1Functional(3) User Contributed Perl Documentation Functional(3)
2
6 Language::Functional - a module which makes Perl slightly more
7 functional
8
10 use Language::Functional ':all';
11 print 'The first ten primes are: ',
12 show(take(10, filter { prime(shift) } integers)), "\n";
13
15 Perl already contains some functional-like functions, such as "map" and
16 "grep". The purpose of this module is to add other functional-like
17 functions to Perl, such as foldl and foldr, as well as the use of
18 infinite lists.
19 Think as to how you would express the first ten prime numbers in a
21 simple way in your favourite programming language? So the example in
22 the synopsis is a killer app, if you will (until I think up a better
23 one ;-).
24 The idea is mostly based on Haskell, from which most of the functions
26 are taken. There are a couple of major omissions: currying and types.
27 Lists (and tuples) are simply Perl list references, none of this 'cons'
28 business, and strings are simple strings, not lists of characters.
29 The idea is to make Perl slightly more functional, rather than
31 completely replace it. Hence, this slots in very well with whatever
32 else your program may be doing, and is very Perl-ish. Other modules are
33 expected to try a much more functional approach.
34
36 The following functions are available. (Note: these should not be
37 called as methods).
38 In each description, I shall give the Haskell definition (if I think it
40 would help) as well as a useful example.
41 show
43 Show returns a string representation of an object. It does not
44 like infinite lists.
45 inc k
47 Increases the value passed by 1.
48 $x = inc 2; # 3
50 In Haskell:
52 inc :: a -> a
54 inc k = 1 + k
55 double k
57 Doubles the passed value.
58 $x = double 3; # 6
60 In Haskell:
62 double :: a -> a
64 double k = k * 2
65 square k
67 Returns the square of the passed value. eg:
68 $x = square 3; # 9
70 In Haskell:
72 square :: a -> a
74 square k = k * k
75 gcd x y
77 Returns the greatest common denominator of two numbers. eg:
78 $x = gcd(144, 1024); # 16
80 In Haskell:
82 gcd :: Integral a => a -> a -> a
84 gcd 0 0 = error "gcd 0 0 is undefined"
85 gcd x y = gcd' (abs x) (abs y)
86 where gcd' x 0 = x
87 gcd' x y = gcd' y (x `rem` y)
88 lcm x y
90 Returns the lowest common multiple of two numbers. eg:
91 $x = lcm(144, 1024); # 9216
93 In Haskell:
95 lcm :: (Integral a) => a -> a -> a
97 lcm _ 0 = 0
98 lcm 0 _ = 0
99 lcm x y = abs ((x `quot` gcd x y) * y)
100 id x
102 The identity function - simply returns the argument. eg:
103 $x = id([1..6]); # [1, 2, 3, 4, 5, 6].
105 In Haskell:
107 id :: a -> a
109 id x = x
110 const k _
112 Returns the first argument of 2 arguments. eg:
113 $x = const(4, 5); # 4
115 In Haskell:
117 const :: a -> b -> a
119 const k _ = k
120 flip f
122 Given a function, flips the two arguments it is passed. Note that
123 this returns a CODEREF, as currying does not yet happen. eg:
124 flip(sub { $_[0] ** $_[1] })->(2, 3) = 9. In Haskell (ie this is
125 what it should really do):
126 flip :: (a -> b -> c) -> b -> a -> c
128 flip f x y = f y x
129 Until p f x
131 Keep on applying f to x until p(x) is true, and then return x at
