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make 0 in ★₀ optional

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rhiannon morris 2023-05-21 20:33:42 +02:00
parent 7c68cd9098
commit 3bbf0366c8
8 changed files with 56 additions and 56 deletions
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10
examples/bool.quox
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@ -2,19 +2,19 @@ load "misc.quox";
namespace bool {
def0 Bool : ★⁰ = {true, false};
def0 Bool : ★ = {true, false};
def boolω : 1.Bool → [ω.Bool] =
λ b ⇒ case1 b return [ω.Bool] of { 'true ⇒ ['true]; 'false ⇒ ['false] };
def if : 0.(A : ★⁰) → 1.Bool → ω.A → ω.A → A =
def if : 0.(A : ★) → 1.Bool → ω.A → ω.A → A =
λ A b t f ⇒ case1 b return A of { 'true ⇒ t; 'false ⇒ f };
-- [todo]: universe lifting
def0 If : 1.Bool → 0.★⁰ → 0.★⁰ → ★⁰ =
λ b T F ⇒ case1 b return ★⁰ of { 'true ⇒ T; 'false ⇒ F };
def0 If : 1.Bool → 0.★ → 0.★ → ★ =
λ b T F ⇒ case1 b return ★ of { 'true ⇒ T; 'false ⇒ F };
def0 T : ω.Bool → ★⁰ = λ b ⇒ If b True False;
def0 T : ω.Bool → ★ = λ b ⇒ If b True False;
def true-not-false : Not ('true ≡ 'false : Bool) =
λ eq ⇒ coe (i ⇒ T (eq @i)) 'true;

28
examples/either.quox
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@ -3,22 +3,22 @@ load "bool.quox";
namespace either {
def0 Tag : ★⁰ = {left, right};
def0 Tag : ★ = {left, right};
def0 Payload : 0.★⁰ → 0.★⁰ → 1.Tag → ★⁰ =
λ A B tag ⇒ case1 tag return ★⁰ of { 'left ⇒ A; 'right ⇒ B };
def0 Payload : 0.★ → 0.★ → 1.Tag → ★ =
λ A B tag ⇒ case1 tag return ★ of { 'left ⇒ A; 'right ⇒ B };
def0 Either : 0.★⁰ → 0.★⁰ → ★⁰ =
def0 Either : 0.★ → 0.★ → ★ =
λ A B ⇒ (tag : Tag) × Payload A B tag;
def Left : 0.(A B : ★⁰) → 1.A → Either A B =
def Left : 0.(A B : ★) → 1.A → Either A B =
λ A B x ⇒ ('left, x);
def Right : 0.(A B : ★⁰) → 1.B → Either A B =
def Right : 0.(A B : ★) → 1.B → Either A B =
λ A B x ⇒ ('right, x);
def elim' :
0.(A B : ★⁰) → 0.(P : 0.(Either A B) → ★⁰) →
0.(A B : ★) → 0.(P : 0.(Either A B) → ★) →
ω.(1.(x : A) → P (Left A B x)) →
ω.(1.(x : B) → P (Right A B x)) →
1.(t : Tag) → 1.(a : Payload A B t) → P (t, a) =
@ -28,7 +28,7 @@ def elim' :
of { 'left ⇒ f; 'right ⇒ g };
def elim :
0.(A B : ★⁰) → 0.(P : 0.(Either A B) → ★⁰) →
0.(A B : ★) → 0.(P : 0.(Either A B) → ★) →
ω.(1.(x : A) → P (Left A B x)) →
ω.(1.(x : B) → P (Right A B x)) →
1.(x : Either A B) → P x =
@ -45,16 +45,16 @@ def Right = either.Right;
namespace dec {
def0 Dec : 0.★⁰ → ★⁰ = λ A ⇒ Either [0.A] [0.Not A];
def0 Dec : 0.★ → ★ = λ A ⇒ Either [0.A] [0.Not A];
def Yes : 0.(A : ★⁰) → 0.A → Dec A = λ A y ⇒ Left [0.A] [0.Not A] [y];
def No : 0.(A : ★⁰) → 0.(Not A) → Dec A = λ A n ⇒ Right [0.A] [0.Not A] [n];
def Yes : 0.(A : ★) → 0.A → Dec A = λ A y ⇒ Left [0.A] [0.Not A] [y];
def No : 0.(A : ★) → 0.(Not A) → Dec A = λ A n ⇒ Right [0.A] [0.Not A] [n];
def0 DecEq : 0.★⁰ → ★⁰ =
def0 DecEq : 0.★ → ★ =
λ A ⇒ ω.(x : A) → ω.(y : A) → Dec (x ≡ y : A);
def elim :
0.(A : ★⁰) → 0.(P : 0.(Dec A) → ★⁰) →
0.(A : ★) → 0.(P : 0.(Dec A) → ★) →
ω.(0.(y : A) → P (Yes A y)) →
ω.(0.(n : Not A) → P (No A n)) →
1.(x : Dec A) → P x =
@ -63,7 +63,7 @@ def elim :
(λ y ⇒ case0 y return y' ⇒ P (Left [0.A] [0.Not A] y') of {[y'] ⇒ f y'})
(λ n ⇒ case0 n return n' ⇒ P (Right [0.A] [0.Not A] n') of {[n'] ⇒ g n'});
def bool : 0.(A : ★⁰) → 1.(Dec A) → Bool =
def bool : 0.(A : ★) → 1.(Dec A) → Bool =
λ A ⇒ elim A (λ _ ⇒ Bool) (λ _ ⇒ 'true) (λ _ ⇒ 'false);
}

