src/HOL/Tools/Lifting/lifting_def.ML
author kuncar
Thu Feb 20 16:56:33 2014 +0100 (2014-02-20)
changeset 55610 9066b603dff6
parent 55609 69ac773a467f
child 55723 f66371633e13
permissions -rw-r--r--
refactoring; generate rep_eq always, not only when it would be accepted by the code generator
kuncar@47308
     1
(*  Title:      HOL/Tools/Lifting/lifting_def.ML
kuncar@47308
     2
    Author:     Ondrej Kuncar
kuncar@47308
     3
kuncar@47308
     4
Definitions for constants on quotient types.
kuncar@47308
     5
*)
kuncar@47308
     6
kuncar@47308
     7
signature LIFTING_DEF =
kuncar@47308
     8
sig
kuncar@51374
     9
  val generate_parametric_transfer_rule:
kuncar@51374
    10
    Proof.context -> thm -> thm -> thm
kuncar@51374
    11
kuncar@47308
    12
  val add_lift_def:
kuncar@53951
    13
    (binding * mixfix) -> typ -> term -> thm -> thm list -> local_theory -> local_theory
kuncar@47308
    14
kuncar@47308
    15
  val lift_def_cmd:
kuncar@53951
    16
    (binding * string option * mixfix) * string * (Facts.ref * Args.src list) list -> local_theory -> Proof.state
kuncar@47308
    17
kuncar@47308
    18
  val can_generate_code_cert: thm -> bool
kuncar@53651
    19
end
kuncar@47308
    20
kuncar@47308
    21
structure Lifting_Def: LIFTING_DEF =
kuncar@47308
    22
struct
kuncar@47308
    23
kuncar@47698
    24
open Lifting_Util
kuncar@47308
    25
kuncar@47308
    26
infix 0 MRSL
kuncar@47308
    27
kuncar@51994
    28
(* Reflexivity prover *)
kuncar@51994
    29
kuncar@55609
    30
fun mono_eq_prover ctxt prop =
kuncar@51994
    31
  let
kuncar@55608
    32
    val rules = ((Transfer.get_relator_eq_raw ctxt) @ (Lifting_Info.get_reflexivity_rules ctxt))
kuncar@51994
    33
  in
kuncar@55609
    34
    SOME (Goal.prove ctxt [] [] prop (K (REPEAT_ALL_NEW (resolve_tac rules) 1)))
kuncar@55609
    35
      handle ERROR _ => NONE
kuncar@51994
    36
  end
kuncar@55609
    37
   
kuncar@51994
    38
fun try_prove_reflexivity ctxt prop =
kuncar@55609
    39
  let
kuncar@55609
    40
    val thy = Proof_Context.theory_of ctxt
kuncar@55609
    41
    val cprop = cterm_of thy prop
kuncar@55609
    42
    val rule = @{thm ge_eq_refl}
kuncar@55609
    43
    val concl_pat = Drule.strip_imp_concl (cprop_of rule)
kuncar@55609
    44
    val insts = Thm.first_order_match (concl_pat, cprop)
kuncar@55609
    45
    val rule = Drule.instantiate_normalize insts rule
kuncar@55609
    46
    val prop = hd (prems_of rule)
kuncar@55609
    47
  in
kuncar@55609
    48
    case mono_eq_prover ctxt prop of
kuncar@55610
    49
      SOME thm => SOME (thm RS rule)
kuncar@55609
    50
      | NONE => NONE
kuncar@55609
    51
  end
kuncar@51994
    52
kuncar@54335
    53
(* 
kuncar@54335
    54
  Generates a parametrized transfer rule.
kuncar@54335
    55
  transfer_rule - of the form T t f
kuncar@54335
    56
  parametric_transfer_rule - of the form par_R t' t
kuncar@54335
    57
  
kuncar@54947
    58
  Result: par_T t' f, after substituing op= for relations in par_R that relate
kuncar@54335
    59
    a type constructor to the same type constructor, it is a merge of (par_R' OO T) t' f
kuncar@54335
    60
    using Lifting_Term.merge_transfer_relations
kuncar@54335
    61
*)
kuncar@51374
    62
kuncar@51374
    63
fun generate_parametric_transfer_rule ctxt transfer_rule parametric_transfer_rule =
kuncar@51374
    64
  let
kuncar@51374
    65
    fun preprocess ctxt thm =
kuncar@51374
    66
      let
kuncar@51374
    67
        val tm = (strip_args 2 o HOLogic.dest_Trueprop o concl_of) thm;
kuncar@51374
    68
        val param_rel = (snd o dest_comb o fst o dest_comb) tm;
kuncar@51374
    69
        val thy = Proof_Context.theory_of ctxt;
kuncar@51374
    70
        val free_vars = Term.add_vars param_rel [];
kuncar@51374
    71
        
kuncar@51374
    72
        fun make_subst (var as (_, typ)) subst = 
kuncar@51374
    73
          let
kuncar@51374
    74
            val [rty, rty'] = binder_types typ
kuncar@51374
    75
          in
kuncar@51374
    76
            if (Term.is_TVar rty andalso is_Type rty') then
kuncar@51374
    77
              (Var var, HOLogic.eq_const rty')::subst
kuncar@51374
    78
            else
kuncar@51374
    79
              subst
kuncar@51374
    80
          end;
kuncar@51374
    81
        
kuncar@51374
    82
        val subst = fold make_subst free_vars [];
kuncar@51374
    83
        val csubst = map (pairself (cterm_of thy)) subst;
kuncar@51374
    84
        val inst_thm = Drule.cterm_instantiate csubst thm;
kuncar@51374
    85
      in
kuncar@51374
    86
        Conv.fconv_rule 
kuncar@51374
    87
          ((Conv.concl_conv (nprems_of inst_thm) o HOLogic.Trueprop_conv o Conv.fun2_conv o Conv.arg1_conv)
wenzelm@54742
    88
            (Raw_Simplifier.rewrite ctxt false (Transfer.get_sym_relator_eq ctxt))) inst_thm
kuncar@51374
    89
      end
kuncar@51374
    90
kuncar@51374
    91
    fun inst_relcomppI thy ant1 ant2 =
kuncar@51374
    92
      let
kuncar@51374
    93
        val t1 = (HOLogic.dest_Trueprop o concl_of) ant1
kuncar@51374
    94
        val t2 = (HOLogic.dest_Trueprop o prop_of) ant2
kuncar@51374
    95
        val fun1 = cterm_of thy (strip_args 2 t1)
kuncar@51374
    96
        val args1 = map (cterm_of thy) (get_args 2 t1)
kuncar@51374
    97
        val fun2 = cterm_of thy (strip_args 2 t2)
kuncar@51374
    98
        val args2 = map (cterm_of thy) (get_args 1 t2)
kuncar@51374
    99
        val relcomppI = Drule.incr_indexes2 ant1 ant2 @{thm relcomppI}
kuncar@51374
   100
        val vars = (rev (Term.add_vars (prop_of relcomppI) []))
kuncar@51374
   101
        val subst = map (apfst ((cterm_of thy) o Var)) (vars ~~ ([fun1] @ args1 @ [fun2] @ args2))
kuncar@51374
   102
      in
kuncar@51374
   103
        Drule.cterm_instantiate subst relcomppI
kuncar@51374
   104
      end
kuncar@51374
   105
wenzelm@54995
   106
    fun zip_transfer_rules ctxt thm =
wenzelm@54995
   107
      let
kuncar@51374
   108
        val thy = Proof_Context.theory_of ctxt
kuncar@51374
   109
        fun mk_POS ty = Const (@{const_name POS}, ty --> ty --> HOLogic.boolT)
kuncar@51374
   110
        val rel = (Thm.dest_fun2 o Thm.dest_arg o cprop_of) thm
kuncar@51374
   111
        val typ = (typ_of o ctyp_of_term) rel
kuncar@51374
   112
        val POS_const = cterm_of thy (mk_POS typ)
kuncar@51374
   113
        val var = cterm_of thy (Var (("X", #maxidx (rep_cterm (rel)) + 1), typ))
kuncar@51374
   114
        val goal = Thm.apply (cterm_of thy HOLogic.Trueprop) (Thm.apply (Thm.apply POS_const rel) var)
kuncar@51374
   115
      in
kuncar@51374
   116
        [Lifting_Term.merge_transfer_relations ctxt goal, thm] MRSL @{thm POS_apply}
kuncar@51374
   117
      end
kuncar@51374
   118
     
kuncar@51374
   119
    val thm = (inst_relcomppI (Proof_Context.theory_of ctxt) parametric_transfer_rule transfer_rule) 
kuncar@51374
   120
                OF [parametric_transfer_rule, transfer_rule]
kuncar@51374
   121
    val preprocessed_thm = preprocess ctxt thm
kuncar@51374
   122
    val orig_ctxt = ctxt
kuncar@51374
   123
    val (fixed_thm, ctxt) = yield_singleton (apfst snd oo Variable.import true) preprocessed_thm ctxt
kuncar@51374
   124
    val assms = cprems_of fixed_thm
kuncar@51374
   125
    val add_transfer_rule = Thm.attribute_declaration Transfer.transfer_add
wenzelm@54995
   126
    val (prems, ctxt) = fold_map Thm.assume_hyps assms ctxt
wenzelm@54995
   127
    val ctxt = Context.proof_map (fold add_transfer_rule prems) ctxt
kuncar@51374
   128
    val zipped_thm =
kuncar@51374
   129
      fixed_thm
kuncar@51374
   130
      |> undisch_all
kuncar@51374
   131
      |> zip_transfer_rules ctxt
kuncar@51374
   132
      |> implies_intr_list assms
kuncar@51374
   133
      |> singleton (Variable.export ctxt orig_ctxt)
kuncar@51374
   134
  in
kuncar@51374
   135
    zipped_thm
kuncar@51374
   136
  end
kuncar@51374
   137
kuncar@51374
   138
fun print_generate_transfer_info msg = 
kuncar@51374
   139
  let
kuncar@51374
   140
    val error_msg = cat_lines 
kuncar@51374
   141
      ["Generation of a parametric transfer rule failed.",
kuncar@51374
   142
      (Pretty.string_of (Pretty.block
kuncar@51374
   143
         [Pretty.str "Reason:", Pretty.brk 2, msg]))]
kuncar@51374
   144
  in
kuncar@51374
   145
    error error_msg
kuncar@51374
   146
  end
kuncar@51374
   147
kuncar@53951
   148
fun map_ter _ x [] = x
kuncar@53951
   149
    | map_ter f _ xs = map f xs
kuncar@53951
   150
kuncar@53951
   151
fun generate_transfer_rules lthy quot_thm rsp_thm def_thm par_thms =
kuncar@51374
   152
  let
kuncar@51374
   153
    val transfer_rule =
kuncar@51374
   154
      ([quot_thm, rsp_thm, def_thm] MRSL @{thm Quotient_to_transfer})
kuncar@51374
   155
      |> Lifting_Term.parametrize_transfer_rule lthy
kuncar@51374
   156
  in
kuncar@53951
   157
    (map_ter (generate_parametric_transfer_rule lthy transfer_rule) [transfer_rule] par_thms
kuncar@53951
   158
    handle Lifting_Term.MERGE_TRANSFER_REL msg => (print_generate_transfer_info msg; [transfer_rule]))
kuncar@51374
   159
  end
kuncar@51374
   160
kuncar@47698
   161
(* Generation of the code certificate from the rsp theorem *)
kuncar@47308
   162
kuncar@47308
