add source locations to inner syntax

examples/misc.quox

@@ -33,4 +33,4 @@ def sym : 0.(A : ★₀) → 0.(x y : A) → 1.(x ≡ y : A) → y ≡ x : A =
 def trans : 0.(A : ★₀) → 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] @0 @1 (eq1 @𝑖) @𝑖 { 0 _ ⇒ eq1 @0; 1 𝑗 ⇒ eq2 @𝑗 };
+    comp [A] @0 @1 (eq1 @𝑖) @𝑖 { 0 _ ⇒ eq1 @0; 1 𝑗 ⇒ eq2 @0 };

exe/Main.idr

@@ -20,9 +20,10 @@ 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 defs $ loadProcessFile file
+    Right res <- fromParserIO ["."] seen suf defs $ loadProcessFile noLoc file
       | Left err => die $ prettyError True True err
     for_ res $ \(name, def) => do
       putDoc $ map termHL $ nest 2 $

lib/Quox/Context.idr

@@ -40,6 +40,10 @@ public export
 NContext : Nat -> Type
 NContext = Context' BaseName
 
+public export
+BContext : Nat -> Type
+BContext = Context' BindName
+
 
 public export
 unsnoc : Context tm (S n) -> (Context tm n, tm n)
@@ -183,6 +187,10 @@ parameters {auto _ : Applicative f}
   traverse f [<]        = pure [<]
   traverse f (tel :< x) = [|traverse f tel :< f x|]
 
+  export %inline
+  traverse' : (a -> f b) -> Telescope' a from to -> f (Telescope' b from to)
+  traverse' f = traverse f
+
   infixl 3 `app`
   ||| like `(<*>)` but with effects
   export
@@ -197,6 +205,7 @@ parameters {auto _ : Applicative f}
   sequence : Telescope (f . tm) from to -> f (Telescope tm from to)
   sequence = traverse id
 
+
 parameters {0 tm1, tm2 : Nat -> Type}
            (f : forall n. tm1 n -> tm2 n)
   export %inline
@@ -207,6 +216,8 @@ parameters {0 tm1, tm2 : Nat -> Type}
   (<$>) : Telescope tm1 from to -> Telescope tm2 from to
   (<$>) = map
 
+
+
 export %inline
 (<*>) : Telescope (\n => tm1 n -> tm2 n) from to ->
         Telescope tm1 from to -> Telescope tm2 from to
@@ -311,3 +322,9 @@ export %inline
 export %inline
 (forall n. PrettyHL (tm n)) => PrettyHL (Telescope tm from to) where
   prettyM tel = separate (hl Delim ";") <$> traverse prettyM (toList tel)
+
+
+namespace BContext
+  export
+  toNames : BContext n -> SnocList BaseName
+  toNames = foldl (\xs, x => xs :< x.name) [<]

lib/Quox/Definition.idr

@@ -3,6 +3,7 @@ module Quox.Definition
 import public Quox.No
 import public Quox.Syntax
 import public Data.SortedMap
+import public Quox.Loc
 import Control.Eff
 import Decidable.Decidable
 
@@ -25,14 +26,18 @@ record Definition where
   qty   : GQty
   type0 : Term 0 0
   body0 : DefBody
+  loc_  : Loc
 
 public export %inline
-mkPostulate : GQty -> (type0 : Term 0 0) -> Definition
+mkPostulate : GQty -> (type0 : Term 0 0) -> Loc -> Definition
-mkPostulate qty type0 = MkDef {qty, type0, body0 = Postulate}
+mkPostulate qty type0 loc_ = MkDef {qty, type0, body0 = Postulate, loc_}
 
 public export %inline
-mkDef : GQty -> (type0, term0 : Term 0 0) -> Definition
+mkDef : GQty -> (type0, term0 : Term 0 0) -> Loc -> Definition
-mkDef qty type0 term0 = MkDef {qty, type0, body0 = Concrete term0}
+mkDef qty type0 term0 loc_ = MkDef {qty, type0, body0 = Concrete term0, loc_}
+
+export Located Definition where def.loc = def.loc_
+export Relocatable Definition where setLoc loc = {loc_ := loc}
 
 
 parameters {d, n : Nat}
@@ -46,7 +51,7 @@ parameters {d, n : Nat}
 
   public export %inline
   toElim : Definition -> Maybe $ Elim d n
-  toElim def = pure $ !def.term :# def.type
+  toElim def = pure $ Ann !def.term def.type def.loc
 
 
 public export %inline
@@ -62,9 +67,13 @@ Definitions : Type
 Definitions = SortedMap Name Definition
 
 public export
-0 DefsReader : Type -> Type
+DefsReader : Type -> Type
 DefsReader = ReaderL DEFS Definitions
 
+public export
+DefsState : Type -> Type
+DefsState = StateL DEFS Definitions
+
 export
 defs : Has DefsReader fs => Eff fs Definitions
 defs = askAt DEFS

lib/Quox/Equal.idr

@@ -9,20 +9,41 @@ import Quox.EffExtra
 
 
 public export
-0 EqModeState : Type -> Type
+EqModeState : Type -> Type
 EqModeState = State EqMode
 
 public export
-0 EqualEff : List (Type -> Type)
+Equal : Type -> Type
-EqualEff = [ErrorEff, EqModeState]
+Equal = Eff [ErrorEff, DefsReader, NameGen]
 
 public export
-0 Equal : Type -> Type
+Equal_ : Type -> Type
-Equal = Eff $ EqualEff
+Equal_ = Eff [ErrorEff, NameGen, EqModeState]
 
 export
-runEqual : EqMode -> Equal a -> Either Error a
+runEqualWith_ : EqMode -> NameSuf -> Equal_ a -> (Either Error a, NameSuf)
-runEqual mode = extract . runExcept . evalState mode
+runEqualWith_ mode suf act =
+  extract $
+  runNameGenWith suf $
+  runExcept $
+  evalState mode act
+
+export
+runEqual_ : EqMode -> Equal_ a -> Either Error a
+runEqual_ mode act = fst $ runEqualWith_ mode 0 act
+
+
+export
+runEqualWith : NameSuf -> Definitions -> Equal a -> (Either Error a, NameSuf)
+runEqualWith suf defs act =
+  extract $
+  runStateAt GEN suf $
+  runReaderAt DEFS defs $
+  runExcept act
+
+export
+runEqual : Definitions -> Equal a -> Either Error a
+runEqual defs act = fst $ runEqualWith 0 defs act
 
 
 export %inline
@@ -30,22 +51,22 @@ mode : Has EqModeState fs => Eff fs EqMode
 mode = get
 
 
-parameters (ctx : EqContext n)
+parameters (loc : Loc) (ctx : EqContext n)
   private %inline
-  clashT : Term 0 n -> Term 0 n -> Term 0 n -> Equal a
+  clashT : Term 0 n -> Term 0 n -> Term 0 n -> Equal_ a
-  clashT ty s t = throw $ ClashT ctx !mode ty s t
+  clashT ty s t = throw $ ClashT loc ctx !mode ty s t
 
   private %inline
-  clashTy : Term 0 n -> Term 0 n -> Equal a
+  clashTy : Term 0 n -> Term 0 n -> Equal_ a
-  clashTy s t = throw $ ClashTy ctx !mode s t
+  clashTy s t = throw $ ClashTy loc ctx !mode s t
 
   private %inline
-  clashE : Elim 0 n -> Elim 0 n -> Equal a
+  clashE : Elim 0 n -> Elim 0 n -> Equal_ a
-  clashE e f = throw $ ClashE ctx !mode e f
+  clashE e f = throw $ ClashE loc ctx !mode e f
 
   private %inline
-  wrongType : Term 0 n -> Term 0 n -> Equal a
+  wrongType : Term 0 n -> Term 0 n -> Equal_ a
-  wrongType ty s = throw $ WrongType ctx ty s
+  wrongType ty s = throw $ WrongType loc ctx ty s
 
 
 public export %inline
@@ -62,8 +83,8 @@ sameTyCon (Enum {}) (Enum {}) = True
 sameTyCon (Enum {}) _         = False
 sameTyCon (Eq   {}) (Eq   {}) = True
 sameTyCon (Eq   {}) _         = False
-sameTyCon Nat       Nat       = True
+sameTyCon (Nat  {}) (Nat  {}) = True
-sameTyCon Nat       _         = False
+sameTyCon (Nat  {}) _         = False
 sameTyCon (BOX  {}) (BOX  {}) = True
 sameTyCon (BOX  {}) _         = False
 sameTyCon (E    {}) (E    {}) = True
@@ -80,37 +101,39 @@ sameTyCon (E    {}) _         = False
 ||| * an enum type is a subsingleton if it has zero or one tags.
 ||| * a box type is a subsingleton if its content is
 public export covering
-isSubSing : Has ErrorEff fs => {n : Nat} ->
+isSubSing : {n : Nat} -> Definitions -> EqContext n -> Term 0 n -> Equal_ Bool
-            Definitions -> EqContext n -> Term 0 n -> Eff fs Bool
 isSubSing defs ctx ty0 = do
-  Element ty0 nc <- whnf defs ctx ty0
+  Element ty0 nc <- whnf defs ctx ty0.loc ty0
   case ty0 of
-    TYPE _        => pure False
+    TYPE {} => pure False
-    Pi _ arg res  => isSubSing defs (extendTy Zero res.name arg ctx) res.term
+    Pi {arg, res, _} =>
-    Sig  fst snd  => isSubSing defs ctx fst `andM`
+      isSubSing defs (extendTy Zero res.name arg ctx) res.term
+    Sig {fst, snd, _} =>
+      isSubSing defs ctx fst `andM`
       isSubSing defs (extendTy Zero snd.name fst ctx) snd.term
-    Enum tags     => pure $ length (SortedSet.toList tags) <= 1
+    Enum {cases, _} =>
+      pure $ length (SortedSet.toList cases) <= 1
     Eq {} => pure True
-    Nat           => pure False
+    Nat {} => pure False
-    BOX  _ ty     => isSubSing defs ctx ty
+    BOX {ty, _} => isSubSing defs ctx ty
-    E    (s :# _) => isSubSing defs ctx s
+    E (Ann {tm, _}) => isSubSing defs ctx tm
     E _ => pure False
-    Lam  _   => pure False
+    Lam  {} => pure False
-    Pair _ _ => pure False
+    Pair {} => pure False
-    Tag  _   => pure False
+    Tag  {} => pure False
-    DLam _   => pure False
+    DLam {} => pure False
-    Zero     => pure False
+    Zero {} => pure False
-    Succ _   => pure False
+    Succ {} => pure False
-    Box  _   => pure False
+    Box  {} => pure False
 
 
 export
 ensureTyCon : Has ErrorEff fs =>
-              (ctx : EqContext n) -> (t : Term 0 n) ->
+              (loc : Loc) -> (ctx : EqContext n) -> (t : Term 0 n) ->
               Eff fs (So (isTyConE t))
-ensureTyCon ctx t = case nchoose $ isTyConE t of
+ensureTyCon loc ctx t = case nchoose $ isTyConE t of
   Left  y => pure y
-  Right n => throw $ NotType (toTyContext ctx) (t // shift0 ctx.dimLen)
+  Right n => throw $ NotType loc (toTyContext ctx) (t // shift0 ctx.dimLen)
 
 ||| performs the minimum work required to recompute the type of an elim.
 |||
@@ -118,10 +141,10 @@ ensureTyCon ctx t = case nchoose $ isTyConE t of
 private covering
 computeElimTypeE : (defs : Definitions) -> EqContext n ->
                    (e : Elim 0 n) -> (0 ne : NotRedex defs e) =>
-                   Equal (Term 0 n)
+                   Equal_ (Term 0 n)
 computeElimTypeE defs ectx e =
   let Val n = ectx.termLen in
-  rethrow $ computeElimType defs (toWhnfContext ectx) e
+  lift $ computeElimType defs (toWhnfContext ectx) e
 
 parameters (defs : Definitions)
   mutual
@@ -131,55 +154,56 @@ parameters (defs : Definitions)
       |||
       ||| ⚠ **assumes that `s`, `t` have already been checked against `ty`**. ⚠
       export covering %inline
-      compare0 : EqContext n -> (ty, s, t : Term 0 n) -> Equal ()
+      compare0 : EqContext n -> (ty, s, t : Term 0 n) -> Equal_ ()
       compare0 ctx ty s t =
         wrapErr (WhileComparingT ctx !mode ty s t) $ do
           let Val n = ctx.termLen
-          Element ty _ <- whnf defs ctx ty
+          Element ty' _ <- whnf defs ctx ty.loc ty
-          Element s  _ <- whnf defs ctx s
+          Element s'  _ <- whnf defs ctx s.loc  s
-          Element t  _ <- whnf defs ctx t
+          Element t'  _ <- whnf defs ctx t.loc  t
-          tty <- ensureTyCon ctx ty
+          tty <- ensureTyCon ty.loc ctx ty'
-          compare0' ctx ty s t
+          compare0' ctx ty' s' t'
 
       ||| converts an elim "Γ ⊢ e" to "Γ, x ⊢ e x", for comparing with
       ||| a lambda "Γ ⊢ λx ⇒ t" that has been converted to "Γ, x ⊢ t".
       private %inline
       toLamBody : Elim d n -> Term d (S n)
-      toLamBody e = E $ weakE 1 e :@ BVT 0
+      toLamBody e = E $ App (weakE 1 e) (BVT 0 e.loc) e.loc
 
       private covering
       compare0' : EqContext n ->
                   (ty, s, t : Term 0 n) ->
                   (0 _ : NotRedex defs ty) => (0 _ : So (isTyConE ty)) =>
                   (0 _ : NotRedex defs s)  => (0 _ : NotRedex defs t) =>
-                  Equal ()
+                  Equal_ ()
-      compare0' ctx (TYPE _) s t = compareType ctx s t
+      compare0' ctx (TYPE {}) s t = compareType ctx s t
 
-      compare0' ctx ty@(Pi {qty, arg, res}) s t {n} = local_ Equal $
+      compare0' ctx ty@(Pi {qty, arg, res, _}) s t {n} = local_ Equal $
         case (s, t) of
           --           Γ, x : A ⊢ s = t : B
           -- -------------------------------------------
           --  Γ ⊢ (λ x ⇒ s) = (λ x ⇒ t) : (π·x : A) → B
-          (Lam b1, Lam b2) => compare0 ctx' res.term b1.term b2.term
+          (Lam b1 {}, Lam b2 {}) =>
+            compare0 ctx' res.term b1.term b2.term
 
           --       Γ, x : A ⊢ s = e x : B
           -- -----------------------------------
           --  Γ ⊢ (λ x ⇒ s) = e : (π·x : A) → B
-          (E e,   Lam b) => eta e b
+          (E e,      Lam b {}) => eta s.loc e b
-          (Lam b, E e)   => eta e b
+          (Lam b {}, E e)      => eta s.loc e b
 
           (E e, E f) => Elim.compare0 ctx e f
 
-          (Lam _, t) => wrongType ctx ty t
+          (Lam {}, t) => wrongType t.loc ctx ty t
-          (E _,   t) => wrongType ctx ty t
+          (E _,    t) => wrongType t.loc ctx ty t
-          (s,     _) => wrongType ctx ty s
+          (s,      _) => wrongType s.loc ctx ty s
         where
           ctx' : EqContext (S n)
           ctx' = extendTy qty res.name arg ctx
 
-          eta : Elim 0 n -> ScopeTerm 0 n -> Equal ()
+          eta : Loc -> Elim 0 n -> ScopeTerm 0 n -> Equal_ ()
-          eta e (S _ (Y b)) = compare0 ctx' res.term (toLamBody e) b
+          eta _   e (S _ (Y b)) = compare0 ctx' res.term (toLamBody e) b
-          eta e (S _ (N _)) = clashT ctx ty s t
+          eta loc e (S _ (N _)) = clashT loc ctx ty s t
 
       compare0' ctx ty@(Sig {fst, snd, _}) s t = local_ Equal $
         case (s, t) of
@@ -188,34 +212,35 @@ parameters (defs : Definitions)
           --     Γ ⊢ (s₁, t₁) = (s₂,t₂) : (x : A) × B
           --
           -- [todo] η for π ≥ 0 maybe
-          (Pair sFst sSnd, Pair tFst tSnd) => do
+          (Pair sFst sSnd {}, Pair tFst tSnd {}) => do
             compare0 ctx fst sFst tFst
-            compare0 ctx (sub1 snd (sFst :# fst)) sSnd tSnd
+            compare0 ctx (sub1 snd (Ann sFst fst fst.loc)) sSnd tSnd
 
           (E e, E f) => Elim.compare0 ctx e f
 
-          (Pair {}, E _)     => clashT ctx ty s t
+          (Pair {}, E _)     => clashT s.loc ctx ty s t
-          (E _,     Pair {}) => clashT ctx ty s t
+          (E _,     Pair {}) => clashT s.loc ctx ty s t
 
-          (Pair {}, t) => wrongType ctx ty t
+          (Pair {}, t) => wrongType t.loc ctx ty t
-          (E _,     t) => wrongType ctx ty t
+          (E _,     t) => wrongType t.loc ctx ty t
-          (s,       _) => wrongType ctx ty s
+          (s,       _) => wrongType s.loc ctx ty s
 
-      compare0' ctx ty@(Enum tags) s t = local_ Equal $
+      compare0' ctx ty@(Enum {}) s t = local_ Equal $
         case (s, t) of
           -- --------------------
           --  Γ ⊢ `t = `t : {ts}
           --
           -- t ∈ ts is in the typechecker, not here, ofc
-          (Tag t1, Tag t2) => unless (t1 == t2) $ clashT ctx ty s t
+          (Tag t1 {}, Tag t2 {}) =>
+            unless (t1 == t2) $ clashT s.loc ctx ty s t
           (E e, E f) => Elim.compare0 ctx e f
 
-          (Tag _, E _)   => clashT ctx ty s t
+          (Tag {}, E _)    => clashT s.loc ctx ty s t
-          (E _,   Tag _) => clashT ctx ty s t
+          (E _,    Tag {}) => clashT s.loc ctx ty s t
 
-          (Tag _, t) => wrongType ctx ty t
+          (Tag {}, t) => wrongType t.loc ctx ty t
-          (E _,   t) => wrongType ctx ty t
+          (E _,    t) => wrongType t.loc ctx ty t
-          (s,     _) => wrongType ctx ty s
+          (s,      _) => wrongType s.loc ctx ty s
 
       compare0' _ (Eq {}) _ _ =
         -- ✨ uip ✨
@@ -224,84 +249,85 @@ parameters (defs : Definitions)
         --  Γ ⊢ e = f : Eq [i ⇒ A] s t
         pure ()
 
-      compare0' ctx Nat s t = local_ Equal $
+      compare0' ctx nat@(Nat {}) s t = local_ Equal $
         case (s, t) of
           -- ---------------
           --  Γ ⊢ 0 = 0 : ℕ
-          (Zero, Zero) => pure ()
+          (Zero {}, Zero {}) => pure ()
 
-          --      Γ ⊢ m = n : ℕ
+          --      Γ ⊢ s = t : ℕ
           -- -------------------------
-          --  Γ ⊢ succ m = succ n : ℕ
+          --  Γ ⊢ succ s = succ t : ℕ
-          (Succ m, Succ n) => compare0 ctx Nat m n
+          (Succ s' {}, Succ t' {}) => compare0 ctx nat s' t'
 
           (E e, E f) => Elim.compare0 ctx e f
 
-          (Zero,   Succ _) => clashT ctx Nat s t
+          (Zero {}, Succ {}) => clashT s.loc ctx nat s t
-          (Zero,   E _)    => clashT ctx Nat s t
+          (Zero {}, E _)     => clashT s.loc ctx nat s t
-          (Succ _, Zero)   => clashT ctx Nat s t
+          (Succ {}, Zero {}) => clashT s.loc ctx nat s t
-          (Succ _, E _)    => clashT ctx Nat s t
+          (Succ {}, E _)     => clashT s.loc ctx nat s t
-          (E _,    Zero)   => clashT ctx Nat s t
+          (E _,     Zero {}) => clashT s.loc ctx nat s t
-          (E _,    Succ _) => clashT ctx Nat s t
+          (E _,     Succ {}) => clashT s.loc ctx nat s t
 
-          (Zero,   t) => wrongType ctx Nat t
+          (Zero {}, t) => wrongType t.loc ctx nat t
-          (Succ _, t) => wrongType ctx Nat t
+          (Succ {}, t) => wrongType t.loc ctx nat t
-          (E _,    t) => wrongType ctx Nat t
+          (E _,     t) => wrongType t.loc ctx nat t
-          (s,      _) => wrongType ctx Nat s
+          (s,       _) => wrongType s.loc ctx nat s
 
-      compare0' ctx ty@(BOX q ty') s t = local_ Equal $
+      compare0' ctx ty@(BOX q ty' {}) s t = local_ Equal $
         case (s, t) of
           --     Γ ⊢ s = t : A
           -- -----------------------
           --  Γ ⊢ [s] = [t] : [π.A]
-          (Box s, Box t) => compare0 ctx ty' s t
+          (Box s' {}, Box t' {}) => compare0 ctx ty' s' t'
 
           (E e, E f) => Elim.compare0 ctx e f
 
-          (Box _, t) => wrongType ctx ty t
+          (Box {}, t) => wrongType t.loc ctx ty t
-          (E   _, t) => wrongType ctx ty t
+          (E   _,  t) => wrongType t.loc ctx ty t
-          (s,     _) => wrongType ctx ty s
+          (s,      _) => wrongType s.loc ctx ty s
 
       compare0' ctx ty@(E _) s t = do
         -- a neutral type can only be inhabited by neutral values
         -- e.g. an abstract value in an abstract type, bound variables, …
-        E e <- pure s | _ => wrongType ctx ty s
+        let E e = s | _ => wrongType s.loc ctx ty s
-        E f <- pure t | _ => wrongType ctx ty t
+            E f = t | _ => wrongType t.loc ctx ty t
         Elim.compare0 ctx e f
 
     ||| compares two types, using the current variance `mode` for universes.
     ||| fails if they are not types, even if they would happen to be equal.
     export covering %inline
-    compareType : EqContext n -> (s, t : Term 0 n) -> Equal ()
+    compareType : EqContext n -> (s, t : Term 0 n) -> Equal_ ()
     compareType ctx s t = do
       let Val n = ctx.termLen
-      Element s _ <- whnf defs ctx s
+      Element s' _ <- whnf defs ctx s.loc s
-      Element t _ <- whnf defs ctx t
+      Element t' _ <- whnf defs ctx t.loc t
-      ts <- ensureTyCon ctx s
+      ts <- ensureTyCon s.loc ctx s'
-      tt <- ensureTyCon ctx t
+      tt <- ensureTyCon t.loc ctx t'
-      st <- either pure (const $ clashTy ctx s t) $ nchoose $ sameTyCon s t
+      st <- either pure (const $ clashTy s.loc ctx s' t') $
-      compareType' ctx s t
+            nchoose $ sameTyCon s' t'
+      compareType' ctx s' t'
 
     private covering
     compareType' : EqContext n -> (s, t : Term 0 n) ->
                    (0 _ : NotRedex defs s) => (0 _ : So (isTyConE s)) =>
                    (0 _ : NotRedex defs t) => (0 _ : So (isTyConE t)) =>
                    (0 _ : So (sameTyCon s t)) =>
-                   Equal ()
+                   Equal_ ()
     -- equality is the same as subtyping, except with the
     -- "≤" in the TYPE rule being replaced with "="
-    compareType' ctx (TYPE k) (TYPE l) =
+    compareType' ctx a@(TYPE k {}) (TYPE l {}) =
       --        𝓀 ≤ ℓ
       -- ----------------------
       --  Γ ⊢ Type 𝓀 <: Type ℓ
-      expectModeU !mode k l
+      expectModeU a.loc !mode k l
 
-    compareType' ctx (Pi {qty = sQty, arg = sArg, res = sRes, _})
+    compareType' ctx a@(Pi {qty = sQty, arg = sArg, res = sRes, _})
                        (Pi {qty = tQty, arg = tArg, res = tRes, _}) = do
       --   Γ ⊢ A₁ :> A₂    Γ, x : A₁ ⊢ B₁ <: B₂
       -- ----------------------------------------
       --  Γ ⊢ (π·x : A₁) → B₁ <: (π·x : A₂) → B₂
-      expectEqualQ sQty tQty
+      expectEqualQ a.loc sQty tQty
       local flip $ compareType ctx sArg tArg -- contra
       compareType (extendTy Zero sRes.name sArg ctx) sRes.term tRes.term
 
@@ -325,21 +351,21 @@ parameters (defs : Definitions)
         Term.compare0 ctx sTy.zero sl tl
         Term.compare0 ctx sTy.one  sr tr
 
-    compareType' ctx s@(Enum tags1) t@(Enum tags2) = do
+    compareType' ctx s@(Enum tags1 {}) t@(Enum tags2 {}) = do
       -- ------------------
       --  Γ ⊢ {ts} <: {ts}
       --
       -- no subtyping based on tag subsets, since that would need
       -- a runtime coercion
-      unless (tags1 == tags2) $ clashTy ctx s t
+      unless (tags1 == tags2) $ clashTy s.loc ctx s t
 
-    compareType' ctx Nat Nat =
+    compareType' ctx (Nat {}) (Nat {}) =
       -- ------------
       --  Γ ⊢ ℕ <: ℕ
       pure ()
 
-    compareType' ctx (BOX pi a) (BOX rh b) = do
+    compareType' ctx (BOX pi a loc) (BOX rh b {}) = do
-      expectEqualQ pi rh
+      expectEqualQ loc pi rh
       compareType ctx a b
 
     compareType' ctx (E e) (E f) = do
@@ -347,13 +373,17 @@ parameters (defs : Definitions)
       -- has been inlined by whnf
       Elim.compare0 ctx e f
 
+    --  Ψ | Γ ⊢₀ e ⇒ Eq [𝑖 ⇒ A] s t
+    -- -----------------------------
+    --  Ψ | Γ ⊢ e @0 = s ⇒ A[0/𝑖]
+    --  Ψ | Γ ⊢ e @1 = s ⇒ A[1/𝑖]
     private covering
     replaceEnd : EqContext n ->
-                 (e : Elim 0 n) -> DimConst -> (0 ne : NotRedex defs e) ->
+                 (e : Elim 0 n) -> Loc -> DimConst -> Loc ->
-                 Equal (Elim 0 n)
+                 (0 ne : NotRedex defs e) -> Equal_ (Elim 0 n)
-    replaceEnd ctx e p ne = do
+    replaceEnd ctx e eloc p ploc ne = do
-      (ty, l, r) <- expectEq defs ctx !(computeElimTypeE defs ctx e)
+      (ty, l, r) <- expectEq defs ctx eloc !(computeElimTypeE defs ctx e)
-      pure $ ends l r p :# dsub1 ty (K p)
+      pure $ Ann (ends l r p) (dsub1 ty (K p ploc)) eloc
 
     namespace Elim
       -- [fixme] the following code ends up repeating a lot of work in the
@@ -364,133 +394,179 @@ parameters (defs : Definitions)
       ||| ⚠ **assumes that they have both been typechecked, and have
       ||| equal types.** ⚠
       export covering %inline
-      compare0 : EqContext n -> (e, f : Elim 0 n) -> Equal ()
+      compare0 : EqContext n -> (e, f : Elim 0 n) -> Equal_ ()
       compare0 ctx e f =
         wrapErr (WhileComparingE ctx !mode e f) $ do
           let Val n = ctx.termLen
-          Element e ne <- whnf defs ctx e
+          Element e' ne <- whnf defs ctx e.loc e
-          Element f nf <- whnf defs ctx f
+          Element f' nf <- whnf defs ctx f.loc f
-          -- [fixme] there is a better way to do this "isSubSing" stuff for sure
+          unless !(isSubSing defs ctx =<< computeElimTypeE defs ctx e') $
-          unless !(isSubSing defs ctx !(computeElimTypeE defs ctx e)) $
+            compare0' ctx e' f' ne nf
-            compare0' ctx e f ne nf
 
       private covering
       compare0' : EqContext n ->
                   (e, f : Elim 0 n) ->
                   (0 ne : NotRedex defs e) -> (0 nf : NotRedex defs f) ->
-                  Equal ()
+                  Equal_ ()
       -- replace applied equalities with the appropriate end first
-      -- e.g. e : Eq [i ⇒ A] s t ⊢ e 𝟎 = s : A‹𝟎/i›
+      -- (see `replaceEnd`)
-      --
+      compare0' ctx (DApp e (K p ploc) loc) f ne nf =
-      -- [todo] maybe have typed whnf and do this (and η???) there instead
+        compare0 ctx !(replaceEnd ctx e loc p ploc $ noOr1 ne) f
-      compare0' ctx (e :% K p) f ne nf =
+      compare0' ctx e (DApp f (K q qloc) loc) ne nf =
-        compare0 ctx !(replaceEnd ctx e p $ noOr1 ne) f
+        compare0 ctx e !(replaceEnd ctx f loc q qloc $ noOr1 nf)
-      compare0' ctx e (f :% K q) ne nf =
-        compare0 ctx e !(replaceEnd ctx f q $ noOr1 nf)
 
-      compare0' ctx e@(F x) f@(F y) _ _ = unless (x == y) $ clashE ctx e f
+      compare0' ctx e@(F x {}) f@(F y {}) _ _ =
-      compare0' ctx e@(F _) f _ _ = clashE ctx e f
+        unless (x == y) $ clashE e.loc ctx e f
+      compare0' ctx e@(F {}) f _ _ = clashE e.loc ctx e f
 
-      compare0' ctx e@(B i) f@(B j) _ _ = unless (i == j) $ clashE ctx e f
+      compare0' ctx e@(B i {}) f@(B j {}) _ _ =
-      compare0' ctx e@(B _) f _ _ = clashE ctx e f
+        unless (i == j) $ clashE e.loc ctx e f
+      compare0' ctx e@(B {}) f _ _ = clashE e.loc ctx e f
 
-      compare0' ctx (e :@ s) (f :@ t) ne nf =
+      --  Ψ | Γ ⊢ e = f ⇒ π.(x : A) → B
+      --  Ψ | Γ ⊢ s = t ⇐ A
+      -- -------------------------------
+      --  Ψ | Γ ⊢ e s = f t ⇒ B[s∷A/x]
+      compare0' ctx (App e s eloc) (App f t floc) ne nf =
         local_ Equal $ do
           compare0 ctx e f
-          (_, arg, _) <- expectPi defs ctx =<<
+          (_, arg, _) <- expectPi defs ctx eloc =<<
                          computeElimTypeE defs ctx e @{noOr1 ne}
           Term.compare0 ctx arg s t
-      compare0' ctx e@(_ :@ _) f _ _ = clashE ctx e f
+      compare0' ctx e@(App {}) f _ _ = clashE e.loc ctx e f
 
-      compare0' ctx (CasePair epi e eret ebody)
+      --  Ψ | Γ ⊢ e = f ⇒ (x : A) × B
-                    (CasePair fpi f fret fbody) ne nf =
+      --  Ψ | Γ, 0.p : (x : A) × B ⊢ Q = R
+      --  Ψ | Γ, x : A, y : B ⊢ s = t ⇐ Q[((x, y) ∷ (x : A) × B)/p]
+      -- -----------------------------------------------------------
+      --    Ψ | Γ ⊢ caseπ e return Q of { (x, y) ⇒ s }
+      --          = caseπ f return R of { (x, y) ⇒ t } ⇒ Q[e/p]
+      compare0' ctx (CasePair epi e eret ebody eloc)
+                    (CasePair fpi f fret fbody {}) ne nf =
         local_ Equal $ do
           compare0 ctx e f
           ety <- computeElimTypeE defs ctx e @{noOr1 ne}
           compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
-          (fst, snd) <- expectSig defs ctx ety
+          (fst, snd) <- expectSig defs ctx eloc ety
           let [< x, y] = ebody.names
           Term.compare0 (extendTyN [< (epi, x, fst), (epi, y, snd.term)] ctx)
-                        (substCasePairRet ety eret)
+                        (substCasePairRet ebody.names ety eret)
                         ebody.term fbody.term
-          expectEqualQ epi fpi
+          expectEqualQ e.loc epi fpi
-      compare0' ctx e@(CasePair {}) f _ _ = clashE ctx e f
+      compare0' ctx e@(CasePair {}) f _ _ = clashE e.loc ctx e f
 
-      compare0' ctx (CaseEnum epi e eret earms)
+      --  Ψ | Γ ⊢ e = f ⇒ {𝐚s}
-                    (CaseEnum fpi f fret farms) ne nf =
+      --  Ψ | Γ, x : {𝐚s} ⊢ Q = R
+      --  Ψ | Γ ⊢ sᵢ = tᵢ ⇐ Q[𝐚ᵢ∷{𝐚s}]
+      -- --------------------------------------------------
+      --  Ψ | Γ ⊢ caseπ e return Q of { '𝐚ᵢ ⇒ sᵢ }
+      --        = caseπ f return R of { '𝐚ᵢ ⇒ tᵢ } ⇒ Q[e/x]
+      compare0' ctx (CaseEnum epi e eret earms eloc)
+                    (CaseEnum fpi f fret farms floc) ne nf =
         local_ Equal $ do
           compare0 ctx e f
           ety <- computeElimTypeE defs ctx e @{noOr1 ne}
           compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
-          for_ !(expectEnum defs ctx ety) $ \t =>
+          for_ !(expectEnum defs ctx eloc ety) $ \t => do
-            compare0 ctx (sub1 eret $ Tag t :# ety)
+            l <- lookupArm eloc t earms
-              !(lookupArm t earms) !(lookupArm t farms)
+            r <- lookupArm floc t farms
-          expectEqualQ epi fpi
+            compare0 ctx (sub1 eret $ Ann (Tag t l.loc) ety l.loc) l r
+          expectEqualQ eloc epi fpi
         where
-          lookupArm : TagVal -> CaseEnumArms d n -> Equal (Term d n)
+          lookupArm : Loc -> TagVal -> CaseEnumArms d n -> Equal_ (Term d n)
-          lookupArm t arms = case lookup t arms of
+          lookupArm loc t arms = case lookup t arms of
             Just arm => pure arm
-            Nothing  => throw $ TagNotIn t (fromList $ keys arms)
+            Nothing  => throw $ TagNotIn loc t (fromList $ keys arms)
-      compare0' ctx e@(CaseEnum {}) f _ _ = clashE ctx e f
+      compare0' ctx e@(CaseEnum {}) f _ _ = clashE e.loc ctx e f
 
-      compare0' ctx (CaseNat epi epi' e eret ezer esuc)
+      --  Ψ | Γ ⊢ e = f ⇒ ℕ
-                    (CaseNat fpi fpi' f fret fzer fsuc) ne nf =
+      --  Ψ | Γ, x : ℕ ⊢ Q = R
+      --  Ψ | Γ ⊢ s₀ = t₀ ⇐ Q[(0 ∷ ℕ)/x]
+      --  Ψ | Γ, x : ℕ, y : Q ⊢ s₁ = t₁ ⇐ Q[(succ x ∷ ℕ)/x]
+      -- -----------------------------------------------------
+      --  Ψ | Γ ⊢ caseπ e return Q of { 0 ⇒ s₀; x, π.y ⇒ s₁ }
+      --        = caseπ f return R of { 0 ⇒ t₀; x, π.y ⇒ t₁ }
+      --        ⇒ Q[e/x]
+      compare0' ctx (CaseNat epi epi' e eret ezer esuc eloc)
+                    (CaseNat fpi fpi' f fret fzer fsuc floc) ne nf =
         local_ Equal $ do
           compare0 ctx e f
           ety <- computeElimTypeE defs ctx e @{noOr1 ne}
           compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
-          compare0 ctx (sub1 eret (Zero :# Nat)) ezer fzer
+          compare0 ctx
+            (sub1 eret (Ann (Zero ezer.loc) (Nat ezer.loc) ezer.loc))
+            ezer fzer
           let [< p, ih] = esuc.names
-          compare0 (extendTyN [< (epi, p, Nat), (epi', ih, eret.term)] ctx)
+          compare0
-                   (substCaseSuccRet eret)
+            (extendTyN [< (epi, p, Nat p.loc), (epi', ih, eret.term)] ctx)
-                   esuc.term fsuc.term
+            (substCaseSuccRet esuc.names eret) esuc.term fsuc.term
-          expectEqualQ epi  fpi
+          expectEqualQ e.loc epi  fpi
-          expectEqualQ epi' fpi'
+          expectEqualQ e.loc epi' fpi'
-      compare0' ctx e@(CaseNat {}) f _ _ = clashE ctx e f
+      compare0' ctx e@(CaseNat {}) f _ _ = clashE e.loc ctx e f
 
-      compare0' ctx (CaseBox epi e eret ebody)
+      --  Ψ | Γ ⊢ e = f ⇒ [ρ. A]
-                    (CaseBox fpi f fret fbody) ne nf =
+      --  Ψ | Γ, x : [ρ. A] ⊢ Q = R
+      --  Ψ | Γ, x : A ⊢ s = t ⇐ Q[([x] ∷ [ρ. A])/x]
+      -- --------------------------------------------------
+      --  Ψ | Γ ⊢ caseπ e return Q of { [x] ⇒ s }
+      --        = caseπ f return R of { [x] ⇒ t } ⇒ Q[e/x]
+      compare0' ctx (CaseBox epi e eret ebody eloc)
+                    (CaseBox fpi f fret fbody floc) ne nf =
         local_ Equal $ do
           compare0 ctx e f
           ety <- computeElimTypeE defs ctx e @{noOr1 ne}
           compareType (extendTy Zero eret.name ety ctx) eret.term fret.term
-          (q, ty) <- expectBOX defs ctx ety
+          (q, ty) <- expectBOX defs ctx eloc ety
           compare0 (extendTy (epi * q) ebody.name ty ctx)
-            (substCaseBoxRet ety eret)
+            (substCaseBoxRet ebody.name ety eret)
             ebody.term fbody.term
-          expectEqualQ epi fpi
+          expectEqualQ eloc epi fpi
-      compare0' ctx e@(CaseBox {}) f _ _ = clashE ctx e f
+      compare0' ctx e@(CaseBox {}) f _ _ = clashE e.loc ctx e f
 
-      compare0' ctx (s :# a) (t :# b) _ _ =
+      --  Ψ | Γ ⊢ s <: t : B
+      -- --------------------------------
+      --  Ψ | Γ ⊢ (s ∷ A) <: (t ∷ B) ⇒ B
+      --
+      -- and similar for :> and A
+      compare0' ctx (Ann s a _) (Ann t b _) _ _ =
         let ty = case !mode of Super => a; _ => b in
         Term.compare0 ctx ty s t
 
-      compare0' ctx (Coe ty1 p1 q1 (E val1)) (Coe ty2 p2 q2 (E val2)) ne nf = do
+      --  Ψ | Γ ⊢ A‹p₁/𝑖› <: B‹p₂/𝑖›
+      --  Ψ | Γ ⊢ A‹q₁/𝑖› <: B‹q₂/𝑖›
+      --  Ψ | Γ ⊢ e <: f ⇒ _
+      --    (non-neutral forms have the coercion already pushed in)
+      -- -----------------------------------------------------------
+      --  Ψ | Γ ⊢ coe [𝑖 ⇒ A] @p₁ @q₁ e
+      --       <: coe [𝑖 ⇒ B] @p₂ @q₂ f ⇒ B‹q₂/𝑖›
+      compare0' ctx (Coe ty1 p1 q1 (E val1) _)
+                    (Coe ty2 p2 q2 (E val2) _) ne nf = do
         compareType ctx (dsub1 ty1 p1) (dsub1 ty2 p2)
         compareType ctx (dsub1 ty1 q1) (dsub1 ty2 q2)
         compare0 ctx val1 val2
-      compare0' ctx e@(Coe {}) f _ _ = clashE ctx e f
+      compare0' ctx e@(Coe {}) f _ _ = clashE e.loc ctx e f
 
-      compare0' ctx (Comp _ _ _ _ (K _) _ _) _ ne _ = void $ absurd $ noOr2 ne
+      -- (no neutral compositions in a closed dctx)
-      compare0' ctx (Comp _ _ _ _ (B i) _ _) _ _ _ = absurd i
+      compare0' _ (Comp {r = K e _, _}) _ ne _ = void $ absurd $ noOr2 ne
-      compare0' ctx _ (Comp _ _ _ _ (K _) _ _) _ nf = void $ absurd $ noOr2 nf
+      compare0' _ (Comp {r = B i _, _}) _ _ _ = absurd i
+      compare0' _ _ (Comp {r = K _ _, _}) _ nf = void $ absurd $ noOr2 nf
 
-      compare0' ctx (TypeCase ty1 ret1 arms1 def1)
+      compare0' ctx (TypeCase ty1 ret1 arms1 def1 eloc)
-                    (TypeCase ty2 ret2 arms2 def2)
+                    (TypeCase ty2 ret2 arms2 def2 floc) ne _ =
-                    ne _ =
         local_ Equal $ do
           compare0 ctx ty1 ty2
-          u <- expectTYPE defs ctx =<< computeElimTypeE defs ctx ty1 @{noOr1 ne}
+          u <- expectTYPE defs ctx eloc =<<
+               computeElimTypeE defs ctx ty1 @{noOr1 ne}
           compareType ctx ret1 ret2
           compareType ctx def1 def2
           for_ allKinds $ \k =>
             compareArm ctx k ret1 u
               (lookupPrecise k arms1) (lookupPrecise k arms2) def1
-      compare0' ctx e@(TypeCase {}) f _ _ = clashE ctx e f
+      compare0' ctx e@(TypeCase {}) f _ _ = clashE e.loc ctx e f
 
-      compare0' ctx   (s :# a) f        _ _ = Term.compare0 ctx a s (E f)
+      compare0' ctx (Ann s a _) f           _ _ = Term.compare0 ctx a s (E f)
-      compare0' ctx e          (t :# b) _ _ = Term.compare0 ctx b (E e) t
+      compare0' ctx e           (Ann t b _) _ _ = Term.compare0 ctx b (E e) t
-      compare0' ctx e@(_ :# _) f        _ _ = clashE ctx e f
+      compare0' ctx e@(Ann {})  f           _ _ = clashE e.loc ctx e f
 
       ||| compare two type-case branches, which came from the arms of the given
       ||| kind. `ret` is the return type of the case expression, and `u` is the
@@ -500,7 +576,7 @@ parameters (defs : Definitions)
                    (ret : Term 0 n) -> (u : Universe) ->
                    (b1, b2 : Maybe (TypeCaseArmBody k 0 n)) ->
                    (def : Term 0 n) ->
-                   Equal ()
+                   Equal_ ()
       compareArm {b1 = Nothing, b2 = Nothing, _} = pure ()
       compareArm ctx k ret u b1 b2 def =
         let def = SN def in
@@ -510,22 +586,22 @@ parameters (defs : Definitions)
       compareArm_ : EqContext n -> (k : TyConKind) ->
                     (ret : Term 0 n) -> (u : Universe) ->
                     (b1, b2 : TypeCaseArmBody k 0 n) ->
-                    Equal ()
+                    Equal_ ()
       compareArm_ ctx KTYPE ret u b1 b2 =
         compare0 ctx ret b1.term b2.term
 
       compareArm_ ctx KPi ret u b1 b2 = do
         let [< a, b] = b1.names
             ctx = extendTyN
-              [< (Zero, a, TYPE u),
+              [< (Zero, a, TYPE u a.loc),
-                 (Zero, b, Arr Zero (BVT 0) (TYPE u))] ctx
+                 (Zero, b, Arr Zero (BVT 0 b.loc) (TYPE u b.loc) b.loc)] ctx
         compare0 ctx (weakT 2 ret) b1.term b2.term
 
       compareArm_ ctx KSig ret u b1 b2 = do
         let [< a, b] = b1.names
             ctx = extendTyN
-              [< (Zero, a, TYPE u),
+              [< (Zero, a, TYPE u a.loc),
-                 (Zero, b, Arr Zero (BVT 0) (TYPE u))] ctx
+                 (Zero, b, Arr Zero (BVT 0 b.loc) (TYPE u b.loc) b.loc)] ctx
         compare0 ctx (weakT 2 ret) b1.term b2.term
 
       compareArm_ ctx KEnum ret u b1 b2 =
@@ -534,70 +610,76 @@ parameters (defs : Definitions)
       compareArm_ ctx KEq ret u b1 b2 = do
         let [< a0, a1, a, l, r] = b1.names
             ctx = extendTyN
-              [< (Zero, a0, TYPE u),
+              [< (Zero, a0, TYPE u a0.loc),
-                 (Zero, a1, TYPE u),
+                 (Zero, a1, TYPE u a1.loc),
-                 (Zero, a,  Eq0 (TYPE u) (BVT 1) (BVT 0)),
+                 (Zero, a,  Eq0 (TYPE u a.loc)
-                 (Zero, l,  BVT 2),
+                                (BVT 1 a0.loc) (BVT 0 a1.loc) a.loc),
-                 (Zero, r,  BVT 2)] ctx
+                 (Zero, l,  BVT 2 a0.loc),
+                 (Zero, r,  BVT 2 a1.loc)] ctx
         compare0 ctx (weakT 5 ret) b1.term b2.term
 
       compareArm_ ctx KNat ret u b1 b2 =
         compare0 ctx ret b1.term b2.term
 
       compareArm_ ctx KBOX ret u b1 b2 = do
-        let ctx = extendTy Zero b1.name (TYPE u) ctx
+        let ctx = extendTy Zero b1.name (TYPE u b1.name.loc) ctx
         compare0 ctx (weakT 1 ret) b1.term b1.term
 
 
-parameters {auto _ : (Has DefsReader fs, Has ErrorEff fs)} (ctx : TyContext d n)
+parameters (loc : Loc) (ctx : TyContext d n)
   -- [todo] only split on the dvars that are actually used anywhere in
   -- the calls to `splits`
 
   parameters (mode : EqMode)
+    private
+    fromEqual_ : Equal_ a -> Equal a
+    fromEqual_ act = lift $ evalState mode act
+
+    private
+    eachFace : Applicative f => (EqContext n -> DSubst d 0 -> f ()) -> f ()
+    eachFace act =
+      for_ (splits loc ctx.dctx) $ \th => act (makeEqContext ctx th) th
+
+    private
+    runCompare : (Definitions -> EqContext n -> DSubst d 0 -> Equal_ ()) ->
+                 Equal ()
+    runCompare act = fromEqual_ $ eachFace $ act !defs
+
     namespace Term
       export covering
-      compare : (ty, s, t : Term d n) -> Eff fs ()
+      compare : (ty, s, t : Term d n) -> Equal ()
-      compare ty s t =
+      compare ty s t = runCompare $ \defs, ectx, th =>
-        map fst $ runState @{Z} mode $
+        compare0 defs ectx (ty // th) (s // th) (t // th)
-          for_ (splits ctx.dctx) $ \th =>
-            let ectx = makeEqContext ctx th in
-            lift $ compare0 !defs ectx (ty // th) (s // th) (t // th)
 
       export covering
-      compareType : (s, t : Term d n) -> Eff fs ()
+      compareType : (s, t : Term d n) -> Equal ()
-      compareType s t =
+      compareType s t = runCompare $ \defs, ectx, th =>
-        map fst $ runState @{Z} mode $
+        compareType defs ectx (s // th) (t // th)
-          for_ (splits ctx.dctx) $ \th =>
-            let ectx = makeEqContext ctx th in
-            lift $ compareType !defs ectx (s // th) (t // th)
 
     namespace Elim
       ||| you don't have to pass the type in but the arguments must still be
       ||| of the same type!!
-      export covering %inline
+      export covering
-      compare : (e, f : Elim d n) -> Eff fs ()
+      compare : (e, f : Elim d n) -> Equal ()
-      compare e f =
+      compare e f = runCompare $ \defs, ectx, th =>
-        map fst $ runState @{Z} mode $
+        compare0 defs ectx (e // th) (f // th)
-          for_ (splits ctx.dctx) $ \th =>
-            let ectx = makeEqContext ctx th in
-            lift $ compare0 !defs ectx (e // th) (f // th)
 
   namespace Term
     export covering %inline
-    equal, sub, super : (ty, s, t : Term d n) -> Eff fs ()
+    equal, sub, super : (ty, s, t : Term d n) -> Equal ()
     equal = compare Equal
     sub   = compare Sub
     super = compare Super
 
     export covering %inline
-    equalType, subtype, supertype : (s, t : Term d n) -> Eff fs ()
+    equalType, subtype, supertype : (s, t : Term d n) -> Equal ()
     equalType = compareType Equal
     subtype   = compareType Sub
     supertype = compareType Super
 
   namespace Elim
     export covering %inline
-    equal, sub, super : (e, f : Elim d n) -> Eff fs ()
+    equal, sub, super : (e, f : Elim d n) -> Equal ()
     equal = compare Equal
     sub   = compare Sub
     super = compare Super

lib/Quox/Loc.idr

@@ -1,7 +1,8 @@
 ||| file locations
 module Quox.Loc
 
-import Text.Bounded
+import public Text.Bounded
+import Data.SortedMap
 import Derive.Prelude
 
