From a7d7542dc646a5fd124ef71e71ce260889f1701b Mon Sep 17 00:00:00 2001 From: Camil Staps Date: Tue, 2 Feb 2016 19:24:50 +0100 Subject: Moved to 1415 directory --- files/practicum/BewijsSubsEnMap.icl | 33 --------------------------------- 1 file changed, 33 deletions(-) delete mode 100644 files/practicum/BewijsSubsEnMap.icl (limited to 'files/practicum/BewijsSubsEnMap.icl') 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: -------- -- cgit v1.2.3