src/HOL/Tools/meson.ML
author paulson
Fri Dec 01 12:23:39 2006 +0100 (2006-12-01)
changeset 21616 296e0c318c3e
parent 21588 cd0dc678a205
child 21646 c07b5b0e8492
permissions -rw-r--r--
Fixed a MAJOR BUG in clause-counting: only Boolean equalities now count as iffs
wenzelm@9869
     1
(*  Title:      HOL/Tools/meson.ML
paulson@9840
     2
    ID:         $Id$
paulson@9840
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
paulson@9840
     4
    Copyright   1992  University of Cambridge
paulson@9840
     5
wenzelm@9869
     6
The MESON resolution proof procedure for HOL.
paulson@9840
     7
paulson@9840
     8
When making clauses, avoids using the rewriter -- instead uses RS recursively
paulson@9840
     9
paulson@9840
    10
NEED TO SORT LITERALS BY # OF VARS, USING ==>I/E.  ELIMINATES NEED FOR
paulson@9840
    11
FUNCTION nodups -- if done to goal clauses too!
paulson@9840
    12
*)
paulson@9840
    13
paulson@15579
    14
signature BASIC_MESON =
paulson@15579
    15
sig
paulson@15579
    16
  val size_of_subgoals	: thm -> int
paulson@15998
    17
  val make_cnf		: thm list -> thm -> thm list
paulson@20417
    18
  val finish_cnf	: thm list -> thm list
paulson@15579
    19
  val make_nnf		: thm -> thm
paulson@17849
    20
  val make_nnf1		: thm -> thm
paulson@15579
    21
  val skolemize		: thm -> thm
paulson@15579
    22
  val make_clauses	: thm list -> thm list
paulson@15579
    23
  val make_horns	: thm list -> thm list
paulson@15579
    24
  val best_prolog_tac	: (thm -> int) -> thm list -> tactic
paulson@15579
    25
  val depth_prolog_tac	: thm list -> tactic
paulson@15579
    26
  val gocls		: thm list -> thm list
paulson@15579
    27
  val skolemize_prems_tac	: thm list -> int -> tactic
paulson@15579
    28
  val MESON		: (thm list -> tactic) -> int -> tactic
paulson@15579
    29
  val best_meson_tac	: (thm -> int) -> int -> tactic
paulson@15579
    30
  val safe_best_meson_tac	: int -> tactic
paulson@15579
    31
  val depth_meson_tac	: int -> tactic
paulson@15579
    32
  val prolog_step_tac'	: thm list -> int -> tactic
paulson@15579
    33
  val iter_deepen_prolog_tac	: thm list -> tactic
paulson@16563
    34
  val iter_deepen_meson_tac	: thm list -> int -> tactic
paulson@15579
    35
  val meson_tac		: int -> tactic
paulson@15579
    36
  val negate_head	: thm -> thm
paulson@15579
    37
  val select_literal	: int -> thm -> thm
paulson@15579
    38
  val skolemize_tac	: int -> tactic
paulson@15579
    39
  val make_clauses_tac	: int -> tactic
paulson@15579
    40
end
paulson@9840
    41
paulson@9840
    42
paulson@15579
    43
structure Meson =
paulson@15579
    44
struct
paulson@9840
    45
paulson@15579
    46
val not_conjD = thm "meson_not_conjD";
paulson@15579
    47
val not_disjD = thm "meson_not_disjD";
paulson@15579
    48
val not_notD = thm "meson_not_notD";
paulson@15579
    49
val not_allD = thm "meson_not_allD";
paulson@15579
    50
val not_exD = thm "meson_not_exD";
paulson@15579
    51
val imp_to_disjD = thm "meson_imp_to_disjD";
paulson@15579
    52
val not_impD = thm "meson_not_impD";
paulson@15579
    53
val iff_to_disjD = thm "meson_iff_to_disjD";
paulson@15579
    54
val not_iffD = thm "meson_not_iffD";
paulson@15579
    55
val conj_exD1 = thm "meson_conj_exD1";
paulson@15579
    56
val conj_exD2 = thm "meson_conj_exD2";
paulson@15579
    57
val disj_exD = thm "meson_disj_exD";
paulson@15579
    58
val disj_exD1 = thm "meson_disj_exD1";
paulson@15579
    59
val disj_exD2 = thm "meson_disj_exD2";
paulson@15579
    60
val disj_assoc = thm "meson_disj_assoc";
paulson@15579
    61
val disj_comm = thm "meson_disj_comm";
paulson@15579
    62
val disj_FalseD1 = thm "meson_disj_FalseD1";
paulson@15579
    63
val disj_FalseD2 = thm "meson_disj_FalseD2";
paulson@9840
    64
paulson@16563
    65
val depth_limit = ref 2000;
paulson@9840
    66
paulson@15579
    67
(**** Operators for forward proof ****)
paulson@15579
    68
paulson@20417
    69
paulson@20417
    70
(** First-order Resolution **)
paulson@20417
    71
paulson@20417
    72
fun typ_pair_of (ix, (sort,ty)) = (TVar (ix,sort), ty);
paulson@20417
    73
fun term_pair_of (ix, (ty,t)) = (Var (ix,ty), t);
paulson@20417
    74
paulson@20417
    75
val Envir.Envir {asol = tenv0, iTs = tyenv0, ...} = Envir.empty 0
paulson@20417
    76
paulson@20417
    77
(*FIXME: currently does not "rename variables apart"*)
paulson@20417
    78
fun first_order_resolve thA thB =
paulson@20417
    79
  let val thy = theory_of_thm thA
paulson@20417
    80
      val tmA = concl_of thA
paulson@20417
    81
      fun match pat = Pattern.first_order_match thy (pat,tmA) (tyenv0,tenv0)
paulson@20417
    82
      val Const("==>",_) $ tmB $ _ = prop_of thB
paulson@20417
    83
      val (tyenv,tenv) = match tmB
paulson@20417
    84
      val ct_pairs = map (pairself (cterm_of thy) o term_pair_of) (Vartab.dest tenv)
paulson@20417
    85
  in  thA RS (cterm_instantiate ct_pairs thB)  end
paulson@20417
    86
  handle _ => raise THM ("first_order_resolve", 0, [thA,thB]);
paulson@18175
    87
paulson@15579
    88
(*raises exception if no rules apply -- unlike RL*)
paulson@18141
    89
fun tryres (th, rls) = 
paulson@18141
