30 lines
594 B
Text
30 lines
594 B
Text
import data.nat
|
|
open nat
|
|
|
|
inductive functor (A B : Type) :=
|
|
mk : (A → B) → functor A B
|
|
|
|
definition functor.to_fun [coercion] {A B : Type} (f : functor A B) : A → B :=
|
|
functor.rec (λ f, f) f
|
|
|
|
inductive struct :=
|
|
mk : Π (A : Type), (A → A → Prop) → struct
|
|
|
|
definition struct.to_sort [coercion] (s : struct) : Type :=
|
|
struct.rec (λA r, A) s
|
|
|
|
definition g (f : nat → nat) (a : nat) := f a
|
|
|
|
constant f : functor nat nat
|
|
|
|
check g (functor.to_fun f) 0
|
|
|
|
check g f 0
|
|
|
|
definition id (A : Type) (a : A) := a
|
|
|
|
constant S : struct
|
|
constant a : S
|
|
|
|
check id (struct.to_sort S) a
|
|
check id S a
|