Basic Haskell: higher-order functions

 

 Functional Programming in Haskell
3rd CCSC Northwest Conference • Fall 2001

Basic Haskell: higher-order functions
bullet Currying
Haskell functions of several arguments are actually "curried", i.e., they are higher-order functions of successive arguments 
> :t take
take :: Int -> [a] -> [a]

> :t take 10
take 10 :: [a] -> [a]

> :t take 10 ['a'..'z']
take 10 (enumFromTo 'a' 'z') :: [Char]

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 Functional Programming in Haskell
3rd CCSC Northwest Conference • Fall 2001

Basic Haskell: higher-order functions
bullet Currying
bullet Infix operators versus prefix functions
Infix operators are just curried functions; by default, symbolic identifiers are written infix and alphabetic ones prefix, but we can over-ride these defaults 
> :t (+)
(+) :: Num a => a -> a -> a

> (+) 10 20
30

> 10 `divMod` 3
(3,1)

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 Functional Programming in Haskell
3rd CCSC Northwest Conference • Fall 2001

Basic Haskell: higher-order functions
bullet Currying
bullet Infix operators versus prefix functions
bullet Operator sections
We can conveniently apply an infix operator to just one argument by enclosing the phrase in parentheses 
> (2^) 10
1024

> (^2) 10
100

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 Functional Programming in Haskell
3rd CCSC Northwest Conference • Fall 2001

Basic Haskell: higher-order functions
bullet Currying
bullet Infix operators versus prefix functions
bullet Operator sections
bullet The map functional
The map functional takes a function as its first argument, then applies it to every element of a list 
> map (^2) [1..10]
[1,4,9,16,25,36,49,64,81,100]

> map (`div` 3) [1..20]
[0,0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6]

> map reverse ["hey", "there", "world"]
["yeh","ereht","dlrow"]

> reverse ["hey", "there", "world"]
["world","there","hey"]

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 Functional Programming in Haskell
3rd CCSC Northwest Conference • Fall 2001

Basic Haskell: higher-order functions
bullet Currying
bullet Infix operators versus prefix functions
bullet Operator sections
bullet The map functional
bullet Higher-order predicates
Predicates (boolean-valued functions) can be extended to lists via the higher-order predicates any and all 
> map even [1..5]
[False,True,False,True,False]

> all even (map (2*) [1..5])
True

> any odd [ x^2 | x<-[1..5] ]
True

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 Functional Programming in Haskell
3rd CCSC Northwest Conference • Fall 2001

Basic Haskell: higher-order functions
bullet Currying
bullet Infix operators versus prefix functions
bullet Operator sections
bullet The map functional
bullet Higher-order predicates
bullet The fold functions
The fold functions foldl and foldr combine elements of a list based on a binary function and an initial value 
> foldr (+) 0 [1..10]
55

> sum [1..10]
55

> foldr (*) 1 [1..5] == 1 * 2 * 3 * 4 * 5 * 1
True

> foldl (&&) True (map even [2,4..10])
True

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 Functional Programming in Haskell
3rd CCSC Northwest Conference • Fall 2001

Basic Haskell: higher-order functions
bullet Currying
bullet Infix operators versus prefix functions
bullet Operator sections
bullet The map functional
bullet Higher-order predicates
bullet The fold functions
bullet Other useful higher-order functions
The standard Prelude defines scores of useful functions, many of which enjoy great generality due to the abstractional capabilities of polymorphic types and higher-order functions 
> zipWith (*) [1..10] [1..10]
[1,4,9,16,25,36,49,64,81,100]

> :t replicate
replicate :: Int -> a -> [a]

> zipWith replicate [1..6] ['a'..'z']
["a","bb","ccc","dddd","eeeee","ffffff"]

> takeWhile (<100) [ 2^n | n<-[1..] ]
[2,4,8,16,32,64]

> :t takeWhile
takeWhile :: (a -> Bool) -> [a] -> [a]

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