src/CCL/ex/Nat.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/CCL/ex/Nat.thy	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,38 @@
+(*  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
+