Haskell/YAHT/Language advanced/Solutions

Partial Application

Function func3 cannot be converted into point-free style. The others look something like:

func1 x = map (*x)

func2 f g = filter f . map g

func4 = map (+2) . filter (`elem` [1..10]) . (5:)

func5 = flip foldr 0 . flip . curry 

You might have been tempted to try to write func2 as filter f . map, trying to eta-reduce off the g. In this case, this isn't possible. This is because the function composition operator (.) has type (b -> c) -> (a -> b) -> (a -> c). In this case, we're trying to use map as the second argument. But map takes two arguments, while (.) expects a function which takes only one.

Instance Declarations

The Eq Class

The Show Class

Other Important Classes

The Ord Class

The Enum Class

The Num Class

The Read Class

Class Contexts

Deriving Classes

Datatypes Revisited

Named Fields

More Lists

Standard List Functions

List Comprehensions

The Final Word on Lists

We can start out with a recursive definition:

and [] = True
and (x:xs) = x && and xs

From here, we can clearly rewrite this as:

and = foldr (&&) True

We can write this recursively as:

concatMap f [] = []
concatMap f (x:xs) = f x ++ concatMap f xs

This hints that we can write this as:

concatMap f = foldr (\a b -> f a ++ b) []

Now, we can do point elimination to get:

     foldr (\a b -> f a ++ b) []
==>  foldr (\a b -> (++) (f a) b) []
==>  foldr (\a -> (++) (f a)) []
==>  foldr (\a -> ((++) . f) a) []
==>  foldr ((++) . f) []