 %default total
@@ -11,53 +12,110 @@ public export
 FileName : Type
 FileName = String
 
+%runElab derive "Bounds" [Ord]
+
 public export
-record Loc' where
+data Loc_ = NoLoc | YesLoc FileName Bounds
+%name Loc_ loc
+%runElab derive "Loc_" [Eq, Ord, Show]
+
+
+||| a wrapper for locations which are always considered equal
+public export
+record Loc where
   constructor L
-  fname : FileName
+  val : Loc_
-  startLine, startCol, endLine, endCol : Int
+%name Loc loc
-%name Loc' loc
+%runElab derive "Loc" [Show]
-%runElab derive "Loc'" [Eq, Ord, Show]
 
-public export
+export %inline Eq  Loc where _ == _ = True
-Loc : Type
+export %inline Ord Loc where compare _ _ = EQ
-Loc = Maybe Loc'
 
-export
+public export %inline
+noLoc : Loc
+noLoc = L NoLoc
+
+public export %inline
 makeLoc : FileName -> Bounds -> Loc
-makeLoc fname (MkBounds {startLine, startCol, endLine, endCol}) =
+makeLoc = L .: YesLoc
-  Just $ L {fname, startLine, startCol, endLine, endCol}
+
 
 export
+onlyStart_ : Loc_ -> Loc_
+onlyStart_ NoLoc = NoLoc
+onlyStart_ (YesLoc fname (MkBounds sl sc _ _)) =
+  YesLoc fname $ MkBounds sl sc sl sc
+
+export %inline
 onlyStart : Loc -> Loc
-onlyStart Nothing = Nothing
+onlyStart = {val $= onlyStart_}
-onlyStart (Just (L fname sl sc _ _)) = Just $ L fname sl sc sl sc
 
 export
+onlyEnd_ : Loc_ -> Loc_
+onlyEnd_ NoLoc = NoLoc
+onlyEnd_ (YesLoc fname (MkBounds _ _ el ec)) =
+  YesLoc fname $ MkBounds el ec el ec
+
+export %inline
 onlyEnd : Loc -> Loc
-onlyEnd Nothing = Nothing
+onlyEnd = {val $= onlyEnd_}
-onlyEnd (Just (L fname _ _ el ec)) = Just $ L fname el ec el ec
 
 
 export
-extend : Loc -> Bounds -> Loc
+extend_ : Loc_ -> Bounds -> Loc_
-extend Nothing _ = Nothing
+extend_ NoLoc _ = NoLoc
-extend (Just (L fname sl1 sc1 el1 ec1)) (MkBounds sl2 sc2 el2 ec2) =
+extend_ (YesLoc fname (MkBounds sl1 sc1 el1 ec1)) (MkBounds sl2 sc2 el2 ec2) =
   let (sl, sc) = (sl1, sc1) `min` (sl2, sc2)
       (el, ec) = (el1, ec1) `max` (el2, ec2)
   in
-  Just $ L fname sl sc el ec
+  YesLoc fname $ MkBounds sl sc el ec
+
+export
+extend : Loc -> Bounds -> Loc
+extend l b = L $ extend_ l.val b
 
 export
 extend' : Loc -> Maybe Bounds -> Loc
 extend' l b = maybe l (extend l) b
 
 
+namespace Loc_
+  export
+  (.bounds) : Loc_ -> Maybe Bounds
+  (YesLoc _ b).bounds = Just b
+  (NoLoc).bounds      = Nothing
+
+namespace Loc
+  export
+  (.bounds) : Loc -> Maybe Bounds
+  l.bounds = l.val.bounds
+
+export %inline
+extendL : Loc -> Loc -> Loc
+extendL l1 l2 = l1 `extend'` l2.bounds
+
+
+infixr 1 `or_`, `or`
+export %inline
+or_ : Loc_ -> Loc_ -> Loc_
+or_ l1@(YesLoc {}) _  = l1
+or_ NoLoc          l2 = l2
+
+export %inline
+or : Loc -> Loc -> Loc
+or (L l1) (L l2) = L $ l1 `or_` l2
+
+
 public export
 interface Located a where (.loc) : a -> Loc
 
-export
+public export
-(.bounds) : Loc -> Maybe Bounds
+0 Located1 : (a -> Type) -> Type
-(Just (L {fname, startLine, startCol, endLine, endCol})).bounds =
+Located1 f = forall x. Located (f x)
-  Just $ MkBounds {startLine, startCol, endLine, endCol}
+
-(Nothing).bounds = Nothing
+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)

lib/Quox/Name.idr

@@ -1,8 +1,10 @@
 module Quox.Name
 
+import Quox.Loc
 import Quox.CharExtra
 import public Data.SnocList
 import Data.List
+import Control.Eff
 import Text.Lexer
 import Derive.Prelude
 
@@ -12,15 +14,21 @@ import Derive.Prelude
 %language ElabReflection
 
 
+public export
+NameSuf : Type
+NameSuf = Nat
+
 public export
 data BaseName
 = UN String         -- user-given name
+| MN String NameSuf -- machine-generated name
 | Unused            -- "_"
 %runElab derive "BaseName" [Eq, Ord]
 
 export
 baseStr : BaseName -> String
 baseStr (UN x)   = x
+baseStr (MN x i) = "\{x}#\{show i}"
 baseStr Unused   = "_"
 
 export Show BaseName where show = baseStr
@@ -83,6 +91,17 @@ export FromString PName where fromString = MakePName [<]
 export FromString Name where fromString = fromPBaseName
 
 
+public export
+record BindName where
+  constructor BN
+  name : BaseName
+  loc_ : Loc
+%runElab derive "BindName" [Eq, Ord, Show]
+
+export Located BindName where n.loc = n.loc_
+export Relocatable BindName where setLoc loc (BN x _) = BN x loc
+
+
 export
 toDotsP : PName -> String
 toDotsP x = fastConcat $ cast $ map (<+> ".") x.mods :< x.base
@@ -140,3 +159,41 @@ isName str =
   case scan name [] (unpack str) of
     Just (_, []) => True
     _            => False
+
+
+public export
+data GenTag = GEN
+
+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
+mn : Has NameGen fs => PBaseName -> Eff fs BaseName
+mn base = do
+  i <- getAt GEN
+  modifyAt GEN S
+  pure $ MN base i
+
+||| generate a fresh binding name with the given base and
+||| (optionally) location `loc`
+export
+mnb : Has NameGen fs =>
+      PBaseName -> {default noLoc loc : Loc} -> Eff fs BindName
+mnb base = 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}

lib/Quox/Parser/FromParser.idr

@@ -1,4 +1,4 @@
-||| take freshly-parsed input, translate it to core, and check it
+||| take freshly-parsed input, scope check, type check, add to env
 module Quox.Parser.FromParser
 
 import Quox.Parser.Syntax
@@ -41,19 +41,19 @@ data StateTag = NS | SEEN
 public export
 FromParserPure : List (Type -> Type)
 FromParserPure =
-  [Except Error, StateL DEFS Definitions, StateL NS Mods]
+  [Except Error, DefsState, StateL NS Mods, NameGen]
 
 public export
-FromParserEff : List (Type -> Type)
+LoadFile' : List (Type -> Type)
-FromParserEff =
+LoadFile' = [IO, StateL SEEN SeenFiles, Reader IncludePath]
-  [Except Error, StateL DEFS Definitions, StateL NS Mods,
-   Reader IncludePath, StateL SEEN SeenFiles, IO]
 
 public export
-FromParser : Type -> Type
+LoadFile : List (Type -> Type)
-FromParser = Eff FromParserEff
+LoadFile = LoadFile' ++ [Except Error]
 
--- [todo] put the locs in the core ast, obv
+public export
+FromParserIO : List (Type -> Type)
+FromParserIO = FromParserPure ++ LoadFile'
 
 
 parameters {auto _ : Functor m} (b : Var n -> m a) (f : PName -> m a)
@@ -70,31 +70,32 @@ parameters {auto _ : Functor m} (b : Var n -> m a) (f : PName -> m a)
 export
 fromPDimWith : Has (Except Error) fs =>
                Context' PatVar d -> PDim -> Eff fs (Dim d)
-fromPDimWith ds (K e _) = pure $ K e
+fromPDimWith ds (K e loc) = pure $ K e loc
-fromPDimWith ds (V i _) =
+fromPDimWith ds (V i loc) =
-  fromBaseName (pure . B) (const $ throw $ DimNotInScope i) ds i
+  fromBaseName (\i => pure $ B i loc)
+               (const $ throw $ DimNotInScope loc i) ds i
 
 private
 avoidDim : Has (Except Error) fs =>
-           Context' PatVar d -> PName -> Eff fs Name
+           Context' PatVar d -> Loc -> PName -> Eff fs Name
-avoidDim ds x =
+avoidDim ds loc x =
-  fromName (const $ throw $ DimNameInTerm x.base) (pure . fromPName) ds x
+  fromName (const $ throw $ DimNameInTerm loc x.base) (pure . fromPName) ds x
 
 private
-resolveName : Mods -> Name -> Eff FromParserPure (Term d n)
+resolveName : Mods -> Loc -> Name -> Eff FromParserPure (Term d n)
-resolveName ns x =
+resolveName ns loc x =
   let here = addMods ns x in
   if isJust $ lookup here !(getAt DEFS) then
-    pure $ FT here
+    pure $ FT here loc
   else do
     let ns :< _ = ns
-      | _ => throw $ TermNotInScope x
+      | _ => throw $ TermNotInScope loc x
-    resolveName ns x
+    resolveName ns loc x
 
 export
-fromPatVar : PatVar -> BaseName
+fromPatVar : PatVar -> BindName
-fromPatVar (Unused _) = Unused
+fromPatVar (Unused loc) = BN Unused loc
-fromPatVar (PV x   _) = UN x
+fromPatVar (PV x   loc) = BN (UN x) loc
 
 export
 fromPQty : PQty -> Qty
@@ -110,93 +111,112 @@ mutual
   fromPTermWith : Context' PatVar d -> Context' PatVar n ->
                   PTerm -> Eff FromParserPure (Term d n)
   fromPTermWith ds ns t0 = case t0 of
-    TYPE k _ =>
+    TYPE k loc =>
-      pure $ TYPE k
+      pure $ TYPE k loc
 
-    Pi pi x s t _ =>
+    Pi pi x s t loc =>
       Pi (fromPQty pi)
         <$> fromPTermWith ds ns s
         <*> fromPTermTScope ds ns [< x] t
+        <*> pure loc
 
-    Lam x s _ =>
+    Lam x s loc =>
-      Lam <$> fromPTermTScope ds ns [< x] s
+      Lam <$> fromPTermTScope ds ns [< x] s <*> pure loc
 
-    App s t _ =>
+    App s t loc =>
-      map E $ (:@) <$> fromPTermElim ds ns s <*> fromPTermWith ds ns t
+      map E $ App
+        <$> fromPTermElim ds ns s
+        <*> fromPTermWith ds ns t
+        <*> pure loc
 
-    Sig x s t _ =>
+    Sig x s t loc =>
-      Sig <$> fromPTermWith ds ns s <*> fromPTermTScope ds ns [< x] t
+      Sig <$> fromPTermWith ds ns s
+          <*> fromPTermTScope ds ns [< x] t
+          <*> pure loc
 
-    Pair s t _ =>
+    Pair s t loc =>
-      Pair <$> fromPTermWith ds ns s <*> fromPTermWith ds ns t
+      Pair <$> fromPTermWith ds ns s <*> fromPTermWith ds ns t <*> pure loc
 
-    Case pi pair (r, ret) (CasePair (x, y) body _) _ =>
+    Case pi pair (r, ret) (CasePair (x, y) body _) loc =>
       map E $ CasePair (fromPQty pi)
         <$> fromPTermElim ds ns pair
         <*> fromPTermTScope ds ns [< r] ret
         <*> fromPTermTScope ds ns [< x, y] body
+        <*> pure loc
 
-    Case pi tag (r, ret) (CaseEnum arms _) _ =>
+    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
+        <*> pure loc
 
-    Nat _ => pure Nat
+    Nat loc => pure $ Nat loc
-    Zero _ => pure Zero
+    Zero loc => pure $ Zero loc
-    Succ n _ => [|Succ $ fromPTermWith ds ns n|]
+    Succ n loc => [|Succ (fromPTermWith ds ns n) (pure loc)|]
 
-    Case pi nat (r, ret) (CaseNat zer (s, pi', ih, suc) _) _ =>
+    Case pi nat (r, ret) (CaseNat zer (s, pi', ih, suc) _) loc =>
       map E $ CaseNat (fromPQty pi) (fromPQty pi')
         <$> fromPTermElim ds ns nat
         <*> fromPTermTScope ds ns [< r] ret
         <*> fromPTermWith ds ns zer
         <*> fromPTermTScope ds ns [< s, ih] suc
+        <*> pure loc
 
-    Enum strs _ =>
+    Enum strs loc =>
       let set = SortedSet.fromList strs in
       if length strs == length (SortedSet.toList set) then
-        pure $ Enum set
+        pure $ Enum set loc
       else
-        throw $ DuplicatesInEnum strs
+        throw $ DuplicatesInEnum loc strs
 
-    Tag str _ => pure $ Tag str
+    Tag str loc => pure $ Tag str loc
 
-    Eq (i, ty) s t _ =>
+    Eq (i, ty) s t loc =>
       Eq <$> fromPTermDScope ds ns [< i] ty
          <*> fromPTermWith ds ns s
          <*> fromPTermWith ds ns t
+         <*> pure loc
 
-    DLam i s _ =>
+    DLam i s loc =>
-      DLam <$> fromPTermDScope ds ns [< i] s
+      DLam <$> fromPTermDScope ds ns [< i] s <*> pure loc
 
-    DApp s p _ =>
+    DApp s p loc =>
-      map E $ (:%) <$> fromPTermElim ds ns s <*> fromPDimWith ds p
+      map E $ DApp
+        <$> fromPTermElim ds ns s
+        <*> fromPDimWith ds p
+        <*> pure loc
 
-    BOX q ty _ => BOX (fromPQty q) <$> fromPTermWith ds ns ty
+    BOX q ty loc => BOX (fromPQty q) <$> fromPTermWith ds ns ty <*> pure loc
 
-    Box val _ => Box <$> fromPTermWith ds ns val
+    Box val loc => Box <$> fromPTermWith ds ns val <*> pure loc
 
-    Case pi box (r, ret) (CaseBox b body _) _ =>
+    Case pi box (r, ret) (CaseBox b body _) loc =>
       map E $ CaseBox (fromPQty pi)
         <$> fromPTermElim ds ns box
         <*> fromPTermTScope ds ns [< r] ret
         <*> fromPTermTScope ds ns [< b] body
+        <*> pure loc
 
-    V x _ =>
+    V x loc =>
-      fromName (pure . E . B) (resolveName !(getAt NS) <=< avoidDim ds) ns x
+      fromName (\i => pure $ E $ B i loc)
+               (resolveName !(getAt NS) loc <=< avoidDim ds loc) ns x
 
-    Ann s a _ =>
+    Ann s a loc =>
-      map E $ (:#) <$> fromPTermWith ds ns s <*> fromPTermWith ds ns a
+      map E $ Ann
+        <$> fromPTermWith ds ns s
+        <*> fromPTermWith ds ns a
+        <*> pure loc
 
-    Coe (i, ty) p q val _ =>
+    Coe (i, ty) p q val loc =>
       map E $ Coe
         <$> fromPTermDScope ds ns [< i] ty
         <*> fromPDimWith ds p
         <*> fromPDimWith ds q
         <*> fromPTermWith ds ns val
+        <*> pure loc
 
-    Comp (i, ty) p q val r (j0, val0) (j1, val1) _ =>
+    Comp (i, ty) p q val r (j0, val0) (j1, val1) loc =>
       map E $ CompH'
         <$> fromPTermDScope ds ns [< i] ty
         <*> fromPDimWith ds p
@@ -205,6 +225,7 @@ mutual
         <*> fromPDimWith ds r
         <*> fromPTermDScope ds ns [< j0] val0
         <*> fromPTermDScope ds ns [< j1] val1
+        <*> pure loc
 
   private
   fromPTermEnumArms : Context' PatVar d -> Context' PatVar n ->
@@ -221,7 +242,7 @@ mutual
     case !(fromPTermWith ds ns e) of
       E e => pure e
       t   => let ctx = MkNameContexts (map fromPatVar ds) (map fromPatVar ns) in
-             throw $ AnnotationNeeded ctx t
+             throw $ AnnotationNeeded t.loc ctx t
 
   -- [todo] use SN if the var is named but still unused
   private
@@ -251,10 +272,10 @@ fromPTerm = fromPTermWith [<] [<]
 
 
 export
-globalPQty : (q : Qty) -> Eff [Except Error] (So $ isGlobal q)
+globalPQty : Loc -> (q : Qty) -> Eff [Except Error] (So $ isGlobal q)
-globalPQty pi = case choose $ isGlobal pi of
+globalPQty loc pi = case choose $ isGlobal pi of
   Left  y => pure y
-  Right _ => throw $ QtyNotGlobal pi
+  Right _ => throw $ QtyNotGlobal loc pi
 
 
 export
@@ -262,30 +283,31 @@ fromPBaseNameNS : PBaseName -> Eff [StateL NS Mods] Name
 fromPBaseNameNS name = pure $ addMods !(getAt NS) $ fromPBaseName name
 
 private
-injTC : TC a -> Eff FromParserPure a
+liftTC : TC a -> Eff FromParserPure a
-injTC act = rethrow $ mapFst WrapTypeError $ runTC !(getAt DEFS) act
+liftTC act = do
+  res <- lift $ runExcept $ runReaderAt DEFS !(getAt DEFS) act
+  rethrow $ mapFst WrapTypeError res
 
 export covering
 fromPDef : PDefinition -> Eff FromParserPure NDefinition
-fromPDef (MkPDef qty pname ptype pterm _) = do
+fromPDef (MkPDef qty pname ptype pterm defLoc) = do
   name <- lift $ fromPBaseNameNS pname
-  let qty = fromPQty qty
+  qtyGlobal <- lift $ globalPQty qty.loc qty.val
-  qtyGlobal <- lift $ globalPQty qty
+  let gqty = Element qty.val qtyGlobal
-  let gqty = Element qty qtyGlobal
+      sqty = globalToSubj gqty
-  let sqty = globalToSubj gqty
   type <- lift $ traverse fromPTerm ptype
   term <- lift $ fromPTerm pterm
   case type of
     Just type => do
-      injTC $ checkTypeC empty type Nothing
+      liftTC $ checkTypeC empty type Nothing
-      injTC $ ignore $ checkC empty sqty term type
+      liftTC $ ignore $ checkC empty sqty term type
-      let def = mkDef gqty type term
+      let def = mkDef gqty type term defLoc
       modifyAt DEFS $ insert name def
       pure (name, def)
     Nothing => do
-      let E elim = term | t => throw $ AnnotationNeeded empty t
+      let E elim = term | _ => throw $ AnnotationNeeded term.loc empty term
-      res <- injTC $ inferC empty sqty elim
+      res <- liftTC $ inferC empty sqty elim
-      let def = mkDef gqty res.type term
+      let def = mkDef gqty res.type term defLoc
       modifyAt DEFS $ insert name def
       pure (name, def)
 
@@ -296,27 +318,23 @@ fromPDecl (PNs  ns)  =
   localAt NS (<+> ns.name) $ concat <$> traverse fromPDecl ns.decls
 
 
-public export
-LoadFile : List (Type -> Type)
-LoadFile = [IO, StateL SEEN SeenFiles, Reader IncludePath, Except Error]
-
 export covering
-loadFile : String -> Eff LoadFile (Maybe String)
+loadFile : Loc -> String -> Eff LoadFile (Maybe String)
-loadFile file =
+loadFile loc file =
   if contains file !(getAt SEEN) then
     pure Nothing
   else do
     Just ifile <- firstExists (map (</> file) !ask)
-      | Nothing => throw $ LoadError file FileNotFound
+      | Nothing => throw $ LoadError loc file FileNotFound
     case !(readFile ifile) of
       Right res => modifyAt SEEN (insert file) $> Just res
-      Left  err => throw $ LoadError ifile err
+      Left  err => throw $ LoadError loc ifile err
 
 mutual
   export covering
-  loadProcessFile : String -> FromParser (List NDefinition)
+  loadProcessFile : Loc -> String -> Eff FromParserIO (List NDefinition)
-  loadProcessFile file =
+  loadProcessFile loc file =
-    case !(lift $ loadFile file) of
+    case !(lift $ loadFile loc file) of
       Just inp => do
         tl <- either (throw . WrapParseError file) pure $ lexParseInput file inp
         concat <$> traverse fromPTopLevel tl
@@ -324,26 +342,29 @@ mutual
 
   ||| populates the `defs` field of the state
   export covering
-  fromPTopLevel : PTopLevel -> FromParser (List NDefinition)
+  fromPTopLevel : PTopLevel -> Eff FromParserIO (List NDefinition)
   fromPTopLevel (PD    decl)     = lift $ fromPDecl decl
-  fromPTopLevel (PLoad file _) = loadProcessFile file
+  fromPTopLevel (PLoad file loc) = loadProcessFile loc file
 
 export
-fromParserPure : Definitions ->
+fromParserPure : NameSuf -> Definitions ->
                  Eff FromParserPure a ->
-                 Either Error (a, Definitions)
+                 (Either Error (a, Definitions), NameSuf)
-fromParserPure defs act =
+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 Definitions ->
+               IncludePath ->
-               FromParser a -> io (Either Error a)
+               IORef SeenFiles -> IORef NameSuf -> IORef Definitions ->
-fromParserIO inc seen defs act =
+               Eff FromParserIO a -> io (Either Error a)
+fromParserIO inc seen suf defs act =
   runIO $
+  runStateIORefAt GEN suf $
   runExcept $
   evalStateAt NS [<] $
   runStateIORefAt SEEN seen $

lib/Quox/Parser/FromParser/Error.idr

@@ -18,33 +18,24 @@ ParseError = Parser.Error
 
 public export
 data Error =
-    AnnotationNeeded (NameContexts d n) (Term d n)
+    AnnotationNeeded Loc (NameContexts d n) (Term d n)
-  | DuplicatesInEnum (List TagVal)
+  | DuplicatesInEnum Loc (List TagVal)
-  | TermNotInScope Name
+  | TermNotInScope Loc Name
-  | DimNotInScope PBaseName
+  | DimNotInScope Loc PBaseName
-  | QtyNotGlobal Qty
+  | QtyNotGlobal Loc Qty
-  | DimNameInTerm PBaseName
+  | DimNameInTerm Loc PBaseName
   | WrapTypeError TypeError
-  | LoadError String FileError
+  | LoadError Loc String FileError
   | WrapParseError String ParseError
 
 
 parameters (unicode, showContext : Bool)
-  export
-  prettyBounds : String -> Bounds -> Doc HL
-  prettyBounds file (MkBounds l1 c1 l2 c2) =
-    hcat [hl Free $ pretty file, hl Delim ":",
-          hl TVar $ pretty l1,   hl Delim ":",
-          hl DVar $ pretty c1,   hl Delim "-",
-          hl TVar $ pretty l2,   hl Delim ":",
-          hl DVar $ pretty c2]
-
   export
   prettyParseError1 : String -> ParsingError _ -> Doc HL
   prettyParseError1 file (Error msg Nothing) =
     pretty msg
   prettyParseError1 file (Error msg (Just bounds)) =
-    asep [prettyBounds file bounds <+> hl Delim ":", pretty msg]
+    hsep [prettyLoc $ makeLoc file bounds, pretty msg]
 
   export
   prettyParseError : String -> ParseError -> Doc HL
@@ -56,33 +47,38 @@ parameters (unicode, showContext : Bool)
 
   export
   prettyError : Error -> Doc HL
-  prettyError (AnnotationNeeded ctx tm) =
+  prettyError (AnnotationNeeded loc ctx tm) =
-    sep ["the term", prettyTerm unicode ctx.dnames ctx.tnames tm,
+    sep [prettyLoc loc <++> "the term",
+         prettyTerm unicode ctx.dnames ctx.tnames tm,
          "needs a type annotation"]
     -- [todo] print the original PTerm instead
 
-  prettyError (DuplicatesInEnum tags) =
+  prettyError (DuplicatesInEnum loc tags) =
-    sep ["duplicate tags in enum type", braces $ fillSep $ map pretty tags]
+    sep [prettyLoc loc <++> "duplicate tags in enum type",
+         braces $ fillSep $ map pretty tags]
 
-  prettyError (DimNotInScope i) =
+  prettyError (DimNotInScope loc i) =
-    sep ["dimension", pretty0 unicode $ DV $ fromString i, "not in scope"]
+    sep [prettyLoc loc <++> "dimension",
+         pretty0 unicode $ DV $ fromString i, "not in scope"]
 
-  prettyError (TermNotInScope x) =
+  prettyError (TermNotInScope loc x) =
-    sep ["term variable", pretty0 unicode $ F x {d = 0, n = 0}, "not in scope"]
+    sep [prettyLoc loc <++> "term variable",
+         hl Free $ pretty0 unicode x, "not in scope"]
 
-  prettyError (QtyNotGlobal pi) =
+  prettyError (QtyNotGlobal loc pi) =
-    sep ["quantity", pretty0 unicode pi,
+    sep [prettyLoc loc <++> "quantity", pretty0 unicode pi,
          "can't be used on a top level declaration"]
 
-  prettyError (DimNameInTerm i) =
+  prettyError (DimNameInTerm loc i) =
-    sep ["dimension variable", pretty0 unicode $ DV $ fromString i,
+    sep [prettyLoc loc <++> "dimension variable",
-         "used in a term context"]
+         pretty0 unicode $ DV $ fromString i, "used in a term context"]
 
   prettyError (WrapTypeError err) =
     Typing.prettyError unicode showContext $ trimContext 2 err
 
-  prettyError (LoadError str err) =
+  prettyError (LoadError loc str err) =
-    vsep [hsep ["couldn't load file", pretty str], fromString $ show err]
+    vsep [hsep [prettyLoc loc, "couldn't load file", pretty str],
+          fromString $ show err]
 
   prettyError (WrapParseError file err) =
     prettyParseError file err

lib/Quox/Parser/Parser.idr

@@ -36,7 +36,7 @@ lexParseWith grm input = do
 export
 withLoc : {c : Bool} -> FileName -> (Grammar c (Loc -> a)) -> Grammar c a
 withLoc fname act = bounds act <&> \res =>
-  if res.isIrrelevant then res.val Nothing
+  if res.isIrrelevant then res.val noLoc
   else res.val $ makeLoc fname res.bounds
 
 export
@@ -241,40 +241,40 @@ casePat fname = withLoc fname $
   <|> delim "[" "]" [|PBox (patVar fname)|]
   <|> fatalError "invalid pattern"
 
-export covering
+export
 term : FileName -> Grammar True PTerm
 -- defined after all the subterm parsers
 
-export covering
+export
 typeLine : FileName -> Grammar True (PatVar, PTerm)
 typeLine fname = do
   resC "["
   mustWork $ do
     i <- patVar fname <* resC "⇒" <|> unused fname
-    t <- term fname <* needRes "]"
+    t <- assert_total term fname <* needRes "]"
     pure (i, t)
 
 ||| box term `[t]` or type `[π.A]`
-export covering
+export
 boxTerm : FileName -> Grammar True PTerm
 boxTerm fname = withLoc fname $ do
   res "["; commit
   q <- optional $ qty fname <* res "."
-  t <- mustWork $ term fname <* needRes "]"
+  t <- mustWork $ assert_total term fname <* needRes "]"
   pure $ maybe (Box t) (\q => BOX q t) q
 
 ||| tuple term like `(a, b)`, or parenthesised single term.
 ||| allows terminating comma. more than two elements are nested on the right:
 ||| `(a, b, c, d) = (a, (b, (c, d)))`.
-export covering
+export
 tupleTerm : FileName -> Grammar True PTerm
 tupleTerm fname = withLoc fname $ do
-  terms <- delimSep1 "(" ")" "," $ term fname
+  terms <- delimSep1 "(" ")" "," $ assert_total term fname
   pure $ \loc => foldr1 (\s, t => Pair s t loc) terms
 
 ||| argument/atomic term: single-token terms, or those with delimiters e.g.
 ||| `[t]`
-export covering
+export
 termArg : FileName -> Grammar True PTerm
 termArg fname = withLoc fname $
       [|TYPE universe1|]
@@ -287,7 +287,7 @@ termArg fname = withLoc fname $
   <|> [|V qname|]
   <|> const <$> tupleTerm fname
 
-export covering
+export
 coeTerm : FileName -> Grammar True PTerm
 coeTerm fname = withLoc fname $ do
   resC "coe"
@@ -298,9 +298,11 @@ public export
 CompBranch : Type
 CompBranch = (DimConst, PatVar, PTerm)
 
-export covering
+export
 compBranch : FileName -> Grammar True CompBranch
-compBranch fname = [|(,,) dimConst (patVar fname) (needRes "⇒" *> term fname)|]
+compBranch fname =
+  [|(,,) dimConst (patVar fname)
+         (needRes "⇒" *> assert_total term fname)|]
 
 private
 checkCompTermBody : (PatVar, PTerm) -> PDim -> PDim -> PTerm -> PDim ->
@@ -313,7 +315,7 @@ checkCompTermBody a p q s r (e0, s0) (e1, s1) bounds =
     (_,    _)    =>
       fatalLoc bounds "body of 'comp' needs one 0 case and one 1 case"
 
-export covering
+export
 compTerm : FileName -> Grammar True PTerm
 compTerm fname = withLoc fname $ do
   resC "comp"
@@ -328,27 +330,27 @@ compTerm fname = withLoc fname $ do
     let body = bounds $ mergeBounds bodyStart bodyEnd
     checkCompTermBody a p q s r s0 s1 body
 
-export covering
+export
 splitUniverseTerm : FileName -> Grammar True PTerm
 splitUniverseTerm fname = withLoc fname $ resC "★" *> mustWork [|TYPE nat|]
 
-export covering
+export
 eqTerm : FileName -> Grammar True PTerm
 eqTerm fname = withLoc fname $
   resC "Eq" *> mustWork [|Eq (typeLine fname) (termArg fname) (termArg fname)|]
 
-export covering
+export
 succTerm : FileName -> Grammar True PTerm
 succTerm fname = withLoc fname $
   resC "succ" *> mustWork [|Succ (termArg fname)|]
 
 ||| a dimension argument with an `@` prefix, or
 ||| a term argument with no prefix
-export covering
+export
 anyArg : FileName -> Grammar True (Either PDim PTerm)
 anyArg fname = dimArg fname <||> termArg fname
 
-export covering
+export
 normalAppTerm : FileName -> Grammar True PTerm
 normalAppTerm fname = withLoc fname $ do
   head <- termArg fname
@@ -360,7 +362,7 @@ where ap : Loc -> PTerm -> Either PDim PTerm -> PTerm
 
 ||| application term `f x @y z`, or other terms that look like application
 ||| like `succ` or `coe`.
-export covering
+export
 appTerm : FileName -> Grammar True PTerm
 appTerm fname =
       coeTerm fname
@@ -370,53 +372,55 @@ appTerm fname =
   <|> succTerm fname
   <|> normalAppTerm fname
 
-export covering
+export
 infixEqTerm : FileName -> Grammar True PTerm
 infixEqTerm fname = withLoc fname $ do
   l <- appTerm fname; commit
-  rest <- optional $
+  rest <- optional $ res "≡" *>
-          res "≡" *> [|(,) (term fname) (needRes ":" *> appTerm fname)|]
+    [|(,) (assert_total term fname) (needRes ":" *> appTerm fname)|]
   let u = Unused $ onlyStart l.loc
   pure $ \loc => maybe l (\rest => Eq (u, snd rest) l (fst rest) loc) rest
 
-export covering
+export
 annTerm : FileName -> Grammar True PTerm
 annTerm fname = withLoc fname $ do
   tm <- infixEqTerm fname; commit
-  ty <- optional $ res "∷" *> term fname
+  ty <- optional $ res "∷" *> assert_total term fname
   pure $ \loc => maybe tm (\ty => Ann tm ty loc) ty
 
-export covering
+export
 lamTerm : FileName -> Grammar True PTerm
 lamTerm fname = withLoc fname $ do
   k <- DLam <$ res "δ" <|> Lam <$ res "λ"
   mustWork $ do
     xs   <- some $ patVar fname;     needRes "⇒"
-    body <- term fname;          commit
+    body <- assert_total term fname; commit
     pure $ \loc => foldr (\x, s => k x s loc) body xs
 
 -- [todo] fix the backtracking in e.g. (F x y z × B)
-export covering
+export
 properBinders : FileName -> Grammar True (List1 PatVar, PTerm)
-properBinders fname = do
+properBinders fname = assert_total $ do
+  -- putting assert_total directly on `term`, in this one function,
+  -- doesn't work. i cannot tell why
   res "("
   xs <- some $ patVar fname; resC ":"
   t  <- term fname;          needRes ")"
   pure (xs, t)
 
-export covering
+export
 piTerm : FileName -> Grammar True PTerm
 piTerm fname = withLoc fname $ do
   q   <- qty fname;               resC "."
   dom <- piBinder;                needRes "→"
-  cod <- term fname; commit
+  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 covering
+export
 sigmaTerm : FileName -> Grammar True PTerm
 sigmaTerm fname =
       (properBinders fname >>= continueDep)
@@ -440,9 +444,10 @@ public export
 PCaseArm : Type
 PCaseArm = (PCasePat, PTerm)
 
-export covering
+export
 caseArm : FileName -> Grammar True PCaseArm
-caseArm fname = [|(,) (casePat fname) (needRes "⇒" *> term fname)|]
+caseArm fname =
+  [|(,) (casePat fname) (needRes "⇒" *> assert_total term fname)|]
 
 export
 checkCaseArms : Loc -> List PCaseArm -> Grammar False PCaseBody
@@ -468,30 +473,30 @@ checkCaseArms loc ((PBox x _, rhs) :: rest) =
   if null rest then pure $ CaseBox x rhs loc
   else fatalError "unexpected pattern after box"
 
-export covering
+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 covering
+export
 caseReturn : FileName -> Grammar True (PatVar, PTerm)
 caseReturn fname = do
   x   <- patVar fname <* resC "⇒" <|> unused fname
-  ret <- term fname
+  ret <- assert_total term fname
   pure (x, ret)
 
-export covering
+export
 caseTerm : FileName -> Grammar True PTerm
 caseTerm fname = withLoc fname $ do
   qty <- caseIntro fname;                     commit
-  head <- mustWork $ term fname;       needRes "return"
+  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 covering
+-- export
 -- term : FileName -> Grammar True PTerm
 term fname = lamTerm fname
          <|> caseTerm fname
@@ -499,7 +504,7 @@ term fname = lamTerm fname
          <|> sigmaTerm fname
 
 
-export covering
+export
 decl : FileName -> Grammar True PDecl
 
 ||| `def` alone means `defω`
@@ -512,7 +517,7 @@ defIntro fname =
          let any = PQ Any $ makeLoc fname pos.bounds
          option any $ qty fname <* needRes "."
 
-export covering
+export
 definition : FileName -> Grammar True PDefinition
 definition fname = withLoc fname $ do
   qty  <- defIntro fname
@@ -522,7 +527,7 @@ definition fname = withLoc fname $ do
   optRes ";"
   pure $ MkPDef qty name type term
 
-export covering
+export
 namespace_ : FileName -> Grammar True PNamespace
 namespace_ fname = withLoc fname $ do
   ns    <- resC "namespace" *> qname; needRes "{"
@@ -531,28 +536,28 @@ namespace_ fname = withLoc fname $ do
 where
   nsInner : Grammar True (List PDecl)
   nsInner = [] <$ resC "}"
-        <|> [|(decl fname <* commit) :: nsInner|]
+        <|> [|(assert_total decl fname <* commit) :: assert_total nsInner|]
 
 decl fname = [|PDef $ definition fname|] <|> [|PNs $ namespace_ fname|]
 
-export covering
+export
 load : FileName -> Grammar True PTopLevel
 load fname = withLoc fname $
   resC "load" *> mustWork [|PLoad strLit|] <* optRes ";"
 
-export covering
+export
 topLevel : FileName -> Grammar True PTopLevel
 topLevel fname = load fname <|> [|PD $ decl fname|]
 
-export covering
+export
 input : FileName -> Grammar False (List PTopLevel)
 input fname = [] <$ eof
-          <|> [|(topLevel fname <* commit) :: input fname|]
+          <|> [|(topLevel fname <* commit) :: assert_total input fname|]
 
-export covering
+export
 lexParseTerm : FileName -> String -> Either Error PTerm
 lexParseTerm = lexParseWith . term
 
-export covering
+export
 lexParseInput : FileName -> String -> Either Error (List PTopLevel)
 lexParseInput = lexParseWith . input

lib/Quox/Parser/Syntax.idr

@@ -33,11 +33,14 @@ isUnused _           = False
 
 
 public export
-data PQty = PQ Qty Loc
+record PQty where
+  constructor PQ
+  val  : Qty
+  loc_ : Loc
 %name PQty qty
 %runElab derive "PQty" [Eq, Ord, Show]
 
-export Located PQty where (PQ _ loc).loc = loc
+export Located PQty where q.loc = q.loc_
 
 namespace PDim
   public export

lib/Quox/Pretty.idr

@@ -1,5 +1,6 @@
 module Quox.Pretty
 
+import Quox.Loc
 import Quox.Name
 
 import public Text.PrettyPrint.Prettyprinter.Doc
@@ -200,6 +201,7 @@ pretty0 unicode = pretty0With unicode [<] [<]
 
 export PrettyHL BaseName where prettyM = pure . pretty . baseStr
 export PrettyHL Name     where prettyM = pure . pretty . toDots
+export PrettyHL BindName where prettyM = prettyM . name
 
 
 export
@@ -278,3 +280,14 @@ epretty @{p} x = Evidence a (p, x)
 
 public export data Lit = L (Doc HL)
 export PrettyHL Lit where prettyM (L doc) = pure doc
+
+
+export
+prettyLoc : Loc -> Doc HL
+prettyLoc (L NoLoc) = hl TVarErr "no location" <+> hl Delim ":"
+prettyLoc (L (YesLoc file (MkBounds l1 c1 l2 c2))) =
+    hcat [hl Free $ pretty file, hl Delim ":",
+          hl TVar $ pretty l1,   hl Delim ":",
+          hl DVar $ pretty c1,   hl Delim "-",
+          hl TVar $ pretty l2,   hl Delim ":",
+          hl DVar $ pretty c2,   hl Delim ":"]

lib/Quox/Reduce.idr

@@ -8,10 +8,25 @@ import Quox.Typing.Error
 import Data.SnocVect
 import Data.Maybe
 import Data.List
+import Control.Eff
 
 %default total
 
 
+-- [fixme] rename this to Whnf and the interface to CanWhnf
+public export
+WhnfM : Type -> Type
+WhnfM = Eff [NameGen, Except Error]
+
+export
+runWhnfWith : NameSuf -> WhnfM a -> (Either Error a, NameSuf)
+runWhnfWith suf act = extract $ runStateAt GEN suf $ runExcept act
+
+export
+runWhnf : WhnfM a -> Either Error a
+runWhnf = fst . runWhnfWith 0
+
+
 public export
 0 RedexTest : TermLike -> Type
 RedexTest tm = {d, n : Nat} -> Definitions -> tm d n -> Bool
@@ -21,12 +36,11 @@ interface Whnf (0 tm : TermLike) (0 isRedex : RedexTest tm) | tm
 where
   whnf : {d, n : Nat} -> (defs : Definitions) ->
          (ctx : WhnfContext d n) ->
-         tm d n -> Either Error (Subset (tm d n) (No . isRedex defs))
+         tm d n -> WhnfM (Subset (tm d n) (No . isRedex defs))
 
 public export %inline
 whnf0 : {d, n : Nat} -> {0 isRedex : RedexTest tm} -> Whnf tm isRedex =>
-        (defs : Definitions) ->
+        (defs : Definitions) -> WhnfContext d n -> tm d n -> WhnfM (tm d n)
-        WhnfContext d n -> tm d n -> Either Error (tm d n)
 whnf0 defs ctx t = fst <$> whnf defs ctx t
 
 public export
@@ -37,8 +51,7 @@ NotRedex defs = No . isRedex defs
 
 public export
 0 NonRedex : (tm : TermLike) -> {isRedex : RedexTest tm} ->
-             Whnf tm isRedex => (d, n : Nat) ->
+             Whnf tm isRedex => (d, n : Nat) -> (defs : Definitions) -> Type
-             (defs : Definitions) -> Type
 NonRedex tm d n defs = Subset (tm d n) (NotRedex defs)
 
 public export %inline
@@ -49,49 +62,49 @@ nred t = Element t nr
 
 public export %inline
 isLamHead : Elim {} -> Bool
-isLamHead (Lam {} :# Pi {}) = True
+isLamHead (Ann (Lam {}) (Pi {}) _) = True
 isLamHead (Coe {})                 = True
 isLamHead _                        = False
 
 public export %inline
 isDLamHead : Elim {} -> Bool
-isDLamHead (DLam {} :# Eq {}) = True
+isDLamHead (Ann (DLam {}) (Eq {}) _) = True
 isDLamHead (Coe {})                  = True
 isDLamHead _                         = False
 
 public export %inline
 isPairHead : Elim {} -> Bool
-isPairHead (Pair {} :# Sig {}) = True
+isPairHead (Ann (Pair {}) (Sig {}) _) = True
 isPairHead (Coe {})                   = True
 isPairHead _                          = False
 
 public export %inline
 isTagHead : Elim {} -> Bool
-isTagHead (Tag t :# Enum _) = True
+isTagHead (Ann (Tag {}) (Enum {}) _) = True
 isTagHead (Coe {})                   = True
 isTagHead _                          = False
 
 public export %inline
 isNatHead : Elim {} -> Bool
-isNatHead (Zero   :# Nat) = True
+isNatHead (Ann (Zero {}) (Nat {}) _) = True
-isNatHead (Succ n :# Nat) = True
+isNatHead (Ann (Succ {}) (Nat {}) _) = True
 isNatHead (Coe {})                   = True
 isNatHead _                          = False
 
 public export %inline
 isBoxHead : Elim {} -> Bool
-isBoxHead (Box {} :# BOX {}) = True
+isBoxHead (Ann (Box {}) (BOX {}) _) = True
 isBoxHead (Coe {})                  = True
 isBoxHead _                         = False
 
 public export %inline
 isE : Term {} -> Bool
-isE (E _) = True
+isE (E {}) = True
 isE _      = False
 
 public export %inline
 isAnn : Elim {} -> Bool
-isAnn (_ :# _) = True
+isAnn (Ann {}) = True
 isAnn _        = False
 
 ||| true if a term is syntactically a type.
@@ -106,8 +119,8 @@ isTyCon (Enum     {}) = True
 isTyCon (Tag   {}) = False
 isTyCon (Eq    {}) = True
 isTyCon (DLam  {}) = False
-isTyCon Nat           = True
+isTyCon (Nat   {}) = True
-isTyCon Zero          = False
+isTyCon (Zero  {}) = False
 isTyCon (Succ  {}) = False
 isTyCon (BOX   {}) = True
 isTyCon (Box   {}) = False
@@ -123,23 +136,23 @@ isTyConE s = isTyCon s || isE s
 ||| true if a term is syntactically a type.
 public export %inline
 isAnnTyCon : Elim {} -> Bool
-isAnnTyCon (ty :# TYPE _) = isTyCon ty
+isAnnTyCon (Ann ty (TYPE {}) _) = isTyCon ty
 isAnnTyCon _                    = False
 
 public export %inline
 isK : Dim d -> Bool
-isK (K _) = True
+isK (K {}) = True
 isK _      = False
 
 
 mutual
   public export
   isRedexE : RedexTest Elim
-  isRedexE defs (F x) {d, n} =
+  isRedexE defs (F {x, _}) {d, n} =
     isJust $ lookupElim x defs {d, n}
-  isRedexE _ (B _) = False
+  isRedexE _ (B {}) = False
-  isRedexE defs (f :@ _) =
+  isRedexE defs (App {fun, _}) =
-    isRedexE defs f || isLamHead f
+    isRedexE defs fun || isLamHead fun
   isRedexE defs (CasePair {pair, _}) =
     isRedexE defs pair || isPairHead pair
   isRedexE defs (CaseEnum {tag, _}) =
@@ -148,10 +161,10 @@ mutual
     isRedexE defs nat || isNatHead nat
   isRedexE defs (CaseBox {box, _}) =
     isRedexE defs box || isBoxHead box
-  isRedexE defs (f :% p) =
+  isRedexE defs (DApp {fun, arg, _}) =
-    isRedexE defs f || isDLamHead f || isK p
+    isRedexE defs fun || isDLamHead fun || isK arg
-  isRedexE defs (t :# a) =
+  isRedexE defs (Ann {tm, ty, _}) =
-    isE t || isRedexT defs t || isRedexT defs a
+    isE tm || isRedexT defs tm || isRedexT defs ty
   isRedexE defs (Coe {val, _}) =
     isRedexT defs val || not (isE val)
   isRedexE defs (Comp {ty, r, _}) =
@@ -165,7 +178,7 @@ mutual
   isRedexT : RedexTest Term
   isRedexT _    (CloT  {}) = True
   isRedexT _    (DCloT {}) = True
-  isRedexT defs (E e)      = isAnn e || isRedexE defs e
+  isRedexT defs (E {e, _}) = isAnn e || isRedexE defs e
   isRedexT _    _          = False
 
 
@@ -203,44 +216,47 @@ 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 ->
+coeScoped : {s : Nat} -> DScopeTerm d n -> Dim d -> Dim d -> Loc ->
             ScopeTermN s d n -> ScopeTermN s d n
-coeScoped ty p q (S names (Y body)) =
+coeScoped ty p q loc (S names (Y body)) =
-  S names $ Y $ E $ Coe (weakDS s ty) p q body
+  S names $ Y $ E $ Coe (weakDS s ty) p q body loc
-coeScoped ty p q (S names (N body)) =
+coeScoped ty p q loc (S names (N body)) =
-  S names $ N $ E $ Coe ty p q body
+  S names $ N $ E $ Coe ty p q body loc
 