    90
  let fun tryall [] = raise THM("tryres", 0, th::rls)
paulson@20417
    91
        | tryall (rl::rls) = (th RS rl handle THM _ => tryall rls)
paulson@18141
    92
  in  tryall rls  end;
paulson@18141
    93
  
paulson@21050
    94
(*Permits forward proof from rules that discharge assumptions. The supplied proof state st,
paulson@21050
    95
  e.g. from conj_forward, should have the form
paulson@21050
    96
    "[| P' ==> ?P; Q' ==> ?Q |] ==> ?P & ?Q"
paulson@21050
    97
  and the effect should be to instantiate ?P and ?Q with normalized versions of P' and Q'.*)
paulson@15579
    98
fun forward_res nf st =
paulson@21050
    99
  let fun forward_tacf [prem] = rtac (nf prem) 1
paulson@21050
   100
        | forward_tacf prems = 
paulson@21050
   101
            error ("Bad proof state in forward_res, please inform lcp@cl.cam.ac.uk:\n" ^
paulson@21050
   102
                   string_of_thm st ^
paulson@21050
   103
                   "\nPremises:\n" ^
paulson@21050
   104
                   cat_lines (map string_of_thm prems))
paulson@21050
   105
  in
paulson@21050
   106
    case Seq.pull (ALLGOALS (METAHYPS forward_tacf) st)
paulson@21050
   107
    of SOME(th,_) => th
paulson@21050
   108
     | NONE => raise THM("forward_res", 0, [st])
paulson@21050
   109
  end;
paulson@15579
   110
paulson@20134
   111
(*Are any of the logical connectives in "bs" present in the term?*)
paulson@20134
   112
fun has_conns bs =
paulson@20134
   113
  let fun has (Const(a,_)) = false
paulson@20134
   114
        | has (Const("Trueprop",_) $ p) = has p
paulson@20134
   115
        | has (Const("Not",_) $ p) = has p
paulson@20134
   116
        | has (Const("op |",_) $ p $ q) = member (op =) bs "op |" orelse has p orelse has q
paulson@20134
   117
        | has (Const("op &",_) $ p $ q) = member (op =) bs "op &" orelse has p orelse has q
paulson@20134
   118
        | has (Const("All",_) $ Abs(_,_,p)) = member (op =) bs "All" orelse has p
paulson@20134
   119
        | has (Const("Ex",_) $ Abs(_,_,p)) = member (op =) bs "Ex" orelse has p
paulson@15579
   120
	| has _ = false
paulson@15579
   121
  in  has  end;
paulson@17716
   122
  
paulson@9840
   123
paulson@15579
   124
(**** Clause handling ****)
paulson@9840
   125
paulson@15579
   126
fun literals (Const("Trueprop",_) $ P) = literals P
paulson@15579
   127
  | literals (Const("op |",_) $ P $ Q) = literals P @ literals Q
paulson@15579
   128
  | literals (Const("Not",_) $ P) = [(false,P)]
paulson@15579
   129
  | literals P = [(true,P)];
paulson@9840
   130
paulson@15579
   131
(*number of literals in a term*)
paulson@15579
   132
val nliterals = length o literals;
paulson@9840
   133
paulson@18389
   134
paulson@18389
   135
(*** Tautology Checking ***)
paulson@18389
   136
paulson@18389
   137
fun signed_lits_aux (Const ("op |", _) $ P $ Q) (poslits, neglits) = 
paulson@18389
   138
      signed_lits_aux Q (signed_lits_aux P (poslits, neglits))
paulson@18389
   139
  | signed_lits_aux (Const("Not",_) $ P) (poslits, neglits) = (poslits, P::neglits)
paulson@18389
   140
  | signed_lits_aux P (poslits, neglits) = (P::poslits, neglits);
paulson@18389
   141
  
paulson@18389
   142
fun signed_lits th = signed_lits_aux (HOLogic.dest_Trueprop (concl_of th)) ([],[]);
paulson@18389
   143
paulson@18389
   144
(*Literals like X=X are tautologous*)
paulson@18389
   145
fun taut_poslit (Const("op =",_) $ t $ u) = t aconv u
paulson@18389
   146
  | taut_poslit (Const("True",_)) = true
paulson@18389
   147
  | taut_poslit _ = false;
paulson@18389
   148
paulson@18389
   149
fun is_taut th =
paulson@18389
   150
  let val (poslits,neglits) = signed_lits th
paulson@18389
   151
  in  exists taut_poslit poslits
paulson@18389
   152
      orelse
wenzelm@20073
   153
      exists (member (op aconv) neglits) (HOLogic.false_const :: poslits)
paulson@19894
   154
  end
paulson@19894
   155
  handle TERM _ => false;	(*probably dest_Trueprop on a weird theorem*)		      
paulson@18389
   156
paulson@18389
   157
paulson@18389
   158
(*** To remove trivial negated equality literals from clauses ***)
paulson@18389
   159
paulson@18389
   160
(*They are typically functional reflexivity axioms and are the converses of
paulson@18389
   161
  injectivity equivalences*)
paulson@18389
   162
  
paulson@18389
   163
val not_refl_disj_D = thm"meson_not_refl_disj_D";
paulson@18389
   164
paulson@20119
   165
(*Is either term a Var that does not properly occur in the other term?*)
paulson@20119
   166
fun eliminable (t as Var _, u) = t aconv u orelse not (Logic.occs(t,u))
paulson@20119
   167
  | eliminable (u, t as Var _) = t aconv u orelse not (Logic.occs(t,u))
paulson@20119
   168
  | eliminable _ = false;
paulson@20119
   169
paulson@18389
   170
fun refl_clause_aux 0 th = th
paulson@18389
   171
  | refl_clause_aux n th =
paulson@18389
   172
       case HOLogic.dest_Trueprop (concl_of th) of
paulson@18389
   173
	  (Const ("op |", _) $ (Const ("op |", _) $ _ $ _) $ _) => 
paulson@18389
   174
            refl_clause_aux n (th RS disj_assoc)    (*isolate an atom as first disjunct*)
paulson@18389
   175
	| (Const ("op |", _) $ (Const("Not",_) $ (Const("op =",_) $ t $ u)) $ _) => 
