src/Pure/meta_simplifier.ML
author nipkow
Thu Aug 23 14:32:48 2001 +0200 (2001-08-23)
changeset 11504 935f9e8de0d0
parent 11371 1d5d181b7e28
child 11505 a410fa8acfca
permissions -rw-r--r--
Traced depth of conditional rewriting
berghofe@10413
     1
(*  Title:      Pure/meta_simplifier.ML
berghofe@10413
     2
    ID:         $Id$
berghofe@10413
     3
    Author:     Tobias Nipkow
berghofe@10413
     4
    Copyright   1994  University of Cambridge
berghofe@10413
     5
berghofe@10413
     6
Meta Simplification
berghofe@10413
     7
*)
berghofe@10413
     8
berghofe@10413
     9
signature META_SIMPLIFIER =
berghofe@10413
    10
sig
berghofe@10413
    11
  exception SIMPLIFIER of string * thm
berghofe@10413
    12
  type meta_simpset
berghofe@10413
    13
  val dest_mss		: meta_simpset ->
berghofe@10413
    14
    {simps: thm list, congs: thm list, procs: (string * cterm list) list}
berghofe@10413
    15
  val empty_mss         : meta_simpset
berghofe@10413
    16
  val clear_mss		: meta_simpset -> meta_simpset
berghofe@10413
    17
  val merge_mss		: meta_simpset * meta_simpset -> meta_simpset
berghofe@10413
    18
  val add_simps         : meta_simpset * thm list -> meta_simpset
berghofe@10413
    19
  val del_simps         : meta_simpset * thm list -> meta_simpset
berghofe@10413
    20
  val mss_of            : thm list -> meta_simpset
berghofe@10413
    21
  val add_congs         : meta_simpset * thm list -> meta_simpset
berghofe@10413
    22
  val del_congs         : meta_simpset * thm list -> meta_simpset
berghofe@10413
    23
  val add_simprocs	: meta_simpset *
berghofe@10413
    24
    (string * cterm list * (Sign.sg -> thm list -> term -> thm option) * stamp) list
berghofe@10413
    25
      -> meta_simpset
berghofe@10413
    26
  val del_simprocs	: meta_simpset *
berghofe@10413
    27
    (string * cterm list * (Sign.sg -> thm list -> term -> thm option) * stamp) list
berghofe@10413
    28
      -> meta_simpset
berghofe@10413
    29
  val add_prems         : meta_simpset * thm list -> meta_simpset
berghofe@10413
    30
  val prems_of_mss      : meta_simpset -> thm list
berghofe@10413
    31
  val set_mk_rews       : meta_simpset * (thm -> thm list) -> meta_simpset
berghofe@10413
    32
  val set_mk_sym        : meta_simpset * (thm -> thm option) -> meta_simpset
berghofe@10413
    33
  val set_mk_eq_True    : meta_simpset * (thm -> thm option) -> meta_simpset
berghofe@10413
    34
  val set_termless      : meta_simpset * (term * term -> bool) -> meta_simpset
berghofe@10413
    35
  val trace_simp        : bool ref
berghofe@10413
    36
  val debug_simp        : bool ref
berghofe@10413
    37
  val rewrite_cterm     : bool * bool * bool
berghofe@10413
    38
                          -> (meta_simpset -> thm -> thm option)
berghofe@10413
    39
                          -> meta_simpset -> cterm -> thm
berghofe@10413
    40
  val rewrite_rule_aux  : (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm
berghofe@10413
    41
  val rewrite_thm       : bool * bool * bool
berghofe@10413
    42
                          -> (meta_simpset -> thm -> thm option)
berghofe@10413
    43
                          -> meta_simpset -> thm -> thm
berghofe@10413
    44
  val rewrite_goals_rule_aux: (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm
berghofe@10413
    45
  val rewrite_goal_rule : bool* bool * bool
berghofe@10413
    46
                          -> (meta_simpset -> thm -> thm option)
berghofe@10413
    47
                          -> meta_simpset -> int -> thm -> thm
berghofe@10413
    48
end;
berghofe@10413
    49
berghofe@10413
    50
structure MetaSimplifier : META_SIMPLIFIER =
berghofe@10413
    51
struct
berghofe@10413
    52
berghofe@10413
    53
(** diagnostics **)
berghofe@10413
    54
berghofe@10413
    55
exception SIMPLIFIER of string * thm;
berghofe@10413
    56
berghofe@10413
    57
fun prnt warn a = if warn then warning a else writeln a;
berghofe@10413
    58
berghofe@10413
    59
fun prtm warn a sign t =
berghofe@10413
    60
  (prnt warn a; prnt warn (Sign.string_of_term sign t));
berghofe@10413
    61
berghofe@10413
    62
fun prctm warn a t =
berghofe@10413
    63
  (prnt warn a; prnt warn (Display.string_of_cterm t));
berghofe@10413
    64
berghofe@10413
    65
fun prthm warn a thm =
berghofe@10413
    66
  let val {sign, prop, ...} = rep_thm thm
berghofe@10413
    67
  in prtm warn a sign prop end;
berghofe@10413
    68
berghofe@10413
    69
val trace_simp = ref false;
berghofe@10413
    70
val debug_simp = ref false;
berghofe@10413
    71
berghofe@10413
    72
fun trace warn a = if !trace_simp then prnt warn a else ();
berghofe@10413
    73
fun debug warn a = if !debug_simp then prnt warn a else ();
berghofe@10413
    74
berghofe@10413
    75
fun trace_term warn a sign t = if !trace_simp then prtm warn a sign t else ();
berghofe@10413
    76
fun trace_cterm warn a t = if !trace_simp then prctm warn a t else ();
berghofe@10413
    77
fun debug_term warn a sign t = if !debug_simp then prtm warn a sign t else ();
berghofe@10413
    78
berghofe@10413
    79
fun trace_thm warn a thm =
berghofe@10413
    80
  let val {sign, prop, ...} = rep_thm thm
berghofe@10413
    81
  in trace_term warn a sign prop end;
berghofe@10413
    82
berghofe@10413
    83
berghofe@10413
    84
berghofe@10413
    85
(** meta simp sets **)
berghofe@10413
    86
berghofe@10413
    87
(* basic components *)
berghofe@10413
    88
berghofe@10413
    89
type rrule = {thm: thm, lhs: term, elhs: cterm, fo: bool, perm: bool};
berghofe@10413
    90
(* thm: the rewrite rule
berghofe@10413
    91
   lhs: the left-hand side
berghofe@10413
    92
   elhs: the etac-contracted lhs.
berghofe@10413
    93
   fo:  use first-order matching
berghofe@10413
    94
   perm: the rewrite rule is permutative
berghofe@10413
    95
Reamrks:
berghofe@10413
    96
  - elhs is used for matching,
berghofe@10413
    97
    lhs only for preservation of bound variable names.
berghofe@10413
    98
  - fo is set iff
berghofe@10413
    99
    either elhs is first-order (no Var is applied),
berghofe@10413
   100
           in which case fo-matching is complete,
berghofe@10413
   101
    or elhs is not a pattern,
berghofe@10413
   102
       in which case there is nothing better to do.
berghofe@10413
   103
*)
berghofe@10413
   104
type cong = {thm: thm, lhs: cterm};
berghofe@10413
   105
type simproc =
berghofe@10413
   106
 {name: string, proc: Sign.sg -> thm list -> term -> thm option, lhs: cterm, id: stamp};
berghofe@10413
   107
berghofe@10413
   108
fun eq_rrule ({thm = thm1, ...}: rrule, {thm = thm2, ...}: rrule) =
berghofe@10413
   109
  #prop (rep_thm thm1) aconv #prop (rep_thm thm2);
berghofe@10413
   110
berghofe@10413
   111
fun eq_cong ({thm = thm1, ...}: cong, {thm = thm2, ...}: cong) = 
berghofe@10413
   112
  #prop (rep_thm thm1) aconv #prop (rep_thm thm2);
berghofe@10413
   113
berghofe@10413
   114
fun eq_prem (thm1, thm2) =
berghofe@10413
   115
  #prop (rep_thm thm1) aconv #prop (rep_thm thm2);
berghofe@10413
   116
berghofe@10413
   117
fun eq_simproc ({id = s1, ...}:simproc, {id = s2, ...}:simproc) = (s1 = s2);
berghofe@10413
   118
berghofe@10413
   119
fun mk_simproc (name, proc, lhs, id) =
berghofe@10413
   120
  {name = name, proc = proc, lhs = lhs, id = id};
berghofe@10413
   121
berghofe@10413
   122
berghofe@10413
   123
(* datatype mss *)
berghofe@10413
   124
berghofe@10413
   125
(*
berghofe@10413
   126
  A "mss" contains data needed during conversion:
berghofe@10413
   127
    rules: discrimination net of rewrite rules;
berghofe@10413
   128
    congs: association list of congruence rules and
berghofe@10413
   129
           a list of `weak' congruence constants.
