src/HOL/Tools/meson.ML
author wenzelm
Sat, 17 Oct 2009 14:43:18 +0200
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(*  Title:      HOL/Tools/meson.ML
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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The MESON resolution proof procedure for HOL.
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When making clauses, avoids using the rewriter -- instead uses RS recursively.
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*)
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signature MESON =
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sig
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  val trace: bool Unsynchronized.ref
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  val term_pair_of: indexname * (typ * 'a) -> term * 'a
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  val first_order_resolve: thm -> thm -> thm
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  val flexflex_first_order: thm -> thm
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  val size_of_subgoals: thm -> int
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  val too_many_clauses: Proof.context option -> term -> bool
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  val make_cnf: thm list -> thm -> Proof.context -> thm list * Proof.context
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  val finish_cnf: thm list -> thm list
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  val make_nnf: Proof.context -> thm -> thm
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  val skolemize: Proof.context -> thm -> thm
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  val is_fol_term: theory -> term -> bool
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  val make_clauses: thm list -> thm list
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  val make_horns: thm list -> thm list
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  val best_prolog_tac: (thm -> int) -> thm list -> tactic
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  val depth_prolog_tac: thm list -> tactic
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  val gocls: thm list -> thm list
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  val skolemize_prems_tac: Proof.context -> thm list -> int -> tactic
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  val MESON: (thm list -> thm list) -> (thm list -> tactic) -> Proof.context -> int -> tactic
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  val best_meson_tac: (thm -> int) -> Proof.context -> int -> tactic
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  val safe_best_meson_tac: Proof.context -> int -> tactic
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  val depth_meson_tac: Proof.context -> int -> tactic
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  val prolog_step_tac': thm list -> int -> tactic
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  val iter_deepen_prolog_tac: thm list -> tactic
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  val iter_deepen_meson_tac: Proof.context -> thm list -> int -> tactic
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  val make_meta_clause: thm -> thm
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  val make_meta_clauses: thm list -> thm list
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  val meson_tac: Proof.context -> thm list -> int -> tactic
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  val negate_head: thm -> thm
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  val select_literal: int -> thm -> thm
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  val skolemize_tac: Proof.context -> int -> tactic
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  val setup: theory -> theory
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end
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structure Meson: MESON =
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struct
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val trace = Unsynchronized.ref false;
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fun trace_msg msg = if ! trace then tracing (msg ()) else ();
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val max_clauses_default = 60;
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val (max_clauses, setup) = Attrib.config_int "max_clauses" max_clauses_default;
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val disj_forward = @{thm disj_forward};
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val disj_forward2 = @{thm disj_forward2};
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val make_pos_rule = @{thm make_pos_rule};
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val make_pos_rule' = @{thm make_pos_rule'};
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val make_pos_goal = @{thm make_pos_goal};
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val make_neg_rule = @{thm make_neg_rule};
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val make_neg_rule' = @{thm make_neg_rule'};
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val make_neg_goal = @{thm make_neg_goal};
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val conj_forward = @{thm conj_forward};
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val all_forward = @{thm all_forward};
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val ex_forward = @{thm ex_forward};
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val choice = @{thm choice};
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val not_conjD = thm "meson_not_conjD";
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val not_disjD = thm "meson_not_disjD";
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val not_notD = thm "meson_not_notD";
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val not_allD = thm "meson_not_allD";
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val not_exD = thm "meson_not_exD";
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val imp_to_disjD = thm "meson_imp_to_disjD";
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val not_impD = thm "meson_not_impD";
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val iff_to_disjD = thm "meson_iff_to_disjD";
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val not_iffD = thm "meson_not_iffD";
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val conj_exD1 = thm "meson_conj_exD1";
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val conj_exD2 = thm "meson_conj_exD2";
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val disj_exD = thm "meson_disj_exD";
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val disj_exD1 = thm "meson_disj_exD1";
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val disj_exD2 = thm "meson_disj_exD2";
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val disj_assoc = thm "meson_disj_assoc";
