[Haskell-cafe] Client-extensible heterogeneous types (Duck-typed variadic functions?)

[Max Bolingbroke]

On 14 October 2010 08:56, Max Bolingbroke <batterseapower at hotmail.com> wrote:
> But if the only operation you ever do on this pair is (.), you may as
> well skolemise and just store (fnA1 . fnA2) directly. What is the
> advantage of doing otherwise?

I forgot to mention that if you *really really* want to program with
the type [exists b. (b -> a, b)] directly you can do it without
defining a new data type to hold the existential package by using CPS
style and making use of the logical law that not(exists a. P[a]) <==>
forall a. not(P[a]):

"""
{-# LANGUAGE Rank2Types, ImpredicativeTypes #-}

foo :: [forall res. (forall b. (b -> Bool, b) -> res) -> res]
foo = [\k -> k (not, True), \k -> k ((<10), 5), \k -> k (uncurry (==),
("Hi", "Hi"))]

main :: IO ()
main = print $ [k (\(f, x) -> f x) | k <- foo]
"""

I pass to each "k" in the "foo" list a continuation that consumes that
item in the list (in this case, a function and its arguments) and
returns a result of uniform type (in this case, Bool).

Cheers,
Max