diff options
| author | Mart Lubbers | 2015-02-06 08:39:37 +0100 |
|---|---|---|
| committer | Mart Lubbers | 2015-02-06 08:39:37 +0100 |
| commit | 379b6353396ca2401241d714733d570629835ffe (patch) | |
| tree | 26652c854a79c627b5f50bc8ac26f9b84f8e196d /files/practicum/BewijsMapFlatten.icl | |
| parent | Merge branch 'master' of https://github.com/dopefishh/fp1 (diff) | |
added practicum files, updated gitignore
Diffstat (limited to 'files/practicum/BewijsMapFlatten.icl')
| -rw-r--r-- | files/practicum/BewijsMapFlatten.icl | 30 |
1 files changed, 30 insertions, 0 deletions
diff --git a/files/practicum/BewijsMapFlatten.icl b/files/practicum/BewijsMapFlatten.icl new file mode 100644 index 0000000..dc74766 --- /dev/null +++ b/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:
|