paulson@20119
   176
	    if eliminable(t,u) 
paulson@20119
   177
	    then refl_clause_aux (n-1) (th RS not_refl_disj_D)  (*Var inequation: delete*)
paulson@18389
   178
	    else refl_clause_aux (n-1) (th RS disj_comm)  (*not between Vars: ignore*)
paulson@18389
   179
	| (Const ("op |", _) $ _ $ _) => refl_clause_aux n (th RS disj_comm)
paulson@18752
   180
	| _ => (*not a disjunction*) th;
paulson@18389
   181
paulson@18389
   182
fun notequal_lits_count (Const ("op |", _) $ P $ Q) = 
paulson@18389
   183
      notequal_lits_count P + notequal_lits_count Q
paulson@18389
   184
  | notequal_lits_count (Const("Not",_) $ (Const("op =",_) $ _ $ _)) = 1
paulson@18389
   185
  | notequal_lits_count _ = 0;
paulson@18389
   186
paulson@18389
   187
(*Simplify a clause by applying reflexivity to its negated equality literals*)
paulson@18389
   188
fun refl_clause th = 
paulson@18389
   189
  let val neqs = notequal_lits_count (HOLogic.dest_Trueprop (concl_of th))
paulson@19894
   190
  in  zero_var_indexes (refl_clause_aux neqs th)  end
paulson@19894
   191
  handle TERM _ => th;	(*probably dest_Trueprop on a weird theorem*)		      
paulson@18389
   192
paulson@18389
   193
paulson@18389
   194
(*** The basic CNF transformation ***)
paulson@18389
   195
paulson@21069
   196
val max_clauses = ref 20;
paulson@21069
   197
paulson@21069
   198
fun sum x y = if x < !max_clauses andalso y < !max_clauses then x+y else !max_clauses;
paulson@21069
   199
fun prod x y = if x < !max_clauses andalso y < !max_clauses then x*y else !max_clauses;
paulson@21069
   200
paulson@19894
   201
(*Estimate the number of clauses in order to detect infeasible theorems*)
paulson@21069
   202
fun signed_nclauses b (Const("Trueprop",_) $ t) = signed_nclauses b t
paulson@21069
   203
  | signed_nclauses b (Const("Not",_) $ t) = signed_nclauses (not b) t
paulson@21069
   204
  | signed_nclauses b (Const("op &",_) $ t $ u) = 
paulson@21069
   205
      if b then sum (signed_nclauses b t) (signed_nclauses b u)
paulson@21069
   206
           else prod (signed_nclauses b t) (signed_nclauses b u)
paulson@21069
   207
  | signed_nclauses b (Const("op |",_) $ t $ u) = 
paulson@21069
   208
      if b then prod (signed_nclauses b t) (signed_nclauses b u)
paulson@21069
   209
           else sum (signed_nclauses b t) (signed_nclauses b u)
paulson@21069
   210
  | signed_nclauses b (Const("op -->",_) $ t $ u) = 
paulson@21069
   211
      if b then prod (signed_nclauses (not b) t) (signed_nclauses b u)
paulson@21069
   212
           else sum (signed_nclauses (not b) t) (signed_nclauses b u)
paulson@21616
   213
  | signed_nclauses b (Const("op =", Type ("fun", [T, _])) $ t $ u) = 
paulson@21616
   214
      if T = HOLogic.boolT then (*Boolean equality is if-and-only-if*)
paulson@21616
   215
	  if b then sum (prod (signed_nclauses (not b) t) (signed_nclauses b u))
paulson@21616
   216
			(prod (signed_nclauses (not b) u) (signed_nclauses b t))
paulson@21616
   217
	       else sum (prod (signed_nclauses b t) (signed_nclauses b u))
paulson@21616
   218
			(prod (signed_nclauses (not b) t) (signed_nclauses (not b) u))
paulson@21616
   219
      else 1 
paulson@21069
   220
  | signed_nclauses b (Const("Ex", _) $ Abs (_,_,t)) = signed_nclauses b t
paulson@21069
   221
  | signed_nclauses b (Const("All",_) $ Abs (_,_,t)) = signed_nclauses b t
paulson@21069
   222
  | signed_nclauses _ _ = 1; (* literal *)
paulson@21069
   223
paulson@21069
   224
val nclauses = signed_nclauses true;
paulson@21069
   225
paulson@21069
   226
fun too_many_clauses t = nclauses t >= !max_clauses;
paulson@19894
   227
paulson@15579
   228
(*Replaces universally quantified variables by FREE variables -- because
paulson@15579
   229
  assumptions may not contain scheme variables.  Later, call "generalize". *)
paulson@15579
   230
fun freeze_spec th =
paulson@20361
   231
  let val newname = gensym "mes_"
paulson@19154
   232
      val spec' = read_instantiate [("x", newname)] spec
paulson@19154
   233
  in  th RS spec'  end;
paulson@9840
   234
paulson@15998
   235
(*Used with METAHYPS below. There is one assumption, which gets bound to prem
paulson@15998
   236
  and then normalized via function nf. The normal form is given to resolve_tac,
paulson@15998
   237
  presumably to instantiate a Boolean variable.*)
paulson@15579
   238
fun resop nf [prem] = resolve_tac (nf prem) 1;
paulson@9840
   239
paulson@20822
   240
(*Any need to extend this list with 
haftmann@21046
   241
  "HOL.type_class","Code_Generator.eq_class","ProtoPure.term"?*)
paulson@18389
   242
val has_meta_conn = 
paulson@18389
   243
    exists_Const (fn (c,_) => c mem_string ["==", "==>", "all", "prop"]);
paulson@20417
   244
paulson@20417
   245
fun apply_skolem_ths (th, rls) = 
paulson@20417
   246
  let fun tryall [] = raise THM("apply_skolem_ths", 0, th::rls)
paulson@20417
   247
        | tryall (rl::rls) = (first_order_resolve th rl handle THM _ => tryall rls)
paulson@20417
   248
  in  tryall rls  end;
paulson@18389
   249
  
paulson@15998
   250
(*Conjunctive normal form, adding clauses from th in front of ths (for foldr).
