List Comprehension

1 List Comprehension

1.1 Simple List Comprehension

> [x^2 | x <- [1..10]]
[1,4,9,16,25,36,49,64,81,100]

>  [ odd x | x <- [1..9]] 
[True,False,True,False,True,False,True,False,True]

1.2 Comprehensions with multiple generators

Comprehensions with multiple generators, separated by commas. The generators are x <- [1, 2, 4] and y <- [4,5].

> [(x, y) | x <- [1, 2, 4], y <- [4,5]]
[(1,4),(1,5),(2,4),(2,5),(4,4),(4,5)]

> [(x-y, x+y) | x <- [1, 2, 4], y <- [4,5]]
[(-3,5),(-4,6),(-2,6),(-3,7),(0,8),(-1,9)]

> [(x/y, x*y) | x <- [1, 2, 4], y <- [4,5]]
[(0.25,4.0),(0.2,5.0),(0.5,8.0),(0.4,10.0),(1.0,16.0),(0.8,20.0)]

1.3 Function Inside List Comprehension

> let f x y = sqrt(x^2 + y^2)

> [ f x y | x <- [1, 2, 4], y <- [4,5]]
[4.123105625617661,5.0990195135927845,4.47213595499958,5.385164807134504,5.656854249492381,6.4031242374328485]

1.4 Comprehension with Guards

Guards or filter is a boolean expression that removes elements that would otherwise have been included in the list comprehension. They restricts the values produced by earlier generators.

Even number sequence

> [x | x <- [1..10], even x]
[2,4,6,8,10]

>  [x | x <- [1,5,12,3,23,11,7,2], x>10] 
[12,23,11]

> [(x,y) | x <- [1,3,5], y <- [2,4,6], x<y]
[(1,2),(1,4),(1,6),(3,4),(3,6),(5,6)]

Odd Number sequence

> [x | x <- [1..10], odd x]
[1,3,5,7,9]

Number factors and Prime Numbers

> let factors n = [ x | x <- [1..n], mod n x == 0]
> 
> factors 15
[1,3,5,15]
> 
> factors 10
[1,2,5,10]
> 
> factors 100
[1,2,4,5,10,20,25,50,100]
> 
> factors 17
[1,17]
> factors 19
[1,19]

> let prime n = factors n == [1, n]
> 
> prime 17
True
> prime 19
True
> prime 20
False
> 

{- Get all prime numbers until number n -}

> let primes_n n = [ x | x <- [1..n], prime x]
> 
> primes_n 10
[2,3,5,7]
> primes_n 100
[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]
>