rhi/quox
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allow multiple names in a binder

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e.g. "(x y : ℕ) × plus x y ≡ 10 : ℕ"

fixes #2
This commit is contained in:
rhiannon morris 2023-04-19 21:36:57 +02:00
parent b4a8438434
commit 3f06e8d68b
8 changed files with 49 additions and 50 deletions
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4
examples/bool.quox
View file

@ -21,8 +21,8 @@ def true-not-false : Not ('true ≡ 'false : Bool) =
-- [todo] infix
def and : ω.Bool → ω.Bool → Bool = λ a b ⇒ if Bool a b 'false;
def or : ω.Bool → ω.Bool → Bool = λ a b ⇒ if Bool a 'true b;
def and : 1.Bool → ω.Bool → Bool = λ a b ⇒ if Bool a b 'false;
def or : 1.Bool → ω.Bool → Bool = λ a b ⇒ if Bool a 'true b;
}

12
examples/either.quox
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@ -5,21 +5,20 @@ namespace either {
def0 Tag : ★₀ = {left, right};
def0 Payload : 0.(A : ★₀) → 0.(B : ★₀) → 1.Tag → ★₀ =
def0 Payload : 0.★₀ → 0.★₀ → 1.Tag → ★₀ =
λ A B tag ⇒ case1 tag return ★₀ of { 'left ⇒ A; 'right ⇒ B };
def0 Either : 0.★₀ → 0.★₀ → ★₀ =
λ A B ⇒ (tag : Tag) × Payload A B tag;
def Left : 0.(A : ★₀) → 0.(B : ★₀) → 1.A → Either A B =
def Left : 0.(A B : ★₀) → 1.A → Either A B =
λ A B x ⇒ ('left, x);
def Right : 0.(A : ★₀) → 0.(B : ★₀) → 1.B → Either A B =
def Right : 0.(A B : ★₀) → 1.B → Either A B =
λ A B x ⇒ ('right, x);
def elim' :
0.(A : ★₀) → 0.(B : ★₀) →
0.(P : 0.(Either A B) → ★₀) →
0.(A B : ★₀) → 0.(P : 0.(Either A B) → ★₀) →
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) =
@ -29,8 +28,7 @@ def elim' :
of { 'left ⇒ f; 'right ⇒ g };
def elim :
0.(A : ★₀) → 0.(B : ★₀) →
0.(P : 0.(Either A B) → ★₀) →
0.(A B : ★₀) → 0.(P : 0.(Either A B) → ★₀) →
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 =

19
examples/list.quox
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@ -18,20 +18,19 @@ def nil : 0.(A : ★₀) → List A =
def cons : 0.(A : ★₀) → 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 : ★₀) → 0.(B : ★₀) →
def foldr' : 0.(A B : ★₀) →
1.B → ω.(1.A → 1.B → B) → 1.(n : ℕ) → 1.(Vec n A) → B =
λ A B z c n ⇒
case1 n return n' ⇒ 1.(Vec n' A) → B of {
zero ⇒
λ nil ⇒ case1 nil return B of { 'nil ⇒ z };
succ n, 1.ih ⇒
λ cons ⇒ case1 cons return B of { (first, rest) ⇒ c first (ih rest) }
};
case1 n return n' ⇒ 1.(Vec n' A) → B of {
zero ⇒
λ nil ⇒ case1 nil return B of { 'nil ⇒ z };
succ n, 1.ih ⇒
λ cons ⇒ case1 cons return B of { (first, rest) ⇒ c first (ih rest) }
};
def foldr : 0.(A : ★₀) → 0.(B : ★₀) →
1.B → ω.(1.A → 1.B → B) → 1.(List A) → B =
def foldr : 0.(A B : ★₀) → 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 };
case1 xs return B of { (len, elems) ⇒ foldr' A B z c len elems };
def sum : 1.(List ℕ) → ℕ = foldr ℕ ℕ 0 nat.plus;

17
examples/misc.quox
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@ -12,10 +12,8 @@ def0 All : 0.(A : ★₀) → 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.(x : A) → 0.(y : A) → 1.(xy : x ≡ y : A) →
Eq [𝑖 ⇒ P (xy @𝑖)] (p x) (p y) =
0.(A : ★₀) → 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 :
@ -25,17 +23,14 @@ def0 eq-f :
λ A P p q x ⇒ p x ≡ q x : P x;
def funext :
0.(A : ★₀) → 0.(P : Pred A) →
0.(p : All A P) → 0.(q : All A P) →
1.(All A (eq-f A P p q)) →
p ≡ q : All A P =
0.(A : ★₀) → 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 : A) → 0.(y : A) →
1.(x ≡ y : A) → y ≡ x : A =
def sym : 0.(A : ★₀) → 0.(x y : A) → 1.(x ≡ y : A) → y ≡ x : A =
λ A x y eq ⇒ δ 𝑖 ⇒ comp [A] @0 @1 (eq @0) @𝑖 { 0 𝑗 ⇒ eq @𝑗; 1 _ ⇒ eq @0 };
def trans : 0.(A : ★₀) → 0.(x : A) → 0.(y : A) → 0.(z : 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 };