berghofe@10413
   130
           A congruence is `weak' if it avoids normalization of some argument.
berghofe@10413
   131
    procs: discrimination net of simplification procedures
berghofe@10413
   132
      (functions that prove rewrite rules on the fly);
berghofe@10413
   133
    bounds: names of bound variables already used
berghofe@10413
   134
      (for generating new names when rewriting under lambda abstractions);
berghofe@10413
   135
    prems: current premises;
berghofe@10413
   136
    mk_rews: mk: turns simplification thms into rewrite rules;
berghofe@10413
   137
             mk_sym: turns == around; (needs Drule!)
berghofe@10413
   138
             mk_eq_True: turns P into P == True - logic specific;
berghofe@10413
   139
    termless: relation for ordered rewriting;
nipkow@11504
   140
    depth: depth of conditional rewriting;
berghofe@10413
   141
*)
berghofe@10413
   142
berghofe@10413
   143
datatype meta_simpset =
berghofe@10413
   144
  Mss of {
berghofe@10413
   145
    rules: rrule Net.net,
berghofe@10413
   146
    congs: (string * cong) list * string list,
berghofe@10413
   147
    procs: simproc Net.net,
berghofe@10413
   148
    bounds: string list,
berghofe@10413
   149
    prems: thm list,
berghofe@10413
   150
    mk_rews: {mk: thm -> thm list,
berghofe@10413
   151
              mk_sym: thm -> thm option,
berghofe@10413
   152
              mk_eq_True: thm -> thm option},
nipkow@11504
   153
    termless: term * term -> bool,
nipkow@11504
   154
    depth: int};
berghofe@10413
   155
nipkow@11504
   156
fun mk_mss (rules, congs, procs, bounds, prems, mk_rews, termless, depth) =
berghofe@10413
   157
  Mss {rules = rules, congs = congs, procs = procs, bounds = bounds,
nipkow@11504
   158
       prems=prems, mk_rews=mk_rews, termless=termless, depth=depth};
berghofe@10413
   159
nipkow@11504
   160
fun upd_rules(Mss{rules,congs,procs,bounds,prems,mk_rews,termless,depth}, rules') =
nipkow@11504
   161
  mk_mss(rules',congs,procs,bounds,prems,mk_rews,termless,depth);
berghofe@10413
   162
berghofe@10413
   163
val empty_mss =
berghofe@10413
   164
  let val mk_rews = {mk = K [], mk_sym = K None, mk_eq_True = K None}
nipkow@11504
   165
  in mk_mss (Net.empty, ([], []), Net.empty, [], [], mk_rews, Term.termless, 0) end;
berghofe@10413
   166
berghofe@10413
   167
fun clear_mss (Mss {mk_rews, termless, ...}) =
nipkow@11504
   168
  mk_mss (Net.empty, ([], []), Net.empty, [], [], mk_rews, termless,0);
berghofe@10413
   169
nipkow@11504
   170
fun incr_depth(Mss{rules,congs,procs,bounds,prems,mk_rews,termless,depth}) =
nipkow@11504
   171
  mk_mss (rules, congs, procs, bounds, prems, mk_rews, termless, depth+1)
nipkow@11504
   172
 
berghofe@10413
   173
berghofe@10413
   174
berghofe@10413
   175
(** simpset operations **)
berghofe@10413
   176
berghofe@10413
   177
(* term variables *)
berghofe@10413
   178
berghofe@10413
   179
val add_term_varnames = foldl_aterms (fn (xs, Var (x, _)) => ins_ix (x, xs) | (xs, _) => xs);
berghofe@10413
   180
fun term_varnames t = add_term_varnames ([], t);
berghofe@10413
   181
berghofe@10413
   182
berghofe@10413
   183
(* dest_mss *)
berghofe@10413
   184
berghofe@10413
   185
fun dest_mss (Mss {rules, congs, procs, ...}) =
berghofe@10413
   186
  {simps = map (fn (_, {thm, ...}) => thm) (Net.dest rules),
berghofe@10413
   187
   congs = map (fn (_, {thm, ...}) => thm) (fst congs),
berghofe@10413
   188
   procs =
berghofe@10413
   189
     map (fn (_, {name, lhs, id, ...}) => ((name, lhs), id)) (Net.dest procs)
berghofe@10413
   190
     |> partition_eq eq_snd
berghofe@10413
   191
     |> map (fn ps => (#1 (#1 (hd ps)), map (#2 o #1) ps))
berghofe@10413
   192
     |> Library.sort_wrt #1};
berghofe@10413
   193
berghofe@10413
   194
nipkow@11504
   195
(* merge_mss *)	      (*NOTE: ignores mk_rews, termless and depth of 2nd mss*)
berghofe@10413
   196
berghofe@10413
   197
fun merge_mss
berghofe@10413
   198
 (Mss {rules = rules1, congs = (congs1,weak1), procs = procs1,
nipkow@11504
   199
       bounds = bounds1, prems = prems1, mk_rews, termless, depth},
berghofe@10413
   200
  Mss {rules = rules2, congs = (congs2,weak2), procs = procs2,
berghofe@10413
   201
       bounds = bounds2, prems = prems2, ...}) =
berghofe@10413
   202
      mk_mss
berghofe@10413
   203
       (Net.merge (rules1, rules2, eq_rrule),
berghofe@10413
   204
        (generic_merge (eq_cong o pairself snd) I I congs1 congs2,
berghofe@10413
   205
        merge_lists weak1 weak2),
berghofe@10413
   206
        Net.merge (procs1, procs2, eq_simproc),
berghofe@10413
   207
        merge_lists bounds1 bounds2,
berghofe@10413
   208
        generic_merge eq_prem I I prems1 prems2,
nipkow@11504
   209
        mk_rews, termless, depth);
berghofe@10413
   210
berghofe@10413
   211
berghofe@10413
   212
(* add_simps *)
berghofe@10413
   213
berghofe@10413
   214
fun mk_rrule2{thm,lhs,elhs,perm} =
berghofe@10413
   215
  let val fo = Pattern.first_order (term_of elhs) orelse not(Pattern.pattern (term_of elhs))
berghofe@10413
   216
  in {thm=thm,lhs=lhs,elhs=elhs,fo=fo,perm=perm} end
berghofe@10413
   217
berghofe@10413
   218
fun insert_rrule(mss as Mss {rules,...},
berghofe@10413
   219
                 rrule as {thm,lhs,elhs,perm}) =
berghofe@10413
   220
  (trace_thm false "Adding rewrite rule:" thm;
berghofe@10413
   221
   let val rrule2 as {elhs,...} = mk_rrule2 rrule
berghofe@10413
   222
       val rules' = Net.insert_term ((term_of elhs, rrule2), rules, eq_rrule)
berghofe@10413
   223
   in upd_rules(mss,rules') end
berghofe@10413
   224
   handle Net.INSERT =>
berghofe@10413
   225
     (prthm true "Ignoring duplicate rewrite rule:" thm; mss));
berghofe@10413
   226
berghofe@10413
   227
fun vperm (Var _, Var _) = true
berghofe@10413
   228
  | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t)
berghofe@10413
   229
  | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2)
berghofe@10413
   230
  | vperm (t, u) = (t = u);
berghofe@10413
   231
berghofe@10413
   232
fun var_perm (t, u) =
berghofe@10413
   233
  vperm (t, u) andalso eq_set (term_varnames t, term_varnames u);
berghofe@10413
   234
berghofe@10413
   235
(* FIXME: it seems that the conditions on extra variables are too liberal if
berghofe@10413
   236
prems are nonempty: does solving the prems really guarantee instantiation of
berghofe@10413
   237
all its Vars? Better: a dynamic check each time a rule is applied.
