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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/BewijsSubsEnMap.icl | |
| parent | week6 camil: working positioning of lines by putting empties at left and righ... (diff) | |
Diffstat (limited to '1415/files/practicum/BewijsSubsEnMap.icl')
| -rw-r--r-- | 1415/files/practicum/BewijsSubsEnMap.icl | 33 |
1 files changed, 33 insertions, 0 deletions
diff --git a/1415/files/practicum/BewijsSubsEnMap.icl b/1415/files/practicum/BewijsSubsEnMap.icl new file mode 100644 index 0000000..43329e3 --- /dev/null +++ b/1415/files/practicum/BewijsSubsEnMap.icl @@ -0,0 +1,33 @@ +Zij gegeven de volgende functie-definities:
+
+subs :: [a] -> [[a]]
+subs [] = [[]] (1.)
+subs [x:xs] = subs xs ++ map (cons x) (subs xs) (2.)
+
+map :: (a -> b) [a] -> [b]
+map f [] = [] (3.)
+map f [x:xs] = [f x : map f xs] (4.)
+
+(++) :: [a] [a] -> [a]
+(++) [] ys = ys (5.)
+(++) [x:xs] ys = [x : xs ++ ys] (6.)
+
+cons :: a [a] -> [a]
+cons x xs = [x : xs] (7.)
+
+
+Bewijs de volgende stelling voor alle functies f en eindige lijsten xs:
+
+ subs (map f xs) = map (map f) (subs xs).
+
+Je kunt gebruik maken van de volgende hulpstellingen (lemma's) die gelden voor alle
+functies f, g en eindige lijsten xs en ys:
+
+map f (xs ++ ys) = map f xs ++ map f ys (8.)
+map g (map f xs) = map (g o f) xs (9.)
+(cons (f a)) o (map f) = (map f) o (cons a) (10.)
+(g o f) x = g (f x) (11.)
+
+
+Bewijs:
+-------
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