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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,11 +1,23 @@ | ||
| ( | ||
| (fun (Pair : forall (A : Type@0) (B : Type@0) -> Type@1) | ||
| (fst : forall (A : Type@0) (B : Type@0) (p : Pair A B) -> A) | ||
| (snd : forall (A : Type@0) (B : Type@0) (p : Pair A B) -> B) | ||
| (p : Pair Nat (forall (x : Nat) -> Nat)) -> | ||
| snd Nat (forall (x : Nat) -> Nat) p (fst Nat (forall (x : Nat) -> Nat) p)) | ||
| (fun (A : Type@0) (B : Type@0) -> forall (C : Type@0) (cons : forall (a : A) (b : B) -> C) -> C) | ||
| (fun (A : Type@0) (B : Type@0) (p : forall (C : Type@0) (cons : forall (a : A) (b : B) -> C) -> C) -> p A (fun (a : A) (b : B) -> a)) | ||
| (fun (A : Type@0) (B : Type@0) (p : forall (C : Type@0) (cons : forall (a : A) (b : B) -> C) -> C) -> p B (fun (a : A) (b : B) -> b)) | ||
| (fun (C : Type@0) (cons : forall (a : Nat) (b : forall (x : Nat) -> Nat) -> C) -> cons 3 (fun (x : Nat) -> succ x)) | ||
| (* Main example *) | ||
| ( | ||
| fun (Pair : forall (A : Type@0) (B : Type@0) -> Type@1) | ||
| (pair : forall (A : Type@0) (B : Type@0) (a : A) (b : B) -> Pair A B) | ||
| (fst : forall (A : Type@0) (B : Type@0) (p : Pair A B) -> A) | ||
| (snd : forall (A : Type@0) (B : Type@0) (p : Pair A B) -> B) -> | ||
| ( | ||
| fun (p : Pair Nat (forall (x : Nat) -> Nat)) -> | ||
| snd Nat (forall (x : Nat) -> Nat) p | ||
| (fst Nat (forall (x : Nat) -> Nat) p) | ||
| ) | ||
| (pair Nat (forall (x : Nat) -> Nat) 3 (fun (x : Nat) -> succ (succ x))) | ||
| ) | ||
| (* Church pair *) | ||
| (fun (A : Type@0) (B : Type@0) -> forall (C : Type@0) (pair : forall (a : A) (b : B) -> C) -> C) | ||
| (* Church pair constructor *) | ||
| (fun (A : Type@0) (B : Type@0) (a : A) (b : B) (C : Type@0) (pair : forall (a : A) (b : B) -> C) -> pair a b) | ||
| (* Church pair fst *) | ||
| (fun (A : Type@0) (B : Type@0) (p : forall (C : Type@0) (pair : forall (a : A) (b : B) -> C) -> C) -> p A (fun (a : A) (b : B) -> a)) | ||
| (* Church pair snd *) | ||
| (fun (A : Type@0) (B : Type@0) (p : forall (C : Type@0) (pair : forall (a : A) (b : B) -> C) -> C) -> p B (fun (a : A) (b : B) -> b)) | ||
| ) : Nat |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,41 @@ | ||
| ( | ||
| (* Main example *) | ||
| ( | ||
| fun (Vec : forall (A : Type@0) (n : Nat) -> Type@2) | ||
| (nil : forall (A : Type@0) -> Vec A 0) | ||
| (cons : forall (A : Type@0) (n : Nat) (head : A) (tail : Vec A n) -> Vec A (succ n)) | ||
| (vecRec : forall (A : Type@0) (n : Nat) (vec : Vec A n) (C : forall (l : Nat) -> Type@1) (nil : C 0) (cons : forall (l : Nat) (a : A) (r : C l) -> C (succ l)) -> C n) -> | ||
| ( | ||
| fun (totalHead : forall (A : Type@0) (n : Nat) (vec : Vec A (succ n)) -> A) | ||
| (vec : Vec (forall (n : Nat) -> Nat) 3) -> | ||
| totalHead ((forall (n : Nat) -> Nat)) 2 vec 4 | ||
| ) | ||
| (* total head function *) | ||
| ( | ||
| fun (A : Type@0) (n : Nat) (vec : Vec A (succ n)) -> | ||
| vecRec A (succ n) vec (fun (l : Nat) -> rec l return r -> Type@0 | zero => Nat | succ l, r => A end) 0 (fun (l : Nat) (a : A) (r : rec l return r -> Type@0 | zero => Nat | succ l, r => A end) -> a) | ||
| ) | ||
| (* example vector *) | ||
| ( | ||
| cons (forall (n : Nat) -> Nat) 2 | ||
| (fun (n : Nat) -> succ (succ (succ n))) | ||
| ( | ||
| cons (forall (n : Nat) -> Nat) 1 | ||
| (fun (n : Nat) -> succ n) | ||
| ( | ||
| cons (forall (n : Nat) -> Nat) 0 | ||
| (fun (n : Nat) -> succ (succ n)) | ||
| (nil (forall (n : Nat) -> Nat)) | ||
| ) | ||
| ) | ||
| ) | ||
| ) | ||
| (* Church vector *) | ||
| (fun (A : Type@0) (n : Nat) -> forall (C : forall (l : Nat) -> Type@1) (nil : C 0) (cons : forall (l : Nat) (a : A) (r : C l) -> C (succ l)) -> C n) | ||
| (* Church vector nil *) | ||
| (fun (A : Type@0) (C : forall (l : Nat) -> Type@1) (nil : C 0) (cons : forall (l : Nat) (a : A) (r : C l) -> C (succ l)) -> nil) | ||
| (* Church vector cons *) | ||
| (fun (A : Type@0) (n : Nat) (head : A) (tail : forall (C : forall (l : Nat) -> Type@1) (nil : C 0) (cons : forall (l : Nat) (a : A) (r : C l) -> C (succ l)) -> C n) (C : forall (l : Nat) -> Type@1) (nil : C 0) (cons : forall (l : Nat) (a : A) (r : C l) -> C (succ l)) -> cons n head (tail C nil cons)) | ||
| (* Church vector recursor *) | ||
| (fun (A : Type@0) (n : Nat) (vec : forall (C : forall (l : Nat) -> Type@1) (nil : C 0) (cons : forall (l : Nat) (a : A) (r : C l) -> C (succ l)) -> C n) (C : forall (l : Nat) -> Type@1) (nil : C 0) (cons : forall (l : Nat) (a : A) (r : C l) -> C (succ l)) -> vec C nil cons) | ||
| ) : Nat |