src/ZF/Inductive_ZF.thy
author wenzelm
Tue Sep 01 22:32:58 2015 +0200 (2015-09-01)
changeset 61076 bdc1e2f0a86a
parent 60770 240563fbf41d
child 63435 7743df69a6b4
permissions -rw-r--r--
eliminated \<Colon>;
     1 (*  Title:      ZF/Inductive_ZF.thy
     2     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     3     Copyright   1993  University of Cambridge
     4 
     5 Inductive definitions use least fixedpoints with standard products and sums
     6 Coinductive definitions use greatest fixedpoints with Quine products and sums
     7 
     8 Sums are used only for mutual recursion;
     9 Products are used only to derive "streamlined" induction rules for relations
    10 *)
    11 
    12 section\<open>Inductive and Coinductive Definitions\<close>
    13 
    14 theory Inductive_ZF
    15 imports Fixedpt QPair Nat_ZF
    16 keywords
    17   "inductive" "coinductive" "inductive_cases" "rep_datatype" "primrec" :: thy_decl and
    18   "domains" "intros" "monos" "con_defs" "type_intros" "type_elims"
    19   "elimination" "induction" "case_eqns" "recursor_eqns"
    20 begin
    21 
    22 lemma def_swap_iff: "a == b ==> a = c \<longleftrightarrow> c = b"
    23   by blast
    24 
    25 lemma def_trans: "f == g ==> g(a) = b ==> f(a) = b"
    26   by simp
    27 
    28 lemma refl_thin: "!!P. a = a ==> P ==> P" .
    29 
    30 ML_file "ind_syntax.ML"
    31 ML_file "Tools/ind_cases.ML"
    32 ML_file "Tools/cartprod.ML"
    33 ML_file "Tools/inductive_package.ML"
    34 ML_file "Tools/induct_tacs.ML"
    35 ML_file "Tools/primrec_package.ML"
    36 
    37 ML \<open>
    38 structure Lfp =
    39   struct
    40   val oper      = @{const lfp}
    41   val bnd_mono  = @{const bnd_mono}
    42   val bnd_monoI = @{thm bnd_monoI}
    43   val subs      = @{thm def_lfp_subset}
    44   val Tarski    = @{thm def_lfp_unfold}
    45   val induct    = @{thm def_induct}
    46   end;
    47 
    48 structure Standard_Prod =
    49   struct
    50   val sigma     = @{const Sigma}
    51   val pair      = @{const Pair}
    52   val split_name = @{const_name split}
    53   val pair_iff  = @{thm Pair_iff}
    54   val split_eq  = @{thm split}
    55   val fsplitI   = @{thm splitI}
    56   val fsplitD   = @{thm splitD}
    57   val fsplitE   = @{thm splitE}
    58   end;
    59 
    60 structure Standard_CP = CartProd_Fun (Standard_Prod);
    61 
    62 structure Standard_Sum =
    63   struct
    64   val sum       = @{const sum}
    65   val inl       = @{const Inl}
    66   val inr       = @{const Inr}
    67   val elim      = @{const case}
    68   val case_inl  = @{thm case_Inl}
    69   val case_inr  = @{thm case_Inr}
    70   val inl_iff   = @{thm Inl_iff}
    71   val inr_iff   = @{thm Inr_iff}
    72   val distinct  = @{thm Inl_Inr_iff}
    73   val distinct' = @{thm Inr_Inl_iff}
    74   val free_SEs  = Ind_Syntax.mk_free_SEs
    75             [distinct, distinct', inl_iff, inr_iff, Standard_Prod.pair_iff]
    76   end;
    77 
    78 
    79 structure Ind_Package =
    80     Add_inductive_def_Fun
    81       (structure Fp=Lfp and Pr=Standard_Prod and CP=Standard_CP
    82        and Su=Standard_Sum val coind = false);
    83 
    84 
    85 structure Gfp =
    86   struct
    87   val oper      = @{const gfp}
    88   val bnd_mono  = @{const bnd_mono}
    89   val bnd_monoI = @{thm bnd_monoI}
    90   val subs      = @{thm def_gfp_subset}
    91   val Tarski    = @{thm def_gfp_unfold}
    92   val induct    = @{thm def_Collect_coinduct}
    93   end;
    94 
    95 structure Quine_Prod =
    96   struct
    97   val sigma     = @{const QSigma}
    98   val pair      = @{const QPair}
    99   val split_name = @{const_name qsplit}
   100   val pair_iff  = @{thm QPair_iff}
   101   val split_eq  = @{thm qsplit}
   102   val fsplitI   = @{thm qsplitI}
   103   val fsplitD   = @{thm qsplitD}
   104   val fsplitE   = @{thm qsplitE}
   105   end;
   106 
   107 structure Quine_CP = CartProd_Fun (Quine_Prod);
   108 
   109 structure Quine_Sum =
   110   struct
   111   val sum       = @{const qsum}
   112   val inl       = @{const QInl}
   113   val inr       = @{const QInr}
   114   val elim      = @{const qcase}
   115   val case_inl  = @{thm qcase_QInl}
   116   val case_inr  = @{thm qcase_QInr}
   117   val inl_iff   = @{thm QInl_iff}
   118   val inr_iff   = @{thm QInr_iff}
   119   val distinct  = @{thm QInl_QInr_iff}
   120   val distinct' = @{thm QInr_QInl_iff}
   121   val free_SEs  = Ind_Syntax.mk_free_SEs
   122             [distinct, distinct', inl_iff, inr_iff, Quine_Prod.pair_iff]
   123   end;
   124 
   125 
   126 structure CoInd_Package =
   127   Add_inductive_def_Fun(structure Fp=Gfp and Pr=Quine_Prod and CP=Quine_CP
   128     and Su=Quine_Sum val coind = true);
   129 
   130 \<close>
   131 
   132 end