[Haskell-cafe] Re: hMapping polymorphic functions

[oleg at pobox.com]

hMapping polymorphic functions is indeed quite challenging, but can
be done. That was the topic of the message 

	Type-class overloaded functions: second-order typeclass programming
	with backtracking
	http://okmij.org/ftp/Haskell/poly2.txt

The challenge is how to avoid specifying the context too early or at
all and keep the context to the bare minimum.

Your particular case is simple however: applying the function
(\x->[x]) that applies literally to any argument type and is defined
only by one case:

> data FnListify = FnListify
>
> instance TypeCast [a] r => Apply FnListify a r where
>     apply _ x = typeCast [x]
>
> list1 = 'a' :*: "a" :*: True :*: HNil
> test1 = hMap FnListify list1

	*Poly2> test1
	"a" :*: (["a"] :*: ([True] :*: HNil))

Within the Poly2 framework, the example becomes

> data FnListify = FnListify
>
> instance TypeCast Otherwise r => GFN n FnListify a r
> instance TypeCast [a] r => Apply (GFnA n FnListify) a r where
>     apply _ x = typeCast [x]
>
> instance TypeCast [a] r => Apply FnListify a r where
>     apply _ x = typeCast [x]
>
> test2 = hMap (GFn FnListify) list1

	*Poly2> test2
	"a" :*: (["a"] :*: ([True] :*: HNil))

The advantage of making things more complicated than they are is that
we can add more clauses to our generic function. For example, we may
choose to handle Booleans in a different way, by negating them.

We add (perhaps in a different module, so the original code remains as
it was)

> data OnlyBool
> instance TypeCast OnlyBool r => GFN Z FnListify a r
> instance Apply OnlyBool Bool HTrue
> instance TypeCast HFalse r => Apply OnlyBool a r
>
> instance Apply (GFnA Z FnListify) Bool Bool where
>     apply _ x = not x

and now,

	*Poly2> test2
	"a" :*: (["a"] :*: (False :*: HNil))


P.S. It may be worth sending me a carbon copy (CC) of any question
relating to HList, OOHaskell, continuations, etc. I can no longer
afford reading every message on Haskell-Cafe (or even every tenth
message).