paulson@15998
   251
  Strips universal quantifiers and breaks up conjunctions.
paulson@15998
   252
  Eliminates existential quantifiers using skoths: Skolemization theorems.*)
paulson@15998
   253
fun cnf skoths (th,ths) =
paulson@18389
   254
  let fun cnf_aux (th,ths) =
wenzelm@21174
   255
  	if not (can HOLogic.dest_Trueprop (prop_of th)) then ths (*meta-level: ignore*)
paulson@20134
   256
        else if not (has_conns ["All","Ex","op &"] (prop_of th))  
paulson@15998
   257
	then th::ths (*no work to do, terminate*)
paulson@16588
   258
	else case head_of (HOLogic.dest_Trueprop (concl_of th)) of
paulson@16588
   259
	    Const ("op &", _) => (*conjunction*)
paulson@20417
   260
		cnf_aux (th RS conjunct1, cnf_aux (th RS conjunct2, ths))
paulson@16588
   261
	  | Const ("All", _) => (*universal quantifier*)
paulson@18389
   262
	        cnf_aux (freeze_spec th,  ths)
paulson@16588
   263
	  | Const ("Ex", _) => 
paulson@16588
   264
	      (*existential quantifier: Insert Skolem functions*)
paulson@20417
   265
	      cnf_aux (apply_skolem_ths (th,skoths), ths)
paulson@16588
   266
	  | Const ("op |", _) => (*disjunction*)
paulson@16588
   267
	      let val tac =
paulson@18389
   268
		  (METAHYPS (resop cnf_nil) 1) THEN
paulson@19154
   269
		   (fn st' => st' |> METAHYPS (resop cnf_nil) 1)
paulson@16588
   270
	      in  Seq.list_of (tac (th RS disj_forward)) @ ths  end 
paulson@16588
   271
	  | _ => (*no work to do*) th::ths 
paulson@19154
   272
      and cnf_nil th = cnf_aux (th,[])
paulson@15998
   273
  in 
paulson@21069
   274
    if too_many_clauses (concl_of th) 
paulson@19894
   275
    then (Output.debug ("cnf is ignoring: " ^ string_of_thm th); ths)
paulson@19894
   276
    else cnf_aux (th,ths)
paulson@15998
   277
  end;
paulson@9840
   278
paulson@16012
   279
(*Convert all suitable free variables to schematic variables, 
paulson@16012
   280
  but don't discharge assumptions.*)
paulson@16173
   281
fun generalize th = Thm.varifyT (forall_elim_vars 0 (forall_intr_frees th));
paulson@16012
   282
paulson@20417
   283
fun make_cnf skoths th = cnf skoths (th, []);
paulson@20417
   284
paulson@20417
   285
(*Generalization, removal of redundant equalities, removal of tautologies.*)
paulson@20417
   286
fun finish_cnf ths = filter (not o is_taut) (map (refl_clause o generalize) ths);
paulson@15998
   287
paulson@9840
   288
paulson@15579
   289
(**** Removal of duplicate literals ****)
paulson@9840
   290
paulson@15579
   291
(*Forward proof, passing extra assumptions as theorems to the tactic*)
paulson@15579
   292
fun forward_res2 nf hyps st =
paulson@15579
   293
  case Seq.pull
paulson@15579
   294
	(REPEAT
paulson@15579
   295
	 (METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1)
paulson@15579
   296
	 st)
paulson@15579
   297
  of SOME(th,_) => th
paulson@15579
   298
   | NONE => raise THM("forward_res2", 0, [st]);
paulson@9840
   299
paulson@15579
   300
(*Remove duplicates in P|Q by assuming ~P in Q
paulson@15579
   301
  rls (initially []) accumulates assumptions of the form P==>False*)
paulson@15579
   302
fun nodups_aux rls th = nodups_aux rls (th RS disj_assoc)
paulson@15579
   303
    handle THM _ => tryres(th,rls)
paulson@15579
   304
    handle THM _ => tryres(forward_res2 nodups_aux rls (th RS disj_forward2),
paulson@15579
   305
			   [disj_FalseD1, disj_FalseD2, asm_rl])
paulson@15579
   306
    handle THM _ => th;
paulson@9840
   307
paulson@15579
   308
(*Remove duplicate literals, if there are any*)
paulson@15579
   309
fun nodups th =
haftmann@20972
   310
  if has_duplicates (op =) (literals (prop_of th))
haftmann@20972
   311
    then nodups_aux [] th
haftmann@20972
   312
    else th;
paulson@9840
   313
paulson@9840
   314
paulson@15579
   315
(**** Generation of contrapositives ****)
paulson@9840
   316
paulson@21102
   317
fun is_left (Const ("Trueprop", _) $ 
paulson@21102
   318
               (Const ("op |", _) $ (Const ("op |", _) $ _ $ _) $ _)) = true
paulson@21102
   319
  | is_left _ = false;
paulson@21102
   320
               
paulson@15579
   321
(*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
paulson@21102
   322
fun assoc_right th = 
paulson@21102
   323
  if is_left (prop_of th) then assoc_right (th RS disj_assoc)
paulson@21102
   324
  else th;
paulson@9840
   325
paulson@15579
   326
(*Must check for negative literal first!*)
paulson@15579
   327
val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
paulson@9840
   328
paulson@15579
   329
(*For ordinary resolution. *)
paulson@15579
   330
val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule'];
