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How to map and filter lists in haskell using list comprehension, primitive recursion, and higher-order functions. It covers various examples of functions that transform and filter lists, such as doubleall, addpairs, multall, applyf, map, lessthanten, halfpairs, and filter. The document also discusses the concept of first-class functions in haskell and how they can be used as arguments or results of functions.
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More generally, for any functionmultAll m lst = [ mx | x <- lst]multAll :: Int -> [Int] -> [Int]addPairs pairList = [[m+n] | (m,n) <- pairList]addPairs :: [(Int,Int)] -> [[Int]]doubleAll lst = [ 2x | x <- lst] doubleAll :: [Int] -> [Int] Applying a transformation to every element of a list:
(^) f (^) of type (^) a -> b , we can define a
function (^) applyF (^) with type (^) [a] -> [b]
(^) by:
applyF lst = [
(^) f x | x <- lst]
More generally, for any functionmultAll m (x:xs) = mx : multAll m xsmultAll m [] = []addPairs ((m,n):rest) = [m+n] : addPairs restaddPairs [] = []doubleAll (x:xs) = 2x : doubleAll xs doubleAll [] = []
(^) f (^) of type (^) a -> b , we can define a
function (^) applyF (^) with type (^) [a] -> [b]
(^) by:
applyF (x:xs) = applyF [] = []
(^) f (^) x : (^) applyF xs
For any property expressed as functionhalfPairs pairList = [(m,n) | (m,n) <- pairList, n == 2*m]halfPairs :: [(Int,Int)] -> [(Int,Int)]lessThanTen lst = [ x | x <- lst, x < 10] lessThanTen :: [Int] -> [Int] Filtering elements from a list:
(^) p (^) of type (^) a -> Bool
, we can
define a function
(^) filterP (^) with type (^) [a] -> [a]
(^) by:
filterP lst = [ x | x <- lst,
(^) p x]
filter p lst = [ x | x <- lst, p x] filter :: (a -> Bool) -> [a] -> [a]^ To be even more generic:
isHalfPair (m,n) = isHalfPair :: (Int,Int) -> Bool^ Examples:filter p lst = [ x | x <- lst, p x] filter :: (a -> Bool) -> [a] -> [a]^ Recall:
(^) (n == 2*m)
filter isDigitfilter isHalfPair [(3,7),(4,8),(5,9),(10,21),(11,22)]
(^) [โaโ, โ3โ, โ7โ, โ\nโ, โbโ, โZโ, โ8โ]
filter not
(^) [True, False, False, False, True]
