Simpler `length`, `sum`, `product` for GHC 7.10 for beginners.

FtpFree.hs

-- Something like this when teaching using GHC
-- so that beginners don't get confused by FTP versions
-- of length, sum, product, etc.
-- Usage: in ghci, `:l FtpFree.hs`

module FtpFree (length, sum, product) where

import  Prelude hiding (length, sum, product)

length :: [a] -> Int
length = foldr (const (+1)) 0
-- length [] = 0
-- length (_:xs) = length xs + 1

sum :: Num a => [a] -> a
sum = foldr (+) 0

product :: Num a => [a] -> a
product = foldr (*) 1




{-
Deriving definition for length:

Start with:
length xs = foldr (\_ x -> x + 1) 0 xs

Eta reduce:
length = foldr (\_ x -> x + 1) 0

Use prefix (+):
length = foldr (\_ x-> (+) 1 x) 0

Eta reduce the lambda:
length = foldr (\_ -> (+) 1 ) 0

Use operator section:
length = foldr (\_ -> (+1) ) 0

This lambda is just const:
length = foldr (const (+1)) 0
-}