berghofe@10413
   238
*)
berghofe@10413
   239
fun rewrite_rule_extra_vars prems elhs erhs =
berghofe@10413
   240
  not (term_varnames erhs subset foldl add_term_varnames (term_varnames elhs, prems))
berghofe@10413
   241
  orelse
berghofe@10413
   242
  not ((term_tvars erhs) subset
berghofe@10413
   243
       (term_tvars elhs  union  List.concat(map term_tvars prems)));
berghofe@10413
   244
berghofe@10413
   245
(*Simple test for looping rewrite rules and stupid orientations*)
berghofe@10413
   246
fun reorient sign prems lhs rhs =
berghofe@10413
   247
   rewrite_rule_extra_vars prems lhs rhs
berghofe@10413
   248
  orelse
berghofe@10413
   249
   is_Var (head_of lhs)
berghofe@10413
   250
  orelse
berghofe@10413
   251
   (exists (apl (lhs, Logic.occs)) (rhs :: prems))
berghofe@10413
   252
  orelse
berghofe@10413
   253
   (null prems andalso
berghofe@10413
   254
    Pattern.matches (#tsig (Sign.rep_sg sign)) (lhs, rhs))
berghofe@10413
   255
    (*the condition "null prems" is necessary because conditional rewrites
berghofe@10413
   256
      with extra variables in the conditions may terminate although
berghofe@10413
   257
      the rhs is an instance of the lhs. Example: ?m < ?n ==> f(?n) == f(?m)*)
berghofe@10413
   258
  orelse
berghofe@10413
   259
   (is_Const lhs andalso not(is_Const rhs))
berghofe@10413
   260
berghofe@10413
   261
fun decomp_simp thm =
berghofe@10413
   262
  let val {sign, prop, ...} = rep_thm thm;
berghofe@10413
   263
      val prems = Logic.strip_imp_prems prop;
berghofe@10413
   264
      val concl = Drule.strip_imp_concl (cprop_of thm);
berghofe@10413
   265
      val (lhs, rhs) = Drule.dest_equals concl handle TERM _ =>
berghofe@10413
   266
        raise SIMPLIFIER ("Rewrite rule not a meta-equality", thm)
berghofe@10413
   267
      val elhs = snd (Drule.dest_equals (cprop_of (Thm.eta_conversion lhs)));
berghofe@10413
   268
      val elhs = if elhs=lhs then lhs else elhs (* try to share *)
berghofe@10413
   269
      val erhs = Pattern.eta_contract (term_of rhs);
berghofe@10413
   270
      val perm = var_perm (term_of elhs, erhs) andalso not (term_of elhs aconv erhs)
berghofe@10413
   271
                 andalso not (is_Var (term_of elhs))
berghofe@10413
   272
  in (sign, prems, term_of lhs, elhs, term_of rhs, perm) end;
berghofe@10413
   273
berghofe@10413
   274
fun mk_eq_True (Mss{mk_rews={mk_eq_True,...},...}) thm =
berghofe@10413
   275
  case mk_eq_True thm of
berghofe@10413
   276
    None => []
berghofe@10413
   277
  | Some eq_True => let val (_,_,lhs,elhs,_,_) = decomp_simp eq_True
berghofe@10413
   278
                    in [{thm=eq_True, lhs=lhs, elhs=elhs, perm=false}] end;
berghofe@10413
   279
berghofe@10413
   280
(* create the rewrite rule and possibly also the ==True variant,
berghofe@10413
   281
   in case there are extra vars on the rhs *)
berghofe@10413
   282
fun rrule_eq_True(thm,lhs,elhs,rhs,mss,thm2) =
berghofe@10413
   283
  let val rrule = {thm=thm, lhs=lhs, elhs=elhs, perm=false}
berghofe@10413
   284
  in if (term_varnames rhs)  subset (term_varnames lhs) andalso
berghofe@10413
   285
        (term_tvars rhs) subset (term_tvars lhs)
berghofe@10413
   286
     then [rrule]
berghofe@10413
   287
     else mk_eq_True mss thm2 @ [rrule]
berghofe@10413
   288
  end;
berghofe@10413
   289
berghofe@10413
   290
fun mk_rrule mss thm =
berghofe@10413
   291
  let val (_,prems,lhs,elhs,rhs,perm) = decomp_simp thm
berghofe@10413
   292
  in if perm then [{thm=thm, lhs=lhs, elhs=elhs, perm=true}] else
berghofe@10413
   293
     (* weak test for loops: *)
berghofe@10413
   294
     if rewrite_rule_extra_vars prems lhs rhs orelse
berghofe@10413
   295
        is_Var (term_of elhs)
berghofe@10413
   296
     then mk_eq_True mss thm
berghofe@10413
   297
     else rrule_eq_True(thm,lhs,elhs,rhs,mss,thm)
berghofe@10413
   298
  end;
berghofe@10413
   299
berghofe@10413
   300
fun orient_rrule mss thm =
berghofe@10413
   301
  let val (sign,prems,lhs,elhs,rhs,perm) = decomp_simp thm
berghofe@10413
   302
  in if perm then [{thm=thm,lhs=lhs,elhs=elhs,perm=true}]
berghofe@10413
   303
     else if reorient sign prems lhs rhs
berghofe@10413
   304
          then if reorient sign prems rhs lhs
berghofe@10413
   305
               then mk_eq_True mss thm
berghofe@10413
   306
               else let val Mss{mk_rews={mk_sym,...},...} = mss
berghofe@10413
   307
                    in case mk_sym thm of
berghofe@10413
   308
                         None => []
berghofe@10413
   309
                       | Some thm' =>
berghofe@10413
   310
                           let val (_,_,lhs',elhs',rhs',_) = decomp_simp thm'
berghofe@10413
   311
                           in rrule_eq_True(thm',lhs',elhs',rhs',mss,thm) end
berghofe@10413
   312
                    end
berghofe@10413
   313
          else rrule_eq_True(thm,lhs,elhs,rhs,mss,thm)
berghofe@10413
   314
  end;
berghofe@10413
   315
berghofe@10413
   316
fun extract_rews(Mss{mk_rews = {mk,...},...},thms) = flat(map mk thms);
berghofe@10413
   317
berghofe@10413
   318
fun orient_comb_simps comb mk_rrule (mss,thms) =
berghofe@10413
   319
  let val rews = extract_rews(mss,thms)
berghofe@10413
   320
      val rrules = flat (map mk_rrule rews)
berghofe@10413
   321
  in foldl comb (mss,rrules) end
berghofe@10413
   322
berghofe@10413
   323
(* Add rewrite rules explicitly; do not reorient! *)
berghofe@10413
   324
fun add_simps(mss,thms) =
berghofe@10413
   325
  orient_comb_simps insert_rrule (mk_rrule mss) (mss,thms);
berghofe@10413
   326
berghofe@10413
   327
fun mss_of thms =
berghofe@10413
   328
  foldl insert_rrule (empty_mss, flat(map (mk_rrule empty_mss) thms));
berghofe@10413
   329
berghofe@10413
   330
fun extract_safe_rrules(mss,thm) =
berghofe@10413
   331
  flat (map (orient_rrule mss) (extract_rews(mss,[thm])));
berghofe@10413
   332
berghofe@10413
   333
fun add_safe_simp(mss,thm) =
berghofe@10413
   334
  foldl insert_rrule (mss, extract_safe_rrules(mss,thm))
berghofe@10413
   335
berghofe@10413
   336
(* del_simps *)
berghofe@10413
   337
berghofe@10413
   338
fun del_rrule(mss as Mss {rules,...},
berghofe@10413
   339
              rrule as {thm, elhs, ...}) =
berghofe@10413
   340
  (upd_rules(mss, Net.delete_term ((term_of elhs, rrule), rules, eq_rrule))
berghofe@10413
   341
   handle Net.DELETE =>
berghofe@10413
   342
     (prthm true "Rewrite rule not in simpset:" thm; mss));
berghofe@10413
   343
berghofe@10413
   344
fun del_simps(mss,thms) =
berghofe@10413
   345
  orient_comb_simps del_rrule (map mk_rrule2 o mk_rrule mss) (mss,thms);
berghofe@10413
   346
berghofe@10413
   347
berghofe@10413
   348
(* add_congs *)
berghofe@10413
   349
berghofe@10413
   350
fun is_full_cong_prems [] varpairs = null varpairs
berghofe@10413
   351
  | is_full_cong_prems (p::prems) varpairs =
berghofe@10413
   352
    (case Logic.strip_assums_concl p of
berghofe@10413
   353
       Const("==",_) $ lhs $ rhs =>
berghofe@10413
   354
         let val (x,xs) = strip_comb lhs and (y,ys) = strip_comb rhs
berghofe@10413
   355
         in is_Var x  andalso  forall is_Bound xs  andalso
berghofe@10413
   356
            null(findrep(xs))  andalso xs=ys andalso
berghofe@10413
   357
            (x,y) mem varpairs andalso
berghofe@10413
   358
            is_full_cong_prems prems (varpairs\(x,y))
berghofe@10413