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val disj_comm = thm "meson_disj_comm";
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val disj_FalseD1 = thm "meson_disj_FalseD1";
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val disj_FalseD2 = thm "meson_disj_FalseD2";
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(**** Operators for forward proof ****)
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(** First-order Resolution **)
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fun typ_pair_of (ix, (sort,ty)) = (TVar (ix,sort), ty);
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fun term_pair_of (ix, (ty,t)) = (Var (ix,ty), t);
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(*FIXME: currently does not "rename variables apart"*)
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fun first_order_resolve thA thB =
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  (case
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    try (fn () =>
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      let val thy = theory_of_thm thA
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          val tmA = concl_of thA
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          val Const("==>",_) $ tmB $ _ = prop_of thB
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          val (tyenv, tenv) = Pattern.first_order_match thy (tmB, tmA) (Vartab.empty, Vartab.empty)
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          val ct_pairs = map (pairself (cterm_of thy) o term_pair_of) (Vartab.dest tenv)
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      in  thA RS (cterm_instantiate ct_pairs thB)  end) () of
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    SOME th => th
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  | NONE => raise THM ("first_order_resolve", 0, [thA, thB]));
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fun flexflex_first_order th =
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  case (tpairs_of th) of
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      [] => th
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    | pairs =>
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        let val thy = theory_of_thm th
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            val (tyenv, tenv) =
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              fold (Pattern.first_order_match thy) pairs (Vartab.empty, Vartab.empty)
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            val t_pairs = map term_pair_of (Vartab.dest tenv)
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            val th' = Thm.instantiate ([], map (pairself (cterm_of thy)) t_pairs) th
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        in  th'  end
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        handle THM _ => th;
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(*Forward proof while preserving bound variables names*)
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fun rename_bvs_RS th rl =
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  let val th' = th RS rl
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  in  Thm.rename_boundvars (concl_of th') (concl_of th) th' end;
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(*raises exception if no rules apply*)
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fun tryres (th, rls) =
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  let fun tryall [] = raise THM("tryres", 0, th::rls)
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        | tryall (rl::rls) = (rename_bvs_RS th rl handle THM _ => tryall rls)
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  in  tryall rls  end;
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(*Permits forward proof from rules that discharge assumptions. The supplied proof state st,
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  e.g. from conj_forward, should have the form
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    "[| P' ==> ?P; Q' ==> ?Q |] ==> ?P & ?Q"
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  and the effect should be to instantiate ?P and ?Q with normalized versions of P' and Q'.*)
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fun forward_res ctxt nf st =
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  let fun forward_tacf [prem] = rtac (nf prem) 1
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        | forward_tacf prems =
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            error (cat_lines
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              ("Bad proof state in forward_res, please inform lcp@cl.cam.ac.uk:" ::
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                Display.string_of_thm ctxt st ::
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                "Premises:" :: map (Display.string_of_thm ctxt) prems))
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  in
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    case Seq.pull (ALLGOALS (OldGoals.METAHYPS forward_tacf) st)
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    of SOME(th,_) => th
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     | NONE => raise THM("forward_res", 0, [st])
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  end;
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(*Are any of the logical connectives in "bs" present in the term?*)
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fun has_conns bs =
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  let fun has (Const(a,_)) = false
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        | has (Const("Trueprop",_) $ p) = has p
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        | has (Const("Not",_) $ p) = has p
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        | has (Const("op |",_) $ p $ q) = member (op =) bs "op |" orelse has p orelse has q
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        | has (Const("op &",_) $ p $ q) = member (op =) bs "op &" orelse has p orelse has q
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        | has (Const("All",_) $ Abs(_,_,p)) = member (op =) bs "All" orelse has p
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        | has (Const("Ex",_) $ Abs(_,_,p)) = member (op =) bs "Ex" orelse has p
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        | has _ = false
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  in  has  end;
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(**** Clause handling ****)
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fun literals (Const("Trueprop",_) $ P) = literals P
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  | literals (Const("op |",_) $ P $ Q) = literals P @ literals Q
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  | literals (Const("Not",_) $ P) = [(false,P)]
