foldl, foldr
f o l d l (+) 0 [ 1 , 2, 3, 4]
0 + [1, 2, 3, 4]
10
foldl, foldr
foldr (:) [5,6] [1,2,3,4]
[1, 2, 3, 4] [5,6]
[4,5,6]
[3,4,5,6]
1 [2,3,4,5,6]
[1,2,3,4,5,6]
Lambda abstrakce, částečná aplikace
f x y = x + y
f = (\x y -> x + y)
a  b = . . .
(e) = (\a b -> ...)
(a e ) = (\b -> a  b) = () a
( b) = (\a -> a  b) = f l i p () b
f l i p :: (a -> b -> c) -> b -> a -> c
f l i p f x y = f y x
Pointfree
(.) :: (b -> c) -> (a -> b) -> a -> c
(f . g) x = f (g x)
(.) f g x = f (g x)
h x = f (g x)
h x = (f . g) x
h = f . ec 77-redukce x
Pointfree - příklady
f u v w x = u v ( w x )
X = f (g x)
x = (f ˇ g) x
= f ˇ g
f u v w x = u v (w x)
f u v w x = (u v . w) x
f u v w x = (u v .) w x
f u v = (u v .)
f u v = (.) (u v)
f u v = ( ( . ) . u) v
f u v = ( ( . ) .) u v
f = ( ( . ) .ú
f = ( ( . ) ( .))
(\a -> b  a) = (b )
po r?-redukci w a x
r?-redukuj eme u a v
(f e) = ((e) f)
f = ( . ) ( . )
Pointfree - příklady
h x y = q y . q x
h x y = q y . q
h x y = (.) (q y) (q
h x y = flip (.) (q x) (q
h x y = (flip (.) (q x) . q)
h x = flip (.) (q x) . q
h x = ( . q ) ( flip (.) (q x))
h x = (. q) ((flip (.) . q) x)
h x = (. q) ((flip (.) . q) x)
h x
h x = f (g x)
h x = (f . g) x
h = f . g
x
x) f b a = flip f a b
y)
y
po r?-redukci y
f.(g.h) = f.g.h((. q) . (flip (.) . q)) x
( . q ) . flip (.) . q po r?-redukci x
Pointfree - příklady h x = f (g x)
h x = (f ˇ g) x
h = f ˇ g
f x y = q y (q x)
f x y = q y (q x)
f x y = flip q (q x) y
f x = flip q (q x)
f b a = flip f a b
po r?-redukci y
f x = flip q (q x)
f x = (flip q . q) x
f = flip q . q po r?-redukci x