@@ -342,6 +389,7 @@ prettyTyCasePat : {opts : _} ->
                   (k : TyConKind) -> BContext (arity k) ->
                   Eff Pretty (Doc opts)
 prettyTyCasePat KTYPE [<] = typeD
+prettyTyCasePat KIOState [<] = ioStateD
 prettyTyCasePat KPi [< a, b] =
   parens . hsep =<< sequence [prettyTBind a, arrowD, prettyTBind b]
 prettyTyCasePat KSig [< a, b] =
@@ -350,6 +398,7 @@ prettyTyCasePat KEnum [<] = hl Syntax $ text "{}"
 prettyTyCasePat KEq [< a0, a1, a, l, r] =
   hsep <$> sequence (eqD :: map prettyTBind [a0, a1, a, l, r])
 prettyTyCasePat KNat [<] = natD
+prettyTyCasePat KString [<] = stringD
 prettyTyCasePat KBOX [< a] = bracks =<< prettyTBind a
 
 
@@ -383,13 +432,13 @@ prettyDisp u = map Just $ hl Universe =<<
   ifUnicode (text $ superscript $ show u) (text $ "^" ++ show u)
 
 
-prettyTerm dnames tnames (TYPE l _) =
-  case !(askAt FLAVOR) of
-    Unicode => do
-      star  <- hl Syntax "★"
-      level <- hl Universe $ text $ superscript $ show l
-      pure $ hcat [star, level]
-    Ascii   => [|hl Syntax "Type" <++> hl Universe (text $ show l)|]
+prettyTerm dnames tnames (TYPE l _) = do
+  type  <- hl Syntax . text =<< ifUnicode "★" "Type"
+  level <- prettyDisp l
+  pure $ maybe type (type <+>) level
+
+prettyTerm dnames tnames (IOState _) =
+  ioStateD
 
 prettyTerm dnames tnames (Pi qty arg res _) =
   parensIfM Outer =<< do
@@ -426,35 +475,31 @@ prettyTerm dnames tnames (Enum cases _) =
 prettyTerm dnames tnames (Tag tag _) =
   prettyTag tag
 
-prettyTerm dnames tnames (Eq (S _ (N ty)) l r _) = do
-  l  <- withPrec InEq $ prettyTerm dnames tnames l
-  r  <- withPrec InEq $ prettyTerm dnames tnames r
-  ty <- withPrec InEq $ prettyTerm dnames tnames ty
-  pure $ sep [l <++> !eqndD, r <++> !colonD, ty]
+prettyTerm dnames tnames (Eq (S _ (N ty)) l r _) =
+  parensIfM Eq =<< do
+    l  <- withPrec InEq $ prettyTerm dnames tnames l
+    r  <- withPrec InEq $ prettyTerm dnames tnames r
+    ty <- withPrec InEq $ prettyTerm dnames tnames ty
+    pure $ sep [l <++> !eqndD, r <++> !colonD, ty]
 
-prettyTerm dnames tnames (Eq ty l r _) = do
-  ty <- prettyTypeLine dnames tnames ty
-  l  <- withPrec Arg $ prettyTerm dnames tnames l
-  r  <- withPrec Arg $ prettyTerm dnames tnames r
-  prettyAppD !eqD [ty, l, r]
+prettyTerm dnames tnames (Eq ty l r _) =
+  parensIfM App =<< do
+    ty <- prettyTypeLine dnames tnames ty
+    l  <- withPrec Arg $ prettyTerm dnames tnames l
+    r  <- withPrec Arg $ prettyTerm dnames tnames r
+    prettyAppD !eqD [ty, l, r]
 
 prettyTerm dnames tnames s@(DLam {}) =
   prettyLambda dnames tnames s
 
-prettyTerm dnames tnames (Nat _) = natD
-prettyTerm dnames tnames (Zero _) = hl Syntax "0"
-prettyTerm dnames tnames (Succ p _) = do
-  succD <- succD
-  let succ : Doc opts -> Eff Pretty (Doc opts)
-      succ t = prettyAppD succD [t]
-      toNat : Term d n -> Eff Pretty (Either (Doc opts) Nat)
-      toNat s with (pushSubsts' s)
-        _ | Zero _   = pure $ Right 0
-        _ | Succ d _ = bitraverse succ (pure . S) =<<
-                       toNat (assert_smaller s d)
-        _ | s'       = map Left . withPrec Arg $
-                       prettyTerm dnames tnames $ assert_smaller s s'
-  either succ (hl Syntax . text . show . S) =<< toNat p
+prettyTerm dnames tnames (NAT _) = natD
+prettyTerm dnames tnames (Nat n _) = hl Syntax $ pshow n
+prettyTerm dnames tnames (Succ p _) =
+  parensIfM App =<<
+  prettyAppD !succD [!(withPrec Arg $ prettyTerm dnames tnames p)]
+
+prettyTerm dnames tnames (STRING _) = stringD
+prettyTerm dnames tnames (Str s _) = prettyStrLit s
 
 prettyTerm dnames tnames (BOX qty ty _) =
   bracks . hcat =<<
@@ -464,7 +509,18 @@ prettyTerm dnames tnames (BOX qty ty _) =
 prettyTerm dnames tnames (Box val _) =
   bracks =<< withPrec Outer (prettyTerm dnames tnames val)
 
-prettyTerm dnames tnames (E e) = prettyElim dnames tnames e
+prettyTerm dnames tnames (Let qty rhs body _) = do
+  let Evidence _ (lets, body) = splitLet [< (qty, body.name, rhs)] body.term
+  heads <- prettyLets dnames tnames lets
+  let tnames = tnames . map (\(_, x, _) => x) lets
+  body <- withPrec Outer $ assert_total prettyTerm dnames tnames body
+  let lines = toList $ heads :< body
+  pure $ ifMultiline (hsep lines) (vsep lines)
+
+prettyTerm dnames tnames (E e) =
+  case the (Elim d n) (pushSubsts' e) of
+    Ann tm _ _ => assert_total prettyTerm dnames tnames tm
+    _          => assert_total prettyElim dnames tnames e
 
 prettyTerm dnames tnames t0@(CloT (Sub t ph)) =
   prettyTerm dnames tnames $ assert_smaller t0 $ pushSubstsWith' id ph t
@@ -491,6 +547,16 @@ prettyElim dnames tnames (CasePair qty pair ret body _) = do
   prettyCase dnames tnames qty pair ret
     [MkCaseArm pat [<] [< x, y] body.term]
 
+prettyElim dnames tnames (Fst pair _) =
+  parensIfM App =<< do
+    pair <- prettyTArg dnames tnames (E pair)
+    prettyAppD !fstD [pair]
+
+prettyElim dnames tnames (Snd pair _) =
+  parensIfM App =<< do
+    pair <- prettyTArg dnames tnames (E pair)
+    prettyAppD !sndD [pair]
+
 prettyElim dnames tnames (CaseEnum qty tag ret arms _) = do
   arms <- for (SortedMap.toList arms) $ \(tag, body) =>
     pure $ MkCaseArm !(prettyTag tag) [<] [<] body
@@ -501,7 +567,7 @@ prettyElim dnames tnames (CaseNat qty qtyIH nat ret zero succ _) = do
       [< p, ih] = succ.names
   spat0 <- [|succD <++> prettyTBind p|]
   ihpat0 <- map hcat $ sequence [prettyQty qtyIH, dotD, prettyTBind ih]
-  spat <- if ih.name == Unused
+  spat <- if ih.val == Unused
           then pure spat0
           else pure $ hsep [spat0 <+> !commaD, ihpat0]
   let sarm = MkCaseArm spat [<] [< p, ih] succ.term
@@ -517,35 +583,31 @@ prettyElim dnames tnames e@(DApp {}) =
   prettyDTApps dnames tnames f xs
 
 prettyElim dnames tnames (Ann tm ty _) =
-  parensIfM Outer =<<
-    hangDSingle !(withPrec AnnL  [|prettyTerm dnames tnames tm <++> annD|])
-                !(withPrec Outer (prettyTerm dnames tnames ty))
+  case the (Term d n) (pushSubsts' tm) of
+    E e => assert_total prettyElim dnames tnames e
+    _   => do
+      tm <- withPrec AnnL  $ assert_total prettyTerm dnames tnames tm
+      ty <- withPrec Outer $ assert_total prettyTerm dnames tnames ty
+      parensIfM Outer =<< hangDSingle (tm <++> !annD) ty
 
 prettyElim dnames tnames (Coe ty p q val _) =
-  parensIfM App =<<
-    if isDefaultDir p q then do
-      ty  <- prettyTypeLine dnames tnames ty
-      val <- prettyTArg dnames tnames val
-      prettyAppD !coeD [ty, val]
-    else do
-      ty  <- prettyTypeLine dnames tnames ty
-      p   <- prettyDArg dnames p
-      q   <- prettyDArg dnames q
-      val <- prettyTArg dnames tnames val
-      prettyAppD !coeD [ty, sep [p, q], val]
+  parensIfM App =<< do
+    ty  <- prettyTypeLine dnames tnames ty
+    p   <- prettyDArg dnames p
+    q   <- prettyDArg dnames q
+    val <- prettyTArg dnames tnames val
+    prettyAppD !coeD [ty, sep [p, q], val]
 
 prettyElim dnames tnames e@(Comp ty p q val r zero one _) =
   parensIfM App =<< do
-    ty   <- prettyTypeLine dnames tnames $ assert_smaller e $ SN ty
+    ty   <- assert_total $ prettyTypeLine dnames tnames $ SN ty
     pq   <- sep <$> sequence [prettyDArg dnames p, prettyDArg dnames q]
     val  <- prettyTArg dnames tnames val
     r    <- prettyDArg dnames r
     arm0 <- [|prettyCompArm dnames tnames Zero zero <+> semiD|]
     arm1 <- prettyCompArm dnames tnames One one
     ind  <- askAt INDENT
-    if isDefaultDir p q
-       then layoutComp [ty]     val r [arm0, arm1]
-       else layoutComp [ty, pq] val r [arm0, arm1]
+    layoutComp [ty, pq] val r [arm0, arm1]
 
 prettyElim dnames tnames (TypeCase ty ret arms def _) = do
   arms <- for (toList arms) $ \(k ** body) => do

lib/Quox/Syntax/Term/Subst.idr

@@ -2,462 +2,383 @@ module Quox.Syntax.Term.Subst
 
 import Quox.No
 import Quox.Syntax.Term.Base
-import Quox.Syntax.Subst
-
 import Data.SnocVect
-import Data.Singleton
 