 
-mutual
+export covering
+Whnf Term Reduce.isRedexT
+
+export covering
+Whnf 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)) =>
-                      Either Error (Term d n)
+                    WhnfM (Term d n)
-    computeElimType (F x) = do
+  computeElimType (F {x, loc}) = do
-      let Just def = lookup x defs | Nothing => Left $ NotInScope x
+    let Just def = lookup x defs | Nothing => throw $ NotInScope loc x
     pure $ def.type
-    computeElimType (B i) = pure $ ctx.tctx !! i
+  computeElimType (B {i, _}) = pure $ ctx.tctx !! i
-    computeElimType (f :@ s) {ne} = do
+  computeElimType (App {fun = f, arg = s, loc}) {ne} = do
-      -- can't use `expectPi` (or `expectEq` below) without making this
-      -- mutual block from hell even worse lol
     Pi {arg, res, _} <- whnf0 defs ctx =<< computeElimType f {ne = noOr1 ne}
-        | t => Left $ ExpectedPi ctx.names t
+      | t => throw $ ExpectedPi loc ctx.names t
-      pure $ sub1 res (s :# arg)
+    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 (f :% p) {ne} = do
+  computeElimType (DApp {fun = f, arg = p, loc}) {ne} = do
     Eq {ty, _} <- whnf0 defs ctx =<< computeElimType f {ne = noOr1 ne}
-        | t => Left $ ExpectedEq ctx.names t
+      | t => throw $ ExpectedEq loc ctx.names t
     pure $ dsub1 ty p
   computeElimType (Coe {ty, q, _}) = pure $ dsub1 ty q
   computeElimType (Comp {ty, _}) = pure ty
   computeElimType (TypeCase {ret, _}) = pure ret
-    computeElimType (_ :# ty) = pure ty
+  computeElimType (Ann {ty, _}) = pure ty
 
 parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext (S d) n)
   ||| for π.(x : A) → B, returns (A, B);
@@ -248,71 +264,79 @@ mutual
   ||| for other intro forms error
   private covering
   tycasePi : (t : Term (S d) n) -> (0 tnf : No (isRedexT defs t)) =>
-               Either Error (Term (S d) n, ScopeTerm (S d) n)
+             WhnfM (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 arg  = E $ typeCase1Y e ty KPi [< "Arg", "Ret"] (BVT 1)
+    let loc  = e.loc
-          res' = typeCase1Y e (Arr Zero arg ty) KPi [< "Arg", "Ret"] (BVT 0)
+        narg = mnb "Arg"; nret = mnb "Ret"
-          res  = SY [< "Arg"] $ E $ weakE 1 res' :@ BVT 0
+        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 = Left $ ExpectedPi ctx.names t
+  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)) =>
-                Either Error (Term (S d) n, ScopeTerm (S d) n)
+              WhnfM (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 fst  = E $ typeCase1Y e ty KSig [< "Fst", "Snd"] (BVT 1)
+    let loc  = e.loc
-          snd' = typeCase1Y e (Arr Zero fst ty) KSig [< "Fst", "Snd"] (BVT 0)
+        nfst = mnb "Fst"; nsnd = mnb "Snd"
-          snd  = SY [< "Fst"] $ E $ weakE 1 snd' :@ BVT 0
+        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 = Left $ ExpectedSig ctx.names t
+  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)) =>
-                Either Error (Term (S d) n)
+              WhnfM (Term (S d) n)
-    tycaseBOX (BOX _ a) = pure a
+  tycaseBOX (BOX {ty, _}) = pure ty
   tycaseBOX (E e) {tnf} = do
     ty <- computeElimType defs ctx e @{noOr2 tnf}
-      pure $ E $ typeCase1Y e ty KBOX [< "Ty"] (BVT 0)
+    pure $ E $ typeCase1Y e ty KBOX [< !(mnb "Ty")] (BVT 0 e.loc) e.loc
-    tycaseBOX t = Left $ ExpectedBOX ctx.names t
+  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)) =>
-               Either Error (Term (S d) n, Term (S d) n, DScopeTerm (S d) n,
+             WhnfM (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 (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 names = [< "A0", "A1", "A", "L", "R"]
+    let loc   = e.loc
-          a0 = E $ typeCase1Y e ty KEq names (BVT 4)
+        names = traverse' (\x => mnb x) [< "A0", "A1", "A", "L", "R"]
-          a1 = E $ typeCase1Y e ty KEq names (BVT 3)
+        a0    = E $ typeCase1Y e ty KEq !names (BVT 4 loc) loc
-          a' = typeCase1Y e (Eq0 ty a0 a1) KEq names (BVT 2)
+        a1    = E $ typeCase1Y e ty KEq !names (BVT 3 loc) loc
-          a  = SY [< "i"] $ E $ dweakE 1 a' :% BV 0
+        a'    = typeCase1Y e (Eq0 ty a0 a1 loc) KEq !names (BVT 2 loc) loc
-          l  = E $ typeCase1Y e a0 KEq names (BVT 1)
+        a     = SY [< !(mnb "i")] $ E $ DApp (dweakE 1 a') (B VZ loc) loc
-          r  = E $ typeCase1Y e a1 KEq names (BVT 0)
+        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 = Left $ ExpectedEq ctx.names t
+  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 `Coe ty p q val :@ s`
+  ||| 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) ->
+  piCoe : (ty : DScopeTerm d n) -> (p, q : Dim d) ->
-            Either Error (Subset (Elim d n) (No . isRedexE defs))
+          (val, s : Term d n) -> Loc ->
-    piCoe sty@(S [< i] ty) p q val s = do
+          WhnfM (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
@@ -321,19 +345,19 @@ mutual
     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
+    let s0   = CoeT i arg q p s s.loc
-          body = E $ (val :# (ty // one p)) :@ E s0
+        body = E $ App (Ann val (ty // one p) val.loc) (E s0) loc
-          s1   = CoeT i (arg // (BV 0 ::: shift 2)) (weakD 1 q) (BV 0)
+        s1   = CoeT i (arg // (BV 0 i.loc ::: shift 2)) (weakD 1 q) (BV 0 i.loc)
-                      (s // shift 1)
+                    (s // shift 1) s.loc
-      whnf defs ctx $ CoeT i (sub1 res s1) p q body
+    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`
+  ||| 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) ->
+           (ret : ScopeTerm d n) -> (body : ScopeTermN 2 d n) -> Loc ->
-             Either Error (Subset (Elim d n) (No . isRedexE defs))
+           WhnfM (Subset (Elim d n) (No . isRedexE defs))
-    sigCoe qty sty@(S [< i] ty) p q val ret body = do
+  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
@@ -345,38 +369,39 @@ mutual
     let ctx1 = extendDim i ctx
     Element ty tynf <- whnf defs ctx1 ty.term
     (tfst, tsnd) <- tycaseSig defs ctx1 ty
-      let a' = CoeT i (weakT 2 tfst) p q (BVT 1)
+    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 // (BV 0 ::: shift 2))
+          (CoeT i (weakT 2 $ tfst // (B VZ noLoc ::: shift 2))
-              (weakD 1 p) (BV 0) (BVT 1) ::: shift 2)
+            (weakD 1 p) (B VZ noLoc) (BVT 1 noLoc) y.loc ::: shift 2)
-          b' = CoeT i tsnd' p q (BVT 0)
+        b' = CoeT i tsnd' p q (BVT 0 noLoc) y.loc
-      whnf defs ctx $ CasePair qty (val :# (ty // one p)) ret $
+    whnf defs ctx $ CasePair qty (Ann val (ty // one p) val.loc) ret
-        ST body.names $ body.term // (a' ::: b' ::: shift 2)
+      (ST body.names $ body.term // (a' ::: b' ::: shift 2)) loc
 
-    ||| reduce a dimension application `Coe ty p q val :% r`
+  ||| 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) ->
+          (r : Dim d) -> Loc ->
-            Either Error (Subset (Elim d n) (No . isRedexE defs))
+          WhnfM (Subset (Elim d n) (No . isRedexE defs))
-    eqCoe sty@(S [< j] ty) p q val r = do
+  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; (r=1) j ⇒ R }
+    --   @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 $ (val :# (ty // one p)) :% 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
+    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) ->
+           (ret : ScopeTerm d n) -> (body : ScopeTerm d n) -> Loc ->
-             Either Error (Subset (Elim d n) (No . isRedexE defs))
+           WhnfM (Subset (Elim d n) (No . isRedexE defs))
-    boxCoe qty sty@(S [< i] ty) p q val ret body = do
+  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
@@ -384,158 +409,317 @@ mutual
     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
+    let a' = CoeT i (weakT 1 ta) p q (BVT 0 noLoc) body.name.loc
-      whnf defs ctx $ CaseBox qty (val :# (ty // one p)) ret $
+    whnf defs ctx $ CaseBox qty (Ann val (ty // one p) val.loc) ret
-        ST body.names $ body.term // (a' ::: shift 1)
+      (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 ->
+                 WhnfM (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 : {n, d : 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 ->
+          WhnfM (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 -> WhnfM Universe
+  unwrapTYPE (TYPE {l, _}) = pure l
+  unwrapTYPE ty = throw $ ExpectedTYPE ty.loc (extendDim i ctx.names) ty
 
 
 export covering
 Whnf Elim Reduce.isRedexE where
-    whnf defs ctx (F x) with (lookupElim x defs) proof eq
+  whnf defs ctx (F x loc) with (lookupElim x defs) proof eq
-      _ | Just y  = whnf defs ctx y
+    _ | Just y  = whnf defs ctx $ setLoc loc y
-      _ | Nothing = pure $ Element (F x) $ rewrite eq in Ah
+    _ | Nothing = pure $ Element (F x loc) $ rewrite eq in Ah
 
-    whnf _ _ (B i) = pure $ nred $ B i
+  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 (f :@ s) = do
+  whnf defs ctx (App f s appLoc) = do
     Element f fnf <- whnf defs ctx f
     case nchoose $ isLamHead f of
       Left _ => case f of
-          Lam body :# Pi {arg, res, _} =>
+        Ann (Lam {body, _}) (Pi {arg, res, _}) floc =>
-            let s = s :# arg in
+          let s = Ann s arg s.loc in
-            whnf defs ctx $ sub1 body s :# sub1 res s
+          whnf defs ctx $ Ann (sub1 body s) (sub1 res s) appLoc
-          Coe ty p q val => piCoe defs ctx ty p q val s
+        Coe ty p q val _ => piCoe defs ctx ty p q val s appLoc
-        Right nlh => pure $ Element (f :@ s) $ fnf `orNo` nlh
+      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) = do
+  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
-          Pair {fst, snd} :# Sig {fst = tfst, snd = tsnd, _} =>
+        Ann (Pair {fst, snd, _}) (Sig {fst = tfst, snd = tsnd, _}) pairLoc =>
-            let fst = fst :# tfst
+          let fst = Ann fst tfst fst.loc
-                snd = snd :# sub1 tsnd fst
+              snd = Ann snd (sub1 tsnd fst) snd.loc
           in
-            whnf defs ctx $ subN body [< fst, snd] :# sub1 ret pair
+          whnf defs ctx $ Ann (subN body [< fst, snd]) (sub1 ret pair) caseLoc
-          Coe ty p q val => do
+        Coe ty p q val _ => do
-            sigCoe defs ctx pi ty p q val ret body
+          sigCoe defs ctx pi ty p q val ret body caseLoc
       Right np =>
-          pure $ Element (CasePair pi pair ret body) $ pairnf `orNo` 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) = do
+  whnf defs ctx (CaseEnum pi tag ret arms caseLoc) = do
     Element tag tagnf <- whnf defs ctx tag
     case nchoose $ isTagHead tag of
-        Left t => case tag of
+      Left _ => case tag of
-          Tag t :# Enum ts =>
+        Ann (Tag t _) (Enum ts _) _ =>
           let ty = sub1 ret tag in
           case lookup t arms of
-              Just arm => whnf defs ctx $ arm :# ty
+            Just arm => whnf defs ctx $ Ann arm ty arm.loc
-              Nothing  => Left $ MissingEnumArm t (keys arms)
+            Nothing  => throw $ MissingEnumArm caseLoc t (keys arms)
-          Coe ty p q val =>
+        Coe ty p q val _ =>
-            -- there is nowhere an equality can be hiding inside an Enum
+          -- there is nowhere an equality can be hiding inside an enum type
-            whnf defs ctx $ CaseEnum pi (val :# dsub1 ty q) ret arms
+          whnf defs ctx $
+            CaseEnum pi (Ann val (dsub1 ty q) val.loc) ret arms caseLoc
       Right nt =>
-          pure $ Element (CaseEnum pi tag ret arms) $ tagnf `orNo` 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) = do
+  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
-            Zero :# Nat => whnf defs ctx (zer :# ty)
+          Ann (Zero _) (Nat _) _ =>
-            Succ n :# Nat =>
+            whnf defs ctx $ Ann zer ty zer.loc
-              let nn = n :# Nat
+          Ann (Succ n succLoc) (Nat natLoc) _ =>
-                  tm = subN suc [< nn, CaseNat pi piIH nn ret zer suc]
+            let nn = Ann n (Nat natLoc) succLoc
+                tm = subN suc [< nn, CaseNat pi piIH nn ret zer suc caseLoc]
             in
-              whnf defs ctx $ tm :# ty
+            whnf defs ctx $ Ann tm ty caseLoc
-            Coe ty p q val =>
+          Coe ty p q val _ =>
             -- same deal as Enum
-              whnf defs ctx $ CaseNat pi piIH (val :# dsub1 ty q) ret zer suc
+            whnf defs ctx $
-        Right nn =>
+              CaseNat pi piIH (Ann val (dsub1 ty q) val.loc) ret zer suc caseLoc
-          pure $ Element (CaseNat pi piIH nat ret zer suc) $ natnf `orNo` nn
+      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) = do
+  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
-          Box val :# BOX q bty =>
+        Ann (Box val boxLoc) (BOX q bty tyLoc) _ =>
           let ty = sub1 ret box in
-            whnf defs ctx $ sub1 body (val :# bty) :# ty
+          whnf defs ctx $ Ann (sub1 body (Ann val bty val.loc)) ty caseLoc
-          Coe ty p q val =>
+        Coe ty p q val _ =>
-            boxCoe defs ctx pi ty p q val ret body
+          boxCoe defs ctx pi ty p q val ret body caseLoc
       Right nb =>
-          pure $ Element (CaseBox pi box ret body) $ boxnf `orNo` nb
+        pure $ Element (CaseBox pi box ret body caseLoc) $ boxnf `orNo` nb
 
   -- ((δ 𝑖 ⇒ s) ∷ Eq [𝑗 ⇒ A] t u) @0 ⇝ t ∷ A‹0/𝑗›
   -- ((δ 𝑖 ⇒ s) ∷ Eq [𝑗 ⇒ A] t u) @1 ⇝ u ∷ A‹1/𝑗›
   -- ((δ 𝑖 ⇒ s) ∷ Eq [𝑗 ⇒ A] t u) @𝑘 ⇝ s‹𝑘/𝑖› ∷ A‹𝑘/𝑗›
   --   (if 𝑘 is a variable)
-    whnf defs ctx (f :% p) = do
+  whnf defs ctx (DApp f p appLoc) = do
     Element f fnf <- whnf defs ctx f
     case nchoose $ isDLamHead f of
       Left _ => case f of
-          DLam body :# Eq {ty = ty, l, r, _} =>
+        Ann (DLam {body, _}) (Eq {ty, l, r, _}) _ =>
-            let body = endsOr l r (dsub1 body p) p in
+          whnf defs ctx $
-            whnf defs ctx $ body :# dsub1 ty p
+            Ann (endsOr (setLoc appLoc l) (setLoc appLoc r) (dsub1 body p) p)
-          Coe ty p' q' val =>
+                (dsub1 ty p) appLoc
-            eqCoe defs ctx ty p' q' val p
+        Coe ty p' q' val _ =>
+          eqCoe defs ctx ty p' q' val p appLoc
       Right ndlh => case p of
-          K e => do
+        K e _ => do
           Eq {l, r, ty, _} <- whnf0 defs ctx =<< computeElimType defs ctx f
-              | ty => Left $ ExpectedEq ctx.names ty
+            | ty => throw $ ExpectedEq ty.loc ctx.names ty
-            whnf defs ctx $ ends (l :# ty.zero) (r :# ty.one) e
+          whnf defs ctx $
-          B _ => pure $ Element (f :% p) $ fnf `orNo` ndlh `orNo` Ah
+            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 (s :# a) = do
+  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 (s :# a) $ ne `orNo` snf `orNo` anf
+        pure $ Element (Ann s a annLoc) $ ne `orNo` snf `orNo` anf
 
-    whnf defs ctx (Coe (S _ (N ty)) _ _ val) =
+  whnf defs ctx (Coe (S _ (N ty)) _ _ val coeLoc) =
-      whnf defs ctx $ val :# ty
+    whnf defs ctx $ Ann val ty coeLoc
-    whnf defs ctx (Coe (S [< i] ty) p q val) = do
+  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
+    pushCoe defs ctx i ty p q val coeLoc
 
-    whnf defs ctx (Comp ty p q val r zero one) =
+  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 $ val :# ty else
+    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 @0 { 0 j ⇒ t; ⋯ } ⇝ t‹q/j› ∷ A
-        -- comp [A] @p @q s { (1=1) 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 $ dsub1 zero q :# ty
+        K Zero _ => whnf defs ctx $ Ann (dsub1 zero q) ty compLoc
-          K One  => whnf defs ctx $ dsub1 one  q :# ty
+        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) $ tynf `orNo` nk
+        pure $ Element (Comp ty p q val r zero one compLoc) $ tynf `orNo` nk
-      -- [todo] anything other than just the boundaries??
 
-    whnf defs ctx (TypeCase ty ret arms def) = do
+  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 ty :# TYPE u = ty in
+      Left  y  =>
-                    reduceTypeCase defs ctx ty u ret arms def
+        let Ann ty (TYPE u _) _ = ty in
-        Right nt => pure $ Element (TypeCase ty ret arms def) $
+        reduceTypeCase defs ctx ty u ret arms def tcLoc
-                             tynf `orNo` retnf `orNo` nt
+      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
@@ -551,8 +735,8 @@ mutual
   whnf _ _ t@(Tag  {}) = pure $ nred t
   whnf _ _ t@(Eq   {}) = pure $ nred t
   whnf _ _ t@(DLam {}) = pure $ nred t
-    whnf _ _    Nat      = pure $ nred Nat
+  whnf _ _ t@(Nat  {}) = pure $ nred t
-    whnf _ _    Zero     = pure $ nred Zero
+  whnf _ _ t@(Zero {}) = pure $ nred t
   whnf _ _ t@(Succ {}) = pure $ nred t
   whnf _ _ t@(BOX  {}) = pure $ nred t
   whnf _ _ t@(Box  {}) = pure $ nred t
@@ -561,150 +745,8 @@ mutual
   whnf defs ctx (E e) = do
     Element e enf <- whnf defs ctx e
     case nchoose $ isAnn e of
-        Left  _  => let tm :# _ = e in pure $ Element tm $ noOr1 $ noOr2 enf
+      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
-
-  ||| 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)) =>
-                   Either Error (Subset (Elim d n) (No . isRedexE defs))
-  reduceTypeCase defs ctx ty u ret arms def = case ty of
-    -- (type-case ★ᵢ ∷ _ return Q of { ★ ⇒ s; ⋯ }) ⇝ s ∷ Q
-    TYPE _ =>
-      whnf defs ctx $ tycaseRhsDef0 def KTYPE arms :# ret
-
-    -- (type-case π.(x : A) → B ∷ ★ᵢ return Q of { (a → b) ⇒ s; ⋯ }) ⇝
-    -- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ ★ᵢ
-    Pi _ arg res =>
-      let arg = arg :# TYPE u
-          res = Lam res :# Arr Zero (TYPE u) (TYPE u)
-      in
-      whnf defs ctx $ subN (tycaseRhsDef def KPi arms) [< arg, res] :# ret
-
-    -- (type-case (x : A) × B ∷ ★ᵢ return Q of { (a × b) ⇒ s; ⋯ }) ⇝
-    -- s[(A ∷ ★ᵢ)/a, ((λ x ⇒ B) ∷ 0.A → ★ᵢ)/b] ∷ ★ᵢ
-    Sig fst snd =>
-      let fst = fst :# TYPE u
-          snd = Lam snd :# Arr Zero (TYPE u) (TYPE u)
-      in
-      whnf defs ctx $ subN (tycaseRhsDef def KSig arms) [< fst, snd] :# ret
-
-    -- (type-case {⋯} ∷ _ return Q of { {} ⇒ s; ⋯ }) ⇝ s ∷ Q
-    Enum _ =>
-      whnf defs ctx $ tycaseRhsDef0 def KEnum arms :# ret
-
-    -- (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 a l r =>
-      let a0 = a.zero; a1 = a.one in
-      whnf defs ctx $
-        subN (tycaseRhsDef def KEq arms)
-          [< a0 :# TYPE u, a1 :# TYPE u,
-             DLam a :# Eq0 (TYPE u) a0 a1, l :# a0, r :# a1]
-        :# ret
-
-    -- (type-case ℕ ∷ _ return Q of { ℕ ⇒ s; ⋯ }) ⇝ s ∷ Q
-    Nat =>
-      whnf defs ctx $ tycaseRhsDef0 def KNat arms :# ret
-
-    -- (type-case [π.A] ∷ ★ᵢ return Q of { [a] ⇒ s; ⋯ }) ⇝ s[(A ∷ ★ᵢ)/a] ∷ Q
-    BOX _ s =>
-      whnf defs ctx $ sub1 (tycaseRhsDef def KBOX arms) (s :# TYPE u) :# ret
-
-  ||| pushes a coercion inside a whnf-ed term
-  private covering
-  pushCoe : {n, d : Nat} -> (defs : Definitions) -> WhnfContext d n ->
-            BaseName ->
-            (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)) =>
-            Either Error (NonRedex Elim d n defs)
-  pushCoe defs ctx i ty p q s =
-    if p == q then whnf defs ctx $ s :# (ty // one q) else
-    case s of
-      -- (coe [_ ⇒ ★ᵢ] @_ @_ ty) ⇝ (ty ∷ ★ᵢ)
-      TYPE {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
-      Pi   {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
-      Sig  {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
-      Enum {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
-      Eq   {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
-      Nat     => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
-      BOX  {} => pure $ nred $ s :# TYPE !(unwrapTYPE ty)
-
-      -- just η expand it. then whnf for (:@) will handle it later
-      -- this is how @xtt does it
-      Lam body => do
-        let body' = CoeT i ty p q $ Lam body
-            term' = [< "y"] :\\ E (weakE 1 body' :@ BVT 0)
-            type' = ty // one q
-        whnf defs ctx $ term' :# type'
-
-      {-
-      -- maybe:
-      -- (coe [i ⇒ π.(x : A) → B] @p @q (λ x ⇒ s)) ⇝
-      -- (λ x ⇒ coe [i ⇒ B[(coe [j ⇒ A‹j/i›] @q @i x)/x]] @p @q s)
-      --   ∷ (π.(x: A‹q/i›) → B‹q/i›)
-      Lam body => do
-        let Pi {qty, arg, res} = ty
-          | _ => Left $ ?err
-        let arg' = ST [< "j"] $ weakT 1 $ arg // (BV 0 ::: shift 2)
-            res' = ST [< i] $ res.term //
-                      (Coe arg' (weakD 1 q) (BV 0) (BVT 0) ::: shift 1)
-            body = ST body.names $ E $ Coe res' p q body.term
-        pure $ Element (Lam body :# Pi qty (arg // one q) (res // one q)) Ah
-      -}
-
-      -- (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 => do
-        let Sig {fst = tfst, snd = tsnd} = ty
-          | _ => Left $ ExpectedSig (extendDim i ctx.names) ty
-        let fst'  = E $ CoeT i tfst p q fst
-            tfst' = tfst // (BV 0 ::: shift 2)
-            tsnd' = sub1 tsnd $ CoeT "j" tfst' (weakD 1 p) (BV 0) $ dweakT 1 fst
-            snd'  = E $ CoeT i tsnd' p q snd
-        pure $
-          Element (Pair fst' snd' :# Sig (tfst // one q) (tsnd // one q)) Ah
-
-      -- η expand like λ
-      DLam body => do
-        let body' = CoeT i ty p q $ DLam body
-            term' = [< "j"] :\\% E (dweakE 1 body' :% BV 0)
-            type' = ty // one q
-        whnf defs ctx $ term' :# type'
-
-      -- (coe [_ ⇒ {⋯}] @_ @_ t) ⇝ (t ∷ {⋯})
-      Tag tag => do
-        let Enum ts = ty
-          | _ => Left $ ExpectedEnum (extendDim i ctx.names) ty
-        pure $ Element (Tag tag :# Enum ts) Ah
-
-      -- (coe [_ ⇒ ℕ] @_ @_ n) ⇝ (n ∷ ℕ)
-      Zero   => pure $ Element (Zero :# Nat) Ah
-      Succ t => pure $ Element (Succ t :# Nat) Ah
-
-      -- (coe [i ⇒ [π.A]] @p @q [s]) ⇝
-      -- [coe [i ⇒ A] @p @q s] ∷ [π. A‹q/i›]
-      Box val => do
-        let BOX {qty, ty = a} = ty
-          | _ => Left $ ExpectedBOX (extendDim i ctx.names) ty
-        pure $ Element (Box (E $ CoeT i a p q s) :# BOX qty (a // one q)) Ah
-
-      E e => pure $ Element (CoeT i ty p q (E e)) (snf `orNo` Ah)
-  where
-    unwrapTYPE : Term (S d) n -> Either Error Universe
-    unwrapTYPE (TYPE u) = pure u
-    unwrapTYPE ty       = Left $ ExpectedTYPE (extendDim i ctx.names) ty

lib/Quox/Syntax/Dim.idr

@@ -1,5 +1,6 @@
 module Quox.Syntax.Dim
 
+import Quox.Loc
 import Quox.Name
 import Quox.Syntax.Var
 import Quox.Syntax.Subst
@@ -17,7 +18,6 @@ import Derive.Prelude
 public export
 data DimConst = Zero | One
 %name DimConst e
-
 %runElab derive "DimConst" [Eq, Ord, Show]
 
 ||| `ends l r e` returns `l` if `e` is `Zero`, or `r` if it is `One`.
@@ -26,23 +26,42 @@ ends : Lazy a -> Lazy a -> DimConst -> a
 ends l r Zero = l
 ends l r One  = r
 
+export Uninhabited (Zero = One)  where uninhabited _ impossible
+export Uninhabited (One  = Zero) where uninhabited _ impossible
+
+public export
+DecEq DimConst where
+  decEq Zero Zero = Yes Refl
+  decEq Zero One  = No absurd
+  decEq One  Zero = No absurd
+  decEq One  One  = Yes Refl
+
 
 public export
 data Dim : Nat -> Type where
-  K : DimConst -> Dim d
+  K : DimConst -> Loc -> Dim d
-  B : Var d -> Dim d
+  B : Var d -> Loc -> Dim d
 %name Dim.Dim p, q
-
 %runElab deriveIndexed "Dim" [Eq, Ord, Show]
 
+export
+Located (Dim d) where
+  (K _ loc).loc = loc
+  (B _ loc).loc = loc
+
+export
+Relocatable (Dim d) where
+  setLoc loc (K e _) = K e loc
+  setLoc loc (B i _) = B i loc
+
 export
 PrettyHL DimConst where
   prettyM = pure . hl Dim . ends "0" "1"
 
 export
 PrettyHL (Dim n) where
-  prettyM (K e) = prettyM e
+  prettyM (K e _) = prettyM e
-  prettyM (B i) = prettyVar DVar DVarErr (!ask).dnames i
+  prettyM (B i _) = prettyVar DVar DVarErr (!ask).dnames i
 
 export
 prettyDim : (dnames : NContext d) -> Dim d -> Doc HL
@@ -60,13 +79,13 @@ prettyDim dnames p =
 ||| - `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 (K e _) = ends l r e
-endsOr l r x (B _) = x
+endsOr l r x (B _ _) = x
 
 
 public export %inline
 toConst : Dim 0 -> DimConst
-toConst (K e) = e
+toConst (K e _) = e
 
 
 public export
@@ -81,52 +100,55 @@ prettyDSubst th =
     !(ifUnicode "⟨" "<") !(ifUnicode "⟩" ">") th
 
 
-public export FromVar Dim where fromVar = B
+public export FromVar Dim where fromVarLoc = B
 
 
 export
 CanShift Dim where
-  K e // _  = K e
+  K e loc // _  = K e loc
-  B i // by = B (i // by)
+  B i loc // by = B (i // by) loc
 
 export
 CanSubstSelf Dim where
-  K e // _  = K e
+  K e loc // _  = K e loc
-  B i // th = th !! i
+  B i loc // th = getLoc th i loc
 
 
-export Uninhabited (Zero = One)  where uninhabited _ impossible
+export Uninhabited (B i loc1 = K e loc2) where uninhabited _ impossible
-export Uninhabited (One  = Zero) where uninhabited _ impossible
+export Uninhabited (K e loc1 = B i loc2) where uninhabited _ impossible
-
-export Uninhabited (B i = K e) where uninhabited _ impossible
-export Uninhabited (K e = B i) where uninhabited _ impossible
-
-public export %inline Injective Dim.B where injective Refl = Refl
-public export %inline Injective Dim.K where injective Refl = Refl
 
 public export
-DecEq DimConst where
+data Eqv : Dim d1 -> Dim d2 -> Type where
-  decEq Zero Zero = Yes Refl
+  EK : K e _ `Eqv` K e _
-  decEq Zero One  = No absurd
+  EB : i `Eqv` j -> B i _ `Eqv` B j _
-  decEq One  Zero = No absurd
+
-  decEq One  One  = Yes Refl
+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
+injectiveK : K e loc1 `Eqv` K f loc2 -> e = f
+injectiveK EK = Refl
 
 public export
-DecEq (Dim d) where
+decEqv : Dec2 Dim.Eqv
-  decEq (K e) (K f) with (decEq e f)
+decEqv (K e _) (K f _) = case decEq e f of
-    _ | Yes prf    = Yes $ cong K prf
+  Yes Refl => Yes EK
-    _ | No  contra = No  $ contra . injective
+  No  n    => No $ n . injectiveK
-  decEq (K e) (B j) = No absurd
+decEqv (B i _) (B j _) = case decEqv i j of
-  decEq (B i) (K f) = No absurd
+  Yes y => Yes $ EB y
-  decEq (B i) (B j) with (decEq i j)
+  No  n => No  $ \(EB y) => n y
-    _ | Yes prf    = Yes $ cong B prf
+decEqv (B _ _) (K _ _) = No absurd
-    _ | No  contra = No  $ contra . injective
+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 : Nat) -> (0 _ : LT i d) => Dim d
+BV : (i : Nat) -> (0 _ : LT i d) => (loc : Loc) -> Dim d
-BV i = B $ V i
+BV i loc = B (V i) loc
 
 
 export

lib/Quox/Syntax/DimEq.idr

@@ -72,7 +72,7 @@ toMaybe (Just x) = Just x
 export
 fromGround' : Context' DimConst d -> DimEq' d
 fromGround' [<]        = [<]
-fromGround' (ctx :< e) = fromGround' ctx :< Just (K e)
+fromGround' (ctx :< e) = fromGround' ctx :< Just (K e noLoc)
 
 export
 fromGround : Context' DimConst d -> DimEq d
@@ -98,8 +98,8 @@ get' : DimEq' d -> Var d -> Maybe (Dim d)
 get' = getWith $ \p, by => map (// by) p
 
 public export %inline
-getVar : DimEq' d -> Var d -> Dim d
+getVar : DimEq' d -> Var d -> Loc -> Dim d
-getVar eqs i = fromMaybe (B i) $ get' eqs i
+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)
@@ -107,8 +107,8 @@ getShift' = getShiftWith $ \p, by => map (// by) p
 
 public export %inline
 get : DimEq' d -> Dim d -> Dim d
-get _   (K e) = K e
+get _   (K e loc) = K e loc
-get eqs (B i) = getVar eqs i
+get eqs (B i loc) = getVar eqs i loc
 
 
 public export %inline
@@ -126,7 +126,7 @@ C eqs     :<? d = C $ eqs :< map (get eqs) d
 
 private %inline
 ifVar : Var d -> Dim d -> Maybe (Dim d) -> Maybe (Dim d)
-ifVar i p = map $ \q => if q == B i then p else q
+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
@@ -135,39 +135,43 @@ checkConst e f eqs = if isYes $ e `decEq` f then C eqs else ZeroIsOne
 
 
 export
-setConst : Var d -> DimConst -> DimEq' d -> DimEq d
+setConst : Var d -> DimConst -> Loc -> DimEq' d -> DimEq d
-setConst VZ e (eqs :< Nothing)    = C $ eqs :< Just (K e)
+setConst VZ e loc (eqs :< Nothing) =
-setConst VZ e (eqs :< Just (K f)) = checkConst e f $ eqs :< Just (K f)
+  C $ eqs :< Just (K e loc)
-setConst VZ e (eqs :< Just (B i)) = setConst i e eqs :<? Just (K e)
+setConst VZ e _ (eqs :< Just (K f loc)) =
-setConst (VS i) e (eqs :< p)      = setConst i e eqs :<? ifVar i (K e) p
+  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' : (i, j : Var d) -> (0 _ : i `LT` j) -> DimEq' d -> DimEq d
+  setVar' : (i, j : Var d) -> (0 _ : i `LT` j) -> Loc -> DimEq' d -> DimEq d
-  setVar' VZ (VS i) LTZ (eqs :< Nothing) =
+  setVar' VZ (VS i) LTZ loc (eqs :< Nothing) =
-    C eqs :<? Just (B i)
+    C eqs :<? Just (B i loc)
-  setVar' VZ (VS i) LTZ (eqs :< Just (K e)) =
+  setVar' VZ (VS i) LTZ loc (eqs :< Just (K e eloc)) =
-    setConst i e eqs :<? Just (K e)
+    setConst i e loc eqs :<? Just (K e eloc)
-  setVar' VZ (VS i) LTZ (eqs :< Just (B j)) =
+  setVar' VZ (VS i) LTZ loc (eqs :< Just (B j jloc)) =
-    setVar i j eqs :<? Just (B (max i j))
+    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) (eqs :< p) =
+  setVar' (VS i) (VS j) (LTS lt) loc (eqs :< p) =
-    setVar' i j lt eqs :<? ifVar i (B j) p
+    setVar' i j lt loc eqs :<? ifVar i (B j loc) p
 
   export %inline
-  setVar : (i, j : Var d) -> DimEq' d -> DimEq d
+  setVar : (i, j : Var d) -> Loc -> Loc -> DimEq' d -> DimEq d
-  setVar i j eqs with (compareP i j) | (compare i.nat j.nat)
+  setVar i j li lj eqs with (compareP i j) | (compare i.nat j.nat)
-    setVar i j eqs | IsLT lt | LT = setVar' i j lt eqs
+    setVar i j li lj eqs | IsLT lt | LT = setVar' i j lt lj eqs
-    setVar i i eqs | IsEQ    | EQ = C eqs
+    setVar i i li lj eqs | IsEQ    | EQ = C eqs
-    setVar i j eqs | IsGT gt | GT = setVar' j i gt eqs
+    setVar i j li lj eqs | IsGT gt | GT = setVar' j i gt li eqs
 
 
 export %inline
 set : (p, q : Dim d) -> DimEq d -> DimEq d
 set _ _ ZeroIsOne = ZeroIsOne
-set (K e) (K f) (C eqs) = checkConst e f eqs
+set (K e eloc) (K f floc) (C eqs) = checkConst e f eqs
-set (K e) (B i) (C eqs) = setConst i e eqs
+set (K e eloc) (B i iloc) (C eqs) = setConst i e eloc eqs
-set (B i) (K e) (C eqs) = setConst i e eqs
+set (B i iloc) (K e eloc) (C eqs) = setConst i e eloc eqs
-set (B i) (B j) (C eqs) = setVar   i j eqs
+set (B i iloc) (B j jloc) (C eqs) = setVar   i j iloc jloc eqs
 
 
 public export %inline
@@ -175,25 +179,26 @@ Split : Nat -> Type
 Split d = (DimEq' d, DSubst (S d) d)
 
 export %inline
-split1 : DimConst -> DimEq' (S d) -> Maybe (Split d)
+split1 : DimConst -> Loc -> DimEq' (S d) -> Maybe (Split d)
-split1 e eqs = case setConst VZ e eqs of
+split1 e loc eqs = case setConst VZ e loc eqs of
   ZeroIsOne    => Nothing
-  C (eqs :< _) => Just (eqs, K e ::: id)
+  C (eqs :< _) => Just (eqs, K e loc ::: id)
 
 export %inline
-split : DimEq' (S d) -> List (Split d)
+split : Loc -> DimEq' (S d) -> List (Split d)
-split eqs = toList (split1 Zero eqs) <+> toList (split1 One eqs)
+split loc eqs = toList (split1 Zero loc eqs) <+> toList (split1 One loc eqs)
-
 
 export
-splits' : DimEq' d -> List (DSubst d 0)
+splits' : Loc -> DimEq' d -> List (DSubst d 0)
-splits' [<]          = [id]
+splits' _   [<]          = [id]
-splits' eqs@(_ :< _) = [th . ph | (eqs', th) <- split eqs, ph <- splits' eqs']
+splits' loc eqs@(_ :< _) =
+  [th . ph | (eqs', th) <- split loc eqs, ph <- splits' loc eqs']
 
+||| the Loc is put into each of the DimConsts
 export %inline
-splits : DimEq d -> List (DSubst d 0)
+splits : Loc -> DimEq d -> List (DSubst d 0)
-splits ZeroIsOne = []
+splits _   ZeroIsOne = []
-splits (C eqs)   = splits' eqs
+splits loc (C eqs)   = splits' loc eqs
 
 
 private
@@ -208,16 +213,16 @@ 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 (K e _) = Refl
-newGet d (B i) = rewrite newGet' d i in 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 Zero _) (C eqs) = Refl
-setSelf (K One)  (C eqs) = Refl
+setSelf (K One _)  (C eqs) = Refl
-setSelf (B i)    (C eqs) with (compareP i i) | (compare i.nat i.nat)
+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
@@ -250,7 +255,7 @@ PrettyHL (DimEq' d) where
     go [<]              = pure [<]
     go (eqs :< Nothing) = local {dnames $= tail} $ go eqs
     go (eqs :< Just p)  = do
-      eq  <- prettyCst (BV {d = 1} 0) (weakD 1 p)
+      eq  <- prettyCst (BV {d = 1} 0 noLoc) (weakD 1 p)
       eqs <- local {dnames $= tail} $ go eqs
       pure $ eqs :< eq
 
@@ -262,16 +267,16 @@ PrettyHL (DimEq d) where
   prettyM (C eqs)   = prettyM eqs
 
 export
-prettyDimEq : NContext d -> DimEq d -> Doc HL
+prettyDimEq : BContext d -> DimEq d -> Doc HL
-prettyDimEq ds = pretty0With False (toSnocList' ds) [<]
+prettyDimEq ds = pretty0With False (toNames ds) [<]
 
 
 public export
 wf' : DimEq' d -> Bool
 wf' [<]                   = True
 wf' (eqs :< Nothing)      = wf' eqs
-wf' (eqs :< Just (K e)) = wf' eqs
+wf' (eqs :< Just (K e _)) = wf' eqs
-wf' (eqs :< Just (B i)) = isNothing (get' eqs i) && wf' eqs
+wf' (eqs :< Just (B i _)) = isNothing (get' eqs i) && wf' eqs
 
 public export
 wf : DimEq d -> Bool

lib/Quox/Syntax/Shift.idr

@@ -35,8 +35,9 @@ public export
 data Eqv : Shift from1 to1 -> Shift from2 to2 -> Type where
   EqSZ : SZ `Eqv` SZ
   EqSS : by `Eqv` bz -> SS by `Eqv` SS bz
-%name Eqv e
+%name Shift.Eqv e
 
+using (by : Shift from to, bz : Shift from to)
   ||| two equivalent shifts are equal if they have the same indices.
   export
   0 fromEqv : by `Eqv` bz -> by = bz
@@ -51,11 +52,11 @@ toEqv Refl {by = (SS by)} = EqSS $ toEqv Refl
 
 
 export
-eqLen : Shift from1 to -> Shift from2 to -> Maybe (from1 = from2)
+cmpLen : Shift from1 to -> Shift from2 to -> Either Ordering (from1 = from2)
-eqLen SZ      SZ      = Just Refl
+cmpLen SZ      SZ      = Right Refl
-eqLen SZ      (SS by) = Nothing
+cmpLen SZ      (SS by) = Left LT
-eqLen (SS by) SZ      = Nothing
+cmpLen (SS by) SZ      = Left GT
-eqLen (SS by) (SS bz) = eqLen by bz
+cmpLen (SS by) (SS bz) = cmpLen by bz
 
 export
 0 shiftDiff : (by : Shift from to) -> to = by.nat + from

lib/Quox/Syntax/Subst.idr

@@ -48,12 +48,16 @@ interface FromVar term => CanSubstSelf term where
   (//) : term from -> Lazy (Subst term from to) -> term to
 
 
-infixl 8 !!
 public export
-(!!) : FromVar term => Subst term from to -> Var from -> term to
+getLoc : FromVar term => Subst term from to -> Var from -> Loc -> term to
-(Shift by) !! i      = fromVar $ shift by i
+getLoc (Shift by) i      loc = fromVarLoc (shift by i) loc
-(t ::: th) !! VZ     = t
+getLoc (t ::: th) VZ     _   = t
-(t ::: th) !! (VS i) = th !! i
+getLoc (t ::: th) (VS i) loc = getLoc th i loc
+
+-- infixl 8 !!
+-- public export
+-- (!!) : FromVar term => Subst term from to -> Var from -> term to
+-- th !! i = getLoc th i noLoc
 
 
 public export
@@ -160,12 +164,16 @@ PrettyHL (f to) => PrettyHL (Subst f from to) where
   prettyM th = prettySubstM prettyM (!ask).tnames TVar "[" "]" 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
-eqShape : Subst env from1 to -> Subst env from2 to -> Maybe (from1 = from2)
+cmpShape : Subst env from1 to -> Subst env from2 to ->
-eqShape (Shift by) (Shift bz) = eqLen by bz
+           Either Ordering (from1 = from2)
-eqShape (Shift by) (t ::: th) = Nothing
+cmpShape (Shift by) (Shift bz) = cmpLen by bz
-eqShape (t ::: th) (Shift by) = Nothing
+cmpShape (Shift _)  (_ ::: _)  = Left LT
-eqShape (t ::: th) (x ::: ph) = cong S <$> eqShape th ph
+cmpShape (_ ::: _)  (Shift _)  = Left GT
+cmpShape (_ ::: th) (_ ::: ph) = cong S <$> cmpShape th ph
 
 
 public export
@@ -175,13 +183,20 @@ record WithSubst tm env n where
   subst : Lazy (Subst env from n)
 
 export
-(forall n. Eq (tm n), Eq (env 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 eqShape s1 s2 of
+    case cmpShape s1 s2 of
-      Just Refl => t1 == t2 && s1 == s2
+      Left  _    => False
-      Nothing   => False
+      Right Refl => t1 == t2 && s1 == s2
+
+export
+(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, s1) (t2, s2)
 
 export %hint
-ShowWithSubst : (forall n. Show (tm n), Show (env n)) =>
+ShowWithSubst : (Show (env n), forall n. Show (tm n)) =>
                 Show (WithSubst tm env n)
 ShowWithSubst = deriveShow

lib/Quox/Syntax/Term/Base.idr

@@ -7,6 +7,7 @@ import public Quox.Syntax.Qty
 import public Quox.Syntax.Dim
 import public Quox.Syntax.Term.TyConKind
 import public Quox.Name
+import public Quox.Loc
 import public Quox.Context
 
 import Quox.Pretty
@@ -63,7 +64,7 @@ ShowScopedBody = deriveShow
 public export
 record Scoped (s : Nat) (f : Nat -> Type) (n : Nat) where
   constructor S
-  names : NContext s
+  names : BContext s
   body  : ScopedBody s f n
 %name Scoped body
 
@@ -88,38 +89,38 @@ mutual
   public export
   data Term : (d, n : Nat) -> Type where
     ||| type of types
-    TYPE : (l : Universe) -> Term d n
+    TYPE : (l : Universe) -> (loc : Loc) -> Term d n
 
     ||| function type
     Pi  : (qty : Qty) -> (arg : Term d n) ->
-          (res : ScopeTerm d n) -> Term d n
+          (res : ScopeTerm d n) -> (loc : Loc) -> Term d n
     ||| function term
-    Lam : (body : ScopeTerm d n) -> Term d n
+    Lam : (body : ScopeTerm d n) -> (loc : Loc) -> Term d n
 
     ||| pair type
-    Sig : (fst : Term d n) -> (snd : ScopeTerm d n) -> Term d n
+    Sig : (fst : Term d n) -> (snd : ScopeTerm d n) -> (loc : Loc) -> Term d n
     ||| pair value
-    Pair : (fst, snd : Term d n) -> Term d n
+    Pair : (fst, snd : Term d n) -> (loc : Loc) -> Term d n
 
     ||| enumeration type
-    Enum : (cases : SortedSet TagVal) -> Term d n
+    Enum : (cases : SortedSet TagVal) -> (loc : Loc) -> Term d n
     ||| enumeration value
-    Tag : (tag : TagVal) -> Term d n
+    Tag : (tag : TagVal) -> (loc : Loc) -> Term d n
 
     ||| equality type
-    Eq : (ty : DScopeTerm d n) -> (l, r : Term d n) -> Term d n
+    Eq : (ty : DScopeTerm d n) -> (l, r : Term d n) -> (loc : Loc) -> Term d n
     ||| equality term
-    DLam : (body : DScopeTerm d n) -> Term d n
+    DLam : (body : DScopeTerm d n) -> (loc : Loc) -> Term d n
 
     ||| natural numbers (temporary until 𝐖 gets added)
-    Nat  : Term d n
+    Nat  : (loc : Loc) -> Term d n
     -- [todo] can these be elims?
-    Zero : Term d n
+    Zero : (loc : Loc) -> Term d n
-    Succ : (p : Term d n) -> Term d n
+    Succ : (p : Term d n) -> (loc : Loc) -> Term d n
 
     ||| "box" (package a value up with a certain quantity)
-    BOX : (qty : Qty) -> (ty : Term d n) -> Term d n
+    BOX : (qty : Qty) -> (ty : Term d n) -> (loc : Loc) -> Term d n
-    Box : (val : Term d n) -> Term d n
+    Box : (val : Term d n) -> (loc : Loc) -> Term d n
 
     ||| elimination
     E : (e : Elim d n) -> Term d n
@@ -134,12 +135,12 @@ mutual
   public export
   data Elim : (d, n : Nat) -> Type where
     ||| free variable
-    F : (x : Name) -> Elim d n
+    F : (x : Name) -> (loc : Loc) -> Elim d n
     ||| bound variable
-    B : (i : Var n) -> Elim d n
+    B : (i : Var n) -> (loc : Loc) -> Elim d n
 
     ||| term application
-    (:@) : (fun : Elim d n) -> (arg : Term d n) -> Elim d n
+    App : (fun : Elim d n) -> (arg : Term d n) -> (loc : Loc) -> Elim d n
 
     ||| pair destruction
     |||
@@ -148,12 +149,14 @@ mutual
     CasePair : (qty : Qty) -> (pair : Elim d n) ->
                (ret : ScopeTerm d n) ->
                (body : ScopeTermN 2 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
@@ -161,33 +164,36 @@ mutual
               (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
-    (:%) : (fun : Elim d n) -> (arg : Dim d) -> Elim d n
+    DApp : (fun : Elim d n) -> (arg : Dim d) -> (loc : Loc) -> Elim d n
 
     ||| type-annotated term
-    (:#) : (tm, ty : Term d n) -> Elim d n
+    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) -> Elim d n
+          (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) -> Elim d n
+           (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
@@ -244,88 +250,211 @@ mutual
 ||| scope which ignores all its binders
 public export %inline
 SN : {s : Nat} -> f n -> Scoped s f n
-SN = S (replicate s Unused) . N
+SN = S (replicate s $ BN Unused noLoc) . N
 
 ||| scope which uses its binders
 public export %inline
-SY : NContext s -> f (s + n) -> Scoped s f n
+SY : BContext s -> f (s + n) -> Scoped s f n
 SY ns = S ns . Y
 
 public export %inline
-name : Scoped 1 f n -> BaseName
+name : Scoped 1 f n -> BindName
 name (S [< x] _) = x
 
 public export %inline
-(.name) : Scoped 1 f n -> BaseName
+(.name) : Scoped 1 f n -> BindName
 s.name = name s
 
 ||| more convenient Pi
 public export %inline
-PiY : (qty : Qty) -> (x : BaseName) ->
+PiY : (qty : Qty) -> (x : BindName) ->
-      (arg : Term d n) -> (res : Term d (S n)) -> Term d n
+      (arg : Term d n) -> (res : Term d (S n)) -> (loc : Loc) -> Term d n
-PiY {qty, x, arg, res} = Pi {qty, arg, res = SY [< x] res}
+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) -> Term d n
+Arr : (qty : Qty) -> (arg, res : Term d n) -> (loc : Loc) -> Term d n
-Arr {qty, arg, res} = Pi {qty, arg, res = SN res}
+Arr {qty, arg, res, loc} = Pi {qty, arg, res = SN res, loc}
 
 ||| more convenient Sig
 public export %inline
-SigY : (x : BaseName) -> (fst : Term d n) ->
+SigY : (x : BindName) -> (fst : Term d n) ->
-       (snd : Term d (S n)) -> Term d n
+       (snd : Term d (S n)) -> (loc : Loc) -> Term d n
-SigY {x, fst, snd} = Sig {fst, snd = SY [< x] snd}
+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) -> Term d n
+And : (fst, snd : Term d n) -> (loc : Loc) -> Term d n
-And {fst, snd} = Sig {fst, snd = SN snd}
+And {fst, snd, loc} = Sig {fst, snd = SN snd, loc}
 
 ||| more convenient Eq
 public export %inline
-EqY : (i : BaseName) -> (ty : Term (S d) n) ->
+EqY : (i : BindName) -> (ty : Term (S d) n) ->
-      (l, r : Term d n) -> Term d n
+      (l, r : Term d n) -> (loc : Loc) -> Term d n
-EqY {i, ty, l, r} = Eq {ty = SY [< i] ty, l, r}
+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) -> Term d n
+Eq0 : (ty, l, r : Term d n) -> (loc : Loc) -> Term d n
-Eq0 {ty, l, r} = Eq {ty = SN ty, l, r}
+Eq0 {ty, l, r, loc} = Eq {ty = SN ty, l, r, loc}
 
 ||| same as `F` but as a term
 public export %inline
-FT : Name -> Term d n
+FT : Name -> (loc : Loc) -> Term d n
-FT = E . F
+FT x loc = E $ F x 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) => Elim d n
+BV : (i : Nat) -> (0 _ : LT i n) => (loc : Loc) -> Elim d n
-BV i = B $ V i
+BV i loc = B (V i) loc
 
 ||| same as `BV` but as a term
 public export %inline
-BVT : (i : Nat) -> (0 _ : LT i n) => Term d n
+BVT : (i : Nat) -> (0 _ : LT i n) => (loc : Loc) -> Term d n
-BVT i = E $ BV i
+BVT i loc = E $ BV i loc
 
 public export
-makeNat : Nat -> Term d n
+makeNat : Nat -> Loc -> Term d n
-makeNat 0 = Zero
+makeNat 0 loc = Zero loc
-makeNat (S k) = Succ $ makeNat k
+makeNat (S k) loc = Succ (makeNat k loc) loc
 
 public export %inline
-enum : List TagVal -> Term d n
+enum : List TagVal -> Loc -> Term d n
-enum = Enum . SortedSet.fromList
+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 -> Elim d n
+           List (TypeCaseArm d n) -> Term d n -> Loc -> Elim d n
-typeCase ty ret arms def = TypeCase ty ret (fromList arms) def
+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) -> NContext (arity k) -> Term d (arity k + n) ->
+             (k : TyConKind) -> BContext (arity k) -> Term d (arity k + n) ->
-             {default Nat def : Term d n} ->
+             (loc : Loc) ->
+             {default (Nat loc) def : Term d n} ->
              Elim d n
-typeCase1Y ty ret k ns body {def} =
+typeCase1Y ty ret k ns body loc = typeCase ty ret [(k ** SY ns body)] def loc
-  typeCase ty ret [(k ** SY ns body)] def
+
+
+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 (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
+  (Lam _ loc).loc       = loc
+  (Sig _ _ loc).loc     = loc
+  (Pair _ _ loc).loc    = loc
+  (Enum _ loc).loc      = loc
+  (Tag _ loc).loc       = loc
+  (Eq _ _ _ loc).loc    = loc
+  (DLam _ loc).loc      = loc
+  (Nat loc).loc         = loc
+  (Zero loc).loc        = loc
+  (Succ _ loc).loc      = loc
+  (BOX _ _ loc).loc     = loc
+  (Box _ loc).loc       = loc
+  (E e).loc             = e.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 _) = F x 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 (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 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 (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 (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)

lib/Quox/Syntax/Term/Pretty.idr

@@ -82,8 +82,8 @@ PrettyHL a => PrettyHL (Binder a) where
 export
 prettyBindType : PrettyHL a => PrettyHL b =>
                  Pretty.HasEnv m =>
-                 Maybe Qty -> BaseName -> a -> Doc HL -> b -> m (Doc HL)
+                 Maybe Qty -> BindName -> a -> Doc HL -> b -> m (Doc HL)
-prettyBindType q x s arr t = do
+prettyBindType q (BN x _) s arr t = do
   bind <- case q of
     Nothing => pretty0M $ MkBinder x s
     Just q  => pretty0M $ MkWithQty q $ MkBinder x s
@@ -92,14 +92,15 @@ prettyBindType q x s arr t = do
 
 export
 prettyArm : PrettyHL a => Pretty.HasEnv m =>
-            BinderSort -> SnocList BaseName -> Doc HL -> a -> m (Doc HL)
+            BinderSort -> SnocList BindName -> Doc HL -> a -> m (Doc HL)
 prettyArm sort xs pat body = do
+  let xs = map name xs
   body <- withPrec Outer $ unders sort xs $ prettyM body
   pure $ hang 2 $ sep [pat <++> !darrowD, body]
 
 export
 prettyLams : PrettyHL a => Pretty.HasEnv m =>
-             Maybe (Doc HL) -> BinderSort -> SnocList BaseName -> a ->
+             Maybe (Doc HL) -> BinderSort -> SnocList BindName -> a ->
              m (Doc HL)
 prettyLams lam sort names body = do
   let var = case sort of T => TVar; D => DVar
@@ -109,13 +110,14 @@ prettyLams lam sort names body = do
 
 
 public export
-data TypeLine a = MkTypeLine BaseName a
+data TypeLine a = MkTypeLine BindName a
 
 export
 PrettyHL a => PrettyHL (TypeLine a) where
-  prettyM (MkTypeLine Unused ty) =
-    bracks <$> pretty0M ty
   prettyM (MkTypeLine i ty) =
+    if i.name == Unused then
+      bracks <$> pretty0M ty
+    else
       map bracks $ withPrec Outer $ prettyLams Nothing D [< i] ty
 
