We start with a few simple function definitions:

>  double x = 2 * x
>  treble x = 3 * x
>  square x = x * x
>  cube x = x * x * x

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Functions as arguments

>  mapp f [] = []
>  mapp f (h:tail) = f h: mapp f tail

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Parametric Polymorphism

>  len:: [a] -> Int
>  len [] = 0
>  len (h:t) = 1 + len t

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Partial Application

>  foo x y = 3 * x + 5 * y

Note that the type of foo is
   Float -> Float -> Float
   
>  goo = foo 3

Note that the type of goo is
   Float -> Float

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Function factory

>  makeAdder n = addN where addN x = x + n
>  add5 = makeAdder 5

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Lambda notation

>  times5 = \x -> 5 * x 

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Composition:

>  times6 = double.treble

>  iter2 f = f.f
>  iter3 f = f. iter2 f
 
>  iter 0 f = id
>  iter n f = f.(iter (n - 1) f)

>  inc x = x + 1
>  add9 = iter 9 inc
 
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Lazy Eval:

>  always0 n = 0
>  result0 = always0 (4 `div` 0) -- = 0

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Streams (infinite lists):

>  ones = 1: ones

>  fromN n = n: fromN (n + 1)
>  intStream = fromN 0

>  nth [] _ = error "empty stream has no elements"
>  nth (h:t) 0 = h
>  nth (h:t) n = nth t (n - 1)

>  odds 
>    = filter odd intStream
>     where
>      odd n = (n `mod` 2) /= 0