--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/ex/binfn.thy Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,52 @@
+(* Title: ZF/bin
+ ID: $Id$
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Copyright 1993 University of Cambridge
+
+Arithmetic on binary integers.
+*)
+
+BinFn = Integ + Bin +
+consts
+ bin_rec :: "[i, i, i, [i,i,i]=>i] => i"
+ integ_of_bin :: "i=>i"
+ bin_succ :: "i=>i"
+ bin_pred :: "i=>i"
+ bin_minus :: "i=>i"
+ bin_add,bin_mult :: "[i,i]=>i"
+
+rules
+
+ bin_rec_def
+ "bin_rec(z,a,b,h) == \
+\ Vrec(z, %z g. bin_case(a, b, %w x. h(w, x, g`w), z))"
+
+ integ_of_bin_def
+ "integ_of_bin(w) == bin_rec(w, $#0, $~($#1), %w x r. $#x $+ r $+ r)"
+
+ bin_succ_def
+ "bin_succ(w0) == bin_rec(w0, Plus$$1, Plus, %w x r. cond(x, r$$0, w$$1))"
+
+ bin_pred_def
+ "bin_pred(w0) == \
+\ bin_rec(w0, Minus, Minus$$0, %w x r. cond(x, w$$0, r$$1))"
+
+ bin_minus_def
+ "bin_minus(w0) == \
+\ bin_rec(w0, Plus, Plus$$1, %w x r. cond(x, bin_pred(r$$0), r$$0))"
+
+ bin_add_def
+ "bin_add(v0,w0) == \
+\ bin_rec(v0, \
+\ lam w:bin. w, \
+\ lam w:bin. bin_pred(w), \
+\ %v x r. lam w1:bin. \
+\ bin_rec(w1, v$$x, bin_pred(v$$x), \
+\ %w y s. (r`cond(x and y, bin_succ(w), w)) \
+\ $$ (x xor y))) ` w0"
+
+ bin_mult_def
+ "bin_mult(v0,w) == \
+\ bin_rec(v0, Plus, bin_minus(w), \
+\ %v x r. cond(x, bin_add(r$$0,w), r$$0))"
+end