132 that point. eg:
133 $x = Until { shift() % 10 == 0 } \&inc, 1; # 10
135 In Haskell:
137 until :: (a -> Bool) -> (a -> a) -> a -> a
139 until p f x = if p x then x else until p f (f x)
140 fst x:xs
142 Returns the first element in a tuple. eg:
143 $x = fst([1, 2]); # 1
145 In Haskell:
147 fst :: (a,b) -> a
149 fst (x,_) = x
150 snd x:y:xs
152 Returns the second element in a tuple. eg:
153 $x = snd([1, 2]); # 2
155 In Haskell:
157 snd :: (a,b) -> a
159 snd (_,y) = y
160 head xs
162 Returns the head (first element) of a list. eg:
163 $x = head([1..6]); # 1
165 In Haskell:
167 head :: [a] -> a
169 head (x:_) = x
170 Last xs
172 Returns the last element of a list. Note the capital L, to make it
173 distinct from the Perl 'last' command. eg:
174 $x = Last([1..6]); # 6
176 In Haskell:
178 last :: [a] -> a
180 last [x] = x
181 last (_:xs) = last xs
182 tail xs
184 Returns a list minus the first element (head). eg:
185 $x = tail([1..6]); # [2, 3, 4, 5, 6]
187 In Haskell:
189 tail :: [a] -> [a]
191 tail (_:xs) = xs
192 init xs
194 Returns a list minus its last element. eg:
195 $x = init([1..6]); # [1, 2, 3, 4, 5]
197 In Haskell:
199 init :: [a] -> [a]
201 init [x] = []
202 init (x:xs) = x : init xs
203 null xs
205 Returns whether or not the list is empty. eg:
206 $x = null([1, 2]); # False
208 In Haskell:
210 null :: [a] -> Bool
212 null [] = True
213 null (_:_) = False
214 Map f xs
216 Evaluates f for each element of the list xs and returns the list
217 composed of the results of each such evaluation. It is very similar
218 to the Perl command 'map', hence the capital M, but also copes with
219 infinite lists. eg:
220 $x = Map { double(shift) } [1..6]; # [2, 4, 6, 8, 10, 12]
222 In Haskell:
224 map :: (a -> b) -> [a] -> [b]
226 map f xs = [ f x | x <- xs ]
227 filter p xs
229 Returns the list of the elements in xs for which p(xs) returns
230 true. It is similar to the Perl command 'grep', but it also copes
231 with infinite lists. eg:
232 $x = filter(\&even, [1..6]); # [2, 4, 6]
234 In Haskell:
236 filter :: (a -> Bool) -> [a] -> [a]
238 filter p xs = [ x | x <- xs, p x ]
239 concat
241 Concatenates lists together into one list. eg:
242 concat([[1..3], [4..6]]); # [1, 2, 3, 4, 5, 6]
244 In Haskell:
246 concat :: [[a]] -> [a]
248 concat = foldr (++) []
249 TODO: Make sure this works with infinite lists!
251 Length
253 Returns the length of a list - only do this with finite lists! eg:
254 $x = Length([1..6]); # 6
256 In Haskell:
258 length :: [a] -> Int
260 length = foldl' (\n _ -> n + 1) 0
261 TODO Make sure this works!
263 foldl f z xs
265 Applies function f to the pairs (z, xs[0]), (f(z, xs[0], xs[1]),
266 (f(f(z, xs[0], xs[1])), xs[2]) and so on. ie it folds from the left
267 and returns the last value. Note that foldl should not be done to
268 infinite lists. eg: the following returns the sum of 1..6:
269 $x = foldl { shift() + shift() } 0, [1..6]; # 21
271 In Haskell:
273 foldl :: (a -> b -> a) -> a -> [b] -> a
275 foldl f z [] = z
276 foldl f z (x:xs) = foldl f (f z x) xs
277 foldl1 f xs
279 This is a variant of foldl where the first value of xs is taken as
280 z. Applies function f to the pairs (xs[0], xs[1]), (f(xs[0], xs[1],
