src/HOL/Tools/meson.ML

-(*  Title:      HOL/ex/meson
+(*  Title:      HOL/Tools/meson.ML
     ID:         $Id$
     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     Copyright   1992  University of Cambridge
 
-The MESON resolution proof procedure for HOL
+The MESON resolution proof procedure for HOL.
 
 When making clauses, avoids using the rewriter -- instead uses RS recursively
 
 NEED TO SORT LITERALS BY # OF VARS, USING ==>I/E.  ELIMINATES NEED FOR
 FUNCTION nodups -- if done to goal clauses too!
 *)
 
-
-(**** LEMMAS : outside the "local" block ****)
-
-(** "Axiom" of Choice, proved using the description operator **)
-
-Goal "ALL x. EX y. Q x y ==> EX f. ALL x. Q x (f x)";
-by (fast_tac (claset() addEs [selectI]) 1);
-qed "choice";
-
-(*** Generation of contrapositives ***)
-
-(*Inserts negated disjunct after removing the negation; P is a literal*)
-val [major,minor] = Goal "~P|Q ==> ((~P==>P) ==> Q)";
-by (rtac (major RS disjE) 1);
-by (rtac notE 1);
-by (etac minor 2);
-by (ALLGOALS assume_tac);
-qed "make_neg_rule";
-
-(*For Plaisted's "Postive refinement" of the MESON procedure*)
-Goal "~P|Q ==> (P ==> Q)";
-by (Blast_tac 1);
-qed "make_refined_neg_rule";
-
-(*P should be a literal*)
-val [major,minor] = Goal "P|Q ==> ((P==>~P) ==> Q)";
-by (rtac (major RS disjE) 1);
-by (rtac notE 1);
-by (etac minor 1);
-by (ALLGOALS assume_tac);
-qed "make_pos_rule";
-
-(*** Generation of a goal clause -- put away the final literal ***)
-
-val [major,minor] = Goal "~P ==> ((~P==>P) ==> False)";
-by (rtac notE 1);
-by (rtac minor 2);
-by (ALLGOALS (rtac major));
-qed "make_neg_goal";
-
-val [major,minor] = Goal "P ==> ((P==>~P) ==> False)";
-by (rtac notE 1);
-by (rtac minor 1);
-by (ALLGOALS (rtac major));
-qed "make_pos_goal";
-
-
-(**** Lemmas for forward proof (like congruence rules) ****)
-
-(*NOTE: could handle conjunctions (faster?) by
-    nf(th RS conjunct2) RS (nf(th RS conjunct1) RS conjI) *)
-val major::prems = Goal
-    "[| P'&Q';  P' ==> P;  Q' ==> Q |] ==> P&Q";
-by (rtac (major RS conjE) 1);
-by (rtac conjI 1);
-by (ALLGOALS (eresolve_tac prems));
-qed "conj_forward";
-
-val major::prems = Goal
-    "[| P'|Q';  P' ==> P;  Q' ==> Q |] ==> P|Q";
-by (rtac (major RS disjE) 1);
-by (ALLGOALS (dresolve_tac prems));
-by (ALLGOALS (eresolve_tac [disjI1,disjI2]));
-qed "disj_forward";
-
-(*Version for removal of duplicate literals*)
-val major::prems = Goal
-    "[| P'|Q';  P' ==> P;  [| Q'; P==>False |] ==> Q |] ==> P|Q";
-by (cut_facts_tac [major] 1);
-by (blast_tac (claset() addIs prems) 1); 
-qed "disj_forward2";
-
-val major::prems = Goal
-    "[| ALL x. P'(x);  !!x. P'(x) ==> P(x) |] ==> ALL x. P(x)";
-by (rtac allI 1);
-by (resolve_tac prems 1);
-by (rtac (major RS spec) 1);
-qed "all_forward";
-
-val major::prems = Goal
-    "[| EX x. P'(x);  !!x. P'(x) ==> P(x) |] ==> EX x. P(x)";
-by (rtac (major RS exE) 1);
-by (rtac exI 1);
-by (eresolve_tac prems 1);
-qed "ex_forward";
-
-(**** END OF LEMMAS ****)
-
 local
 
  (*Prove theorems using fast_tac*)
- fun prove_fun s = 
+ fun prove_fun s =
      prove_goal (the_context ()) s
-	  (fn prems => [ cut_facts_tac prems 1, Fast_tac 1 ]);
+          (fn prems => [ cut_facts_tac prems 1, Fast_tac 1 ]);
 
  (**** Negation Normal Form ****)
 
  (*** de Morgan laws ***)
 

    of Some(th,_) => th
     | None => raise THM("forward_res", 0, [st]);
 
