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SSL Hex_Bin_Examples.thySprache: Isabelle |
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(* Title: HOL/ex/Hex_Bin_Examples.thy Author: Gerwin Klein, NICTA *) section ‹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: 🍋‹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
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2026-05-26