diff options
Diffstat (limited to 'files/practicum/BewijsSubsEnMap.icl')
-rw-r--r-- | files/practicum/BewijsSubsEnMap.icl | 33 |
1 files changed, 0 insertions, 33 deletions
diff --git a/files/practicum/BewijsSubsEnMap.icl b/files/practicum/BewijsSubsEnMap.icl deleted file mode 100644 index 43329e3..0000000 --- a/files/practicum/BewijsSubsEnMap.icl +++ /dev/null @@ -1,33 +0,0 @@ -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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