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