Re: [Haskell-cafe] On to applicative

2010/8/31 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

We say that m has type Maybe Integer, so :: is pronounced 'has type'. We also say that m is a value. Just is a type constructor, Maybe Int is a type, and Just 7, like m, is a value. So we don't talk about instance here. Informally you could say that 7 is an instance of Int, but in Haskell we use 'instance' to mean something (precisely) else. This pharse is correct w.r.t to the use of 'instance' in Haskell: Maybe is an instance of the Functor class.

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?

Note that for Maybe, the instance is define with instance Functor Maybe where ... Note how the type argument of Maybe is not given. But above, when you create a value, it has type Maybe Int, not only Maybe. So for the ((->) r) case, you still want to "complete" it. E.g. m :: Maybe Int -- not just Maybe (+) :: (->) Int Int -- and not only (->) Int Cheers, Thu

Michael

--- On Tue, 8/31/10, Vo Minh Thu wrote:

From: Vo Minh Thu Subject: Re: [Haskell-cafe] On to applicative To: "michael rice" Cc: haskell-cafe@haskell.org Date: Tuesday, August 31, 2010, 1:50 PM

2010/8/31 michael rice

...

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 wrote:

From: Vo Minh Thu Subject: Re: [Haskell-cafe] On to applicative To: "michael rice" Cc: haskell-cafe@haskell.org Date: Tuesday, August 31, 2010, 1:17 PM

2010/8/31 michael rice

...

"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