14
examples/list.quox
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@ -2,23 +2,23 @@ load "nat.quox";
namespace list {
def0 Vec : 0.ℕ → 0.★⁰ → ★⁰ =
def0 Vec : 0.ℕ → 0.★ → ★ =
λ n A ⇒
caseω n return ★⁰ of {
caseω n return ★ of {
zero ⇒ {nil};
succ _, 0.Tail ⇒ A × Tail
};
def0 List : 0.★⁰ → ★⁰ =
def0 List : 0.★ → ★ =
λ A ⇒ (len : ℕ) × Vec len A;
def nil : 0.(A : ★⁰) → List A =
def nil : 0.(A : ★) → List A =
λ A ⇒ (0, 'nil);
def cons : 0.(A : ★⁰) → 1.A → 1.(List A) → List A =
def cons : 0.(A : ★) → 1.A → 1.(List A) → List A =
λ A x xs ⇒ case1 xs return List A of { (len, elems) ⇒ (succ len, x, elems) };
def foldr' : 0.(A B : ★⁰) →
def foldr' : 0.(A B : ★) →
1.B → ω.(1.A → 1.B → B) → 1.(n : ℕ) → 1.(Vec n A) → B =
λ A B z c n ⇒
case1 n return n' ⇒ 1.(Vec n' A) → B of {
@ -28,7 +28,7 @@ def foldr' : 0.(A B : ★⁰) →
λ cons ⇒ case1 cons return B of { (first, rest) ⇒ c first (ih rest) }
};
def foldr : 0.(A B : ★⁰) → 1.B → ω.(1.A → 1.B → B) → 1.(List A) → B =
def foldr : 0.(A B : ★) → 1.B → ω.(1.A → 1.B → B) → 1.(List A) → B =
λ A B z c xs ⇒
case1 xs return B of { (len, elems) ⇒ foldr' A B z c len elems };

