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--------------------------------------------------------------------------------
-- | Author : Bjoern Peemoeller
--   Version: July 2013
--
-- This module provides some utility functions for function application.
--------------------------------------------------------------------------------

module Data.Function (fix, on) where

-- | `fix f` is the least fixed point of the function `f`,
-- i.e. the least defined `x` such that `f x = x`.
fix :: (a -> a) -> a
fix f = let x = f x in x

-- | `on f g x y` applies the binary operation `f` to the results of
-- applying operation `g` to two arguments `x` and `y`.
-- Thus, it transforms two inputs and combines the outputs.
---
--     (*) `on` f = \x y -> f x * f y
---
-- A typical usage of this operation is:
---
--     sortBy ((<=) `on` fst)
on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
on op f x y = f x `op` f y