 %default total
 
+namespace CanDSubst
+  public export
+  interface CanDSubst (0 tm : TermLike) where
+    (//) : tm d1 n -> Lazy (DSubst d1 d2) -> tm d2 n
 
-infixl 8 ///
+||| does the minimal reasonable work:
+||| - deletes the closure around an atomic constant like `TYPE`
+||| - deletes an identity substitution
+||| - composes (lazily) with an existing top-level dim-closure
+||| - otherwise, wraps in a new closure
+export
+CanDSubst Term where
+  s                // Shift SZ = s
+  TYPE l loc       // _        = TYPE l loc
+  DCloT (Sub s ph) // th       = DCloT $ Sub s $ ph . th
+  s                // th       = DCloT $ Sub s th
 
-parameters {0 f : Nat -> Nat -> Type}
-  private
-  th0 : f 0 0 -> Thinned2 f d n
-  th0 = Th2 zero zero
+private
+subDArgs : Elim d1 n -> DSubst d1 d2 -> Elim d2 n
+subDArgs (DApp f d loc) th = DApp (subDArgs f th) (d // th) loc
+subDArgs e              th = DCloE $ Sub e th
 
-  private
-  th1 : {d, n : Nat} -> f d n -> Thinned2 f d n
-  th1 = Th2 id' id'
+||| does the minimal reasonable work:
+||| - deletes the closure around a term variable
+||| - deletes an identity substitution
+||| - composes (lazily) with an existing top-level dim-closure
+||| - immediately looks up bound variables in a
+|||   top-level sequence of dimension applications
+||| - otherwise, wraps in a new closure
+export
+CanDSubst Elim where
+  e                // Shift SZ = e
+  F x u loc        // _        = F x u loc
+  B i loc          // _        = B i loc
+  e@(DApp {})      // th       = subDArgs e th
+  DCloE (Sub e ph) // th       = DCloE $ Sub e $ ph . th
+  e                // th       = DCloE $ Sub e th
 
-private dsubTerm : {d1, d2, n : Nat} -> Term d1 n -> DSubst d1 d2 -> TermT d2 n
-private dsubElim : {d1, d2, n : Nat} -> Elim d1 n -> DSubst d1 d2 -> ElimT d2 n
+namespace DSubst.ScopeTermN
+  export %inline
+  (//) : ScopeTermN s d1 n -> Lazy (DSubst d1 d2) ->
+         ScopeTermN s d2 n
+  S ns (Y body) // th = S ns $ Y $ body // th
+  S ns (N body) // th = S ns $ N $ body // th
 
-dsubTerm (TYPE l loc) th = th0 $ TYPE l loc
-dsubTerm (Enum strs loc) th = th0 $ Enum strs loc
-dsubTerm (Tag str loc) th = th0 $ Tag str loc
-dsubTerm (Nat loc) th = th0 $ Nat loc
-dsubTerm (Zero loc) th = th0 $ Zero loc
-dsubTerm (E e) th =
-  let Th2 dope tope e' = dsubElim e th in
-  Th2 dope tope $ E e'
-dsubTerm (DCloT (Sub t ph)) th = th1 $ DCloT $ Sub t $ ph . th
-dsubTerm t th = th1 $ DCloT $ Sub t th
+namespace DSubst.DScopeTermN
+  export %inline
+  (//) : {s : Nat} ->
+         DScopeTermN s d1 n -> Lazy (DSubst d1 d2) ->
+         DScopeTermN s d2 n
+  S ns (Y body) // th = S ns $ Y $ body // pushN s (locs $ toList' ns) th
+  S ns (N body) // th = S ns $ N $ body // th
 
-dsubElim (F x l loc) th = th0 $ F x l loc
-dsubElim (B loc) th = Th2 zero id' $ B loc
-dsubElim (DCloE (Sub e ph)) th = th1 $ DCloE $ Sub e $ ph . th
-dsubElim e th = th1 $ DCloE $ Sub e th
 
-mutual
-  namespace Term
-    export
-    (///) : {d1, d2, n : Nat} -> TermT d1 n -> DSubst d1 d2 -> TermT d2 n
-    Th2 dope tope term /// th =
-      let Val tscope = appOpe n tope; Val dscope = appOpe d1 dope
-          Th2 dope' tope' term' = dsubTerm term (select dope th)
-      in
-      Th2 dope' (tope . tope') term'
+export %inline FromVar (Elim d) where fromVarLoc = B
+export %inline FromVar (Term d) where fromVarLoc = E .: fromVarLoc
 
-  namespace Elim
-    export
-    (///) : {d1, d2, n : Nat} -> ElimT d1 n -> DSubst d1 d2 -> ElimT d2 n
-    Th2 dope tope elim /// th =
-      let Val tscope = appOpe n tope; Val dscope = appOpe d1 dope
-          Th2 dope' tope' elim' = dsubElim elim (select dope th)
-      in
-      Th2 dope' (tope . tope') elim'
+
+||| does the minimal reasonable work:
+||| - deletes the closure around a *free* name
+||| - deletes an identity substitution
+||| - composes (lazily) with an existing top-level closure
+||| - immediately looks up a bound variable
+||| - otherwise, wraps in a new closure
+export
+CanSubstSelf (Elim d) where
+  F x u loc       // _  = F x u loc
+  B i loc         // th = getLoc th i loc
+  CloE (Sub e ph) // th = assert_total CloE $ Sub e $ ph . th
+  e               // th = case force th of
+                               Shift SZ => e
+                               th       => CloE $ Sub e th
+
+namespace CanTSubst
+  public export
+  interface CanTSubst (0 tm : TermLike) where
+    (//) : tm d n1 -> Lazy (TSubst d n1 n2) -> tm d n2
+
+||| does the minimal reasonable work:
+||| - deletes the closure around an atomic constant like `TYPE`
+||| - deletes an identity substitution
+||| - composes (lazily) with an existing top-level closure
+||| - goes inside `E` in case it is a simple variable or something
+||| - otherwise, wraps in a new closure
+export
+CanTSubst Term where
+  TYPE l loc      // _  = TYPE l loc
+  E e             // th = E $ e // th
+  CloT (Sub s ph) // th = CloT $ Sub s $ ph . th
+  s               // th = case force th of
+                               Shift SZ => s
+                               th       => CloT $ Sub s th
+
+namespace ScopeTermN
+  export %inline
+  (//) : {s : Nat} ->
+         ScopeTermN s d n1 -> Lazy (TSubst d n1 n2) ->
+         ScopeTermN s d n2
+  S ns (Y body) // th = S ns $ Y $ body // pushN s (locs $ toList' ns) th
+  S ns (N body) // th = S ns $ N $ body // th
+
+namespace DScopeTermN
+  export %inline
+  (//) : {s : Nat} ->
+         DScopeTermN s d n1 -> Lazy (TSubst d n1 n2) -> DScopeTermN s d n2
+  S ns (Y body) // th = S ns $ Y $ body // map (// shift s) th
+  S ns (N body) // th = S ns $ N $ body // th
+
+export %inline CanShift (Term d) where s // by = s // Shift by
+export %inline CanShift (Elim d) where e // by = e // Shift by
+
+export %inline CanShift (flip Term n) where s // by = s // Shift by
+export %inline CanShift (flip Elim n) where e // by = e // Shift by
+
+export %inline
+{s : Nat} -> CanShift (ScopeTermN s d) where
+  b // by = b // Shift by
+
+
+export %inline
+comp : DSubst d1 d2 -> TSubst d1 n1 mid -> TSubst d2 mid n2 -> TSubst d2 n1 n2
+comp th ps ph = map (// th) ps . ph
+
+
+public export %inline
+dweakT : (by : Nat) -> Term d n -> Term (by + d) n
+dweakT by t = t // shift by
+
+public export %inline
+dweakS : (by : Nat) -> ScopeTermN s d n -> ScopeTermN s (by + d) n
+dweakS by t = t // shift by
+
+public export %inline
+dweakDS : {s : Nat} -> (by : Nat) ->
+          DScopeTermN s d n -> DScopeTermN s (by + d) n
+dweakDS by t = t // shift by
+
+public export %inline
+dweakE : (by : Nat) -> Elim d n -> Elim (by + d) n
+dweakE by t = t // shift by
+
+
+public export %inline
+weakT : (by : Nat) -> Term d n -> Term d (by + n)
+weakT by t = t // shift by
+
+public export %inline
+weakS : {s : Nat} -> (by : Nat) -> ScopeTermN s d n -> ScopeTermN s d (by + n)
+weakS by t = t // shift by
+
+public export %inline
+weakDS : {s : Nat} -> (by : Nat) ->
+         DScopeTermN s d n -> DScopeTermN s d (by + n)
+weakDS by t = t // shift by
+
+public export %inline
+weakE : (by : Nat) -> Elim d n -> Elim d (by + n)
+weakE by t = t // shift by
+
+
+parameters {auto _ : CanShift f} {s : Nat}
+  export %inline
+  getTerm : ScopedBody s f n -> f (s + n)
+  getTerm (Y b) = b
+  getTerm (N b) = b // fromNat s
+
+  export %inline
+  (.term) : Scoped s f n -> f (s + n)
+  t.term = getTerm t.body
+
+namespace ScopeTermBody
+  export %inline
+  getTerm0 : ScopedBody 0 f n -> f n
+  getTerm0 (Y b) = b
+  getTerm0 (N b) = b
+
+namespace ScopeTermN
+  export %inline
+  (.term0) : Scoped 0 f n -> f n
+  t.term0 = getTerm0 t.body
+
+export %inline
+subN : ScopeTermN s d n -> SnocVect s (Elim d n) -> Term d n
+subN (S _ (Y body)) es = body // fromSnocVect es
+subN (S _ (N body)) _  = body
+
+export %inline
+sub1 : ScopeTerm d n -> Elim d n -> Term d n
+sub1 t e = subN t [< e]
+
+export %inline
+dsubN : DScopeTermN s d n -> SnocVect s (Dim d) -> Term d n
+dsubN (S _ (Y body)) ps = body // fromSnocVect ps
+dsubN (S _ (N body)) _  = body
+
+export %inline
+dsub1 : DScopeTerm d n -> Dim d -> Term d n
+dsub1 t p = dsubN t [< p]
+
+
+public export %inline
+(.zero) : (body : DScopeTerm d n) -> {default body.loc loc : Loc} -> Term d n
+body.zero = dsub1 body $ K Zero loc
+
+public export %inline
+(.one) : (body : DScopeTerm d n) -> {default body.loc loc : Loc} -> Term d n
+body.one = dsub1 body $ K One loc
 