   359
         end
berghofe@10413
   360
     | _ => false);
berghofe@10413
   361
berghofe@10413
   362
fun is_full_cong thm =
berghofe@10413
   363
let val prems = prems_of thm
berghofe@10413
   364
    and concl = concl_of thm
berghofe@10413
   365
    val (lhs,rhs) = Logic.dest_equals concl
berghofe@10413
   366
    val (f,xs) = strip_comb lhs
berghofe@10413
   367
    and (g,ys) = strip_comb rhs
berghofe@10413
   368
in
berghofe@10413
   369
  f=g andalso null(findrep(xs@ys)) andalso length xs = length ys andalso
berghofe@10413
   370
  is_full_cong_prems prems (xs ~~ ys)
berghofe@10413
   371
end
berghofe@10413
   372
nipkow@11504
   373
fun add_cong (Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, thm) =
berghofe@10413
   374
  let
berghofe@10413
   375
    val (lhs, _) = Drule.dest_equals (Drule.strip_imp_concl (cprop_of thm)) handle TERM _ =>
berghofe@10413
   376
      raise SIMPLIFIER ("Congruence not a meta-equality", thm);
berghofe@10413
   377
(*   val lhs = Pattern.eta_contract lhs; *)
berghofe@10413
   378
    val (a, _) = dest_Const (head_of (term_of lhs)) handle TERM _ =>
berghofe@10413
   379
      raise SIMPLIFIER ("Congruence must start with a constant", thm);
berghofe@10413
   380
    val (alist,weak) = congs
berghofe@10413
   381
    val alist2 = overwrite_warn (alist, (a,{lhs=lhs, thm=thm}))
berghofe@10413
   382
           ("Overwriting congruence rule for " ^ quote a);
berghofe@10413
   383
    val weak2 = if is_full_cong thm then weak else a::weak
berghofe@10413
   384
  in
nipkow@11504
   385
    mk_mss (rules,(alist2,weak2),procs,bounds,prems,mk_rews,termless,depth)
berghofe@10413
   386
  end;
berghofe@10413
   387
berghofe@10413
   388
val (op add_congs) = foldl add_cong;
berghofe@10413
   389
berghofe@10413
   390
berghofe@10413
   391
(* del_congs *)
berghofe@10413
   392
nipkow@11504
   393
fun del_cong (Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, thm) =
berghofe@10413
   394
  let
berghofe@10413
   395
    val (lhs, _) = Logic.dest_equals (concl_of thm) handle TERM _ =>
berghofe@10413
   396
      raise SIMPLIFIER ("Congruence not a meta-equality", thm);
berghofe@10413
   397
(*   val lhs = Pattern.eta_contract lhs; *)
berghofe@10413
   398
    val (a, _) = dest_Const (head_of lhs) handle TERM _ =>
berghofe@10413
   399
      raise SIMPLIFIER ("Congruence must start with a constant", thm);
berghofe@10413
   400
    val (alist,_) = congs
berghofe@10413
   401
    val alist2 = filter (fn (x,_)=> x<>a) alist
berghofe@10413
   402
    val weak2 = mapfilter (fn(a,{thm,...}) => if is_full_cong thm then None
berghofe@10413
   403
                                              else Some a)
berghofe@10413
   404
                   alist2
berghofe@10413
   405
  in
nipkow@11504
   406
    mk_mss (rules,(alist2,weak2),procs,bounds,prems,mk_rews,termless,depth)
berghofe@10413
   407
  end;
berghofe@10413
   408
berghofe@10413
   409
val (op del_congs) = foldl del_cong;
berghofe@10413
   410
berghofe@10413
   411
berghofe@10413
   412
(* add_simprocs *)
berghofe@10413
   413
nipkow@11504
   414
fun add_proc (mss as Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth},
berghofe@10413
   415
    (name, lhs, proc, id)) =
berghofe@10413
   416
  let val {sign, t, ...} = rep_cterm lhs
berghofe@10413
   417
  in (trace_term false ("Adding simplification procedure " ^ quote name ^ " for")
berghofe@10413
   418
      sign t;
berghofe@10413
   419
    mk_mss (rules, congs,
berghofe@10413
   420
      Net.insert_term ((t, mk_simproc (name, proc, lhs, id)), procs, eq_simproc)
berghofe@10413
   421
        handle Net.INSERT => 
berghofe@10413
   422
	    (warning ("Ignoring duplicate simplification procedure \"" 
berghofe@10413
   423
	              ^ name ^ "\""); 
berghofe@10413
   424
	     procs),
nipkow@11504
   425
        bounds, prems, mk_rews, termless,depth))
berghofe@10413
   426
  end;
berghofe@10413
   427
berghofe@10413
   428
fun add_simproc (mss, (name, lhss, proc, id)) =
berghofe@10413
   429
  foldl add_proc (mss, map (fn lhs => (name, lhs, proc, id)) lhss);
berghofe@10413
   430
berghofe@10413
   431
val add_simprocs = foldl add_simproc;
berghofe@10413
   432
berghofe@10413
   433
berghofe@10413
   434
(* del_simprocs *)
berghofe@10413
   435
nipkow@11504
   436
fun del_proc (mss as Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth},
berghofe@10413
   437
    (name, lhs, proc, id)) =
berghofe@10413
   438
  mk_mss (rules, congs,
berghofe@10413
   439
    Net.delete_term ((term_of lhs, mk_simproc (name, proc, lhs, id)), procs, eq_simproc)
berghofe@10413
   440
      handle Net.DELETE => 
berghofe@10413
   441
	  (warning ("Simplification procedure \"" ^ name ^
berghofe@10413
   442
		       "\" not in simpset"); procs),
nipkow@11504
   443
      bounds, prems, mk_rews, termless, depth);
berghofe@10413
   444
berghofe@10413
   445
fun del_simproc (mss, (name, lhss, proc, id)) =
berghofe@10413
   446
  foldl del_proc (mss, map (fn lhs => (name, lhs, proc, id)) lhss);
berghofe@10413
   447
berghofe@10413
   448
val del_simprocs = foldl del_simproc;
berghofe@10413
   449
berghofe@10413
   450
berghofe@10413
   451
(* prems *)
berghofe@10413
   452
nipkow@11504
   453
fun add_prems (Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, thms) =
nipkow@11504
   454
  mk_mss (rules, congs, procs, bounds, thms @ prems, mk_rews, termless, depth);
berghofe@10413
   455
berghofe@10413
   456
fun prems_of_mss (Mss {prems, ...}) = prems;
berghofe@10413
   457
berghofe@10413
   458
berghofe@10413
   459
(* mk_rews *)
berghofe@10413
   460
berghofe@10413
   461
fun set_mk_rews
nipkow@11504
   462
  (Mss {rules, congs, procs, bounds, prems, mk_rews, termless, depth}, mk) =
berghofe@10413
   463
    mk_mss (rules, congs, procs, bounds, prems,
berghofe@10413
   464
            {mk=mk, mk_sym= #mk_sym mk_rews, mk_eq_True= #mk_eq_True mk_rews},
nipkow@11504
   465
            termless, depth);
berghofe@10413
   466
berghofe@10413
   467
fun set_mk_sym
nipkow@11504
   468
  (Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, mk_sym) =
berghofe@10413
   469
    mk_mss (rules, congs, procs, bounds, prems,
berghofe@10413
   470
            {mk= #mk mk_rews, mk_sym= mk_sym, mk_eq_True= #mk_eq_True mk_rews},
nipkow@11504
   471
            termless,depth);
berghofe@10413
   472
berghofe@10413
   473
fun set_mk_eq_True
nipkow@11504
   474
  (Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, mk_eq_True) =
berghofe@10413
   475
    mk_mss (rules, congs, procs, bounds, prems,
berghofe@10413
   476
            {mk= #mk mk_rews, mk_sym= #mk_sym mk_rews, mk_eq_True= mk_eq_True},
nipkow@11504
   477
            termless,depth);
berghofe@10413
   478
berghofe@10413
   479
(* termless *)
berghofe@10413
   480
berghofe@10413
   481
fun set_termless
nipkow@11504
   482
  (Mss {rules, congs, procs, bounds, prems, mk_rews, depth, ...}, termless) =
nipkow@11504
   483
    mk_mss (rules, congs, procs, bounds, prems, mk_rews, termless, depth);
berghofe@10413
   484
berghofe@10413
   485
berghofe@10413
   486
berghofe@10413
   487
(** rewriting **)
berghofe@10413
   488
berghofe@10413
   489
(*
berghofe@10413
   490
  Uses conversions, see:
berghofe@10413
   491
    L C Paulson, A higher-order implementation of rewriting,
berghofe@10413
   492
    Science of Computer Programming 3 (1983), pages 119-149.