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  | literals P = [(true,P)];
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(*number of literals in a term*)
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val nliterals = length o literals;
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(*** Tautology Checking ***)
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fun signed_lits_aux (Const ("op |", _) $ P $ Q) (poslits, neglits) =
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      signed_lits_aux Q (signed_lits_aux P (poslits, neglits))
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  | signed_lits_aux (Const("Not",_) $ P) (poslits, neglits) = (poslits, P::neglits)
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  | signed_lits_aux P (poslits, neglits) = (P::poslits, neglits);
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fun signed_lits th = signed_lits_aux (HOLogic.dest_Trueprop (concl_of th)) ([],[]);
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(*Literals like X=X are tautologous*)
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fun taut_poslit (Const("op =",_) $ t $ u) = t aconv u
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  | taut_poslit (Const("True",_)) = true
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  | taut_poslit _ = false;
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fun is_taut th =
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  let val (poslits,neglits) = signed_lits th
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  in  exists taut_poslit poslits
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      orelse
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      exists (member (op aconv) neglits) (HOLogic.false_const :: poslits)
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  end
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  handle TERM _ => false;       (*probably dest_Trueprop on a weird theorem*)
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(*** To remove trivial negated equality literals from clauses ***)
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(*They are typically functional reflexivity axioms and are the converses of
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  injectivity equivalences*)
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val not_refl_disj_D = thm"meson_not_refl_disj_D";
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(*Is either term a Var that does not properly occur in the other term?*)
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fun eliminable (t as Var _, u) = t aconv u orelse not (Logic.occs(t,u))
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  | eliminable (u, t as Var _) = t aconv u orelse not (Logic.occs(t,u))
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  | eliminable _ = false;
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fun refl_clause_aux 0 th = th
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  | refl_clause_aux n th =
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       case HOLogic.dest_Trueprop (concl_of th) of
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          (Const ("op |", _) $ (Const ("op |", _) $ _ $ _) $ _) =>
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            refl_clause_aux n (th RS disj_assoc)    (*isolate an atom as first disjunct*)
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        | (Const ("op |", _) $ (Const("Not",_) $ (Const("op =",_) $ t $ u)) $ _) =>
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            if eliminable(t,u)
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            then refl_clause_aux (n-1) (th RS not_refl_disj_D)  (*Var inequation: delete*)
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            else refl_clause_aux (n-1) (th RS disj_comm)  (*not between Vars: ignore*)
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        | (Const ("op |", _) $ _ $ _) => refl_clause_aux n (th RS disj_comm)
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        | _ => (*not a disjunction*) th;
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fun notequal_lits_count (Const ("op |", _) $ P $ Q) =
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      notequal_lits_count P + notequal_lits_count Q
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  | notequal_lits_count (Const("Not",_) $ (Const("op =",_) $ _ $ _)) = 1
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  | notequal_lits_count _ = 0;
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(*Simplify a clause by applying reflexivity to its negated equality literals*)
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fun refl_clause th =
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  let val neqs = notequal_lits_count (HOLogic.dest_Trueprop (concl_of th))
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  in  zero_var_indexes (refl_clause_aux neqs th)  end
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  handle TERM _ => th;  (*probably dest_Trueprop on a weird theorem*)
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(*** Removal of duplicate literals ***)
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(*Forward proof, passing extra assumptions as theorems to the tactic*)
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fun forward_res2 ctxt nf hyps st =
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  case Seq.pull
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        (REPEAT
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         (OldGoals.METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1)
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         st)
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  of SOME(th,_) => th
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   | NONE => raise THM("forward_res2", 0, [st]);
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(*Remove duplicates in P|Q by assuming ~P in Q
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  rls (initially []) accumulates assumptions of the form P==>False*)
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fun nodups_aux ctxt rls th = nodups_aux ctxt rls (th RS disj_assoc)
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    handle THM _ => tryres(th,rls)
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    handle THM _ => tryres(forward_res2 ctxt (nodups_aux ctxt) rls (th RS disj_forward2),
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                           [disj_FalseD1, disj_FalseD2, asm_rl])
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    handle THM _ => th;
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(*Remove duplicate literals, if there are any*)
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fun nodups ctxt th =
