[Haskell-cafe] Unique functor instance
voigt at tcs.inf.tu-dresden.de
Tue Nov 25 08:42:14 EST 2008
Claus Reinke wrote:
>> Luke Palmer wrote:
>>> I've been wondering, is it ever possible to have two (extensionally)
>>> different Functor instances for the same type? I do mean in Haskell;
>>> i.e. (,) doesn't count. I've failed to either come up with any
>>> examples or prove that they all must be the same using the laws.
>> For "not-too-exotic" datatypes, in particular for algebraic data types
>> with polynomial structure (no exponentials, embedded function types, and
>> other nasties), I would conjecture that indeed there is always exactly
>> one Functor instance satisfying the identity and composition laws.
> Are identity and composition sufficient to guarantee that the
> mapped function is actually applied?
> instance Functor f where fmap _ x = x
Such an fmap will not have the required type
(a -> b) -> f a -> f b
Consider "fmap even". Then a=Int, b=Bool, x::f Int,
(fmap even x)::f Bool, type error since you assumed fmap even x = x !
Dr. Janis Voigtlaender
mailto:voigt at tcs.inf.tu-dresden.de
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