berghofe@10413
   493
*)
berghofe@10413
   494
berghofe@10413
   495
type prover = meta_simpset -> thm -> thm option;
berghofe@10413
   496
type termrec = (Sign.sg_ref * term list) * term;
berghofe@10413
   497
type conv = meta_simpset -> termrec -> termrec;
berghofe@10413
   498
berghofe@10413
   499
val dest_eq = Drule.dest_equals o cprop_of;
berghofe@10413
   500
val lhs_of = fst o dest_eq;
berghofe@10413
   501
val rhs_of = snd o dest_eq;
berghofe@10413
   502
berghofe@10413
   503
fun beta_eta_conversion t =
berghofe@10413
   504
  let val thm = beta_conversion true t;
berghofe@10413
   505
  in transitive thm (eta_conversion (rhs_of thm)) end;
berghofe@10413
   506
berghofe@10413
   507
fun check_conv msg thm thm' =
berghofe@10413
   508
  let
berghofe@10413
   509
    val thm'' = transitive thm (transitive
berghofe@10413
   510
      (symmetric (beta_eta_conversion (lhs_of thm'))) thm')
berghofe@10413
   511
  in (if msg then trace_thm false "SUCCEEDED" thm' else (); Some thm'') end
berghofe@10413
   512
  handle THM _ =>
berghofe@10413
   513
    let val {sign, prop = _ $ _ $ prop0, ...} = rep_thm thm;
berghofe@10413
   514
    in
berghofe@10413
   515
      (trace_thm false "Proved wrong thm (Check subgoaler?)" thm';
berghofe@10413
   516
       trace_term false "Should have proved:" sign prop0;
berghofe@10413
   517
       None)
berghofe@10413
   518
    end;
berghofe@10413
   519
berghofe@10413
   520
berghofe@10413
   521
(* mk_procrule *)
berghofe@10413
   522
berghofe@10413
   523
fun mk_procrule thm =
berghofe@10413
   524
  let val (_,prems,lhs,elhs,rhs,_) = decomp_simp thm
berghofe@10413
   525
  in if rewrite_rule_extra_vars prems lhs rhs
berghofe@10413
   526
     then (prthm true "Extra vars on rhs:" thm; [])
berghofe@10413
   527
     else [mk_rrule2{thm=thm, lhs=lhs, elhs=elhs, perm=false}]
berghofe@10413
   528
  end;
berghofe@10413
   529
berghofe@10413
   530
berghofe@10413
   531
(* conversion to apply the meta simpset to a term *)
berghofe@10413
   532
berghofe@10413
   533
(* Since the rewriting strategy is bottom-up, we avoid re-normalizing already
berghofe@10413
   534
   normalized terms by carrying around the rhs of the rewrite rule just
berghofe@10413
   535
   applied. This is called the `skeleton'. It is decomposed in parallel
berghofe@10413
   536
   with the term. Once a Var is encountered, the corresponding term is
berghofe@10413
   537
   already in normal form.
berghofe@10413
   538
   skel0 is a dummy skeleton that is to enforce complete normalization.
berghofe@10413
   539
*)
berghofe@10413
   540
val skel0 = Bound 0;
berghofe@10413
   541
berghofe@10413
   542
(* Use rhs as skeleton only if the lhs does not contain unnormalized bits.
berghofe@10413
   543
   The latter may happen iff there are weak congruence rules for constants
berghofe@10413
   544
   in the lhs.
berghofe@10413
   545
*)
berghofe@10413
   546
fun uncond_skel((_,weak),(lhs,rhs)) =
berghofe@10413
   547
  if null weak then rhs (* optimization *)
berghofe@10413
   548
  else if exists_Const (fn (c,_) => c mem weak) lhs then skel0
berghofe@10413
   549
       else rhs;
berghofe@10413
   550
berghofe@10413
   551
(* Behaves like unconditional rule if rhs does not contain vars not in the lhs.
berghofe@10413
   552
   Otherwise those vars may become instantiated with unnormalized terms
berghofe@10413
   553
   while the premises are solved.
berghofe@10413
   554
*)
berghofe@10413
   555
fun cond_skel(args as (congs,(lhs,rhs))) =
berghofe@10413
   556
  if term_varnames rhs subset term_varnames lhs then uncond_skel(args)
berghofe@10413
   557
  else skel0;
berghofe@10413
   558
berghofe@10413
   559
(*
berghofe@10413
   560
  we try in order:
berghofe@10413
   561
    (1) beta reduction
berghofe@10413
   562
    (2) unconditional rewrite rules
berghofe@10413
   563
    (3) conditional rewrite rules
berghofe@10413
   564
    (4) simplification procedures
berghofe@10413
   565
berghofe@10413
   566
  IMPORTANT: rewrite rules must not introduce new Vars or TVars!
