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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/BewijsMeppenEnTippen.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:
-
-:: BTree a = Tip a | Bin (BTree a) (BTree a)
-
-map :: (a -> b) [a] -> [b]
-map f [] = [] (1.)
-map f [x:xs] = [f x : map f xs] (2.)
-
-mapbtree :: (a -> b) (BTree a) -> BTree b
-mapbtree f (Tip a) = Tip (f a) (3.)
-mapbtree f (Bin t1 t2) = Bin (mapbtree f t1) (mapbtree f t2) (4.)
-
-foldbtree :: (a a -> a) (BTree a) -> a
-foldbtree f (Tip x) = x (5.)
-foldbtree f (Bin t1 t2) = f (foldbtree f t1) (foldbtree f t2) (6.)
-
-tips :: (BTree a) -> [a]
-tips t = foldbtree (++) (mapbtree unit t) (7.)
-
-unit :: a -> [a]
-unit x = [x] (8.)
-
-
-Te bewijzen:
- voor alle functies f, voor alle eindige bomen t:
-
- map f (tips t) = tips (mapbtree f t)
-
-Bewijs: