PointFree programming

Question

I want to know if it is possible to convert a recursive function into point free definition.

If we take an easy recursive function.

factorial :: int-> int
factorial 0=1
factorial n+1= (n+1) *factorial n

IF we have non recursive def.

factorial :: int-> int
factorial n= product [1..n]  
   <=> factorial n = product.enumFromTo 1 n 
   <=> factorial   = product.enumFromTo 1  

But how can i do the same on the recursive definition?

Reason why i am asking is that i want to make transformationsApply pointfree.

transformationsApply :: Eq a => a -> ([a] -> [a]) -> [([a], [a])] -> [a] -> Maybe [a]
transformationsApply _ _ [] _= Nothing
transformationsApply wc func ((a,b):xs) (y:ys)
   = orElse (transformationApply wc func (y:ys) (a,b)) 
            (transformationsApply wc func xs (y:ys))

transformationApply used above is defined as

transformationApply :: Eq a => a -> (([a] -> [a]) -> ([a] -> (([a], [a]) -> Maybe [a])))

transformationApply wc func xs (a,b) 
   = mmap ((substitute wc b).func) (match wc a xs)

Answer 1

I would suggest to keep your code more readable than to try converting it to incomprehensible pointfree form.

The easiest way to convert a function to pointfree form is to ask lambdabot. Now when you have recursive function you can convert that to non-recursive using fix. Here is the example of fact function (A direct conversion from what lambdabot gave) and you can see how readable it is.

import Control.Monad
import Data.Function


if' :: Bool -> a -> a -> a
if' True  x _ = x
if' False _ y = y

fact = fix $ ap (flip if' 1 . (0 ==)) . ap (*) . (. subtract 1)