berghofe@10413
   567
berghofe@10413
   568
*)
berghofe@10413
   569
berghofe@10413
   570
fun rewritec (prover, signt, maxt)
nipkow@11504
   571
             (mss as Mss{rules, procs, termless, prems, congs, depth,...}) t =
berghofe@10413
   572
  let
berghofe@10413
   573
    val eta_thm = Thm.eta_conversion t;
berghofe@10413
   574
    val eta_t' = rhs_of eta_thm;
berghofe@10413
   575
    val eta_t = term_of eta_t';
berghofe@10413
   576
    val tsigt = Sign.tsig_of signt;
berghofe@10413
   577
    fun rew {thm, lhs, elhs, fo, perm} =
berghofe@10413
   578
      let
berghofe@10413
   579
        val {sign, prop, maxidx, ...} = rep_thm thm;
berghofe@10413
   580
        val _ = if Sign.subsig (sign, signt) then ()
berghofe@10413
   581
                else (prthm true "Ignoring rewrite rule from different theory:" thm;
berghofe@10413
   582
                      raise Pattern.MATCH);
berghofe@10413
   583
        val (rthm, elhs') = if maxt = ~1 then (thm, elhs)
berghofe@10413
   584
          else (Thm.incr_indexes (maxt+1) thm, Thm.cterm_incr_indexes (maxt+1) elhs);
berghofe@10413
   585
        val insts = if fo then Thm.cterm_first_order_match (elhs', eta_t')
berghofe@10413
   586
                          else Thm.cterm_match (elhs', eta_t');
berghofe@10413
   587
        val thm' = Thm.instantiate insts (Thm.rename_boundvars lhs eta_t rthm);
berghofe@10413
   588
        val prop' = #prop (rep_thm thm');
berghofe@10413
   589
        val unconditional = (Logic.count_prems (prop',0) = 0);
berghofe@10413
   590
        val (lhs', rhs') = Logic.dest_equals (Logic.strip_imp_concl prop')
berghofe@10413
   591
      in
nipkow@11295
   592
        if perm andalso not (termless (rhs', lhs'))
nipkow@11295
   593
        then (trace_thm false "Cannot apply permutative rewrite rule:" thm;
nipkow@11295
   594
              trace_thm false "Term does not become smaller:" thm'; None)
berghofe@10413
   595
        else
nipkow@11504
   596
          let val ds = "[" ^ string_of_int depth ^ "]"
nipkow@11504
   597
          in trace_thm false "Applying instance of rewrite rule:" thm;
berghofe@10413
   598
           if unconditional
berghofe@10413
   599
           then
nipkow@11504
   600
             (trace_thm false (ds ^ "Rewriting:") thm';
berghofe@10413
   601
              let val lr = Logic.dest_equals prop;
berghofe@10413
   602
                  val Some thm'' = check_conv false eta_thm thm'
berghofe@10413
   603
              in Some (thm'', uncond_skel (congs, lr)) end)
berghofe@10413
   604
           else
nipkow@11504
   605
             (trace_thm false (ds ^ "Trying to rewrite:") thm';
nipkow@11504
   606
              case prover (incr_depth mss) thm' of
nipkow@11504
   607
                None       => (trace_thm false (ds ^ "FAILED") thm'; None)
berghofe@10413
   608
              | Some thm2 =>
berghofe@10413
   609
                  (case check_conv true eta_thm thm2 of
berghofe@10413
   610
                     None => None |
berghofe@10413
   611
                     Some thm2' =>
berghofe@10413
   612
                       let val concl = Logic.strip_imp_concl prop
berghofe@10413
   613
                           val lr = Logic.dest_equals concl
nipkow@11504
   614
                       in Some (thm2', cond_skel (congs, lr)) end))
nipkow@11504
   615
          end
berghofe@10413
   616
      end
berghofe@10413
   617
berghofe@10413
   618
    fun rews [] = None
berghofe@10413
   619
      | rews (rrule :: rrules) =
berghofe@10413
   620
          let val opt = rew rrule handle Pattern.MATCH => None
berghofe@10413
   621
          in case opt of None => rews rrules | some => some end;
berghofe@10413
   622
berghofe@10413
   623
    fun sort_rrules rrs = let
berghofe@10413
   624
      fun is_simple({thm, ...}:rrule) = case #prop (rep_thm thm) of 
berghofe@10413
   625
                                      Const("==",_) $ _ $ _ => true
berghofe@10413
   626
                                      | _                   => false 
berghofe@10413
   627
      fun sort []        (re1,re2) = re1 @ re2
berghofe@10413
   628
        | sort (rr::rrs) (re1,re2) = if is_simple rr 
berghofe@10413
   629
                                     then sort rrs (rr::re1,re2)
berghofe@10413
   630
                                     else sort rrs (re1,rr::re2)
berghofe@10413
   631
    in sort rrs ([],[]) end
berghofe@10413
   632
berghofe@10413
   633
    fun proc_rews ([]:simproc list) = None
berghofe@10413
   634
      | proc_rews ({name, proc, lhs, ...} :: ps) =
berghofe@10413
   635
          if Pattern.matches tsigt (term_of lhs, term_of t) then
berghofe@10413
   636
            (debug_term false ("Trying procedure " ^ quote name ^ " on:") signt eta_t;
berghofe@10413
   637
             case proc signt prems eta_t of
berghofe@10413
   638
               None => (debug false "FAILED"; proc_rews ps)
berghofe@10413
   639
             | Some raw_thm =>
berghofe@10413
   640
                 (trace_thm false ("Procedure " ^ quote name ^ " produced rewrite rule:") raw_thm;
berghofe@10413
   641
                  (case rews (mk_procrule raw_thm) of
nipkow@11291
   642
                    None => (trace_cterm false "IGNORED - does not match" t; proc_rews ps)
berghofe@10413
   643
                  | some => some)))
berghofe@10413
   644
          else proc_rews ps;
berghofe@10413
   645
  in case eta_t of
berghofe@10413
   646
       Abs _ $ _ => Some (transitive eta_thm
berghofe@10413
   647
         (beta_conversion false (rhs_of eta_thm)), skel0)
berghofe@10413
   648
     | _ => (case rews (sort_rrules (Net.match_term rules eta_t)) of
berghofe@10413
   649
               None => proc_rews (Net.match_term procs eta_t)
berghofe@10413
   650
             | some => some)
berghofe@10413
   651
  end;
berghofe@10413
   652
berghofe@10413
   653
berghofe@10413
   654
(* conversion to apply a congruence rule to a term *)
berghofe@10413
   655
berghofe@10413
   656
fun congc (prover,signt,maxt) {thm=cong,lhs=lhs} t =
berghofe@10413
   657
  let val {sign, ...} = rep_thm cong
berghofe@10413
   658
      val _ = if Sign.subsig (sign, signt) then ()
berghofe@10413
   659
                 else error("Congruence rule from different theory")
berghofe@10413
   660
      val rthm = if maxt = ~1 then cong else Thm.incr_indexes (maxt+1) cong;
berghofe@10413
   661
      val rlhs = fst (Drule.dest_equals (Drule.strip_imp_concl (cprop_of rthm)));
berghofe@10413
   662
      val insts = Thm.cterm_match (rlhs, t)
berghofe@10413
   663
      (* Pattern.match can raise Pattern.MATCH;
berghofe@10413
   664
         is handled when congc is called *)
berghofe@10413
   665
      val thm' = Thm.instantiate insts (Thm.rename_boundvars (term_of rlhs) (term_of t) rthm);
berghofe@10413
   666
      val unit = trace_thm false "Applying congruence rule:" thm';
berghofe@10413
   667
      fun err (msg, thm) = (prthm false msg thm; error "Failed congruence proof!")
berghofe@10413
   668
  in case prover thm' of
berghofe@10413
   669
       None => err ("Could not prove", thm')
berghofe@10413
   670
     | Some thm2 => (case check_conv true (beta_eta_conversion t) thm2 of
berghofe@10413
   671
          None => err ("Should not have proved", thm2)
berghofe@10413
   672
        | Some thm2' => thm2')
berghofe@10413
   673
  end;
berghofe@10413
   674
berghofe@10413
   675
val (cA, (cB, cC)) =
berghofe@10413
   676
  apsnd dest_equals (dest_implies (hd (cprems_of Drule.imp_cong)));
berghofe@10413
   677
berghofe@10413
   678
fun transitive' thm1 None = Some thm1
berghofe@10413
   679
  | transitive' thm1 (Some thm2) = Some (transitive thm1 thm2);
berghofe@10413
   680
berghofe@10413
   681
fun bottomc ((simprem,useprem,mutsimp), prover, sign, maxidx) =
berghofe@10413
   682
  let
berghofe@10413
   683
    fun botc skel mss t =
berghofe@10413
   684
          if is_Var skel then None
berghofe@10413
   685
          else
berghofe@10413
   686
          (case subc skel mss t of
berghofe@10413
   687
             some as Some thm1 =>
berghofe@10413
   688
               (case rewritec (prover, sign, maxidx) mss (rhs_of thm1) of
berghofe@10413
   689
                  Some (thm2, skel2) =>
berghofe@10413
   690
                    transitive' (transitive thm1 thm2)
berghofe@10413
   691
