[Haskell-cafe] Functors [Comments from OCaml Hacker Brian Hurt]

[Eugene Kirpichov]

2009/1/17 Andrew Coppin <andrewcoppin at btinternet.com>:
> Eugene Kirpichov wrote:
>>
>> No, a functor is a more wide notion than that, it has nothing to do
>> with collections.
>> An explanation more close to truth would be "A structure is a functor
>> if it provides a way to convert a structure over X to a structure over
>> Y, given a function X -> Y, while preserving the underlying
>> 'structure'", where preserving structure means being compatible with
>> composition and identity.
>>
>
> As far as I'm aware, constraints like "while preserving the underlying
> structure" are not expressible in Haskell.

Yes, but they are expressible in your mind so that you can recognize a
functor and design you program so that it does satisfy this
constraint, thus removing a large faulty piece of the design space.

Also, you can write a QuickCheck test for fmap (f . g) = fmap f . fmap
g and fmap id = id.

>
>> instance (Monad m) => Functor m where
>>  fmap f ma = do a <- ma; return (f a)
>>
>
> While that's quite interesting from a mathematical point of view, how is
> this "useful" for programming purposes?

In the same sense as monoids are, see my previous message.

If you mean the usefulness of a Functor typeclass in Haskell, it's in
the fact that everywhere where you'd like to convert a structure over
X to a structure over Y (for example, the result of a monadic
computation), you simply write 'fmap f structure' and it works the
right way, if the structure has an instance for Functor (many
structures do). I know I'm being a bit abstract, but that's the way I
percept it.

do filename <- toLowerCase `fmap` readLine
    ....

>
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