[Haskell-cafe] Polyvariadic composition
Ryan Ingram
ryani.spam at gmail.com
Tue Jul 31 02:23:30 CEST 2012
My completely off-the-cuff guess is that
a a b b
isn't considered more or less specific than
(x -> a) ar (x -> b) br
since they both apply some constraint on the types. For example, it's not
immediately clear that the first instance can't be used for (x -> a) (x ->
a) (x -> b) (x -> b)
Whereas when you say
a ar b br
the type
(x -> a) ar (x -> b) br
is strictly more specific, so the overlapping instance can be chosen.
Remember instance selection is done entirely via the instance head, so
instance X a a
is not the same as
instance (a ~ b) => X a b
The first case supplies an instance for any two equal types, and the second
case supplies an instance for *any two types*, then throws an error if the
compiler can't prove that the two types are equal.
For example, without overlapping instances, you can write
class X a b where foo :: a -> b
instance X a a where foo = id
instance X Int Bool where foo = (== 0)
But if instead you specify
instance (a ~ b) => X a b where foo = id
you can't specify the Int Bool instance without overlap.
-- ryan
On Mon, Jul 30, 2012 at 12:32 PM, Artyom Kazak <artyom.kazak at gmail.com>wrote:
> Hello,
>
> I have accidentally written my version of polyvariadic composition
> combinator, `mcomp`. It differs from Oleg’s version (
> http://okmij.org/ftp/Haskell/**polyvariadic.html#polyvar-comp<http://okmij.org/ftp/Haskell/polyvariadic.html#polyvar-comp>) in three aspects: a) it is simpler, b) it works without enumerating basic
> cases (all existing types, in other words), and c) it needs more type
> extensions.
>
> {-# LANGUAGE
>> MultiParamTypeClasses
>> , FunctionalDependencies
>> , FlexibleInstances
>> , UndecidableInstances
>> , TypeFamilies , OverlappingInstances
>> #-}
>>
>> class Mcomp a ar b br | a br -> b where
>> mcomp :: a -> (ar -> br) -> b
>>
>> instance (a ~ ar, b ~ br) => Mcomp a ar b br where
>> mcomp a f = f a
>>
>> instance (Mcomp a ar b br) => Mcomp (x -> a) ar (x -> b) br where
>> mcomp a f = \x -> mcomp (a x) f
>>
>
> My question is: why doesn’t it work when I replace
>
> instance (a ~ ar, b ~ br) => Mcomp a ar b br
>
> with
>
> instance Mcomp a a b b
>
> ? I thought that equal letters mean equal types…
>
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