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| author | Camil Staps | 2016-02-02 19:24:50 +0100 |
|---|---|---|
| committer | Camil Staps | 2016-02-02 19:24:50 +0100 |
| commit | a7d7542dc646a5fd124ef71e71ce260889f1701b (patch) | |
| tree | 04ed89503bbb3cc9933273a1326a53ca724c3492 /1415/files/practicum/BewijsMapFlatten.icl | |
| parent | week6 camil: working positioning of lines by putting empties at left and righ... (diff) | |
Diffstat (limited to '1415/files/practicum/BewijsMapFlatten.icl')
| -rw-r--r-- | 1415/files/practicum/BewijsMapFlatten.icl | 30 |
1 files changed, 30 insertions, 0 deletions
diff --git a/1415/files/practicum/BewijsMapFlatten.icl b/1415/files/practicum/BewijsMapFlatten.icl new file mode 100644 index 0000000..dc74766 --- /dev/null +++ b/1415/files/practicum/BewijsMapFlatten.icl @@ -0,0 +1,30 @@ +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:
|