[Haskell-beginners] Functors in Haskell

Dimitri DeFigueiredo defigueiredo at ucdavis.edu
Tue Apr 29 19:05:13 UTC 2014

Wow, this makes it very clear!

So, the object mapping is provided by the type constructor and the arrow 
mapping by fmap.

Thanks :-)

Em 29/04/14 12:35, Rein Henrichs escreveu:
> Yes, this is reasonable, but it might be useful to be a bit more 
> explicit about the categories involved.
> An instance of Functor is a functor which maps objects and arrows in 
> the category of Hask (of Haskell types and functions) to... objects 
> and arrows in the category of Hask. It is an endofunctor. The object 
> mapping must map a type to a type and therefore must have the kind * 
> -> *. This means that it is a type constructor, e.g., Maybe. The arrow 
> mapping must map arrows to arrows, which means it must map functions 
> to functions. fmap provides this mapping and the Functor laws in 
> Haskell are of course equivalent to the laws from category theory.
> And while the inclusion of bottom is problematic for Hask, it is still 
> possible to reason about it in a "morally correct" way 
> (http://www.cse.chalmers.se/~nad/publications/danielsson-et-al-popl2006.pdf 
> <http://www.cse.chalmers.se/%7Enad/publications/danielsson-et-al-popl2006.pdf>).
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