src/HOL/ex/Hex_Bin_Examples.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/ex/Hex_Bin_Examples.thy	Fri Oct 06 03:49:36 2006 +0200
@@ -0,0 +1,47 @@
+(*  Title:      HOL/ex/Hex_Bin_Examples.thy
+    ID:         $Id$
+    Author:     Gerwin Klein, NICTA
+*)
+
+header {* Examples for hexadecimal and binary numerals *}
+
+theory Hex_Bin_Examples imports Main 
+begin
+
+
+text "Hex and bin numerals can be used like normal decimal numerals in input"
+lemma "0xFF = 255" by (rule refl)
+lemma "0xF = 0b1111" by (rule refl)
+
+text {* 
+  Just like decimal numeral they are polymorphic, for arithmetic 
+  they need to be constrained
+*}
+lemma "0x0A + 0x10 = (0x1A :: nat)" by simp
+
+text "The number of leading zeros is irrelevant"
+lemma "0b00010000 = 0x10" by (rule refl) 
+
+text "Unary minus works as for decimal numerals"
+lemma "- 0x0A = - 10" by (rule refl)
+
+text {*
+  Hex and bin numerals are printed as decimal: @{term "0b10"}
+*}
+term "0b10"
+term "0x0A"
+
+text {* 
+  The numerals 0 and 1 are syntactically different from the 
+  constants 0 and 1. For the usual numeric types, their values 
+  are the same, though.
+*}
+lemma "0x01 = 1" oops 
+lemma "0x00 = 0" oops 
+
+lemma "0x01 = (1::nat)" by simp
+lemma "0b0000 = (0::int)" by simp
+
+
+end
+