 
@@ -142,28 +144,28 @@ prettyTuple = map (parens . align . separate commaD) . traverse prettyM
 
 export
 prettyArms : PrettyHL a => Pretty.HasEnv m =>
-             BinderSort -> List (SnocList BaseName, Doc HL, a) -> m (Doc HL)
+             BinderSort -> List (SnocList BindName, Doc HL, a) -> m (Doc HL)
 prettyArms s =
   map (braces . aseparate semiD) .
   traverse (\(xs, l, r) => prettyArm s xs l r)
 
 export
 prettyCase' : (PrettyHL a, PrettyHL b, PrettyHL c, Pretty.HasEnv m) =>
-              Doc HL -> a -> BaseName -> b ->
+              Doc HL -> a -> BindName -> b ->
-              List (SnocList BaseName, Doc HL, c) ->
+              List (SnocList BindName, Doc HL, c) ->
               m (Doc HL)
 prettyCase' intro elim r ret arms = do
   elim  <- pretty0M elim
-  ret   <- case r of
+  ret   <- case r.name of
-    Unused => under T r $ pretty0M ret
+    Unused => under T r.name $ pretty0M ret
     _      => prettyLams Nothing T [< r] ret
   arms  <- prettyArms T arms
   pure $ asep [intro <++> elim, returnD <++> ret, ofD <++> arms]
 
 export
 prettyCase : (PrettyHL a, PrettyHL b, PrettyHL c, Pretty.HasEnv m) =>
-             Qty -> a -> BaseName -> b ->
+             Qty -> a -> BindName -> b ->
-             List (SnocList BaseName, Doc HL, c) ->
+             List (SnocList BindName, Doc HL, c) ->
              m (Doc HL)
 prettyCase pi elim r ret arms = do
   caseq <- (caseD <+>) <$> prettySuffix pi
@@ -197,13 +199,13 @@ prettyBoxVal : PrettyHL a => Pretty.HasEnv m => a -> m (Doc HL)
 prettyBoxVal val = bracks <$> pretty0M val
 
 export
-prettyCompPat : Pretty.HasEnv m => DimConst -> BaseName -> m (Doc HL)
+prettyCompPat : Pretty.HasEnv m => DimConst -> BindName -> m (Doc HL)
-prettyCompPat e j = hsep <$> sequence [pretty0M e, pretty0M $ DV j]
+prettyCompPat e j = hsep <$> sequence [pretty0M e, pretty0M $ DV j.name]
 
 export
 toNatLit : Term d n -> Maybe Nat
-toNatLit Zero     = Just 0
+toNatLit (Zero _)   = Just 0
-toNatLit (Succ n) = [|S $ toNatLit n|]
+toNatLit (Succ n _) = [|S $ toNatLit n|]
 toNatLit _          = Nothing
 
 private
@@ -216,69 +218,69 @@ parameters (showSubsts : Bool)
   export covering
   [TermSubst] PrettyHL (Term d n) using ElimSubst
   where
-    prettyM (TYPE l) =
+    prettyM (TYPE l _) =
       pure $ !typeD <+> hl Syntax !(prettyUnivSuffix l)
 
-    prettyM (Pi qty s (S _ (N t))) = do
+    prettyM (Pi qty s (S _ (N t)) _) = do
       dom <- pretty0M $ MkWithQty qty s
       cod <- withPrec AnnR $ prettyM t
       parensIfM AnnR $ asep [dom <++> !arrowD, cod]
 
-    prettyM (Pi qty s (S [< x] (Y t))) =
+    prettyM (Pi qty s (S [< x] (Y t)) _) =
       prettyBindType (Just qty) x s !arrowD t
 
-    prettyM (Lam (S x t)) =
+    prettyM (Lam (S x t) _) =
       let GotLams {names, body, _} = getLams' x t.term Refl in
       prettyLams (Just !lamD) T (toSnocList' names) body
 
-    prettyM (Sig s (S _ (N t))) = do
+    prettyM (Sig s (S _ (N t)) _) = do
       s <- withPrec InTimes $ prettyM s
       t <- withPrec Times   $ prettyM t
       parensIfM Times $ asep [s <++> !timesD, t]
 
-    prettyM (Sig s (S [< x] (Y t))) =
+    prettyM (Sig s (S [< x] (Y t)) _) =
       prettyBindType Nothing x s !timesD t
 
-    prettyM (Pair s t) =
+    prettyM (Pair s t _) =
       let GotPairs {init, last, _} = getPairs' [< s] t in
       prettyTuple $ toList $ init :< last
 
-    prettyM (Enum tags) =
+    prettyM (Enum tags _) =
       pure $ delims "{" "}" . aseparate comma $ map prettyTagBare $
         Prelude.toList tags
 
-    prettyM (Tag t) =
+    prettyM (Tag t _) =
       pure $ prettyTag t
 
-    prettyM (Eq (S _ (N ty)) l r) = do
+    prettyM (Eq (S _ (N ty)) l r _) = do
       l  <- withPrec InEq $ prettyM l
       r  <- withPrec InEq $ prettyM r
       ty <- withPrec InEq $ prettyM ty
       parensIfM Eq $ asep [l <++> !eqndD, r <++> colonD, ty]
 
-    prettyM (Eq (S [< i] (Y ty)) l r) = do
+    prettyM (Eq (S [< i] (Y ty)) l r _) = do
       prettyApps Nothing (L eqD)
         [epretty $ MkTypeLine i ty, epretty l, epretty r]
 
-    prettyM (DLam (S i t)) =
+    prettyM (DLam (S i t) _) =
       let GotDLams {names, body, _} = getDLams' i t.term Refl in
       prettyLams (Just !dlamD) D (toSnocList' names) body
 
-    prettyM Nat = natD
+    prettyM (Nat _) = natD
 
-    prettyM Zero = pure $ hl Syntax "0"
+    prettyM (Zero _) = pure $ hl Syntax "0"
 
-    prettyM (Succ n) =
+    prettyM (Succ n _) =
       case toNatLit n of
         Just n  => pure $ hl Syntax $ pretty $ S n
         Nothing => prettyApps Nothing (L succD) [n]
 
-    prettyM (BOX pi ty) = do
+    prettyM (BOX pi ty _) = do
       pi <- pretty0M pi
       ty <- pretty0M ty
       pure $ bracks $ hcat [pi, dotD, align ty]
 
-    prettyM (Box val) = prettyBoxVal val
+    prettyM (Box val _) = prettyBoxVal val
 
     prettyM (E e) = prettyM e
 
@@ -299,49 +301,49 @@ parameters (showSubsts : Bool)
   export covering
   [ElimSubst] PrettyHL (Elim d n) using TermSubst
   where
-    prettyM (F x) =
+    prettyM (F x _) =
       hl' Free <$> prettyM x
 
-    prettyM (B i) =
+    prettyM (B i _) =
       prettyVar TVar TVarErr (!ask).tnames i
 
-    prettyM (e :@ s) =
+    prettyM (App e s _) =
       let GotArgs {fun, args, _} = getArgs' e [s] in
       prettyApps Nothing fun args
 
-    prettyM (CasePair pi p (S [< r] ret) (S [< x, y] body)) = do
+    prettyM (CasePair pi p (S [< r] ret) (S [< x, y] body) _) = do
       pat <- parens . separate commaD <$> traverse (hlF TVar . prettyM) [x, y]
       prettyCase pi p r ret.term [([< x, y], pat, body.term)]
 
-    prettyM (CaseEnum pi t (S [< r] ret) arms) =
+    prettyM (CaseEnum pi t (S [< r] ret) arms _) =
       prettyCase pi t r ret.term
         [([<], prettyTag t, b) | (t, b) <- SortedMap.toList arms]
 
-    prettyM (CaseNat pi pi' nat (S [< r] ret) zer (S [< s, ih] suc)) =
+    prettyM (CaseNat pi pi' nat (S [< r] ret) zer (S [< s, ih] suc) _) =
       prettyCase pi nat r ret.term
         [([<],       zeroD,    eterm zer),
          ([< s, ih], !succPat, eterm suc.term)]
     where
       succPat : m (Doc HL)
       succPat = case (ih, pi') of
-        (Unused, Zero) => pure $ succD <++> !(pretty0M s)
+        (BN Unused _, Zero) => pure $ succD <++> !(pretty0M s)
         _ => pure $ asep [succD <++> !(pretty0M s) <+> comma,
                           !(pretty0M $ MkWithQty pi' ih)]
 
-    prettyM (CaseBox pi box (S [< r] ret) (S [< u] body)) =
+    prettyM (CaseBox pi box (S [< r] ret) (S [< u] body) _) =
       prettyCase pi box r ret.term
-        [([< u], !(prettyBoxVal $ TV u), body.term)]
+        [([< u], !(prettyBoxVal $ TV u.name), body.term)]
 
-    prettyM (e :% d) =
+    prettyM (DApp e d _) =
       let GotDArgs {fun, args, _} = getDArgs' e [d] in
       prettyApps (Just "@") fun args
 
-    prettyM (s :# a) = do
+    prettyM (Ann s a _) = do
       s <- withPrec AnnL $ prettyM s
       a <- withPrec AnnR $ prettyM a
       parensIfM AnnR $ hang 2 $ s <++> !annD <%%> a
 
-    prettyM (Coe (S [< i] ty) p q val) =
+    prettyM (Coe (S [< i] ty) p q val _) =
       let ty = case ty of
             Y ty => epretty $ MkTypeLine i ty
             N ty => epretty ty
@@ -352,9 +354,9 @@ parameters (showSubsts : Bool)
          (Just "@", epretty q),
          (Nothing,  epretty val)]
 
-    prettyM (Comp ty p q val r (S [< z] zero) (S [< o] one)) = do
+    prettyM (Comp ty p q val r (S [< z] zero) (S [< o] one) _) = do
       apps <- prettyApps' (L compD)
-        [(Nothing,  epretty $ MkTypeLine Unused ty),
+        [(Nothing,  epretty $ MkTypeLine (BN Unused noLoc) ty),
          (Just "@", epretty p),
          (Just "@", epretty q),
          (Nothing,  epretty val),
@@ -364,25 +366,26 @@ parameters (showSubsts : Bool)
          ([< o], !(prettyCompPat One  o), one.term)]
       pure $ apps <++> arms
 
-    prettyM (TypeCase ty ret arms def) = do
+    prettyM (TypeCase ty ret arms def _) = do
       arms <- traverse fromArm (toList arms)
-      prettyCase' typecaseD ty Unused ret $
+      prettyCase' typecaseD ty (BN Unused noLoc) ret $
         arms ++ [([<], hl Syntax "_", eterm def)]
     where
-      v : BaseName -> Doc HL
+      v : BindName -> Doc HL
-      v = pretty0 True . TV
+      v = pretty0 True . TV . name
 
-      tyCasePat : (k : TyConKind) -> NContext (arity k) -> m (Doc HL)
+      tyCasePat : (k : TyConKind) -> BContext (arity k) -> m (Doc HL)
       tyCasePat KTYPE [<] = typeD
       tyCasePat KPi   [< a, b] = pure $ parens $ hsep [v a, !arrowD, v b]
       tyCasePat KSig  [< a, b] = pure $ parens $ hsep [v a, !arrowD, v b]
       tyCasePat KEnum [<]   = pure $ hl Syntax "{}"
-      tyCasePat KEq   vars  = prettyApps Nothing (L eqD) $ map TV $ toList' vars
       tyCasePat KNat  [<]   = natD
       tyCasePat KBOX  [< a] = pure $ bracks $ v a
+      tyCasePat KEq   vars  =
+        prettyApps Nothing (L eqD) $ map (TV . name) $ toList' vars
 
       fromArm : TypeCaseArm d n ->
-                m (SnocList BaseName, Doc HL, Exists (Term d))
+                m (SnocList BindName, Doc HL, Exists (Term d))
       fromArm (k ** S ns t) =
         pure (toSnocList' ns, !(tyCasePat k ns), eterm t.term)
 
@@ -414,7 +417,7 @@ PrettyHL (Elim d n) where prettyM = prettyM @{ElimSubst False}
 
 export covering
 prettyTerm : (unicode : Bool) ->
-             (dnames : NContext d) -> (tnames : NContext n) ->
+             (dnames : BContext d) -> (tnames : BContext n) ->
              Term d n -> Doc HL
 prettyTerm unicode dnames tnames term =
-  pretty0With unicode (toSnocList' dnames) (toSnocList' tnames) term
+  pretty0With unicode (toNames dnames) (toNames tnames) term

lib/Quox/Syntax/Term/Split.idr

@@ -13,7 +13,7 @@ import public Data.Vect
 
 public export %inline
 isLam : Term {} -> Bool
-isLam (Lam _) = True
+isLam (Lam {}) = True
 isLam _        = False
 
 public export
@@ -23,7 +23,7 @@ NotLam = No . isLam
 
 public export %inline
 isDLam : Term {} -> Bool
-isDLam (DLam _) = True
+isDLam (DLam {}) = True
 isDLam _         = False
 
 public export
@@ -43,7 +43,7 @@ NotPair = No . isPair
 
 public export %inline
 isApp : Elim {} -> Bool
-isApp (_ :@ _) = True
+isApp (App {}) = True
 isApp _        = False
 
 public export
@@ -53,7 +53,7 @@ NotApp = No . isApp
 
 public export %inline
 isDApp : Elim {} -> Bool
-isDApp (_ :% _) = True
+isDApp (DApp {}) = True
 isDApp _         = False
 
 public export
@@ -61,11 +61,13 @@ public export
 NotDApp = No . isDApp
 
 
-infixl 9 :@@
+-- infixl 9 :@@
-||| apply multiple arguments at once
+-- ||| apply multiple arguments at once
-public export %inline
+-- public export %inline
-(:@@) : Elim d n -> List (Term d n) -> Elim d n
+-- (:@@) : Elim d n -> List (Term d n) -> Elim d n
-f :@@ ss = foldl (:@) f ss
+-- f :@@ ss = foldl app f ss where
+--   app : Elim d n -> Term d n -> Elim d n
+--   app f s = App f s (f.loc `extend'` s.loc.bounds)
 
 public export
 record GetArgs d n where
@@ -85,7 +87,7 @@ mutual
   getArgsNc : (e : Elim d n) -> (0 nc : NotClo e) =>
               List (Term d n) -> GetArgs d n
   getArgsNc fun args = case nchoose $ isApp fun of
-    Left  y => let f :@ a = fun in getArgs' f (a :: args)
+    Left  y => let App f a _ = fun in getArgs' f (a :: args)
     Right n => GotArgs {fun, args, notApp = n}
 
 ||| splits an application into its head and arguments. if it's not an
@@ -96,11 +98,13 @@ getArgs : Elim d n -> GetArgs d n
 getArgs e = getArgs' e []
 
 
-infixl 9 :%%
+-- infixl 9 :%%
-||| apply multiple dimension arguments at once
+-- ||| apply multiple dimension arguments at once
-public export %inline
+-- public export %inline
-(:%%) : Elim d n -> List (Dim d) -> Elim d n
+-- (:%%) : Elim d n -> List (Dim d) -> Elim d n
-f :%% ss = foldl (:%) f ss
+-- f :%% ss = foldl dapp f ss where
+--   dapp : Elim d n -> Dim d -> Elim d n
+--   dapp f p = DApp f p (f.loc `extend'` p.loc.bounds)
 
 public export
 record GetDArgs d n where
@@ -120,7 +124,7 @@ mutual
   getDArgsNc : (e : Elim d n) -> (0 nc : NotClo e) =>
                List (Dim d) -> GetDArgs d n
   getDArgsNc fun args = case nchoose $ isDApp fun of
-    Left  y => let f :% d = fun in getDArgs' f (d :: args)
+    Left  y => let DApp f d _ = fun in getDArgs' f (d :: args)
     Right n => GotDArgs {fun, args, notDApp = n}
 
 ||| splits a dimension application into its head and arguments. if it's not an
@@ -130,33 +134,33 @@ getDArgs : Elim d n -> GetDArgs d n
 getDArgs e = getDArgs' e []
 
 
-infixr 1 :\\
+-- infixr 1 :\\
-public export
+-- public export
-absN : NContext m -> Term d (m + n) -> Term d n
+-- absN : BContext m -> Term d (m + n) -> Term d n
-absN [<]       s = s
+-- absN [<]       s = s
-absN (xs :< x) s = absN xs $ Lam $ ST [< x] s
+-- absN (xs :< x) s = absN xs $ Lam (ST [< x] s) ?absloc
 
-public export %inline
+-- public export %inline
-(:\\) : NContext m -> Term d (m + n) -> Term d n
+-- (:\\) : BContext m -> Term d (m + n) -> Term d n
-(:\\) = absN
+-- (:\\) = absN
 
 
-infixr 1 :\\%
+-- infixr 1 :\\%
-public export
+-- public export
-dabsN : NContext m -> Term (m + d) n -> Term d n
+-- dabsN : BContext m -> Term (m + d) n -> Term d n
-dabsN [<]       s = s
+-- dabsN [<]       s = s
-dabsN (xs :< x) s = dabsN xs $ DLam $ DST [< x] s
+-- dabsN (xs :< x) s = dabsN xs $ DLam (DST [< x] s) ?dabsLoc
 
-public export %inline
+-- public export %inline
-(:\\%) : NContext m -> Term (m + d) n -> Term d n
+-- (:\\%) : BContext m -> Term (m + d) n -> Term d n
-(:\\%) = dabsN
+-- (:\\%) = dabsN
 
 
 public export
 record GetLams d n where
   constructor GotLams
   {0 lams, rest : Nat}
-  names    : NContext lams
+  names    : BContext lams
   body     : Term d rest
   0 eq     : lams + n = rest
   0 notLam : NotLam body
@@ -164,7 +168,7 @@ record GetLams d n where
 mutual
   export %inline
   getLams' : forall lams, rest.
-             NContext lams -> Term d rest -> (0 eq : lams + n = rest) ->
+             BContext lams -> Term d rest -> (0 eq : lams + n = rest) ->
              GetLams d n
   getLams' xs s0 eq =
     let Element s nc = pushSubsts s0 in
@@ -172,12 +176,12 @@ mutual
 
   private
   getLamsNc : forall lams, rest.
-              NContext lams ->
+              BContext lams ->
               (t : Term d rest) -> (0 nc : NotClo t) =>
               (0 eq : lams + n = rest) ->
               GetLams d n
   getLamsNc xs s Refl = case nchoose $ isLam s of
-    Left  y => let Lam (S [< x] body) = s in
+    Left  y => let Lam (S [< x] body) _ = s in
                getLams' (xs :< x) (assert_smaller s body.term) Refl
     Right n => GotLams xs s Refl n
 
@@ -190,7 +194,7 @@ public export
 record GetDLams d n where
   constructor GotDLams
   {0 lams, rest : Nat}
-  names     : NContext lams
+  names     : BContext lams
   body      : Term rest n
   0 eq      : lams + d = rest
   0 notDLam : NotDLam body
@@ -198,7 +202,7 @@ record GetDLams d n where
 mutual
   export %inline
   getDLams' : forall lams, rest.
-              NContext lams -> Term rest n -> (0 eq : lams + d = rest) ->
+              BContext lams -> Term rest n -> (0 eq : lams + d = rest) ->
               GetDLams d n
   getDLams' xs s0 eq =
     let Element s nc = pushSubsts s0 in
@@ -206,12 +210,12 @@ mutual
 
   private
   getDLamsNc : forall lams, rest.
-               NContext lams ->
+               BContext lams ->
                (t : Term rest n) -> (0 nc : NotClo t) =>
                (0 eq : lams + d = rest) ->
                GetDLams d n
   getDLamsNc is s Refl = case nchoose $ isDLam s of
-    Left  y => let DLam (S [< i] body) = s in
+    Left  y => let DLam (S [< i] body) _ = s in
                getDLams' (is :< i) (assert_smaller s body.term) Refl
     Right n => GotDLams is s Refl n
 
@@ -238,7 +242,7 @@ mutual
                (t : Term d n) -> (0 nc : NotClo t) =>
                GetPairs d n
   getPairsNc ss t = case nchoose $ isPair t of
-    Left  y => let Pair s t = t in
+    Left  y => let Pair s t _ = t in
                getPairs' (ss :< s) t
     Right n => GotPairs ss t n
 

lib/Quox/Syntax/Term/Subst.idr

@@ -20,13 +20,13 @@ namespace CanDSubst
 export
 CanDSubst Term where
   s                // Shift SZ = s
-  TYPE l           // _        = TYPE l
+  TYPE l loc       // _        = TYPE l loc
   DCloT (Sub s ph) // th       = DCloT $ Sub s $ ph . th
   s                // th       = DCloT $ Sub s th
 
 private
 subDArgs : Elim dfrom n -> DSubst dfrom dto -> Elim dto n
-subDArgs (f :% d) th = subDArgs f th :% (d // th)
+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:
@@ -39,9 +39,9 @@ subDArgs e        th = DCloE $ Sub e th
 export
 CanDSubst Elim where
   e                // Shift SZ = e
-  F x              // _        = F x
+  F x loc          // _        = F x loc
-  B i              // _        = B i
+  B i loc          // _        = B i loc
-  f :% d           // th       = subDArgs (f :% d) th
+  e@(DApp {})      // th       = subDArgs e th
   DCloE (Sub e ph) // th       = DCloE $ Sub e $ ph . th
   e                // th       = DCloE $ Sub e th
 
@@ -61,8 +61,8 @@ namespace DSubst.DScopeTermN
   S ns (N body) // th = S ns $ N $ body // th
 
 
-export %inline FromVar (Elim d) where fromVar = B
+export %inline FromVar (Elim d) where fromVarLoc = B
-export %inline FromVar (Term d) where fromVar = E . fromVar
+export %inline FromVar (Term d) where fromVarLoc = E .: fromVar
 
 
 ||| does the minimal reasonable work:
@@ -73,8 +73,8 @@ export %inline FromVar (Term d) where fromVar = E . fromVar
 ||| - otherwise, wraps in a new closure
 export
 CanSubstSelf (Elim d) where
-  F x             // _  = F x
+  F x loc         // _  = F x loc
-  B i             // th = th !! i
+  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
@@ -93,7 +93,7 @@ namespace CanTSubst
 ||| - otherwise, wraps in a new closure
 export
 CanTSubst Term where
-  TYPE l          // _  = TYPE l
+  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
@@ -192,12 +192,12 @@ dsub1 t p = dsubN t [< p]
 
 
 public export %inline
-(.zero) : DScopeTerm d n -> Term d n
+(.zero) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n
-body.zero = dsub1 body $ K Zero
+body.zero = dsub1 body $ K Zero loc
 
 public export %inline
-(.one) : DScopeTerm d n -> Term d n
+(.one) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n
-body.one = dsub1 body $ K One
+body.one = dsub1 body $ K One loc
 
 
 public export
@@ -251,29 +251,34 @@ mutual
 mutual
   export
   PushSubsts Term Subst.isCloT where
-    pushSubstsWith th ph (TYPE l) =
+    pushSubstsWith th ph (TYPE l loc) =
-      nclo $ TYPE l
+      nclo $ TYPE l loc
-    pushSubstsWith th ph (Pi qty a body) =
+    pushSubstsWith th ph (Pi qty a body loc) =
-      nclo $ Pi qty (a // th // ph) (body // th // ph)
+      nclo $ Pi qty (a // th // ph) (body // th // ph) loc
-    pushSubstsWith th ph (Lam body) =
+    pushSubstsWith th ph (Lam body loc) =
-      nclo $ Lam (body // th // ph)
+      nclo $ Lam (body // th // ph) loc
-    pushSubstsWith th ph (Sig a b) =
+    pushSubstsWith th ph (Sig a b loc) =
-      nclo $ Sig (a // th // ph) (b // th // ph)
+      nclo $ Sig (a // th // ph) (b // th // ph) loc
-    pushSubstsWith th ph (Pair s t) =
+    pushSubstsWith th ph (Pair s t loc) =
-      nclo $ Pair (s // th // ph) (t // th // ph)
+      nclo $ Pair (s // th // ph) (t // th // ph) loc
-    pushSubstsWith th ph (Enum tags) =
+    pushSubstsWith th ph (Enum tags loc) =
-      nclo $ Enum tags
+      nclo $ Enum tags loc
-    pushSubstsWith th ph (Tag tag) =
+    pushSubstsWith th ph (Tag tag loc) =
-      nclo $ Tag tag
+      nclo $ Tag tag loc
-    pushSubstsWith th ph (Eq ty l r) =
+    pushSubstsWith th ph (Eq ty l r loc) =
-      nclo $ Eq (ty // th // ph) (l // th // ph) (r // th // ph)
+      nclo $ Eq (ty // th // ph) (l // th // ph) (r // th // ph) loc
-    pushSubstsWith th ph (DLam body) =
+    pushSubstsWith th ph (DLam body loc) =
-      nclo $ DLam (body // th // ph)
+      nclo $ DLam (body // th // ph) loc
-    pushSubstsWith _ _ Nat = nclo Nat
+    pushSubstsWith _ _ (Nat loc) =
-    pushSubstsWith _ _ Zero = nclo Zero
+      nclo $ Nat loc
-    pushSubstsWith th ph (Succ n) = nclo $ Succ $ n // th // ph
+    pushSubstsWith _ _ (Zero loc) =
-    pushSubstsWith th ph (BOX pi ty) = nclo $ BOX pi $ ty // th // ph
+      nclo $ Zero loc
-    pushSubstsWith th ph (Box val) = nclo $ Box $ val // th // ph
+    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)) =
@@ -283,38 +288,38 @@ mutual
 
   export
   PushSubsts Elim Subst.isCloE where
-    pushSubstsWith th ph (F x) =
+    pushSubstsWith th ph (F x loc) =
-      nclo $ F x
+      nclo $ F x loc
-    pushSubstsWith th ph (B i) =
+    pushSubstsWith th ph (B i loc) =
-      let res = ph !! i in
+      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 (f :@ s) =
+    pushSubstsWith th ph (App f s loc) =
-      nclo $ (f // th // ph) :@ (s // th // ph)
+      nclo $ App (f // th // ph) (s // th // ph) loc
-    pushSubstsWith th ph (CasePair pi p r b) =
+    pushSubstsWith th ph (CasePair pi p r b loc) =
-      nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph)
+      nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph) loc
-    pushSubstsWith th ph (CaseEnum pi t r arms) =
+    pushSubstsWith th ph (CaseEnum pi t r arms loc) =
       nclo $ CaseEnum pi (t // th // ph) (r // th // ph)
-               (map (\b => b // th // ph) arms)
+               (map (\b => b // th // ph) arms) loc
-    pushSubstsWith th ph (CaseNat pi pi' n r z s) =
+    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)
+               (z // th // ph) (s // th // ph) loc
-    pushSubstsWith th ph (CaseBox pi x r b) =
+    pushSubstsWith th ph (CaseBox pi x r b loc) =
-      nclo $ CaseBox pi (x // th // ph) (r // th // ph) (b // th // ph)
+      nclo $ CaseBox pi (x // th // ph) (r // th // ph) (b // th // ph) loc
-    pushSubstsWith th ph (f :% d) =
+    pushSubstsWith th ph (DApp f d loc) =
-      nclo $ (f // th // ph) :% (d // th)
+      nclo $ DApp (f // th // ph) (d // th) loc
-    pushSubstsWith th ph (s :# a) =
+    pushSubstsWith th ph (Ann s a loc) =
-      nclo $ (s // th // ph) :# (a // th // ph)
+      nclo $ Ann (s // th // ph) (a // th // ph) loc
-    pushSubstsWith th ph (Coe ty p q val) =
+    pushSubstsWith th ph (Coe ty p q val loc) =
-      nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph)
+      nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph) loc
-    pushSubstsWith th ph (Comp ty p q val r zero one) =
+    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)
+                  (zero // th // ph) (one // th // ph) loc
-    pushSubstsWith th ph (TypeCase ty ret arms def) =
+    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)
+        (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)) =
@@ -323,14 +328,19 @@ mutual
 
 private %inline
 CompHY : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
-        (r : Dim d) -> (zero, one : DScopeTerm d n) -> Elim d n
+         (r : Dim d) -> (zero, one : DScopeTerm d n) -> (loc : Loc) -> Elim d n
-CompHY {ty, p, q, val, r, zero, one} =
+CompHY {ty, p, q, val, r, zero, one, loc} =
-  let ty' = SY ty.names $ ty.term // (B VZ ::: shift 2) in
+  -- [fixme] maintain location of existing B VZ
+  let ty' = SY ty.names $ ty.term // (B VZ noLoc ::: shift 2) in
   Comp {
     ty = dsub1 ty q, p, q,
-    val = E $ Coe ty p q val, r,
+    val = E $ Coe ty p q val val.loc, r,
-    zero = SY zero.names $ E $ Coe ty' (B VZ) (weakD 1 q) zero.term,
+    -- [fixme] better locations for these vars?
-    one  = SY one.names  $ E $ Coe ty' (B VZ) (weakD 1 q) one.term
+    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
@@ -338,26 +348,28 @@ 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} =
+CompH' {ty, p, q, val, r, zero, one, loc} =
   case dsqueeze ty of
-    S _ (N ty) => Comp   {ty, p, q, val, r, zero, one}
+    S _ (N ty) => Comp   {ty, p, q, val, r, zero, one, loc}
-    S _ (Y _)  => CompHY {ty, p, q, val, r, zero, one}
+    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; (r=1) j ⇒ t₁ }
+||| 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) {
+||| comp [A‹q/i›] @p @q (coe [i ⇒ A] @p @q s) @r {
-|||   (r=0) j ⇒ coe [i ⇒ A] @j @q t₀;
+|||   0 j ⇒ coe [i ⇒ A] @j @q t₀;
-|||   (r=1) j ⇒ coe [i ⇒ A] @j @q t₁
+|||   1 j ⇒ coe [i ⇒ A] @j @q t₁
 ||| }
 public export %inline
-CompH : (i : BaseName) -> (ty : Term (S d) n) ->
+CompH : (i : BindName) -> (ty : Term (S d) n) ->
         (p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
-        (j0 : BaseName) -> (zero : Term (S d) n) ->
+        (j0 : BindName) -> (zero : Term (S d) n) ->
-        (j1 : BaseName) -> (one : 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} =
+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}
+          zero = SY [< j0] zero, one = SY [< j0] one, loc}

lib/Quox/Syntax/Term/Tighten.idr

@@ -18,6 +18,12 @@ Tighten (Shift from) where
   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 <$> tighten p i <*> pure loc
+
+
 export
 tightenSub : (forall m, n. OPE m n -> env n -> Maybe (env m)) ->
              OPE to1 to2 -> Subst env from to2 -> Maybe (Subst env from to1)
@@ -46,23 +52,35 @@ tightenDScope f p (S names (N body)) = S names . N <$> f p body
 mutual
   private
   tightenT : OPE n1 n2 -> Term d n2 -> Maybe (Term d n1)
-  tightenT p (TYPE l) = pure $ TYPE l
+  tightenT p (TYPE l loc) = pure $ TYPE l loc
-  tightenT p (Pi qty arg res) =
+  tightenT p (Pi qty arg res loc) =
-    Pi qty <$> tightenT p arg <*> tightenS p res
+    Pi qty <$> tightenT p arg <*> tightenS p res <*> pure loc
-  tightenT p (Lam body) = Lam <$> tightenS p body
+  tightenT p (Lam body loc) =
-  tightenT p (Sig fst snd) = Sig <$> tightenT p fst <*> tightenS p snd
+    Lam <$> tightenS p body <*> pure loc
-  tightenT p (Pair fst snd) = Pair <$> tightenT p fst <*> tightenT p snd
+  tightenT p (Sig fst snd loc) =
-  tightenT p (Enum cases) = pure $ Enum cases
+    Sig <$> tightenT p fst <*> tightenS p snd <*> pure loc
-  tightenT p (Tag tag) = pure $ Tag tag
+  tightenT p (Pair fst snd loc) =
-  tightenT p (Eq ty l r) =
+    Pair <$> tightenT p fst <*> tightenT p snd <*> pure loc
-    Eq <$> tightenDS p ty <*> tightenT p l <*> tightenT p r
+  tightenT p (Enum cases loc) =
-  tightenT p (DLam body) = DLam <$> tightenDS p body
+    pure $ Enum cases loc
-  tightenT p Nat = pure Nat
+  tightenT p (Tag tag loc) =
-  tightenT p Zero = pure Zero
+    pure $ Tag tag loc
-  tightenT p (Succ s) = Succ <$> tightenT p s
+  tightenT p (Eq ty l r loc) =
-  tightenT p (BOX qty ty) = BOX qty <$> tightenT p ty
+    Eq <$> tightenDS p ty <*> tightenT p l <*> tightenT p r <*> pure loc
-  tightenT p (Box val) = Box <$> tightenT p val
+  tightenT p (DLam body loc) =
-  tightenT p (E e) = assert_total $ E <$> tightenE p e
+    DLam <$> 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
@@ -72,45 +90,57 @@ mutual
 
   private
   tightenE : OPE n1 n2 -> Elim d n2 -> Maybe (Elim d n1)
-  tightenE p (F x) = pure $ F x
+  tightenE p (F x loc) =
-  tightenE p (B i) = [|B $ tighten p i|]
+    pure $ F x loc
-  tightenE p (fun :@ arg) = [|tightenE p fun :@ tightenT p arg|]
+  tightenE p (B i loc) =
-  tightenE p (CasePair qty pair ret body) =
+    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 <$> tightenE p pair
                  <*> tightenS p ret
                  <*> tightenS p body
-  tightenE p (CaseEnum qty tag ret arms) =
+                 <*> pure loc
+  tightenE p (CaseEnum qty tag ret arms loc) =
     CaseEnum qty <$> tightenE p tag
                  <*> tightenS p ret
                  <*> traverse (tightenT p) arms
-  tightenE p (CaseNat qty qtyIH nat ret zero succ) =
+                 <*> pure loc
+  tightenE p (CaseNat qty qtyIH nat ret zero succ loc) =
     CaseNat qty qtyIH
       <$> tightenE p nat
       <*> tightenS p ret
       <*> tightenT p zero
       <*> tightenS p succ
-  tightenE p (CaseBox qty box ret body) =
+      <*> pure loc
+  tightenE p (CaseBox qty box ret body loc) =
     CaseBox qty <$> tightenE p box
                 <*> tightenS p ret
                 <*> tightenS p body
-  tightenE p (fun :% arg) = (:% arg) <$> tightenE p fun
+                <*> pure loc
-  tightenE p (tm :# ty) = [|tightenT p tm :# tightenT p ty|]
+  tightenE p (DApp fun arg loc) =
-  tightenE p (Coe ty q0 q1 val) =
+    DApp <$> 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
-  tightenE p (Comp ty q0 q1 val r zero one) =
+        <*> pure loc
+  tightenE p (Comp ty q0 q1 val r zero one loc) =
     Comp <$> tightenT p ty
          <*> pure q0 <*> pure q1
          <*> tightenT p val
          <*> pure r
          <*> tightenDS p zero
          <*> tightenDS p one
-  tightenE p (TypeCase ty ret arms def) =
+         <*> pure loc
+  tightenE p (TypeCase ty ret arms def loc) =
     TypeCase <$> 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
@@ -130,35 +160,40 @@ mutual
 export Tighten (Elim d) where tighten p e = tightenE p e
 export Tighten (Term d) where tighten p t = tightenT p t
 
-export
-Tighten Dim where
-  tighten p (K e) = pure $ K e
-  tighten p (B i) = B <$> tighten p i
-
 
 mutual
   export
   dtightenT : OPE d1 d2 -> Term d2 n -> Maybe (Term d1 n)
-  dtightenT p (TYPE l) = pure $ TYPE l
+  dtightenT p (TYPE l loc) =
-  dtightenT p (Pi qty arg res) =
+    pure $ TYPE l loc
-    Pi qty <$> dtightenT p arg <*> dtightenS p res
+  dtightenT p (Pi qty arg res loc) =
-  dtightenT p (Lam body) =
+    Pi qty <$> dtightenT p arg <*> dtightenS p res <*> pure loc
-    Lam <$> dtightenS p body
+  dtightenT p (Lam body loc) =
-  dtightenT p (Sig fst snd) =
+    Lam <$> dtightenS p body <*> pure loc
-    Sig <$> dtightenT p fst <*> dtightenS p snd
+  dtightenT p (Sig fst snd loc) =
-  dtightenT p (Pair fst snd) =
+    Sig <$> dtightenT p fst <*> dtightenS p snd <*> pure loc
-    Pair <$> dtightenT p fst <*> dtightenT p snd
+  dtightenT p (Pair fst snd loc) =
-  dtightenT p (Enum cases) = pure $ Enum cases
+    Pair <$> dtightenT p fst <*> dtightenT p snd <*> pure loc
-  dtightenT p (Tag tag) = pure $ Tag tag
+  dtightenT p (Enum cases loc) =
-  dtightenT p (Eq ty l r) =
+    pure $ Enum cases loc
-    Eq <$> dtightenDS p ty <*> dtightenT p l <*> dtightenT p r
+  dtightenT p (Tag tag loc) =
-  dtightenT p (DLam body) = DLam <$> dtightenDS p body
+    pure $ Tag tag loc
-  dtightenT p Nat = pure Nat
+  dtightenT p (Eq ty l r loc) =
-  dtightenT p Zero = pure Zero
+    Eq <$> dtightenDS p ty <*> dtightenT p l <*> dtightenT p r <*> pure loc
-  dtightenT p (Succ s) = Succ <$> dtightenT p s
+  dtightenT p (DLam body loc) =
-  dtightenT p (BOX qty ty) = BOX qty <$> dtightenT p ty
+    DLam <$> dtightenDS p body <*> pure loc
-  dtightenT p (Box val) = Box <$> dtightenT p val
+  dtightenT p (Nat loc) =
-  dtightenT p (E e) = assert_total $ E <$> dtightenE p e
+    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
@@ -169,38 +204,48 @@ mutual
 
   export
   dtightenE : OPE d1 d2 -> Elim d2 n -> Maybe (Elim d1 n)
-  dtightenE p (F x) = pure $ F x
+  dtightenE p (F x loc) =
-  dtightenE p (B i) = pure $ B i
+    pure $ F x loc
-  dtightenE p (fun :@ arg) = [|dtightenE p fun :@ dtightenT p arg|]
+  dtightenE p (B i loc) =
-  dtightenE p (CasePair qty pair ret body) =
+    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
-  dtightenE p (CaseEnum qty tag ret arms) =
+                 <*> pure loc
+  dtightenE p (CaseEnum qty tag ret arms loc) =
     CaseEnum qty <$> dtightenE p tag
                  <*> dtightenS p ret
                  <*> traverse (dtightenT p) arms
-  dtightenE p (CaseNat qty qtyIH nat ret zero succ) =
+                 <*> pure loc
+  dtightenE p (CaseNat qty qtyIH nat ret zero succ loc) =
     CaseNat qty qtyIH
       <$> dtightenE p nat
       <*> dtightenS p ret
       <*> dtightenT p zero
       <*> dtightenS p succ
-  dtightenE p (CaseBox qty box ret body) =
+      <*> pure loc
+  dtightenE p (CaseBox qty box ret body loc) =
     CaseBox qty <$> dtightenE p box
                 <*> dtightenS p ret
                 <*> dtightenS p body
-  dtightenE p (fun :% arg) = [|dtightenE p fun :% tighten p arg|]
+                <*> pure loc
-  dtightenE p (tm :# ty) = [|dtightenT p tm :# dtightenT p ty|]
+  dtightenE p (DApp fun arg loc) =
-  dtightenE p (Coe ty q0 q1 val) =
+    DApp <$> dtightenE p fun <*> tighten p arg <*> pure loc
-    [|Coe (dtightenDS p ty) (tighten p q0) (tighten p q1) (dtightenT p val)|]
+  dtightenE p (Ann tm ty loc) =
-  dtightenE p (Comp ty q0 q1 val r zero one) =
+    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)|]
+           (dtightenDS p zero) (dtightenDS p one) (pure loc)|]
-  dtightenE p (TypeCase ty ret arms def) =
+  dtightenE p (TypeCase ty ret arms def loc) =
     [|TypeCase (dtightenE p ty) (dtightenT p ret)
-               (traverse (dtightenS p) arms) (dtightenT p def)|]
+               (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
@@ -226,46 +271,55 @@ 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} -> NContext s -> f (s + n) -> Scoped s f n
+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} -> NContext s -> Term (s + d) n -> DScopeTermN s d n
+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 : BaseName) ->
+PiT : (qty : Qty) -> (x : BindName) ->
-      (arg : Term d n) -> (res : Term d (S n)) -> Term d n
+      (arg : Term d n) -> (res : Term d (S n)) -> (loc : Loc) -> Term d n
-PiT {qty, x, arg, res} = Pi {qty, arg, res = ST [< x] res}
+PiT {qty, x, arg, res, loc} = Pi {qty, arg, res = ST [< x] res, loc}
 
 public export %inline
-SigT : (x : BaseName) -> (fst : Term d n) ->
+LamT : (x : BindName) -> (body : Term d (S n)) -> (loc : Loc) -> Term d n
-       (snd : Term d (S n)) -> Term d n
+LamT {x, body, loc} = Lam {body = ST [< x] body, loc}
-SigT {x, fst, snd} = Sig {fst, snd = ST [< x] snd}
 
 public export %inline
-EqT : (i : BaseName) -> (ty : Term (S d) n) ->
+SigT : (x : BindName) -> (fst : Term d n) ->
-      (l, r : Term d n) -> Term d n
+       (snd : Term d (S n)) -> (loc : Loc) -> Term d n
-EqT {i, ty, l, r} = Eq {ty = DST [< i] ty, l, r}
+SigT {x, fst, snd, loc} = Sig {fst, snd = ST [< x] snd, loc}
 
 public export %inline
-CoeT : (i : BaseName) -> (ty : Term (S d) n) ->
+EqT : (i : BindName) -> (ty : Term (S d) n) ->
-       (p, q : Dim d) -> (val : Term d n) -> Elim d n
+      (l, r : Term d n) -> (loc : Loc) -> Term d n
-CoeT {i, ty, p, q, val} = Coe {ty = DST [< i] ty, p, q, val}
+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) -> NContext (arity k) -> Term d (arity k + n) ->
+             (k : TyConKind) -> BContext (arity k) -> Term d (arity k + n) ->
-             {default Nat def : Term d n} ->
+             (loc : Loc) ->
+             {default (Nat loc) def : Term d n} ->
              Elim d n
-typeCase1T ty ret k ns body {def} =
+typeCase1T ty ret k ns body loc {def} =
-  typeCase ty ret [(k ** ST ns body)] def
+  typeCase ty ret [(k ** ST ns body)] def loc
 
 
 export

lib/Quox/Syntax/Var.idr

@@ -1,6 +1,7 @@
 module Quox.Syntax.Var
 
-import Quox.Name
+import public Quox.Loc
+import public Quox.Name
 import Quox.Pretty
 import Quox.OPE
 
@@ -42,6 +43,23 @@ export Uninhabited (VZ   = VS i) where uninhabited _ impossible
 export Uninhabited (VS i = VZ)   where uninhabited _ impossible
 
 
+public export
+data Eqv : Var m -> Var n -> Type where
+  EZ : VZ `Eqv` VZ
+  ES : i `Eqv` j -> VS i `Eqv` VS j
+%name Var.Eqv e
+
+export
+decEqv : Dec2 Eqv
+decEqv VZ     VZ     = Yes EZ
+decEqv VZ     (VS i) = No $ \case _ impossible
+decEqv (VS i) VZ     = No $ \case _ impossible
+decEqv (VS i) (VS j) =
+  case decEqv i j of
+    Yes y => Yes $ ES y
+    No  n => No  $ \(ES y) => n y
+
+
 private
 lookupS : Nat -> SnocList a -> Maybe a
 lookupS _     [<]       = Nothing
@@ -148,9 +166,13 @@ weakIsSpec p i = toNatInj $ trans (weakCorrect p i) (sym $ weakSpecCorrect p i)
 
 
 public export
-interface FromVar f where %inline fromVar : Var n -> f n
+interface FromVar f where %inline fromVarLoc : Var n -> Loc -> f n
 
-public export FromVar Var where fromVar = id
+public export %inline
+fromVar : FromVar f => Var n -> {default noLoc loc : Loc} -> f n
+fromVar x = fromVarLoc x loc
+
+public export FromVar Var where fromVarLoc x _ = x
 
 export
 tabulateV : {0 tm : Nat -> Type} -> (forall n. Var n -> tm n) ->

lib/Quox/Typechecker.idr

@@ -13,22 +13,26 @@ import Quox.EffExtra
 
 public export
 0 TCEff : List (Type -> Type)
-TCEff = [ErrorEff, DefsReader]
+TCEff = [ErrorEff, DefsReader, NameGen]
 
 public export
 0 TC : Type -> Type
 TC = Eff TCEff
 
+export
+runTCWith : NameSuf -> Definitions -> TC a -> (Either Error a, NameSuf)
+runTCWith = runEqualWith
+
 export
 runTC : Definitions -> TC a -> Either Error a
-runTC defs =
+runTC = runEqual
-  extract . runExcept . runReaderAt DEFS defs
 
 
+parameters (loc : Loc)
   export
   popQs : Has ErrorEff fs => QContext s -> QOutput (s + n) -> Eff fs (QOutput n)
   popQs [<]         qout         = pure qout
-popQs (pis :< pi) (qout :< rh) = do expectCompatQ rh pi; popQs pis qout
+  popQs (pis :< pi) (qout :< rh) = do expectCompatQ loc rh pi; popQs pis qout
 
   export %inline
   popQ : Has ErrorEff fs => Qty -> QOutput (S n) -> Eff fs (QOutput n)
@@ -47,29 +51,32 @@ lubs ctx []        = Just $ zeroFor ctx
 lubs ctx (x :: xs) = lubs1 $ x ::: xs
 