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  if has_duplicates (op =) (literals (prop_of th))
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    then nodups_aux ctxt [] th
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    else th;
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(*** The basic CNF transformation ***)
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fun too_many_clauses ctxto t = 
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 let
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  val max_cl = case ctxto of SOME ctxt => Config.get ctxt max_clauses
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                           | NONE => max_clauses_default
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  fun sum x y = if x < max_cl andalso y < max_cl then x+y else max_cl;
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  fun prod x y = if x < max_cl andalso y < max_cl then x*y else max_cl;
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  (*Estimate the number of clauses in order to detect infeasible theorems*)
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  fun signed_nclauses b (Const("Trueprop",_) $ t) = signed_nclauses b t
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    | signed_nclauses b (Const("Not",_) $ t) = signed_nclauses (not b) t
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    | signed_nclauses b (Const("op &",_) $ t $ u) =
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        if b then sum (signed_nclauses b t) (signed_nclauses b u)
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             else prod (signed_nclauses b t) (signed_nclauses b u)
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    | signed_nclauses b (Const("op |",_) $ t $ u) =
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        if b then prod (signed_nclauses b t) (signed_nclauses b u)
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             else sum (signed_nclauses b t) (signed_nclauses b u)
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    | signed_nclauses b (Const("op -->",_) $ t $ u) =
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        if b then prod (signed_nclauses (not b) t) (signed_nclauses b u)
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             else sum (signed_nclauses (not b) t) (signed_nclauses b u)
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    | signed_nclauses b (Const("op =", Type ("fun", [T, _])) $ t $ u) =
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        if T = HOLogic.boolT then (*Boolean equality is if-and-only-if*)
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            if b then sum (prod (signed_nclauses (not b) t) (signed_nclauses b u))
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                          (prod (signed_nclauses (not b) u) (signed_nclauses b t))
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                 else sum (prod (signed_nclauses b t) (signed_nclauses b u))
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                          (prod (signed_nclauses (not b) t) (signed_nclauses (not b) u))
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        else 1
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    | signed_nclauses b (Const("Ex", _) $ Abs (_,_,t)) = signed_nclauses b t
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    | signed_nclauses b (Const("All",_) $ Abs (_,_,t)) = signed_nclauses b t
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    | signed_nclauses _ _ = 1; (* literal *)
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 in 
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  signed_nclauses true t >= max_cl
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 end;
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(*Replaces universally quantified variables by FREE variables -- because
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  assumptions may not contain scheme variables.  Later, generalize using Variable.export. *)
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local  
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  val spec_var = Thm.dest_arg (Thm.dest_arg (#2 (Thm.dest_implies (Thm.cprop_of spec))));
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  val spec_varT = #T (Thm.rep_cterm spec_var);
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  fun name_of (Const ("All", _) $ Abs(x,_,_)) = x | name_of _ = Name.uu;
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in  
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  fun freeze_spec th ctxt =
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    let
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      val cert = Thm.cterm_of (ProofContext.theory_of ctxt);
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      val ([x], ctxt') = Variable.variant_fixes [name_of (HOLogic.dest_Trueprop (concl_of th))] ctxt;
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      val spec' = Thm.instantiate ([], [(spec_var, cert (Free (x, spec_varT)))]) spec;
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    in (th RS spec', ctxt') end
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end;
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(*Used with METAHYPS below. There is one assumption, which gets bound to prem
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  and then normalized via function nf. The normal form is given to resolve_tac,
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  instantiate a Boolean variable created by resolution with disj_forward. Since
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  (nf prem) returns a LIST of theorems, we can backtrack to get all combinations.*)
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fun resop nf [prem] = resolve_tac (nf prem) 1;
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(*Any need to extend this list with
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  "HOL.type_class","HOL.eq_class","Pure.term"?*)
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val has_meta_conn =
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    exists_Const (member (op =) ["==", "==>", "=simp=>", "all", "prop"] o #1);
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fun apply_skolem_ths (th, rls) =
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  let fun tryall [] = raise THM("apply_skolem_ths", 0, th::rls)
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        | tryall (rl::rls) = (first_order_resolve th rl handle THM _ => tryall rls)
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  in  tryall rls  end;
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(*Conjunctive normal form, adding clauses from th in front of ths (for foldr).
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  Strips universal quantifiers and breaks up conjunctions.
