[Haskell-cafe] On to applicative

[michael rice]

I'm not sure if my terminology is correct or even if my question makes sense, but I can create "instances" of Maybe, List, IO, and Either.

Prelude Data.Either> let m = Just 7
Prelude Data.Either> :t m
m :: Maybe Integer

Prelude Data.Either> let l = 2:[]
Prelude Data.Either> :t l
l :: [Integer]

Prelude Data.Either> let g = getLine
Prelude Data.Either> :t g
g :: IO String

Prelude Data.Either> let e = Right "abc"
Prelude Data.Either> :t e
e :: Either a [Char]

All these instances are functors, each with its own version of fmap that can be applied to it.

How can I similarly create an instance of (->) so I can apply (->)'s version of fmap

instance Functor ((->) r) where  
    fmap f g = (\x -> f (g x))

to it?

Michael

--- On Tue, 8/31/10, Vo Minh Thu <noteed at gmail.com> wrote:

From: Vo Minh Thu <noteed at gmail.com>
Subject: Re: [Haskell-cafe] On to applicative
To: "michael rice" <nowgate at yahoo.com>
Cc: haskell-cafe at haskell.org
Date: Tuesday, August 31, 2010, 1:50 PM

2010/8/31 michael rice <nowgate at yahoo.com>
>
> So it's a type constructor, not a type? Could you please provide a simple example of its usage?

Sure, although I'm sure you've come by some already.

-- the identity function
id :: a -> a
-- often, we write it like this:
-- id x = x
-- but here we see the relationship between the ananymous function
syntax and the function type:
id = \x -> x

In fact, if you write in prefix form, it is quite familiar:
f :: (->) Int Bool
e = Either String Float

Cheers,
Thu

> Michael
>
> --- On Tue, 8/31/10, Vo Minh Thu <noteed at gmail.com> wrote:
>
> From: Vo Minh Thu <noteed at gmail.com>
> Subject: Re: [Haskell-cafe] On to applicative
> To: "michael rice" <nowgate at yahoo.com>
> Cc: haskell-cafe at haskell.org
> Date: Tuesday, August 31, 2010, 1:17 PM
>
> 2010/8/31 michael rice <nowgate at yahoo.com>
> >
> > "Learn You a Haskell ..."  says that (->) is a type just like Either. Where can I find its type definition?
>
> You can't define it *in* Haskell as user code. It is a built-in infix
> type constructor (Either or Maybe are type constructors too, not just
> types). In fact, if you want to implement a simple, typed functional
> language, you'll find it is the only built-in type constructor you
> have to implement (as the implementor of the language).
>
> Also,
>   Show a => a
> is a type too, but you won't find a definition for 'a' or for '=>'.
> All those things are defined by the language.
>
> Cheers,
> Thu
>



      
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