src/ZF/Inductive_ZF.thy
 author wenzelm Wed Aug 22 22:55:41 2012 +0200 (2012-08-22 ago) changeset 48891 c0eafbd55de3 parent 46950 d0181abdbdac child 56146 8453d35e4684 permissions -rw-r--r--
prefer ML_file over old uses;
```     1 (*  Title:      ZF/Inductive_ZF.thy
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```     2     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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```     3     Copyright   1993  University of Cambridge
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```     4
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```     5 Inductive definitions use least fixedpoints with standard products and sums
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```     6 Coinductive definitions use greatest fixedpoints with Quine products and sums
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```     7
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```     8 Sums are used only for mutual recursion;
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```     9 Products are used only to derive "streamlined" induction rules for relations
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```    10 *)
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```    11
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```    12 header{*Inductive and Coinductive Definitions*}
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```    13
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```    14 theory Inductive_ZF
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```    15 imports Fixedpt QPair Nat_ZF
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```    16 keywords
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```    17   "inductive" "coinductive" "rep_datatype" "primrec" :: thy_decl and
```
```    18   "inductive_cases" :: thy_script and
```
```    19   "domains" "intros" "monos" "con_defs" "type_intros" "type_elims"
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```    20   "elimination" "induction" "case_eqns" "recursor_eqns"
```
```    21 begin
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```    22
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```    23 lemma def_swap_iff: "a == b ==> a = c \<longleftrightarrow> c = b"
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```    24   by blast
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```    25
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```    26 lemma def_trans: "f == g ==> g(a) = b ==> f(a) = b"
```
```    27   by simp
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```    28
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```    29 lemma refl_thin: "!!P. a = a ==> P ==> P" .
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```    30
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```    31 ML_file "ind_syntax.ML"
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```    32 ML_file "Tools/ind_cases.ML"
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```    33 ML_file "Tools/cartprod.ML"
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```    34 ML_file "Tools/inductive_package.ML"
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```    35 ML_file "Tools/induct_tacs.ML"
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```    36 ML_file "Tools/primrec_package.ML"
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```    37
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```    38 setup IndCases.setup
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```    39 setup DatatypeTactics.setup
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```    40
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```    41 ML {*
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```    42 structure Lfp =
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```    43   struct
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```    44   val oper      = @{const lfp}
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```    45   val bnd_mono  = @{const bnd_mono}
```
```    46   val bnd_monoI = @{thm bnd_monoI}
```
```    47   val subs      = @{thm def_lfp_subset}
```
```    48   val Tarski    = @{thm def_lfp_unfold}
```
```    49   val induct    = @{thm def_induct}
```
```    50   end;
```
```    51
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```    52 structure Standard_Prod =
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```    53   struct
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```    54   val sigma     = @{const Sigma}
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```    55   val pair      = @{const Pair}
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```    56   val split_name = @{const_name split}
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```    57   val pair_iff  = @{thm Pair_iff}
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```    58   val split_eq  = @{thm split}
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```    59   val fsplitI   = @{thm splitI}
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```    60   val fsplitD   = @{thm splitD}
```
```    61   val fsplitE   = @{thm splitE}
```
```    62   end;
```
```    63
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```    64 structure Standard_CP = CartProd_Fun (Standard_Prod);
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```    65
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```    66 structure Standard_Sum =
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```    67   struct
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```    68   val sum       = @{const sum}
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```    69   val inl       = @{const Inl}
```
```    70   val inr       = @{const Inr}
```
```    71   val elim      = @{const case}
```
```    72   val case_inl  = @{thm case_Inl}
```
```    73   val case_inr  = @{thm case_Inr}
```
```    74   val inl_iff   = @{thm Inl_iff}
```
```    75   val inr_iff   = @{thm Inr_iff}
```
```    76   val distinct  = @{thm Inl_Inr_iff}
```
```    77   val distinct' = @{thm Inr_Inl_iff}
```
```    78   val free_SEs  = Ind_Syntax.mk_free_SEs
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```    79             [distinct, distinct', inl_iff, inr_iff, Standard_Prod.pair_iff]
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```    80   end;
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```    81
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```    82
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```    83 structure Ind_Package =
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```    84     Add_inductive_def_Fun
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```    85       (structure Fp=Lfp and Pr=Standard_Prod and CP=Standard_CP
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```    86        and Su=Standard_Sum val coind = false);
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```    87
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```    88
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```    89 structure Gfp =
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```    90   struct
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```    91   val oper      = @{const gfp}
```
```    92   val bnd_mono  = @{const bnd_mono}
```
```    93   val bnd_monoI = @{thm bnd_monoI}
```
```    94   val subs      = @{thm def_gfp_subset}
```
```    95   val Tarski    = @{thm def_gfp_unfold}
```
```    96   val induct    = @{thm def_Collect_coinduct}
```
```    97   end;
```
```    98
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```    99 structure Quine_Prod =
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```   100   struct
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```   101   val sigma     = @{const QSigma}
```
```   102   val pair      = @{const QPair}
```
```   103   val split_name = @{const_name qsplit}
```
```   104   val pair_iff  = @{thm QPair_iff}
```
```   105   val split_eq  = @{thm qsplit}
```
```   106   val fsplitI   = @{thm qsplitI}
```
```   107   val fsplitD   = @{thm qsplitD}
```
```   108   val fsplitE   = @{thm qsplitE}
```
```   109   end;
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```   110
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```   111 structure Quine_CP = CartProd_Fun (Quine_Prod);
```
```   112
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```   113 structure Quine_Sum =
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```   114   struct
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```   115   val sum       = @{const qsum}
```
```   116   val inl       = @{const QInl}
```
```   117   val inr       = @{const QInr}
```
```   118   val elim      = @{const qcase}
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```   119   val case_inl  = @{thm qcase_QInl}
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```   120   val case_inr  = @{thm qcase_QInr}
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```   121   val inl_iff   = @{thm QInl_iff}
```
```   122   val inr_iff   = @{thm QInr_iff}
```
```   123   val distinct  = @{thm QInl_QInr_iff}
```
```   124   val distinct' = @{thm QInr_QInl_iff}
```
```   125   val free_SEs  = Ind_Syntax.mk_free_SEs
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```   126             [distinct, distinct', inl_iff, inr_iff, Quine_Prod.pair_iff]
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```   127   end;
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```   128
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```   129
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```   130 structure CoInd_Package =
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```   131   Add_inductive_def_Fun(structure Fp=Gfp and Pr=Quine_Prod and CP=Quine_CP
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```   132     and Su=Quine_Sum val coind = true);
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```   133
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```   134 *}
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```   135
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```   136 end
```