24
examples/misc.quox
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@ -1,36 +1,36 @@
def0 True : ★⁰ = {true};
def0 True : ★ = {true};
def0 False : ★⁰ = {};
def0 Not : 0.★⁰ → ★⁰ = λ A ⇒ ω.A → False;
def0 False : ★ = {};
def0 Not : 0.★ → ★ = λ A ⇒ ω.A → False;
def void : 0.(A : ★⁰) → 0.False → A =
def void : 0.(A : ★) → 0.False → A =
λ A v ⇒ case0 v return A of { };
def0 Pred : 0.★⁰ → ★¹ = λ A ⇒ 0.A → ★⁰;
def0 Pred : 0.★ → ★¹ = λ A ⇒ 0.A → ★;
def0 All : 0.(A : ★⁰) → 0.(Pred A) → ★¹ =
def0 All : 0.(A : ★) → 0.(Pred A) → ★¹ =
λ A P ⇒ 1.(x : A) → P x;
def cong :
0.(A : ★⁰) → 0.(P : Pred A) → 1.(p : All A P) →
0.(A : ★) → 0.(P : Pred A) → 1.(p : All A P) →
0.(x y : A) → 1.(xy : x ≡ y : A) → Eq (𝑖 ⇒ P (xy @𝑖)) (p x) (p y) =
λ A P p x y xy ⇒ δ 𝑖 ⇒ p (xy @𝑖);
def0 eq-f :
0.(A : ★⁰) → 0.(P : Pred A) →
0.(A : ★) → 0.(P : Pred A) →
0.(p : All A P) → 0.(q : All A P) →
0.A → ★⁰ =
0.A → ★ =
λ A P p q x ⇒ p x ≡ q x : P x;
def funext :
0.(A : ★⁰) → 0.(P : Pred A) → 0.(p q : All A P) →
0.(A : ★) → 0.(P : Pred A) → 0.(p q : All A P) →
1.(All A (eq-f A P p q)) → p ≡ q : All A P =
λ A P p q eq ⇒ δ 𝑖 ⇒ λ x ⇒ eq x @𝑖;
def sym : 0.(A : ★⁰) → 0.(x y : A) → 1.(x ≡ y : A) → y ≡ x : A =
def sym : 0.(A : ★) → 0.(x y : A) → 1.(x ≡ y : A) → y ≡ x : A =
λ A x y eq ⇒ δ 𝑖 ⇒ comp A (eq @0) @𝑖 { 0 𝑗 ⇒ eq @𝑗; 1 _ ⇒ eq @0 };
def trans : 0.(A : ★⁰) → 0.(x y z : A) →
def trans : 0.(A : ★) → 0.(x y z : A) →
ω.(x ≡ y : A) → ω.(y ≡ z : A) → x ≡ z : A =
λ A x y z eq1 eq2 ⇒ δ 𝑖 ⇒
comp A (eq1 @𝑖) @𝑖 { 0 _ ⇒ eq1 @0; 1 𝑗 ⇒ eq2 @𝑗 };

4
examples/nat.quox
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@ -37,8 +37,8 @@ def0 succ-inj : 0.(m n : ℕ) → 0.(succ m ≡ succ n : ℕ) → m ≡ n : ℕ
λ m n eq ⇒ δ 𝑖 ⇒ pred (eq @𝑖);
def0 IsSucc : 0.ℕ → ★⁰ =
λ n ⇒ caseω n return ★⁰ of { zero ⇒ False; succ _ ⇒ True };
def0 IsSucc : 0.ℕ → ★ =
λ n ⇒ caseω n return ★ of { zero ⇒ False; succ _ ⇒ True };
def isSucc? : ω.(n : ℕ) → Dec (IsSucc n) =
λ n ⇒

