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src/HOL/ex/Hex_Bin_Examples.thy

author | wenzelm |

Sun, 02 Nov 2014 18:21:45 +0100 | |

changeset 58889 | 5b7a9633cfa8 |

parent 41460 | ea56b98aee83 |

child 61343 | 5b5656a63bd6 |

permissions | -rw-r--r-- |

modernized header uniformly as section;

(* 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: @{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