d4f2bb77b8
To make the equation compiler more convenient to use, we will add a couple of preprocessing steps. This commit adds the first one of them. In this step, we use type inference to refine pattern variables, and we relax the restrictions on inaccessible annotations. We will also add a preprocessing step that implements the "complete transition" step before we execute the elim_match step.
58 lines
1.6 KiB
Text
58 lines
1.6 KiB
Text
open nat
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inductive Vec (A : Type) : nat → Type
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| nil {} : Vec 0
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| cons : Π {n}, A → Vec n → Vec (succ n)
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open Vec
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def append1 {A : Type} : Π {m n : nat}, Vec A m -> Vec A n -> Vec A (n + m)
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| _ m nil ys := ys
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| _ m (cons x xs) ys := cons x (append1 xs ys)
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def append2 {A : Type} : Π {m n : nat}, Vec A m -> Vec A n -> Vec A (n + m)
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| _ _ nil ys := ys
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| _ _ (cons x xs) ys := cons x (append2 xs ys)
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def append3 {A : Type} : Π {m n : nat}, Vec A m -> Vec A n -> Vec A (n + m)
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| ._ m nil ys := ys
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| ._ m (cons x xs) ys := cons x (append1 xs ys)
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inductive Fin : nat → Type
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| fzero : Π {n}, Fin (nat.succ n)
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open Fin
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def fmin1 : Π {n : nat} (x y : Fin n), Fin n
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| ._ fzero fzero := fzero
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def fmin2 : Π {n : nat} (x y : Fin n), Fin n
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| _ fzero fzero := fzero
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def fmin3 : Π {n : nat} (x y : Fin n), Fin n
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| n fzero fzero := fzero
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def fmin4 : Π {n : nat} (x y : Fin n), Fin n
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| .(succ n) (@fzero n) (@fzero .(n)) := fzero
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def fmin5 : Π {n : nat} (x y : Fin n), Fin n
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| .(succ n) (@fzero .(n)) (@fzero n) := fzero
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def fmin6 : Π {n : nat} (x y : Fin n), Fin n
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| .(succ _) fzero fzero := fzero
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example (n : nat) (x y : Fin n) : fmin1 x y = fmin2 x y :=
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begin cases x, cases y, refl end
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example (n : nat) (x y : Fin n) : fmin1 x y = fmin3 x y :=
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begin cases x, cases y, refl end
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example (n : nat) (x y : Fin n) : fmin1 x y = fmin4 x y :=
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begin cases x, cases y, refl end
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example (n : nat) (x y : Fin n) : fmin1 x y = fmin5 x y :=
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begin cases x, cases y, refl end
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example (n : nat) (x y : Fin n) : fmin1 x y = fmin6 x y :=
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begin cases x, cases y, refl end
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