src/HOL/Codatatype/Tools/bnf_gfp_util.ML
author blanchet
Tue Sep 11 18:39:47 2012 +0200 (2012-09-11)
changeset 49286 dde4967c9233
parent 49275 ce87d6a901eb
child 49509 163914705f8d
permissions -rw-r--r--
added "defaults" option
     1 (*  Title:      HOL/Codatatype/Tools/bnf_gfp_util.ML
     2     Author:     Dmitriy Traytel, TU Muenchen
     3     Copyright   2012
     4 
     5 Library for the codatatype construction.
     6 *)
     7 
     8 signature BNF_GFP_UTIL =
     9 sig
    10   val mk_rec_simps: int -> thm -> thm list -> thm list list
    11 
    12   val dest_listT: typ -> typ
    13 
    14   val mk_Cons: term -> term -> term
    15   val mk_Shift: term -> term -> term
    16   val mk_Succ: term -> term -> term
    17   val mk_Times: term * term -> term
    18   val mk_append: term * term -> term
    19   val mk_congruent: term -> term -> term
    20   val mk_clists: term -> term
    21   val mk_diag: term -> term
    22   val mk_equiv: term -> term -> term
    23   val mk_fromCard: term -> term -> term
    24   val mk_list_rec: term -> term -> term
    25   val mk_nat_rec: term -> term -> term
    26   val mk_pickWP: term -> term -> term -> term -> term -> term
    27   val mk_prefCl: term -> term
    28   val mk_proj: term -> term
    29   val mk_quotient: term -> term -> term
    30   val mk_shift: term -> term -> term
    31   val mk_size: term -> term
    32   val mk_thePull: term -> term -> term -> term -> term
    33   val mk_toCard: term -> term -> term
    34   val mk_undefined: typ -> term
    35   val mk_univ: term -> term
    36 
    37   val mk_specN: int -> thm -> thm
    38 
    39   val mk_InN_Field: int -> int -> thm
    40   val mk_InN_inject: int -> int -> thm
    41   val mk_InN_not_InM: int -> int -> thm
    42 end;
    43 
    44 structure BNF_GFP_Util : BNF_GFP_UTIL =
    45 struct
    46 
    47 open BNF_Util
    48 
    49 val mk_append = HOLogic.mk_binop @{const_name append};
    50 
    51 fun mk_equiv B R =
    52   Const (@{const_name equiv}, fastype_of B --> fastype_of R --> HOLogic.boolT) $ B $ R;
    53 
    54 fun mk_Sigma (A, B) =
    55   let
    56     val AT = fastype_of A;
    57     val BT = fastype_of B;
    58     val ABT = mk_relT (HOLogic.dest_setT AT, HOLogic.dest_setT (range_type BT));
    59   in Const (@{const_name Sigma}, AT --> BT --> ABT) $ A $ B end;
    60 
    61 fun mk_diag A =
    62   let
    63     val AT = fastype_of A;
    64     val AAT = mk_relT (HOLogic.dest_setT AT, HOLogic.dest_setT AT);
    65   in Const (@{const_name diag}, AT --> AAT) $ A end;
    66 
    67 fun mk_Times (A, B) =
    68   let val AT = HOLogic.dest_setT (fastype_of A);
    69   in mk_Sigma (A, Term.absdummy AT B) end;
    70 
    71 fun dest_listT (Type (@{type_name list}, [T])) = T
    72   | dest_listT T = raise TYPE ("dest_setT: set type expected", [T], []);
    73 
    74 fun mk_Succ Kl kl =
    75   let val T = fastype_of kl;
    76   in
    77     Const (@{const_name Succ},
    78       HOLogic.mk_setT T --> T --> HOLogic.mk_setT (dest_listT T)) $ Kl $ kl
    79   end;
    80 
    81 fun mk_Shift Kl k =
    82   let val T = fastype_of Kl;
    83   in
    84     Const (@{const_name Shift}, T --> dest_listT (HOLogic.dest_setT T) --> T) $ Kl $ k
    85   end;
    86 
    87 fun mk_shift lab k =
    88   let val T = fastype_of lab;
    89   in
    90     Const (@{const_name shift}, T --> dest_listT (Term.domain_type T) --> T) $ lab $ k
    91   end;
    92 
    93 fun mk_prefCl A =
    94   Const (@{const_name prefCl}, fastype_of A --> HOLogic.boolT) $ A;
    95 
    96 fun mk_clists r =
    97   let val T = fastype_of r;
    98   in Const (@{const_name clists}, T --> mk_relT (`I (HOLogic.listT (fst (dest_relT T))))) $ r end;
