ex/InSort.thy

some more sorting algorithms

(*  Title: 	HOL/ex/insort.thy
    ID:         $Id$
    Author: 	Tobias Nipkow
    Copyright   1994 TU Muenchen

Insertion sort
*)

InSort  =  Sorting +

consts
  ins :: "[['a,'a]=>bool, 'a, 'a list] => 'a list"
  insort :: "[['a,'a]=>bool, 'a list] => 'a list"

rules
  ins_Nil  "ins(f,x,[]) = [x]"
  ins_Cons "ins(f,x,Cons(y,ys)) =   \
\	       if(f(x,y), Cons(x,Cons(y,ys)), Cons(y, ins(f,x,ys)))"

  insort_Nil  "insort(f,[]) = []"
  insort_Cons "insort(f,Cons(x,xs)) = ins(f,x,insort(f,xs))"
end