author | wenzelm |
Fri, 17 Nov 2006 02:20:03 +0100 | |
changeset 21404 | eb85850d3eb7 |
parent 19736 | d8d0f8f51d69 |
child 21871 | 9ce66839d9f1 |
permissions | -rw-r--r-- |
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(* Title: HOL/Library/Char_ord.thy |
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ID: $Id$ |
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Author: Norbert Voelker |
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*) |
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header {* Order on characters *} |
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theory Char_ord |
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imports Product_ord |
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begin |
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text {* Conversions between nibbles and integers in [0..15]. *} |
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consts |
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nibble_to_int:: "nibble \<Rightarrow> int" |
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primrec |
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"nibble_to_int Nibble0 = 0" |
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"nibble_to_int Nibble1 = 1" |
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"nibble_to_int Nibble2 = 2" |
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"nibble_to_int Nibble3 = 3" |
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"nibble_to_int Nibble4 = 4" |
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"nibble_to_int Nibble5 = 5" |
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"nibble_to_int Nibble6 = 6" |
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"nibble_to_int Nibble7 = 7" |
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"nibble_to_int Nibble8 = 8" |
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"nibble_to_int Nibble9 = 9" |
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"nibble_to_int NibbleA = 10" |
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"nibble_to_int NibbleB = 11" |
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"nibble_to_int NibbleC = 12" |
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"nibble_to_int NibbleD = 13" |
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"nibble_to_int NibbleE = 14" |
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"nibble_to_int NibbleF = 15" |
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definition |
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more robust syntax for definition/abbreviation/notation;
wenzelm
parents:
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changeset
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int_to_nibble :: "int \<Rightarrow> nibble" where |
eb85850d3eb7
more robust syntax for definition/abbreviation/notation;
wenzelm
parents:
19736
diff
changeset
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"int_to_nibble x = (let y = x mod 16 in |
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if y = 0 then Nibble0 else |
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if y = 1 then Nibble1 else |
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if y = 2 then Nibble2 else |
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if y = 3 then Nibble3 else |
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if y = 4 then Nibble4 else |
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if y = 5 then Nibble5 else |
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if y = 6 then Nibble6 else |
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if y = 7 then Nibble7 else |
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if y = 8 then Nibble8 else |
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if y = 9 then Nibble9 else |
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if y = 10 then NibbleA else |
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if y = 11 then NibbleB else |
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if y = 12 then NibbleC else |
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if y = 13 then NibbleD else |
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if y = 14 then NibbleE else |
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NibbleF)" |
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lemma int_to_nibble_nibble_to_int: "int_to_nibble(nibble_to_int x) = x" |
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by (cases x) (auto simp: int_to_nibble_def Let_def) |
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lemma inj_nibble_to_int: "inj nibble_to_int" |
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by (rule inj_on_inverseI) (rule int_to_nibble_nibble_to_int) |
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lemmas nibble_to_int_eq = inj_nibble_to_int [THEN inj_eq] |
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lemma nibble_to_int_ge_0: "0 \<le> nibble_to_int x" |
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by (cases x) auto |
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lemma nibble_to_int_less_16: "nibble_to_int x < 16" |
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by (cases x) auto |
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text {* Conversion between chars and int pairs. *} |
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consts |
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char_to_int_pair :: "char \<Rightarrow> int \<times> int" |
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primrec |
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"char_to_int_pair (Char a b) = (nibble_to_int a, nibble_to_int b)" |
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lemma inj_char_to_int_pair: "inj char_to_int_pair" |
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apply (rule inj_onI) |
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apply (case_tac x, case_tac y) |
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apply (auto simp: nibble_to_int_eq) |
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done |
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lemmas char_to_int_pair_eq = inj_char_to_int_pair [THEN inj_eq] |
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text {* Instantiation of order classes *} |
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instance char :: ord .. |
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defs (overloaded) |
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char_le_def: "c \<le> d \<equiv> (char_to_int_pair c \<le> char_to_int_pair d)" |
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char_less_def: "c < d \<equiv> (char_to_int_pair c < char_to_int_pair d)" |
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lemmas char_ord_defs = char_less_def char_le_def |
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instance char :: order |
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by default (auto simp: char_ord_defs char_to_int_pair_eq order_less_le) |
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instance char :: linorder |
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by default (auto simp: char_le_def) |
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end |