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  Eliminates existential quantifiers using skoths: Skolemization theorems.*)
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fun cnf skoths ctxt (th,ths) =
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  let val ctxtr = Unsynchronized.ref ctxt
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      fun cnf_aux (th,ths) =
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        if not (can HOLogic.dest_Trueprop (prop_of th)) then ths (*meta-level: ignore*)
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        else if not (has_conns ["All","Ex","op &"] (prop_of th))
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        then nodups ctxt th :: ths (*no work to do, terminate*)
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        else case head_of (HOLogic.dest_Trueprop (concl_of th)) of
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            Const ("op &", _) => (*conjunction*)
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                cnf_aux (th RS conjunct1, cnf_aux (th RS conjunct2, ths))
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          | Const ("All", _) => (*universal quantifier*)
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                let val (th',ctxt') = freeze_spec th (!ctxtr)
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                in  ctxtr := ctxt'; cnf_aux (th', ths) end
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          | Const ("Ex", _) =>
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              (*existential quantifier: Insert Skolem functions*)
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              cnf_aux (apply_skolem_ths (th,skoths), ths)
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          | Const ("op |", _) =>
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              (*Disjunction of P, Q: Create new goal of proving ?P | ?Q and solve it using
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                all combinations of converting P, Q to CNF.*)
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              let val tac =
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                  OldGoals.METAHYPS (resop cnf_nil) 1 THEN
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                   (fn st' => st' |> OldGoals.METAHYPS (resop cnf_nil) 1)
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              in  Seq.list_of (tac (th RS disj_forward)) @ ths  end
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          | _ => nodups ctxt th :: ths  (*no work to do*)
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      and cnf_nil th = cnf_aux (th,[])
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      val cls = 
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            if too_many_clauses (SOME ctxt) (concl_of th)
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            then (trace_msg (fn () => "cnf is ignoring: " ^ Display.string_of_thm ctxt th); ths)
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            else cnf_aux (th,ths)
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  in  (cls, !ctxtr)  end;
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fun make_cnf skoths th ctxt = cnf skoths ctxt (th, []);
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(*Generalization, removal of redundant equalities, removal of tautologies.*)
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fun finish_cnf ths = filter (not o is_taut) (map refl_clause ths);
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(**** Generation of contrapositives ****)
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fun is_left (Const ("Trueprop", _) $
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               (Const ("op |", _) $ (Const ("op |", _) $ _ $ _) $ _)) = true
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  | is_left _ = false;
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   366
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(*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
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   368
fun assoc_right th =
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  if is_left (prop_of th) then assoc_right (th RS disj_assoc)
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  else th;
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(*Must check for negative literal first!*)
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val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
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(*For ordinary resolution. *)
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val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule'];
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(*Create a goal or support clause, conclusing False*)
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fun make_goal th =   (*Must check for negative literal first!*)
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    make_goal (tryres(th, clause_rules))
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  handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
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(*Sort clauses by number of literals*)
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fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2);
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fun sort_clauses ths = sort (make_ord fewerlits) ths;
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(*True if the given type contains bool anywhere*)
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fun has_bool (Type("bool",_)) = true
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  | has_bool (Type(_, Ts)) = exists has_bool Ts
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  | has_bool _ = false;
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   393
(*Is the string the name of a connective? Really only | and Not can remain,
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  since this code expects to be called on a clause form.*)
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   395
val is_conn = member (op =)
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   396
    ["Trueprop", "op &", "op |", "op -->", "Not",
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   397
     "All", "Ex", "Ball", "Bex"];
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   398
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diff changeset
   399
(*True if the term contains a function--not a logical connective--where the type
20524
1493053fc111 Tweaks to is_fol_term, the first-order test. We don't count "=" as a connective
paulson
parents: 20417
diff changeset
   400
  of any argument contains bool.*)
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   401
val has_bool_arg_const =
15613
ab90e95ae02e meson now checks that problems are first-order
paulson
parents: 15581
diff changeset
   402
    exists_Const
ab90e95ae02e meson now checks that problems are first-order
paulson
parents: 15581
diff changeset
   403
      (fn (c,T) => not(is_conn c) andalso exists (has_bool) (binder_types T));
22381
cb145d434284 The first-order test now tests for the obscure case of a polymorphic constant like 1 being
paulson
parents: 22360
diff changeset
   404
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   405
(*A higher-order instance of a first-order constant? Example is the definition of
22381
cb145d434284 The first-order test now tests for the obscure case of a polymorphic constant like 1 being
paulson
parents: 22360
diff changeset
   406
  HOL.one, 1, at a function type in theory SetsAndFunctions.*)
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   407
fun higher_inst_const thy (c,T) =
22381
cb145d434284 The first-order test now tests for the obscure case of a polymorphic constant like 1 being
paulson
parents: 22360
diff changeset
   408
  case binder_types T of
cb145d434284 The first-order test now tests for the obscure case of a polymorphic constant like 1 being
paulson
parents: 22360
diff changeset
   409
      [] => false (*not a function type, OK*)
cb145d434284 The first-order test now tests for the obscure case of a polymorphic constant like 1 being
paulson
parents: 22360
diff changeset
   410
    | Ts => length (binder_types (Sign.the_const_type thy c)) <> length Ts;
cb145d434284 The first-order test now tests for the obscure case of a polymorphic constant like 1 being
paulson
parents: 22360
diff changeset
   411
24742
73b8b42a36b6 removal of some "ref"s from res_axioms.ML; a side-effect is that the ordering
paulson
parents: 24300
diff changeset
   412
(*Returns false if any Vars in the theorem mention type bool.