 
  (*Are any of the constants in "bs" present in the term?*)
- fun has_consts bs = 
+ fun has_consts bs =
    let fun has (Const(a,_)) = a mem bs
-	 | has (f$u) = has f orelse has u
-	 | has (Abs(_,_,t)) = has t
-	 | has _ = false
+         | has (f$u) = has f orelse has u
+         | has (Abs(_,_,t)) = has t
+         | has _ = false
    in  has  end;
 
 
  (**** Clause handling ****)
 

  (*to detect, and remove, tautologous clauses*)
  fun taut_lits [] = false
    | taut_lits ((flg,t)::ts) = (not flg,t) mem ts orelse taut_lits ts;
 
  (*Include False as a literal: an occurrence of ~False is a tautology*)
- fun is_taut th = taut_lits ((true, HOLogic.false_const) :: 
-			     literals (prop_of th));
+ fun is_taut th = taut_lits ((true, HOLogic.false_const) ::
+                             literals (prop_of th));
 
  (*Generation of unique names -- maxidx cannot be relied upon to increase!
    Cannot rely on "variant", since variables might coincide when literals
-   are joined to make a clause... 
+   are joined to make a clause...
    19 chooses "U" as the first variable name*)
  val name_ref = ref 19;
 
  (*Replaces universally quantified variables by FREE variables -- because
    assumptions may not contain scheme variables.  Later, call "generalize". *)
  fun freeze_spec th =
    let val sth = th RS spec
        val newname = (name_ref := !name_ref + 1;
-		      radixstring(26, "A", !name_ref))
+                      radixstring(26, "A", !name_ref))
    in  read_instantiate [("x", newname)] sth  end;
 
  fun resop nf [prem] = resolve_tac (nf prem) 1;
 
  (*Conjunctive normal form, detecting tautologies early.
    Strips universal quantifiers and breaks up conjunctions. *)
- fun cnf_aux seen (th,ths) = 
+ fun cnf_aux seen (th,ths) =
    if taut_lits (literals(prop_of th) @ seen)  then ths
    else if not (has_consts ["All","op &"] (prop_of th))  then th::ths
    else (*conjunction?*)
-	 cnf_aux seen (th RS conjunct1, 
-		       cnf_aux seen (th RS conjunct2, ths))
+         cnf_aux seen (th RS conjunct1,
+                       cnf_aux seen (th RS conjunct2, ths))
    handle THM _ => (*universal quant?*)
-	 cnf_aux  seen (freeze_spec th,  ths)
+         cnf_aux  seen (freeze_spec th,  ths)
    handle THM _ => (*disjunction?*)
-     let val tac = 
-	 (METAHYPS (resop (cnf_nil seen)) 1) THEN
-	 (fn st' => st' |>
-		 METAHYPS (resop (cnf_nil (literals (concl_of st') @ seen))) 1)
+     let val tac =
+         (METAHYPS (resop (cnf_nil seen)) 1) THEN
+         (fn st' => st' |>
+                 METAHYPS (resop (cnf_nil (literals (concl_of st') @ seen))) 1)
      in  Seq.list_of (tac (th RS disj_forward)) @ ths  end
  and cnf_nil seen th = cnf_aux seen (th,[]);
 
  (*Top-level call to cnf -- it's safe to reset name_ref*)
- fun cnf (th,ths) = 
+ fun cnf (th,ths) =
     (name_ref := 19;  cnf (th RS conjunct1, cnf (th RS conjunct2, ths))
      handle THM _ => (*not a conjunction*) cnf_aux [] (th, ths));
 
  (**** Removal of duplicate literals ****)
 
  (*Forward proof, passing extra assumptions as theorems to the tactic*)
  fun forward_res2 nf hyps st =
    case Seq.pull
-	 (REPEAT 
-	  (METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1) 
-	  st)
+         (REPEAT
+          (METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1)
+          st)
    of Some(th,_) => th
     | None => raise THM("forward_res2", 0, [st]);
 
  (*Remove duplicates in P|Q by assuming ~P in Q
    rls (initially []) accumulates assumptions of the form P==>False*)
  fun nodups_aux rls th = nodups_aux rls (th RS disj_assoc)
      handle THM _ => tryres(th,rls)
      handle THM _ => tryres(forward_res2 nodups_aux rls (th RS disj_forward2),
-			    [disj_FalseD1, disj_FalseD2, asm_rl])
+                            [disj_FalseD1, disj_FalseD2, asm_rl])
      handle THM _ => th;
 
  (*Remove duplicate literals, if there are any*)
  fun nodups th =
      if null(findrep(literals(prop_of th))) then th

 
  (**** Generation of contrapositives ****)
 
  (*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
  fun assoc_right th = assoc_right (th RS disj_assoc)
-	 handle THM _ => th;
+         handle THM _ => th;
 
  (*Must check for negative literal first!*)
  val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
 