                      (botc skel2 mss (rhs_of thm2))
berghofe@10413
   692
                | None => some)
berghofe@10413
   693
           | None =>
berghofe@10413
   694
               (case rewritec (prover, sign, maxidx) mss t of
berghofe@10413
   695
                  Some (thm2, skel2) => transitive' thm2
berghofe@10413
   696
                    (botc skel2 mss (rhs_of thm2))
berghofe@10413
   697
                | None => None))
berghofe@10413
   698
berghofe@10413
   699
    and try_botc mss t =
berghofe@10413
   700
          (case botc skel0 mss t of
berghofe@10413
   701
             Some trec1 => trec1 | None => (reflexive t))
berghofe@10413
   702
berghofe@10413
   703
    and subc skel
nipkow@11504
   704
          (mss as Mss{rules,congs,procs,bounds,prems,mk_rews,termless,depth}) t0 =
berghofe@10413
   705
       (case term_of t0 of
berghofe@10413
   706
           Abs (a, T, t) =>
berghofe@10413
   707
             let val b = variant bounds a
wenzelm@10767
   708
                 val (v, t') = Thm.dest_abs (Some ("." ^ b)) t0
nipkow@11504
   709
                 val mss' = mk_mss (rules, congs, procs, b :: bounds, prems, mk_rews, termless,depth)
berghofe@10413
   710
                 val skel' = case skel of Abs (_, _, sk) => sk | _ => skel0
berghofe@10413
   711
             in case botc skel' mss' t' of
berghofe@10413
   712
                  Some thm => Some (abstract_rule a v thm)
berghofe@10413
   713
                | None => None
berghofe@10413
   714
             end
berghofe@10413
   715
         | t $ _ => (case t of
berghofe@10413
   716
             Const ("==>", _) $ _  =>
berghofe@10413
   717
               let val (s, u) = Drule.dest_implies t0
berghofe@10413
   718
               in impc (s, u, mss) end
berghofe@10413
   719
           | Abs _ =>
berghofe@10413
   720
               let val thm = beta_conversion false t0
berghofe@10413
   721
               in case subc skel0 mss (rhs_of thm) of
berghofe@10413
   722
                    None => Some thm
berghofe@10413
   723
                  | Some thm' => Some (transitive thm thm')
berghofe@10413
   724
               end
berghofe@10413
   725
           | _  =>
berghofe@10413
   726
               let fun appc () =
berghofe@10413
   727
                     let
berghofe@10413
   728
                       val (tskel, uskel) = case skel of
berghofe@10413
   729
                           tskel $ uskel => (tskel, uskel)
berghofe@10413
   730
                         | _ => (skel0, skel0);
wenzelm@10767
   731
                       val (ct, cu) = Thm.dest_comb t0
berghofe@10413
   732
                     in
berghofe@10413
   733
                     (case botc tskel mss ct of
berghofe@10413
   734
                        Some thm1 =>
berghofe@10413
   735
                          (case botc uskel mss cu of
berghofe@10413
   736
                             Some thm2 => Some (combination thm1 thm2)
berghofe@10413
   737
                           | None => Some (combination thm1 (reflexive cu)))
berghofe@10413
   738
                      | None =>
berghofe@10413
   739
                          (case botc uskel mss cu of
berghofe@10413
   740
                             Some thm1 => Some (combination (reflexive ct) thm1)
berghofe@10413
   741
                           | None => None))
berghofe@10413
   742
                     end
berghofe@10413
   743
                   val (h, ts) = strip_comb t
berghofe@10413
   744
               in case h of
berghofe@10413
   745
                    Const(a, _) =>
berghofe@10413
   746
                      (case assoc_string (fst congs, a) of
berghofe@10413
   747
                         None => appc ()
berghofe@10413
   748
                       | Some cong =>
berghofe@10413
   749
(* post processing: some partial applications h t1 ... tj, j <= length ts,
berghofe@10413
   750
   may be a redex. Example: map (%x.x) = (%xs.xs) wrt map_cong *)
berghofe@10413
   751
                          (let
berghofe@10413
   752
                             val thm = congc (prover mss, sign, maxidx) cong t0;
berghofe@10413
   753
                             val t = rhs_of thm;
wenzelm@10767
   754
                             val (cl, cr) = Thm.dest_comb t
berghofe@10413
   755
                             val dVar = Var(("", 0), dummyT)
berghofe@10413
   756
                             val skel =
berghofe@10413
   757
                               list_comb (h, replicate (length ts) dVar)
berghofe@10413
   758
                           in case botc skel mss cl of
berghofe@10413
   759
                                None => Some thm
berghofe@10413
   760
                              | Some thm' => Some (transitive thm
berghofe@10413
   761
                                  (combination thm' (reflexive cr)))
berghofe@10413
   762
                           end handle TERM _ => error "congc result"
berghofe@10413
   763
                                    | Pattern.MATCH => appc ()))
berghofe@10413
   764
                  | _ => appc ()
berghofe@10413
   765
               end)
berghofe@10413
   766
         | _ => None)
berghofe@10413
   767
berghofe@10413
   768
    and impc args =
berghofe@10413
   769
      if mutsimp
berghofe@10413
   770
      then let val (prem, conc, mss) = args
berghofe@10413
   771
           in apsome snd (mut_impc ([], prem, conc, mss)) end
berghofe@10413
   772
      else nonmut_impc args
berghofe@10413
   773
berghofe@10413
   774
    and mut_impc (prems, prem, conc, mss) = (case botc skel0 mss prem of
berghofe@10413
   775
        None => mut_impc1 (prems, prem, conc, mss)
berghofe@10413
   776
      | Some thm1 =>
berghofe@10413
   777
          let val prem1 = rhs_of thm1
berghofe@10413
   778
          in (case mut_impc1 (prems, prem1, conc, mss) of
berghofe@10413
   779
              None => Some (None,
berghofe@10413
   780
                combination (combination refl_implies thm1) (reflexive conc))
berghofe@10413
   781
            | Some (x, thm2) => Some (x, transitive (combination (combination
berghofe@10413
   782
                refl_implies thm1) (reflexive conc)) thm2))
berghofe@10413
   783
          end)
berghofe@10413
   784
berghofe@10413
   785
    and mut_impc1 (prems, prem1, conc, mss) =
berghofe@10413
   786
      let
berghofe@10413
   787
        fun uncond ({thm, lhs, elhs, perm}) =
berghofe@10413
   788
          if Thm.no_prems thm then Some lhs else None
berghofe@10413
   789
berghofe@10413
   790
        val (lhss1, mss1) =
berghofe@10413
   791
          if maxidx_of_term (term_of prem1) <> ~1
berghofe@10413
   792
          then (trace_cterm true
berghofe@10413
   793
            "Cannot add premise as rewrite rule because it contains (type) unknowns:" prem1;
berghofe@10413
   794
                ([],mss))
berghofe@10413
   795
          else let val thm = assume prem1
berghofe@10413
   796
                   val rrules1 = extract_safe_rrules (mss, thm)
berghofe@10413
   797
                   val lhss1 = mapfilter uncond rrules1
berghofe@10413
   798
                   val mss1 = foldl insert_rrule (add_prems (mss, [thm]), rrules1)
berghofe@10413
   799
               in (lhss1, mss1) end
berghofe@10413
   800
berghofe@10413
   801
        fun disch1 thm =
berghofe@10413
   802
          let val (cB', cC') = dest_eq thm
berghofe@10413
   803
          in
berghofe@10413
   804
            implies_elim (Thm.instantiate
berghofe@10413
   805
              ([], [(cA, prem1), (cB, cB'), (cC, cC')]) Drule.imp_cong)
berghofe@10413
   806
              (implies_intr prem1 thm)
berghofe@10413
   807
          end
berghofe@10413
   808
berghofe@10413
   809
        fun rebuild None = (case rewritec (prover, sign, maxidx) mss
berghofe@10413
   810
            (mk_implies (prem1, conc)) of
berghofe@10413
   811
              None => None
berghofe@11371
   812
            | Some (thm, _) => 
berghofe@11371
   813
                let val (prem, conc) = Drule.dest_implies (rhs_of thm)
berghofe@11371
   814
                in (case mut_impc (prems, prem, conc, mss) of
berghofe@11371
   815
                    None => Some (None, thm)
berghofe@11371
   816
                  | Some (x, thm') => Some (x, transitive thm thm'))
berghofe@11371
   817
                end handle TERM _ => Some (None, thm))
berghofe@10413
