[Agda] Fin n -> Fin n extensional?

[Thorsten Altenkirch]

As discussed it is not. However, there is an alternative representation of
(Fin n -> Fin m) which is extensional, namely "Vec (Fin m) n². It is not
hard to define 

	lam : (Fin n -> Fin m) -> Vec (Fin m) n
	app : Vec (Fin m) n -> Fin n -> Fin m

but this is only a retract. However, we can prove

	(f g : Vec (Fin m) n) -> ((i : Fin n) -> app f i == app g i) -> f == g

Thorsten

On 18/02/2015 14:25, "Jacques Carette" <carette at mcmaster.ca> wrote:

>Does anyone have a proof in Agda that functions at type (Fin n -> Fin n)
>are extensional?
>Jacques
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