   163
fun get_body_types (Type ("fun", [_, U]), Type ("fun", [_, V])) = get_body_types (U, V)
kuncar@47308
   164
  | get_body_types (U, V)  = (U, V)
kuncar@47308
   165
kuncar@47308
   166
fun get_binder_types (Type ("fun", [T, U]), Type ("fun", [V, W])) = (T, V) :: get_binder_types (U, W)
kuncar@47308
   167
  | get_binder_types _ = []
kuncar@47308
   168
kuncar@47937
   169
fun get_binder_types_by_rel (Const (@{const_name "fun_rel"}, _) $ _ $ S) (Type ("fun", [T, U]), Type ("fun", [V, W])) = 
kuncar@47937
   170
    (T, V) :: get_binder_types_by_rel S (U, W)
kuncar@47937
   171
  | get_binder_types_by_rel _ _ = []
kuncar@47937
   172
kuncar@47937
   173
fun get_body_type_by_rel (Const (@{const_name "fun_rel"}, _) $ _ $ S) (Type ("fun", [_, U]), Type ("fun", [_, V])) = 
kuncar@47937
   174
    get_body_type_by_rel S (U, V)
kuncar@47937
   175
  | get_body_type_by_rel _ (U, V)  = (U, V)
kuncar@47937
   176
kuncar@47308
   177
fun force_rty_type ctxt rty rhs = 
kuncar@47308
   178
  let
kuncar@47308
   179
    val thy = Proof_Context.theory_of ctxt
kuncar@47308
   180
    val rhs_schematic = singleton (Variable.polymorphic ctxt) rhs
kuncar@47308
   181
    val rty_schematic = fastype_of rhs_schematic
kuncar@47308
   182
    val match = Sign.typ_match thy (rty_schematic, rty) Vartab.empty
kuncar@47308
   183
  in
kuncar@47308
   184
    Envir.subst_term_types match rhs_schematic
kuncar@47308
   185
  end
kuncar@47308
   186
kuncar@47308
   187
fun unabs_def ctxt def = 
kuncar@47308
   188
  let
kuncar@47308
   189
    val (_, rhs) = Thm.dest_equals (cprop_of def)
kuncar@47308
   190
    fun dest_abs (Abs (var_name, T, _)) = (var_name, T)
kuncar@47308
   191
      | dest_abs tm = raise TERM("get_abs_var",[tm])
kuncar@47308
   192
    val (var_name, T) = dest_abs (term_of rhs)
kuncar@47308
   193
    val (new_var_names, ctxt') = Variable.variant_fixes [var_name] ctxt
kuncar@47308
   194
    val thy = Proof_Context.theory_of ctxt'
kuncar@47308
   195
    val refl_thm = Thm.reflexive (cterm_of thy (Free (hd new_var_names, T)))
kuncar@47308
   196
  in
kuncar@47308
   197
    Thm.combination def refl_thm |>
kuncar@47308
   198
    singleton (Proof_Context.export ctxt' ctxt)
kuncar@47308
   199
  end
kuncar@47308
   200
kuncar@47308
   201
fun unabs_all_def ctxt def = 
kuncar@47308
   202
  let
kuncar@47308
   203
    val (_, rhs) = Thm.dest_equals (cprop_of def)
kuncar@47308
   204
    val xs = strip_abs_vars (term_of rhs)
kuncar@47308
   205
  in  
kuncar@47308
   206
    fold (K (unabs_def ctxt)) xs def
kuncar@47308
   207
  end
kuncar@47308
   208
kuncar@47308
   209
val map_fun_unfolded = 
kuncar@47308
   210
  @{thm map_fun_def[abs_def]} |>
kuncar@47308
   211
  unabs_def @{context} |>
kuncar@47308
   212
  unabs_def @{context} |>
kuncar@47308
   213
  Local_Defs.unfold @{context} [@{thm comp_def}]
kuncar@47308
   214
kuncar@47308
   215
fun unfold_fun_maps ctm =
kuncar@47308
   216
  let
kuncar@47308
   217
    fun unfold_conv ctm =
kuncar@47308
   218
      case (Thm.term_of ctm) of
kuncar@47308
   219
        Const (@{const_name "map_fun"}, _) $ _ $ _ => 
kuncar@47308
   220
          (Conv.arg_conv unfold_conv then_conv Conv.rewr_conv map_fun_unfolded) ctm
kuncar@47308
   221
        | _ => Conv.all_conv ctm
kuncar@47308
   222
  in
kuncar@47937
   223
    (Conv.fun_conv unfold_conv) ctm
kuncar@47937
   224
  end
kuncar@47937
   225
kuncar@47937
   226
fun unfold_fun_maps_beta ctm =
kuncar@47937
   227
  let val try_beta_conv = Conv.try_conv (Thm.beta_conversion false)
kuncar@47937
   228
  in 
kuncar@47937
   229
    (unfold_fun_maps then_conv try_beta_conv) ctm 
kuncar@47308
   230
  end
kuncar@47308
   231
kuncar@47308
   232
fun prove_rel ctxt rsp_thm (rty, qty) =
kuncar@47308
   233
  let
kuncar@47308
   234
    val ty_args = get_binder_types (rty, qty)
kuncar@47308
   235
    fun disch_arg args_ty thm = 
kuncar@47308
   236
      let
kuncar@47504
   237
        val quot_thm = Lifting_Term.prove_quot_thm ctxt args_ty
kuncar@47308
   238
      in
kuncar@47308
   239
        [quot_thm, thm] MRSL @{thm apply_rsp''}
kuncar@47308
   240
      end
kuncar@47308
   241
  in
kuncar@47308
   242
    fold disch_arg ty_args rsp_thm
kuncar@47308
   243
  end
kuncar@47308
   244
kuncar@47308
   245
exception CODE_CERT_GEN of string
kuncar@47308
   246
kuncar@47308
   247
fun simplify_code_eq ctxt def_thm = 
kuncar@48024
   248
  Local_Defs.unfold ctxt [@{thm o_apply}, @{thm map_fun_def}, @{thm id_apply}] def_thm
kuncar@47308
   249
kuncar@47852
   250
(*
kuncar@47852
   251
  quot_thm - quotient theorem (Quotient R Abs Rep T).