 
-||| context extension with no names or quantities
-private
-CtxExtension0' : Nat -> Nat -> Nat -> Type
-CtxExtension0' s d n = Context (Term d . (+ n)) s
-
-private
-addNames0 : Context (Term d . (+ n)) s -> NContext s -> CtxExtension d n (s + n)
-addNames0 [<] [<] = [<]
-addNames0 (ts :< t) (xs :< x) = addNames0 ts xs :< (Zero, x, t)
-
 export
-typecaseTel : (k : TyConKind) -> Universe -> CtxExtension0' (arity k) d n
+typecaseTel : (k : TyConKind) -> BContext (arity k) -> Universe ->
-typecaseTel k u = case k of
+              CtxExtension d n (arity k + n)
+typecaseTel k xs u = case k of
   KTYPE => [<]
   -- A : ★ᵤ, B : 0.A → ★ᵤ
-  KPi => [< TYPE u, Arr Zero (BVT 0) (TYPE u)]
+  KPi =>
-  KSig => [< TYPE u, Arr Zero (BVT 0) (TYPE u)]
+    let [< a, b] = xs in
+    [< (Zero, a, TYPE u a.loc),
+       (Zero, b, Arr Zero (BVT 0 b.loc) (TYPE u b.loc) b.loc)]
+  KSig =>
+    let [< a, b] = xs in
+    [< (Zero, a, TYPE u a.loc),
+       (Zero, b, Arr Zero (BVT 0 b.loc) (TYPE u b.loc) b.loc)]
   KEnum => [<]
   -- A₀ : ★ᵤ, A₁ : ★ᵤ, A : (A₀ ≡ A₁ : ★ᵤ), L : A₀, R : A₀
-  KEq => [< TYPE u, TYPE u, Eq0 (TYPE u) (BVT 1) (BVT 0), BVT 2, BVT 2]
+  KEq =>
+    let [< a0, a1, a, l, r] = xs in
+    [< (Zero, a0, TYPE u a0.loc),
+       (Zero, a1, TYPE u a1.loc),
+       (Zero, a,  Eq0 (TYPE u a.loc) (BVT 1 a.loc) (BVT 0 a.loc) a.loc),
+       (Zero, l,  BVT 2 l.loc),
+       (Zero, r,  BVT 2 r.loc)]
   KNat => [<]
   -- A : ★ᵤ
-  KBOX => [< TYPE u]
+  KBOX => let [< a] = xs in [< (Zero, a, TYPE u a.loc)]
 
 
 mutual
@@ -149,8 +156,8 @@ mutual
                 (subj : Term d n) -> (0 nc : NotClo subj) => Term d n ->
                 TC (CheckResult' n)
   toCheckType ctx sg t ty = do
-    u <- expectTYPE !defs ctx ty
+    u <- expectTYPE !defs ctx ty.loc ty
-    expectEqualQ Zero sg.fst
+    expectEqualQ t.loc Zero sg.fst
     checkTypeNoWrap ctx t (Just u)
     pure $ zeroFor ctx
 
@@ -159,70 +166,70 @@ mutual
            (subj : Term d n) -> (0 nc : NotClo subj) => Term d n ->
            TC (CheckResult' n)
 
-  check' ctx sg t@(TYPE _) ty = toCheckType ctx sg t ty
+  check' ctx sg t@(TYPE {}) ty = toCheckType ctx sg t ty
 
   check' ctx sg t@(Pi {}) ty = toCheckType ctx sg t ty
 
-  check' ctx sg (Lam body) ty = do
+  check' ctx sg (Lam body loc) ty = do
-    (qty, arg, res) <- expectPi !defs ctx ty
+    (qty, arg, res) <- expectPi !defs ctx ty.loc ty
     -- if Ψ | Γ, x : A ⊢ σ · t ⇐ B ⊳ Σ, ρ·x
     -- with ρ ≤ σπ
     let qty' = sg.fst * qty
     qout <- checkC (extendTy qty' body.name arg ctx) sg body.term res.term
     -- then Ψ | Γ ⊢ σ · (λx ⇒ t) ⇐ (π·x : A) → B ⊳ Σ
-    popQ qty' qout
+    popQ loc qty' qout
 
   check' ctx sg t@(Sig {}) ty = toCheckType ctx sg t ty
 
-  check' ctx sg (Pair fst snd) ty = do
+  check' ctx sg (Pair fst snd loc) ty = do
-    (tfst, tsnd) <- expectSig !defs ctx ty
+    (tfst, tsnd) <- expectSig !defs ctx ty.loc ty
     -- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ₁
     qfst <- checkC ctx sg fst tfst
-    let tsnd = sub1 tsnd (fst :# tfst)
+    let tsnd = sub1 tsnd (Ann fst tfst fst.loc)
     -- if Ψ | Γ ⊢ σ · t ⇐ B[s] ⊳ Σ₂
     qsnd <- checkC ctx sg snd tsnd
     -- then Ψ | Γ ⊢ σ · (s, t) ⇐ (x : A) × B ⊳ Σ₁ + Σ₂
     pure $ qfst + qsnd
 
-  check' ctx sg t@(Enum _) ty = toCheckType ctx sg t ty
+  check' ctx sg t@(Enum {}) ty = toCheckType ctx sg t ty
 
-  check' ctx sg (Tag t) ty = do
+  check' ctx sg (Tag t loc) ty = do
-    tags <- expectEnum !defs ctx ty
+    tags <- expectEnum !defs ctx ty.loc ty
     -- if t ∈ ts
-    unless (t `elem` tags) $ throw $ TagNotIn t tags
+    unless (t `elem` tags) $ throw $ TagNotIn loc t tags
     -- then Ψ | Γ ⊢ σ · t ⇐ {ts} ⊳ 𝟎
     pure $ zeroFor ctx
 
   check' ctx sg t@(Eq {}) ty = toCheckType ctx sg t ty
 
-  check' ctx sg (DLam body) ty = do
+  check' ctx sg (DLam body loc) ty = do
-    (ty, l, r) <- expectEq !defs ctx ty
+    (ty, l, r) <- expectEq !defs ctx ty.loc ty
     let ctx' = extendDim body.name ctx
         ty   = ty.term
         body = body.term
     -- if Ψ, i | Γ ⊢ σ · t ⇐ A ⊳ Σ
     qout <- checkC ctx' sg body ty
     -- if Ψ, i, i = 0 | Γ ⊢ t = l : A
-    equal (eqDim (BV 0) (K Zero) ctx') ty body (dweakT 1 l)
+    lift $ equal loc (eqDim (B VZ loc) (K Zero loc) ctx') ty body (dweakT 1 l)
     -- if Ψ, i, i = 1 | Γ ⊢ t = r : A
-    equal (eqDim (BV 0) (K One)  ctx') ty body (dweakT 1 r)
+    lift $ equal loc (eqDim (B VZ loc) (K One loc)  ctx') ty body (dweakT 1 r)
     -- then Ψ | Γ ⊢ σ · (δ i ⇒ t) ⇐ Eq [i ⇒ A] l r ⊳ Σ
     pure qout
 
-  check' ctx sg Nat ty = toCheckType ctx sg Nat ty
+  check' ctx sg t@(Nat {}) ty = toCheckType ctx sg t ty
 
-  check' ctx sg Zero ty = do
+  check' ctx sg (Zero {}) ty = do
-    expectNat !defs ctx ty
+    expectNat !defs ctx ty.loc ty
     pure $ zeroFor ctx
 
-  check' ctx sg (Succ n) ty = do
+  check' ctx sg (Succ n {}) ty = do
-    expectNat !defs ctx ty
+    expectNat !defs ctx ty.loc ty
-    checkC ctx sg n Nat
+    checkC ctx sg n ty
 
   check' ctx sg t@(BOX {}) ty = toCheckType ctx sg t ty
 
-  check' ctx sg (Box val) ty = do
+  check' ctx sg (Box val loc) ty = do
-    (q, ty) <- expectBOX !defs ctx ty
+    (q, ty) <- expectBOX !defs ctx ty.loc ty
     -- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ
     valout <- checkC ctx sg val ty
     -- then Ψ | Γ ⊢ σ · [s] ⇐ [π.A] ⊳ πΣ
@@ -232,7 +239,7 @@ mutual
     -- if Ψ | Γ ⊢ σ · e ⇒ A' ⊳ Σ
     infres <- inferC ctx sg e
     -- if Ψ | Γ ⊢ A' <: A
-    subtype ctx infres.type ty
+    lift $ subtype e.loc ctx infres.type ty
     -- then Ψ | Γ ⊢ σ · e ⇐ A ⊳ Σ
     pure infres.qout
 
@@ -241,13 +248,13 @@ mutual
                (subj : Term d n) -> (0 nc : NotClo subj) =>
                Maybe Universe -> TC ()
 
-  checkType' ctx (TYPE k) u = do
+  checkType' ctx (TYPE k loc) u = do
     -- if 𝓀 < ℓ then Ψ | Γ ⊢₀ Type 𝓀 ⇐ Type ℓ
     case u of
-      Just l  => unless (k < l) $ throw $ BadUniverse k l
+      Just l  => unless (k < l) $ throw $ BadUniverse loc k l
       Nothing => pure ()
 
-  checkType' ctx (Pi qty arg res) u = do
+  checkType' ctx (Pi qty arg res _) u = do
     -- if Ψ | Γ ⊢₀ A ⇐ Type ℓ
     checkTypeC ctx arg u
     -- if Ψ | Γ, x : A ⊢₀ B ⇐ Type ℓ
@@ -255,9 +262,9 @@ mutual
     -- then Ψ | Γ ⊢₀ (π·x : A) → B ⇐ Type ℓ
 
   checkType' ctx t@(Lam {}) u =
-    throw $ NotType ctx t
+    throw $ NotType t.loc ctx t
 
-  checkType' ctx (Sig fst snd) u = do
+  checkType' ctx (Sig fst snd _) u = do
     -- if Ψ | Γ ⊢₀ A ⇐ Type ℓ
     checkTypeC ctx fst u
     -- if Ψ | Γ, x : A ⊢₀ B ⇐ Type ℓ
@@ -265,15 +272,15 @@ mutual
     -- then Ψ | Γ ⊢₀ (x : A) × B ⇐ Type ℓ
 
   checkType' ctx t@(Pair {}) u =
-    throw $ NotType ctx t
+    throw $ NotType t.loc ctx t
 
-  checkType' ctx (Enum _) u = pure ()
+  checkType' ctx (Enum {}) u = pure ()
     -- Ψ | Γ ⊢₀ {ts} ⇐ Type ℓ
 
   checkType' ctx t@(Tag {}) u =
-    throw $ NotType ctx t
+    throw $ NotType t.loc ctx t
 
-  checkType' ctx (Eq t l r) u = do
+  checkType' ctx (Eq t l r _) u = do
     -- if Ψ, i | Γ ⊢₀ A ⇐ Type ℓ
     case t.body of
       Y t' => checkTypeC (extendDim t.name ctx) t' u
@@ -285,50 +292,31 @@ mutual
     -- then Ψ | Γ ⊢₀ Eq [i ⇒ A] l r ⇐ Type ℓ
 
   checkType' ctx t@(DLam {}) u =
-    throw $ NotType ctx t
+    throw $ NotType t.loc ctx t
 
-  checkType' ctx Nat u = pure ()
+  checkType' ctx (Nat {}) u = pure ()
-  checkType' ctx Zero u = throw $ NotType ctx Zero
+  checkType' ctx t@(Zero {}) u = throw $ NotType t.loc ctx t
-  checkType' ctx t@(Succ _) u = throw $ NotType ctx t
+  checkType' ctx t@(Succ {}) u = throw $ NotType t.loc ctx t
 
-  checkType' ctx (BOX q ty) u = checkType ctx ty u
+  checkType' ctx (BOX q ty _) u = checkType ctx ty u
-  checkType' ctx t@(Box _) u = throw $ NotType ctx t
+  checkType' ctx t@(Box {}) u = throw $ NotType t.loc ctx t
 
   checkType' ctx (E e) u = do
     -- if Ψ | Γ ⊢₀ E ⇒ Type ℓ
     infres <- inferC ctx szero e
     -- if Ψ | Γ ⊢ Type ℓ <: Type 𝓀
     case u of
-      Just u  => subtype ctx infres.type (TYPE u)
+      Just u  => lift $ subtype e.loc ctx infres.type (TYPE u noLoc)
-      Nothing => ignore $
+      Nothing => ignore $ expectTYPE !defs ctx e.loc infres.type
-        expectTYPE !defs ctx infres.type
     -- then Ψ | Γ ⊢₀ E ⇐ Type 𝓀
 
-  private covering
-  check0ScopeN : {s : Nat} ->
-                 TyContext d n -> CtxExtension0' s d n ->
-                 ScopeTermN s d n -> Term d n -> TC ()
-  check0ScopeN ctx ext (S _     (N body)) ty = check0 ctx body ty
-  check0ScopeN ctx ext (S names (Y body)) ty =
-    check0 (extendTyN (addNames0 ext names) ctx) body (weakT s ty)
-
-  private covering
-  check0Scope : TyContext d n -> Term d n ->
-                ScopeTerm d n -> Term d n -> TC ()
-  check0Scope ctx t = check0ScopeN ctx [< t]
-
-
-  private covering
-  checkTypeScopeN : TyContext d n -> CtxExtension0' s d n ->
-                    ScopeTermN s d n -> Maybe Universe -> TC ()
-  checkTypeScopeN ctx ext (S _     (N body)) u = checkType ctx body u
-  checkTypeScopeN ctx ext (S names (Y body)) u =
-    checkType (extendTyN (addNames0 ext names) ctx) body u
 
   private covering
   checkTypeScope : TyContext d n -> Term d n ->
                    ScopeTerm d n -> Maybe Universe -> TC ()
-  checkTypeScope ctx s = checkTypeScopeN ctx [< s]
+  checkTypeScope ctx s (S _     (N body)) u = checkType ctx body u
+  checkTypeScope ctx s (S [< x] (Y body)) u =
+    checkType (extendTy Zero x s ctx) body u
 
 
   private covering
@@ -336,16 +324,16 @@ mutual
            (subj : Elim d n) -> (0 nc : NotClo subj) =>
            TC (InferResult' d n)
 
-  infer' ctx sg (F x) = do
+  infer' ctx sg (F x loc) = do
     -- if π·x : A {≔ s} in global context
-    g <- lookupFree x !defs
+    g <- lookupFree x loc !defs
     -- if σ ≤ π
-    expectCompatQ sg.fst g.qty.fst
+    expectCompatQ loc sg.fst g.qty.fst
     -- then Ψ | Γ ⊢ σ · x ⇒ A ⊳ 𝟎
     let Val d = ctx.dimLen; Val n = ctx.termLen
     pure $ InfRes {type = g.type, qout = zeroFor ctx}
 
-  infer' ctx sg (B i) =
+  infer' ctx sg (B i _) =
     -- if x : A ∈ Γ
     -- then Ψ | Γ ⊢ σ · x ⇒ A ⊳ (𝟎, σ·x, 𝟎)
     pure $ lookupBound sg.fst i ctx.tctx
@@ -357,19 +345,19 @@ mutual
       let InfRes {type, qout} = lookupBound pi i ctx in
       InfRes {type = weakT 1 type, qout = qout :< Zero}
 
-  infer' ctx sg (fun :@ arg) = do
+  infer' ctx sg (App fun arg loc) = do
     -- if Ψ | Γ ⊢ σ · f ⇒ (π·x : A) → B ⊳ Σ₁
     funres <- inferC ctx sg fun
-    (qty, argty, res) <- expectPi !defs ctx funres.type
+    (qty, argty, res) <- expectPi !defs ctx fun.loc funres.type
     -- if Ψ | Γ ⊢ σ ⨴ π · s ⇐ A ⊳ Σ₂
     argout <- checkC ctx (subjMult sg qty) arg argty
     -- then Ψ | Γ ⊢ σ · f s ⇒ B[s] ⊳ Σ₁ + πΣ₂
     pure $ InfRes {
-      type = sub1 res $ arg :# argty,
+      type = sub1 res $ Ann arg argty arg.loc,
       qout = funres.qout + qty * argout
     }
 
-  infer' ctx sg (CasePair pi pair ret body) = do
+  infer' ctx sg (CasePair pi pair ret body loc) = do
     -- no check for 1 ≤ π, since pairs have a single constructor.
     -- e.g. at 0 the components are also 0 in the body
     --
@@ -377,27 +365,28 @@ mutual
     pairres <- inferC ctx sg pair
     -- if Ψ | Γ, p : (x : A) × B ⊢₀ ret ⇐ Type
     checkTypeC (extendTy Zero ret.name pairres.type ctx) ret.term Nothing
-    (tfst, tsnd) <- expectSig !defs ctx pairres.type
+    (tfst, tsnd) <- expectSig !defs ctx pair.loc pairres.type
     -- if Ψ | Γ, x : A, y : B ⊢ σ · body ⇐
     --    ret[(x, y) ∷ (x : A) × B/p] ⊳ Σ₂, ρ₁·x, ρ₂·y
     -- with ρ₁, ρ₂ ≤ πσ
     let [< x, y]  = body.names
         pisg    = pi * sg.fst
         bodyctx = extendTyN [< (pisg, x, tfst), (pisg, y, tsnd.term)] ctx
-        bodyty  = substCasePairRet pairres.type ret
+        bodyty  = substCasePairRet body.names pairres.type ret
-    bodyout <- checkC bodyctx sg body.term bodyty >>= popQs [< pisg, pisg]
+    bodyout <- checkC bodyctx sg body.term bodyty >>=
+               popQs loc [< pisg, pisg]
     -- then Ψ | Γ ⊢ σ · caseπ ⋯ ⇒ ret[pair/p] ⊳ πΣ₁ + Σ₂
     pure $ InfRes {
       type = sub1 ret pair,
       qout = pi * pairres.qout + bodyout
     }
 
-  infer' ctx sg (CaseEnum pi t ret arms) {d, n} = do
+  infer' ctx sg (CaseEnum pi t ret arms loc) {d, n} = do
     -- if Ψ | Γ ⊢ σ · t ⇒ {ts} ⊳ Σ₁
     tres <- inferC ctx sg t
-    ttags <- expectEnum !defs ctx tres.type
+    ttags <- expectEnum !defs ctx t.loc tres.type
     -- if 1 ≤ π, OR there is only zero or one option
-    unless (length (SortedSet.toList ttags) <= 1) $ expectCompatQ One pi
+    unless (length (SortedSet.toList ttags) <= 1) $ expectCompatQ loc One pi
     -- if Ψ | Γ, x : {ts} ⊢₀ A ⇐ Type
     checkTypeC (extendTy Zero ret.name tres.type ctx) ret.term Nothing
     -- if for each "a ⇒ s" in arms,
@@ -405,109 +394,109 @@ mutual
     -- with Σ₂ = lubs Σᵢ
     let arms = SortedMap.toList arms
     let armTags = SortedSet.fromList $ map fst arms
-    unless (ttags == armTags) $ throw $ BadCaseEnum ttags armTags
+    unless (ttags == armTags) $ throw $ BadCaseEnum loc ttags armTags
     armres <- for arms $ \(a, s) =>
-      checkC ctx sg s (sub1 ret (Tag a :# tres.type))
+      checkC ctx sg s $ sub1 ret $ Ann (Tag a s.loc) tres.type s.loc
     let Just armout = lubs ctx armres
-          | _ => throw $ BadQtys "case arms" ctx $
+          | _ => throw $ BadQtys loc "case arms" ctx $
-              zipWith (\qs, (t, rhs) => (qs, Tag t)) armres arms
+              zipWith (\qs, (t, rhs) => (qs, Tag t noLoc)) armres arms
     pure $ InfRes {
       type = sub1 ret t,
       qout = pi * tres.qout + armout
     }
 
-  infer' ctx sg (CaseNat pi pi' n ret zer suc) = do
+  infer' ctx sg (CaseNat pi pi' n ret zer suc loc) = do
     -- if 1 ≤ π
-    expectCompatQ One pi
+    expectCompatQ loc One pi
     -- if Ψ | Γ ⊢ σ · n ⇒ ℕ ⊳ Σn
     nres <- inferC ctx sg n
-    expectNat !defs ctx nres.type
+    let nat = nres.type
+    expectNat !defs ctx n.loc nat
     -- if Ψ | Γ, n : ℕ ⊢₀ A ⇐ Type
-    checkTypeC (extendTy Zero ret.name Nat ctx) ret.term Nothing
+    checkTypeC (extendTy Zero ret.name nat ctx) ret.term Nothing
     -- if Ψ | Γ ⊢ σ · zer ⇐ A[0 ∷ ℕ/n] ⊳ Σz
-    zerout <- checkC ctx sg zer (sub1 ret (Zero :# Nat))
+    zerout <- checkC ctx sg zer $ sub1 ret $ Ann (Zero zer.loc) nat zer.loc
     -- if Ψ | Γ, n : ℕ, ih : A ⊢ σ · suc ⇐ A[succ p ∷ ℕ/n] ⊳ Σs, ρ₁.p, ρ₂.ih
     -- with ρ₂ ≤ π'σ, (ρ₁ + ρ₂) ≤ πσ
     let [< p, ih] = suc.names
         pisg      = pi * sg.fst
-        sucCtx    = extendTyN [< (pisg, p, Nat), (pi', ih, ret.term)] ctx
+        sucCtx    = extendTyN [< (pisg, p, Nat p.loc), (pi', ih, ret.term)] ctx
-        sucType   = substCaseSuccRet ret
+        sucType   = substCaseSuccRet suc.names ret
     sucout :< qp :< qih <- checkC sucCtx sg suc.term sucType
-    expectCompatQ qih (pi' * sg.fst)
+    expectCompatQ loc qih (pi' * sg.fst)
     -- [fixme] better error here
-    expectCompatQ (qp + qih) pisg
+    expectCompatQ loc (qp + qih) pisg
     -- then Ψ | Γ ⊢ caseπ ⋯ ⇒ A[n] ⊳ πΣn + Σz + ωΣs
     pure $ InfRes {
       type = sub1 ret n,
       qout = pi * nres.qout + zerout + Any * sucout
     }
 
-  infer' ctx sg (CaseBox pi box ret body) = do
+  infer' ctx sg (CaseBox pi box ret body loc) = do
     -- if Ψ | Γ ⊢ σ · b ⇒ [ρ.A] ⊳ Σ₁
     boxres <- inferC ctx sg box
-    (q, ty) <- expectBOX !defs ctx boxres.type
+    (q, ty) <- expectBOX !defs ctx box.loc boxres.type
     -- if Ψ | Γ, x : [ρ.A] ⊢₀ R ⇐ Type
     checkTypeC (extendTy Zero ret.name boxres.type ctx) ret.term Nothing
     -- if Ψ | Γ, x : A ⊢ t ⇐ R[[x] ∷ [ρ.A/x]] ⊳ Σ₂, ς·x
     --   with ς ≤ ρπσ
     let qpisg    = q * pi * sg.fst
         bodyCtx  = extendTy qpisg body.name ty ctx
-        bodyType = substCaseBoxRet ty ret
+        bodyType = substCaseBoxRet body.name ty ret
-    bodyout <- checkC bodyCtx sg body.term bodyType >>= popQ qpisg
+    bodyout <- checkC bodyCtx sg body.term bodyType >>= popQ loc qpisg
     -- then Ψ | Γ ⊢ caseπ ⋯ ⇒ R[b/x] ⊳ Σ₁ + Σ₂
     pure $ InfRes {
       type = sub1 ret box,
       qout = boxres.qout + bodyout
     }
 
-  infer' ctx sg (fun :% dim) = do
+  infer' ctx sg (DApp fun dim loc) = do
     -- if Ψ | Γ ⊢ σ · f ⇒ Eq [𝑖 ⇒ A] l r ⊳ Σ
     InfRes {type, qout} <- inferC ctx sg fun
-    ty <- fst <$> expectEq !defs ctx type
+    ty <- fst <$> expectEq !defs ctx fun.loc type
     -- then Ψ | Γ ⊢ σ · f p ⇒ A‹p/𝑖› ⊳ Σ
     pure $ InfRes {type = dsub1 ty dim, qout}
 
-  infer' ctx sg (Coe (S [< i] ty) p q val) = do
+  infer' ctx sg (Coe ty p q val loc) = do
-    let ty = ty.term
+    checkType (extendDim ty.name ctx) ty.term Nothing
-    checkType (extendDim i ctx) ty Nothing
+    qout <- checkC ctx sg val $ dsub1 ty p
-    qout <- checkC ctx sg val (ty // one p)
+    pure $ InfRes {type = dsub1 ty q, qout}
-    pure $ InfRes {type = ty // one q, qout}
 
-  infer' ctx sg (Comp ty p q val r (S [< j0] val0) (S [< j1] val1)) = do
+  infer' ctx sg (Comp ty p q val r (S [< j0] val0) (S [< j1] val1) loc) = do
     checkType ctx ty Nothing
     qout <- checkC ctx sg val ty
     let ty'  = dweakT 1 ty; val' = dweakT 1 val; p' = weakD 1 p
-        ctx0 = extendDim j0 $ eqDim r (K Zero) ctx
+        ctx0 = extendDim j0 $ eqDim r (K Zero j0.loc) ctx
         val0 = val0.term
     qout0 <- check ctx0 sg val0 ty'
-    equal (eqDim (BV 0) p' ctx0) ty' val0 val'
+    lift $ equal loc (eqDim (B VZ p.loc) p' ctx0) ty' val0 val'
-    let ctx1 = extendDim j0 $ eqDim r (K One) ctx
+    let ctx1 = extendDim j1 $ eqDim r (K One j1.loc) ctx
         val1  = val1.term
     qout1 <- check ctx1 sg val1 ty'
-    equal (eqDim (BV 0) p' ctx1) ty' val1 val'
+    lift $ equal loc (eqDim (B VZ p.loc) p' ctx1) ty' val1 val'
     let qout0' = toMaybe $ map (, val0 // one p) qout0
         qout1' = toMaybe $ map (, val1 // one p) qout1
         qouts  = (qout, val) :: catMaybes [qout0', qout1']
     let Just qout = lubs ctx $ map fst qouts
-      | Nothing => throw $ BadQtys "composition" ctx qouts
+      | Nothing => throw $ BadQtys loc "composition" ctx qouts
     pure $ InfRes {type = ty, qout}
 
-  infer' ctx sg (TypeCase ty ret arms def) = do
+  infer' ctx sg (TypeCase ty ret arms def loc) = do
     -- if σ = 0
-    expectEqualQ Zero sg.fst
+    expectEqualQ loc Zero sg.fst
     -- if Ψ, Γ ⊢₀ e ⇒ Type u
-    u <- expectTYPE !defs ctx . type =<< inferC ctx szero ty
+    u <- expectTYPE !defs ctx ty.loc . type =<< inferC ctx szero ty
     -- if Ψ, Γ ⊢₀ C ⇐ Type (non-dependent return type)
     checkTypeC ctx ret Nothing
     -- if Ψ, Γ' ⊢₀ A ⇐ C for each rhs A
     for_ allKinds $ \k =>
       for_ (lookupPrecise k arms) $ \(S names t) =>
-        check0 (extendTyN (addNames0 (typecaseTel k u) names) ctx)
+        check0 (extendTyN (typecaseTel k names u) ctx)
                t.term (weakT (arity k) ret)
     -- then Ψ, Γ ⊢₀ type-case ⋯ ⇒ C
     pure $ InfRes {type = ret, qout = zeroFor ctx}
 
-  infer' ctx sg (term :# type) = do
+  infer' ctx sg (Ann term type loc) = do
     -- if Ψ | Γ ⊢₀ A ⇐ Type ℓ
     checkTypeC ctx type Nothing
     -- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ

lib/Quox/Typing.idr

@@ -39,111 +39,122 @@ InferResult eqs d n = IfConsistent eqs $ InferResult' d n
 
 
 export
-lookupFree : Has ErrorEff fs => Name -> Definitions -> Eff fs Definition
+lookupFree : Has ErrorEff fs => Name -> Loc -> Definitions -> Eff fs Definition
-lookupFree x defs = maybe (throw $ NotInScope x) pure $ lookup x defs
+lookupFree x loc defs = maybe (throw $ NotInScope loc x) pure $ lookup x defs
 
 
 public export
-substCasePairRet : Term d n -> ScopeTerm d n -> Term d (2 + n)
+substCasePairRet : BContext 2 -> Term d n -> ScopeTerm d n -> Term d (2 + n)
-substCasePairRet dty retty =
+substCasePairRet [< x, y] dty retty =
-  let arg = Pair (BVT 1) (BVT 0) :# (dty // fromNat 2) in
+  let tm = Pair (BVT 1 x.loc) (BVT 0 y.loc) $ x.loc `extendL` y.loc
+      arg = Ann tm (dty // fromNat 2) tm.loc
+  in
   retty.term // (arg ::: shift 2)
 
 public export
-substCaseSuccRet : ScopeTerm d n -> Term d (2 + n)
+substCaseSuccRet : BContext 2 -> ScopeTerm d n -> Term d (2 + n)
-substCaseSuccRet retty = retty.term // (Succ (BVT 1) :# Nat ::: shift 2)
+substCaseSuccRet [< p, ih] retty =
+  let arg = Ann (Succ (BVT 1 p.loc) p.loc) (Nat noLoc) $ p.loc `extendL` ih.loc
+  in
+  retty.term // (arg ::: shift 2)
 
 public export
-substCaseBoxRet : Term d n -> ScopeTerm d n -> Term d (S n)
+substCaseBoxRet : BindName -> Term d n -> ScopeTerm d n -> Term d (S n)
-substCaseBoxRet dty retty =
+substCaseBoxRet x dty retty =
-  retty.term // (Box (BVT 0) :# weakT 1 dty ::: shift 1)
+  let arg = Ann (Box (BVT 0 x.loc) x.loc) (weakT 1 dty) x.loc in
+  retty.term // (arg ::: shift 1)
 
 
-parameters (defs : Definitions) {auto _ : Has ErrorEff fs}
+parameters (defs : Definitions) {auto _ : (Has ErrorEff fs, Has NameGen fs)}
   namespace TyContext
-   parameters (ctx : TyContext d n)
+   parameters (ctx : TyContext d n) (loc : Loc)
     export covering
     whnf : {0 isRedex : RedexTest tm} -> Whnf tm isRedex =>
            tm d n -> Eff fs (NonRedex tm d n defs)
-    whnf = let Val n = ctx.termLen; Val d = ctx.dimLen in
+    whnf tm = do
-           rethrow . whnf defs (toWhnfContext ctx)
+      let Val n = ctx.termLen; Val d = ctx.dimLen
+      res <- lift $ runExcept $ whnf defs (toWhnfContext ctx) tm
+      rethrow res
 
     private covering %macro
-    expect : (forall d, n. NameContexts d n -> Term d n -> Error) ->
+    expect : (forall d, n. Loc -> NameContexts d n -> Term d n -> Error) ->
              TTImp -> TTImp -> Elab (Term d n -> Eff fs a)
     expect k l r = do
       f <- check `(\case ~(l) => Just ~(r); _ => Nothing)
-      pure $ \t => maybe (throw $ k ctx.names t) pure . f . fst =<< whnf t
+      pure $ \t => maybe (throw $ k loc ctx.names t) pure . f . fst =<< whnf t
 
     export covering %inline
     expectTYPE : Term d n -> Eff fs Universe
-    expectTYPE = expect ExpectedTYPE `(TYPE l) `(l)
+    expectTYPE = expect ExpectedTYPE `(TYPE {l, _}) `(l)
 
     export covering %inline
     expectPi : Term d n -> Eff fs (Qty, Term d n, ScopeTerm d n)
-    expectPi = expect ExpectedPi `(Pi {qty, arg, res}) `((qty, arg, res))
+    expectPi = expect ExpectedPi `(Pi {qty, arg, res, _}) `((qty, arg, res))
 
     export covering %inline
     expectSig : Term d n -> Eff fs (Term d n, ScopeTerm d n)
-    expectSig = expect ExpectedSig `(Sig {fst, snd}) `((fst, snd))
+    expectSig = expect ExpectedSig `(Sig {fst, snd, _}) `((fst, snd))
 
     export covering %inline
     expectEnum : Term d n -> Eff fs (SortedSet TagVal)
-    expectEnum = expect ExpectedEnum `(Enum ts) `(ts)
+    expectEnum = expect ExpectedEnum `(Enum {cases, _}) `(cases)
 
     export covering %inline
     expectEq : Term d n -> Eff fs (DScopeTerm d n, Term d n, Term d n)
-    expectEq = expect ExpectedEq `(Eq {ty, l, r}) `((ty, l, r))
+    expectEq = expect ExpectedEq `(Eq {ty, l, r, _}) `((ty, l, r))
 
     export covering %inline
     expectNat : Term d n -> Eff fs ()
-    expectNat = expect ExpectedNat `(Nat) `(())
+    expectNat = expect ExpectedNat `(Nat {}) `(())
 
     export covering %inline
     expectBOX : Term d n -> Eff fs (Qty, Term d n)
-    expectBOX = expect ExpectedBOX `(BOX {qty, ty}) `((qty, ty))
+    expectBOX = expect ExpectedBOX `(BOX {qty, ty, _}) `((qty, ty))
 
 
   namespace EqContext
-   parameters (ctx : EqContext n)
+   parameters (ctx : EqContext n) (loc : Loc)
     export covering
     whnf : {0 isRedex : RedexTest tm} -> Whnf tm isRedex =>
            tm 0 n -> Eff fs (NonRedex tm 0 n defs)
-    whnf = let Val n = ctx.termLen in rethrow . whnf defs (toWhnfContext ctx)
+    whnf tm = do
+      let Val n = ctx.termLen
+      res <- lift $ runExcept $ whnf defs (toWhnfContext ctx) tm
+      rethrow res
 
     private covering %macro
-    expect : (forall d, n. NameContexts d n -> Term d n -> Error) ->
+    expect : (forall d, n. Loc -> NameContexts d n -> Term d n -> Error) ->
              TTImp -> TTImp -> Elab (Term 0 n -> Eff fs a)
     expect k l r = do
       f <- check `(\case ~(l) => Just ~(r); _ => Nothing)
       pure $ \t =>
-        let err = throw $ k ctx.names (t // shift0 ctx.dimLen) in
+        let err = throw $ k loc ctx.names (t // shift0 ctx.dimLen) in
         maybe err pure . f . fst =<< whnf t
 
     export covering %inline
     expectTYPE : Term 0 n -> Eff fs Universe
-    expectTYPE = expect ExpectedTYPE `(TYPE l) `(l)
+    expectTYPE = expect ExpectedTYPE `(TYPE {l, _}) `(l)
 
     export covering %inline
     expectPi : Term 0 n -> Eff fs (Qty, Term 0 n, ScopeTerm 0 n)
-    expectPi = expect ExpectedPi `(Pi {qty, arg, res}) `((qty, arg, res))
+    expectPi = expect ExpectedPi `(Pi {qty, arg, res, _}) `((qty, arg, res))
 
     export covering %inline
     expectSig : Term 0 n -> Eff fs (Term 0 n, ScopeTerm 0 n)
-    expectSig = expect ExpectedSig `(Sig {fst, snd}) `((fst, snd))
+    expectSig = expect ExpectedSig `(Sig {fst, snd, _}) `((fst, snd))
 
     export covering %inline
     expectEnum : Term 0 n -> Eff fs (SortedSet TagVal)
-    expectEnum = expect ExpectedEnum `(Enum ts) `(ts)
+    expectEnum = expect ExpectedEnum `(Enum {cases, _}) `(cases)
 
     export covering %inline
     expectEq : Term 0 n -> Eff fs (DScopeTerm 0 n, Term 0 n, Term 0 n)
-    expectEq = expect ExpectedEq `(Eq {ty, l, r}) `((ty, l, r))
+    expectEq = expect ExpectedEq `(Eq {ty, l, r, _}) `((ty, l, r))
 
     export covering %inline
     expectNat : Term 0 n -> Eff fs ()
-    expectNat = expect ExpectedNat `(Nat) `(())
+    expectNat = expect ExpectedNat `(Nat {}) `(())
 
     export covering %inline
     expectBOX : Term 0 n -> Eff fs (Qty, Term 0 n)
-    expectBOX = expect ExpectedBOX `(BOX {qty, ty}) `((qty, ty))
+    expectBOX = expect ExpectedBOX `(BOX {qty, ty, _}) `((qty, ty))

lib/Quox/Typing/Context.idr

@@ -31,9 +31,9 @@ record TyContext d n where
   {auto dimLen  : Singleton d}
   {auto termLen : Singleton n}
   dctx   : DimEq d
-  dnames : NContext d
+  dnames : BContext d
   tctx   : TContext d n
-  tnames : NContext n
+  tnames : BContext n
   qtys   : QContext n -- only used for printing
 %name TyContext ctx
 
@@ -44,9 +44,9 @@ record EqContext n where
   {dimLen : Nat}
   {auto termLen : Singleton n}
   dassign : DimAssign dimLen -- only used for printing
-  dnames  : NContext dimLen -- only used for printing
+  dnames  : BContext dimLen -- only used for printing
   tctx    : TContext 0 n
-  tnames  : NContext n
+  tnames  : BContext n
   qtys    : QContext n -- only used for printing
 %name EqContext ctx
 
@@ -54,8 +54,8 @@ record EqContext n where
 public export
 record WhnfContext d n where
   constructor MkWhnfContext
-  dnames : NContext d
+  dnames : BContext d
-  tnames : NContext n
+  tnames : BContext n
   tctx   : TContext d n
 %name WhnfContext ctx
 
@@ -76,7 +76,7 @@ extendLen (tel :< _) x = [|S $ extendLen tel x|]
 
 public export
 CtxExtension : Nat -> Nat -> Nat -> Type
-CtxExtension d = Telescope ((Qty, BaseName,) . Term d)
+CtxExtension d = Telescope ((Qty, BindName,) . Term d)
 
 namespace TyContext
   public export %inline
@@ -101,11 +101,11 @@ namespace TyContext
     }
 
   export %inline
-  extendTy : Qty -> BaseName -> Term d n -> TyContext d n -> TyContext d (S n)
+  extendTy : Qty -> BindName -> Term d n -> TyContext d n -> TyContext d (S n)
   extendTy q x s = extendTyN [< (q, x, s)]
 
   export %inline
-  extendDim : BaseName -> TyContext d n -> TyContext (S d) n
+  extendDim : BindName -> TyContext d n -> TyContext (S d) n
   extendDim x (MkTyContext {dimLen, dctx, dnames, tctx, tnames, qtys}) =
     MkTyContext {
       dctx   = dctx :<? Nothing,
@@ -142,7 +142,7 @@ namespace QOutput
 export
 makeDAssign : DSubst d 0 -> DimAssign d
 makeDAssign (Shift SZ)     = [<]
-makeDAssign (K e ::: th) = makeDAssign th :< e
+makeDAssign (K e _ ::: th) = makeDAssign th :< e
 
 export
 makeEqContext' : {d : Nat} -> TyContext d n -> DSubst d 0 -> EqContext n
@@ -172,8 +172,7 @@ namespace EqContext
   null ctx = null ctx.dnames && null ctx.tnames
 
   export %inline
-  extendTyN : Telescope (\n => (Qty, BaseName, Term 0 n)) from to ->
+  extendTyN : CtxExtension 0 from to -> EqContext from -> EqContext to
-              EqContext from -> EqContext to
   extendTyN xss (MkEqContext {termLen, dassign, dnames, tctx, tnames, qtys}) =
     let (qs, xs, ss) = unzip3 xss in
     MkEqContext {
@@ -185,11 +184,11 @@ namespace EqContext
     }
 
   export %inline
-  extendTy : Qty -> BaseName -> Term 0 n -> EqContext n -> EqContext (S n)
+  extendTy : Qty -> BindName -> Term 0 n -> EqContext n -> EqContext (S n)
   extendTy q x s = extendTyN [< (q, x, s)]
 
   export %inline
-  extendDim : BaseName -> DimConst -> EqContext n -> EqContext n
+  extendDim : BindName -> DimConst -> EqContext n -> EqContext n
   extendDim x e (MkEqContext {dassign, dnames, tctx, tnames, qtys}) =
     MkEqContext {dassign = dassign :< e, dnames = dnames :< x,
                  tctx, tnames, qtys}
@@ -214,7 +213,7 @@ namespace WhnfContext
   empty = MkWhnfContext [<] [<] [<]
 
   export
-  extendDimN : {s : Nat} -> NContext s -> WhnfContext d n ->
+  extendDimN : {s : Nat} -> BContext s -> WhnfContext d n ->
                WhnfContext (s + d) n
   extendDimN ns (MkWhnfContext {dnames, tnames, tctx}) =
     MkWhnfContext {
@@ -224,16 +223,16 @@ namespace WhnfContext
     }
 
   export
-  extendDim : BaseName -> WhnfContext d n -> WhnfContext (S d) n
+  extendDim : BindName -> WhnfContext d n -> WhnfContext (S d) n
   extendDim i = extendDimN [< i]
 
 
 private
-data CtxBinder a = MkCtxBinder BaseName a
+data CtxBinder a = MkCtxBinder BindName a
 
 PrettyHL a => PrettyHL (CtxBinder a) where
   prettyM (MkCtxBinder x t) = pure $
-    sep [hsep [!(pretty0M $ TV x), colonD], !(pretty0M t)]
+    sep [hsep [!(pretty0M $ TV x.name), colonD], !(pretty0M t)]
 
 parameters (unicode : Bool)
   private
@@ -241,16 +240,16 @@ parameters (unicode : Bool)
   pipeD = hl Syntax "|"
 
   export covering
-  prettyTContext : NContext d ->
+  prettyTContext : BContext d ->
-                   QContext n -> NContext n ->
+                   QContext n -> BContext n ->
                    TContext d n -> Doc HL
   prettyTContext ds qs xs ctx = separate comma $ toList $ go qs xs ctx where
-    go : QContext m -> NContext m -> TContext d m -> SnocList (Doc HL)
+    go : QContext m -> BContext m -> TContext d m -> SnocList (Doc HL)
     go [<]       [<]       [<] = [<]
     go (qs :< q) (xs :< x) (ctx :< t) =
       let bind = MkWithQty q $ MkCtxBinder x t in
       go qs xs ctx :<
-      runPrettyWith unicode (toSnocList' ds) (toSnocList' xs) (pretty0M bind)
+      runPrettyWith unicode (toNames ds) (toNames xs) (pretty0M bind)
 
   export covering
   prettyTyContext : TyContext d n -> Doc HL

lib/Quox/Typing/Error.idr

@@ -1,5 +1,6 @@
 module Quox.Typing.Error
 
+import Quox.Loc
 import Quox.Syntax
 import Quox.Typing.Context
 import Quox.Typing.EqMode
@@ -12,8 +13,8 @@ import Control.Eff
 public export
 record NameContexts d n where
   constructor MkNameContexts
-  dnames : NContext d
+  dnames : BContext d
-  tnames : NContext n
+  tnames : BContext n
 
 namespace NameContexts
   export
@@ -21,11 +22,11 @@ namespace NameContexts
   empty = MkNameContexts [<] [<]
 
   export
-  extendDimN : NContext s -> NameContexts d n -> NameContexts (s + d) n
+  extendDimN : BContext s -> NameContexts d n -> NameContexts (s + d) n
   extendDimN xs = {dnames $= (++ toSnocVect' xs)}
 
   export
-  extendDim : BaseName -> NameContexts d n -> NameContexts (S d) n
+  extendDim : BindName -> NameContexts d n -> NameContexts (S d) n
   extendDim i = extendDimN [< i]
 
 namespace TyContext
@@ -54,30 +55,30 @@ namespace WhnfContext
 
 public export
 data Error
-= ExpectedTYPE (NameContexts d n) (Term d n)
+= ExpectedTYPE Loc (NameContexts d n) (Term d n)
-| ExpectedPi   (NameContexts d n) (Term d n)
+| ExpectedPi   Loc (NameContexts d n) (Term d n)
-| ExpectedSig  (NameContexts d n) (Term d n)
+| ExpectedSig  Loc (NameContexts d n) (Term d n)
-| ExpectedEnum (NameContexts d n) (Term d n)
+| ExpectedEnum Loc (NameContexts d n) (Term d n)
-| ExpectedEq   (NameContexts d n) (Term d n)
+| ExpectedEq   Loc (NameContexts d n) (Term d n)
-| ExpectedNat  (NameContexts d n) (Term d n)
+| ExpectedNat  Loc (NameContexts d n) (Term d n)
-| ExpectedBOX  (NameContexts d n) (Term d n)
+| ExpectedBOX  Loc (NameContexts d n) (Term d n)
-| BadUniverse  Universe Universe
+| BadUniverse  Loc Universe Universe
-| TagNotIn     TagVal (SortedSet TagVal)
+| TagNotIn     Loc TagVal (SortedSet TagVal)
-| BadCaseEnum  (SortedSet TagVal) (SortedSet TagVal)
+| BadCaseEnum  Loc (SortedSet TagVal) (SortedSet TagVal)
-| BadQtys      String (TyContext d n) (List (QOutput n, Term d n))
+| BadQtys      Loc String (TyContext d n) (List (QOutput n, Term d n))
 
 -- first term arg of ClashT is the type
-| ClashT  (EqContext n) EqMode (Term 0 n) (Term 0 n) (Term 0 n)
+| ClashT  Loc (EqContext n) EqMode (Term 0 n) (Term 0 n) (Term 0 n)
-| ClashTy (EqContext n) EqMode (Term 0 n) (Term 0 n)
+| ClashTy Loc (EqContext n) EqMode (Term 0 n) (Term 0 n)
-| ClashE  (EqContext n) EqMode (Elim 0 n) (Elim 0 n)
+| ClashE  Loc (EqContext n) EqMode (Elim 0 n) (Elim 0 n)
-| ClashU  EqMode Universe Universe
+| ClashU  Loc EqMode Universe Universe
-| ClashQ  Qty Qty
+| ClashQ  Loc Qty Qty
-| NotInScope Name
+| NotInScope Loc Name
 
-| NotType (TyContext d n) (Term d n)
+| NotType Loc (TyContext d n) (Term d n)
-| WrongType (EqContext n) (Term 0 n) (Term 0 n)
+| WrongType Loc (EqContext n) (Term 0 n) (Term 0 n)
 
-| MissingEnumArm TagVal (List TagVal)
+| MissingEnumArm Loc TagVal (List TagVal)
 
 -- extra context
 | WhileChecking
@@ -166,18 +167,18 @@ expect : Has (Except e) fs =>
          (a -> a -> e) -> (a -> a -> Bool) -> a -> a -> Eff fs ()
 expect err cmp x y = unless (x `cmp` y) $ throw $ err x y
 
-parameters {auto _ : Has ErrorEff fs}
+parameters {auto _ : Has ErrorEff fs} (loc : Loc)
   export %inline
   expectEqualQ : Qty -> Qty -> Eff fs ()
-  expectEqualQ = expect ClashQ (==)
+  expectEqualQ = expect (ClashQ loc) (==)
 
   export %inline
   expectCompatQ : Qty -> Qty -> Eff fs ()
-  expectCompatQ = expect ClashQ compat
+  expectCompatQ = expect (ClashQ loc) compat
 
   export %inline
   expectModeU : EqMode -> Universe -> Universe -> Eff fs ()
-  expectModeU mode = expect (ClashU mode) $ ucmp mode
+  expectModeU mode = expect (ClashU loc mode) $ ucmp mode
 
 
 private
@@ -207,8 +208,8 @@ parameters (unicode : Bool)
   dstermn ctx (S i t) = termn (extendDimN i ctx) t.term
 
   private
-  filterSameQtys : NContext n -> List (QOutput n, z) ->
+  filterSameQtys : BContext n -> List (QOutput n, z) ->
-                   Exists $ \n' => (NContext n', List (QOutput n', z))
+                   Exists $ \n' => (BContext n', List (QOutput n', z))
   filterSameQtys [<]       qts = Evidence 0 ([<], qts)
   filterSameQtys (ns :< n) qts =
     let (qs, qts) = unzip $ map (\(qs :< q, t) => (q, qs, t)) qts
@@ -224,7 +225,7 @@ parameters (unicode : Bool)
 
   private
   printCaseQtys : TyContext d n ->
-                  NContext n' -> List (QOutput n', Term d n) ->
+                  BContext n' -> List (QOutput n', Term d n) ->
                   List (Doc HL)
   printCaseQtys ctx ns qts =
     let Evidence l (ns, qts) = filterSameQtys ns qts in
@@ -233,94 +234,97 @@ parameters (unicode : Bool)
     commaList : PrettyHL a => Context' a l -> Doc HL
     commaList = hseparate comma . map (pretty0 unicode) . toList'
 
-    line : NContext l -> (QOutput l, Term d n) -> Doc HL
+    line : BContext l -> (QOutput l, Term d n) -> Doc HL
     line ns (qs, t) =
       "-" <++> asep ["the term", termn ctx.names t,
-                     "uses variables", commaList $ TV <$> ns,
+                     "uses variables", commaList $ (TV . name) <$> ns,
                      "with quantities", commaList qs]
 