 
 public export
-TSubst : Nat -> Nat -> Nat -> Type
-TSubst = Subst2 Elim
+0 CloTest : TermLike -> Type
+CloTest tm = forall d, n. tm d n -> Bool
 
+public export
+interface PushSubsts (0 tm : TermLike) (0 isClo : CloTest tm) | tm where
+  pushSubstsWith : DSubst d1 d2 -> TSubst d2 n1 n2 ->
+                   tm d1 n1 -> Subset (tm d2 n2) (No . isClo)
 
-public export %inline FromVar (Elim 0) where var = B
+public export
+0 NotClo : {isClo : CloTest tm} -> PushSubsts tm isClo => Pred (tm d n)
+NotClo = No . isClo
 
-export CanSubstSelf2 Elim
+public export
+0 NonClo : (tm : TermLike) -> {isClo : CloTest tm} ->
+           PushSubsts tm isClo => TermLike
+NonClo tm d n = Subset (tm d n) NotClo
 
-private subTerm : {d, n1, n2 : Nat} -> Term d n1 -> TSubst d n1 n2 -> TermT d n2
-private subElim : {d, n1, n2 : Nat} -> Elim d n1 -> TSubst d n1 n2 -> ElimT d n2
+public export %inline
+nclo : {isClo : CloTest tm} -> (0 _ : PushSubsts tm isClo) =>
+       (t : tm d n) -> (0 nc : NotClo t) => NonClo tm d n
+nclo t = Element t nc
 
-subTerm (TYPE l loc) th = th0 $ TYPE l loc
-subTerm (Nat loc) th = th0 $ Nat loc
-subTerm (Zero loc) th = th0 $ Zero loc
-subTerm (E e) th = let Th2 dope tope e' = subElim e th in Th2 dope tope $ E e'
-subTerm (CloT (Sub2 s ph)) th = th1 $ CloT $ Sub2 s $ ph .% th
-subTerm s th = th1 $ CloT $ Sub2 s th
+parameters {0 isClo : CloTest tm} {auto _ : PushSubsts tm isClo}
+  ||| if the input term has any top-level closures, push them under one layer of
+  ||| syntax
+  export %inline
+  pushSubsts : tm d n -> NonClo tm d n
+  pushSubsts s = pushSubstsWith id id s
 
-subElim (F x k loc) th = th0 $ F x k loc
-subElim (B loc) [< e] = e
-subElim (CloE (Sub2 e ph)) th = th1 $ CloE $ Sub2 e $ ph .% th
-subElim e th = th1 $ CloE $ Sub2 e th
+  export %inline
+  pushSubstsWith' : DSubst d1 d2 -> TSubst d2 n1 n2 -> tm d1 n1 -> tm d2 n2
+  pushSubstsWith' th ph x = fst $ pushSubstsWith th ph x
 
+  export %inline
+  pushSubsts' : tm d n -> tm d n
+  pushSubsts' s = fst $ pushSubsts s
 
+mutual
+  public export
+  isCloT : CloTest Term
+  isCloT (CloT  {}) = True
+  isCloT (DCloT {}) = True
+  isCloT (E e)      = isCloE e
+  isCloT _          = False
+
+  public export
+  isCloE : CloTest Elim
+  isCloE (CloE  {}) = True
+  isCloE (DCloE {}) = True
+  isCloE _          = False
 
 export
-CanSubstSelf2 Elim where
-  Th2 dope tope elim // th =
-    let
-        th' = select tope th
-    in
-    ?sube2
+PushSubsts Elim Subst.isCloE where
+  pushSubstsWith th ph (F x u loc) =
+    nclo $ F x u loc
+  pushSubstsWith th ph (B i loc) =
+    let res = getLoc ph i loc in
+    case nchoose $ isCloE res of
+      Left  yes => assert_total pushSubsts res
+      Right no  => Element res no
+  pushSubstsWith th ph (App f s loc) =
+    nclo $ App (f // th // ph) (s // th // ph) loc
+  pushSubstsWith th ph (CasePair pi p r b loc) =
+    nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph) loc
+  pushSubstsWith th ph (Fst pair loc) =
+    nclo $ Fst (pair // th // ph) loc
+  pushSubstsWith th ph (Snd pair loc) =
+    nclo $ Snd (pair // th // ph) loc
+  pushSubstsWith th ph (CaseEnum pi t r arms loc) =
+    nclo $ CaseEnum pi (t // th // ph) (r // th // ph)
+             (map (\b => b // th // ph) arms) loc
+  pushSubstsWith th ph (CaseNat pi pi' n r z s loc) =
+    nclo $ CaseNat pi pi' (n // th // ph) (r // th // ph)
+             (z // th // ph) (s // th // ph) loc
+  pushSubstsWith th ph (CaseBox pi x r b loc) =
+    nclo $ CaseBox pi (x // th // ph) (r // th // ph) (b // th // ph) loc
+  pushSubstsWith th ph (DApp f d loc) =
+    nclo $ DApp (f // th // ph) (d // th) loc
+  pushSubstsWith th ph (Ann s a loc) =
+    nclo $ Ann (s // th // ph) (a // th // ph) loc
+  pushSubstsWith th ph (Coe ty p q val loc) =
+    nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph) loc
+  pushSubstsWith th ph (Comp ty p q val r zero one loc) =
+    nclo $ Comp (ty // th // ph) (p // th) (q // th)
+                (val // th // ph) (r // th)
+                (zero // th // ph) (one // th // ph) loc
+  pushSubstsWith th ph (TypeCase ty ret arms def loc) =
+    nclo $ TypeCase (ty // th // ph) (ret  // th // ph)
+      (map (\t => t // th // ph) arms) (def // th // ph) loc
+  pushSubstsWith th ph (CloE (Sub e ps)) =
+    pushSubstsWith th (comp th ps ph) e
+  pushSubstsWith th ph (DCloE (Sub e ps)) =
+    pushSubstsWith (ps . th) ph e
 