kuncar@47852
   252
  returns: whether the Lifting package is capable to generate code for the abstract type
kuncar@47852
   253
    represented by quot_thm
kuncar@47852
   254
*)
kuncar@47852
   255
kuncar@47308
   256
fun can_generate_code_cert quot_thm  =
kuncar@47951
   257
  case quot_thm_rel quot_thm of
kuncar@47308
   258
    Const (@{const_name HOL.eq}, _) => true
kuncar@47308
   259
    | Const (@{const_name invariant}, _) $ _  => true
kuncar@47308
   260
    | _ => false
kuncar@47308
   261
kuncar@55610
   262
fun generate_rep_eq ctxt def_thm rsp_thm (rty, qty) =
kuncar@47308
   263
  let
kuncar@47937
   264
    val unfolded_def = Conv.fconv_rule (Conv.arg_conv unfold_fun_maps_beta) def_thm
kuncar@47308
   265
    val unabs_def = unabs_all_def ctxt unfolded_def
kuncar@55610
   266
  in  
kuncar@55610
   267
    if body_type rty = body_type qty then 
kuncar@55610
   268
      SOME (simplify_code_eq ctxt unabs_def)
kuncar@55610
   269
    else 
kuncar@55610
   270
      let
kuncar@55610
   271
        val thy = Proof_Context.theory_of ctxt
kuncar@55610
   272
        val quot_thm = Lifting_Term.prove_quot_thm ctxt (get_body_types (rty, qty))
kuncar@55610
   273
        val fun_rel = prove_rel ctxt rsp_thm (rty, qty)
kuncar@55610
   274
        val rep_abs_thm = [quot_thm, fun_rel] MRSL @{thm Quotient_rep_abs_eq}
kuncar@55610
   275
      in
kuncar@55610
   276
        case mono_eq_prover ctxt (hd(prems_of rep_abs_thm)) of
kuncar@55610
   277
          SOME mono_eq_thm =>
kuncar@55610
   278
            let
kuncar@55610
   279
              val rep_abs_eq = mono_eq_thm RS rep_abs_thm
kuncar@55610
   280
              val rep = (cterm_of thy o quot_thm_rep) quot_thm
kuncar@55610
   281
              val rep_refl = Thm.reflexive rep RS @{thm meta_eq_to_obj_eq}
kuncar@55610
   282
              val repped_eq = [rep_refl, unabs_def RS @{thm meta_eq_to_obj_eq}] MRSL @{thm cong}
kuncar@55610
   283
              val code_cert = [repped_eq, rep_abs_eq] MRSL trans
kuncar@55610
   284
            in
kuncar@55610
   285
              SOME (simplify_code_eq ctxt code_cert)
kuncar@55610
   286
            end
kuncar@55610
   287
          | NONE => NONE
kuncar@55610
   288
      end
kuncar@47308
   289
  end
kuncar@47308
   290
kuncar@47937
   291
fun generate_abs_eq ctxt def_thm rsp_thm quot_thm =
kuncar@47308
   292
  let
kuncar@47937
   293
    val abs_eq_with_assms =
kuncar@47937
   294
      let
kuncar@47951
   295
        val (rty, qty) = quot_thm_rty_qty quot_thm
kuncar@47951
   296
        val rel = quot_thm_rel quot_thm
kuncar@47937
   297
        val ty_args = get_binder_types_by_rel rel (rty, qty)
kuncar@47937
   298
        val body_type = get_body_type_by_rel rel (rty, qty)
kuncar@47937
   299
        val quot_ret_thm = Lifting_Term.prove_quot_thm ctxt body_type
kuncar@47937
   300
        
kuncar@47937
   301
        val rep_abs_folded_unmapped_thm = 
kuncar@47937
   302
          let
kuncar@47937
   303
            val rep_id = [quot_thm, def_thm] MRSL @{thm Quotient_Rep_eq}
kuncar@47937
   304
            val ctm = Thm.dest_equals_lhs (cprop_of rep_id)
kuncar@47937
   305
            val unfolded_maps_eq = unfold_fun_maps ctm
kuncar@47937
   306
            val t1 = [quot_thm, def_thm, rsp_thm] MRSL @{thm Quotient_rep_abs_fold_unmap}
kuncar@47937
   307
            val prems_pat = (hd o Drule.cprems_of) t1
kuncar@47937
   308
            val insts = Thm.first_order_match (prems_pat, cprop_of unfolded_maps_eq)
kuncar@47937
   309
          in
kuncar@47937
   310
            unfolded_maps_eq RS (Drule.instantiate_normalize insts t1)
kuncar@47937
   311
          end
kuncar@47937
   312
      in
kuncar@47937
   313
        rep_abs_folded_unmapped_thm
kuncar@47937
   314
        |> fold (fn _ => fn thm => thm RS @{thm fun_relD2}) ty_args
kuncar@47937
   315
        |> (fn x => x RS (@{thm Quotient_rel_abs2} OF [quot_ret_thm]))
kuncar@47937
   316
      end
kuncar@47937
   317
    
