src/HOL/ex/Qsort.thy

+(*  Title: 	HOL/ex/qsort.thy
+    ID:         $Id$
+    Author: 	Tobias Nipkow
+    Copyright   1994 TU Muenchen
+
+Quicksort
+*)
+
+Qsort = Sorting +
+consts
+  qsort  :: "[['a,'a] => bool, 'a list] => 'a list"
+
+rules
+
+qsort_Nil  "qsort le [] = []"
+qsort_Cons "qsort le (x#xs) = qsort le [y:xs . ~le x y] @ \
+\                            (x# qsort le [y:xs . le x y])"
+
+(* computational induction.
+   The dependence of p on x but not xs is intentional.
+*)
+qsort_ind
+ "[| P([]); \
+\    !!x xs. [| P([y:xs . ~p x y]); P([y:xs . p x y]) |] ==> \
+\            P(x#xs) |] \
+\ ==> P(xs)"
+end