[Haskell-cafe] Dealing with invertible functions

[Ivan Zakharyaschev]

Le lundi 29 juin 2015 11:19:57 UTC+3, Clinton Mead a écrit :
>
> I was trying to think of a way to deal with invertible functions, say if I 
> want to set up a one-to-one mapping from A<->B without having to maintain 
> two sets of functions (and worry about them getting out of sync).
>
> So I thought about making an "invertible" function. This is a function 
> that knows it's own inverse, and you can compose them and get the inverses 
> for free. Of course you need to set up the base functions manually, but 
> then after that the composed functions don't have to be maintained 
> separately both ways.
>
> Below I'm going to include some code, and I have a few questions:
>
> 1) Am I (badly) reinventing the wheel.
>

Perhaps 
http://hackage.haskell.org/package/TypeCompose-0.9.10/docs/Data-Bijection.html#t::-60--45--62-: 


2) Is there otherwise something terrible with this approach.
> 3) I ended up wanting a function with signature "f a b -> a -> b". This 
> feels strangly like applicative but not exactly. Am I reinventing the wheel 
> here also or should I be doing this differently?
>
> Perhaps, there is an analogue of your function application (for 
bijections, <$>) in Arrow, which is a class of Data.Bijection.Bijection. 
Probably not in Category though. (I've just stumbled upon a similar 
discussion at http://programmers.stackexchange.com/a/215503/11591 ; with 
similar requirements: "There's a common reason why I can't use Applicative 
or Arrow (or Monad) - I can't wrap a normal function (in general) because 
values of my type *represent* a function but are *represented* by data, and 
won't support arbitrary functions if if there was a way to translate." You, 
too, can't inject an arbitrary function because you have to manually write 
the inverse.)

class KindaApplicative f where
>   (<$>) :: f a b -> a -> b
>
> instance KindaApplicative InvertibleFunction where
>   (InvertibleFunction f _) <$> x = f x
>


Best wishes,
Ivan Z. 
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