--- namespace CanDSubst
---   public export
---   interface CanDSubst (0 tm : TermLike) where
---     (//) : {d1 : Nat} -> Thinned2 tm d1 n -> Lazy (DSubst d1 d2) ->
---            Thinned2 tm d2 n
-
--- ||| does the minimal reasonable work:
--- ||| - deletes the closure around an atomic constant like `TYPE`
--- ||| - deletes an identity substitution
--- ||| - composes (lazily) with an existing top-level dim-closure
--- ||| - otherwise, wraps in a new closure
--- export
--- CanDSubst Term where
---   Th2 _ _ (TYPE l loc)       // _        = Th2 zero zero $ TYPE l loc
---   Th2 i j (DCloT (Sub s ph)) // th       =
---     Th2 ?i' j $ DCloT $ Sub s $ ph . ?th'
---   Th2 i j s                  // th       = ?sdf -- DCloT $ Sub s th
-
--- -- private
--- -- subDArgs : Elim d1 n -> DSubst d1 d2 -> Elim d2 n
--- -- subDArgs (DApp f d loc) th = DApp (subDArgs f th) (d // th) loc
--- -- subDArgs e              th = DCloE $ Sub e th
-
--- -- ||| does the minimal reasonable work:
--- -- ||| - deletes the closure around a term variable
--- -- ||| - deletes an identity substitution
--- -- ||| - composes (lazily) with an existing top-level dim-closure
--- -- ||| - immediately looks up bound variables in a
--- -- |||   top-level sequence of dimension applications
--- -- ||| - otherwise, wraps in a new closure
--- -- export
--- -- CanDSubst Elim where
--- --   e                // Shift SZ = e
--- --   F x u loc        // _        = F x u loc
--- --   B i loc          // _        = B i loc
--- --   e@(DApp {})      // th       = subDArgs e th
--- --   DCloE (Sub e ph) // th       = DCloE $ Sub e $ ph . th
--- --   e                // th       = DCloE $ Sub e th
-
--- -- namespace DSubst.ScopeTermN
--- --   export %inline
--- --   (//) : ScopeTermN s d1 n -> Lazy (DSubst d1 d2) ->
--- --          ScopeTermN s d2 n
--- --   S ns (Y body) // th = S ns $ Y $ body // th
--- --   S ns (N body) // th = S ns $ N $ body // th
-
--- -- namespace DSubst.DScopeTermN
--- --   export %inline
--- --   (//) : {s : Nat} ->
--- --          DScopeTermN s d1 n -> Lazy (DSubst d1 d2) ->
--- --          DScopeTermN s d2 n
--- --   S ns (Y body) // th = S ns $ Y $ body // pushN s th
--- --   S ns (N body) // th = S ns $ N $ body // th
+export
+PushSubsts Term Subst.isCloT where
+  pushSubstsWith th ph (TYPE l loc) =
+    nclo $ TYPE l loc
+  pushSubstsWith th ph (IOState loc) =
+    nclo $ IOState loc
+  pushSubstsWith th ph (Pi qty a body loc) =
+    nclo $ Pi qty (a // th // ph) (body // th // ph) loc
+  pushSubstsWith th ph (Lam body loc) =
+    nclo $ Lam (body // th // ph) loc
+  pushSubstsWith th ph (Sig a b loc) =
+    nclo $ Sig (a // th // ph) (b // th // ph) loc
+  pushSubstsWith th ph (Pair s t loc) =
+    nclo $ Pair (s // th // ph) (t // th // ph) loc
+  pushSubstsWith th ph (Enum tags loc) =
+    nclo $ Enum tags loc
+  pushSubstsWith th ph (Tag tag loc) =
+    nclo $ Tag tag loc
+  pushSubstsWith th ph (Eq ty l r loc) =
+    nclo $ Eq (ty // th // ph) (l // th // ph) (r // th // ph) loc
+  pushSubstsWith th ph (DLam body loc) =
+    nclo $ DLam (body // th // ph) loc
+  pushSubstsWith _ _ (NAT loc) =
+    nclo $ NAT loc
+  pushSubstsWith _ _ (Nat n loc) =
+    nclo $ Nat n loc
+  pushSubstsWith th ph (Succ n loc) =
+    nclo $ Succ (n // th // ph) loc
+  pushSubstsWith _ _ (STRING loc) =
+    nclo $ STRING loc
+  pushSubstsWith _ _ (Str s loc) =
+    nclo $ Str s loc
+  pushSubstsWith th ph (BOX pi ty loc) =
+    nclo $ BOX pi (ty // th // ph) loc
+  pushSubstsWith th ph (Box val loc) =
+    nclo $ Box (val // th // ph) loc
+  pushSubstsWith th ph (E e) =
+    let Element e nc = pushSubstsWith th ph e in nclo $ E e
+  pushSubstsWith th ph (Let qty rhs body loc) =
+    nclo $ Let qty (rhs // th // ph) (body // th // ph) loc
+  pushSubstsWith th ph (CloT (Sub s ps)) =
+    pushSubstsWith th (comp th ps ph) s
+  pushSubstsWith th ph (DCloT (Sub s ps)) =
+    pushSubstsWith (ps . th) ph s
 
 
--- -- export %inline FromVar (Elim d) where fromVarLoc = B
--- -- export %inline FromVar (Term d) where fromVarLoc = E .: fromVar
+||| heterogeneous comp, in terms of Comp and Coe
+public export %inline
+CompH' : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
+         (r : Dim d) -> (zero, one : DScopeTerm d n) -> (loc : Loc) -> Elim d n
+CompH' {ty, p, q, val, r, zero, one, loc} =
+  let ty' = SY ty.names $ ty.term // (B VZ ty.name.loc ::: shift 2) in
+  Comp {
+    ty = dsub1 ty q, p, q,
+    val = E $ Coe ty p q val val.loc, r,
+    zero = SY zero.names $ E $
+      Coe ty' (B VZ zero.loc) (weakD 1 q) zero.term zero.loc,
+    one = SY one.names $ E $
+      Coe ty' (B VZ one.loc) (weakD 1 q) one.term one.loc,
+    loc
+  }
 