kuncar@47937
   318
    val prems = prems_of abs_eq_with_assms
kuncar@47937
   319
    val indexed_prems = map_index (apfst (fn x => x + 1)) prems
kuncar@51994
   320
    val indexed_assms = map (apsnd (try_prove_reflexivity ctxt)) indexed_prems
kuncar@47937
   321
    val proved_assms = map (apsnd the) (filter (is_some o snd) indexed_assms)
kuncar@47937
   322
    val abs_eq = fold_rev (fn (i, assms) => fn thm => assms RSN (i, thm)) proved_assms abs_eq_with_assms
kuncar@47308
   323
  in
kuncar@47937
   324
    simplify_code_eq ctxt abs_eq
kuncar@47937
   325
  end
kuncar@47937
   326
kuncar@47937
   327
fun define_code_using_abs_eq abs_eq_thm lthy =
kuncar@47937
   328
  if null (Logic.strip_imp_prems(prop_of abs_eq_thm)) then
kuncar@47937
   329
    (snd oo Local_Theory.note) ((Binding.empty, [Code.add_default_eqn_attrib]), [abs_eq_thm]) lthy
kuncar@47937
   330
  else
kuncar@47937
   331
    lthy
kuncar@47937
   332
  
kuncar@51374
   333
fun define_code_using_rep_eq opt_rep_eq_thm lthy = 
kuncar@51374
   334
  case opt_rep_eq_thm of
kuncar@47937
   335
    SOME rep_eq_thm =>   
kuncar@47308
   336
      let
kuncar@47308
   337
        val add_abs_eqn_attribute = 
kuncar@47308
   338
          Thm.declaration_attribute (fn thm => Context.mapping (Code.add_abs_eqn thm) I)
kuncar@47308
   339
        val add_abs_eqn_attrib = Attrib.internal (K add_abs_eqn_attribute);
kuncar@47308
   340
      in
kuncar@47937
   341
        (snd oo Local_Theory.note) ((Binding.empty, [add_abs_eqn_attrib]), [rep_eq_thm]) lthy
kuncar@47308
   342
      end
kuncar@47937
   343
    | NONE => lthy
kuncar@47937
   344
kuncar@47937
   345
fun has_constr ctxt quot_thm =
kuncar@47937
   346
  let
kuncar@47937
   347
    val thy = Proof_Context.theory_of ctxt
kuncar@47951
   348
    val abs_fun = quot_thm_abs quot_thm
kuncar@47937
   349
  in
kuncar@47937
   350
    if is_Const abs_fun then
kuncar@47937
   351
      Code.is_constr thy ((fst o dest_Const) abs_fun)
kuncar@47308
   352
    else
kuncar@47937
   353
      false
kuncar@47308
   354
  end
kuncar@47308
   355
kuncar@47937
   356
fun has_abstr ctxt quot_thm =
kuncar@47308
   357
  let
kuncar@47937
   358
    val thy = Proof_Context.theory_of ctxt
kuncar@47951
   359
    val abs_fun = quot_thm_abs quot_thm
kuncar@47308
   360
  in
kuncar@47937
   361
    if is_Const abs_fun then
kuncar@47937
   362
      Code.is_abstr thy ((fst o dest_Const) abs_fun)
kuncar@47937
   363
    else
kuncar@47937
   364
      false
kuncar@47308
   365
  end
kuncar@47308
   366
kuncar@51374
   367
fun define_code abs_eq_thm opt_rep_eq_thm (rty, qty) lthy =
kuncar@47937
   368
  let
kuncar@47937
   369
    val (rty_body, qty_body) = get_body_types (rty, qty)
kuncar@47937
   370
  in
kuncar@47937
   371
    if rty_body = qty_body then
kuncar@47937
   372
      if null (Logic.strip_imp_prems(prop_of abs_eq_thm)) then
kuncar@47937
   373
        (snd oo Local_Theory.note) ((Binding.empty, [Code.add_default_eqn_attrib]), [abs_eq_thm]) lthy
kuncar@47937
   374
      else
kuncar@51374
   375
        (snd oo Local_Theory.note) ((Binding.empty, [Code.add_default_eqn_attrib]), [the opt_rep_eq_thm]) lthy
kuncar@47937
   376
    else
kuncar@47937
   377
      let 
kuncar@47937
   378
        val body_quot_thm = Lifting_Term.prove_quot_thm lthy (rty_body, qty_body)
kuncar@47937
   379
      in
kuncar@47937
   380
        if has_constr lthy body_quot_thm then
kuncar@47937
   381
          define_code_using_abs_eq abs_eq_thm lthy
kuncar@47937
   382
        else if has_abstr lthy body_quot_thm then
kuncar@51374
   383
          define_code_using_rep_eq opt_rep_eq_thm lthy
kuncar@47937
   384
        else
kuncar@47937
   385
          lthy
kuncar@47937
   386
      end
kuncar@47937
   387
  end
kuncar@47308
   388
kuncar@47852
   389
(*
kuncar@47852
   390
  Defines an operation on an abstract type in terms of a corresponding operation 
kuncar@47852
   391
    on a representation type.
