Tom Pledger wrote: > K. Fritz Ruehr writes: > : > | But Jerzy Karczmarczuk enlightened me as to the full generality possible > | along these lines (revealing the whole truth under the influence of at > | least one beer, as I recall). Namely, one can define a sequence of > | functions (let's use a better notation now, with "c" for composition): > | > | c1 = (.) -- good old composition > | c2 = (.) . (.) -- my (.<) from above > | c3 = (.) . (.) . (.) > | c4 = (.) . (.) . (.) . (.) > | -- etc. > > Nice! > > There's also > > c0 = ($) > > which is clearer if you use 'non-pointfree' notation > > ... > c2 f g x y = f (g x y) > c1 f g x = f (g x) > c0 f g = f g > > - Tom
Note also that chains of these operators can be used in a somewhat readable way. For example, suppose we have: f1 :: Int -> Int f2 :: Int -> Int -> Int f3 :: Int -> Int -> Int -> Int f :: Int -> Int -> Int -> Int -> Int f1 x = -x f2 x y = x - y f3 x y z = x * (y - z) f a b c d = f2 (f1 (f3 a b c)) d We can define `f` in a point-free style: f = f2 `c1` f1 `c3` f3 Each function in the composition, from innermost (rightmost) to outermost (leftmost), takes the intermediate result so far (or, for the innermost function, the first argument) plus zero or more additional arguments from those that remain, as determined by the composition operator to its left. Note that the composition operators need to be left-associative (as they are by default) for this to work. -- Dean _______________________________________________ Haskell mailing list [EMAIL PROTECTED] http://www.haskell.org/mailman/listinfo/haskell