    99 
   100 fun mk_toCard A r =
   101   let
   102     val AT = fastype_of A;
   103     val rT = fastype_of r;
   104   in
   105     Const (@{const_name toCard},
   106       AT --> rT --> HOLogic.dest_setT AT --> fst (dest_relT rT)) $ A $ r
   107   end;
   108 
   109 fun mk_fromCard A r =
   110   let
   111     val AT = fastype_of A;
   112     val rT = fastype_of r;
   113   in
   114     Const (@{const_name fromCard},
   115       AT --> rT --> fst (dest_relT rT) --> HOLogic.dest_setT AT) $ A $ r
   116   end;
   117 
   118 fun mk_Cons x xs =
   119   let val T = fastype_of xs;
   120   in Const (@{const_name Cons}, dest_listT T --> T --> T) $ x $ xs end;
   121 
   122 fun mk_size t = HOLogic.size_const (fastype_of t) $ t;
   123 
   124 fun mk_quotient A R =
   125   let val T = fastype_of A;
   126   in Const (@{const_name quotient}, T --> fastype_of R --> HOLogic.mk_setT T) $ A $ R end;
   127 
   128 fun mk_proj R =
   129   let val ((AT, BT), T) = `dest_relT (fastype_of R);
   130   in Const (@{const_name proj}, T --> AT --> HOLogic.mk_setT BT) $ R end;
   131 
   132 fun mk_univ f =
   133   let val ((AT, BT), T) = `dest_funT (fastype_of f);
   134   in Const (@{const_name univ}, T --> HOLogic.mk_setT AT --> BT) $ f end;
   135 
   136 fun mk_congruent R f =
   137   Const (@{const_name congruent}, fastype_of R --> fastype_of f --> HOLogic.boolT) $ R $ f;
   138 
   139 fun mk_undefined T = Const (@{const_name undefined}, T);
   140 
   141 fun mk_nat_rec Zero Suc =
   142   let val T = fastype_of Zero;
   143   in Const (@{const_name nat_rec}, T --> fastype_of Suc --> HOLogic.natT --> T) $ Zero $ Suc end;
   144 
   145 fun mk_list_rec Nil Cons =
   146   let
   147     val T = fastype_of Nil;
   148     val (U, consT) = `(Term.domain_type) (fastype_of Cons);
   149   in
   150     Const (@{const_name list_rec}, T --> consT --> HOLogic.listT U --> T) $ Nil $ Cons
   151   end;
   152 
   153 fun mk_thePull B1 B2 f1 f2 =
   154   let
   155     val fT1 = fastype_of f1;
   156     val fT2 = fastype_of f2;
   157     val BT1 = domain_type fT1;
   158     val BT2 = domain_type fT2;
   159   in
   160     Const (@{const_name thePull}, HOLogic.mk_setT BT1 --> HOLogic.mk_setT BT2 --> fT1 --> fT2 -->
   161       mk_relT (BT1, BT2)) $ B1 $ B2 $ f1 $ f2
   162   end;
   163 
   164 fun mk_pickWP A f1 f2 b1 b2 =
   165   let
   166     val fT1 = fastype_of f1;
   167     val fT2 = fastype_of f2;
   168     val AT = domain_type fT1;
   169     val BT1 = range_type fT1;
   170     val BT2 = range_type fT2;
   171   in
   172     Const (@{const_name pickWP}, HOLogic.mk_setT AT --> fT1 --> fT2 --> BT1 --> BT2 --> AT) $
   173       A $ f1 $ f2 $ b1 $ b2
   174   end;
   175 
   176 fun mk_InN_not_InM 1 _ = @{thm Inl_not_Inr}
   177   | mk_InN_not_InM n m =
   178     if n > m then mk_InN_not_InM m n RS @{thm not_sym}
   179     else mk_InN_not_InM (n - 1) (m - 1) RS @{thm not_arg_cong_Inr};
   180 
   181 fun mk_InN_Field 1 1 = @{thm TrueE[OF TrueI]}
   182   | mk_InN_Field _ 1 = @{thm Inl_Field_csum}
   183   | mk_InN_Field 2 2 = @{thm Inr_Field_csum}
   184   | mk_InN_Field n m = mk_InN_Field (n - 1) (m - 1) RS @{thm Inr_Field_csum};
   185 
   186 fun mk_InN_inject 1 _ = @{thm TrueE[OF TrueI]}
   187   | mk_InN_inject _ 1 = @{thm Inl_inject}
   188   | mk_InN_inject 2 2 = @{thm Inr_inject}
   189   | mk_InN_inject n m = @{thm Inr_inject} RS mk_InN_inject (n - 1) (m - 1);
   190 
   191 fun mk_specN 0 thm = thm
   192   | mk_specN n thm = mk_specN (n - 1) (thm RS spec);
   193 
   194 fun mk_rec_simps n rec_thm defs = map (fn i =>
   195   map (fn def => def RS rec_thm RS mk_nthI n i RS fun_cong) defs) (1 upto n);
   196 
   197 end;