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authorCamil Staps2016-02-02 19:24:50 +0100
committerCamil Staps2016-02-02 19:24:50 +0100
commita7d7542dc646a5fd124ef71e71ce260889f1701b (patch)
tree04ed89503bbb3cc9933273a1326a53ca724c3492 /files/practicum/BewijsMapFlatten.icl
parentweek6 camil: working positioning of lines by putting empties at left and righ... (diff)
Moved to 1415 directoryHEADmaster
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-Zij gegeven:
-
-(++) :: [a] [a] -> [a]
-(++) [] xs = xs (1)
-(++) [y:ys] xs = [y : ys ++ xs] (2)
-
-map :: (a -> b) [a] -> [b]
-map f [] = [] (3)
-map f [x:xs] = [f x : map f xs] (4)
-
-flatten :: [[a]] -> [a]
-flatten [] = [] (5)
-flatten [x:xs] = x ++ (flatten xs) (6)
-
-1.
-Te bewijzen:
- voor iedere functie f, eindige lijst as en bs:
-
- map f (as ++ bs) = (map f as) ++ (map f bs)
-
-Bewijs:
-
-
-2.
-Te bewijzen:
- voor iedere functie f, voor iedere eindige lijst xs:
-
- flatten (map (map f) xs) = map f (flatten xs)
-
-Bewijs: