[Haskell-cafe] Re: Function composition

[Jorge Marques Pelizzoni]

Adapting my previous class sample with these ideas, we have:

class Multicompose t1 t2 t3 | t1 t2 -> t3 where
	infixr 9 +.
	(+.)::t1 -> t2 -> t3

instance Multicompose t1 t2 t3 => Multicompose t1 (a -> t2) (a -> t3) where
	(+.) = (.).(+.)

instance Multicompose (b -> c) (a -> b) (a -> c) where
	(+.) = (.)

The only advantage is having the compiler calculate the number of
compositions.

Cheers,

Jorge.

Stuart Cook escreveu:
> On 10/4/07, Dominic Steinitz <dominic.steinitz at blueyonder.co.uk> wrote:
>> Look at the type of (.).(.).(.)
>
> Indeed, this generalizes to functions of any arity on the "RHS":
>
>   Prelude> :t (.)
>   (.) :: (b -> c) -> (a -> b) -> a -> c
>
>   Prelude> :t (.).(.)
>   (.).(.) :: (b -> c) -> (a -> a1 -> b) -> a -> a1 -> c
>
>   Prelude> :t (.).(.).(.)
>   (.).(.).(.) :: (b -> c) -> (a -> a1 -> a2 -> b) -> a -> a1 -> a2 -> c
>
>   Prelude> :t (.).(.).(.).(.)
>   (.).(.).(.).(.) :: (b -> c) -> (a -> a1 -> a2 -> a3 -> b) -> a -> a1
> -> a2 -> a3 -> c
>
>
> Of course, if you want higher-arity functions anywhere *other* than
> the head of your composition chain, you'll have to resort to tupling
> and uncurrying.
>
>
> Stuart
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Jorge M. Pelizzoni
ICMC - Universidade de São Paulo