   -- [todo] only show some contexts, probably
   export
   prettyError : (showContext : Bool) -> Error -> Doc HL
   prettyError showContext = \case
-    ExpectedTYPE ctx s =>
+    ExpectedTYPE loc ctx s =>
-      sep ["expected a type universe, but got", termn ctx s]
+      sep [prettyLoc loc <++> "expected a type universe, but got", termn ctx s]
 
-    ExpectedPi ctx s =>
+    ExpectedPi loc ctx s =>
-      sep ["expected a function type, but got", termn ctx s]
+      sep [prettyLoc loc <++> "expected a function type, but got", termn ctx s]
 
-    ExpectedSig ctx s =>
+    ExpectedSig loc ctx s =>
-      sep ["expected a pair type, but got", termn ctx s]
+      sep [prettyLoc loc <++> "expected a pair type, but got", termn ctx s]
 
-    ExpectedEnum ctx s =>
+    ExpectedEnum loc ctx s =>
-      sep ["expected an enumeration type, but got", termn ctx s]
+      sep [prettyLoc loc <++> "expected an enumeration type, but got",
+           termn ctx s]
 
-    ExpectedEq ctx s =>
+    ExpectedEq loc ctx s =>
-      sep ["expected an equality type, but got", termn ctx s]
+      sep [prettyLoc loc <++> "expected an equality type, but got", termn ctx s]
 
-    ExpectedNat ctx s {d, n} =>
+    ExpectedNat loc ctx s {d, n} =>
-      sep ["expected the type", pretty0 unicode $ Nat {d, n},
+      sep [prettyLoc loc <++> "expected the type",
-           "but got", termn ctx s]
+           pretty0 unicode $ Nat noLoc {d, n}, "but got", termn ctx s]
 
-    ExpectedBOX ctx s =>
+    ExpectedBOX loc ctx s =>
-      sep ["expected a box type, but got", termn ctx s]
+      sep [prettyLoc loc <++> "expected a box type, but got", termn ctx s]
 
-    BadUniverse k l =>
+    BadUniverse loc k l =>
-      sep ["the universe level", prettyUniverse k,
+      sep [prettyLoc loc <++> "the universe level", prettyUniverse k,
            "is not strictly less than", prettyUniverse l]
 
-    TagNotIn tag set =>
+    TagNotIn loc tag set =>
-      sep [sep ["tag", prettyTag tag, "is not contained in"],
+      sep [hsep [prettyLoc loc, "tag", prettyTag tag, "is not contained in"],
-           termn empty (Enum set)]
+           termn empty (Enum set noLoc)]
 
-    BadCaseEnum type arms =>
+    BadCaseEnum loc type arms =>
-      sep ["case expression has head of type", termn empty (Enum type),
+      sep [prettyLoc loc <++> "case expression has head of type",
-           "but cases for", termn empty (Enum arms)]
+           termn empty (Enum type noLoc),
+           "but cases for", termn empty (Enum arms noLoc)]
 
-    BadQtys what ctx arms =>
+    BadQtys loc what ctx arms =>
       hang 4 $ sep $
-        ("inconsistent variable usage in" <++> fromString what) ::
+        hsep [prettyLoc loc, "inconsistent variable usage in", fromString what]
-        printCaseQtys ctx ctx.tnames arms
+          :: printCaseQtys ctx ctx.tnames arms
 
-    ClashT ctx mode ty s t =>
+    ClashT loc ctx mode ty s t =>
       inEContext ctx $
-      sep ["the term", termn ctx.names0 s,
+      sep [prettyLoc loc <++> "the term", termn ctx.names0 s,
            hsep ["is not", prettyMode mode], termn ctx.names0 t,
            "at type", termn ctx.names0 ty]
 
-    ClashTy ctx mode a b =>
+    ClashTy loc ctx mode a b =>
       inEContext ctx $
-      sep ["the type", termn ctx.names0 a,
+      sep [prettyLoc loc <++> "the type", termn ctx.names0 a,
            hsep ["is not", prettyMode mode], termn ctx.names0 b]
 
-    ClashE ctx mode e f =>
+    ClashE loc ctx mode e f =>
       inEContext ctx $
-      sep ["the term", termn ctx.names0 $ E e,
+      sep [prettyLoc loc <++> "the term", termn ctx.names0 $ E e,
            hsep ["is not", prettyMode mode], termn ctx.names0 $ E f]
 
-    ClashU mode k l =>
+    ClashU loc mode k l =>
-      sep ["the universe level", prettyUniverse k,
+      sep [prettyLoc loc <++> "the universe level", prettyUniverse k,
            hsep ["is not", prettyMode mode], prettyUniverse l]
 
-    ClashQ pi rh =>
+    ClashQ loc pi rh =>
-      sep ["the quantity", pretty0 unicode pi,
+      sep [prettyLoc loc <++> "the quantity", pretty0 unicode pi,
            "is not equal to", pretty0 unicode rh]
 
-    NotInScope x =>
+    NotInScope loc x =>
-      hsep [hl' Free $ pretty0 unicode x, "is not in scope"]
+      hsep [prettyLoc loc, hl' Free $ pretty0 unicode x, "is not in scope"]
 
-    NotType ctx s =>
+    NotType loc ctx s =>
       inTContext ctx $
-      sep ["the term", termn ctx.names s, "is not a type"]
+      sep [prettyLoc loc <++> "the term", termn ctx.names s, "is not a type"]
 
-    WrongType ctx ty s =>
+    WrongType loc ctx ty s =>
       inEContext ctx $
-      sep ["the term", termn ctx.names0 s,
+      sep [prettyLoc loc <++> "the term", termn ctx.names0 s,
            "cannot have type", termn ctx.names0 ty]
 
-    MissingEnumArm tag tags =>
+    MissingEnumArm loc tag tags =>
-      sep [hsep ["the tag", hl Tag $ pretty tag, "is not contained in"],
+      sep [hsep [prettyLoc loc, "the tag", hl Tag $ pretty tag,
-           termn empty $ Enum $ fromList tags]
+                 "is not contained in"],
+           termn empty $ Enum (fromList tags) noLoc]
 
     WhileChecking ctx pi s a err =>
       vsep [inTContext ctx $

tests/AstExtra.idr

@@ -0,0 +1,33 @@
+module AstExtra
+
+import Quox.Syntax
+import Quox.Parser.Syntax
+import Quox.Typing.Context
+
+prefix 9 ^
+public export
+(^) : (Loc -> a) -> a
+(^) a = a noLoc
+
+public export
+FromString BindName where fromString str = BN (fromString str) noLoc
+
+public export
+FromString PatVar where fromString x = PV x noLoc
+
+public export
+empty01 : TyContext 0 0
+empty01 = eqDim (^K Zero) (^K One) empty
+
+
+anys : {n : Nat} -> QContext n
+anys {n = 0}   = [<]
+anys {n = S n} = anys :< Any
+
+public export
+ctx, ctx01 : {n : Nat} -> Context (\n => (BindName, Term 0 n)) n ->
+             TyContext 0 n
+ctx tel = let (ns, ts) = unzip tel in
+          MkTyContext new [<] ts ns anys
+ctx01 tel = let (ns, ts) = unzip tel in
+            MkTyContext ZeroIsOne [<] ts ns anys

tests/Tests/DimEq.idr

@@ -2,6 +2,7 @@ module Tests.DimEq
 
 import Quox.Syntax.DimEq
 import PrettyExtra
+import AstExtra
 
 import TAP
 import Data.Maybe
@@ -95,9 +96,9 @@ tests = "dimension constraints" :- [
     testPrettyD ii new "𝑖",
     testPrettyD iijj (fromGround [< Zero, One])
       "𝑖, 𝑗, 𝑖 = 0, 𝑗 = 1",
-    testPrettyD iijj (C [< Just (K Zero), Nothing])
+    testPrettyD iijj (C [< Just (^K Zero), Nothing])
       "𝑖, 𝑗, 𝑖 = 0",
-    testPrettyD iijjkk (C [< Nothing, Just (BV 0), Just (BV 1)])
+    testPrettyD iijjkk (C [< Nothing, Just (^BV 0), Just (^BV 1)])
       "𝑖, 𝑗, 𝑘, 𝑗 = 𝑖, 𝑘 = 𝑖"
   ],
 
@@ -108,56 +109,56 @@ tests = "dimension constraints" :- [
     testNeq [<] new ZeroIsOne,
     testNeq iijj new ZeroIsOne,
     testSet iijj
-      (C [< Nothing, Just (BV 0)])
+      (C [< Nothing, Just (^BV 0)])
-      new [(BV 1, BV 0)],
+      new [(^BV 1, ^BV 0)],
     testSet iijj
-      (C [< Nothing, Just (BV 0)])
+      (C [< Nothing, Just (^BV 0)])
-      new [(BV 0, BV 1)],
+      new [(^BV 0, ^BV 1)],
     testNeq iijj
       new
-      (C [< Nothing, Just (BV 0)]),
+      (C [< Nothing, Just (^BV 0)]),
     testSet [<]
       ZeroIsOne
-      new [(K Zero, K One)],
+      new [(^K Zero, ^K One)],
     testSet iijjkk
-      (C [< Nothing, Just (BV 0), Just (BV 1)])
+      (C [< Nothing, Just (^BV 0), Just (^BV 1)])
-      new [(BV 0, BV 1), (BV 1, BV 2)],
+      new [(^BV 0, ^BV 1), (^BV 1, ^BV 2)],
     testSet iijjkk
-      (C [< Nothing, Just (BV 0), Just (BV 1)])
+      (C [< Nothing, Just (^BV 0), Just (^BV 1)])
-      new [(BV 0, BV 1), (BV 0, BV 2)],
+      new [(^BV 0, ^BV 1), (^BV 0, ^BV 2)],
     testSet iijjkk
-      (C [< Nothing, Nothing, Just (BV 0)])
+      (C [< Nothing, Nothing, Just (^BV 0)])
-      new [(BV 0, BV 1), (BV 0, BV 1)],
+      new [(^BV 0, ^BV 1), (^BV 0, ^BV 1)],
     testSet iijj
-      (C [< Just (K Zero), Just (K Zero)])
+      (C [< Just (^K Zero), Just (^K Zero)])
-      new [(BV 1, K Zero), (BV 0, BV 1)],
+      new [(^BV 1, ^K Zero), (^BV 0, ^BV 1)],
     testSet iijjkk
-      (C [< Just (K Zero), Just (K Zero), Just (K Zero)])
+      (C [< Just (^K Zero), Just (^K Zero), Just (^K Zero)])
-      new [(BV 2, K Zero), (BV 1, BV 2), (BV 0, BV 1)],
+      new [(^BV 2, ^K Zero), (^BV 1, ^BV 2), (^BV 0, ^BV 1)],
     testSet iijjkk
-      (C [< Just (K Zero), Just (K Zero), Just (K Zero)])
+      (C [< Just (^K Zero), Just (^K Zero), Just (^K Zero)])
-      new [(BV 2, K Zero), (BV 0, BV 1), (BV 1, BV 2)],
+      new [(^BV 2, ^K Zero), (^BV 0, ^BV 1), (^BV 1, ^BV 2)],
     testSet iijjkk
-      (C [< Just (K Zero), Just (K Zero), Just (K Zero)])
+      (C [< Just (^K Zero), Just (^K Zero), Just (^K Zero)])
-      new [(BV 0, BV 2), (BV 1, K Zero), (BV 2, BV 1)],
+      new [(^BV 0, ^BV 2), (^BV 1, ^K Zero), (^BV 2, ^BV 1)],
     testSet iijjkk
-      (C [< Nothing, Just (BV 0), Just (BV 1)])
+      (C [< Nothing, Just (^BV 0), Just (^BV 1)])
-      new [(BV 0, BV 2), (BV 2, BV 1)],
+      new [(^BV 0, ^BV 2), (^BV 2, ^BV 1)],
     testSet iijjkkll
-      (C [< Nothing, Just (BV 0), Just (BV 1), Just (BV 2)])
+      (C [< Nothing, Just (^BV 0), Just (^BV 1), Just (^BV 2)])
-      new [(BV 2, BV 1), (BV 3, BV 0), (BV 2, BV 3)],
+      new [(^BV 2, ^BV 1), (^BV 3, ^BV 0), (^BV 2, ^BV 3)],
     testSet iijjkk
-      (C [< Just (K One), Just (K One), Just (K One)])
+      (C [< Just (^K One), Just (^K One), Just (^K One)])
-      (C [< Just (K One), Nothing, Just (BV 0)])
+      (C [< Just (^K One), Nothing, Just (^BV 0)])
-      [(BV 1, BV 2)],
+      [(^BV 1, ^BV 2)],
     testSet iijj
       ZeroIsOne
-      (C [< Just (K One), Just (K Zero)])
+      (C [< Just (^K One), Just (^K Zero)])
-      [(BV 1, BV 0)],
+      [(^BV 1, ^BV 0)],
     testSet iijj
       ZeroIsOne
-      (C [< Nothing, Just (BV 0)])
+      (C [< Nothing, Just (^BV 0)])
-      [(BV 1, K Zero), (BV 0, K One)]
+      [(^BV 1, ^K Zero), (^BV 0, ^K One)]
   ],
 
   "wf" :- [
@@ -165,9 +166,9 @@ tests = "dimension constraints" :- [
     testWf ii ZeroIsOne,
     testWf [<] new,
     testWf iijjkk new,
-    testWf iijjkk (C [< Nothing, Just (BV 0), Just (BV 1)]),
+    testWf iijjkk (C [< Nothing, Just (^BV 0), Just (^BV 1)]),
-    testNwf iijjkk (C [< Nothing, Just (BV 0), Just (BV 0)]),
+    testNwf iijjkk (C [< Nothing, Just (^BV 0), Just (^BV 0)]),
-    testWf iijj (C [< Just (K Zero), Just (K Zero)]),
+    testWf iijj (C [< Just (^K Zero), Just (^K Zero)]),
-    testNwf iijj (C [< Just (K Zero), Just (BV 0)])
+    testNwf iijj (C [< Just (^K Zero), Just (^BV 0)])
   ]
 ]

tests/Tests/Equal.idr

@@ -5,52 +5,40 @@ import Quox.Typechecker
 import public TypingImpls
 import TAP
 import Quox.EffExtra
+import AstExtra
+
 
 defGlobals : Definitions
 defGlobals = fromList
-  [("A", mkPostulate gzero $ TYPE 0),
+  [("A", ^mkPostulate gzero (^TYPE 0)),
-   ("B", mkPostulate gzero $ TYPE 0),
+   ("B", ^mkPostulate gzero (^TYPE 0)),
-   ("a", mkPostulate gany $ FT "A"),
+   ("a", ^mkPostulate gany (^FT "A")),
-   ("a'", mkPostulate gany $ FT "A"),
+   ("a'", ^mkPostulate gany (^FT "A")),
-   ("b", mkPostulate gany $ FT "B"),
+   ("b", ^mkPostulate gany (^FT "B")),
-   ("f", mkPostulate gany $ Arr One (FT "A") (FT "A")),
+   ("f", ^mkPostulate gany (^Arr One (^FT "A") (^FT "A"))),
-   ("id", mkDef gany (Arr One (FT "A") (FT "A")) ([< "x"] :\\ BVT 0)),
+   ("id", ^mkDef gany (^Arr One (^FT "A") (^FT "A")) (^LamY "x" (^BVT 0))),
-   ("eq-AB", mkPostulate gzero $ Eq0 (TYPE 0) (FT "A") (FT "B")),
+   ("eq-AB", ^mkPostulate gzero (^Eq0 (^TYPE 0) (^FT "A") (^FT "B"))),
-   ("two", mkDef gany Nat (Succ (Succ Zero)))]
+   ("two", ^mkDef gany (^Nat) (^Succ (^Succ (^Zero))))]
 
-parameters (label : String) (act : Lazy (TC ()))
+parameters (label : String) (act : Equal ())
            {default defGlobals globals : Definitions}
   testEq : Test
-  testEq = test label $ runTC globals act
+  testEq = test label $ runEqual globals act
 
   testNeq : Test
   testNeq = testThrows label (const True) $ runTC globals act $> "()"
 
 
-parameters (0 d : Nat) (ctx : TyContext d n)
+parameters (ctx : TyContext d n)
-  subTD, equalTD : Term d n -> Term d n -> Term d n -> TC ()
+  subT, equalT : Term d n -> Term d n -> Term d n -> TC ()
-  subTD ty s t = Term.sub ctx ty s t
+  subT ty s t = lift $ Term.sub noLoc ctx ty s t
-  equalTD ty s t = Term.equal ctx ty s t
+  equalT ty s t = lift $ Term.equal noLoc ctx ty s t
-  equalTyD : Term d n -> Term d n -> TC ()
+  equalTy : Term d n -> Term d n -> TC ()
-  equalTyD s t = Term.equalType ctx s t
+  equalTy s t = lift $ Term.equalType noLoc ctx s t
 
-  subED, equalED : Elim d n -> Elim d n -> TC ()
+  subE, equalE : Elim d n -> Elim d n -> TC ()
-  subED e f = Elim.sub ctx e f
+  subE e f = lift $ Elim.sub noLoc ctx e f
-  equalED e f = Elim.equal ctx e f
+  equalE e f = lift $ Elim.equal noLoc ctx e f
-
-parameters (ctx : TyContext 0 n)
-  subT, equalT : Term 0 n -> Term 0 n -> Term 0 n -> TC ()
-  subT = subTD 0 ctx
-  equalT = equalTD 0 ctx
-  equalTy : Term 0 n -> Term 0 n -> TC ()
-  equalTy = equalTyD 0 ctx
-
-  subE, equalE : Elim 0 n -> Elim 0 n -> TC ()
-  subE = subED 0 ctx
-  equalE = equalED 0 ctx
-
-empty01 : TyContext 0 0
-empty01 = eqDim (K Zero) (K One) empty
 
 
 export
@@ -61,410 +49,434 @@ tests = "equality & subtyping" :- [
 
   "universes" :- [
     testEq "★₀ = ★₀" $
-      equalT empty (TYPE 1) (TYPE 0) (TYPE 0),
+      equalT empty (^TYPE 1) (^TYPE 0) (^TYPE 0),
     testNeq "★₀ ≠ ★₁" $
-      equalT empty (TYPE 2) (TYPE 0) (TYPE 1),
+      equalT empty (^TYPE 2) (^TYPE 0) (^TYPE 1),
     testNeq "★₁ ≠ ★₀" $
-      equalT empty (TYPE 2) (TYPE 1) (TYPE 0),
+      equalT empty (^TYPE 2) (^TYPE 1) (^TYPE 0),
     testEq "★₀ <: ★₀" $
-      subT empty (TYPE 1) (TYPE 0) (TYPE 0),
+      subT empty (^TYPE 1) (^TYPE 0) (^TYPE 0),
     testEq "★₀ <: ★₁" $
-      subT empty (TYPE 2) (TYPE 0) (TYPE 1),
+      subT empty (^TYPE 2) (^TYPE 0) (^TYPE 1),
     testNeq "★₁ ≮: ★₀" $
-      subT empty (TYPE 2) (TYPE 1) (TYPE 0)
+      subT empty (^TYPE 2) (^TYPE 1) (^TYPE 0)
   ],
 
   "function types" :- [
-    note #""𝐴 ⊸ 𝐵" for (1·𝐴) → 𝐵"#,
+    note "cumulativity",
-    note #""𝐴 ⇾ 𝐵" for (0·𝐴) → 𝐵"#,
+    testEq "0.★₀ → ★₀ = 0.★₀ → ★₀" $
-    testEq "★₀ ⇾ ★₀ = ★₀ ⇾ ★₀" $
+      let tm = ^Arr Zero (^TYPE 0) (^TYPE 0) in
-      let tm = Arr Zero (TYPE 0) (TYPE 0) in
+      equalT empty (^TYPE 1) tm tm,
-      equalT empty (TYPE 1) tm tm,
+    testEq "0.★₀ → ★₀ <: 0.★₀ → ★₀" $
-    testEq "★₀ ⇾ ★₀ <: ★₀ ⇾ ★₀" $
+      let tm = ^Arr Zero (^TYPE 0) (^TYPE 0) in
-      let tm = Arr Zero (TYPE 0) (TYPE 0) in
+      subT empty (^TYPE 1) tm tm,
-      subT empty (TYPE 1) tm tm,
+    testNeq "0.★₁ → ★₀ ≠ 0.★₀ → ★₀" $
-    testNeq "★₁ ⊸ ★₀ ≠ ★₀ ⇾ ★₀" $
+      let tm1 = ^Arr Zero (^TYPE 1) (^TYPE 0)
-      let tm1 = Arr Zero (TYPE 1) (TYPE 0)
+          tm2 = ^Arr Zero (^TYPE 0) (^TYPE 0) in
-          tm2 = Arr Zero (TYPE 0) (TYPE 0) in
+      equalT empty (^TYPE 2) tm1 tm2,
-      equalT empty (TYPE 2) tm1 tm2,
+    testEq "1.★₁ → ★₀ <: 1.★₀ → ★₀" $
-    testEq "★₁ ⊸ ★₀ <: ★₀ ⊸ ★₀" $
+      let tm1 = ^Arr One (^TYPE 1) (^TYPE 0)
-      let tm1 = Arr One (TYPE 1) (TYPE 0)
+          tm2 = ^Arr One (^TYPE 0) (^TYPE 0) in
-          tm2 = Arr One (TYPE 0) (TYPE 0) in
+      subT empty (^TYPE 2) tm1 tm2,
-      subT empty (TYPE 2) tm1 tm2,
+    testEq "1.★₀ → ★₀ <: 1.★₀ → ★₁" $
-    testEq "★₀ ⊸ ★₀ <: ★₀ ⊸ ★₁" $
+      let tm1 = ^Arr One (^TYPE 0) (^TYPE 0)
-      let tm1 = Arr One (TYPE 0) (TYPE 0)
+          tm2 = ^Arr One (^TYPE 0) (^TYPE 1) in
-          tm2 = Arr One (TYPE 0) (TYPE 1) in
+      subT empty (^TYPE 2) tm1 tm2,
-      subT empty (TYPE 2) tm1 tm2,
+    testEq "1.★₀ → ★₀ <: 1.★₀ → ★₁" $
-    testEq "★₀ ⊸ ★₀ <: ★₀ ⊸ ★₁" $
+      let tm1 = ^Arr One (^TYPE 0) (^TYPE 0)
-      let tm1 = Arr One (TYPE 0) (TYPE 0)
+          tm2 = ^Arr One (^TYPE 0) (^TYPE 1) in
-          tm2 = Arr One (TYPE 0) (TYPE 1) in
+      subT empty (^TYPE 2) tm1 tm2,
-      subT empty (TYPE 2) tm1 tm2,
+    testEq "1.A → B = 1.A → B" $
-    testEq "A ⊸ B = A ⊸ B" $
+      let tm = ^Arr One (^FT "A") (^FT "B") in
-      let tm = Arr One (FT "A") (FT "B") in
+      equalT empty (^TYPE 0) tm tm,
-      equalT empty (TYPE 0) tm tm,
+    testEq "1.A → B <: 1.A → B" $
-    testEq "A ⊸ B <: A ⊸ B" $
+      let tm = ^Arr One (^FT "A") (^FT "B") in
-      let tm = Arr One (FT "A") (FT "B") in
+      subT empty (^TYPE 0) tm tm,
-      subT empty (TYPE 0) tm tm,
     note "incompatible quantities",
-    testNeq "★₀ ⊸ ★₀ ≠ ★₀ ⇾ ★₁" $
+    testNeq "1.★₀ → ★₀ ≠ 0.★₀ → ★₁" $
-      let tm1 = Arr Zero (TYPE 0) (TYPE 0)
+      let tm1 = ^Arr Zero (^TYPE 0) (^TYPE 0)
-          tm2 = Arr Zero (TYPE 0) (TYPE 1) in
+          tm2 = ^Arr Zero (^TYPE 0) (^TYPE 1) in
-      equalT empty (TYPE 2) tm1 tm2,
+      equalT empty (^TYPE 2) tm1 tm2,
-    testNeq "A ⇾ B ≠ A ⊸ B" $
+    testNeq "0.A → B ≠ 1.A → B" $
-      let tm1 = Arr Zero (FT "A") (FT "B")
+      let tm1 = ^Arr Zero (^FT "A") (^FT "B")
-          tm2 = Arr One  (FT "A") (FT "B") in
+          tm2 = ^Arr One  (^FT "A") (^FT "B") in
-      equalT empty (TYPE 0) tm1 tm2,
+      equalT empty (^TYPE 0) tm1 tm2,
-    testNeq "A ⇾ B ≮: A ⊸ B" $
+    testNeq "0.A → B ≮: 1.A → B" $
-      let tm1 = Arr Zero (FT "A") (FT "B")
+      let tm1 = ^Arr Zero (^FT "A") (^FT "B")
-          tm2 = Arr One  (FT "A") (FT "B") in
+          tm2 = ^Arr One  (^FT "A") (^FT "B") in
-      subT empty (TYPE 0) tm1 tm2,
+      subT empty (^TYPE 0) tm1 tm2,
-    testEq "0=1 ⊢ A ⇾ B = A ⊸ B" $
+    testEq "0=1 ⊢ 0.A → B = 1.A → B" $
-      let tm1 = Arr Zero (FT "A") (FT "B")
+      let tm1 = ^Arr Zero (^FT "A") (^FT "B")
-          tm2 = Arr One  (FT "A") (FT "B") in
+          tm2 = ^Arr One  (^FT "A") (^FT "B") in
-      equalT empty01 (TYPE 0) tm1 tm2,
+      equalT empty01 (^TYPE 0) tm1 tm2,
-    todo "dependent function types",
+    todo "dependent function types"
-    note "[todo] should π ≤ ρ ⊢ (ρ·A) → B <: (π·A) → B?"
   ],
 
   "lambda" :- [
-    testEq "λ x ⇒ [x] = λ x ⇒ [x]" $
+    testEq "λ x ⇒ x = λ x ⇒ x" $
-      equalT empty (Arr One (FT "A") (FT "A"))
+      equalT empty (^Arr One (^FT "A") (^FT "A"))
-        ([< "x"] :\\ BVT 0)
+        (^LamY "x" (^BVT 0))
-        ([< "x"] :\\ BVT 0),
+        (^LamY "x" (^BVT 0)),
-    testEq "λ x ⇒ [x] <: λ x ⇒ [x]" $
+    testEq "λ x ⇒ x <: λ x ⇒ x" $
-      subT empty (Arr One (FT "A") (FT "A"))
+      subT empty (^Arr One (^FT "A") (^FT "A"))
-        ([< "x"] :\\ BVT 0)
+        (^LamY "x" (^BVT 0))
-        ([< "x"] :\\ BVT 0),
+        (^LamY "x" (^BVT 0)),
-    testEq "λ x ⇒ [x] = λ y ⇒ [y]" $
+    testEq "λ x ⇒ x = λ y ⇒ y" $
-      equalT empty (Arr One (FT "A") (FT "A"))
+      equalT empty (^Arr One (^FT "A") (^FT "A"))
-        ([< "x"] :\\ BVT 0)
+        (^LamY "x" (^BVT 0))
-        ([< "y"] :\\ BVT 0),
+        (^LamY "y" (^BVT 0)),
-    testEq "λ x ⇒ [x] <: λ y ⇒ [y]" $
+    testEq "λ x ⇒ x <: λ y ⇒ y" $
-      equalT empty (Arr One (FT "A") (FT "A"))
+      subT empty (^Arr One (^FT "A") (^FT "A"))
-        ([< "x"] :\\ BVT 0)
+        (^LamY "x" (^BVT 0))
-        ([< "y"] :\\ BVT 0),
+        (^LamY "y" (^BVT 0)),
-    testNeq "λ x y ⇒ [x] ≠ λ x y ⇒ [y]" $
+    testNeq "λ x y ⇒ x ≠ λ x y ⇒ y" $
-      equalT empty (Arr One (FT "A") $ Arr One (FT "A") (FT "A"))
+      equalT empty
-        ([< "x", "y"] :\\ BVT 1)
+        (^Arr One (^FT "A") (^Arr One (^FT "A") (^FT "A")))
-        ([< "x", "y"] :\\ BVT 0),
+        (^LamY "x" (^LamY "y" (^BVT 1)))
-    testEq "λ x ⇒ [a] = λ x ⇒ [a]  (Y vs N)" $
+        (^LamY "x" (^LamY "y" (^BVT 0))),
-      equalT empty (Arr Zero (FT "B") (FT "A"))
+    testEq "λ x ⇒ a = λ x ⇒ a  (Y vs N)" $
-        (Lam $ SY [< "x"] $ FT "a")
+      equalT empty
-        (Lam $ SN         $ FT "a"),
+        (^Arr Zero (^FT "B") (^FT "A"))
-    testEq "λ x ⇒ [f [x]] = [f]  (η)" $
+        (^LamY "x" (^FT "a"))
-      equalT empty (Arr One (FT "A") (FT "A"))
+        (^LamN     (^FT "a")),
-        ([< "x"] :\\ E (F "f" :@ BVT 0))
+    testEq "λ x ⇒ f x = f  (η)" $
-        (FT "f")
+      equalT empty
+        (^Arr One (^FT "A") (^FT "A"))
+        (^LamY "x" (E $ ^App (^F "f") (^BVT 0)))
+        (^FT "f")
   ],
 
   "eq type" :- [
     testEq "(★₀ ≡ ★₀ : ★₁) = (★₀ ≡ ★₀ : ★₁)" $
-      let tm = Eq0 (TYPE 1) (TYPE 0) (TYPE 0) in
+      let tm = ^Eq0 (^TYPE 1) (^TYPE 0) (^TYPE 0) in
-      equalT empty (TYPE 2) tm tm,
+      equalT empty (^TYPE 2) tm tm,
     testEq "A ≔ ★₁ ⊢ (★₀ ≡ ★₀ : ★₁) = (★₀ ≡ ★₀ : A)"
-        {globals = fromList [("A", mkDef gzero (TYPE 2) (TYPE 1))]} $
+        {globals = fromList [("A", ^mkDef gzero (^TYPE 2) (^TYPE 1))]} $
-      equalT empty (TYPE 2)
+      equalT empty (^TYPE 2)
-        (Eq0 (TYPE 1) (TYPE 0) (TYPE 0))
+        (^Eq0 (^TYPE 1) (^TYPE 0) (^TYPE 0))
-        (Eq0 (FT "A") (TYPE 0) (TYPE 0)),
+        (^Eq0 (^FT "A") (^TYPE 0) (^TYPE 0)),
     todo "dependent equality types"
   ],
 
   "equalities and uip" :-
   let refl : Term d n -> Term d n -> Elim d n
-      refl a x = (DLam $ S [< "_"] $ N x) :# (Eq0 a x x)
+      refl a x = ^Ann (^DLam (SN x)) (^Eq0 a x x)
   in
   [
-    note #""refl [A] x" is an abbreviation for "(δ i ⇒ x) ∷ (x ≡ x : A)""#,
     note "binds before ∥ are globals, after it are BVs",
-    testEq "refl [A] a = refl [A] a" $
+    note #"refl A x is an abbreviation for "(δ i ⇒ x) ∷ (x ≡ x : A)""#,
-      equalE empty (refl (FT "A") (FT "a")) (refl (FT "A") (FT "a")),
+    testEq "refl A a = refl A a" $
+      equalE empty (refl (^FT "A") (^FT "a")) (refl (^FT "A") (^FT "a")),
 
     testEq "p : (a ≡ a' : A), q : (a ≡ a' : A) ∥ ⊢ p = q  (free)"
            {globals =
-              let def = mkPostulate gzero $ Eq0 (FT "A") (FT "a") (FT "a'") in
+              let def = ^mkPostulate gzero (^Eq0 (^FT "A") (^FT "a") (^FT "a'"))
-              defGlobals `mergeLeft` fromList [("p", def), ("q", def)]} $
+              in defGlobals `mergeLeft` fromList [("p", def), ("q", def)]} $
-      equalE empty (F "p") (F "q"),
+      equalE empty (^F "p") (^F "q"),
 
     testEq "∥ x : (a ≡ a' : A), y : (a ≡ a' : A) ⊢ x = y  (bound)" $
-      let ty : forall n. Term 0 n := Eq0 (FT "A") (FT "a") (FT "a'") in
+      let ty : forall n. Term 0 n := ^Eq0 (^FT "A") (^FT "a") (^FT "a'") in
       equalE (extendTyN [< (Any, "x", ty), (Any, "y", ty)] empty)
-        (BV 0) (BV 1),
+        (^BV 0) (^BV 1),
 
-    testEq "∥ x : [(a ≡ a' : A) ∷ Type 0], y : [ditto] ⊢ x = y" $
+    testEq "∥ x : (a ≡ a' : A) ∷ Type 0, y : [ditto] ⊢ x = y" $
       let ty : forall n. Term 0 n :=
-            E (Eq0 (FT "A") (FT "a") (FT "a'") :# TYPE 0) in
+            E $ ^Ann (^Eq0 (^FT "A") (^FT "a") (^FT "a'")) (^TYPE 0) in
       equalE (extendTyN [< (Any, "x", ty), (Any, "y", ty)] empty)
-        (BV 0) (BV 1),
+        (^BV 0) (^BV 1),
 
     testEq "E ≔ a ≡ a' : A, EE ≔ E ∥ x : EE, y : EE ⊢ x = y"
            {globals = defGlobals `mergeLeft` fromList
-              [("E", mkDef gzero (TYPE 0) (Eq0 (FT "A") (FT "a") (FT "a'"))),
+              [("E", ^mkDef gzero (^TYPE 0)
-               ("EE", mkDef gzero (TYPE 0) (FT "E"))]} $
+                        (^Eq0 (^FT "A") (^FT "a") (^FT "a'"))),
-      equalE (extendTyN [< (Any, "x", FT "EE"), (Any, "y", FT "EE")] empty)
+               ("EE", ^mkDef gzero (^TYPE 0) (^FT "E"))]} $
-        (BV 0) (BV 1),
+      equalE (extendTyN [< (Any, "x", ^FT "EE"), (Any, "y", ^FT "EE")] empty)
+        (^BV 0) (^BV 1),
 
     testEq "E ≔ a ≡ a' : A, EE ≔ E ∥ x : EE, y : E ⊢ x = y"
            {globals = defGlobals `mergeLeft` fromList
-              [("E", mkDef gzero (TYPE 0) (Eq0 (FT "A") (FT "a") (FT "a'"))),
+              [("E", ^mkDef gzero (^TYPE 0)
-               ("EE", mkDef gzero (TYPE 0) (FT "E"))]} $
+                        (^Eq0 (^FT "A") (^FT "a") (^FT "a'"))),
-      equalE (extendTyN [< (Any, "x", FT "EE"), (Any, "y", FT "E")] empty)
+               ("EE", ^mkDef gzero (^TYPE 0) (^FT "E"))]} $
-        (BV 0) (BV 1),
+      equalE (extendTyN [< (Any, "x", ^FT "EE"), (Any, "y", ^FT "E")] empty)
+        (^BV 0) (^BV 1),
 
     testEq "E ≔ a ≡ a' : A ∥ x : E, y : E ⊢ x = y"
            {globals = defGlobals `mergeLeft` fromList
-              [("E", mkDef gzero (TYPE 0) (Eq0 (FT "A") (FT "a") (FT "a'")))]} $
+              [("E", ^mkDef gzero (^TYPE 0)
-      equalE (extendTyN [< (Any, "x", FT "E"), (Any, "y", FT "E")] empty)
+                        (^Eq0 (^FT "A") (^FT "a") (^FT "a'")))]} $
-        (BV 0) (BV 1),
+      equalE (extendTyN [< (Any, "x", ^FT "E"), (Any, "y", ^FT "E")] empty)
+        (^BV 0) (^BV 1),
 
     testEq "E ≔ a ≡ a' : A ∥ x : (E×E), y : (E×E) ⊢ x = y"
            {globals = defGlobals `mergeLeft` fromList
-              [("E", mkDef gzero (TYPE 0) (Eq0 (FT "A") (FT "a") (FT "a'")))]} $
+              [("E", ^mkDef gzero (^TYPE 0)
-      let ty : forall n. Term 0 n :=
+                        (^Eq0 (^FT "A") (^FT "a") (^FT "a'")))]} $
-            Sig (FT "E") $ S [< "_"] $ N $ FT "E" in
+      let ty : forall n. Term 0 n := ^Sig (^FT "E") (SN $ ^FT "E") in
       equalE (extendTyN [< (Any, "x", ty), (Any, "y", ty)] empty)
-        (BV 0) (BV 1),
+        (^BV 0) (^BV 1),
 
-    testEq "E ≔ a ≡ a' : A, W ≔ E × E ∥ x : W, y : W ⊢ x = y"
+    testEq "E ≔ a ≡ a' : A, W ≔ E × E ∥ x : W, y : E×E ⊢ x = y"
            {globals = defGlobals `mergeLeft` fromList
-              [("E", mkDef gzero (TYPE 0) (Eq0 (FT "A") (FT "a") (FT "a'"))),
+              [("E", ^mkDef gzero (^TYPE 0)
-               ("W", mkDef gzero (TYPE 0) (FT "E" `And` FT "E"))]} $
+                      (^Eq0 (^FT "A") (^FT "a") (^FT "a'"))),
+               ("W", ^mkDef gzero (^TYPE 0) (^And (^FT "E") (^FT "E")))]} $
       equalE
-        (extendTyN [< (Any, "x", FT "W"), (Any, "y", FT "W")] empty)
+        (extendTyN [< (Any, "x", ^FT "W"),
-        (BV 0) (BV 1)
+                      (Any, "y", ^And (^FT "E") (^FT "E"))] empty)
+        (^BV 0) (^BV 1)
   ],
 
   "term closure" :- [
-    testEq "[#0]{} = [#0] : A" $
+    note "bold numbers for de bruijn indices",
-      equalT (extendTy Any "x" (FT "A") empty)
+    testEq "𝟎{} = 𝟎 : A" $
-        (FT "A")
+      equalT (extendTy Any "x" (^FT "A") empty)
-        (CloT (Sub (BVT 0) id))
+        (^FT "A")
-        (BVT 0),
+        (CloT (Sub (^BVT 0) id))
-    testEq "[#0]{a} = [a] : A" $
+        (^BVT 0),
-      equalT empty (FT "A")
+    testEq "𝟎{a} = a : A" $
-        (CloT (Sub (BVT 0) (F "a" ::: id)))
+      equalT empty (^FT "A")
-        (FT "a"),
+        (CloT (Sub (^BVT 0) (^F "a" ::: id)))
-    testEq "[#0]{a,b} = [a] : A" $
+        (^FT "a"),
-      equalT empty (FT "A")
+    testEq "𝟎{a,b} = a : A" $
-        (CloT (Sub (BVT 0) (F "a" ::: F "b" ::: id)))
+      equalT empty (^FT "A")
-        (FT "a"),
+        (CloT (Sub (^BVT 0) (^F "a" ::: ^F "b" ::: id)))
-    testEq "[#1]{a,b} = [b] : A" $
+        (^FT "a"),
-      equalT empty (FT "A")
+    testEq "𝟏{a,b} = b : A" $
-        (CloT (Sub (BVT 1) (F "a" ::: F "b" ::: id)))
+      equalT empty (^FT "A")
-        (FT "b"),
+        (CloT (Sub (^BVT 1) (^F "a" ::: ^F "b" ::: id)))
-    testEq "(λy ⇒ [#1]){a} = λy ⇒ [a] : B ⇾ A  (N)" $
+        (^FT "b"),
-      equalT empty (Arr Zero (FT "B") (FT "A"))
+    testEq "(λy ⇒ 𝟏){a} = λy ⇒ a : 0.B → A  (N)" $
-        (CloT (Sub (Lam $ S [< "y"] $ N $ BVT 0) (F "a" ::: id)))
+      equalT empty (^Arr Zero (^FT "B") (^FT "A"))
-        (Lam $ S [< "y"] $ N $ FT "a"),
+        (CloT (Sub (^LamN (^BVT 0)) (^F "a" ::: id)))
-    testEq "(λy ⇒ [#1]){a} = λy ⇒ [a] : B ⇾ A  (Y)" $
+        (^LamN (^FT "a")),
-      equalT empty (Arr Zero (FT "B") (FT "A"))
+    testEq "(λy ⇒ 𝟏){a} = λy ⇒ a : 0.B → A  (Y)" $
-        (CloT (Sub ([< "y"] :\\ BVT 1) (F "a" ::: id)))
+      equalT empty (^Arr Zero (^FT "B") (^FT "A"))
-        ([< "y"] :\\ FT "a")
+        (CloT (Sub (^LamY "y" (^BVT 1)) (^F "a" ::: id)))
+        (^LamY "y" (^FT "a"))
   ],
 
   "term d-closure" :- [
-    testEq "★₀‹𝟎› = ★₀ : ★₁" $
+    testEq "★₀‹0› = ★₀ : ★₁" $
-      equalTD 1
+      equalT (extendDim "𝑗" empty)
-        (extendDim "𝑗" empty)
+        (^TYPE 1) (DCloT (Sub (^TYPE 0) (^K Zero ::: id))) (^TYPE 0),
-        (TYPE 1) (DCloT (Sub (TYPE 0) (K Zero ::: id))) (TYPE 0),
+    testEq "(δ i ⇒ a)‹0› = (δ i ⇒ a) : (a ≡ a : A)" $
-    testEq "(δ i ⇒ a)‹𝟎› = (δ i ⇒ a) : (a ≡ a : A)" $
+      equalT (extendDim "𝑗" empty)
-      equalTD 1
+        (^Eq0 (^FT "A") (^FT "a") (^FT "a"))
-        (extendDim "𝑗" empty)
+        (DCloT (Sub (^DLamN (^FT "a")) (^K Zero ::: id)))
-        (Eq0 (FT "A") (FT "a") (FT "a"))
+        (^DLamN (^FT "a")),
-        (DCloT (Sub ([< "i"] :\\% FT "a") (K Zero ::: id)))
-        ([< "i"] :\\% FT "a"),
     note "it is hard to think of well-typed terms with big dctxs"
   ],
 
   "free var" :-
   let au_bu = fromList
-        [("A", mkDef gany (TYPE 1) (TYPE 0)),
+        [("A", ^mkDef gany (^TYPE 1) (^TYPE 0)),
-         ("B", mkDef gany (TYPE 1) (TYPE 0))]
+         ("B", ^mkDef gany (^TYPE 1) (^TYPE 0))]
       au_ba = fromList
-        [("A", mkDef gany (TYPE 1) (TYPE 0)),
+        [("A", ^mkDef gany (^TYPE 1) (^TYPE 0)),
-         ("B", mkDef gany (TYPE 1) (FT "A"))]
+         ("B", ^mkDef gany (^TYPE 1) (^FT "A"))]
   in [
     testEq "A = A" $
-      equalE empty (F "A") (F "A"),
+      equalE empty (^F "A") (^F "A"),
     testNeq "A ≠ B" $
-      equalE empty (F "A") (F "B"),
+      equalE empty (^F "A") (^F "B"),
     testEq "0=1 ⊢ A = B" $
-      equalE empty01 (F "A") (F "B"),
+      equalE empty01 (^F "A") (^F "B"),
     testEq "A : ★₁ ≔ ★₀ ⊢ A = (★₀ ∷ ★₁)" {globals = au_bu} $
-      equalE empty (F "A") (TYPE 0 :# TYPE 1),
+      equalE empty (^F "A") (^Ann (^TYPE 0) (^TYPE 1)),
-    testEq "A : ★₁ ≔ ★₀ ⊢ [A] = ★₀" {globals = au_bu} $
+    testEq "A : ★₁ ≔ ★₀ ⊢ A = ★₀" {globals = au_bu} $
-      equalT empty (TYPE 1) (FT "A") (TYPE 0),
+      equalT empty (^TYPE 1) (^FT "A") (^TYPE 0),
     testEq "A ≔ ★₀, B ≔ ★₀ ⊢ A = B" {globals = au_bu} $
-      equalE empty (F "A") (F "B"),
+      equalE empty (^F "A") (^F "B"),
     testEq "A ≔ ★₀, B ≔ A ⊢ A = B" {globals = au_ba} $
-      equalE empty (F "A") (F "B"),
+      equalE empty (^F "A") (^F "B"),
     testEq "A <: A" $
-      subE empty (F "A") (F "A"),
+      subE empty (^F "A") (^F "A"),
     testNeq "A ≮: B" $
-      subE empty (F "A") (F "B"),
+      subE empty (^F "A") (^F "B"),
     testEq "A : ★₃ ≔ ★₀, B : ★₃ ≔ ★₂ ⊢ A <: B"
-        {globals = fromList [("A", mkDef gany (TYPE 3) (TYPE 0)),
+        {globals = fromList [("A", ^mkDef gany (^TYPE 3) (^TYPE 0)),
-                             ("B", mkDef gany (TYPE 3) (TYPE 2))]} $
+                             ("B", ^mkDef gany (^TYPE 3) (^TYPE 2))]} $
-      subE empty (F "A") (F "B"),
+      subE empty (^F "A") (^F "B"),
     note "(A and B in different universes)",
     testEq "A : ★₁ ≔ ★₀, B : ★₃ ≔ ★₂ ⊢ A <: B"
-        {globals = fromList [("A", mkDef gany (TYPE 1) (TYPE 0)),
+        {globals = fromList [("A", ^mkDef gany (^TYPE 1) (^TYPE 0)),
-                             ("B", mkDef gany (TYPE 3) (TYPE 2))]} $
+                             ("B", ^mkDef gany (^TYPE 3) (^TYPE 2))]} $
-      subE empty (F "A") (F "B"),
+      subE empty (^F "A") (^F "B"),
     testEq "0=1 ⊢ A <: B" $
-      subE empty01 (F "A") (F "B")
+      subE empty01 (^F "A") (^F "B")
   ],
 
   "bound var" :- [
-    testEq "#0 = #0" $
+    note "bold numbers for de bruijn indices",
-      equalE (extendTy Any "A" (TYPE 0) empty) (BV 0) (BV 0),
+    testEq "𝟎 = 𝟎" $
-    testEq "#0 <: #0" $
+      equalE (extendTy Any "A" (^TYPE 0) empty) (^BV 0) (^BV 0),
-      subE (extendTy Any "A" (TYPE 0) empty) (BV 0) (BV 0),
+    testEq "𝟎 <: 𝟎" $
-    testNeq "#0 ≠ #1" $
+      subE (extendTy Any "A" (^TYPE 0) empty) (^BV 0) (^BV 0),
-      equalE (extendTyN [< (Any, "A", TYPE 0), (Any, "B", TYPE 0)] empty)
+    testNeq "𝟎 ≠ 𝟏" $
-        (BV 0) (BV 1),
+      equalE (extendTyN [< (Any, "A", ^TYPE 0), (Any, "B", ^TYPE 0)] empty)
-    testNeq "#0 ≮: #1" $
+        (^BV 0) (^BV 1),
-      subE (extendTyN [< (Any, "A", TYPE 0), (Any, "B", TYPE 0)] empty)
+    testNeq "𝟎 ≮: 𝟏" $
-        (BV 0) (BV 1),
+      subE (extendTyN [< (Any, "A", ^TYPE 0), (Any, "B", ^TYPE 0)] empty)
-    testEq "0=1 ⊢ #0 = #1" $
+        (^BV 0) (^BV 1),
-      equalE (extendTyN [< (Any, "A", TYPE 0), (Any, "B", TYPE 0)] empty01)
+    testEq "0=1 ⊢ 𝟎 = 𝟏" $
-        (BV 0) (BV 1)
+      equalE (extendTyN [< (Any, "A", ^TYPE 0), (Any, "B", ^TYPE 0)] empty01)
+        (^BV 0) (^BV 1)
   ],
 