-
--- -- ||| does the minimal reasonable work:
--- -- ||| - deletes the closure around a *free* name
--- -- ||| - deletes an identity substitution
--- -- ||| - composes (lazily) with an existing top-level closure
--- -- ||| - immediately looks up a bound variable
--- -- ||| - otherwise, wraps in a new closure
--- -- export
--- -- CanSubstSelf (Elim d) where
--- --   F x u loc       // _  = F x u loc
--- --   B i loc         // th = getLoc th i loc
--- --   CloE (Sub e ph) // th = assert_total CloE $ Sub e $ ph . th
--- --   e               // th = case force th of
--- --                                Shift SZ => e
--- --                                th       => CloE $ Sub e th
-
--- -- namespace CanTSubst
--- --   public export
--- --   interface CanTSubst (0 tm : TermLike) where
--- --     (//) : tm d n1 -> Lazy (TSubst d n1 n2) -> tm d n2
-
--- -- ||| does the minimal reasonable work:
--- -- ||| - deletes the closure around an atomic constant like `TYPE`
--- -- ||| - deletes an identity substitution
--- -- ||| - composes (lazily) with an existing top-level closure
--- -- ||| - goes inside `E` in case it is a simple variable or something
--- -- ||| - otherwise, wraps in a new closure
--- -- export
--- -- CanTSubst Term where
--- --   TYPE l loc      // _  = TYPE l loc
--- --   E e             // th = E $ e // th
--- --   CloT (Sub s ph) // th = CloT $ Sub s $ ph . th
--- --   s               // th = case force th of
--- --                                Shift SZ => s
--- --                                th       => CloT $ Sub s th
-
--- -- namespace ScopeTermN
--- --   export %inline
--- --   (//) : {s : Nat} ->
--- --          ScopeTermN s d n1 -> Lazy (TSubst d n1 n2) ->
--- --          ScopeTermN s d n2
--- --   S ns (Y body) // th = S ns $ Y $ body // pushN s th
--- --   S ns (N body) // th = S ns $ N $ body // th
-
--- -- namespace DScopeTermN
--- --   export %inline
--- --   (//) : {s : Nat} ->
--- --          DScopeTermN s d n1 -> Lazy (TSubst d n1 n2) -> DScopeTermN s d n2
--- --   S ns (Y body) // th = S ns $ Y $ body // map (// shift s) th
--- --   S ns (N body) // th = S ns $ N $ body // th
-
--- -- export %inline CanShift (Term d) where s // by = s // Shift by
--- -- export %inline CanShift (Elim d) where e // by = e // Shift by
-
--- -- export %inline
--- -- {s : Nat} -> CanShift (ScopeTermN s d) where
--- --   b // by = b // Shift by
-
-
--- -- export %inline
--- -- comp : DSubst d1 d2 -> TSubst d1 n1 mid -> TSubst d2 mid n2 -> TSubst d2 n1 n2
--- -- comp th ps ph = map (// th) ps . ph
-
-
--- -- public export %inline
--- -- dweakT : (by : Nat) -> Term d n -> Term (by + d) n
--- -- dweakT by t = t // shift by
-
--- -- public export %inline
--- -- dweakE : (by : Nat) -> Elim d n -> Elim (by + d) n
--- -- dweakE by t = t // shift by
-
-
--- -- public export %inline
--- -- weakT : (by : Nat) -> Term d n -> Term d (by + n)
--- -- weakT by t = t // shift by
-
--- -- public export %inline
--- -- weakE : (by : Nat) -> Elim d n -> Elim d (by + n)
--- -- weakE by t = t // shift by
-
-
--- -- parameters {s : Nat}
--- --   namespace ScopeTermBody
--- --     export %inline
--- --     (.term) : ScopedBody s (Term d) n -> Term d (s + n)
--- --     (Y b).term = b
--- --     (N b).term = weakT s b
-
--- --   namespace ScopeTermN
--- --     export %inline
--- --     (.term) : ScopeTermN s d n -> Term d (s + n)
--- --     t.term = t.body.term
-
--- --   namespace DScopeTermBody
--- --     export %inline
--- --     (.term) : ScopedBody s (\d => Term d n) d -> Term (s + d) n
--- --     (Y b).term = b
--- --     (N b).term = dweakT s b
-
--- --   namespace DScopeTermN
--- --     export %inline
--- --     (.term) : DScopeTermN s d n -> Term (s + d) n
--- --     t.term = t.body.term
-
-
--- -- export %inline
--- -- subN : ScopeTermN s d n -> SnocVect s (Elim d n) -> Term d n
--- -- subN (S _ (Y body)) es = body // fromSnocVect es
--- -- subN (S _ (N body)) _  = body
-
--- -- export %inline
--- -- sub1 : ScopeTerm d n -> Elim d n -> Term d n
--- -- sub1 t e = subN t [< e]
-
--- -- export %inline
--- -- dsubN : DScopeTermN s d n -> SnocVect s (Dim d) -> Term d n
--- -- dsubN (S _ (Y body)) ps = body // fromSnocVect ps
--- -- dsubN (S _ (N body)) _  = body
-
--- -- export %inline
--- -- dsub1 : DScopeTerm d n -> Dim d -> Term d n
--- -- dsub1 t p = dsubN t [< p]
-
-
--- -- public export %inline
--- -- (.zero) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n
--- -- body.zero = dsub1 body $ K Zero loc
-
--- -- public export %inline
--- -- (.one) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n
--- -- body.one = dsub1 body $ K One loc
-
-
--- -- public export
--- -- 0 CloTest : TermLike -> Type
--- -- CloTest tm = forall d, n. tm d n -> Bool
-
--- -- interface PushSubsts (0 tm : TermLike) (0 isClo : CloTest tm) | tm where
--- --   pushSubstsWith : DSubst d1 d2 -> TSubst d2 n1 n2 ->
--- --                    tm d1 n1 -> Subset (tm d2 n2) (No . isClo)
-
--- -- public export
--- -- 0 NotClo : {isClo : CloTest tm} -> PushSubsts tm isClo => Pred (tm d n)
--- -- NotClo = No . isClo
-
--- -- public export
--- -- 0 NonClo : (tm : TermLike) -> {isClo : CloTest tm} ->
--- --            PushSubsts tm isClo => TermLike
--- -- NonClo tm d n = Subset (tm d n) NotClo
-
--- -- public export %inline
--- -- nclo : {isClo : CloTest tm} -> (0 _ : PushSubsts tm isClo) =>
--- --        (t : tm d n) -> (0 nc : NotClo t) => NonClo tm d n
--- -- nclo t = Element t nc
-
--- -- parameters {0 isClo : CloTest tm} {auto _ : PushSubsts tm isClo}
--- --   ||| if the input term has any top-level closures, push them under one layer of
--- --   ||| syntax
--- --   export %inline
--- --   pushSubsts : tm d n -> NonClo tm d n
--- --   pushSubsts s = pushSubstsWith id id s
-
--- --   export %inline
--- --   pushSubstsWith' : DSubst d1 d2 -> TSubst d2 n1 n2 -> tm d1 n1 -> tm d2 n2
--- --   pushSubstsWith' th ph x = fst $ pushSubstsWith th ph x
-
--- --   export %inline
--- --   pushSubsts' : tm d n -> tm d n
--- --   pushSubsts' s = fst $ pushSubsts s
-
--- -- mutual
--- --   public export
--- --   isCloT : CloTest Term
--- --   isCloT (CloT  {}) = True
--- --   isCloT (DCloT {}) = True
--- --   isCloT (E e)      = isCloE e
--- --   isCloT _          = False
-
--- --   public export
--- --   isCloE : CloTest Elim
--- --   isCloE (CloE  {}) = True
--- --   isCloE (DCloE {}) = True
--- --   isCloE _          = False
-
--- -- mutual
--- --   export
--- --   PushSubsts Term Subst.isCloT where
--- --     pushSubstsWith th ph (TYPE l loc) =
--- --       nclo $ TYPE l loc
--- --     pushSubstsWith th ph (Pi qty a body loc) =
--- --       nclo $ Pi qty (a // th // ph) (body // th // ph) loc
--- --     pushSubstsWith th ph (Lam body loc) =
--- --       nclo $ Lam (body // th // ph) loc
--- --     pushSubstsWith th ph (Sig a b loc) =
--- --       nclo $ Sig (a // th // ph) (b // th // ph) loc
--- --     pushSubstsWith th ph (Pair s t loc) =
--- --       nclo $ Pair (s // th // ph) (t // th // ph) loc
--- --     pushSubstsWith th ph (Enum tags loc) =
--- --       nclo $ Enum tags loc
--- --     pushSubstsWith th ph (Tag tag loc) =
--- --       nclo $ Tag tag loc
--- --     pushSubstsWith th ph (Eq ty l r loc) =
--- --       nclo $ Eq (ty // th // ph) (l // th // ph) (r // th // ph) loc
--- --     pushSubstsWith th ph (DLam body loc) =
--- --       nclo $ DLam (body // th // ph) loc
--- --     pushSubstsWith _ _ (Nat loc) =
--- --       nclo $ Nat loc
--- --     pushSubstsWith _ _ (Zero loc) =
--- --       nclo $ Zero loc
--- --     pushSubstsWith th ph (Succ n loc) =
--- --       nclo $ Succ (n // th // ph) loc
--- --     pushSubstsWith th ph (BOX pi ty loc) =
--- --       nclo $ BOX pi (ty // th // ph) loc
--- --     pushSubstsWith th ph (Box val loc) =
--- --       nclo $ Box (val // th // ph) loc
--- --     pushSubstsWith th ph (E e) =
--- --       let Element e nc = pushSubstsWith th ph e in nclo $ E e
--- --     pushSubstsWith th ph (CloT (Sub s ps)) =
--- --       pushSubstsWith th (comp th ps ph) s
--- --     pushSubstsWith th ph (DCloT (Sub s ps)) =
--- --       pushSubstsWith (ps . th) ph s
-
--- --   export
--- --   PushSubsts Elim Subst.isCloE where
--- --     pushSubstsWith th ph (F x u loc) =
--- --       nclo $ F x u loc
--- --     pushSubstsWith th ph (B i loc) =
--- --       let res = getLoc ph i loc in
--- --       case nchoose $ isCloE res of
--- --         Left  yes => assert_total pushSubsts res
--- --         Right no  => Element res no
--- --     pushSubstsWith th ph (App f s loc) =
--- --       nclo $ App (f // th // ph) (s // th // ph) loc
--- --     pushSubstsWith th ph (CasePair pi p r b loc) =
--- --       nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph) loc
--- --     pushSubstsWith th ph (CaseEnum pi t r arms loc) =
--- --       nclo $ CaseEnum pi (t // th // ph) (r // th // ph)
--- --                (map (\b => b // th // ph) arms) loc
--- --     pushSubstsWith th ph (CaseNat pi pi' n r z s loc) =
--- --       nclo $ CaseNat pi pi' (n // th // ph) (r // th // ph)
--- --                (z // th // ph) (s // th // ph) loc
--- --     pushSubstsWith th ph (CaseBox pi x r b loc) =
--- --       nclo $ CaseBox pi (x // th // ph) (r // th // ph) (b // th // ph) loc
--- --     pushSubstsWith th ph (DApp f d loc) =
--- --       nclo $ DApp (f // th // ph) (d // th) loc
--- --     pushSubstsWith th ph (Ann s a loc) =
--- --       nclo $ Ann (s // th // ph) (a // th // ph) loc
--- --     pushSubstsWith th ph (Coe ty p q val loc) =
--- --       nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph) loc
--- --     pushSubstsWith th ph (Comp ty p q val r zero one loc) =
--- --       nclo $ Comp (ty // th // ph) (p // th) (q // th)
--- --                   (val // th // ph) (r // th)
--- --                   (zero // th // ph) (one // th // ph) loc
--- --     pushSubstsWith th ph (TypeCase ty ret arms def loc) =
--- --       nclo $ TypeCase (ty // th // ph) (ret  // th // ph)
--- --         (map (\t => t // th // ph) arms) (def // th // ph) loc
--- --     pushSubstsWith th ph (CloE (Sub e ps)) =
--- --       pushSubstsWith th (comp th ps ph) e
--- --     pushSubstsWith th ph (DCloE (Sub e ps)) =
--- --       pushSubstsWith (ps . th) ph e
-
-
--- -- private %inline
--- -- CompHY : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
--- --          (r : Dim d) -> (zero, one : DScopeTerm d n) -> (loc : Loc) -> Elim d n
--- -- CompHY {ty, p, q, val, r, zero, one, loc} =
--- --   let ty' = SY ty.names $ ty.term // (B VZ ty.loc ::: shift 2) in
--- --   Comp {
--- --     ty = dsub1 ty q, p, q,
--- --     val = E $ Coe ty p q val val.loc, r,
--- --     -- [fixme] better locations for these vars?
--- --     zero = SY zero.names $ E $
--- --       Coe ty' (B VZ zero.loc) (weakD 1 q) zero.term zero.loc,
--- --     one = SY one.names $ E $
--- --       Coe ty' (B VZ one.loc) (weakD 1 q) one.term one.loc,
--- --     loc
--- --   }
-
--- -- public export %inline
--- -- CompH' : (ty : DScopeTerm d n) ->
--- --          (p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
--- --          (zero : DScopeTerm d n) ->
--- --          (one : DScopeTerm d n) ->
--- --          (loc : Loc) ->
--- --          Elim d n
--- -- CompH' {ty, p, q, val, r, zero, one, loc} =
--- --   case dsqueeze ty of
--- --     S _ (N ty) => Comp   {ty, p, q, val, r, zero, one, loc}
--- --     S _ (Y _)  => CompHY {ty, p, q, val, r, zero, one, loc}
-
--- -- ||| heterogeneous composition, using Comp and Coe (and subst)
--- -- |||
--- -- ||| comp [i ⇒ A] @p @q s @r { 0 j ⇒ t₀; 1 j ⇒ t₁ }
--- -- ||| ≔
--- -- ||| comp [A‹q/i›] @p @q (coe [i ⇒ A] @p @q s) @r {
--- -- |||   0 j ⇒ coe [i ⇒ A] @j @q t₀;
--- -- |||   1 j ⇒ coe [i ⇒ A] @j @q t₁
--- -- ||| }
--- -- public export %inline
--- -- CompH : (i : BindName) -> (ty : Term (S d) n) ->
--- --         (p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
--- --         (j0 : BindName) -> (zero : Term (S d) n) ->
--- --         (j1 : BindName) -> (one : Term (S d) n) ->
--- --         (loc : Loc) ->
--- --         Elim d n
--- -- CompH {i, ty, p, q, val, r, j0, zero, j1, one, loc} =
--- --   CompH' {ty = SY [< i] ty, p, q, val, r,
--- --           zero = SY [< j0] zero, one = SY [< j0] one, loc}
+||| heterogeneous comp, in terms of Comp and Coe
+public export %inline
+CompH : (i : BindName) -> (ty : Term (S d) n) ->
+        (p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
+        (j0 : BindName) -> (zero : Term (S d) n) ->
+        (j1 : BindName) -> (one : Term (S d) n) ->
+        (loc : Loc) -> Elim d n
+CompH {i, ty, p, q, val, r, j0, zero, j1, one, loc} =
+  CompH' {ty = SY [< i] ty, p, q, val, r,
+          zero = SY [< j0] zero, one = SY [< j1] one, loc}

