src/HOL/ex/Hex_Bin_Examples.thy
 author wenzelm Sun Nov 02 18:21:45 2014 +0100 (2014-11-02) changeset 58889 5b7a9633cfa8 parent 41460 ea56b98aee83 child 61343 5b5656a63bd6 permissions -rw-r--r--
```     1 (*  Title:      HOL/ex/Hex_Bin_Examples.thy
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```     2     Author:     Gerwin Klein, NICTA
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```     3 *)
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```     4
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```     5 section {* Examples for hexadecimal and binary numerals *}
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```     6
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```     7 theory Hex_Bin_Examples imports Main
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```     8 begin
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```     9
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```    10
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```    11 text "Hex and bin numerals can be used like normal decimal numerals in input"
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```    12 lemma "0xFF = 255" by (rule refl)
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```    13 lemma "0xF = 0b1111" by (rule refl)
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```    14
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```    15 text {*
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```    16   Just like decimal numeral they are polymorphic, for arithmetic
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```    17   they need to be constrained
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```    18 *}
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```    19 lemma "0x0A + 0x10 = (0x1A :: nat)" by simp
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```    20
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```    21 text "The number of leading zeros is irrelevant"
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```    22 lemma "0b00010000 = 0x10" by (rule refl)
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```    23
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```    24 text "Unary minus works as for decimal numerals"
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```    25 lemma "- 0x0A = - 10" by (rule refl)
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```    26
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```    27 text {*
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```    28   Hex and bin numerals are printed as decimal: @{term "0b10"}
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```    29 *}
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```    30 term "0b10"
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```    31 term "0x0A"
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```    32
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```    33 text {*
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```    34   The numerals 0 and 1 are syntactically different from the
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```    35   constants 0 and 1. For the usual numeric types, their values
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```    36   are the same, though.
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```    37 *}
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```    38 lemma "0x01 = 1" oops
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```    39 lemma "0x00 = 0" oops
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```    40
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```    41 lemma "0x01 = (1::nat)" by simp
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```    42 lemma "0b0000 = (0::int)" by simp
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```    43
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```    44
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```    45 end
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```    46
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