   "application" :- [
-    testEq "f [a] = f [a]" $
+    testEq "f a = f a" $
-      equalE empty (F "f" :@ FT "a") (F "f" :@ FT "a"),
+      equalE empty (^App (^F "f") (^FT "a")) (^App (^F "f") (^FT "a")),
-    testEq "f [a] <: f [a]" $
+    testEq "f a <: f a" $
-      subE empty (F "f" :@ FT "a") (F "f" :@ FT "a"),
+      subE empty (^App (^F "f") (^FT "a")) (^App (^F "f") (^FT "a")),
-    testEq "(λ x ⇒ [x] ∷ A ⊸ A) a = ([a ∷ A] ∷ A)  (β)" $
+    testEq "(λ x ⇒ x ∷ 1.A → A) a = ((a ∷ A) ∷ A)  (β)" $
       equalE empty
-        ((([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
+        (^App (^Ann (^LamY "x" (^BVT 0)) (^Arr One (^FT "A") (^FT "A")))
-        (E (FT "a" :# FT "A") :# FT "A"),
+              (^FT "a"))
-    testEq "(λ x ⇒ [x] ∷ A ⊸ A) a = a  (βυ)" $
+        (^Ann (E $ ^Ann (^FT "a") (^FT "A")) (^FT "A")),
+    testEq "(λ x ⇒ x ∷ A ⊸ A) a = a  (βυ)" $
       equalE empty
-        ((([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
+        (^App (^Ann (^LamY "x" (^BVT 0)) (^Arr One (^FT "A") (^FT "A")))
-        (F "a"),
+              (^FT "a"))
-    testEq "(λ g ⇒ [g [a]] ∷ ⋯)) [f] = (λ y ⇒ [f [y]] ∷ ⋯) [a]  (β↘↙)" $
+        (^F "a"),
-      let a = FT "A"; a2a = (Arr One a a) in
+    testEq "((λ g ⇒ g a) ∷ 1.(1.A → A) → A) f = ((λ y ⇒ f y) ∷ 1.A → A) a  # β↘↙" $
+      let a = ^FT "A"; a2a = ^Arr One a a; aa2a = ^Arr One a2a a in
       equalE empty
-        ((([< "g"] :\\ E (BV 0 :@ FT "a")) :# Arr One a2a a) :@ FT "f")
+        (^App (^Ann (^LamY "g" (E $ ^App (^BV 0) (^FT "a"))) aa2a) (^FT "f"))
-        ((([< "y"] :\\ E (F "f" :@ BVT 0)) :# a2a) :@ FT "a"),
+        (^App (^Ann (^LamY "y" (E $ ^App (^F "f") (^BVT 0))) a2a) (^FT "a")),
-    testEq "(λ x ⇒ [x] ∷ A ⊸ A) a <: a" $
+    testEq "((λ x ⇒ x) ∷ 1.A → A) a <: a" $
       subE empty
-        ((([< "x"] :\\ BVT 0) :# (Arr One (FT "A") (FT "A"))) :@ FT "a")
+        (^App (^Ann (^LamY "x" (^BVT 0)) (^Arr One (^FT "A") (^FT "A")))
-        (F "a"),
+              (^FT "a"))
-    note "id : A ⊸ A ≔ λ x ⇒ [x]",
+        (^F "a"),
-    testEq "id [a] = a" $ equalE empty (F "id" :@ FT "a") (F "a"),
+    note "id : A ⊸ A ≔ λ x ⇒ x",
-    testEq "id [a] <: a" $ subE empty (F "id" :@ FT "a") (F "a")
+    testEq "id a = a" $ equalE empty (^App (^F "id") (^FT "a")) (^F "a"),
+    testEq "id a <: a" $ subE empty (^App (^F "id") (^FT "a")) (^F "a")
   ],
 
   "dim application" :- [
     testEq "eq-AB @0 = eq-AB @0" $
-      equalE empty (F "eq-AB" :% K Zero) (F "eq-AB" :% K Zero),
+      equalE empty
+        (^DApp (^F "eq-AB") (^K Zero))
+        (^DApp (^F "eq-AB") (^K Zero)),
     testNeq "eq-AB @0 ≠ eq-AB @1" $
-      equalE empty (F "eq-AB" :% K Zero) (F "eq-AB" :% K One),
+      equalE empty
+        (^DApp (^F "eq-AB") (^K Zero))
+        (^DApp (^F "eq-AB") (^K One)),
     testEq "𝑖 | ⊢ eq-AB @𝑖 = eq-AB @𝑖" $
-      equalED 1
+      equalE
         (extendDim "𝑖" empty)
-        (F "eq-AB" :% BV 0) (F "eq-AB" :% BV 0),
+        (^DApp (^F "eq-AB") (^BV 0))
+        (^DApp (^F "eq-AB") (^BV 0)),
     testNeq "𝑖 | ⊢ eq-AB @𝑖 ≠ eq-AB @0" $
-      equalED 1
+      equalE (extendDim "𝑖" empty)
-        (extendDim "𝑖" empty)
+        (^DApp (^F "eq-AB") (^BV 0))
-        (F "eq-AB" :% BV 0) (F "eq-AB" :% K Zero),
+        (^DApp (^F "eq-AB") (^K Zero)),
     testEq "𝑖, 𝑖=0 | ⊢ eq-AB @𝑖 = eq-AB @0" $
-      equalED 1
+      equalE (eqDim (^BV 0) (^K Zero) $ extendDim "𝑖" empty)
-        (eqDim (BV 0) (K Zero) $ extendDim "𝑖" empty)
+        (^DApp (^F "eq-AB") (^BV 0))
-        (F "eq-AB" :% BV 0) (F "eq-AB" :% K Zero),
+        (^DApp (^F "eq-AB") (^K Zero)),
     testNeq "𝑖, 𝑖=1 | ⊢ eq-AB @𝑖 ≠ eq-AB @0" $
-      equalED 1
+      equalE (eqDim (^BV 0) (^K One) $ extendDim "𝑖" empty)
-        (eqDim (BV 0) (K One) $ extendDim "𝑖" empty)
+        (^DApp (^F "eq-AB") (^BV 0))
-        (F "eq-AB" :% BV 0) (F "eq-AB" :% K Zero),
+        (^DApp (^F "eq-AB") (^K Zero)),
     testNeq "𝑖, 𝑗 | ⊢ eq-AB @𝑖 ≠ eq-AB @𝑗" $
-      equalED 2
+      equalE (extendDim "𝑗" $ extendDim "𝑖" empty)
-        (extendDim "𝑗" $ extendDim "𝑖" empty)
+        (^DApp (^F "eq-AB") (^BV 1))
-        (F "eq-AB" :% BV 1) (F "eq-AB" :% BV 0),
+        (^DApp (^F "eq-AB") (^BV 0)),
     testEq "𝑖, 𝑗, 𝑖=𝑗 | ⊢ eq-AB @𝑖 = eq-AB @𝑗" $
-      equalED 2
+      equalE (eqDim (^BV 0) (^BV 1) $ extendDim "𝑗" $ extendDim "𝑖" empty)
-        (eqDim (BV 0) (BV 1) $ extendDim "𝑗" $ extendDim "𝑖" empty)
+        (^DApp (^F "eq-AB") (^BV 1))
-        (F "eq-AB" :% BV 1) (F "eq-AB" :% BV 0),
+        (^DApp (^F "eq-AB") (^BV 0)),
     testEq "𝑖, 𝑗, 𝑖=0, 𝑗=0 | ⊢ eq-AB @𝑖 = eq-AB @𝑗" $
-      equalED 2
+      equalE
-        (eqDim (BV 0) (K Zero) $ eqDim (BV 1) (K Zero) $
+        (eqDim (^BV 0) (^K Zero) $ eqDim (^BV 1) (^K Zero) $
           extendDim "𝑗" $ extendDim "𝑖" empty)
-        (F "eq-AB" :% BV 1) (F "eq-AB" :% BV 0),
+        (^DApp (^F "eq-AB") (^BV 1))
+        (^DApp (^F "eq-AB") (^BV 0)),
     testEq "0=1 | ⊢ eq-AB @𝑖 = eq-AB @𝑗" $
-      equalED 2
+      equalE (extendDim "𝑗" $ extendDim "𝑖" empty01)
-        (extendDim "𝑗" $ extendDim "𝑖" empty01)
+        (^DApp (^F "eq-AB") (^BV 1))
-        (F "eq-AB" :% BV 1) (F "eq-AB" :% BV 0),
+        (^DApp (^F "eq-AB") (^BV 0)),
-    testEq "eq-AB @0 = A" $ equalE empty (F "eq-AB" :% K Zero) (F "A"),
+    testEq "eq-AB @0 = A" $
-    testEq "eq-AB @1 = B" $ equalE empty (F "eq-AB" :% K One)  (F "B"),
+      equalE empty (^DApp (^F "eq-AB") (^K Zero)) (^F "A"),
-    testEq "((δ i ⇒ a) ∷ a ≡ a) @0 = a" $
+    testEq "eq-AB @1 = B" $
+      equalE empty (^DApp (^F "eq-AB") (^K One)) (^F "B"),
+    testEq "((δ i ⇒ a) ∷ a ≡ a : A) @0 = a" $
       equalE empty
-        (((DLam $ SN $ FT "a") :# Eq0 (FT "A") (FT "a") (FT "a")) :% K Zero)
+        (^DApp (^Ann (^DLamN (^FT "a")) (^Eq0 (^FT "A") (^FT "a") (^FT "a")))
-        (F "a"),
+               (^K Zero))
-    testEq "((δ i ⇒ a) ∷ a ≡ a) @0 = ((δ i ⇒ a) ∷ a ≡ a) @1" $
+        (^F "a"),
+    testEq "((δ i ⇒ a) ∷ a ≡ a : A) @0 = ((δ i ⇒ a) ∷ a ≡ a : A) @1" $
       equalE empty
-        (((DLam $ SN $ FT "a") :# Eq0 (FT "A") (FT "a") (FT "a")) :% K Zero)
+        (^DApp (^Ann (^DLamN (^FT "a")) (^Eq0 (^FT "A") (^FT "a") (^FT "a")))
-        (((DLam $ SN $ FT "a") :# Eq0 (FT "A") (FT "a") (FT "a")) :% K One)
+               (^K Zero))
+        (^DApp (^Ann (^DLamN (^FT "a")) (^Eq0 (^FT "A") (^FT "a") (^FT "a")))
+               (^K One))
   ],
 
   "annotation" :- [
-    testEq "(λ x ⇒ f [x]) ∷ A ⊸ A = [f] ∷ A ⊸ A" $
+    testEq "(λ x ⇒ f x) ∷ 1.A → A = f ∷ 1.A → A" $
       equalE empty
-        (([< "x"] :\\ E (F "f" :@ BVT 0)) :# Arr One (FT "A") (FT "A"))
+        (^Ann (^LamY "x" (E $ ^App (^F "f") (^BVT 0)))
-        (FT "f" :# Arr One (FT "A") (FT "A")),
+              (^Arr One (^FT "A") (^FT "A")))
-    testEq "[f] ∷ A ⊸ A = f" $
+        (^Ann (^FT "f") (^Arr One (^FT "A") (^FT "A"))),
-      equalE empty (FT "f" :# Arr One (FT "A") (FT "A")) (F "f"),
+    testEq "f ∷ 1.A → A = f" $
-    testEq "(λ x ⇒ f [x]) ∷ A ⊸ A = f" $
       equalE empty
-        (([< "x"] :\\ E (F "f" :@ BVT 0)) :# Arr One (FT "A") (FT "A"))
+        (^Ann (^FT "f") (^Arr One (^FT "A") (^FT "A")))
-        (F "f")
+        (^F "f"),
+    testEq "(λ x ⇒ f x) ∷ 1.A → A = f" $
+      equalE empty
+        (^Ann (^LamY "x" (E $ ^App (^F "f") (^BVT 0)))
+              (^Arr One (^FT "A") (^FT "A")))
+        (^F "f")
   ],
 
   "natural type" :- [
-    testEq "ℕ = ℕ" $ equalTy empty Nat Nat,
+    testEq "ℕ = ℕ" $ equalTy empty (^Nat) (^Nat),
-    testEq "ℕ = ℕ : ★₀" $ equalT empty (TYPE 0) Nat Nat,
+    testEq "ℕ = ℕ : ★₀" $ equalT empty (^TYPE 0) (^Nat) (^Nat),
-    testEq "ℕ = ℕ : ★₆₉" $ equalT empty (TYPE 69) Nat Nat,
+    testEq "ℕ = ℕ : ★₆₉" $ equalT empty (^TYPE 69) (^Nat) (^Nat),
-    testNeq "ℕ ≠ {}" $ equalTy empty Nat (enum []),
+    testNeq "ℕ ≠ {}" $ equalTy empty (^Nat) (^enum []),
-    testEq "0=1 ⊢ ℕ = {}" $ equalTy empty01 Nat (enum [])
+    testEq "0=1 ⊢ ℕ = {}" $ equalTy empty01 (^Nat) (^enum [])
   ],
 
   "natural numbers" :- [
-    testEq "zero = zero" $ equalT empty Nat Zero Zero,
+    testEq "0 = 0" $ equalT empty (^Nat) (^Zero) (^Zero),
     testEq "succ two = succ two" $
-      equalT empty Nat (Succ (FT "two")) (Succ (FT "two")),
+      equalT empty (^Nat) (^Succ (^FT "two")) (^Succ (^FT "two")),
     testNeq "succ two ≠ two" $
-      equalT empty Nat (Succ (FT "two")) (FT "two"),
+      equalT empty (^Nat) (^Succ (^FT "two")) (^FT "two"),
-    testNeq "zero ≠ succ zero" $
+    testNeq "0 ≠ 1" $
-      equalT empty Nat Zero (Succ Zero),
+      equalT empty (^Nat) (^Zero) (^Succ (^Zero)),
-    testEq "0=1 ⊢ zero = succ zero" $
+    testEq "0=1 ⊢ 0 = 1" $
-      equalT empty01 Nat Zero (Succ Zero)
+      equalT empty01 (^Nat) (^Zero) (^Succ (^Zero))
   ],
 
   "natural elim" :- [
     testEq "caseω 0 return {a,b} of {zero ⇒ 'a; succ _ ⇒ 'b} = 'a" $
       equalT empty
-        (enum ["a", "b"])
+        (^enum ["a", "b"])
-        (E $ CaseNat Any Zero (Zero :# Nat)
+        (E $ ^CaseNat Any Zero (^Ann (^Zero) (^Nat))
-          (SN $ enum ["a", "b"])
+          (SN $ ^enum ["a", "b"])
-          (Tag "a")
+          (^Tag "a")
-          (SN $ Tag "b"))
+          (SN $ ^Tag "b"))
-        (Tag "a"),
+        (^Tag "a"),
     testEq "caseω 1 return {a,b} of {zero ⇒ 'a; succ _ ⇒ 'b} = 'b" $
       equalT empty
-        (enum ["a", "b"])
+        (^enum ["a", "b"])
-        (E $ CaseNat Any Zero (Succ Zero :# Nat)
+        (E $ ^CaseNat Any Zero (^Ann (^Succ (^Zero)) (^Nat))
-          (SN $ enum ["a", "b"])
+          (SN $ ^enum ["a", "b"])
-          (Tag "a")
+          (^Tag "a")
-          (SN $ Tag "b"))
+          (SN $ ^Tag "b"))
-        (Tag "b"),
+        (^Tag "b"),
     testEq "caseω 4 return ℕ of {0 ⇒ 0; succ n ⇒ n} = 3" $
       equalT empty
-        Nat
+        (^Nat)
-        (E $ CaseNat Any Zero (makeNat 4 :# Nat)
+        (E $ ^CaseNat Any Zero (^Ann (^makeNat 4) (^Nat))
-          (SN Nat)
+          (SN $ ^Nat)
-          Zero
+          (^Zero)
-          (SY [< "n", Unused] $ BVT 1))
+          (SY [< "n", ^BN Unused] $ ^BVT 1))
-        (makeNat 3)
+        (^makeNat 3)
   ],
 
   todo "pair types",
@@ -472,24 +484,24 @@ tests = "equality & subtyping" :- [
   "pairs" :- [
     testEq "('a, 'b) = ('a, 'b) : {a} × {b}" $
       equalT empty
-        (enum ["a"] `And` enum ["b"])
+        (^And (^enum ["a"]) (^enum ["b"]))
-        (Tag "a" `Pair` Tag "b")
+        (^Pair (^Tag "a") (^Tag "b"))
-        (Tag "a" `Pair` Tag "b"),
+        (^Pair (^Tag "a") (^Tag "b")),
     testNeq "('a, 'b) ≠ ('b, 'a) : {a,b} × {a,b}" $
       equalT empty
-        (enum ["a", "b"] `And` enum ["a", "b"])
+        (^And (^enum ["a", "b"]) (^enum ["a", "b"]))
-        (Tag "a" `Pair` Tag "b")
+        (^Pair (^Tag "a") (^Tag "b"))
-        (Tag "b" `Pair` Tag "a"),
+        (^Pair (^Tag "b") (^Tag "a")),
     testEq "0=1 ⊢ ('a, 'b) = ('b, 'a) : {a,b} × {a,b}" $
       equalT empty01
-        (enum ["a", "b"] `And` enum ["a", "b"])
+        (^And (^enum ["a", "b"]) (^enum ["a", "b"]))
-        (Tag "a" `Pair` Tag "b")
+        (^Pair (^Tag "a") (^Tag "b"))
-        (Tag "b" `Pair` Tag "a"),
+        (^Pair (^Tag "b") (^Tag "a")),
     testEq "0=1 ⊢ ('a, 'b) = ('b, 'a) : ℕ" $
       equalT empty01
-        Nat
+        (^Nat)
-        (Tag "a" `Pair` Tag "b")
+        (^Pair (^Tag "a") (^Tag "b"))
-        (Tag "b" `Pair` Tag "a")
+        (^Pair (^Tag "b") (^Tag "a"))
   ],
 
   todo "pair elim",
@@ -503,61 +515,60 @@ tests = "equality & subtyping" :- [
   todo "box elim",
 
   "elim closure" :- [
-    testEq "#0{a} = a" $
+    note "bold numbers for de bruijn indices",
-      equalE empty (CloE (Sub (BV 0) (F "a" ::: id))) (F "a"),
+    testEq "𝟎{a} = a" $
-    testEq "#1{a} = #0" $
+      equalE empty (CloE (Sub (^BV 0) (^F "a" ::: id))) (^F "a"),
-      equalE (extendTy Any "x" (FT "A") empty)
+    testEq "𝟏{a} = 𝟎" $
-        (CloE (Sub (BV 1) (F "a" ::: id))) (BV 0)
+      equalE (extendTy Any "x" (^FT "A") empty)
+        (CloE (Sub (^BV 1) (^F "a" ::: id))) (^BV 0)
   ],
 
   "elim d-closure" :- [
+    note "bold numbers for de bruijn indices",
     note "0·eq-AB : (A ≡ B : ★₀)",
-    testEq "(eq-AB #0)‹𝟎› = eq-AB 𝟎" $
+    testEq "(eq-AB @𝟎)‹0› = eq-AB @0" $
-      equalED 1
+      equalE empty
-        (extendDim "𝑖" empty)
+        (DCloE (Sub (^DApp (^F "eq-AB") (^BV 0)) (^K Zero ::: id)))
-        (DCloE (Sub (F "eq-AB" :% BV 0) (K Zero ::: id)))
+        (^DApp (^F "eq-AB") (^K Zero)),
-        (F "eq-AB" :% K Zero),
+    testEq "(eq-AB @𝟎)‹0› = A" $
-    testEq "(eq-AB #0)‹𝟎› = A" $
+      equalE empty
-      equalED 1
+        (DCloE (Sub (^DApp (^F "eq-AB") (^BV 0)) (^K Zero ::: id)))
-        (extendDim "𝑖" empty)
+        (^F "A"),
-        (DCloE (Sub (F "eq-AB" :% BV 0) (K Zero ::: id))) (F "A"),
+    testEq "(eq-AB @𝟎)‹1› = B" $
-    testEq "(eq-AB #0)‹𝟏› = B" $
+      equalE empty
-      equalED 1
+        (DCloE (Sub (^DApp (^F "eq-AB") (^BV 0)) (^K One ::: id)))
-        (extendDim "𝑖" empty)
+        (^F "B"),
-        (DCloE (Sub (F "eq-AB" :% BV 0) (K One ::: id))) (F "B"),
+    testNeq "(eq-AB @𝟎)‹1› ≠ A" $
-    testNeq "(eq-AB #0)‹𝟏› ≠ A" $
+      equalE empty
-      equalED 1
+        (DCloE (Sub (^DApp (^F "eq-AB") (^BV 0)) (^K One ::: id)))
-        (extendDim "𝑖" empty)
+        (^F "A"),
-        (DCloE (Sub (F "eq-AB" :% BV 0) (K One ::: id))) (F "A"),
+    testEq "(eq-AB @𝟎)‹𝟎,0› = (eq-AB 𝟎)" $
-    testEq "(eq-AB #0)‹#0,𝟎› = (eq-AB #0)" $
+      equalE (extendDim "𝑖" empty)
-      equalED 2
+        (DCloE (Sub (^DApp (^F "eq-AB") (^BV 0)) (^BV 0 ::: ^K Zero ::: id)))
-        (extendDim "𝑗" $ extendDim "𝑖" empty)
+        (^DApp (^F "eq-AB") (^BV 0)),
-        (DCloE (Sub (F "eq-AB" :% BV 0) (BV 0 ::: K Zero ::: id)))
+    testNeq "(eq-AB 𝟎)‹0› ≠ (eq-AB 0)" $
-        (F "eq-AB" :% BV 0),
+      equalE (extendDim "𝑖" empty)
-    testNeq "(eq-AB #0)‹𝟎› ≠ (eq-AB 𝟎)" $
+        (DCloE (Sub (^DApp (^F "eq-AB") (^BV 0)) (^BV 0 ::: ^K Zero ::: id)))
-      equalED 2
+        (^DApp (^F "eq-AB") (^K Zero)),
-        (extendDim "𝑗" $ extendDim "𝑖" empty)
+    testEq "𝟎‹0› = 𝟎  # term and dim vars distinct" $
-        (DCloE (Sub (F "eq-AB" :% BV 0) (BV 0 ::: K Zero ::: id)))
+      equalE
-        (F "eq-AB" :% K Zero),
+        (extendTy Any "x" (^FT "A") empty)
-    testEq "#0‹𝟎› = #0  # term and dim vars distinct" $
+        (DCloE (Sub (^BV 0) (^K Zero ::: id))) (^BV 0),
-      equalED 1
+    testEq "a‹0› = a" $
-        (extendTy Any "x" (FT "A") $ extendDim "𝑖" empty)
+      equalE empty
-        (DCloE (Sub (BV 0) (K Zero ::: id))) (BV 0),
+        (DCloE (Sub (^F "a") (^K Zero ::: id))) (^F "a"),
-    testEq "a‹𝟎› = a" $
+    testEq "(f a)‹0› = f‹0› a‹0›" $
-      equalED 1 (extendDim "𝑖" empty)
+      let th = ^K Zero ::: id in
-        (DCloE (Sub (F "a") (K Zero ::: id))) (F "a"),
+      equalE empty
-    testEq "(f [a])‹𝟎› = f‹𝟎› [a]‹𝟎›" $
+        (DCloE (Sub (^App (^F "f") (^FT "a")) th))
-      let th = K Zero ::: id in
+        (^App (DCloE (Sub (^F "f") th)) (DCloT (Sub (^FT "a") th)))
-      equalED 1 (extendDim "𝑖" empty)
-        (DCloE (Sub (F "f" :@ FT "a") th))
-        (DCloE (Sub (F "f") th) :@ DCloT (Sub (FT "a") th))
   ],
 
   "clashes" :- [
-    testNeq "★₀ ≠ ★₀ ⇾ ★₀" $
+    testNeq "★₀ ≠ 0.★₀ → ★₀" $
-      equalT empty (TYPE 1) (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)),
+      equalT empty (^TYPE 1) (^TYPE 0) (^Arr Zero (^TYPE 0) (^TYPE 0)),
-    testEq "0=1 ⊢ ★₀ = ★₀ ⇾ ★₀" $
+    testEq "0=1 ⊢ ★₀ = 0.★₀ → ★₀" $
-      equalT empty01 (TYPE 1) (TYPE 0) (Arr Zero (TYPE 0) (TYPE 0)),
+      equalT empty01 (^TYPE 1) (^TYPE 0) (^Arr Zero (^TYPE 0) (^TYPE 0)),
     todo "others"
   ]
 ]

tests/Tests/FromPTerm.idr

@@ -4,8 +4,9 @@ import Quox.Parser.FromParser
 import Quox.Parser
 import TypingImpls
 import Tests.Parser as TParser
-import TAP
 import Quox.EffExtra
+import TAP
+import AstExtra
 
 import System.File
 import Derive.Prelude
@@ -49,6 +50,11 @@ parameters {c : Bool} {auto _ : Show b}
     parses : Test
     parses = parsesWith $ const True
 
+    %macro
+    parseMatch : TTImp -> Elab Test
+    parseMatch pat =
+      parsesWith <$> check `(\case ~(pat) => True; _ => False)
+
     parsesAs : Eq b => b -> Test
     parsesAs exp = parsesWith (== exp)
 
@@ -59,11 +65,9 @@ parameters {c : Bool} {auto _ : Show b}
       either (const $ Right ()) (Left . ExpectedFail . show) $ fromP pres
 
 
-FromString PatVar where fromString x = PV x Nothing
-
 runFromParser : {default empty defs : Definitions} ->
                 Eff FromParserPure a -> Either FromParser.Error a
-runFromParser = map fst . fromParserPure defs
+runFromParser = map fst . fst . fromParserPure 0 defs
 
 export
 tests : Test
@@ -72,30 +76,35 @@ tests = "PTerm → Term" :- [
   let fromPDim = runFromParser . fromPDimWith [< "𝑖", "𝑗"]
   in [
     note "dim ctx: [𝑖, 𝑗]",
-    parsesAs dim fromPDim "𝑖" (BV 1),
+    parseMatch dim fromPDim "𝑖" `(B (VS VZ) _),
-    parsesAs dim fromPDim "𝑗" (BV 0),
+    parseMatch dim fromPDim "𝑗" `(B VZ _),
     parseFails dim fromPDim "𝑘",
-    parsesAs dim fromPDim "0" (K Zero),
+    parseMatch dim fromPDim "0" `(K Zero _),
-    parsesAs dim fromPDim "1" (K One)
+    parseMatch dim fromPDim "1" `(K One _)
   ],
 
   "terms" :-
-  let defs = fromList [("f", mkDef gany Nat Zero)]
+  let defs = fromList [("f", mkDef gany (Nat noLoc) (Zero noLoc) noLoc)]
         -- doesn't have to be well typed yet, just well scoped
       fromPTerm = runFromParser {defs} .
                   fromPTermWith [< "𝑖", "𝑗"] [< "A", "x", "y", "z"]
   in [
     note "dim ctx: [𝑖, 𝑗]; term ctx: [A, x, y, z]",
-    parsesAs term fromPTerm "x" $ BVT 2,
+    parseMatch term fromPTerm "x" `(E $ B (VS $ VS VZ) _),
     parseFails term fromPTerm "𝑖",
-    parsesAs term fromPTerm "f" $ FT "f",
+    parseMatch term fromPTerm "f" `(E $ F "f" _),
-    parsesAs term fromPTerm "λ w ⇒ w" $ [< "w"] :\\ BVT 0,
+    parseMatch term fromPTerm "λ w ⇒ w"
-    parsesAs term fromPTerm "λ w ⇒ x" $ [< "w"] :\\ BVT 3,
+      `(Lam (S _ $ Y $ E $ B VZ _) _),
-    parsesAs term fromPTerm "λ x ⇒ x" $ [< "x"] :\\ BVT 0,
+    parseMatch term fromPTerm "λ w ⇒ x"
-    parsesAs term fromPTerm "λ a b ⇒ f a b" $
+      `(Lam (S _ $ N $ E $ B (VS $ VS VZ) _) _),
-      [< "a", "b"] :\\ E (F "f" :@@ [BVT 1, BVT 0]),
+    parseMatch term fromPTerm "λ x ⇒ x"
-    parsesAs term fromPTerm "f @𝑖" $
+      `(Lam (S _ $ Y $ E $ B VZ _) _),
-      E $ F "f" :% BV 1
+    parseMatch term fromPTerm "λ a b ⇒ f a b"
+      `(Lam (S _ $ Y $
+          Lam (S _ $ Y $
+            E $ App (App (F "f" _) (E $ B (VS VZ) _) _) (E $ B VZ _) _) _) _),
+    parseMatch term fromPTerm "f @𝑖" $
+      `(E $ DApp (F "f" _) (B (VS VZ) _) _)
   ],
 
   todo "everything else"

tests/Tests/PrettyTerm.idr

@@ -23,128 +23,179 @@ parameters (ds : NContext d) (ns : NContext n)
                  {default str label : String} -> Test
   testPrettyE1 e str {label} = testPrettyT1 (E e) str {label}
 
+
+prefix 9 ^
+(^) : (Loc -> a) -> a
+(^) a = a noLoc
+
+FromString BindName where fromString str = BN (fromString str) noLoc
+
+
 export
 tests : Test
 tests = "pretty printing terms" :- [
   "free vars" :- [
-    testPrettyE1 [<] [<] (F "x") "x",
+    testPrettyE1 [<] [<] (^F "x") "x",
-    testPrettyE1 [<] [<] (F $ MakeName [< "A", "B", "C"] "x") "A.B.C.x"
+    testPrettyE1 [<] [<] (^F (MakeName [< "A", "B", "C"] "x")) "A.B.C.x"
   ],
 
   "bound vars" :- [
-    testPrettyE1 [< "𝑖", "𝑗"] [< "x", "y"] (BV 0) "y",
+    testPrettyE1 [< "𝑖", "𝑗"] [< "x", "y"] (^BV 0) "y",
-    testPrettyE1 [< "𝑖", "𝑗"] [< "x", "y"] (BV 1) "x",
+    testPrettyE1 [< "𝑖", "𝑗"] [< "x", "y"] (^BV 1) "x",
-    testPrettyE1 [< "𝑖", "𝑗"] [< "x", "y"] (F "eq" :% BV 1) "eq @𝑖",
+    testPrettyE1 [< "𝑖", "𝑗"] [< "x", "y"]
-    testPrettyE1 [< "𝑖", "𝑗"] [< "x", "y"] (F "eq" :% BV 1 :% BV 0) "eq @𝑖 @𝑗"
+      (^DApp (^F "eq") (^BV 1))
+      "eq @𝑖",
+    testPrettyE1 [< "𝑖", "𝑗"] [< "x", "y"]
+      (^DApp (^DApp (^F "eq") (^BV 1)) (^BV 0))
+      "eq @𝑖 @𝑗"
   ],
 
   "applications" :- [
-    testPrettyE1 [<] [<] (F "f" :@ FT "x") "f x",
+    testPrettyE1 [<] [<]
-    testPrettyE1 [<] [<] (F "f" :@@ [FT "x", FT "y"]) "f x y",
+      (^App (^F "f") (^FT "x"))
-    testPrettyE1 [<] [<] (F "f" :% K Zero) "f @0",
+      "f x",
-    testPrettyE1 [<] [<] (F "f" :@ FT "x" :% K Zero) "f x @0",
+    testPrettyE1 [<] [<]
-    testPrettyE1 [<] [<] (F "g" :% K One :@ FT "y") "g @1 y"
+      (^App (^App (^F "f") (^FT "x")) (^FT "y"))
+      "f x y",
+    testPrettyE1 [<] [<]
+      (^DApp (^F "f") (^K Zero))
+      "f @0",
+    testPrettyE1 [<] [<]
+      (^DApp (^App (^F "f") (^FT "x")) (^K Zero))
+      "f x @0",
+    testPrettyE1 [<] [<]
+      (^App (^DApp (^F "g") (^K One)) (^FT "y"))
+      "g @1 y"
   ],
 
   "lambda" :- [
-    testPrettyT [<] [<] ([< "x"] :\\ BVT 0) "λ x ⇒ x" "fun x => x",
-    testPrettyT [<] [<] (Lam $ SN $ FT "a") "λ _ ⇒ a" "fun _ => a",
-    testPrettyT [<] [< "y"] ([< "x"] :\\ BVT 1) "λ x ⇒ y" "fun x => y",
     testPrettyT [<] [<]
-      ([< "x", "y", "f"] :\\ E (BV 0 :@@ [BVT 2, BVT 1]))
+      (^LamY "x" (^BVT 0))
+      "λ x ⇒ x"
+      "fun x => x",
+    testPrettyT [<] [<]
+      (^LamN (^FT "a"))
+      "λ _ ⇒ a"
+      "fun _ => a",
+    testPrettyT [<] [< "y"]
+      (^LamY "x" (^BVT 1))
+      "λ x ⇒ y"
+      "fun x => y",
+    testPrettyT [<] [<]
+      (^LamY "x" (^LamY "y" (^LamY "f"
+        (E $ ^App (^App (^BV 0) (^BVT 2)) (^BVT 1)))))
       "λ x y f ⇒ f x y"
       "fun x y f => f x y",
-    testPrettyT [<] [<] (DLam $ SN $ FT "a") "δ _ ⇒ a" "dfun _ => a",
-    testPrettyT [<] [<] ([< "i"] :\\% FT "x") "δ i ⇒ x" "dfun i => x",
     testPrettyT [<] [<]
-      ([< "x"] :\\ [< "i"] :\\% E (BV 0 :% BV 0))
+      (^DLam (SN (^FT "a")))
+      "δ _ ⇒ a"
+      "dfun _ => a",
+    testPrettyT [<] [<]
+      (^DLamY "i" (^FT "x"))
+      "δ i ⇒ x"
+      "dfun i => x",
+    testPrettyT [<] [<]
+      (^LamY "x" (^DLamY "i" (E $ ^DApp (^BV 0) (^BV 0))))
       "λ x ⇒ δ i ⇒ x @i"
       "fun x => dfun i => x @i"
   ],
 
   "type universes" :- [
-    testPrettyT [<] [<] (TYPE 0) "★₀" "Type0",
+    testPrettyT [<] [<] (^TYPE 0) "★₀" "Type0",
-    testPrettyT [<] [<] (TYPE 100) "★₁₀₀" "Type100"
+    testPrettyT [<] [<] (^TYPE 100) "★₁₀₀" "Type100"
   ],
 
   "function types" :- [
-    testPrettyT [<] [<] (Arr One (FT "A") (FT "B")) "1.A → B" "1.A -> B",
     testPrettyT [<] [<]
-      (PiY One "x" (FT "A") (E $ F "B" :@ BVT 0))
+      (^Arr One (^FT "A") (^FT "B"))
+      "1.A → B"
+      "1.A -> B",
+    testPrettyT [<] [<]
+      (^PiY One "x" (^FT "A") (E $ ^App (^F "B") (^BVT 0)))
       "1.(x : A) → B x"
       "1.(x : A) -> B x",
     testPrettyT [<] [<]
-      (PiY Zero "A" (TYPE 0) $ Arr Any (BVT 0) (BVT 0))
+      (^PiY Zero "A" (^TYPE 0) (^Arr Any (^BVT 0) (^BVT 0)))
       "0.(A : ★₀) → ω.A → A"
       "0.(A : Type0) -> #.A -> A",
     testPrettyT [<] [<]
-      (Arr Any (Arr Any (FT "A") (FT "A")) (FT "A"))
+      (^Arr Any (^Arr Any (^FT "A") (^FT "A")) (^FT "A"))
       "ω.(ω.A → A) → A"
       "#.(#.A -> A) -> A",
     testPrettyT [<] [<]
-      (Arr Any (FT "A") (Arr Any (FT "A") (FT "A")))
+      (^Arr Any (^FT "A") (^Arr Any (^FT "A") (^FT "A")))
       "ω.A → ω.A → A"
       "#.A -> #.A -> A",
     testPrettyT [<] [<]
-      (PiY Zero "P" (Arr Zero (FT "A") (TYPE 0)) (E $ BV 0 :@ FT "a"))
+      (^PiY Zero "P" (^Arr Zero (^FT "A") (^TYPE 0))
+        (E $ ^App (^BV 0) (^FT "a")))
       "0.(P : 0.A → ★₀) → P a"
       "0.(P : 0.A -> Type0) -> P a"
   ],
 
   "pair types" :- [
-    testPrettyT [<] [<] (FT "A" `And` FT "B") "A × B" "A ** B",
     testPrettyT [<] [<]
-      (SigY "x" (FT "A") (E $ F "B" :@ BVT 0))
+      (^And (^FT "A") (^FT "B"))
+      "A × B"
+      "A ** B",
+    testPrettyT [<] [<]
+      (^SigY "x" (^FT "A") (E $ ^App (^F "B") (^BVT 0)))
       "(x : A) × B x"
       "(x : A) ** B x",
     testPrettyT [<] [<]
-      (SigY "x" (FT "A") $
+      (^SigY "x" (^FT "A")
-       SigY "y" (E $ F "B" :@ BVT 0) $
+        (^SigY "y" (E $ ^App (^F "B") (^BVT 0))
-       E $ F "C" :@@ [BVT 1, BVT 0])
+          (E $ ^App (^App (^F "C") (^BVT 1)) (^BVT 0))))
       "(x : A) × (y : B x) × C x y"
       "(x : A) ** (y : B x) ** C x y",
     todo "non-dependent, left and right nested"
   ],
 
   "pairs" :- [
-    testPrettyT1 [<] [<] (Pair (FT "A") (FT "B")) "(A, B)",
+    testPrettyT1 [<] [<]
-    testPrettyT1 [<] [<] (Pair (FT "A") (Pair (FT "B") (FT "C"))) "(A, B, C)",
+      (^Pair (^FT "A") (^FT "B"))
-    testPrettyT1 [<] [<] (Pair (Pair (FT "A") (FT "B")) (FT "C")) "((A, B), C)",
+      "(A, B)",
+    testPrettyT1 [<] [<]
+      (^Pair (^FT "A") (^Pair (^FT "B") (^FT "C")))
+      "(A, B, C)",
+    testPrettyT1 [<] [<]
+      (^Pair (^Pair (^FT "A") (^FT "B")) (^FT "C"))
+      "((A, B), C)",
     testPrettyT [<] [<]
-      (Pair ([< "x"] :\\ BVT 0) (Arr One (FT "B₁") (FT "B₂")))
+      (^Pair (^LamY "x" (^BVT 0)) (^Arr One (^FT "B₁") (^FT "B₂")))
       "(λ x ⇒ x, 1.B₁ → B₂)"
       "(fun x => x, 1.B₁ -> B₂)"
   ],
 
   "enum types" :- [
-    testPrettyT1 [<] [<] (enum []) "{}",
+    testPrettyT1 [<] [<] (^enum []) "{}",
-    testPrettyT1 [<] [<] (enum ["a"]) "{a}",
+    testPrettyT1 [<] [<] (^enum ["a"]) "{a}",
-    testPrettyT1 [<] [<] (enum ["aa", "bb", "cc"]) "{aa, bb, cc}",
+    testPrettyT1 [<] [<] (^enum ["aa", "bb", "cc"]) "{aa, bb, cc}",
-    testPrettyT1 [<] [<] (enum ["a b c"]) #"{"a b c"}"#,
+    testPrettyT1 [<] [<] (^enum ["a b c"]) #"{"a b c"}"#,
-    testPrettyT1 [<] [<] (enum ["\"", ",", "\\"]) #" {"\"", ",", \} "#
+    testPrettyT1 [<] [<] (^enum ["\"", ",", "\\"]) #" {"\"", ",", \} "#
       {label = #"{"\"", ",", \}  # ｢\｣ is an identifier"#}
   ],
 
   "tags" :- [
-    testPrettyT1 [<] [<] (Tag "a") "'a",
+    testPrettyT1 [<] [<] (^Tag "a") "'a",
-    testPrettyT1 [<] [<] (Tag "hello") "'hello",
+    testPrettyT1 [<] [<] (^Tag "hello") "'hello",
-    testPrettyT1 [<] [<] (Tag "qualified.tag") "'qualified.tag",
+    testPrettyT1 [<] [<] (^Tag "qualified.tag") "'qualified.tag",
-    testPrettyT1 [<] [<] (Tag "non-identifier tag") #"'"non-identifier tag""#,
+    testPrettyT1 [<] [<] (^Tag "non-identifier tag") #"'"non-identifier tag""#,
-    testPrettyT1 [<] [<] (Tag #"""#) #" '"\"" "#
+    testPrettyT1 [<] [<] (^Tag #"""#) #" '"\"" "#
   ],
 
   todo "equality types",
 
   "case" :- [
     testPrettyE [<] [<]
-      (CasePair One (F "a") (SN $ TYPE 1) (SN $ TYPE 0))
+      (^CasePair One (^F "a") (SN $ ^TYPE 1) (SN $ ^TYPE 0))
       "case1 a return ★₁ of { (_, _) ⇒ ★₀ }"
       "case1 a return Type1 of { (_, _) => Type0 }",
     testPrettyT [<] [<]
-      ([< "u"] :\\
+      (^LamY "u" (E $
-        E (CaseEnum One (F "u")
+        ^CaseEnum One (^F "u")
-            (SY [< "x"] $ Eq0 (enum ["tt"]) (BVT 0) (Tag "tt"))
+          (SY [< "x"] $ ^Eq0 (^enum ["tt"]) (^BVT 0) (^Tag "tt"))
-            (fromList [("tt", [< Unused] :\\% Tag "tt")])))
+          (fromList [("tt", ^DLamN (^Tag "tt"))])))
       "λ u ⇒ case1 u return x ⇒ x ≡ 'tt : {tt} of { 'tt ⇒ δ _ ⇒ 'tt }"
       """
         fun u =>
@@ -155,27 +206,30 @@ tests = "pretty printing terms" :- [
   "type-case" :- [
     testPrettyE [<] [<]
       {label = "type-case ℕ ∷ ★₀ return ★₀ of { ⋯ }"}
-      (TypeCase (Nat :# TYPE 0) (TYPE 0) empty Nat)
+      (^TypeCase (^Ann (^Nat) (^TYPE 0)) (^TYPE 0) empty (^Nat))
       "type-case ℕ ∷ ★₀ return ★₀ of { _ ⇒ ℕ }"
       "type-case Nat :: Type0 return Type0 of { _ => Nat }"
   ],
 
   "annotations" :- [
-    testPrettyE [<] [<] (FT "a" :# FT "A") "a ∷ A" "a :: A",
     testPrettyE [<] [<]
-      (FT "a" :# E (FT "A" :# FT "𝐀"))
+      (^Ann (^FT "a") (^FT "A"))
+      "a ∷ A"
+      "a :: A",
+    testPrettyE [<] [<]
+      (^Ann (^FT "a") (E $ ^Ann (^FT "A") (^FT "𝐀")))
       "a ∷ A ∷ 𝐀"
       "a :: A :: 𝐀",
     testPrettyE [<] [<]
-      (E (FT "α" :# FT "a") :# FT "A")
+      (^Ann (E $ ^Ann (^FT "α") (^FT "a")) (^FT "A"))
       "(α ∷ a) ∷ A"
       "(α :: a) :: A",
     testPrettyE [<] [<]
-      (([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A"))
+      (^Ann (^LamY "x" (^BVT 0)) (^Arr One (^FT "A") (^FT "A")))
       "(λ x ⇒ x) ∷ 1.A → A"
       "(fun x => x) :: 1.A -> A",
     testPrettyE [<] [<]
-      (Arr One (FT "A") (FT "A") :# TYPE 7)
+      (^Ann (^Arr One (^FT "A") (^FT "A")) (^TYPE 7))
       "(1.A → A) ∷ ★₇"
       "(1.A -> A) :: Type7"
   ]

tests/Tests/Reduce.idr

@@ -3,7 +3,12 @@ module Tests.Reduce
 import Quox.Syntax as Lib
 import Quox.Equal
 import TypingImpls
+import AstExtra
 import TAP
+import Control.Eff
+
+%hide Prelude.App
+%hide Pretty.App
 
 
 parameters {0 isRedex : RedexTest tm} {auto _ : Whnf tm isRedex} {d, n : Nat}
@@ -12,7 +17,7 @@ parameters {0 isRedex : RedexTest tm} {auto _ : Whnf tm isRedex} {d, n : Nat}
   private
   testWhnf : String -> WhnfContext d n -> tm d n -> tm d n -> Test
   testWhnf label ctx from to = test "\{label}  (whnf)" $ do
-    result <- bimap toInfo fst $ whnf defs ctx from
+    result <- mapFst toInfo $ runWhnf $ whnf0 defs ctx from
     unless (result == to) $ Left [("exp", show to), ("got", show result)]
 
   private
@@ -20,7 +25,7 @@ parameters {0 isRedex : RedexTest tm} {auto _ : Whnf tm isRedex} {d, n : Nat}
   testNoStep label ctx e = testWhnf label ctx e e
 
 private
-ctx : Context (\n => (BaseName, Term 0 n)) n -> WhnfContext 0 n
+ctx : Context (\n => (BindName, Term 0 n)) n -> WhnfContext 0 n
 ctx xs = let (ns, ts) = unzip xs in MkWhnfContext [<] ns ts
 
 
@@ -28,91 +33,101 @@ export
 tests : Test
 tests = "whnf" :- [
   "head constructors" :- [
-    testNoStep "★₀" empty $ TYPE 0,
+    testNoStep "★₀" empty $ ^TYPE 0,
-    testNoStep "[A] ⊸ [B]" empty $
+    testNoStep "1.A → B" empty $
-      Arr One (FT "A") (FT "B"),
+      ^Arr One (^FT "A") (^FT "B"),
-    testNoStep "(x: [A]) ⊸ [B [x]]" empty $
+    testNoStep "(x: A) ⊸ B x" empty $
-      Pi One (FT "A") (S [< "x"] $ Y $ E $ F "B" :@ BVT 0),
+      ^PiY One "x" (^FT "A") (E $ ^App (^F "B") (^BVT 0)),
-    testNoStep "λx. [x]" empty $
+    testNoStep "λ x ⇒ x" empty $
-      Lam $ S [< "x"] $ Y $ BVT 0,
+      ^LamY "x" (^BVT 0),
-    testNoStep "[f [a]]" empty $
+    testNoStep "f a" empty $
-      E $ F "f" :@ FT "a"
+      E $ ^App (^F "f") (^FT "a")
   ],
 
   "neutrals" :- [
-    testNoStep "x" (ctx [< ("A", Nat)]) $ BV 0,
+    testNoStep "x" (ctx [< ("A", ^Nat)]) $ ^BV 0,
-    testNoStep "a"       empty $ F "a",
+    testNoStep "a"       empty $ ^F "a",
-    testNoStep "f [a]"   empty $ F "f" :@ FT "a",
+    testNoStep "f a"     empty $ ^App (^F "f") (^FT "a"),
-    testNoStep "★₀ ∷ ★₁" empty $ TYPE 0 :# TYPE 1
+    testNoStep "★₀ ∷ ★₁" empty $ ^Ann (^TYPE 0) (^TYPE 1)
   ],
 
   "redexes" :- [
-    testWhnf "[a] ∷ [A]" empty
+    testWhnf "a ∷ A" empty
-      (FT "a" :# FT "A")
+      (^Ann (^FT "a") (^FT "A"))
-      (F "a"),
+      (^F "a"),
-    testWhnf "[★₁ ∷ ★₃]" empty
+    testWhnf "★₁ ∷ ★₃" empty
-      (E (TYPE 1 :# TYPE 3))
+      (E $ ^Ann (^TYPE 1) (^TYPE 3))
-      (TYPE 1),
+      (^TYPE 1),
-    testWhnf "(λx. [x] ∷ [A] ⊸ [A]) [a]" empty
+    testWhnf "(λ x ⇒ x ∷ 1.A → A) a" empty
-      ((([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
+      (^App (^Ann (^LamY "x" (^BVT 0)) (^Arr One (^FT "A") (^FT "A")))
-      (F "a")
+            (^FT "a"))
+      (^F "a")
   ],
 
   "definitions" :- [
     testWhnf "a  (transparent)" empty
-      {defs = fromList [("a", mkDef gzero (TYPE 1) (TYPE 0))]}
+      {defs = fromList [("a", ^mkDef gzero (^TYPE 1) (^TYPE 0))]}
-      (F "a") (TYPE 0 :# TYPE 1)
+      (^F "a") (^Ann (^TYPE 0) (^TYPE 1)),
+    testNoStep "a  (opaque)" empty
+      {defs = fromList [("a", ^mkPostulate gzero (^TYPE 1))]}
+      (^F "a")
   ],
 
   "elim closure" :- [
-    testWhnf "x{}" (ctx [< ("A", Nat)])
+    testWhnf "x{}" (ctx [< ("x", ^Nat)])
-      (CloE (Sub (BV 0) id))
+      (CloE (Sub (^BV 0) id))
-      (BV 0),
+      (^BV 0),
     testWhnf "x{a/x}" empty
-      (CloE (Sub (BV 0) (F "a" ::: id)))
+      (CloE (Sub (^BV 0) (^F "a" ::: id)))
-      (F "a"),
+      (^F "a"),
-    testWhnf "x{x/x,a/y}" (ctx [< ("A", Nat)])
+    testWhnf "x{a/y}" (ctx [< ("x", ^Nat)])
-      (CloE (Sub (BV 0) (BV 0 ::: F "a" ::: id)))
+      (CloE (Sub (^BV 0) (^BV 0 ::: ^F "a" ::: id)))
-      (BV 0),
+      (^BV 0),
     testWhnf "x{(y{a/y})/x}" empty
-      (CloE (Sub (BV 0) ((CloE (Sub (BV 0) (F "a" ::: id))) ::: id)))
+      (CloE (Sub (^BV 0) ((CloE (Sub (^BV 0) (^F "a" ::: id))) ::: id)))
-      (F "a"),
+      (^F "a"),
     testWhnf "(x y){f/x,a/y}" empty
-      (CloE (Sub (BV 0 :@ BVT 1) (F "f" ::: F "a" ::: id)))
+      (CloE (Sub (^App (^BV 0) (^BVT 1)) (^F "f" ::: ^F "a" ::: id)))
-      (F "f" :@ FT "a"),
+      (^App (^F "f") (^FT "a")),
-    testWhnf "([y] ∷ [x]){A/x}" (ctx [< ("A", Nat)])
+    testWhnf "(y ∷ x){A/x}" (ctx [< ("x", ^Nat)])
-      (CloE (Sub (BVT 1 :# BVT 0) (F "A" ::: id)))
+      (CloE (Sub (^Ann (^BVT 1) (^BVT 0)) (^F "A" ::: id)))
-      (BV 0),
+      (^BV 0),
-    testWhnf "([y] ∷ [x]){A/x,a/y}" empty
+    testWhnf "(y ∷ x){A/x,a/y}" empty
-      (CloE (Sub (BVT 1 :# BVT 0) (F "A" ::: F "a" ::: id)))
+      (CloE (Sub (^Ann (^BVT 1) (^BVT 0)) (^F "A" ::: ^F "a" ::: id)))
-      (F "a")
+      (^F "a")
   ],
 