paulson@9840
   331
paulson@15579
   332
(*Create a goal or support clause, conclusing False*)
paulson@15579
   333
fun make_goal th =   (*Must check for negative literal first!*)
paulson@15579
   334
    make_goal (tryres(th, clause_rules))
paulson@15579
   335
  handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
paulson@9840
   336
paulson@15579
   337
(*Sort clauses by number of literals*)
paulson@15579
   338
fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2);
paulson@9840
   339
paulson@18389
   340
fun sort_clauses ths = sort (make_ord fewerlits) ths;
paulson@9840
   341
paulson@15581
   342
(*True if the given type contains bool anywhere*)
paulson@15581
   343
fun has_bool (Type("bool",_)) = true
paulson@15581
   344
  | has_bool (Type(_, Ts)) = exists has_bool Ts
paulson@15581
   345
  | has_bool _ = false;
paulson@15581
   346
  
paulson@20524
   347
(*Is the string the name of a connective? Really only | and Not can remain, 
paulson@20524
   348
  since this code expects to be called on a clause form.*)  
wenzelm@19875
   349
val is_conn = member (op =)
paulson@20524
   350
    ["Trueprop", "op &", "op |", "op -->", "Not", 
paulson@15613
   351
     "All", "Ex", "Ball", "Bex"];
paulson@15613
   352
paulson@20524
   353
(*True if the term contains a function--not a logical connective--where the type 
paulson@20524
   354
  of any argument contains bool.*)
paulson@15613
   355
val has_bool_arg_const = 
paulson@15613
   356
    exists_Const
paulson@15613
   357
      (fn (c,T) => not(is_conn c) andalso exists (has_bool) (binder_types T));
paulson@15908
   358
      
paulson@21102
   359
(*Raises an exception if any Vars in the theorem mention type bool. 
paulson@21102
   360
  Also rejects functions whose arguments are Booleans or other functions.*)
paulson@19204
   361
fun is_fol_term t =
paulson@19204
   362
    not (exists (has_bool o fastype_of) (term_vars t)  orelse
paulson@19204
   363
	 not (Term.is_first_order ["all","All","Ex"] t) orelse
paulson@19204
   364
	 has_bool_arg_const t  orelse  
paulson@19204
   365
	 has_meta_conn t);
paulson@19204
   366
paulson@21102
   367
fun rigid t = not (is_Var (head_of t));
paulson@21102
   368
paulson@21102
   369
fun ok4horn (Const ("Trueprop",_) $ (Const ("op |", _) $ t $ _)) = rigid t
paulson@21102
   370
  | ok4horn (Const ("Trueprop",_) $ t) = rigid t
paulson@21102
   371
  | ok4horn _ = false;
paulson@21102
   372
paulson@15579
   373
(*Create a meta-level Horn clause*)
paulson@21102
   374
fun make_horn crules th = 
paulson@21102
   375
  if ok4horn (concl_of th) 
paulson@21102
   376
  then make_horn crules (tryres(th,crules)) handle THM _ => th
paulson@21102
   377
  else th;
paulson@9840
   378
paulson@16563
   379
(*Generate Horn clauses for all contrapositives of a clause. The input, th,
paulson@16563
   380
  is a HOL disjunction.*)
paulson@15579
   381
fun add_contras crules (th,hcs) =
paulson@15579
   382
  let fun rots (0,th) = hcs
paulson@15579
   383
	| rots (k,th) = zero_var_indexes (make_horn crules th) ::
paulson@15579
   384
			rots(k-1, assoc_right (th RS disj_comm))
paulson@15862
   385
  in case nliterals(prop_of th) of
paulson@15579
   386
	1 => th::hcs
paulson@15579
   387
      | n => rots(n, assoc_right th)
paulson@15579
   388
  end;
paulson@9840
   389
paulson@15579
   390
(*Use "theorem naming" to label the clauses*)
paulson@15579
   391
fun name_thms label =
paulson@15579
   392
    let fun name1 (th, (k,ths)) =
paulson@15579
   393
	  (k-1, Thm.name_thm (label ^ string_of_int k, th) :: ths)
paulson@9840
   394
paulson@15579
   395
    in  fn ths => #2 (foldr name1 (length ths, []) ths)  end;
paulson@9840
   396
paulson@16563
   397
(*Is the given disjunction an all-negative support clause?*)
paulson@15579
   398
fun is_negative th = forall (not o #1) (literals (prop_of th));
paulson@9840
   399
paulson@15579
   400
val neg_clauses = List.filter is_negative;
paulson@9840
   401
paulson@9840
   402
paulson@15579
   403
(***** MESON PROOF PROCEDURE *****)
paulson@9840
   404
paulson@15579
   405
fun rhyps (Const("==>",_) $ (Const("Trueprop",_) $ A) $ phi,
paulson@15579
   406
	   As) = rhyps(phi, A::As)
paulson@15579
   407
  | rhyps (_, As) = As;
paulson@9840
   408
paulson@15579
   409
(** Detecting repeated assumptions in a subgoal **)
paulson@9840
   410
paulson@15579
   411
(*The stringtree detects repeated assumptions.*)
wenzelm@16801
   412
fun ins_term (net,t) = Net.insert_term (op aconv) (t,t) net;
paulson@9840
   413
paulson@15579
   414
(*detects repetitions in a list of terms*)
paulson@15579
   415
fun has_reps [] = false