281 xs[2]), (f(f(xs[0], xs[1], xs[2])), xs[3]) and so on. ie it folds
282 from the left and returns the last value. Note that foldl should
283 not be done to infinite lists. eg: the following returns the sum of
284 1..6:
285 $x = foldl1 { shift() + shift() } [1..6]; # 21
287 In Haskell:
289 foldl1 :: (a -> a -> a) -> [a] -> a
291 foldl1 f (x:xs) = foldl f x xs
292 scanl f q xs
294 Returns a list of all the intermedia values that foldl would
295 compute. ie returns the list z, f(z, xs[0]), f(f(z, xs[0]),
296 xs[1]), f(f(f(z, xs[0]), xs[1]), xs[2]) and so on. eg:
297 $x = scanl { shift() + shift() }, 0, [1..6]; # [0, 1, 3, 6, 10, 15, 21]
299 In Haskell:
301 scanl :: (a -> b -> a) -> a -> [b] -> [a]
303 scanl f q xs = q : (case xs of
304 [] -> []
305 x:xs -> scanl f (f q x) xs)
306 scanl1 f xs
308 This is a variant of scanl where the first value of xs is taken as
309 q. Returns a list of all the intermedia values that foldl would
310 compute. ie returns the list f(xs[0], xs[1]), f(f(xs[0], xs[1]),
311 xs[2]), f(f(f(xs[0], xs[1]), xs[2]), xs[3]) and so on. eg:
312 $x = scanl1 { shift() + shift() } [1..6]; # [1, 3, 6, 10, 15, 21]
314 In Haskell:
316 scanl1 :: (a -> a -> a) -> [a] -> [a]
318 scanl1 f (x:xs) = scanl f x xs
319 foldr f z xs
321 This is similar to foldl but is folding from the right instead of
322 the left. Note that foldr should not be done to infinite lists.
323 eg: the following returns the sum of 1..6
324 $x = foldr { shift() + shift() } 0, [1..6] ; # 21
326 In Haskell:
328 foldr :: (a -> b -> b) -> b -> [a] -> b
330 foldr f z [] = z
331 foldr f z (x:xs) = f x (foldr f z xs)
332 foldr1 f xs
334 This is similar to foldr1 but is folding from the right instead of
335 the left. Note that foldr1 should not be done on infinite lists.
336 eg:
337 $x = foldr1 { shift() + shift() } [1..6]; # 21
339 In Haskell:
341 foldr1 :: (a -> a -> a) -> [a] -> a
343 foldr1 f [x] = x
344 foldr1 f (x:xs) = f x (foldr1 f xs)
345 scanr f z xs
347 This is similar to scanl but is scanning and folding from the right
348 instead of the left. Note that scanr should not be done on infinite
349 lists. eg:
350 $x = scanr { shift() + shift() } 0, [1..6];
352 # [0, 6, 11, 15, 18, 20, 21]
353 In Haskell:
355 scanr :: (a -> b -> b) -> b -> [a] -> [b]
357 scanr f q0 [] = [q0]
358 scanr f q0 (x:xs) = f x q : qs
359 where qs@(q:_) = scanr f q0 xs
360 scanr1 f xs
362 This is similar to scanl1 but is scanning and folding from the
363 right instead of the left. Note that scanr1 should not be done on
364 infinite lists. eg:
365 $x = scanr1 { shift() + shift() } [1..6];
367 # [6, 11, 15, 18, 20, 21]
368 In Haskell:
370 scanr1 :: (a -> a -> a) -> [a] -> [a]
372 scanr1 f [x] = [x]
373 scanr1 f (x:xs) = f x q : qs
374 where qs@(q:_) = scanr1 f xs
375 iterate f x
377 This returns the infinite list (x, f(x), f(f(x)), f(f(f(x)))...)
378 and so on. eg:
379 $x = take(8, iterate { shift() * 2 } 1);
381 # [1, 2, 4, 8, 16, 32, 64, 128]
382 In Haskell:
384 iterate :: (a -> a) -> a -> [a]
386 iterate f x = x : iterate f (f x)
387 repeat x
389 This returns the infinite list where all elements are x. eg:
390 $x = take(4, repeat(42)); # [42, 42, 42, 42].
