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

---
 1415/fp1/week7/mart/BewijsMeppenEnTippen.icl | 29 ++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)
 create mode 100644 1415/fp1/week7/mart/BewijsMeppenEnTippen.icl

(limited to '1415/fp1/week7/mart/BewijsMeppenEnTippen.icl')

diff --git a/1415/fp1/week7/mart/BewijsMeppenEnTippen.icl b/1415/fp1/week7/mart/BewijsMeppenEnTippen.icl
new file mode 100644
index 0000000..720ff4d
--- /dev/null
+++ b/1415/fp1/week7/mart/BewijsMeppenEnTippen.icl
@@ -0,0 +1,29 @@
+Zij gegeven:
+
+:: BTree a              = Tip a | Bin (BTree a) (BTree a)
+
+map                     :: (a -> b) [a] -> [b]
+map f []                = []                                    (1.)
+map f [x:xs]            = [f x : map f xs]                      (2.)
+
+mapbtree                :: (a -> b) (BTree a) -> BTree b
+mapbtree f (Tip a)      = Tip (f a)                             (3.)
+mapbtree f (Bin t1 t2)  = Bin (mapbtree f t1) (mapbtree f t2)   (4.)
+
+foldbtree               :: (a a -> a) (BTree a) -> a
+foldbtree f (Tip x)     = x                                     (5.)
+foldbtree f (Bin t1 t2) = f (foldbtree f t1) (foldbtree f t2)   (6.)
+
+tips                    :: (BTree a) -> [a]
+tips t                  = foldbtree (++) (mapbtree unit t)      (7.)
+
+unit                    :: a -> [a]
+unit x                  = [x]                                   (8.)
+
+
+Te bewijzen:
+    voor alle functies f, voor alle eindige bomen t:
+    
+        map f (tips t) = tips (mapbtree f t)
+
+Bewijs:
-- 
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