lib/Quox/Syntax/Term/Tighten.idr

@@ -1,334 +0,0 @@
-module Quox.Syntax.Term.Tighten
-
-import Quox.Syntax.Term.Base
-import Quox.Syntax.Subst
-import public Quox.OPE
-
-%default total
-
-
-export
-Tighten (Shift f) where
-  -- `OPE m n` is a spicy `m ≤ n`,
-  -- and `Shift f n` is a (different) spicy `f ≤ n`
-  -- so the value is `f ≤ m` (as a `Shift`), if that is the case
-  tighten _        SZ      = Nothing
-  tighten Id       by      = Just by
-  tighten (Drop p) (SS by) = tighten p by
-  tighten (Keep p) (SS by) = [|SS $ tighten p by|]
-
-
-export
-Tighten Dim where
-  tighten p (K e loc) = pure $ K e loc
-  tighten p (B i loc) = B <$> tighten p i <*> pure loc
-
-
-export
-tightenSub : (forall m, n. OPE m n -> env n -> Maybe (env m)) ->
-             OPE t1 t2 -> Subst env f t2 -> Maybe (Subst env f t1)
-tightenSub f p (Shift by) = [|Shift $ tighten p by|]
-tightenSub f p (t ::: th) = [|f p t !::: tightenSub f p th|]
-
-export
-Tighten env => Tighten (Subst env f) where
-  tighten p th = tightenSub tighten p th
-
-
-export
-tightenScope : (forall m, n. OPE m n -> f n -> Maybe (f m)) ->
-               {s : Nat} -> OPE m n -> Scoped s f n -> Maybe (Scoped s f m)
-tightenScope f p (S names (Y body)) = SY names <$> f (keepN s p) body
-tightenScope f p (S names (N body)) = S names . N <$> f p body
-
-export
-tightenDScope : {0 f : Nat -> Nat -> Type} ->
-                (forall m, n, k. OPE m n -> f n k -> Maybe (f m k)) ->
-                OPE m n -> Scoped s (f n) k -> Maybe (Scoped s (f m) k)
-tightenDScope f p (S names (Y body)) = SY names <$> f p body
-tightenDScope f p (S names (N body)) = S names . N <$> f p body
-
-
-mutual
-  private
-  tightenT : OPE n1 n2 -> Term d n2 -> Maybe (Term d n1)
-  tightenT p (TYPE l loc) = pure $ TYPE l loc
-  tightenT p (Pi qty arg res loc) =
-    Pi qty <$> tightenT p arg <*> tightenS p res <*> pure loc
-  tightenT p (Lam body loc) =
-    Lam <$> tightenS p body <*> pure loc
-  tightenT p (Sig fst snd loc) =
-    Sig <$> tightenT p fst <*> tightenS p snd <*> pure loc
-  tightenT p (Pair fst snd loc) =
-    Pair <$> tightenT p fst <*> tightenT p snd <*> pure loc
-  tightenT p (Enum cases loc) =
-    pure $ Enum cases loc
-  tightenT p (Tag tag loc) =
-    pure $ Tag tag loc
-  tightenT p (Eq ty l r loc) =
-    Eq <$> tightenDS p ty <*> tightenT p l <*> tightenT p r <*> pure loc
-  tightenT p (DLam body loc) =
-    DLam <$> tightenDS p body <*> pure loc
-  tightenT p (Nat loc) =
-    pure $ Nat loc
-  tightenT p (Zero loc) =
-    pure $ Zero loc
-  tightenT p (Succ s loc) =
-    Succ <$> tightenT p s <*> pure loc
-  tightenT p (BOX qty ty loc) =
-    BOX qty <$> tightenT p ty <*> pure loc
-  tightenT p (Box val loc) =
-    Box <$> tightenT p val <*> pure loc
-  tightenT p (E e) =
-    assert_total $ E <$> tightenE p e
-  tightenT p (CloT (Sub tm th)) = do
-    th <- assert_total $ tightenSub tightenE p th
-    pure $ CloT $ Sub tm th
-  tightenT p (DCloT (Sub tm th)) = do
-    tm <- tightenT p tm
-    pure $ DCloT $ Sub tm th
-
-  private
-  tightenE : OPE n1 n2 -> Elim d n2 -> Maybe (Elim d n1)
-  tightenE p (F x u loc) =
-    pure $ F x u loc
-  tightenE p (B i loc) =
-    B <$> tighten p i <*> pure loc
-  tightenE p (App fun arg loc) =
-    App <$> tightenE p fun <*> tightenT p arg <*> pure loc
-  tightenE p (CasePair qty pair ret body loc) =
-    CasePair qty <$> tightenE p pair
-                 <*> tightenS p ret
-                 <*> tightenS p body
-                 <*> pure loc
-  tightenE p (CaseEnum qty tag ret arms loc) =
-    CaseEnum qty <$> tightenE p tag
-                 <*> tightenS p ret
-                 <*> traverse (tightenT p) arms
-                 <*> pure loc
-  tightenE p (CaseNat qty qtyIH nat ret zero succ loc) =
-    CaseNat qty qtyIH
-      <$> tightenE p nat
-      <*> tightenS p ret
-      <*> tightenT p zero
-      <*> tightenS p succ
-      <*> pure loc
-  tightenE p (CaseBox qty box ret body loc) =
-    CaseBox qty <$> tightenE p box
-                <*> tightenS p ret
-                <*> tightenS p body
-                <*> pure loc
-  tightenE p (DApp fun arg loc) =
-    DApp <$> tightenE p fun <*> pure arg <*> pure loc
-  tightenE p (Ann tm ty loc) =
-    Ann <$> tightenT p tm <*> tightenT p ty <*> pure loc
-  tightenE p (Coe ty q0 q1 val loc) =
-    Coe <$> tightenDS p ty
-        <*> pure q0 <*> pure q1
-        <*> tightenT p val
-        <*> pure loc
-  tightenE p (Comp ty q0 q1 val r zero one loc) =
-    Comp <$> tightenT p ty
-         <*> pure q0 <*> pure q1
-         <*> tightenT p val
-         <*> pure r
-         <*> tightenDS p zero
-         <*> tightenDS p one
-         <*> pure loc
-  tightenE p (TypeCase ty ret arms def loc) =
-    TypeCase <$> tightenE p ty
-             <*> tightenT p ret
-             <*> traverse (tightenS p) arms
-             <*> tightenT p def
-             <*> pure loc
-  tightenE p (CloE (Sub el th)) = do
-    th <- assert_total $ tightenSub tightenE p th
-    pure $ CloE $ Sub el th
-  tightenE p (DCloE (Sub el th)) = do
-    el <- tightenE p el
-    pure $ DCloE $ Sub el th
-
-  export
-  tightenS : {s : Nat} -> OPE m n ->
-             ScopeTermN s f n -> Maybe (ScopeTermN s f m)
-  tightenS = assert_total $ tightenScope tightenT
-
-  export
-  tightenDS : OPE m n -> DScopeTermN s f n -> Maybe (DScopeTermN s f m)
-  tightenDS = assert_total $ tightenDScope tightenT {f = \n, d => Term d n}
-
-export Tighten (Elim d) where tighten p e = tightenE p e
-export Tighten (Term d) where tighten p t = tightenT p t
-
-
-mutual
-  export
-  dtightenT : OPE d1 d2 -> Term d2 n -> Maybe (Term d1 n)
-  dtightenT p (TYPE l loc) =
-    pure $ TYPE l loc
-  dtightenT p (Pi qty arg res loc) =
-    Pi qty <$> dtightenT p arg <*> dtightenS p res <*> pure loc
-  dtightenT p (Lam body loc) =
-    Lam <$> dtightenS p body <*> pure loc
-  dtightenT p (Sig fst snd loc) =
-    Sig <$> dtightenT p fst <*> dtightenS p snd <*> pure loc
-  dtightenT p (Pair fst snd loc) =
-    Pair <$> dtightenT p fst <*> dtightenT p snd <*> pure loc
-  dtightenT p (Enum cases loc) =
-    pure $ Enum cases loc
-  dtightenT p (Tag tag loc) =
-    pure $ Tag tag loc
-  dtightenT p (Eq ty l r loc) =
-    Eq <$> dtightenDS p ty <*> dtightenT p l <*> dtightenT p r <*> pure loc
-  dtightenT p (DLam body loc) =
-    DLam <$> dtightenDS p body <*> pure loc
-  dtightenT p (Nat loc) =
-    pure $ Nat loc
-  dtightenT p (Zero loc) =
-    pure $ Zero loc
-  dtightenT p (Succ s loc) =
-    Succ <$> dtightenT p s <*> pure loc
-  dtightenT p (BOX qty ty loc) =
-    BOX qty <$> dtightenT p ty <*> pure loc
-  dtightenT p (Box val loc) =
-    Box <$> dtightenT p val <*> pure loc
-  dtightenT p (E e) =
-    assert_total $ E <$> dtightenE p e
-  dtightenT p (CloT (Sub tm th)) = do
-    tm <- dtightenT p tm
-    th <- assert_total $ traverse (dtightenE p) th
-    pure $ CloT $ Sub tm th
-  dtightenT p (DCloT (Sub tm th)) = do
-    th <- tighten p th
-    pure $ DCloT $ Sub tm th
-
-  export
-  dtightenE : OPE d1 d2 -> Elim d2 n -> Maybe (Elim d1 n)
-  dtightenE p (F x u loc) =
-    pure $ F x u loc
-  dtightenE p (B i loc) =
-    pure $ B i loc
-  dtightenE p (App fun arg loc) =
-    App <$> dtightenE p fun <*> dtightenT p arg <*> pure loc
-  dtightenE p (CasePair qty pair ret body loc) =
-    CasePair qty <$> dtightenE p pair
-                 <*> dtightenS p ret
-                 <*> dtightenS p body
-                 <*> pure loc
-  dtightenE p (CaseEnum qty tag ret arms loc) =
-    CaseEnum qty <$> dtightenE p tag
-                 <*> dtightenS p ret
-                 <*> traverse (dtightenT p) arms
-                 <*> pure loc
-  dtightenE p (CaseNat qty qtyIH nat ret zero succ loc) =
-    CaseNat qty qtyIH
-      <$> dtightenE p nat
-      <*> dtightenS p ret
-      <*> dtightenT p zero
-      <*> dtightenS p succ
-      <*> pure loc
-  dtightenE p (CaseBox qty box ret body loc) =
-    CaseBox qty <$> dtightenE p box
-                <*> dtightenS p ret
-                <*> dtightenS p body
-                <*> pure loc
-  dtightenE p (DApp fun arg loc) =
-    DApp <$> dtightenE p fun <*> tighten p arg <*> pure loc
-  dtightenE p (Ann tm ty loc) =
-    Ann <$> dtightenT p tm <*> dtightenT p ty <*> pure loc
-  dtightenE p (Coe ty q0 q1 val loc) =
-    [|Coe (dtightenDS p ty) (tighten p q0) (tighten p q1) (dtightenT p val)
-          (pure loc)|]
-  dtightenE p (Comp ty q0 q1 val r zero one loc) =
-    [|Comp (dtightenT p ty) (tighten p q0) (tighten p q1)
-           (dtightenT p val) (tighten p r)
-           (dtightenDS p zero) (dtightenDS p one) (pure loc)|]
-  dtightenE p (TypeCase ty ret arms def loc) =
-    [|TypeCase (dtightenE p ty) (dtightenT p ret)
-               (traverse (dtightenS p) arms) (dtightenT p def) (pure loc)|]
-  dtightenE p (CloE (Sub el th)) = do
-    el <- dtightenE p el
-    th <- assert_total $ traverse (dtightenE p) th
-    pure $ CloE $ Sub el th
-  dtightenE p (DCloE (Sub el th)) = do
-    th <- tighten p th
-    pure $ DCloE $ Sub el th
-
-  export
-  dtightenS : OPE d1 d2 -> ScopeTermN s d2 n -> Maybe (ScopeTermN s d1 n)
-  dtightenS = assert_total $ tightenDScope dtightenT {f = Term}
-
-  export
-  dtightenDS : {s : Nat} -> OPE d1 d2 ->
-               DScopeTermN s d2 n -> Maybe (DScopeTermN s d1 n)
-  dtightenDS = assert_total $ tightenScope dtightenT
-
-
-export [TermD] Tighten (\d => Term d n) where tighten p t = dtightenT p t
-export [ElimD] Tighten (\d => Elim d n) where tighten p e = dtightenE p e
-
-
--- versions of SY, etc, that try to tighten and use SN automatically
-
-public export
-ST : Tighten f => {s : Nat} -> BContext s -> f (s + n) -> Scoped s f n
-ST names body =
-  case tightenN s body of
-    Just body => S names $ N body
-    Nothing   => S names $ Y body
-
-public export
-DST : {s : Nat} -> BContext s -> Term (s + d) n -> DScopeTermN s d n
-DST names body =
-  case tightenN @{TermD} s body of
-    Just body => S names $ N body
-    Nothing   => S names $ Y body
-
-public export %inline
-PiT : (qty : Qty) -> (x : BindName) ->
-      (arg : Term d n) -> (res : Term d (S n)) -> (loc : Loc) -> Term d n
-PiT {qty, x, arg, res, loc} = Pi {qty, arg, res = ST [< x] res, loc}
-
-public export %inline
-LamT : (x : BindName) -> (body : Term d (S n)) -> (loc : Loc) -> Term d n
-LamT {x, body, loc} = Lam {body = ST [< x] body, loc}
-
-public export %inline
-SigT : (x : BindName) -> (fst : Term d n) ->
-       (snd : Term d (S n)) -> (loc : Loc) -> Term d n
-SigT {x, fst, snd, loc} = Sig {fst, snd = ST [< x] snd, loc}
-
-public export %inline
-EqT : (i : BindName) -> (ty : Term (S d) n) ->
-      (l, r : Term d n) -> (loc : Loc) -> Term d n
-EqT {i, ty, l, r, loc} = Eq {ty = DST [< i] ty, l, r, loc}
-
-public export %inline
-DLamT : (i : BindName) -> (body : Term (S d) n) -> (loc : Loc) -> Term d n
-DLamT {i, body, loc} = DLam {body = DST [< i] body, loc}
-
-public export %inline
-CoeT : (i : BindName) -> (ty : Term (S d) n) ->
-       (p, q : Dim d) -> (val : Term d n) -> (loc : Loc) -> Elim d n
-CoeT {i, ty, p, q, val, loc} = Coe {ty = DST [< i] ty, p, q, val, loc}
-
-public export %inline
-typeCase1T : Elim d n -> Term d n ->
-             (k : TyConKind) -> BContext (arity k) -> Term d (arity k + n) ->
-             (loc : Loc) ->
-             {default (Nat loc) def : Term d n} ->
-             Elim d n
-typeCase1T ty ret k ns body loc {def} =
-  typeCase ty ret [(k ** ST ns body)] def loc
-
-
-export
-squeeze : {s : Nat} -> ScopeTermN s d n -> ScopeTermN s d n
-squeeze (S names (Y body)) = S names $ maybe (Y body) N $ tightenN s body
-squeeze (S names (N body)) = S names $ N body
-
-export
-dsqueeze : {s : Nat} -> DScopeTermN s d n -> DScopeTermN s d n
-dsqueeze (S names (Y body)) =
-  S names $ maybe (Y body) N $ tightenN s body @{TermD}
-dsqueeze (S names (N body)) = S names $ N body