392 In Haskell:
394 repeat :: a -> [a]
396 repeat x = xs where xs = x:xs
397 replicate n x
399 Returns a list containing n times the element x. eg:
400 $x = replicate(5, 1); # [1, 1, 1, 1, 1]
402 In Haskell:
404 replicate :: Int -> a -> [a]
406 replicate n x = take n (repeat x)
407 take n xs
409 Returns a list containing the first n elements from the list xs.
410 eg:
411 $x = take(2, [1..6]); # [1, 2]
413 In Haskell:
415 take :: Int -> [a] -> [a]
417 take 0 _ = []
418 take _ [] = []
419 take n (x:xs) | n>0 = x : take (n-1) xs
420 take _ _ = error "Prelude.take: negative argument"
421 drop n xs
423 Returns a list containing xs with the first n elements missing. eg:
424 $x = drop(2, [1..6]); # [3, 4, 5, 6]
426 In Haskell:
428 drop :: Int -> [a] -> [a]
430 drop 0 xs = xs
431 drop _ [] = []
432 drop n (_:xs) | n>0 = drop (n-1) xs
433 drop _ _ = error "Prelude.drop: negative argument"
434 splitAt n xs
436 Splits the list xs into two lists at element n. eg:
437 $x = splitAt(2, [1..6]);# [[1, 2], [3, 4, 5, 6]]
439 In Haskell:
441 splitAt :: Int -> [a] -> ([a], [a])
443 splitAt 0 xs = ([],xs)
444 splitAt _ [] = ([],[])
445 splitAt n (x:xs) | n>0 = (x:xs',xs'') where (xs',xs'') = splitAt (n-1) xs
446 splitAt _ _ = error "Prelude.splitAt: negative argument"
447 takeWhile p xs
449 Takes elements from xs while p(that element) is true. Returns the
450 list. eg:
451 $x = takeWhile { shift() <= 4 } [1..6]; # [1, 2, 3, 4]
453 In Haskell:
455 takeWhile :: (a -> Bool) -> [a] -> [a]
457 takeWhile p [] = []
458 takeWhile p (x:xs)
459 | p x = x : takeWhile p xs
460 | otherwise = []
461 dropWhile p xs
463 Drops elements from the head of xs while p(that element) is true.
464 Returns the list. eg:
465 $x = dropWhile { shift() <= 4 } [1..6]; # [5, 6]
467 In Haskell:
469 dropWhile :: (a -> Bool) -> [a] -> [a]
471 dropWhile p [] = []
472 dropWhile p xs@(x:xs')
473 | p x = dropWhile p xs'
474 | otherwise = xs
475 span p xs
477 Splits xs into two lists, the first containing the first few
478 elements for which p(that element) is true. eg:
479 $x = span { shift() <= 4 }, [1..6];
481 # [[1, 2, 3, 4], [5, 6]]
482 In Haskell:
484 span :: (a -> Bool) -> [a] -> ([a],[a])
486 span p [] = ([],[])
487 span p xs@(x:xs')
488 | p x = (x:ys, zs)
489 | otherwise = ([],xs)
490 where (ys,zs) = span p xs'
491 break p xs
493 Splits xs into two lists, the first containing the first few
494 elements for which p(that element) is false. eg:
495 $x = break { shift() >= 4 }, [1..6]; # [[1, 2, 3], [4, 5, 6]]
497 In Haskell:
499 break :: (a -> Bool) -> [a] -> ([a],[a])
501 break p = span (not . p)
502 lines s
504 Breaks the string s into multiple strings, split at line
505 boundaries. eg:
506 $x = lines("A\nB\nC"); # ['A', 'B', 'C']
508 In Haskell:
510 lines :: String -> [String]
512 lines "" = []
513 lines s = let (l,s') = break ('\n'==) s
514 in l : case s' of [] -> []
515 (_:s'') -> lines s''
516 words s
518 Breaks the string s into multiple strings, split at whitespace
519 boundaries. eg:
520 $x = words("hey how random"); # ['hey', 'how', 'random']
522 In Haskell:
524 words :: String -> [String]
526 words s = case dropWhile isSpace s of
527 "" -> []
528 s' -> w : words s''
529 where (w,s'') = break isSpace s'
530 unlines xs
532 Does the opposite of unlines, that is: joins multiple strings into
533 one, joined by newlines. eg:
534 $x = unlines(['A', 'B', 'C']); # "A\nB\nC";
536 In Haskell:
538 unlines :: [String] -> String
540 unlines = concatMap (\l -> l ++ "\n")
541 (note that strings in Perl are not lists of characters, so this
543 approach will not actually work...)