kuncar@47852
   392
kuncar@47852
   393
  var - a binding and a mixfix of the new constant being defined
kuncar@47852
   394
  qty - an abstract type of the new constant
kuncar@47852
   395
  rhs - a term representing the new constant on the raw level
kuncar@47937
   396
  rsp_thm - a respectfulness theorem in the internal tagged form (like '(R ===> R ===> R) f f'),
kuncar@47852
   397
    i.e. "(Lifting_Term.equiv_relation (fastype_of rhs, qty)) $ rhs $ rhs"
kuncar@54335
   398
  par_thms - a parametricity theorem for rhs
kuncar@47852
   399
*)
kuncar@47308
   400
kuncar@53951
   401
fun add_lift_def var qty rhs rsp_thm par_thms lthy =
kuncar@47308
   402
  let
kuncar@47308
   403
    val rty = fastype_of rhs
kuncar@47937
   404
    val quot_thm = Lifting_Term.prove_quot_thm lthy (rty, qty)
kuncar@47951
   405
    val absrep_trm =  quot_thm_abs quot_thm
kuncar@47308
   406
    val rty_forced = (domain_type o fastype_of) absrep_trm
kuncar@47308
   407
    val forced_rhs = force_rty_type lthy rty_forced rhs
wenzelm@53207
   408
    val lhs = Free (Binding.name_of (#1 var), qty)
kuncar@47308
   409
    val prop = Logic.mk_equals (lhs, absrep_trm $ forced_rhs)
kuncar@47308
   410
    val (_, prop') = Local_Defs.cert_def lthy prop
kuncar@47308
   411
    val (_, newrhs) = Local_Defs.abs_def prop'
kuncar@47308
   412
kuncar@47308
   413
    val ((_, (_ , def_thm)), lthy') = 
kuncar@47308
   414
      Local_Theory.define (var, ((Thm.def_binding (#1 var), []), newrhs)) lthy
kuncar@47308
   415
kuncar@53951
   416
    val transfer_rules = generate_transfer_rules lthy' quot_thm rsp_thm def_thm par_thms
huffman@49975
   417
kuncar@47937
   418
    val abs_eq_thm = generate_abs_eq lthy' def_thm rsp_thm quot_thm
kuncar@51374
   419
    val opt_rep_eq_thm = generate_rep_eq lthy' def_thm rsp_thm (rty_forced, qty)
huffman@47351
   420
kuncar@47545
   421
    fun qualify defname suffix = Binding.qualified true suffix defname
kuncar@47308
   422
kuncar@47545
   423
    val lhs_name = (#1 var)
kuncar@47308
   424
    val rsp_thm_name = qualify lhs_name "rsp"
kuncar@47937
   425
    val abs_eq_thm_name = qualify lhs_name "abs_eq"
kuncar@47937
   426
    val rep_eq_thm_name = qualify lhs_name "rep_eq"
kuncar@51374
   427
    val transfer_rule_name = qualify lhs_name "transfer"
huffman@47373
   428
    val transfer_attr = Attrib.internal (K Transfer.transfer_add)
kuncar@47308
   429
  in
kuncar@47308
   430
    lthy'
kuncar@47308
   431
      |> (snd oo Local_Theory.note) ((rsp_thm_name, []), [rsp_thm])
kuncar@53951
   432
      |> (snd oo Local_Theory.note) ((transfer_rule_name, [transfer_attr]), transfer_rules)
kuncar@47937
   433
      |> (snd oo Local_Theory.note) ((abs_eq_thm_name, []), [abs_eq_thm])
kuncar@51374
   434
      |> (case opt_rep_eq_thm of 
kuncar@47937
   435
            SOME rep_eq_thm => (snd oo Local_Theory.note) ((rep_eq_thm_name, []), [rep_eq_thm])
kuncar@47937
   436
            | NONE => I)
kuncar@51374
   437
      |> define_code abs_eq_thm opt_rep_eq_thm (rty_forced, qty)
kuncar@47308
   438
  end
kuncar@47308
   439
kuncar@47308
   440
fun mk_readable_rsp_thm_eq tm lthy =
kuncar@47308
   441
  let
kuncar@47308
   442
    val ctm = cterm_of (Proof_Context.theory_of lthy) tm
kuncar@47308
   443
    
kuncar@47308
   444
    fun simp_arrows_conv ctm =
kuncar@47308
   445
      let
kuncar@47308
   446
        val unfold_conv = Conv.rewrs_conv 
kuncar@49626
   447
          [@{thm fun_rel_eq_invariant[THEN eq_reflection]}, 
kuncar@49626
   448
            @{thm fun_rel_eq[THEN eq_reflection]},
kuncar@49626
   449
            @{thm fun_rel_eq_rel[THEN eq_reflection]}, 
kuncar@47308
   450
            @{thm fun_rel_def[THEN eq_reflection]}]
kuncar@47308
   451
        fun binop_conv2 cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
kuncar@47634
   452
        val invariant_commute_conv = Conv.bottom_conv
kuncar@47634
   453
          (K (Conv.try_conv (Conv.rewrs_conv (Lifting_Info.get_invariant_commute_rules lthy)))) lthy
kuncar@49626
   454
        val relator_eq_conv = Conv.bottom_conv