22
examples/pair.quox
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@ -1,35 +1,35 @@
namespace pair {
def0 Σ : 0.(A : ★⁰) → 0.(0.A → ★⁰) → ★⁰ = λ A B ⇒ (x : A) × B x;
def0 Σ : 0.(A : ★) → 0.(0.A → ★) → ★ = λ A B ⇒ (x : A) × B x;
def fst : 0.(A : ★⁰) → 0.(B : 0.A → ★⁰) → ω.(Σ A B) → A =
def fst : 0.(A : ★) → 0.(B : 0.A → ★) → ω.(Σ A B) → A =
λ A B p ⇒ caseω p return A of { (x, _) ⇒ x };
def snd : 0.(A : ★⁰) → 0.(B : 0.A → ★⁰) → ω.(p : Σ A B) → B (fst A B p) =
def snd : 0.(A : ★) → 0.(B : 0.A → ★) → ω.(p : Σ A B) → B (fst A B p) =
λ A B p ⇒ caseω p return p' ⇒ B (fst A B p') of { (_, y) ⇒ y };
def uncurry :
0.(A : ★⁰) → 0.(B : 0.A → ★⁰) → 0.(C : 0.(x : A) → 0.(B x) → ★⁰) →
0.(A : ★) → 0.(B : 0.A → ★) → 0.(C : 0.(x : A) → 0.(B x) → ★) →
1.(f : 1.(x : A) → 1.(y : B x) → C x y) →
1.(p : Σ A B) → C (fst A B p) (snd A B p) =
λ A B C f p ⇒
case1 p return p' ⇒ C (fst A B p') (snd A B p') of { (x, y) ⇒ f x y };
def uncurry' :
0.(A B C : ★⁰) → 1.(1.A → 1.B → C) → 1.(A × B) → C =
0.(A B C : ★) → 1.(1.A → 1.B → C) → 1.(A × B) → C =
λ A B C ⇒ uncurry A (λ _ ⇒ B) (λ _ _ ⇒ C);
def curry :
0.(A : ★⁰) → 0.(B : 0.A → ★⁰) → 0.(C : 0.(Σ A B) → ★⁰) →
0.(A : ★) → 0.(B : 0.A → ★) → 0.(C : 0.(Σ A B) → ★) →
1.(f : 1.(p : Σ A B) → C p) → 1.(x : A) → 1.(y : B x) → C (x, y) =
λ A B C f x y ⇒ f (x, y);
def curry' :
0.(A B C : ★⁰) → 1.(1.(A × B) → C) → 1.A → 1.B → C =
0.(A B C : ★) → 1.(1.(A × B) → C) → 1.A → 1.B → C =
λ A B C ⇒ curry A (λ _ ⇒ B) (λ _ ⇒ C);
def0 fst-snd :
0.(A : ★⁰) → 0.(B : 0.A → ★⁰) →
0.(A : ★) → 0.(B : 0.A → ★) →
1.(p : Σ A B) → p ≡ (fst A B p, snd A B p) : Σ A B =
λ A B p ⇒
case1 p
@ -37,14 +37,14 @@ def0 fst-snd :
of { (x, y) ⇒ δ 𝑖 ⇒ (x, y) };
def map :
0.(A A' : ★⁰) →
0.(B : 0.A → ★⁰) → 0.(B' : 0.A' → ★⁰) →
0.(A A' : ★) →
0.(B : 0.A → ★) → 0.(B' : 0.A' → ★) →
1.(f : 1.A → A') → 1.(g : 0.(x : A) → 1.(B x) → B' (f x)) →
1.(Σ A B) → Σ A' B' =
λ A A' B B' f g p ⇒
case1 p return Σ A' B' of { (x, y) ⇒ (f x, g x y) };
def map' : 0.(A A' B B' : ★⁰) →
def map' : 0.(A A' B B' : ★) →
1.(1.A → A') → 1.(1.B → B') → 1.(A × B) → A' × B' =
λ A A' B B' f g ⇒ map A A' (λ _ ⇒ B) (λ _ ⇒ B') f (λ _ ⇒ g);

6
lib/Quox/Parser/Parser.idr
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@ -274,7 +274,7 @@ tupleTerm fname = withLoc fname $ do
export
universe1 : Grammar True Universe
universe1 = universeTok <|> res "★" *> super
universe1 = universeTok <|> res "★" *> option 0 super
||| argument/atomic term: single-token terms, or those with delimiters e.g.
||| `[t]`
@ -359,8 +359,8 @@ compTerm fname = withLoc fname $ do
export
splitUniverseTerm : FileName -> Grammar True PTerm
splitUniverseTerm fname =
withLoc fname $ resC "★" *> mustWork [|TYPE $ nat <|> super|]
-- having super here looks redundant, but when parsing a non-atomic term
withLoc fname $ resC "★" *> [|TYPE $ option 0 $ nat <|> super|]
-- some of this looks redundant, but when parsing a non-atomic term
-- this branch will be taken first
export

4
tests/Tests/Parser.idr
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@ -116,8 +116,8 @@ tests = "parser" :- [
parseMatch term "Type4" `(TYPE 4 _),
parseMatch term "Type 100" `(TYPE 100 _),
parseMatch term "(Type 1000)" `(TYPE 1000 _),
parseFails term "Type",
parseFails term "★"
parseMatch term "Type" `(TYPE 0 _),
parseMatch term "★" `(TYPE 0 _)
],
"applications" :- [