paulson@15579
   416
  | has_reps [_] = false
paulson@15579
   417
  | has_reps [t,u] = (t aconv u)
paulson@15579
   418
  | has_reps ts = (Library.foldl ins_term (Net.empty, ts);  false)
wenzelm@19875
   419
		  handle Net.INSERT => true;
paulson@9840
   420
paulson@15579
   421
(*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*)
paulson@18508
   422
fun TRYING_eq_assume_tac 0 st = Seq.single st
paulson@18508
   423
  | TRYING_eq_assume_tac i st =
paulson@18508
   424
       TRYING_eq_assume_tac (i-1) (eq_assumption i st)
paulson@18508
   425
       handle THM _ => TRYING_eq_assume_tac (i-1) st;
paulson@18508
   426
paulson@18508
   427
fun TRYALL_eq_assume_tac st = TRYING_eq_assume_tac (nprems_of st) st;
paulson@9840
   428
paulson@15579
   429
(*Loop checking: FAIL if trying to prove the same thing twice
paulson@15579
   430
  -- if *ANY* subgoal has repeated literals*)
paulson@15579
   431
fun check_tac st =
paulson@15579
   432
  if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st)
paulson@15579
   433
  then  Seq.empty  else  Seq.single st;
paulson@9840
   434
paulson@9840
   435
paulson@15579
   436
(* net_resolve_tac actually made it slower... *)
paulson@15579
   437
fun prolog_step_tac horns i =
paulson@15579
   438
    (assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
paulson@18508
   439
    TRYALL_eq_assume_tac;
paulson@9840
   440
paulson@9840
   441
(*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*)
paulson@15579
   442
fun addconcl(prem,sz) = size_of_term(Logic.strip_assums_concl prem) + sz
paulson@15579
   443
paulson@15579
   444
fun size_of_subgoals st = foldr addconcl 0 (prems_of st);
paulson@15579
   445
paulson@9840
   446
paulson@9840
   447
(*Negation Normal Form*)
paulson@9840
   448
val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD,
wenzelm@9869
   449
               not_impD, not_iffD, not_allD, not_exD, not_notD];
paulson@15581
   450
paulson@21102
   451
fun ok4nnf (Const ("Trueprop",_) $ (Const ("Not", _) $ t)) = rigid t
paulson@21102
   452
  | ok4nnf (Const ("Trueprop",_) $ t) = rigid t
paulson@21102
   453
  | ok4nnf _ = false;
paulson@21102
   454
paulson@21102
   455
fun make_nnf1 th = 
paulson@21102
   456
  if ok4nnf (concl_of th) 
paulson@21102
   457
  then make_nnf1 (tryres(th, nnf_rls))
wenzelm@9869
   458
    handle THM _ =>
paulson@15581
   459
        forward_res make_nnf1
wenzelm@9869
   460
           (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
paulson@21102
   461
    handle THM _ => th
paulson@21102
   462
  else th;
paulson@9840
   463
paulson@20018
   464
(*The simplification removes defined quantifiers and occurrences of True and False. 
paulson@20018
   465
  nnf_ss also includes the one-point simprocs,
paulson@18405
   466
  which are needed to avoid the various one-point theorems from generating junk clauses.*)
paulson@19894
   467
val nnf_simps =
paulson@20018
   468
     [simp_implies_def, Ex1_def, Ball_def, Bex_def, if_True, 
paulson@19894
   469
      if_False, if_cancel, if_eq_cancel, cases_simp];
paulson@19894
   470
val nnf_extra_simps =
paulson@19894
   471
      thms"split_ifs" @ ex_simps @ all_simps @ simp_thms;
paulson@18405
   472
paulson@18405
   473
val nnf_ss =
paulson@19894
   474
    HOL_basic_ss addsimps nnf_extra_simps 
paulson@19894
   475
                 addsimprocs [defALL_regroup,defEX_regroup,neq_simproc,let_simproc];
paulson@15872
   476
paulson@21050
   477
fun make_nnf th = case prems_of th of
paulson@21050
   478
    [] => th |> rewrite_rule (map safe_mk_meta_eq nnf_simps)
paulson@21102
   479
	     |> simplify nnf_ss  
paulson@21050
   480
	     |> make_nnf1
paulson@21050
   481
  | _ => raise THM ("make_nnf: premises in argument", 0, [th]);
paulson@15581
   482
paulson@15965
   483
(*Pull existential quantifiers to front. This accomplishes Skolemization for
paulson@15965
   484
  clauses that arise from a subgoal.*)
wenzelm@9869
   485
fun skolemize th =
paulson@20134
   486
  if not (has_conns ["Ex"] (prop_of th)) then th
quigley@15773
   487
  else (skolemize (tryres(th, [choice, conj_exD1, conj_exD2,
quigley@15679
   488
                              disj_exD, disj_exD1, disj_exD2])))
wenzelm@9869
   489
    handle THM _ =>
wenzelm@9869
   490
        skolemize (forward_res skolemize
wenzelm@9869
   491
                   (tryres (th, [conj_forward, disj_forward, all_forward])))
paulson@9840
   492
    handle THM _ => forward_res skolemize (th RS ex_forward);
paulson@9840
   493
paulson@9840
   494
paulson@9840
   495
(*Make clauses from a list of theorems, previously Skolemized and put into nnf.