kuncar@49626
   455
          (K (Conv.try_conv (Conv.rewrs_conv (Transfer.get_relator_eq lthy)))) lthy
kuncar@47308
   456
      in
kuncar@47308
   457
        case (Thm.term_of ctm) of
kuncar@47308
   458
          Const (@{const_name "fun_rel"}, _) $ _ $ _ => 
kuncar@49626
   459
            (binop_conv2 simp_arrows_conv simp_arrows_conv then_conv unfold_conv) ctm
kuncar@49626
   460
          | _ => (invariant_commute_conv then_conv relator_eq_conv) ctm
kuncar@47308
   461
      end
kuncar@47937
   462
    
kuncar@47308
   463
    val unfold_ret_val_invs = Conv.bottom_conv 
kuncar@47308
   464
      (K (Conv.try_conv (Conv.rewr_conv @{thm invariant_same_args}))) lthy 
wenzelm@51314
   465
    val simp_conv = HOLogic.Trueprop_conv (Conv.fun2_conv simp_arrows_conv)
kuncar@47308
   466
    val univq_conv = Conv.rewr_conv @{thm HOL.all_simps(6)[symmetric, THEN eq_reflection]}
kuncar@47308
   467
    val univq_prenex_conv = Conv.top_conv (K (Conv.try_conv univq_conv)) lthy
kuncar@47308
   468
    val beta_conv = Thm.beta_conversion true
kuncar@47308
   469
    val eq_thm = 
kuncar@47308
   470
      (simp_conv then_conv univq_prenex_conv then_conv beta_conv then_conv unfold_ret_val_invs) ctm
kuncar@47308
   471
  in
wenzelm@54742
   472
    Object_Logic.rulify lthy (eq_thm RS Drule.equal_elim_rule2)
kuncar@47308
   473
  end
kuncar@47308
   474
kuncar@47607
   475
fun rename_to_tnames ctxt term =
kuncar@47607
   476
  let
kuncar@47607
   477
    fun all_typs (Const ("all", _) $ Abs (_, T, t)) = T :: all_typs t
kuncar@47607
   478
      | all_typs _ = []
kuncar@47308
   479
kuncar@47607
   480
    fun rename (Const ("all", T1) $ Abs (_, T2, t)) (new_name :: names) = 
kuncar@47607
   481
        (Const ("all", T1) $ Abs (new_name, T2, rename t names)) 
kuncar@47607
   482
      | rename t _ = t
kuncar@47607
   483
kuncar@47607
   484
    val (fixed_def_t, _) = yield_singleton (Variable.importT_terms) term ctxt
kuncar@47607
   485
    val new_names = Datatype_Prop.make_tnames (all_typs fixed_def_t)
kuncar@47607
   486
  in
kuncar@47607
   487
    rename term new_names
kuncar@47607
   488
  end
kuncar@47308
   489
kuncar@47852
   490
(*
kuncar@47852
   491
kuncar@47852
   492
  lifting_definition command. It opens a proof of a corresponding respectfulness 
kuncar@47852
   493
  theorem in a user-friendly, readable form. Then add_lift_def is called internally.
kuncar@47852
   494
kuncar@47852
   495
*)
kuncar@47852
   496
kuncar@53951
   497
fun lift_def_cmd (raw_var, rhs_raw, par_xthms) lthy =
kuncar@47308
   498
  let
kuncar@51994
   499
    val ((binding, SOME qty, mx), lthy) = yield_singleton Proof_Context.read_vars raw_var lthy 
kuncar@51994
   500
    val rhs = (Syntax.check_term lthy o Syntax.parse_term lthy) rhs_raw
kuncar@51994
   501
    val rsp_rel = Lifting_Term.equiv_relation lthy (fastype_of rhs, qty)
kuncar@47308
   502
    val rty_forced = (domain_type o fastype_of) rsp_rel;
kuncar@51994
   503
    val forced_rhs = force_rty_type lthy rty_forced rhs;
kuncar@47308
   504
    val internal_rsp_tm = HOLogic.mk_Trueprop (rsp_rel $ forced_rhs $ forced_rhs)
kuncar@51994
   505
    val opt_proven_rsp_thm = try_prove_reflexivity lthy internal_rsp_tm
kuncar@53951
   506
    val par_thms = Attrib.eval_thms lthy par_xthms
kuncar@51994
   507
    
kuncar@51994
   508
    fun after_qed internal_rsp_thm lthy = 
kuncar@53951
   509
      add_lift_def (binding, mx) qty rhs internal_rsp_thm par_thms lthy
kuncar@47308
   510
kuncar@47308
   511
  in
kuncar@51374
   512
    case opt_proven_rsp_thm of
kuncar@51994
   513
      SOME thm => Proof.theorem NONE (K (after_qed thm)) [] lthy
kuncar@51994
   514
      | NONE =>  
kuncar@51994
   515
        let
kuncar@51994
   516
          val readable_rsp_thm_eq = mk_readable_rsp_thm_eq internal_rsp_tm lthy
kuncar@51994
   517
          val (readable_rsp_tm, _) = Logic.dest_implies (prop_of readable_rsp_thm_eq)
kuncar@51994
   518
          val readable_rsp_tm_tnames = rename_to_tnames lthy readable_rsp_tm
kuncar@51994
   519
      
kuncar@51994
   520
