(* Title: HOL/ex/Hex_Bin_Examples.thy
Author: Gerwin Klein, NICTA
*)
section \<open>Examples for hexadecimal and binary numerals\<close>
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 \<open>
Just like decimal numeral they are polymorphic, for arithmetic
they need to be constrained
\<close>
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 \<open>
Hex and bin numerals are printed as decimal: \<^term>\<open>0b10\<close>
\<close>
term "0b10"
term "0x0A"
text \<open>
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.
\<close>
lemma "0x01 = 1" oops
lemma "0x00 = 0" oops
lemma "0x01 = (1::nat)" by simp
lemma "0b0000 = (0::int)" by simp
end