lib/Quox/Syntax/Term/TyConKind.idr

@@ -9,7 +9,8 @@ import Generics.Derive
 
 
 public export
-data TyConKind = KTYPE | KPi | KSig | KEnum | KEq | KNat | KBOX
+data TyConKind =
+  KTYPE | KIOState | KPi | KSig | KEnum | KEq | KNat | KString | KBOX
 %name TyConKind k
 %runElab derive "TyConKind" [Eq.Eq, Ord.Ord, Show.Show, Generic, Meta, DecEq]
 
@@ -25,10 +26,12 @@ allKinds = %runElab do
 ||| in `type-case`, how many variables are bound in this branch
 public export %inline
 arity : TyConKind -> Nat
-arity KTYPE = 0
-arity KPi   = 2
-arity KSig  = 2
-arity KEnum = 0
-arity KEq   = 5
-arity KNat  = 0
-arity KBOX  = 1
+arity KTYPE    = 0
+arity KIOState = 0
+arity KPi      = 2
+arity KSig     = 2
+arity KEnum    = 0
+arity KEq      = 5
+arity KNat     = 0
+arity KString  = 0
+arity KBOX     = 1

lib/Quox/Thin.idr

@@ -1,13 +0,0 @@
-module Quox.Thin
-
-import public Quox.Thin.Base
-import public Quox.Thin.View
-import public Quox.Thin.Eqv
-import public Quox.Thin.Cons
-import public Quox.Thin.List
-import public Quox.Thin.Append
-import public Quox.Thin.Comp
-import public Quox.Thin.Cover
-import public Quox.Thin.Coprod
-import public Quox.Thin.Split
-import public Quox.Thin.Term