paulson@9840
   496
  The resulting clauses are HOL disjunctions.*)
wenzelm@9869
   497
fun make_clauses ths =
paulson@15998
   498
    (sort_clauses (map (generalize o nodups) (foldr (cnf[]) [] ths)));
quigley@15773
   499
paulson@16563
   500
(*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*)
wenzelm@9869
   501
fun make_horns ths =
paulson@9840
   502
    name_thms "Horn#"
wenzelm@19046
   503
      (distinct Drule.eq_thm_prop (foldr (add_contras clause_rules) [] ths));
paulson@9840
   504
paulson@9840
   505
(*Could simply use nprems_of, which would count remaining subgoals -- no
paulson@9840
   506
  discrimination as to their size!  With BEST_FIRST, fails for problem 41.*)
paulson@9840
   507
wenzelm@9869
   508
fun best_prolog_tac sizef horns =
paulson@9840
   509
    BEST_FIRST (has_fewer_prems 1, sizef) (prolog_step_tac horns 1);
paulson@9840
   510
wenzelm@9869
   511
fun depth_prolog_tac horns =
paulson@9840
   512
    DEPTH_FIRST (has_fewer_prems 1) (prolog_step_tac horns 1);
paulson@9840
   513
paulson@9840
   514
(*Return all negative clauses, as possible goal clauses*)
paulson@9840
   515
fun gocls cls = name_thms "Goal#" (map make_goal (neg_clauses cls));
paulson@9840
   516
paulson@15008
   517
fun skolemize_prems_tac prems =
paulson@9840
   518
    cut_facts_tac (map (skolemize o make_nnf) prems)  THEN'
paulson@9840
   519
    REPEAT o (etac exE);
paulson@9840
   520
paulson@18141
   521
(*Expand all definitions (presumably of Skolem functions) in a proof state.*)
paulson@18141
   522
fun expand_defs_tac st =
paulson@18141
   523
  let val defs = filter (can dest_equals) (#hyps (crep_thm st))
wenzelm@20288
   524
  in  PRIMITIVE (LocalDefs.def_export false defs) st  end;
paulson@18141
   525
paulson@16588
   526
(*Basis of all meson-tactics.  Supplies cltac with clauses: HOL disjunctions*)
paulson@16588
   527
fun MESON cltac i st = 
paulson@16588
   528
  SELECT_GOAL
paulson@18141
   529
    (EVERY [rtac ccontr 1,
paulson@16588
   530
	    METAHYPS (fn negs =>
paulson@16588
   531
		      EVERY1 [skolemize_prems_tac negs,
paulson@18141
   532
			      METAHYPS (cltac o make_clauses)]) 1,
paulson@18141
   533
            expand_defs_tac]) i st
paulson@20417
   534
  handle THM _ => no_tac st;	(*probably from make_meta_clause, not first-order*)		      
paulson@9840
   535
paulson@9840
   536
(** Best-first search versions **)
paulson@9840
   537
paulson@16563
   538
(*ths is a list of additional clauses (HOL disjunctions) to use.*)
wenzelm@9869
   539
fun best_meson_tac sizef =
wenzelm@9869
   540
  MESON (fn cls =>
paulson@9840
   541
         THEN_BEST_FIRST (resolve_tac (gocls cls) 1)
paulson@9840
   542
                         (has_fewer_prems 1, sizef)
paulson@9840
   543
                         (prolog_step_tac (make_horns cls) 1));
paulson@9840
   544
paulson@9840
   545
(*First, breaks the goal into independent units*)
paulson@9840
   546
val safe_best_meson_tac =
wenzelm@9869
   547
     SELECT_GOAL (TRY Safe_tac THEN
paulson@9840
   548
                  TRYALL (best_meson_tac size_of_subgoals));
paulson@9840
   549
paulson@9840
   550
(** Depth-first search version **)
paulson@9840
   551
paulson@9840
   552
val depth_meson_tac =
wenzelm@9869
   553
     MESON (fn cls => EVERY [resolve_tac (gocls cls) 1,
paulson@9840
   554
                             depth_prolog_tac (make_horns cls)]);
paulson@9840
   555
paulson@9840
   556
paulson@9840
   557
(** Iterative deepening version **)
paulson@9840
   558
paulson@9840
   559
(*This version does only one inference per call;
paulson@9840
   560
  having only one eq_assume_tac speeds it up!*)
wenzelm@9869
   561
fun prolog_step_tac' horns =
paulson@9840
   562
    let val (horn0s, hornps) = (*0 subgoals vs 1 or more*)
paulson@9840
   563
            take_prefix Thm.no_prems horns
paulson@9840
   564
        val nrtac = net_resolve_tac horns
paulson@9840
   565
    in  fn i => eq_assume_tac i ORELSE
paulson@9840
   566
                match_tac horn0s i ORELSE  (*no backtracking if unit MATCHES*)
paulson@9840
   567
                ((assume_tac i APPEND nrtac i) THEN check_tac)
paulson@9840
   568
    end;
paulson@9840
   569
wenzelm@9869
   570
fun iter_deepen_prolog_tac horns =
paulson@9840
   571
    ITER_DEEPEN (has_fewer_prems 1) (prolog_step_tac' horns);
paulson@9840
   572
paulson@21095
   573
fun iter_deepen_meson_tac ths = MESON 
paulson@21095
   574
 (fn cls =>
paulson@21095
   575
      case (gocls (cls@ths)) of
paulson@21095
   576
	   [] => no_tac  (*no goal clauses*)
paulson@21095
   577
	 | goes => 
paulson@21095
   578
	     let val horns = make_horns (cls@ths)
paulson@21095
   579
	         val _ = if !Output.show_debug_msgs 
paulson@21095
   580
	                 then Output.debug ("meson method called:\n" ^ 
paulson@21095
   581
	     	                  space_implode "\n" (map string_of_thm (cls@ths)) ^ 
paulson@21095
   582
	     	                  "\nclauses:\n" ^ 
paulson@21095
   583
	     	                  space_implode "\n" (map string_of_thm horns))
paulson@21095
   584
	     	         else ()
paulson@21095
   585
	     in THEN_ITER_DEEPEN (resolve_tac goes 1) (has_fewer_prems 1) (prolog_step_tac' horns)
paulson@21095
   586
	     end
paulson@21095
   587
 );
paulson@9840