  (*For Plaisted's postive refinement.  [currently unused] *)
  val refined_clause_rules = [disj_assoc, make_refined_neg_rule, make_pos_rule];
 
  (*Create a goal or support clause, conclusing False*)
  fun make_goal th =   (*Must check for negative literal first!*)
-     make_goal (tryres(th, clause_rules)) 
+     make_goal (tryres(th, clause_rules))
    handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
 
  (*Sort clauses by number of literals*)
  fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2);
 

 
  (*Convert all suitable free variables to schematic variables*)
  fun generalize th = forall_elim_vars 0 (forall_intr_frees th);
 
  (*Create a meta-level Horn clause*)
- fun make_horn crules th = make_horn crules (tryres(th,crules)) 
-			   handle THM _ => th;
+ fun make_horn crules th = make_horn crules (tryres(th,crules))
+                           handle THM _ => th;
 
  (*Generate Horn clauses for all contrapositives of a clause*)
- fun add_contras crules (th,hcs) = 
+ fun add_contras crules (th,hcs) =
    let fun rots (0,th) = hcs
-	 | rots (k,th) = zero_var_indexes (make_horn crules th) ::
-			 rots(k-1, assoc_right (th RS disj_comm))
+         | rots (k,th) = zero_var_indexes (make_horn crules th) ::
+                         rots(k-1, assoc_right (th RS disj_comm))
    in case nliterals(prop_of th) of
-	 1 => th::hcs
+         1 => th::hcs
        | n => rots(n, assoc_right th)
    end;
 
  (*Use "theorem naming" to label the clauses*)
- fun name_thms label = 
+ fun name_thms label =
      let fun name1 (th, (k,ths)) =
-	   (k-1, Thm.name_thm (label ^ string_of_int k, th) :: ths)
+           (k-1, Thm.name_thm (label ^ string_of_int k, th) :: ths)
 
      in  fn ths => #2 (foldr name1 (ths, (length ths, [])))  end;
 
  (*Find an all-negative support clause*)
  fun is_negative th = forall (not o #1) (literals (prop_of th));

 
 
  (***** MESON PROOF PROCEDURE *****)
 
  fun rhyps (Const("==>",_) $ (Const("Trueprop",_) $ A) $ phi,
-	    As) = rhyps(phi, A::As)
+            As) = rhyps(phi, A::As)
    | rhyps (_, As) = As;
 
  (** Detecting repeated assumptions in a subgoal **)
 
  (*The stringtree detects repeated assumptions.*)

  (*detects repetitions in a list of terms*)
  fun has_reps [] = false
    | has_reps [_] = false
    | has_reps [t,u] = (t aconv u)
    | has_reps ts = (foldl ins_term (Net.empty, ts);  false)
-		   handle INSERT => true; 
+                   handle INSERT => true;
 
  (*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*)
  fun TRYALL_eq_assume_tac 0 st = Seq.single st
-   | TRYALL_eq_assume_tac i st = 
-	TRYALL_eq_assume_tac (i-1) (eq_assumption i st)
-	handle THM _ => TRYALL_eq_assume_tac (i-1) st;
+   | TRYALL_eq_assume_tac i st =
+        TRYALL_eq_assume_tac (i-1) (eq_assumption i st)
+        handle THM _ => TRYALL_eq_assume_tac (i-1) st;
 
  (*Loop checking: FAIL if trying to prove the same thing twice
    -- if *ANY* subgoal has repeated literals*)
- fun check_tac st = 
+ fun check_tac st =
    if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st)
    then  Seq.empty  else  Seq.single st;
 
 
  (* net_resolve_tac actually made it slower... *)
- fun prolog_step_tac horns i = 
+ fun prolog_step_tac horns i =
      (assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
      TRYALL eq_assume_tac;
 
 
 in

 fun size_of_subgoals st = foldr addconcl (prems_of st, 0)
 end;
 
 (*Negation Normal Form*)
 val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD,
-	       not_impD, not_iffD, not_allD, not_exD, not_notD];
+               not_impD, not_iffD, not_allD, not_exD, not_notD];
 fun make_nnf th = make_nnf (tryres(th, nnf_rls))
-    handle THM _ => 
-	forward_res make_nnf
-	   (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
+    handle THM _ =>
+        forward_res make_nnf
+           (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
     handle THM _ => th;
 
 (*Pull existential quantifiers (Skolemization)*)
-fun skolemize th = 
+fun skolemize th =
   if not (has_consts ["Ex"] (prop_of th)) then th
   else skolemize (tryres(th, [choice, conj_exD1, conj_exD2,
-			      disj_exD, disj_exD1, disj_exD2]))
-    handle THM _ => 
-	skolemize (forward_res skolemize
-		   (tryres (th, [conj_forward, disj_forward, all_forward])))
+                              disj_exD, disj_exD1, disj_exD2]))
+    handle THM _ =>
+        skolemize (forward_res skolemize
+                   (tryres (th, [conj_forward, disj_forward, all_forward])))
     handle THM _ => forward_res skolemize (th RS ex_forward);
 