lib/Quox/Thin/Append.idr

@@ -1,27 +0,0 @@
-module Quox.Thin.Append
-
-import public Quox.Thin.Base
-import public Quox.Thin.View
-import Data.DPair
-
-%default total
-
-public export
-app' : OPE m1 n1 mask1 -> OPE m2 n2 mask2 -> Exists (OPE (m1 + m2) (n1 + n2))
-app' Stop             ope2 = Evidence _ ope2
-app' (Drop ope1 Refl) ope2 = Evidence _ $ Drop (app' ope1 ope2).snd Refl
-app' (Keep ope1 Refl) ope2 = Evidence _ $ Keep (app' ope1 ope2).snd Refl
-
-public export
-(++) : {n1, n2, mask1, mask2 : Nat} ->
-       (0 ope1 : OPE m1 n1 mask1) -> (0 ope2 : OPE m2 n2 mask2) ->
-       Subset Nat (OPE (m1 + m2) (n1 + n2))
-ope1 ++ ope2 with %syntactic (view ope1)
-  Stop           ++ ope2 | StopV = Element _ ope2
-  Drop ope1 Refl ++ ope2 | DropV mask ope1 =
-    Element _ $ Drop (ope1 ++ ope2).snd Refl
-  Keep ope1 Refl ++ ope2 | KeepV mask ope1 =
-    Element _ $ Keep (ope1 ++ ope2).snd Refl
-
--- [todo] this mask is just (mask1 << n2) | mask2
--- prove it and add %transform

lib/Quox/Thin/Base.idr

@@ -1,81 +0,0 @@
-module Quox.Thin.Base
-
-import Data.Fin
-import Data.DPair
-
-%default total
-
-||| "order preserving embeddings", for recording a correspondence between a
-||| smaller scope and part of a larger one. the third argument is a bitmask
-||| representing this OPE, unique for a given `n`.
-public export
-data OPE : (m, n, mask : Nat) -> Type where
-  [search m n]
-  Stop : OPE 0 0 0
-  Drop : OPE m n mask -> mask' = mask + mask       -> OPE m     (S n) mask'
-  Keep : OPE m n mask -> mask' = (S (mask + mask)) -> OPE (S m) (S n) mask'
-%name OPE ope
-
-export
-Show (OPE m n mask) where
-  showPrec d Stop            = "Stop"
-  showPrec d (Drop ope Refl) = showCon d "Drop" $ showArg ope ++ " Refl"
-  showPrec d (Keep ope Refl) = showCon d "Keep" $ showArg ope ++ " Refl"
-
-public export %inline
-drop : OPE m n mask -> OPE m (S n) (mask + mask)
-drop ope = Drop ope Refl
-
-public export %inline
-keep : OPE m n mask -> OPE (S m) (S n) (S (mask + mask))
-keep ope = Keep ope Refl
-
-
-public export
-data IsStop : OPE m n mask -> Type where ItIsStop : IsStop Stop
-
-public export
-data IsDrop : OPE m n mask -> Type where ItIsDrop : IsDrop (Drop ope eq)
-
-public export
-data IsKeep : OPE m n mask -> Type where ItIsKeep : IsKeep (Keep ope eq)
-
-
-export
-0 zeroIsStop : (ope : OPE m 0 mask) -> IsStop ope
-zeroIsStop Stop = ItIsStop
-
-
-||| everything selected
-public export
-id : {m : Nat} -> Subset Nat (OPE m m)
-id {m = 0}   = Element _ Stop
-id {m = S m} = Element _ $ Keep id.snd Refl
-
-public export %inline
-0 id' : {m : Nat} -> OPE m m (fst (Base.id {m}))
-id' = id.snd
-
-||| nothing selected
-public export
-zero : {m : Nat} -> OPE 0 m 0
-zero {m = 0}   = Stop
-zero {m = S m} = Drop zero Refl
-
-||| a single slot selected
-public export
-one : Fin n -> Subset Nat (OPE 1 n)
-one FZ     = Element _ $ keep zero
-one (FS i) = Element _ $ drop (one i).snd
-
-public export %inline
-0 one' : (i : Fin n) -> OPE 1 n (one i).fst
-one' i = (one i).snd
-
-
-public export
-record SomeOPE n where
-  constructor MkOPE
-  {0 scope : Nat}
-  {mask : Nat}
-  0 ope : OPE scope n mask

lib/Quox/Thin/Comp.idr

@@ -1,55 +0,0 @@
-module Quox.Thin.Comp
-
-import public Quox.Thin.Base
-import public Quox.Thin.View
-import Quox.NatExtra
-import Data.Singleton
-
-%default total
-
-||| inductive definition of OPE composition
-public export
-data Comp : (l : OPE n p mask1) -> (r : OPE m n mask2) ->
-            (res : OPE m p mask3) -> Type where
-  [search l r]
-  StopZ : Comp Stop Stop Stop
-  DropZ : Comp a b c -> Comp (Drop a Refl) b (Drop c Refl)
-  KeepZ : Comp a b c -> Comp (Keep a Refl) (Keep b Refl) (Keep c Refl)
-  KDZ   : Comp a b c -> Comp (Keep a Refl) (Drop b Refl) (Drop c Refl)
-
-public export
-record CompResult (ope1 : OPE n p mask1) (ope2 : OPE m n mask2) where
-  constructor MkComp
-  {mask : Nat}
-  {0 ope : OPE m p mask}
-  0 comp : Comp ope1 ope2 ope
-%name CompResult comp
-
-||| compose two OPEs, if the middle scope size is already known at runtime
-export
-comp' : {n, p, mask1, mask2 : Nat} ->
-        (0 ope1 : OPE n p mask1) -> (0 ope2 : OPE m n mask2) ->
-        CompResult ope1 ope2
-comp' ope1 ope2 with %syntactic (view ope1) | (view ope2)
-  comp' Stop Stop | StopV | StopV =
-    MkComp StopZ
-  comp' (Drop ope1 Refl) ope2 | DropV _ ope1 | _ =
-    MkComp $ DropZ (comp' ope1 ope2).comp
-  comp' (Keep ope1 Refl) (Drop ope2 Refl) | KeepV _ ope1 | DropV _ ope2 =
-    MkComp $ KDZ (comp' ope1 ope2).comp
-  comp' (Keep ope1 Refl) (Keep ope2 Refl) | KeepV _ ope1 | KeepV _ ope2 =
-    MkComp $ KeepZ (comp' ope1 ope2).comp
-
-||| compose two OPEs, after recomputing the middle scope size using `appOpe`
-export
-comp : {p, mask1, mask2 : Nat} ->
-       (0 ope1 : OPE n p mask1) -> (0 ope2 : OPE m n mask2) ->
-       CompResult ope1 ope2
-comp ope1 ope2 = let Val n = appOpe p ope1 in comp' ope1 ope2
-
--- [todo] is there a quick way to compute the mask of comp?
-
-export
-0 (.) : (ope1 : OPE n p mask1) -> (ope2 : OPE m n mask2) ->
-        OPE m p (comp ope1 ope2).mask
-ope1 . ope2 = (comp ope1 ope2).ope

lib/Quox/Thin/Cons.idr

@@ -1,74 +0,0 @@
-module Quox.Thin.Cons
-
-import public Quox.Thin.Base
-import Quox.Thin.Eqv
-import Quox.Thin.View
-import Data.DPair
-import Control.Relation
-
-%default total
-
-
-public export
-data IsHead : (ope : OPE m (S n) mask) -> Bool -> Type where
-  [search ope]
-  DropH : IsHead (Drop ope eq) False
-  KeepH : IsHead (Keep ope eq) True
-
-public export
-data IsTail : (full : OPE m (S n) mask) -> OPE m' n mask' -> Type where
-  [search full]
-  DropT : IsTail (Drop ope eq) ope
-  KeepT : IsTail (Keep ope eq) ope
-
-public export
-record Uncons (ope : OPE m (S n) mask) where
-  constructor MkUncons
-  0 head : Bool
-  {tailMask : Nat}
-  0 tail : OPE scope n tailMask
-  {auto isHead : IsHead ope head}
-  {auto 0 isTail : IsTail ope tail}
-
-public export
-uncons : {n, mask : Nat} -> (0 ope : OPE m (S n) mask) -> Uncons ope
-uncons ope with %syntactic (view ope)
-  uncons (Drop ope Refl) | DropV _ ope = MkUncons False ope
-  uncons (Keep ope Refl) | KeepV _ ope = MkUncons True  ope
-
-public export
-head : {n, mask : Nat} -> (0 ope : OPE m (S n) mask) -> Exists $ IsHead ope
-head ope = Evidence _ (uncons ope).isHead
-
-public export
-record Tail (ope : OPE m (S n) mask) where
-  constructor MkTail
-  {tailMask : Nat}
-  0 tail : OPE scope n tailMask
-  {auto 0 isTail : IsTail ope tail}
-
-public export
-tail : {n, mask : Nat} -> (0 ope : OPE m (S n) mask) -> Tail ope
-tail ope = let u = uncons ope in MkTail u.tail @{u.isTail}
-
-
-export
-cons : {mask : Nat} -> (head : Bool) -> (0 tail : OPE m n mask) ->
-       Subset Nat (OPE (if head then S m else m) (S n))
-cons False tail = Element _ $ drop tail
-cons True  tail = Element _ $ keep tail
-
-export
-0 consEquiv' : (self : OPE m' (S n) mask') ->
-               (head : Bool) -> (tail : OPE m n mask) ->
-               IsHead self head -> IsTail self tail ->
-               (cons head tail).snd `Eqv` self
-consEquiv' (Drop tail _) False tail DropH DropT = EqvDrop reflexive
-consEquiv' (Keep tail _) True  tail KeepH KeepT = EqvKeep reflexive
-
-export
-0 consEquiv : (full : OPE m' (S n) mask') ->
-              (cons (uncons full).head (uncons full).tail).snd `Eqv` full
-consEquiv full with %syntactic (uncons full)
-  _ | MkUncons head tail {isHead, isTail} =
-    consEquiv' full head tail isHead isTail