   588
paulson@16563
   589
fun meson_claset_tac ths cs =
paulson@16563
   590
  SELECT_GOAL (TRY (safe_tac cs) THEN TRYALL (iter_deepen_meson_tac ths));
wenzelm@9869
   591
paulson@16563
   592
val meson_tac = CLASET' (meson_claset_tac []);
wenzelm@9869
   593
wenzelm@9869
   594
paulson@14813
   595
(**** Code to support ordinary resolution, rather than Model Elimination ****)
paulson@14744
   596
paulson@15008
   597
(*Convert a list of clauses (disjunctions) to meta-level clauses (==>), 
paulson@15008
   598
  with no contrapositives, for ordinary resolution.*)
paulson@14744
   599
paulson@14744
   600
(*Rules to convert the head literal into a negated assumption. If the head
paulson@14744
   601
  literal is already negated, then using notEfalse instead of notEfalse'
paulson@14744
   602
  prevents a double negation.*)
paulson@14744
   603
val notEfalse = read_instantiate [("R","False")] notE;
paulson@14744
   604
val notEfalse' = rotate_prems 1 notEfalse;
paulson@14744
   605
paulson@15448
   606
fun negated_asm_of_head th = 
paulson@14744
   607
    th RS notEfalse handle THM _ => th RS notEfalse';
paulson@14744
   608
paulson@14744
   609
(*Converting one clause*)
paulson@15581
   610
fun make_meta_clause th = 
paulson@21102
   611
  negated_asm_of_head (make_horn resolution_clause_rules th);
paulson@21102
   612
  
paulson@14744
   613
fun make_meta_clauses ths =
paulson@14744
   614
    name_thms "MClause#"
wenzelm@19046
   615
      (distinct Drule.eq_thm_prop (map make_meta_clause ths));
paulson@14744
   616
paulson@14744
   617
(*Permute a rule's premises to move the i-th premise to the last position.*)
paulson@14744
   618
fun make_last i th =
paulson@14744
   619
  let val n = nprems_of th 
paulson@14744
   620
  in  if 1 <= i andalso i <= n 
paulson@14744
   621
      then Thm.permute_prems (i-1) 1 th
paulson@15118
   622
      else raise THM("select_literal", i, [th])
paulson@14744
   623
  end;
paulson@14744
   624
paulson@14744
   625
(*Maps a rule that ends "... ==> P ==> False" to "... ==> ~P" while suppressing
paulson@14744
   626
  double-negations.*)
paulson@14744
   627
val negate_head = rewrite_rule [atomize_not, not_not RS eq_reflection];
paulson@14744
   628
paulson@14744
   629
(*Maps the clause  [P1,...Pn]==>False to [P1,...,P(i-1),P(i+1),...Pn] ==> ~P*)
paulson@14744
   630
fun select_literal i cl = negate_head (make_last i cl);
paulson@14744
   631
paulson@18508
   632
paulson@14813
   633
(*Top-level Skolemization. Allows part of the conversion to clauses to be
paulson@14813
   634
  expressed as a tactic (or Isar method).  Each assumption of the selected 
paulson@14813
   635
  goal is converted to NNF and then its existential quantifiers are pulled
paulson@14813
   636
  to the front. Finally, all existential quantifiers are eliminated, 
paulson@14813
   637
  leaving !!-quantified variables. Perhaps Safe_tac should follow, but it
paulson@14813
   638
  might generate many subgoals.*)
mengj@18194
   639
paulson@19204
   640
fun skolemize_tac i st = 
paulson@19204
   641
  let val ts = Logic.strip_assums_hyp (List.nth (prems_of st, i-1))
paulson@19204
   642
  in 
paulson@19204
   643
     EVERY' [METAHYPS
quigley@15773
   644
	    (fn hyps => (cut_facts_tac (map (skolemize o make_nnf) hyps) 1
paulson@14813
   645
                         THEN REPEAT (etac exE 1))),
paulson@19204
   646
            REPEAT_DETERM_N (length ts) o (etac thin_rl)] i st
paulson@19204
   647
  end
paulson@19204
   648
  handle Subscript => Seq.empty;
mengj@18194
   649
paulson@15118
   650
(*Top-level conversion to meta-level clauses. Each clause has  
paulson@15118
   651
  leading !!-bound universal variables, to express generality. To get 
paulson@15118
   652
  disjunctions instead of meta-clauses, remove "make_meta_clauses" below.*)
paulson@15008
   653
val make_clauses_tac = 
paulson@15008
   654
  SUBGOAL
paulson@15008
   655
    (fn (prop,_) =>
paulson@15008
   656
     let val ts = Logic.strip_assums_hyp prop
paulson@15008
   657
     in EVERY1 
paulson@15008
   658
	 [METAHYPS
paulson@15008
   659
	    (fn hyps => 
paulson@15151
   660
              (Method.insert_tac
paulson@15118
   661
                (map forall_intr_vars 
paulson@15118
   662
                  (make_meta_clauses (make_clauses hyps))) 1)),
paulson@15008
   663
	  REPEAT_DETERM_N (length ts) o (etac thin_rl)]
paulson@15008
   664
     end);
paulson@16563
   665
     
paulson@16563
   666
     
paulson@16563
   667
(*** setup the special skoklemization methods ***)
wenzelm@9869
   668
paulson@16563
   669
(*No CHANGED_PROP here, since these always appear in the preamble*)
wenzelm@9869
   670
paulson@16563
   671
val skolemize_setup =
wenzelm@18708
   672
  Method.add_methods
wenzelm@21588
   673
    [("skolemize", Method.no_args (Method.SIMPLE_METHOD' skolemize_tac),
wenzelm@18708
   674
      "Skolemization into existential quantifiers"),
wenzelm@21588
   675
     ("make_clauses", Method.no_args (Method.SIMPLE_METHOD' make_clauses_tac), 
wenzelm@18708
   676
      "Conversion to !!-quantified meta-level clauses")];
paulson@9840
   677
paulson@9840
   678
end;
wenzelm@9869
   679
paulson@15579
   680
structure BasicMeson: BASIC_MESON = Meson;
paulson@15579
   681
open BasicMeson;