   "term closure" :- [
-    testWhnf "(λy. x){a/x}" empty
+    testWhnf "(λ y ⇒ x){a/x}" empty
-      (CloT (Sub (Lam $ S [< "y"] $ N $ BVT 0) (F "a" ::: id)))
+      (CloT (Sub (^LamN (^BVT 0)) (^F "a" ::: id)))
-      (Lam $ S [< "y"] $ N $ FT "a"),
+      (^LamN (^FT "a")),
     testWhnf "(λy. y){a/x}" empty
-      (CloT (Sub ([< "y"] :\\ BVT 0) (F "a" ::: id)))
+      (CloT (Sub (^LamY "y" (^BVT 0)) (^F "a" ::: id)))
-      ([< "y"] :\\ BVT 0)
+      (^LamY "y" (^BVT 0))
   ],
 
-  "looking inside […]" :- [
+  "looking inside `E`" :- [
-    testWhnf "[(λx. x ∷ A ⊸ A) [a]]" empty
+    testWhnf "(λx. x ∷ A ⊸ A) a" empty
-      (E $ (([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
+      (E $ ^App (^Ann (^LamY "x" (^BVT 0)) (^Arr One (^FT "A") (^FT "A")))
-      (FT "a")
+              (^FT "a"))
+      (^FT "a")
   ],
 
   "nested redex" :- [
-    note "whnf only looks at top level redexes",
+    testNoStep "λ y ⇒ ((λ x ⇒ x) ∷ 1.A → A) y" empty $
-    testNoStep "λy. [(λx. [x] ∷ [A] ⊸ [A]) [y]]" empty $
+      ^LamY "y" (E $
-      [< "y"] :\\ E ((([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ BVT 0),
+        ^App (^Ann (^LamY "x" (^BVT 0)) (^Arr One (^FT "A") (^FT "A")))
-    testNoStep "f [(λx. [x] ∷ [A] ⊸ [A]) [a]]" empty $
+             (^BVT 0)),
-      F "a" :@
+    testNoStep "f (((λ x ⇒ x) ∷ 1.A → A) a)" empty $
-      E ((([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a"),
+      ^App (^F "f")
-    testNoStep "λx. [y [x]]{x/x,a/y}" (ctx [< ("A", Nat)]) $
+        (E $ ^App (^Ann (^LamY "x" (^BVT 0)) (^Arr One (^FT "A") (^FT "A")))
-      [< "x"] :\\ CloT (Sub (E $ BV 1 :@ BVT 0) (BV 0 ::: F "a" ::: id)),
+              (^FT "a")),
-    testNoStep "f ([y [x]]{x/x,a/y})" (ctx [< ("A", Nat)]) $
+    testNoStep "λx. (y x){x/x,a/y}" (ctx [< ("y", ^Nat)]) $
-      F "f" :@ CloT (Sub (E $ BV 1 :@ BVT 0) (BV 0 ::: F "a" ::: id))
+      ^LamY "x" (CloT $ Sub (E $ ^App (^BV 1) (^BVT 0))
+                            (^BV 0 ::: ^F "a" ::: id)),
+    testNoStep "f (y x){x/x,a/y}" (ctx [< ("y", ^Nat)]) $
+      ^App (^F "f")
+        (CloT (Sub (E $ ^App (^BV 1) (^BVT 0))
+                   (^BV 0 ::: ^F "a" ::: id)))
   ]
 ]

tests/Tests/Typechecker.idr

@@ -5,6 +5,11 @@ import Quox.Typechecker as Lib
 import public TypingImpls
 import TAP
 import Quox.EffExtra
+import AstExtra
+
+
+%hide Prelude.App
+%hide Pretty.App
 
 
 data Error'
@@ -28,64 +33,75 @@ ToInfo Error' where
 M = Eff [Except Error', DefsReader]
 
 inj : TC a -> M a
-inj = rethrow . mapFst TCError <=< lift . runExcept
+inj act = rethrow $ mapFst TCError $ runTC !defs act
 
 
 reflTy : Term d n
 reflTy =
-  PiY Zero "A" (TYPE 0) $
+  ^PiY Zero "A" (^TYPE 0)
-  PiY One  "x" (BVT 0)  $
+    (^PiY One  "x" (^BVT 0)
-  Eq0 (BVT 1) (BVT 0) (BVT 0)
+      (^Eq0 (^BVT 1) (^BVT 0) (^BVT 0)))
 
 reflDef : Term d n
-reflDef = [< "A","x"] :\\ [< "i"] :\\% BVT 0
+reflDef = ^LamY "A" (^LamY "x" (^DLamY "i" (^BVT 0)))
 
 
 fstTy : Term d n
 fstTy =
-  (PiY Zero "A" (TYPE 1) $
+  ^PiY Zero "A" (^TYPE 1)
-   PiY Zero "B" (Arr Any (BVT 0) (TYPE 1)) $
+    (^PiY Zero "B" (^Arr Any (^BVT 0) (^TYPE 1))
-   Arr Any (SigY "x" (BVT 1) $ E $ BV 1 :@ BVT 0) (BVT 1))
+      (^Arr Any (^SigY "x" (^BVT 1) (E $ ^App (^BV 1) (^BVT 0))) (^BVT 1)))
 
 fstDef : Term d n
 fstDef =
-  ([< "A","B","p"] :\\
+  ^LamY "A" (^LamY "B" (^LamY "p"
-    E (CasePair Any (BV 0) (SN $ BVT 2) (SY [< "x","y"] $ BVT 1)))
+    (E $ ^CasePair Any (^BV 0) (SN $ ^BVT 2)
+      (SY [< "x", "y"] $ ^BVT 1))))
 
 sndTy : Term d n
 sndTy =
-  (PiY Zero "A" (TYPE 1) $
+  ^PiY Zero "A" (^TYPE 1)
-   PiY Zero "B" (Arr Any (BVT 0) (TYPE 1)) $
+    (^PiY Zero "B" (^Arr Any (^BVT 0) (^TYPE 1))
-   PiY Any  "p" (SigY "x" (BVT 1) $ E $ BV 1 :@ BVT 0) $
+      (^PiY Any "p" (^SigY "x" (^BVT 1) (E $ ^App (^BV 1) (^BVT 0)))
-   E (BV 1 :@ E (F "fst" :@@ [BVT 2, BVT 1, BVT 0])))
+        (E $ ^App (^BV 1)
+          (E $ ^App (^App (^App (^F "fst") (^BVT 2)) (^BVT 1)) (^BVT 0)))))
 
 sndDef : Term d n
 sndDef =
-  ([< "A","B","p"] :\\
+  -- λ A B p ⇒ caseω p return p' ⇒ B (fst A B p') of { (x, y) ⇒ y }
-    E (CasePair Any (BV 0)
+  ^LamY "A" (^LamY "B" (^LamY "p"
-        (SY [< "p"] $ E $ BV 2 :@ E (F "fst" :@@ [BVT 3, BVT 2, BVT 0]))
+    (E $ ^CasePair Any (^BV 0)
-        (SY [< "x","y"] $ BVT 0)))
+      (SY [< "p"] $ E $
+        ^App (^BV 2)
+          (E $ ^App (^App (^App (^F "fst") (^BVT 3)) (^BVT 2)) (^BVT 0)))
+      (SY [< "x", "y"] $ ^BVT 0))))
+
+nat : Term d n
+nat = ^Nat
 
 
 defGlobals : Definitions
 defGlobals = fromList
-  [("A",  mkPostulate gzero $ TYPE 0),
+  [("A",  ^mkPostulate gzero (^TYPE 0)),
-   ("B",  mkPostulate gzero $ TYPE 0),
+   ("B",  ^mkPostulate gzero (^TYPE 0)),
-   ("C",  mkPostulate gzero $ TYPE 1),
+   ("C",  ^mkPostulate gzero (^TYPE 1)),
-   ("D",  mkPostulate gzero $ TYPE 1),
+   ("D",  ^mkPostulate gzero (^TYPE 1)),
-   ("P",  mkPostulate gzero $ Arr Any (FT "A") (TYPE 0)),
+   ("P",  ^mkPostulate gzero (^Arr Any (^FT "A") (^TYPE 0))),
-   ("a",  mkPostulate gany  $ FT "A"),
+   ("a",  ^mkPostulate gany  (^FT "A")),
-   ("a'", mkPostulate gany  $ FT "A"),
+   ("a'", ^mkPostulate gany  (^FT "A")),
-   ("b",  mkPostulate gany  $ FT "B"),
+   ("b",  ^mkPostulate gany  (^FT "B")),
-   ("f",  mkPostulate gany  $ Arr One (FT "A") (FT "A")),
+   ("f",  ^mkPostulate gany  (^Arr One (^FT "A") (^FT "A"))),
-   ("fω", mkPostulate gany  $ Arr Any (FT "A") (FT "A")),
+   ("fω", ^mkPostulate gany  (^Arr Any (^FT "A") (^FT "A"))),
-   ("g",  mkPostulate gany  $ Arr One (FT "A") (FT "B")),
+   ("g",  ^mkPostulate gany  (^Arr One (^FT "A") (^FT "B"))),
-   ("f2", mkPostulate gany  $ Arr One (FT "A") $ Arr One (FT "A") (FT "B")),
+   ("f2", ^mkPostulate gany
-   ("p",  mkPostulate gany  $ PiY One "x" (FT "A") $ E $ F "P" :@ BVT 0),
+      (^Arr One (^FT "A") (^Arr One (^FT "A") (^FT "B")))),
-   ("q",  mkPostulate gany  $ PiY One "x" (FT "A") $ E $ F "P" :@ BVT 0),
+   ("p",  ^mkPostulate gany
-   ("refl", mkDef gany reflTy reflDef),
+      (^PiY One "x" (^FT "A") (E $ ^App (^F "P") (^BVT 0)))),
-   ("fst",  mkDef gany fstTy fstDef),
+   ("q",  ^mkPostulate gany
-   ("snd",  mkDef gany sndTy sndDef)]
+      (^PiY One "x" (^FT "A") (E $ ^App (^F "P") (^BVT 0)))),
+   ("refl", ^mkDef gany reflTy reflDef),
+   ("fst",  ^mkDef gany fstTy fstDef),
+   ("snd",  ^mkDef gany sndTy sndDef)]
 
 parameters (label : String) (act : Lazy (M ()))
            {default defGlobals globals : Definitions}
@@ -98,23 +114,10 @@ parameters (label : String) (act : Lazy (M ()))
     (extract $ runExcept $ runReaderAt DEFS globals act) $> "()"
 
 
-anys : {n : Nat} -> QContext n
-anys {n = 0}   = [<]
-anys {n = S n} = anys :< Any
-
-ctx, ctx01 : {n : Nat} -> Context (\n => (BaseName, Term 0 n)) n ->
-             TyContext 0 n
-ctx tel = let (ns, ts) = unzip tel in
-          MkTyContext new [<] ts ns anys
-ctx01 tel = let (ns, ts) = unzip tel in
-            MkTyContext ZeroIsOne [<] ts ns anys
-
-empty01 : TyContext 0 0
-empty01 = eqDim (K Zero) (K One) empty
-
 inferredTypeEq : TyContext d n -> (exp, got : Term d n) -> M ()
 inferredTypeEq ctx exp got =
-  wrapErr (const $ WrongInfer exp got) $ inj $ equalType ctx exp got
+  wrapErr (const $ WrongInfer exp got) $ inj $ lift $
+    equalType noLoc ctx exp got
 
 qoutEq : (exp, got : QOutput n) -> M ()
 qoutEq qout res = unless (qout == res) $ throw $ WrongQOut qout res
@@ -156,153 +159,168 @@ tests : Test
 tests = "typechecker" :- [
   "universes" :- [
     testTC "0 · ★₀ ⇐ ★₁  # by checkType" $
-      checkType_ empty (TYPE 0) (Just 1),
+      checkType_ empty (^TYPE 0) (Just 1),
     testTC "0 · ★₀ ⇐ ★₁  # by check" $
-      check_ empty szero (TYPE 0) (TYPE 1),
+      check_ empty szero (^TYPE 0) (^TYPE 1),
     testTC "0 · ★₀ ⇐ ★₂" $
-      checkType_ empty (TYPE 0) (Just 2),
+      checkType_ empty (^TYPE 0) (Just 2),
     testTC "0 · ★₀ ⇐ ★_" $
-      checkType_ empty (TYPE 0) Nothing,
+      checkType_ empty (^TYPE 0) Nothing,
     testTCFail "0 · ★₁ ⇍ ★₀" $
-      checkType_ empty (TYPE 1) (Just 0),
+      checkType_ empty (^TYPE 1) (Just 0),
     testTCFail "0 · ★₀ ⇍ ★₀" $
-      checkType_ empty (TYPE 0) (Just 0),
+      checkType_ empty (^TYPE 0) (Just 0),
     testTC "0=1 ⊢ 0 · ★₁ ⇐ ★₀" $
-      checkType_ empty01 (TYPE 1) (Just 0),
+      checkType_ empty01 (^TYPE 1) (Just 0),
     testTCFail "1 · ★₀ ⇍ ★₁  # by check" $
-      check_ empty sone (TYPE 0) (TYPE 1)
+      check_ empty sone (^TYPE 0) (^TYPE 1)
   ],
 
   "function types" :- [
-    note "A, B : ★₀;  C, D : ★₁;  P : A ⇾ ★₀",
+    note "A, B : ★₀;  C, D : ★₁;  P : 0.A → ★₀",
-    testTC "0 · A ⊸ B ⇐ ★₀" $
+    testTC "0 · 1.A → B ⇐ ★₀" $
-      check_ empty szero (Arr One (FT "A") (FT "B")) (TYPE 0),
+      check_ empty szero (^Arr One (^FT "A") (^FT "B")) (^TYPE 0),
     note "subtyping",
-    testTC "0 · A ⊸ B ⇐ ★₁" $
+    testTC "0 · 1.A → B ⇐ ★₁" $
-      check_ empty szero (Arr One (FT "A") (FT "B")) (TYPE 1),
+      check_ empty szero (^Arr One (^FT "A") (^FT "B")) (^TYPE 1),
-    testTC "0 · C ⊸ D ⇐ ★₁" $
+    testTC "0 · 1.C → D ⇐ ★₁" $
-      check_ empty szero (Arr One (FT "C") (FT "D")) (TYPE 1),
+      check_ empty szero (^Arr One (^FT "C") (^FT "D")) (^TYPE 1),
-    testTCFail "0 · C ⊸ D ⇍ ★₀" $
+    testTCFail "0 · 1.C → D ⇍ ★₀" $
-      check_ empty szero (Arr One (FT "C") (FT "D")) (TYPE 0),
+      check_ empty szero (^Arr One (^FT "C") (^FT "D")) (^TYPE 0),
-    testTC "0 · (1·x : A) → P x ⇐ ★₀" $
+    testTC "0 · 1.(x : A) → P x ⇐ ★₀" $
       check_ empty szero
-        (PiY One "x" (FT "A") $ E $ F "P" :@ BVT 0)
+        (^PiY One "x" (^FT "A") (E $ ^App (^F "P") (^BVT 0)))
-        (TYPE 0),
+        (^TYPE 0),
-    testTCFail "0 · A ⊸ P ⇍ ★₀" $
+    testTCFail "0 · 1.A → P ⇍ ★₀" $
-      check_ empty szero (Arr One (FT "A") $ FT "P") (TYPE 0),
+      check_ empty szero (^Arr One (^FT "A") (^FT "P")) (^TYPE 0),
-    testTC "0=1 ⊢ 0 · A ⊸ P ⇐ ★₀" $
+    testTC "0=1 ⊢ 0 · 1.A → P ⇐ ★₀" $
-      check_ empty01 szero (Arr One (FT "A") $ FT "P") (TYPE 0)
+      check_ empty01 szero (^Arr One (^FT "A") (^FT "P")) (^TYPE 0)
   ],
 
   "pair types" :- [
-    note #""A × B" for "(_ : A) × B""#,
     testTC "0 · A × A ⇐ ★₀" $
-      check_ empty szero (FT "A" `And` FT "A") (TYPE 0),
+      check_ empty szero (^And (^FT "A") (^FT "A")) (^TYPE 0),
     testTCFail "0 · A × P ⇍ ★₀" $
-      check_ empty szero (FT "A" `And` FT "P") (TYPE 0),
+      check_ empty szero (^And (^FT "A") (^FT "P")) (^TYPE 0),
     testTC "0 · (x : A) × P x ⇐ ★₀" $
       check_ empty szero
-        (SigY "x" (FT "A") $ E $ F "P" :@ BVT 0) (TYPE 0),
+        (^SigY "x" (^FT "A") (E $ ^App (^F "P") (^BVT 0)))
+        (^TYPE 0),
     testTC "0 · (x : A) × P x ⇐ ★₁" $
       check_ empty szero
-        (SigY "x" (FT "A") $ E $ F "P" :@ BVT 0) (TYPE 1),
+        (^SigY "x" (^FT "A") (E $ ^App (^F "P") (^BVT 0)))
+        (^TYPE 1),
     testTC "0 · (A : ★₀) × A ⇐ ★₁" $
-      check_ empty szero (SigY "A" (TYPE 0) $ BVT 0) (TYPE 1),
+      check_ empty szero
+        (^SigY "A" (^TYPE 0) (^BVT 0))
+        (^TYPE 1),
     testTCFail "0 · (A : ★₀) × A ⇍ ★₀" $
-      check_ empty szero (SigY "A" (TYPE 0) $ BVT 0) (TYPE 0),
+      check_ empty szero
+        (^SigY "A" (^TYPE 0) (^BVT 0))
+        (^TYPE 0),
     testTCFail "1 · A × A ⇍ ★₀" $
-      check_ empty sone (FT "A" `And` FT "A") (TYPE 0)
+      check_ empty sone
+        (^And (^FT "A") (^FT "A"))
+        (^TYPE 0)
   ],
 
   "enum types" :- [
-    testTC "0 · {} ⇐ ★₀" $ check_ empty szero (enum []) (TYPE 0),
+    testTC "0 · {} ⇐ ★₀" $ check_ empty szero (^enum []) (^TYPE 0),
-    testTC "0 · {} ⇐ ★₃" $ check_ empty szero (enum []) (TYPE 3),
+    testTC "0 · {} ⇐ ★₃" $ check_ empty szero (^enum []) (^TYPE 3),
     testTC "0 · {a,b,c} ⇐ ★₀" $
-      check_ empty szero (enum ["a", "b", "c"]) (TYPE 0),
+      check_ empty szero (^enum ["a", "b", "c"]) (^TYPE 0),
     testTC "0 · {a,b,c} ⇐ ★₃" $
-      check_ empty szero (enum ["a", "b", "c"]) (TYPE 3),
+      check_ empty szero (^enum ["a", "b", "c"]) (^TYPE 3),
-    testTCFail "1 · {} ⇍ ★₀" $ check_ empty sone (enum []) (TYPE 0),
+    testTCFail "1 · {} ⇍ ★₀" $ check_ empty sone (^enum []) (^TYPE 0),
-    testTC "0=1 ⊢ 1 · {} ⇐ ★₀" $ check_ empty01 sone (enum []) (TYPE 0)
+    testTC "0=1 ⊢ 1 · {} ⇐ ★₀" $ check_ empty01 sone (^enum []) (^TYPE 0)
   ],
 
   "free vars" :- [
     note "A : ★₀",
     testTC "0 · A ⇒ ★₀" $
-      inferAs empty szero (F "A") (TYPE 0),
+      inferAs empty szero (^F "A") (^TYPE 0),
     testTC "0 · [A] ⇐ ★₀" $
-      check_ empty szero (FT "A") (TYPE 0),
+      check_ empty szero (^FT "A") (^TYPE 0),
     note "subtyping",
     testTC "0 · [A] ⇐ ★₁" $
-      check_ empty szero (FT "A") (TYPE 1),
+      check_ empty szero (^FT "A") (^TYPE 1),
     note "(fail) runtime-relevant type",
     testTCFail "1 · A ⇏ ★₀" $
-      infer_ empty sone (F "A"),
+      infer_ empty sone (^F "A"),
     testTC "1 . f ⇒ 1.A → A" $
-      inferAs empty sone (F "f") (Arr One (FT "A") (FT "A")),
+      inferAs empty sone (^F "f") (^Arr One (^FT "A") (^FT "A")),
     testTC "1 . f ⇐ 1.A → A" $
-      check_ empty sone (FT "f") (Arr One (FT "A") (FT "A")),
+      check_ empty sone (^FT "f") (^Arr One (^FT "A") (^FT "A")),
     testTCFail "1 . f ⇍ 0.A → A" $
-      check_ empty sone (FT "f") (Arr Zero (FT "A") (FT "A")),
+      check_ empty sone (^FT "f") (^Arr Zero (^FT "A") (^FT "A")),
     testTCFail "1 . f ⇍ ω.A → A" $
-      check_ empty sone (FT "f") (Arr Any (FT "A") (FT "A")),
+      check_ empty sone (^FT "f") (^Arr Any (^FT "A") (^FT "A")),
     testTC "1 . (λ x ⇒ f x) ⇐ 1.A → A" $
       check_ empty sone
-        ([< "x"] :\\ E (F "f" :@ BVT 0))
+        (^LamY "x" (E $ ^App (^F "f") (^BVT 0)))
-        (Arr One (FT "A") (FT "A")),
+        (^Arr One (^FT "A") (^FT "A")),
     testTC "1 . (λ x ⇒ f x) ⇐ ω.A → A" $
       check_ empty sone
-        ([< "x"] :\\ E (F "f" :@ BVT 0))
+        (^LamY "x" (E $ ^App (^F "f") (^BVT 0)))
-        (Arr Any (FT "A") (FT "A")),
+        (^Arr Any (^FT "A") (^FT "A")),
     testTCFail "1 . (λ x ⇒ f x) ⇍ 0.A → A" $
       check_ empty sone
-        ([< "x"] :\\ E (F "f" :@ BVT 0))
+        (^LamY "x" (E $ ^App (^F "f") (^BVT 0)))
-        (Arr Zero (FT "A") (FT "A")),
+        (^Arr Zero (^FT "A") (^FT "A")),
     testTC "1 . fω ⇒ ω.A → A" $
-      inferAs empty sone (F "fω") (Arr Any (FT "A") (FT "A")),
+      inferAs empty sone (^F "fω") (^Arr Any (^FT "A") (^FT "A")),
     testTC "1 . (λ x ⇒ fω x) ⇐ ω.A → A" $
       check_ empty sone
-        ([< "x"] :\\ E (F "fω" :@ BVT 0))
+        (^LamY "x" (E $ ^App (^F "fω") (^BVT 0)))
-        (Arr Any (FT "A") (FT "A")),
+        (^Arr Any (^FT "A") (^FT "A")),
     testTCFail "1 . (λ x ⇒ fω x) ⇍ 0.A → A" $
       check_ empty sone
-        ([< "x"] :\\ E (F "fω" :@ BVT 0))
+        (^LamY "x" (E $ ^App (^F "fω") (^BVT 0)))
-        (Arr Zero (FT "A") (FT "A")),
+        (^Arr Zero (^FT "A") (^FT "A")),
     testTCFail "1 . (λ x ⇒ fω x) ⇍ 1.A → A" $
       check_ empty sone
-        ([< "x"] :\\ E (F "fω" :@ BVT 0))
+        (^LamY "x" (E $ ^App (^F "fω") (^BVT 0)))
-        (Arr One (FT "A") (FT "A")),
+        (^Arr One (^FT "A") (^FT "A")),
     note "refl : (0·A : ★₀) → (1·x : A) → (x ≡ x : A) ≔ (λ A x ⇒ δ _ ⇒ x)",
-    testTC "1 · refl ⇒ ⋯" $ inferAs empty sone (F "refl") reflTy,
+    testTC "1 · refl ⇒ ⋯" $ inferAs empty sone (^F "refl") reflTy,
-    testTC "1 · [refl] ⇐ ⋯" $ check_ empty sone (FT "refl") reflTy
+    testTC "1 · [refl] ⇐ ⋯" $ check_ empty sone (^FT "refl") reflTy
   ],
 
   "bound vars" :- [
     testTC "x : A ⊢ 1 · x ⇒ A ⊳ 1·x" $
-      inferAsQ {n = 1} (ctx [< ("x", FT "A")]) sone
+      inferAsQ (ctx [< ("x", ^FT "A")]) sone
-        (BV 0) (FT "A") [< One],
+        (^BV 0) (^FT "A") [< One],
-    testTC "x : A ⊢ 1 · [x] ⇐ A ⊳ 1·x" $
+    testTC "x : A ⊢ 1 · x ⇐ A ⊳ 1·x" $
-      checkQ {n = 1} (ctx [< ("x", FT "A")]) sone (BVT 0) (FT "A") [< One],
+      checkQ (ctx [< ("x", ^FT "A")]) sone (^BVT 0) (^FT "A") [< One],
-    note "f2 : A ⊸ A ⊸ B",
+    note "f2 : 1.A → 1.A → B",
-    testTC "x : A ⊢ 1 · f2 [x] [x] ⇒ B ⊳ ω·x" $
+    testTC "x : A ⊢ 1 · f2 x x ⇒ B ⊳ ω·x" $
-      inferAsQ {n = 1} (ctx [< ("x", FT "A")]) sone
+      inferAsQ (ctx [< ("x", ^FT "A")]) sone
-        (F "f2" :@@ [BVT 0, BVT 0]) (FT "B") [< Any]
+        (^App (^App (^F "f2") (^BVT 0)) (^BVT 0)) (^FT "B") [< Any]
   ],
 
   "lambda" :- [
     note "linear & unrestricted identity",
-    testTC "1 · (λ x ⇒ x) ⇐ A ⊸ A" $
-      check_ empty sone ([< "x"] :\\ BVT 0) (Arr One (FT "A") (FT "A")),
     testTC "1 · (λ x ⇒ x) ⇐ A → A" $
-      check_ empty sone ([< "x"] :\\ BVT 0) (Arr Any (FT "A") (FT "A")),
+      check_ empty sone
+        (^LamY "x" (^BVT 0))
+        (^Arr One (^FT "A") (^FT "A")),
+    testTC "1 · (λ x ⇒ x) ⇐ ω.A → A" $
+      check_ empty sone
+        (^LamY "x" (^BVT 0))
+        (^Arr Any (^FT "A") (^FT "A")),
     note "(fail) zero binding used relevantly",
-    testTCFail "1 · (λ x ⇒ x) ⇍ A ⇾ A" $
+    testTCFail "1 · (λ x ⇒ x) ⇍ 0.A → A" $
-      check_ empty sone ([< "x"] :\\ BVT 0) (Arr Zero (FT "A") (FT "A")),
+      check_ empty sone
+        (^LamY "x" (^BVT 0))
+        (^Arr Zero (^FT "A") (^FT "A")),
     note "(but ok in overall erased context)",
     testTC "0 · (λ x ⇒ x) ⇐ A ⇾ A" $
-      check_ empty szero ([< "x"] :\\ BVT 0) (Arr Zero (FT "A") (FT "A")),
+      check_ empty szero
+        (^LamY "x" (^BVT 0))
+        (^Arr Zero (^FT "A") (^FT "A")),
     testTC "1 · (λ A x ⇒ refl A x) ⇐ ⋯  # (type of refl)" $
       check_ empty sone
-        ([< "A", "x"] :\\ E (F "refl" :@@ [BVT 1, BVT 0]))
+        (^LamY "A" (^LamY "x" (E $ ^App (^App (^F "refl") (^BVT 1)) (^BVT 0))))
         reflTy,
     testTC "1 · (λ A x ⇒ δ i ⇒ x) ⇐ ⋯  # (def. and type of refl)" $
       check_ empty sone reflDef reflTy
@@ -310,148 +328,153 @@ tests = "typechecker" :- [
 
   "pairs" :- [
     testTC "1 · (a, a) ⇐ A × A" $
-      check_ empty sone (Pair (FT "a") (FT "a")) (FT "A" `And` FT "A"),
+      check_ empty sone
+        (^Pair (^FT "a") (^FT "a")) (^And (^FT "A") (^FT "A")),
     testTC "x : A ⊢ 1 · (x, x) ⇐ A × A ⊳ ω·x" $
-      checkQ (ctx [< ("x", FT "A")]) sone
+      checkQ (ctx [< ("x", ^FT "A")]) sone
-        (Pair (BVT 0) (BVT 0)) (FT "A" `And` FT "A") [< Any],
+        (^Pair (^BVT 0) (^BVT 0)) (^And (^FT "A") (^FT "A")) [< Any],
     testTC "1 · (a, δ i ⇒ a) ⇐ (x : A) × (x ≡ a)" $
       check_ empty sone
-        (Pair (FT "a") ([< "i"] :\\% FT "a"))
+        (^Pair (^FT "a") (^DLamN (^FT "a")))
-        (SigY "x" (FT "A") $ Eq0 (FT "A") (BVT 0) (FT "a"))
+        (^SigY "x" (^FT "A") (^Eq0 (^FT "A") (^BVT 0) (^FT "a")))
   ],
 
   "unpairing" :- [
     testTC "x : A × A ⊢ 1 · (case1 x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ 1·x" $
-      inferAsQ (ctx [< ("x", FT "A" `And` FT "A")]) sone
+      inferAsQ (ctx [< ("x", ^And (^FT "A") (^FT "A"))]) sone
-        (CasePair One (BV 0) (SN $ FT "B")
+        (^CasePair One (^BV 0) (SN $ ^FT "B")
-          (SY [< "l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
+          (SY [< "l", "r"] $ E $ ^App (^App (^F "f2") (^BVT 1)) (^BVT 0)))
-        (FT "B") [< One],
+        (^FT "B") [< One],
     testTC "x : A × A ⊢ 1 · (caseω x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ ω·x" $
-      inferAsQ (ctx [< ("x", FT "A" `And` FT "A")]) sone
+      inferAsQ (ctx [< ("x", ^And (^FT "A") (^FT "A"))]) sone
-        (CasePair Any (BV 0) (SN $ FT "B")
+        (^CasePair Any (^BV 0) (SN $ ^FT "B")
-          (SY [< "l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
+          (SY [< "l", "r"] $ E $ ^App (^App (^F "f2") (^BVT 1)) (^BVT 0)))
-        (FT "B") [< Any],
+        (^FT "B") [< Any],
     testTC "x : A × A ⊢ 0 · (caseω x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ 0·x" $
-      inferAsQ (ctx [< ("x", FT "A" `And` FT "A")]) szero
+      inferAsQ (ctx [< ("x", ^And (^FT "A") (^FT "A"))]) szero
-        (CasePair Any (BV 0) (SN $ FT "B")
+        (^CasePair Any (^BV 0) (SN $ ^FT "B")
-          (SY [< "l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
+          (SY [< "l", "r"] $ E $ ^App (^App (^F "f2") (^BVT 1)) (^BVT 0)))
-        (FT "B") [< Zero],
+        (^FT "B") [< Zero],
     testTCFail "x : A × A ⊢ 1 · (case0 x return B of (l,r) ⇒ f2 l r) ⇏" $
-      infer_ (ctx [< ("x", FT "A" `And` FT "A")]) sone
+      infer_ (ctx [< ("x", ^And (^FT "A") (^FT "A"))]) sone
-        (CasePair Zero (BV 0) (SN $ FT "B")
+        (^CasePair Zero (^BV 0) (SN $ ^FT "B")
-          (SY [< "l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0])),
+          (SY [< "l", "r"] $ E $ ^App (^App (^F "f2") (^BVT 1)) (^BVT 0))),
     testTC "x : A × B ⊢ 1 · (caseω x return A of (l,r) ⇒ l) ⇒ A ⊳ ω·x" $
-      inferAsQ (ctx [< ("x", FT "A" `And` FT "B")]) sone
+      inferAsQ (ctx [< ("x", ^And (^FT "A") (^FT "B"))]) sone
-        (CasePair Any (BV 0) (SN $ FT "A")
+        (^CasePair Any (^BV 0) (SN $ ^FT "A")
-          (SY [< "l", "r"] $ BVT 1))
+          (SY [< "l", "r"] $ ^BVT 1))
-        (FT "A") [< Any],
+        (^FT "A") [< Any],
     testTC "x : A × B ⊢ 0 · (case1 x return A of (l,r) ⇒ l) ⇒ A ⊳ 0·x" $
-      inferAsQ (ctx [< ("x", FT "A" `And` FT "B")]) szero
+      inferAsQ (ctx [< ("x", ^And (^FT "A") (^FT "B"))]) szero
-        (CasePair One (BV 0) (SN $ FT "A")
+        (^CasePair One (^BV 0) (SN $ ^FT "A")
-          (SY [< "l", "r"] $ BVT 1))
+          (SY [< "l", "r"] $ ^BVT 1))
-        (FT "A") [< Zero],
+        (^FT "A") [< Zero],
     testTCFail "x : A × B ⊢ 1 · (case1 x return A of (l,r) ⇒ l) ⇏" $
-      infer_ (ctx [< ("x", FT "A" `And` FT "B")]) sone
+      infer_ (ctx [< ("x", ^And (^FT "A") (^FT "B"))]) sone
-        (CasePair One (BV 0) (SN $ FT "A")
+        (^CasePair One (^BV 0) (SN $ ^FT "A")
-          (SY [< "l", "r"] $ BVT 1)),
+          (SY [< "l", "r"] $ ^BVT 1)),
     note "fst : (0·A : ★₁) → (0·B : A ↠ ★₁) → ((x : A) × B x) ↠ A",
     note "    ≔ (λ A B p ⇒ caseω p return A of (x, y) ⇒ x)",
     testTC "0 · ‹type of fst› ⇐ ★₂" $
-      check_ empty szero fstTy (TYPE 2),
+      check_ empty szero fstTy (^TYPE 2),
     testTC "1 · ‹def of fst› ⇐ ‹type of fst›" $
       check_ empty sone fstDef fstTy,
     note "snd : (0·A : ★₁) → (0·B : A ↠ ★₁) → (ω·p : (x : A) × B x) → B (fst A B p)",
     note "    ≔ (λ A B p ⇒ caseω p return p ⇒ B (fst A B p) of (x, y) ⇒ y)",
     testTC "0 · ‹type of snd› ⇐ ★₂" $
-      check_ empty szero sndTy (TYPE 2),
+      check_ empty szero sndTy (^TYPE 2),
     testTC "1 · ‹def of snd› ⇐ ‹type of snd›" $
       check_ empty sone sndDef sndTy,
     testTC "0 · snd ★₀ (λ x ⇒ x) ⇒ (ω·p : (A : ★₀) × A) → fst ★₀ (λ x ⇒ x) p" $
       inferAs empty szero
-        (F "snd" :@@ [TYPE 0, [< "x"] :\\ BVT 0])
+        (^App (^App (^F "snd") (^TYPE 0)) (^LamY "x" (^BVT 0)))
-        (PiY Any "A" (SigY "A" (TYPE 0) $ BVT 0) $
+        (^PiY Any "p" (^SigY "A" (^TYPE 0) (^BVT 0))
-                (E $ F "fst" :@@ [TYPE 0, [< "x"] :\\ BVT 0, BVT 0]))
+          (E $ ^App (^App (^App (^F "fst") (^TYPE 0)) (^LamY "x" (^BVT 0)))
+                    (^BVT 0)))
   ],
 
   "enums" :- [
     testTC "1 · 'a ⇐ {a}" $
-      check_ empty sone (Tag "a") (enum ["a"]),
+      check_ empty sone (^Tag "a") (^enum ["a"]),
     testTC "1 · 'a ⇐ {a, b, c}" $
-      check_ empty sone (Tag "a") (enum ["a", "b", "c"]),
+      check_ empty sone (^Tag "a") (^enum ["a", "b", "c"]),
     testTCFail "1 · 'a ⇍ {b, c}" $
-      check_ empty sone (Tag "a") (enum ["b", "c"]),
+      check_ empty sone (^Tag "a") (^enum ["b", "c"]),
     testTC "0=1 ⊢ 1 · 'a ⇐ {b, c}" $
-      check_ empty01 sone (Tag "a") (enum ["b", "c"])
+      check_ empty01 sone (^Tag "a") (^enum ["b", "c"])
   ],
 
   "enum matching" :- [
     testTC "ω.x : {tt} ⊢ 1 · case1 x return {tt} of { 'tt ⇒ 'tt } ⇒ {tt}" $
-      inferAs (ctx [< ("x", enum ["tt"])]) sone
+      inferAs (ctx [< ("x", ^enum ["tt"])]) sone
-        (CaseEnum One (BV 0) (SN (enum ["tt"])) $
+        (^CaseEnum One (^BV 0) (SN (^enum ["tt"]))
-          singleton "tt" (Tag "tt"))
+          (singleton "tt" (^Tag "tt")))
-        (enum ["tt"]),
+        (^enum ["tt"]),
     testTCFail "ω.x : {tt} ⊢ 1 · case1 x return {tt} of { 'ff ⇒ 'tt } ⇏" $
-      infer_ (ctx [< ("x", enum ["tt"])]) sone
+      infer_ (ctx [< ("x", ^enum ["tt"])]) sone
-        (CaseEnum One (BV 0) (SN (enum ["tt"])) $
+        (^CaseEnum One (^BV 0) (SN (^enum ["tt"]))
-          singleton "ff" (Tag "tt"))
+          (singleton "ff" (^Tag "tt")))
   ],
 
   "equality types" :- [
     testTC "0 · ℕ ≡ ℕ : ★₀ ⇐ Type" $
-      checkType_ empty (Eq0 (TYPE 0) Nat Nat) Nothing,
+      checkType_ empty (^Eq0 (^TYPE 0) nat nat) Nothing,
     testTC "0 · ℕ ≡ ℕ : ★₀ ⇐ ★₁" $
-      check_ empty szero (Eq0 (TYPE 0) Nat Nat) (TYPE 1),
+      check_ empty szero (^Eq0 (^TYPE 0) nat nat) (^TYPE 1),
     testTCFail "1 · ℕ ≡ ℕ : ★₀ ⇍ ★₁" $
-      check_ empty sone (Eq0 (TYPE 0) Nat Nat) (TYPE 1),
+      check_ empty sone (^Eq0 (^TYPE 0) nat nat) (^TYPE 1),
     testTC "0 · ℕ ≡ ℕ : ★₀ ⇐ ★₂" $
-      check_ empty szero (Eq0 (TYPE 0) Nat Nat) (TYPE 2),
+      check_ empty szero (^Eq0 (^TYPE 0) nat nat) (^TYPE 2),
     testTC "0 · ℕ ≡ ℕ : ★₁ ⇐ ★₂" $
-      check_ empty szero (Eq0 (TYPE 1) Nat Nat) (TYPE 2),
+      check_ empty szero (^Eq0 (^TYPE 1) nat nat) (^TYPE 2),
     testTCFail "0 · ℕ ≡ ℕ : ★₁ ⇍ ★₁" $
-      check_ empty szero (Eq0 (TYPE 1) Nat Nat) (TYPE 1),
+      check_ empty szero (^Eq0 (^TYPE 1) nat nat) (^TYPE 1),
     testTCFail "0 ≡ 'beep : {beep} ⇍ Type" $
-      checkType_ empty (Eq0 (enum ["beep"]) Zero (Tag "beep")) Nothing,
+      checkType_ empty
+        (^Eq0 (^enum ["beep"]) (^Zero) (^Tag "beep"))
+        Nothing,
     testTC "ab : A ≡ B : ★₀, x : A, y : B ⊢ 0 · Eq [i ⇒ ab i] x y ⇐ ★₀" $
-      check_ (ctx [< ("ab", Eq0 (TYPE 0) (FT "A") (FT "B")),
+      check_ (ctx [< ("ab", ^Eq0 (^TYPE 0) (^FT "A") (^FT "B")),
-                     ("x", FT "A"), ("y", FT "B")]) szero
+                     ("x", ^FT "A"), ("y", ^FT "B")]) szero
-        (Eq (SY [< "i"] $ E $ BV 2 :% BV 0) (BVT 1) (BVT 0))
+        (^EqY "i" (E $ ^DApp (^BV 2) (^BV 0)) (^BVT 1) (^BVT 0))
-        (TYPE 0),
+        (^TYPE 0),
     testTCFail "ab : A ≡ B : ★₀, x : A, y : B ⊢ Eq [i ⇒ ab i] y x ⇍ Type" $
-      checkType_ (ctx [< ("ab", Eq0 (TYPE 0) (FT "A") (FT "B")),
+      check_ (ctx [< ("ab", ^Eq0 (^TYPE 0) (^FT "A") (^FT "B")),
-                         ("x", FT "A"), ("y", FT "B")])
+                     ("x", ^FT "A"), ("y", ^FT "B")]) szero
-        (Eq (SY [< "i"] $ E $ BV 2 :% BV 0) (BVT 0) (BVT 1))
+        (^EqY "i" (E $ ^DApp (^BV 2) (^BV 0)) (^BVT 0) (^BVT 1))
-        Nothing
+        (^TYPE 0)
   ],
 
   "equalities" :- [
     testTC "1 · (δ i ⇒ a) ⇐ a ≡ a" $
-      check_ empty sone (DLam $ SN $ FT "a")
+      check_ empty sone (^DLamN (^FT "a"))
-        (Eq0 (FT "A") (FT "a") (FT "a")),
+        (^Eq0 (^FT "A") (^FT "a") (^FT "a")),
-    testTC "0 · (λ p q ⇒ δ i ⇒ p) ⇐ (ω·p q : a ≡ a') → p ≡ q" $
+    testTC "0 · (λ p q ⇒ δ i ⇒ p) ⇐ (ω·p q : a ≡ a') → p ≡ q  # uip" $
       check_ empty szero
-        ([< "p","q"] :\\ [< "i"] :\\% BVT 1)
+        (^LamY "p" (^LamY "q" (^DLamN (^BVT 1))))
-        (PiY Any "p" (Eq0 (FT "A") (FT "a") (FT "a")) $
+        (^PiY Any "p" (^Eq0 (^FT "A") (^FT "a") (^FT "a"))
-         PiY Any "q" (Eq0 (FT "A") (FT "a") (FT "a")) $
+          (^PiY Any "q" (^Eq0 (^FT "A") (^FT "a") (^FT "a"))
-         Eq0 (Eq0 (FT "A") (FT "a") (FT "a")) (BVT 1) (BVT 0)),
+            (^Eq0 (^Eq0 (^FT "A") (^FT "a") (^FT "a")) (^BVT 1) (^BVT 0)))),
-    testTC "0 · (λ p q ⇒ δ i ⇒ q) ⇐ (ω·p q : a ≡ a') → p ≡ q" $
+    testTC "0 · (λ p q ⇒ δ i ⇒ q) ⇐ (ω·p q : a ≡ a') → p ≡ q  # uip(2)" $
       check_ empty szero
-        ([< "p","q"] :\\ [< "i"] :\\% BVT 0)
+        (^LamY "p" (^LamY "q" (^DLamN (^BVT 0))))
-        (PiY Any "p" (Eq0 (FT "A") (FT "a") (FT "a")) $
+        (^PiY Any "p" (^Eq0 (^FT "A") (^FT "a") (^FT "a"))
-         PiY Any "q" (Eq0 (FT "A") (FT "a") (FT "a")) $
+          (^PiY Any "q" (^Eq0 (^FT "A") (^FT "a") (^FT "a"))
-         Eq0 (Eq0 (FT "A") (FT "a") (FT "a")) (BVT 1) (BVT 0))
+            (^Eq0 (^Eq0 (^FT "A") (^FT "a") (^FT "a")) (^BVT 1) (^BVT 0))))
   ],
 
   "natural numbers" :- [
-    testTC "0 · ℕ ⇐ ★₀" $ check_ empty szero Nat (TYPE 0),
+    testTC "0 · ℕ ⇐ ★₀" $ check_ empty szero nat (^TYPE 0),
-    testTC "0 · ℕ ⇐ ★₇" $ check_ empty szero Nat (TYPE 7),
+    testTC "0 · ℕ ⇐ ★₇" $ check_ empty szero nat (^TYPE 7),
-    testTCFail "1 · ℕ ⇍ ★₀" $ check_ empty sone Nat (TYPE 0),
+    testTCFail "1 · ℕ ⇍ ★₀" $ check_ empty sone nat (^TYPE 0),
-    testTC "1 · zero ⇐ ℕ" $ check_ empty sone Zero Nat,
+    testTC "1 · zero ⇐ ℕ" $ check_ empty sone (^Zero) nat,
-    testTCFail "1 · zero ⇍ ℕ×ℕ" $ check_ empty sone Zero (Nat `And` Nat),
+    testTCFail "1 · zero ⇍ ℕ×ℕ" $ check_ empty sone (^Zero) (^And nat nat),
     testTC "ω·n : ℕ ⊢ 1 · succ n ⇐ ℕ" $
-      check_ (ctx [< ("n", Nat)]) sone (Succ (BVT 0)) Nat,
+      check_ (ctx [< ("n", nat)]) sone (^Succ (^BVT 0)) nat,
     testTC "1 · λ n ⇒ succ n ⇐ 1.ℕ → ℕ" $
-      check_ empty sone ([< "n"] :\\ Succ (BVT 0)) (Arr One Nat Nat),
+      check_ empty sone
-    todo "nat elim"
+        (^LamY "n" (^Succ (^BVT 0)))
+        (^Arr One nat nat)
   ],
 
   "natural elim" :- [
@@ -459,25 +482,28 @@ tests = "typechecker" :- [
     note "    ⇐ 1.ℕ → ℕ",
     testTC "pred" $
       check_ empty sone
-        ([< "n"] :\\ E (CaseNat One Zero (BV 0) (SN Nat)
+        (^LamY "n" (E $
-            Zero (SY [< "n", Unused] $ BVT 1)))
+          ^CaseNat One Zero (^BV 0) (SN nat)
-        (Arr One Nat Nat),
+            (^Zero) (SY [< "n", ^BN Unused] $ ^BVT 1)))
+        (^Arr One nat nat),
     note "1 · λ m n ⇒ case1 m return ℕ of { zero ⇒ n; succ _, 1.p ⇒ succ p }",
     note "    ⇐ 1.ℕ → 1.ℕ → 1.ℕ",
     testTC "plus" $
       check_ empty sone
-        ([< "m", "n"] :\\ E (CaseNat One One (BV 1) (SN Nat)
+        (^LamY "m" (^LamY "n" (E $
-          (BVT 0) (SY [< Unused, "p"] $ Succ $ BVT 0)))
+          ^CaseNat One One (^BV 1) (SN nat)
-        (Arr One Nat $ Arr One Nat Nat)
+            (^BVT 0)
+            (SY [< ^BN Unused, "p"] $ ^Succ (^BVT 0)))))
+        (^Arr One nat (^Arr One nat nat))
   ],
 
   "box types" :- [
     testTC "0 · [0.ℕ] ⇐ ★₀" $
-      check_ empty szero (BOX Zero Nat) (TYPE 0),
+      check_ empty szero (^BOX Zero nat) (^TYPE 0),
     testTC "0 · [0.★₀] ⇐ ★₁" $
-      check_ empty szero (BOX Zero (TYPE 0)) (TYPE 1),
+      check_ empty szero (^BOX Zero (^TYPE 0)) (^TYPE 1),
     testTCFail "0 · [0.★₀] ⇍ ★₀" $
-      check_ empty szero (BOX Zero (TYPE 0)) (TYPE 0)
+      check_ empty szero (^BOX Zero (^TYPE 0)) (^TYPE 0)
   ],
 
   todo "box values",
@@ -486,10 +512,14 @@ tests = "typechecker" :- [
   "type-case" :- [
     testTC "0 · type-case ℕ ∷ ★₀ return ★₀ of { _ ⇒ ℕ } ⇒ ★₀" $
       inferAs empty szero
-        (TypeCase (Nat :# TYPE 0) (TYPE 0) empty Nat)
+        (^TypeCase (^Ann nat (^TYPE 0)) (^TYPE 0) empty nat)
-        (TYPE 0)
+        (^TYPE 0)
   ],
 
+  todo "add the examples dir to the tests"
+]
+
+{-
   "misc" :- [
     note "0·A : Type, 0·P : A → Type, ω·p : (1·x : A) → P x",
     note "⊢",
@@ -524,4 +554,4 @@ tests = "typechecker" :- [
     --     return A
     --     of { }
   ]
-]
+-}

tests/quox-tests.ipkg

@@ -5,6 +5,7 @@ depends = base, contrib, elab-util, snocvect, quox-lib, tap, eff
 executable = quox-tests
 main = Tests
 modules =
+  AstExtra,
   TypingImpls,
   PrettyExtra,
   Tests.DimEq,