On Thu, 2009-01-22 at 16:11 +0100, Ketil Malde wrote:
One wart that was briefly mentioned during the Great Monoid Naming Thread of 2009 is the need to wrap types in newtypes to provide multiple instances of the same class with different semantics -- the archetypical example being Integer as a monoid over addition as well as multiplication.
I was just wondering if not phantom types might serve here as an alternative way to go about that. Here's a small example illustrating it:
---------------------------------------- {-# LANGUAGE EmptyDataDecls #-} {-# LANGUAGE FlexibleInstances #-}
module Monoids where import Data.Monoid
data Foo a = Foo Integer deriving (Show, Eq)
data Additive data Multiplicative
instance Monoid (Foo Additive) where mappend (Foo x) (Foo y) = Foo (x+y) mempty = Foo 0
instance Monoid (Foo Multiplicative) where mappend (Foo x) (Foo y) = Foo (x*y) mempty = Foo 1
instance Num (Foo a) where fromInteger x = Foo x Foo x + Foo y = Foo (x+y) Foo x * Foo y = Foo (x*y) signum (Foo x) = Foo (signum x) ----------------------------------------
Loading this into ghci, you get: *Monoids> mconcat [1,2]
<interactive>:1:0: Ambiguous type variable `t' in the constraints: `Monoid t' arising from a use of `mconcat' at <interactive>:1:0-12 `Num t' arising from the literal `2' at <interactive>:1:11 Probable fix: add a type signature that fixes these type variable(s) *Monoids> mconcat [1,2::Foo Additive] Foo 3 *Monoids> mconcat [1,2::Foo Multiplicative] Foo 2
(This can of course be prettified a bit by omitting the constructor from the Show instance).
Any thought about this, pro/contra the newtype method?
The old wiki had an excellent page that has not been replicated either verbatim or in spirit in the new wiki. http://web.archive.org/web/20060831090007/http://www.haskell.org/hawiki/Comm... This lists many small tips and tricks that Haskell programmers have discovered/used throughout the years. This particular example is an example of using wrapper types to attach a phantom type as described here: http://web.archive.org/web/20070614230306/http://haskell.org/hawiki/WrapperT...