 
 (*Make clauses from a list of theorems, previously Skolemized and put into nnf.
   The resulting clauses are HOL disjunctions.*)
-fun make_clauses ths = 
+fun make_clauses ths =
     sort_clauses (map (generalize o nodups) (foldr cnf (ths,[])));
 
 (*Convert a list of clauses to (contrapositive) Horn clauses*)
-fun make_horns ths = 
+fun make_horns ths =
     name_thms "Horn#"
       (gen_distinct eq_thm (foldr (add_contras clause_rules) (ths,[])));
 
 (*Could simply use nprems_of, which would count remaining subgoals -- no
   discrimination as to their size!  With BEST_FIRST, fails for problem 41.*)
 
-fun best_prolog_tac sizef horns = 
+fun best_prolog_tac sizef horns =
     BEST_FIRST (has_fewer_prems 1, sizef) (prolog_step_tac horns 1);
 
-fun depth_prolog_tac horns = 
+fun depth_prolog_tac horns =
     DEPTH_FIRST (has_fewer_prems 1) (prolog_step_tac horns 1);
 
 (*Return all negative clauses, as possible goal clauses*)
 fun gocls cls = name_thms "Goal#" (map make_goal (neg_clauses cls));
 
 
-fun skolemize_tac prems = 
+fun skolemize_tac prems =
     cut_facts_tac (map (skolemize o make_nnf) prems)  THEN'
     REPEAT o (etac exE);
 
 (*Shell of all meson-tactics.  Supplies cltac with clauses: HOL disjunctions*)
 fun MESON cltac = SELECT_GOAL

                     EVERY1 [skolemize_tac negs,
                             METAHYPS (cltac o make_clauses)])]);
 
 (** Best-first search versions **)
 
-fun best_meson_tac sizef = 
-  MESON (fn cls => 
+fun best_meson_tac sizef =
+  MESON (fn cls =>
          THEN_BEST_FIRST (resolve_tac (gocls cls) 1)
                          (has_fewer_prems 1, sizef)
                          (prolog_step_tac (make_horns cls) 1));
 
 (*First, breaks the goal into independent units*)
 val safe_best_meson_tac =
-     SELECT_GOAL (TRY Safe_tac THEN 
+     SELECT_GOAL (TRY Safe_tac THEN
                   TRYALL (best_meson_tac size_of_subgoals));
 
 (** Depth-first search version **)
 
 val depth_meson_tac =
-     MESON (fn cls => EVERY [resolve_tac (gocls cls) 1, 
+     MESON (fn cls => EVERY [resolve_tac (gocls cls) 1,
                              depth_prolog_tac (make_horns cls)]);
 
 
 
 (** Iterative deepening version **)
 
 (*This version does only one inference per call;
   having only one eq_assume_tac speeds it up!*)
-fun prolog_step_tac' horns = 
+fun prolog_step_tac' horns =
     let val (horn0s, hornps) = (*0 subgoals vs 1 or more*)
             take_prefix Thm.no_prems horns
         val nrtac = net_resolve_tac horns
     in  fn i => eq_assume_tac i ORELSE
                 match_tac horn0s i ORELSE  (*no backtracking if unit MATCHES*)
                 ((assume_tac i APPEND nrtac i) THEN check_tac)
     end;
 
-fun iter_deepen_prolog_tac horns = 
+fun iter_deepen_prolog_tac horns =
     ITER_DEEPEN (has_fewer_prems 1) (prolog_step_tac' horns);
 
-val iter_deepen_meson_tac = 
-  MESON (fn cls => 
+val iter_deepen_meson_tac =
+  MESON (fn cls =>
          (THEN_ITER_DEEPEN (resolve_tac (gocls cls) 1)
                            (has_fewer_prems 1)
                            (prolog_step_tac' (make_horns cls))));
 
-val meson_tac =
-     SELECT_GOAL (TRY Safe_tac THEN 
-                  TRYALL (iter_deepen_meson_tac));
+fun meson_claset_tac cs =
+  SELECT_GOAL (TRY (safe_tac cs) THEN TRYALL iter_deepen_meson_tac);
+
+val meson_tac = CLASET' meson_claset_tac;
+
+
+(* proof method setup *)
+
+local
+
+fun meson_meth ctxt =
+  Method.SIMPLE_METHOD' HEADGOAL (CHANGED o meson_claset_tac (Classical.get_local_claset ctxt));
+
+in
+
+val meson_setup =
+ [Method.add_methods
+  [("meson", Method.ctxt_args meson_meth, "The MESON resolution proof procedure")]];
 
 end;
+
+end;