7
examples/nat.quox
View file

@ -33,8 +33,7 @@ def pred : 1.ℕ → ℕ = λ n ⇒ case1 n return ℕ of { zero ⇒ zero; succ
def pred-succ : ω.(n : ℕ) → pred (succ n) ≡ n : ℕ =
λ n ⇒ δ 𝑖 ⇒ n;
def0 succ-inj : 0.(m : ℕ) → 0.(n : ℕ) →
0.(succ m ≡ succ n : ℕ) → m ≡ n : ℕ =
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);
@ -94,14 +93,14 @@ def0 plus-zero : 0.(m : ℕ) → m ≡ plus m 0 : ℕ =
succ _, ω.ih ⇒ δ 𝑖 ⇒ succ (ih @𝑖)
};
def0 plus-succ : 0.(m : ℕ) → 0.(n : ℕ) → succ (plus m n) ≡ plus m (succ n) : ℕ =
def0 plus-succ : 0.(m n : ℕ) → succ (plus m n) ≡ plus m (succ n) : ℕ =
λ m n ⇒
caseω m return m' ⇒ succ (plus m' n) ≡ plus m' (succ n) : ℕ of {
zero ⇒ δ _ ⇒ succ n;
succ _, ω.ih ⇒ δ 𝑖 ⇒ succ (ih @𝑖)
};
def0 plus-comm : 0.(m : ℕ) → 0.(n : ℕ) → plus m n ≡ plus n m : ℕ =
def0 plus-comm : 0.(m n : ℕ) → plus m n ≡ plus n m : ℕ =
λ m n ⇒
caseω m return m' ⇒ plus m' n ≡ plus n m' : ℕ of {
zero ⇒ plus-zero n;

23
examples/pair.quox
View file

@ -2,12 +2,10 @@ namespace pair {
def0 Σ : 0.(A : ★₀) → 0.(0.A → ★₀) → ★₀ = 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) → 0.(B : 0.A → ★₀) → 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) → 0.(B : 0.A → ★₀) → 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 :
@ -17,11 +15,19 @@ def uncurry :
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 =
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) →
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 =
λ A B C ⇒ curry A (λ _ ⇒ B) (λ _ ⇒ C);
def0 fst-snd :
0.(A : ★₀) → 0.(B : 0.A → ★₀) →
1.(p : Σ A B) → p ≡ (fst A B p, snd A B p) : Σ A B =
@ -31,18 +37,15 @@ def0 fst-snd :
of { (x, y) ⇒ δ 𝑖 ⇒ (x, y) };
def map :
0.(A : ★₀) → 0.(A' : ★₀) →
0.(A A' : ★₀) →
0.(B : 0.A → ★₀) → 0.(B' : 0.A' → ★₀) →
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 : ★₀) → 0.(A' : ★₀) →
0.(B : ★₀) → 0.(B' : ★₀) →
1.(f : 1.A → A') → 1.(g : 1.B → B') →
1.(A × B) → A' × B' =
def map' : 0.(A A' B B' : ★₀) →
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);
}

13
lib/Quox/Parser/Parser.idr
View file

@ -242,19 +242,20 @@ mutual
bindTerm : Grammar True PTerm
bindTerm = pi <|> sigma
where
binderHead = parens {commit = False} [|MkPair bname (resC ":" *> term)|]
binderHead =
parens {commit = False} [|MkPair (some bname) (resC ":" *> term)|]
pi, sigma : Grammar True PTerm
pi = [|makePi (qty <* res ".") domain (resC "→" *> term)|]
where
makePi : Qty -> (BName, PTerm) -> PTerm -> PTerm
makePi q (x, s) t = Pi q x s t
domain = binderHead <|> [|(Nothing,) aTerm|]
makePi : Qty -> (List1 BName, PTerm) -> PTerm -> PTerm
makePi q (xs, s) t = foldr (\x => Pi q x s) t xs
domain = binderHead <|> [|(Nothing ::: [],) aTerm|]
sigma = [|makeSigma binderHead (resC "×" *> annTerm)|]
where
makeSigma : (BName, PTerm) -> PTerm -> PTerm
makeSigma (x, s) t = Sig x s t
makeSigma : (List1 BName, PTerm) -> PTerm -> PTerm
makeSigma (xs, s) t = foldr (\x => Sig x s) t xs
private covering
annTerm : Grammar True PTerm

4
tests/Tests/Parser.idr
View file

@ -148,6 +148,8 @@ tests = "parser" :- [
Pi Any (Just "x") (V "A") (V "B" :@ V "x"),
parsesAs term "#.(x : A) -> B x" $
Pi Any (Just "x") (V "A") (V "B" :@ V "x"),
parsesAs term "1.(x y : A) -> B x" $
Pi One (Just "x") (V "A") $ Pi One (Just "y") (V "A") (V "B" :@ V "x"),
parseFails term "(x : A) → B x",
parsesAs term "1.A → B"
(Pi One Nothing (V "A") (V "B")),
@ -158,6 +160,8 @@ tests = "parser" :- [
Sig (Just "x") (V "A") (V "B" :@ V "x"),
parsesAs term "(x : A) ** B x" $
Sig (Just "x") (V "A") (V "B" :@ V "x"),
parsesAs term "(x y : A) × B x" $
Sig (Just "x") (V "A") $ Sig (Just "y") (V "A") (V "B" :@ V "x"),
parseFails term "1.(x : A) × B x",
parsesAs term "A × B" $
Sig Nothing (V "A") (V "B"),