initial week 7 commit

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

diff --git a/week7/mart/BinSearchTree.dcl b/week7/mart/BinSearchTree.dcl
new file mode 100644 (file)
index 0000000..2e480bb
--- /dev/null
+++ b/week7/mart/BinSearchTree.dcl
@@ -0,0 +1,7 @@
+definition module BinSearchTree\r
+\r
+import StdClass\r
+import BinTree\r
+\r
+is_geordend     :: // meest algemene type\r
+is_gebalanceerd :: // meest algemene type\r

diff --git a/week7/mart/BinSearchTree.icl b/week7/mart/BinSearchTree.icl
new file mode 100644 (file)
index 0000000..92e7548
--- /dev/null
+++ b/week7/mart/BinSearchTree.icl
@@ -0,0 +1,52 @@
+implementation module BinSearchTree\r
+\r
+import StdEnv\r
+import BinTree\r
+\r
+z0 = Leaf\r
+z1 = insertTree 50 z0\r
+z2 = insertTree 10 z1\r
+z3 = insertTree 75 z2\r
+z4 = insertTree 80 z3\r
+z5 = insertTree 77 z4\r
+z6 = insertTree 10 z5\r
+z7 = insertTree 75 z6\r
+z8 = deleteTree 50 z7\r
+\r
+//  Uit het diktaat, blz. 73:\r
+insertTree :: a (Tree a) -> Tree a | Ord a\r
+insertTree e Leaf = Node e Leaf Leaf\r
+insertTree e (Node x le ri)\r
+| e <= x = Node x (insertTree e le) ri\r
+| e >  x = Node x le (insertTree e ri)\r
+\r
+deleteTree :: a (Tree a) -> (Tree a) | Eq, Ord a\r
+deleteTree e Leaf = Leaf\r
+deleteTree e (Node x le ri)\r
+| e <  x = Node x (deleteTree e le) ri\r
+| e == x = join le ri\r
+| e >  x = Node x le (deleteTree e ri)\r
+where\r
+       join :: (Tree a) (Tree a) -> (Tree a)\r
+       join Leaf b2 = b2\r
+       join b1 b2 = Node x b1` b2\r
+       where\r
+               (x,b1`) = largest b1\r
+               \r
+               largest :: (Tree a) -> (a,(Tree a))\r
+               largest (Node x b1 Leaf) = (x,b1)\r
+               largest (Node x b1 b2)   = (y,Node x b1 b2`)\r
+               where\r
+                       (y,b2`) = largest b2\r
+\r
+\r
+is_geordend :: // meest algemene type\r
+is_geordend ...\r
+\r
+Start = map is_geordend [t0,t1,t2,t3,t4,t5,t6,t7]\r
+\r
+\r
+is_gebalanceerd :: // meest algemene type\r
+is_gebalanceerd ...\r
+\r
+//Start = map is_gebalanceerd [t0,t1,t2,t3,t4,t5,t6,t7]\r