   818
          | rebuild (Some thm2) =
berghofe@10413
   819
            let val thm = disch1 thm2
berghofe@10413
   820
            in (case rewritec (prover, sign, maxidx) mss (rhs_of thm) of
berghofe@10413
   821
                 None => Some (None, thm)
berghofe@10413
   822
               | Some (thm', _) =>
berghofe@10413
   823
                   let val (prem, conc) = Drule.dest_implies (rhs_of thm')
berghofe@10413
   824
                   in (case mut_impc (prems, prem, conc, mss) of
berghofe@10413
   825
                       None => Some (None, transitive thm thm')
berghofe@10413
   826
                     | Some (x, thm'') =>
berghofe@10413
   827
                         Some (x, transitive (transitive thm thm') thm''))
berghofe@10413
   828
                   end handle TERM _ => Some (None, transitive thm thm'))
berghofe@10413
   829
            end
berghofe@10413
   830
berghofe@10413
   831
        fun simpconc () =
berghofe@10413
   832
          let val (s, t) = Drule.dest_implies conc
berghofe@10413
   833
          in case mut_impc (prems @ [prem1], s, t, mss1) of
berghofe@10413
   834
               None => rebuild None
berghofe@10413
   835
             | Some (Some i, thm2) =>
berghofe@10413
   836
                  let
berghofe@10413
   837
                    val (prem, cC') = Drule.dest_implies (rhs_of thm2);
berghofe@10413
   838
                    val thm2' = transitive (disch1 thm2) (Thm.instantiate
berghofe@10413
   839
                      ([], [(cA, prem1), (cB, prem), (cC, cC')])
berghofe@10413
   840
                      Drule.swap_prems_eq)
berghofe@10413
   841
                  in if i=0 then apsome (apsnd (transitive thm2'))
berghofe@10413
   842
                       (mut_impc1 (prems, prem, mk_implies (prem1, cC'), mss))
berghofe@10413
   843
                     else Some (Some (i-1), thm2')
berghofe@10413
   844
                  end
berghofe@10413
   845
             | Some (None, thm) => rebuild (Some thm)
berghofe@10413
   846
          end handle TERM _ => rebuild (botc skel0 mss1 conc)
berghofe@10413
   847
berghofe@10413
   848
      in
berghofe@10413
   849
        let
berghofe@10413
   850
          val tsig = Sign.tsig_of sign
berghofe@10413
   851
          fun reducible t =
berghofe@10413
   852
            exists (fn lhs => Pattern.matches_subterm tsig (lhs, term_of t)) lhss1;
berghofe@10413
   853
        in case dropwhile (not o reducible) prems of
berghofe@10413
   854
            [] => simpconc ()
berghofe@10413
   855
          | red::rest => (trace_cterm false "Can now reduce premise:" red;
berghofe@10413
   856
              Some (Some (length rest), reflexive (mk_implies (prem1, conc))))
berghofe@10413
   857
        end
berghofe@10413
   858
      end
berghofe@10413
   859
berghofe@10413
   860
     (* legacy code - only for backwards compatibility *)
berghofe@10413
   861
     and nonmut_impc (prem, conc, mss) =
berghofe@10413
   862
       let val thm1 = if simprem then botc skel0 mss prem else None;
berghofe@10413
   863
           val prem1 = if_none (apsome rhs_of thm1) prem;
berghofe@10413
   864
           val maxidx1 = maxidx_of_term (term_of prem1)
berghofe@10413
   865
           val mss1 =
berghofe@10413
   866
             if not useprem then mss else
berghofe@10413
   867
             if maxidx1 <> ~1
berghofe@10413
   868
             then (trace_cterm true
berghofe@10413
   869
               "Cannot add premise as rewrite rule because it contains (type) unknowns:" prem1;
berghofe@10413
   870
                   mss)
berghofe@10413
   871
             else let val thm = assume prem1
berghofe@10413
   872
                  in add_safe_simp (add_prems (mss, [thm]), thm) end
berghofe@10413
   873
       in (case botc skel0 mss1 conc of
berghofe@10413
   874
           None => (case thm1 of
berghofe@10413
   875
               None => None
berghofe@10413
   876
             | Some thm1' => Some (combination
berghofe@10413
   877
                 (combination refl_implies thm1') (reflexive conc)))
berghofe@10413
   878
         | Some thm2 =>
berghofe@10413
   879
           let
berghofe@10413
   880
             val conc2 = rhs_of thm2;
berghofe@10413
   881
             val thm2' = implies_elim (Thm.instantiate
berghofe@10413
   882
               ([], [(cA, prem1), (cB, conc), (cC, conc2)]) Drule.imp_cong)
berghofe@10413
   883
               (implies_intr prem1 thm2)
berghofe@10413
   884
           in (case thm1 of
berghofe@10413
   885
               None => Some thm2'
berghofe@10413
   886
             | Some thm1' => Some (transitive (combination
berghofe@10413
   887
                 (combination refl_implies thm1') (reflexive conc)) thm2'))
berghofe@10413
   888
           end)
berghofe@10413
   889
       end
berghofe@10413
   890
berghofe@10413
   891
 in try_botc end;
berghofe@10413
   892
berghofe@10413
   893
berghofe@10413
   894
(*** Meta-rewriting: rewrites t to u and returns the theorem t==u ***)
berghofe@10413
   895
berghofe@10413
   896
(*
berghofe@10413
   897
  Parameters:
berghofe@10413
   898
    mode = (simplify A,
berghofe@10413
   899
            use A in simplifying B,
berghofe@10413
   900
            use prems of B (if B is again a meta-impl.) to simplify A)
berghofe@10413
   901
           when simplifying A ==> B
berghofe@10413
   902
    mss: contains equality theorems of the form [|p1,...|] ==> t==u
berghofe@10413
   903
    prover: how to solve premises in conditional rewrites and congruences
berghofe@10413
   904
*)
berghofe@10413
   905
berghofe@10413
   906
(* FIXME: check that #bounds(mss) does not "occur" in ct already *)
berghofe@10413
   907
berghofe@10413
   908
fun rewrite_cterm mode prover mss ct =
berghofe@10413
   909
  let val {sign, t, maxidx, ...} = rep_cterm ct
berghofe@10413
   910
  in bottomc (mode, prover, sign, maxidx) mss ct end
berghofe@10413
   911
  handle THM (s, _, thms) =>
berghofe@10413
   912
    error ("Exception THM was raised in simplifier:\n" ^ s ^ "\n" ^
berghofe@10413
   913
      Pretty.string_of (pretty_thms thms));
berghofe@10413
   914
berghofe@10413
   915
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
berghofe@10413
   916
(*Do not rewrite flex-flex pairs*)
berghofe@10413
   917
fun goals_conv pred cv =
berghofe@10413
   918
  let fun gconv i ct =
berghofe@10413
   919
        let val (A,B) = Drule.dest_implies ct
berghofe@10413
   920
            val (thA,j) = case term_of A of
berghofe@10413
   921
                  Const("=?=",_)$_$_ => (reflexive A, i)
berghofe@10413
   922
                | _ => (if pred i then cv A else reflexive A, i+1)
berghofe@10413
   923
        in  combination (combination refl_implies thA) (gconv j B) end
berghofe@10413
   924
        handle TERM _ => reflexive ct
berghofe@10413
   925
  in gconv 1 end;
berghofe@10413
   926
berghofe@10413
   927
(*Use a conversion to transform a theorem*)
berghofe@10413
   928
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
berghofe@10413
   929
berghofe@10413
   930
(*Rewrite a theorem*)
berghofe@10413
   931
fun rewrite_rule_aux _ [] = (fn th => th)
berghofe@10413
   932
  | rewrite_rule_aux prover thms =
berghofe@10413
   933
      fconv_rule (rewrite_cterm (true,false,false) prover (mss_of thms));
berghofe@10413
   934
berghofe@10413
   935
fun rewrite_thm mode prover mss = fconv_rule (rewrite_cterm mode prover mss);
berghofe@10413
   936
berghofe@10413
   937
(*Rewrite the subgoals of a proof state (represented by a theorem) *)
berghofe@10413
   938
fun rewrite_goals_rule_aux _ []   th = th
berghofe@10413
   939
  | rewrite_goals_rule_aux prover thms th =
berghofe@10413
   940
      fconv_rule (goals_conv (K true) (rewrite_cterm (true, true, false) prover
berghofe@10413
   941
        (mss_of thms))) th;
berghofe@10413
   942
berghofe@10413
   943
(*Rewrite the subgoal of a proof state (represented by a theorem) *)
berghofe@10413
   944
fun rewrite_goal_rule mode prover mss i thm =
berghofe@10413
   945
  if 0 < i  andalso  i <= nprems_of thm
berghofe@10413
   946
  then fconv_rule (goals_conv (fn j => j=i) (rewrite_cterm mode prover mss)) thm
berghofe@10413
   947
  else raise THM("rewrite_goal_rule",i,[thm]);
berghofe@10413
   948
berghofe@10413
   949
end;
berghofe@10413
   950
berghofe@10413
   951
open MetaSimplifier;