author | haftmann |
Mon, 02 Dec 2019 17:15:16 +0000 | |
changeset 71195 | d50a718ccf35 |
parent 70901 | 94a0c47b8553 |
child 71759 | 816e52bbfa60 |
permissions | -rw-r--r-- |
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(* Title: HOL/Library/Type_Length.thy |
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Author: John Matthews, Galois Connections, Inc., Copyright 2006 |
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*) |
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section \<open>Assigning lengths to types by type classes\<close> |
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theory Type_Length |
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imports Numeral_Type |
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begin |
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text \<open> |
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The aim of this is to allow any type as index type, but to provide a |
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default instantiation for numeral types. This independence requires |
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some duplication with the definitions in \<^file>\<open>Numeral_Type.thy\<close>. |
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\<close> |
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class len0 = |
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fixes len_of :: "'a itself \<Rightarrow> nat" |
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syntax "_type_length" :: "type \<Rightarrow> nat" (\<open>(1LENGTH/(1'(_')))\<close>) |
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translations "LENGTH('a)" \<rightharpoonup> |
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"CONST len_of (CONST Pure.type :: 'a itself)" |
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print_translation \<open> |
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let |
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fun len_of_itself_tr' ctxt [Const (\<^const_syntax>\<open>Pure.type\<close>, Type (_, [T]))] = |
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Syntax.const \<^syntax_const>\<open>_type_length\<close> $ Syntax_Phases.term_of_typ ctxt T |
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in [(\<^const_syntax>\<open>len_of\<close>, len_of_itself_tr')] end |
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\<close> |
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text \<open>Some theorems are only true on words with length greater 0.\<close> |
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class len = len0 + |
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assumes len_gt_0 [iff]: "0 < LENGTH('a)" |
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begin |
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lemma len_not_eq_0 [simp]: |
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"LENGTH('a) \<noteq> 0" |
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by simp |
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end |
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instantiation num0 and num1 :: len0 |
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begin |
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definition len_num0: "len_of (_ :: num0 itself) = 0" |
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definition len_num1: "len_of (_ :: num1 itself) = 1" |
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instance .. |
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end |
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instantiation bit0 and bit1 :: (len0) len0 |
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begin |
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definition len_bit0: "len_of (_ :: 'a::len0 bit0 itself) = 2 * LENGTH('a)" |
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definition len_bit1: "len_of (_ :: 'a::len0 bit1 itself) = 2 * LENGTH('a) + 1" |
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instance .. |
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end |
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lemmas len_of_numeral_defs [simp] = len_num0 len_num1 len_bit0 len_bit1 |
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instance num1 :: len |
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by standard simp |
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instance bit0 :: (len) len |
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by standard simp |
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instance bit1 :: (len0) len |
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by standard simp |
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instantiation Enum.finite_1 :: len |
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begin |
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definition |
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"len_of_finite_1 (x :: Enum.finite_1 itself) \<equiv> (1 :: nat)" |
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instance |
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by standard (auto simp: len_of_finite_1_def) |
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end |
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instantiation Enum.finite_2 :: len |
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begin |
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definition |
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"len_of_finite_2 (x :: Enum.finite_2 itself) \<equiv> (2 :: nat)" |
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instance |
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by standard (auto simp: len_of_finite_2_def) |
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end |
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instantiation Enum.finite_3 :: len |
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begin |
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definition |
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"len_of_finite_3 (x :: Enum.finite_3 itself) \<equiv> (4 :: nat)" |
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instance |
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by standard (auto simp: len_of_finite_3_def) |
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end |
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lemma length_not_greater_eq_2_iff [simp]: |
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\<open>\<not> 2 \<le> LENGTH('a::len) \<longleftrightarrow> LENGTH('a) = 1\<close> |
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by (auto simp add: not_le dest: less_2_cases) |
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end |