(* Title: HOL/ex/Hex_Bin_Examples.thy ID: $Id: Hex_Bin_Examples.thy,v 1.1 2006/10/06 01:49:36 kleing Exp $ 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
lemma
(255::'a) = (255::'a)
lemma
(15::'a) = (15::'a)
lemma
10 + 16 = 26
lemma
(16::'a) = (16::'a)
lemma
- (10::'a) = - (10::'a)
lemma
Numeral1 = 1
lemma
Numeral0 = 0