src/ZF/Inductive_ZF.thy
 author wenzelm Sat Mar 01 14:10:15 2008 +0100 (2008-03-01 ago) changeset 26189 9808cca5c54d parent 26056 6a0801279f4c child 26190 cf51a23c0cd0 permissions -rw-r--r--
misc cleanup of embedded ML code;
use more antiquotations;
tuned;
```     1 (*  Title:      ZF/Inductive_ZF.thy
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```     2     ID:         \$Id\$
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```     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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```     4     Copyright   1993  University of Cambridge
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```     5
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```     6 Inductive definitions use least fixedpoints with standard products and sums
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```     7 Coinductive definitions use greatest fixedpoints with Quine products and sums
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```     8
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```     9 Sums are used only for mutual recursion;
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```    10 Products are used only to derive "streamlined" induction rules for relations
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```    11 *)
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```    12
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```    13 header{*Inductive and Coinductive Definitions*}
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```    14
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```    15 theory Inductive_ZF
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```    16 imports Fixedpt QPair Nat_ZF
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```    17 uses
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```    18   ("ind_syntax.ML")
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```    19   ("Tools/cartprod.ML")
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```    20   ("Tools/ind_cases.ML")
```
```    21   ("Tools/inductive_package.ML")
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```    22   ("Tools/induct_tacs.ML")
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```    23   ("Tools/primrec_package.ML")
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```    24 begin
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```    25
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```    26 lemma def_swap_iff: "a == b ==> a = c <-> c = b"
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```    27   by blast
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```    28
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```    29 lemma def_trans: "f == g ==> g(a) = b ==> f(a) = b"
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```    30   by simp
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```    31
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```    32 lemma refl_thin: "!!P. a = a ==> P ==> P" .
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```    33
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```    34 use "ind_syntax.ML"
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```    35 use "Tools/cartprod.ML"
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```    36 use "Tools/ind_cases.ML"
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```    37 use "Tools/inductive_package.ML"
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```    38 use "Tools/induct_tacs.ML"
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```    39 use "Tools/primrec_package.ML"
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```    40
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```    41 setup IndCases.setup
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```    42 setup DatatypeTactics.setup
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```    43
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```    44 ML_setup {*
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```    45 val iT = Ind_Syntax.iT
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```    46 and oT = FOLogic.oT;
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```    47
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```    48 structure Lfp =
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```    49   struct
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```    50   val oper      = @{const lfp}
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```    51   val bnd_mono  = @{const bnd_mono}
```
```    52   val bnd_monoI = @{thm bnd_monoI}
```
```    53   val subs      = @{thm def_lfp_subset}
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```    54   val Tarski    = @{thm def_lfp_unfold}
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```    55   val induct    = @{thm def_induct}
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```    56   end;
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```    57
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```    58 structure Standard_Prod =
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```    59   struct
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```    60   val sigma     = @{const Sigma}
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```    61   val pair      = @{const Pair}
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```    62   val split_name = @{const_name split}
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```    63   val pair_iff  = @{thm Pair_iff}
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```    64   val split_eq  = @{thm split}
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```    65   val fsplitI   = @{thm splitI}
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```    66   val fsplitD   = @{thm splitD}
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```    67   val fsplitE   = @{thm splitE}
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```    68   end;
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```    69
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```    70 structure Standard_CP = CartProd_Fun (Standard_Prod);
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```    71
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```    72 structure Standard_Sum =
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```    73   struct
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```    74   val sum       = @{const sum}
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```    75   val inl       = @{const Inl}
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```    76   val inr       = @{const Inr}
```
```    77   val elim      = @{const case}
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```    78   val case_inl  = @{thm case_Inl}
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```    79   val case_inr  = @{thm case_Inr}
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```    80   val inl_iff   = @{thm Inl_iff}
```
```    81   val inr_iff   = @{thm Inr_iff}
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```    82   val distinct  = @{thm Inl_Inr_iff}
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```    83   val distinct' = @{thm Inr_Inl_iff}
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```    84   val free_SEs  = Ind_Syntax.mk_free_SEs
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```    85             [distinct, distinct', inl_iff, inr_iff, Standard_Prod.pair_iff]
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```    86   end;
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```    87
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```    88
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```    89 structure Ind_Package =
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```    90     Add_inductive_def_Fun
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```    91       (structure Fp=Lfp and Pr=Standard_Prod and CP=Standard_CP
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```    92        and Su=Standard_Sum val coind = false);
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```    93
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```    94
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```    95 structure Gfp =
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```    96   struct
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```    97   val oper      = @{const gfp}
```
```    98   val bnd_mono  = @{const bnd_mono}
```
```    99   val bnd_monoI = @{thm bnd_monoI}
```
```   100   val subs      = @{thm def_gfp_subset}
```
```   101   val Tarski    = @{thm def_gfp_unfold}
```
```   102   val induct    = @{thm def_Collect_coinduct}
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```   103   end;
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```   104
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```   105 structure Quine_Prod =
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```   106   struct
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```   107   val sigma     = @{const QSigma}
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```   108   val pair      = @{const QPair}
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```   109   val split_name = @{const_name qsplit}
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```   110   val pair_iff  = @{thm QPair_iff}
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```   111   val split_eq  = @{thm qsplit}
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```   112   val fsplitI   = @{thm qsplitI}
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```   113   val fsplitD   = @{thm qsplitD}
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```   114   val fsplitE   = @{thm qsplitE}
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```   115   end;
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```   116
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```   117 structure Quine_CP = CartProd_Fun (Quine_Prod);
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```   118
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```   119 structure Quine_Sum =
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```   120   struct
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```   121   val sum       = @{const qsum}
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```   122   val inl       = @{const QInl}
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```   123   val inr       = @{const QInr}
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```   124   val elim      = @{const qcase}
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```   125   val case_inl  = @{thm qcase_QInl}
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```   126   val case_inr  = @{thm qcase_QInr}
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```   127   val inl_iff   = @{thm QInl_iff}
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```   128   val inr_iff   = @{thm QInr_iff}
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```   129   val distinct  = @{thm QInl_QInr_iff}
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```   130   val distinct' = @{thm QInr_QInl_iff}
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```   131   val free_SEs  = Ind_Syntax.mk_free_SEs
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```   132             [distinct, distinct', inl_iff, inr_iff, Quine_Prod.pair_iff]
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```   133   end;
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```   134
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```   135
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```   136 structure CoInd_Package =
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```   137   Add_inductive_def_Fun(structure Fp=Gfp and Pr=Quine_Prod and CP=Quine_CP
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```   138     and Su=Quine_Sum val coind = true);
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```   139
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```   140 *}
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```   141
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```   142 end
```