544 unwords ws
546 Does the opposite of unwords, that is: joins multiple strings into
547 one, joined by a space. eg:
548 $x = unwords(["hey","how","random"]); # 'hey how random'
550 In Haskell:
552 unwords :: [String] -> String
554 unwords [] = []
555 unwords ws = foldr1 (\w s -> w ++ ' ':s) ws
556 Reverse xs
558 Returns a list containing the elements of xs in reverse order. Note
559 the capital R, so as not to clash with the Perl command 'reverse'.
560 You should not try to Reverse an infinite list. eg:
561 $x = Reverse([1..6]); # [6, 5, 4, 3, 2, 1]
563 In Haskell:
565 reverse :: [a] -> [a]
567 reverse = foldl (flip (:)) []
568 And xs
570 Returns true if all the elements in xs are true. Returns false
571 otherwise. Note the capital A, so as not to clash with the Perl
572 command 'and'. You should not try to And an infinite list (unless
573 you expect it to fail, as it will short-circuit). eg:
574 $x = And([1, 1, 1]); # 1
576 In Haskell:
578 and :: [Bool] -> Bool
580 and = foldr (&&) True
581 Or xs
583 Returns true if one of the elements in xs is true. Returns false
584 otherwise. Note the capital O, so as not to clash with the Perl
585 command 'or'. You may try to Or an infinite list as it will short-
586 circuit (unless you expect it to fail, that is). eg:
587 $x = Or([0, 0, 1]); # 1
589 In Haskell:
591 or :: [Bool] -> Bool
593 or = foldr (||) False
594 any p xs
596 Returns true if one of p(each element of xs) are true. Returns
597 false otherwise. You should not try to And an infinite list (unless
598 you expect it to fail, as it will short-circuit). eg:
599 $x = any { even(shift) } [1, 2, 3]; # 1
601 In Haskell:
603 any :: (a -> Bool) -> [a] -> Bool
605 any p = or . map p
606 all p xs
608 Returns true if all of the p(each element of xs) is true. Returns
609 false otherwise. You may try to Or an infinite list as it will
610 short-circuit (unless you expect it to fail, that is). eg:
611 $x = all { odd(shift) } [1, 1, 3]; # 1
613 In Haskell:
615 all :: (a -> Bool) -> [a] -> Bool
617 all p = and . map p
618 elem x xs
620 Returns true is x is present in xs. You probably should not do
621 this with infinite lists. Note that this assumes x and xs are
622 numbers. eg:
623 $x = elem(2, [1, 2, 3]); # 1
625 In Haskell:
627 elem :: Eq a => a -> [a] -> Bool
629 elem = any . (==)
630 notElem x xs
632 Returns true if x is not present in x. You should not do this with
633 infinite lists. Note that this assumes that x and xs are numbers.