          fun after_qed' thm_list lthy = 
kuncar@51994
   521
            let
kuncar@51994
   522
              val internal_rsp_thm = Goal.prove lthy [] [] internal_rsp_tm 
wenzelm@54742
   523
                  (fn {context = ctxt, ...} =>
wenzelm@54742
   524
                    rtac readable_rsp_thm_eq 1 THEN Proof_Context.fact_tac ctxt (hd thm_list) 1)
kuncar@51994
   525
            in
kuncar@51994
   526
              after_qed internal_rsp_thm lthy
kuncar@51994
   527
            end
kuncar@51994
   528
        in
kuncar@51994
   529
          Proof.theorem NONE after_qed' [[(readable_rsp_tm_tnames,[])]] lthy
kuncar@51994
   530
        end 
kuncar@47308
   531
  end
kuncar@47308
   532
kuncar@47379
   533
fun quot_thm_err ctxt (rty, qty) pretty_msg =
kuncar@47379
   534
  let
kuncar@47379
   535
    val error_msg = cat_lines
kuncar@47379
   536
       ["Lifting failed for the following types:",
kuncar@47379
   537
        Pretty.string_of (Pretty.block
kuncar@47379
   538
         [Pretty.str "Raw type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty]),
kuncar@47379
   539
        Pretty.string_of (Pretty.block
kuncar@47379
   540
         [Pretty.str "Abstract type:", Pretty.brk 2, Syntax.pretty_typ ctxt qty]),
kuncar@47379
   541
        "",
kuncar@47379
   542
        (Pretty.string_of (Pretty.block
kuncar@47379
   543
         [Pretty.str "Reason:", Pretty.brk 2, pretty_msg]))]
kuncar@47379
   544
  in
kuncar@47379
   545
    error error_msg
kuncar@47379
   546
  end
kuncar@47379
   547
kuncar@47504
   548
fun check_rty_err ctxt (rty_schematic, rty_forced) (raw_var, rhs_raw) =
kuncar@47379
   549
  let
kuncar@47504
   550
    val (_, ctxt') = yield_singleton Proof_Context.read_vars raw_var ctxt 
kuncar@47504
   551
    val rhs = (Syntax.check_term ctxt' o Syntax.parse_term ctxt') rhs_raw
kuncar@47379
   552
    val error_msg = cat_lines
kuncar@47379
   553
       ["Lifting failed for the following term:",
kuncar@47379
   554
        Pretty.string_of (Pretty.block
kuncar@47379
   555
         [Pretty.str "Term:", Pretty.brk 2, Syntax.pretty_term ctxt rhs]),
kuncar@47379
   556
        Pretty.string_of (Pretty.block
kuncar@47504
   557
         [Pretty.str "Type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty_schematic]),
kuncar@47379
   558
        "",
kuncar@47379
   559
        (Pretty.string_of (Pretty.block
kuncar@47379
   560
         [Pretty.str "Reason:", 
kuncar@47379
   561
          Pretty.brk 2, 
kuncar@51957
   562
          Pretty.str "The type of the term cannot be instantiated to",
kuncar@47379
   563
          Pretty.brk 1,
kuncar@47504
   564
          Pretty.quote (Syntax.pretty_typ ctxt rty_forced),
kuncar@47379
   565
          Pretty.str "."]))]
kuncar@47379
   566
    in
kuncar@47379
   567
      error error_msg
kuncar@47379
   568
    end
kuncar@47379
   569
kuncar@53951
   570
fun lift_def_cmd_with_err_handling (raw_var, rhs_raw, par_xthms) lthy =
kuncar@53951
   571
  (lift_def_cmd (raw_var, rhs_raw, par_xthms) lthy
kuncar@47379
   572
    handle Lifting_Term.QUOT_THM (rty, qty, msg) => quot_thm_err lthy (rty, qty) msg)
kuncar@47504
   573
    handle Lifting_Term.CHECK_RTY (rty_schematic, rty_forced) => 
kuncar@47504
   574
      check_rty_err lthy (rty_schematic, rty_forced) (raw_var, rhs_raw)
kuncar@47379
   575
kuncar@47308
   576
(* parser and command *)
kuncar@47308
   577
val liftdef_parser =
kuncar@51374
   578
  (((Parse.binding -- (@{keyword "::"} |-- (Parse.typ >> SOME) -- Parse.opt_mixfix')) >> Parse.triple2)
kuncar@53951
   579
    --| @{keyword "is"} -- Parse.term -- 
kuncar@53951
   580
      Scan.optional (@{keyword "parametric"} |-- Parse.!!! Parse_Spec.xthms1) []) >> Parse.triple1
kuncar@47308
   581
val _ =
kuncar@47308
   582
  Outer_Syntax.local_theory_to_proof @{command_spec "lift_definition"}
kuncar@47308
   583
    "definition for constants over the quotient type"
kuncar@47379
   584
      (liftdef_parser >> lift_def_cmd_with_err_handling)
kuncar@47308
   585
kuncar@47308
   586
kuncar@53651
   587
end (* structure *)