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(* Title: HOL/ex/Hex_Bin_Examples.thy
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Author: Gerwin Klein, NICTA
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*)
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section \<open>Examples for hexadecimal and binary numerals\<close>
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theory Hex_Bin_Examples imports Main
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begin
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text "Hex and bin numerals can be used like normal decimal numerals in input"
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lemma "0xFF = 255" by (rule refl)
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lemma "0xF = 0b1111" by (rule refl)
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text \<open>
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Just like decimal numeral they are polymorphic, for arithmetic
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they need to be constrained
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\<close>
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lemma "0x0A + 0x10 = (0x1A :: nat)" by simp
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text "The number of leading zeros is irrelevant"
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lemma "0b00010000 = 0x10" by (rule refl)
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text "Unary minus works as for decimal numerals"
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lemma "- 0x0A = - 10" by (rule refl)
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text \<open>
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Hex and bin numerals are printed as decimal: \<^term>\<open>0b10\<close>
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\<close>
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term "0b10"
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term "0x0A"
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text \<open>
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The numerals 0 and 1 are syntactically different from the
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constants 0 and 1. For the usual numeric types, their values
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are the same, though.
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\<close>
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lemma "0x01 = 1" oops
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lemma "0x00 = 0" oops
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lemma "0x01 = (1::nat)" by simp
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lemma "0b0000 = (0::int)" by simp
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end
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