634 eg:
635 $x = notElem(2, [1, 1, 3]); # 1
637 In Haskell:
639 notElem :: Eq a => a -> [a] -> Bool
641 notElem = all . (/=)
642 lookup key xys
644 This returns the value of the key in xys, where xys is a list of
645 key, value pairs. It returns undef if the key was not found. You
646 should not do this with infinite lists. Note that this assumes that
647 the keys are strings. eg:
648 $x = lookup(3, [1..6]); # 4
650 In Haskell:
652 lookup :: Eq a => a -> [(a,b)] -> Maybe b
654 lookup k [] = Nothing
655 lookup k ((x,y):xys)
656 | k==x = Just y
657 | otherwise = lookup k xys
658 TODO: Make sure this works with infinite lists
660 minimum xs
662 Returns the minimum value in xs. You should not do this with a
663 infinite list. eg:
664 $x = minimum([1..6]); # 1
666 In Haskell:
668 minimum :: Ord a => [a] -> a
670 minimum = foldl1 min
671 maximum xs
673 Returns the maximum value in xs. You should not do this with an
674 infinite list. eg: maximum([1..6]) = 6. In Haskell:
675 maximum :: Ord a => [a] -> a
677 maximum = foldl1 max
678 sum xs
680 Returns the sum of the elements of xs. You should not do this with
681 an infinite list. eg: sum([1..6]) = 21. In Haskell:
682 sum :: Num a => [a] -> a
684 sum = foldl' (+) 0
685 product xs
687 Returns the products of the elements of xs. You should not do this
688 with an infinite list. eg: product([1..6]) = 720. In Haskell:
689 product :: Num a => [a] -> a
691 product = foldl' (*) 1
692 zip as bs
694 Zips together two lists into one list. Should not be done with
695 infinite lists. eg: zip([1..6], [7..12]) = [1, 7, 2, 8, 3, 9, 4,
696 10, 5, 11, 6, 12]. In Haskell:
697 zip :: [a] -> [b] -> [(a,b)]
699 zip = zipWith (\a b -> (a,b))
700 zipWith :: (a->b->c) -> [a]->[b]->[c]
702 zipWith z (a:as) (b:bs) = z a b : zipWith z as bs
703 zipWith _ _ _ = []
704 zip3 as bs cs
706 Zips together three lists into one. Should not be done with
707 infinite lists. eg: zip3([1..2], [3..4], [5..6]) = [1, 3, 5, 2, 4,
708 6]. In Haskell:
709 zip3 :: [a] -> [b] -> [c] -> [(a,b,c)]
711 zip3 = zipWith3 (\a b c -> (a,b,c))
712 zipWith3 :: (a->b->c->d) -> [a]->[b]->[c]->[d]
714 zipWith3 z (a:as) (b:bs) (c:cs)
715 = z a b c : zipWith3 z as bs cs
716 zipWith3 _ _ _ _ = []
717 unzip abs
719 Unzips one list into two. Should not be done with infinite lists.
720 eg: unzip([1,7,2,8,3,9,4,10,5,11,6,12]) = ([1, 2, 3, 4, 5, 6], [7,
721 8, 9, 10, 11, 12]).
722 unzip :: [(a,b)] -> ([a],[b])
724 unzip = foldr (\(a,b) ~(as,bs) -> (a:as, b:bs)) ([], [])
725 unzip abcs
727 Unzips one list into three. Should not be done with infinite lists.
728 eg: unzip3([1,3,5,2,4,6]) = ([1, 2], [3, 4], [5, 6]). In Haskell:
729 unzip3 :: [(a,b,c)] -> ([a],[b],[c])
731 unzip3 = foldr (\(a,b,c) ~(as,bs,cs) -> (a:as,b:bs,c:cs))
732 ([],[],[])
733 integers
735 A useful function that returns an infinite list containing all the
736 integers. eg: integers = (1, 2, 3, 4, 5, ...).
737 factors x
739 A useful function that returns the factors of x. eg: factors(100)
740 = [1, 2, 4, 5, 10, 20, 25, 50, 100]. In Haskell:
741 factors x = [n | n <- [1..x], x `mod` n == 0]
743 prime x
745 A useful function that returns, rather unefficiently, if x is a
746 prime number or not. It is rather useful while used as a filter,
747 eg: take(10, filter("prime", integers)) = [2, 3, 5, 7, 11, 13, 17,
748 19, 23, 29]. In Haskell:
749 primes = [n | n <- [2..], length (factors n) == 2]
751
753 Leon Brocard <acme@astray.com>
754
756 Copyright (C) 1999-2008, Leon Brocard
757
759 This module is free software; you can redistribute it or modify it
760 under the same terms as Perl itself.
761perl v5.32.0 2020-07-28 Functional(3)