Multiple functions applied to a single value
Graham Klyne
gk at ninebynine.org
Thu Nov 27 14:56:03 EST 2003
There's a possible programming idiom that I repeatedly find myself thinking
about as I write my code. It feels like a kind of dual of fold, except
that it's not necessarily confined to lists. I'm wondering if anything
like this is discussed in the literature, or implemented in the libraries...
Scene-setting: broadly speaking, fold takes a function and applies it to
several values, and combines the results in some way. What I'm thinking of
is a combinator or suchlike that takes two or more functions, applies them
(separately) to a single value, then combines the results of those
combinations.
One function that I have defined and use in my code is called 'flist':
flist :: [a->b] -> a -> [b]
flist fs a = map ($ a) fs
(which is similar to Monad.ap, except that the 'a' parameter is not a
list/monad). I could imagine combining this with a fold in some cases.
A more generalized form of this that works with arbitrary monads was
suggested by Derek Elkin:
fmonad :: Monad m => m (a->b) -> a -> m b
fmonad fm a =
do { f <- fm
; return $ f a
}
But not all cases I encounter involve lists or monads. A different case
might look like this:
> eval :: (b->c->d) -> (a->b) -> (a->c) -> (a->d)
> eval f g1 g2 a = f (g1 a) (g2 a)
So, for example, a function to test of the two elements of a pair are the
same might be:
> pairSame = eval (==) fst snd
giving:
> pairSame (1,2) -- false
> pairSame (3,3) -- true
Or a function to subtract the second and subsequent elements of a list from
the first:
> firstDiffRest = eval (-) head (sum . tail)
> firstDiffRest [10,4,3,2,1] -- 0
That's about as far as I've taken this, but it feels as if it might be part
of a more general pattern. Hence my question: is there anything like this
in the libraries?
#g
------------
Graham Klyne
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