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Re: Icon

On Thu, Dec 20, 2001 at 06:09:52PM -0500, Guy Steele wrote:
> See?  it's easy!  :-)

It's even easier in Haskell:

module M where

-- use some standard monad combinators
import Monad

-- define the monad type, which is precisely of the form Guy described.
-- Here r is a type parameter for the ultimate return value, and a is
-- the type of value that this M will generate.
newtype M r a = M { runM :: (a -> r -> r) -> r -> r }

-- make it a monad, meaning:
instance Monad (M r) where
    -- a pure value is converted to an M by applying the success 
    -- continuation to it
    return x = M (\sc -> sc x)
    -- when we want to operate on an M, we simply apply it to a success
    -- continuation that applies the function
    M m >>= f = M (\sc -> m (\x -> runM (f x) sc))

instance MonadPlus (M r) where
    -- A failure means simply returning the failure value
    mzero = M (\sc fc -> fc)
    -- while combining two Ms means giving one's return value as the other's 
    -- failure argument (. means function composition)
    M m `mplus` M m' = M (\sc -> m sc . m' sc)

-- Some silly cruft to use numerical operations conveniently
instance (Num n) => Eq (M r n)
instance (Num n) => Show (M r n)
instance (Num n) => Num (M r n) where
    (+) = liftM2 (+)

-- A set of values is defined by making each of the pure values an M (by 
-- return), and then combining them with mplus (msum = foldl mplus mzero)
to lower upper = msum (map return [lower..upper])


This technique is described in detail in Ralf Hinze's ICFP 2000 paper

Here's an example:

M> runM (to 1 3 + to 4 6) (:) []

Here we used list construction as the way to combine values. Another

M> runM (to 1 3 + to 4 6) (\a b -> print a >> b) (return ())

Here we use first-class IO actions as the return value, which is a
characteristic feature of Haskell.

Note that there is no need for any syntax transformations, this is pure
Haskell. You can get surprisingly far without macros when just about
everything is a first-class value...

Lauri Alanko