blob: ae7f746778c7f0d45ad154163072afb4a52058aa (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
|
Generalizable Variables T A.
Inductive path `(a: A): A -> Type := idpath: path a a.
Class TMonad (T: Type -> Type) := {
bind: forall {A B: Type}, (T A) -> (A -> T B) -> T B;
ret: forall {A: Type}, A -> T A;
ret_unit_left: forall {A B: Type} (k: A -> T B) (a: A),
path (bind (ret a) k) (k a)
}.
Let T_fzip `{TMonad T} := fun (A B: Type) (f: T (A -> B)) (t: T A)
=> bind t (fun a => bind f (fun g => ret (g a) )).
Let T_pure `{TMonad T} := @ret _ _.
Let T_pure_id `{TMonad T} {A: Type} (t: A -> A) (x: T A):
path (T_fzip A A (T_pure (A -> A) t) x) x.
unfold T_fzip, T_pure.
Fail rewrite (ret_unit_left (fun g a => ret (g a)) (fun x => x)).
|
