--- a/src/CCL/ex/nat.thy Sat Apr 05 16:00:00 2003 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,38 +0,0 @@
-(* Title: CCL/ex/nat.thy
- ID: $Id$
- Author: Martin Coen, Cambridge University Computer Laboratory
- Copyright 1993 University of Cambridge
-
-Programs defined over the natural numbers
-*)
-
-Nat = Wfd +
-
-consts
-
- not :: "i=>i"
- "#+","#*","#-",
- "##","#<","#<=" :: "[i,i]=>i" (infixr 60)
- ackermann :: "[i,i]=>i"
-
-rules
-
- not_def "not(b) == if b then false else true"
-
- add_def "a #+ b == nrec(a,b,%x g.succ(g))"
- mult_def "a #* b == nrec(a,zero,%x g.b #+ g)"
- sub_def "a #- b == letrec sub x y be ncase(y,x,%yy.ncase(x,zero,%xx.sub(xx,yy))) \
-\ in sub(a,b)"
- le_def "a #<= b == letrec le x y be ncase(x,true,%xx.ncase(y,false,%yy.le(xx,yy))) \
-\ in le(a,b)"
- lt_def "a #< b == not(b #<= a)"
-
- div_def "a ## b == letrec div x y be if x #< y then zero else succ(div(x#-y,y)) \
-\ in div(a,b)"
- ack_def
- "ackermann(a,b) == letrec ack n m be ncase(n,succ(m),%x. \
-\ ncase(m,ack(x,succ(zero)),%y.ack(x,ack(succ(x),y))))\
-\ in ack(a,b)"
-
-end
-