21102
7f2ebe5c5b72 Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents: 21095
diff changeset
   413
  Also rejects functions whose arguments are Booleans or other functions.*)
22381
cb145d434284 The first-order test now tests for the obscure case of a polymorphic constant like 1 being
paulson
parents: 22360
diff changeset
   414
fun is_fol_term thy t =
cb145d434284 The first-order test now tests for the obscure case of a polymorphic constant like 1 being
paulson
parents: 22360
diff changeset
   415
    Term.is_first_order ["all","All","Ex"] t andalso
29267
8615b4f54047 use exists_subterm directly;
wenzelm
parents: 28397
diff changeset
   416
    not (exists_subterm (fn Var (_, T) => has_bool T | _ => false) t  orelse
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   417
         has_bool_arg_const t  orelse
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   418
         exists_Const (higher_inst_const thy) t orelse
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   419
         has_meta_conn t);
19204
b8f7de7ef629 Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents: 19154
diff changeset
   420
21102
7f2ebe5c5b72 Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents: 21095
diff changeset
   421
fun rigid t = not (is_Var (head_of t));
7f2ebe5c5b72 Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents: 21095
diff changeset
   422
7f2ebe5c5b72 Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents: 21095
diff changeset
   423
fun ok4horn (Const ("Trueprop",_) $ (Const ("op |", _) $ t $ _)) = rigid t
7f2ebe5c5b72 Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents: 21095
diff changeset
   424
  | ok4horn (Const ("Trueprop",_) $ t) = rigid t
7f2ebe5c5b72 Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents: 21095
diff changeset
   425
  | ok4horn _ = false;
7f2ebe5c5b72 Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents: 21095
diff changeset
   426
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   427
(*Create a meta-level Horn clause*)
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   428
fun make_horn crules th =
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   429
  if ok4horn (concl_of th)
21102
7f2ebe5c5b72 Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents: 21095
diff changeset
   430
  then make_horn crules (tryres(th,crules)) handle THM _ => th
7f2ebe5c5b72 Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents: 21095
diff changeset
   431
  else th;
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   432
16563
a92f96951355 meson method taking an argument list
paulson
parents: 16173
diff changeset
   433
(*Generate Horn clauses for all contrapositives of a clause. The input, th,
a92f96951355 meson method taking an argument list
paulson
parents: 16173
diff changeset
   434
  is a HOL disjunction.*)
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   435
fun add_contras crules (th,hcs) =
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   436
  let fun rots (0,th) = hcs
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   437
        | rots (k,th) = zero_var_indexes (make_horn crules th) ::
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   438
                        rots(k-1, assoc_right (th RS disj_comm))
15862
67574c1b15a0 removed unnecessary (?) check
paulson
parents: 15779
diff changeset
   439
  in case nliterals(prop_of th) of
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   440
        1 => th::hcs
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   441
      | n => rots(n, assoc_right th)
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   442
  end;
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   443
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   444
(*Use "theorem naming" to label the clauses*)
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   445
fun name_thms label =
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   446
    let fun name1 (th, (k,ths)) =
27865
27a8ad9612a3 moved basic thm operations from structure PureThy to Thm (cf. more_thm.ML);
wenzelm
parents: 27239
diff changeset
   447
          (k-1, Thm.put_name_hint (label ^ string_of_int k) th :: ths)
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29684
diff changeset
   448
    in  fn ths => #2 (List.foldr name1 (length ths, []) ths)  end;
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   449
16563
a92f96951355 meson method taking an argument list
paulson
parents: 16173
diff changeset
   450
(*Is the given disjunction an all-negative support clause?*)
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   451
fun is_negative th = forall (not o #1) (literals (prop_of th));
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   452
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   453
val neg_clauses = List.filter is_negative;
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   454
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   455
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   456
(***** MESON PROOF PROCEDURE *****)
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   457
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   458
fun rhyps (Const("==>",_) $ (Const("Trueprop",_) $ A) $ phi,
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   459
           As) = rhyps(phi, A::As)
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   460
  | rhyps (_, As) = As;
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   461
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   462
(** Detecting repeated assumptions in a subgoal **)
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   463
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   464
(*The stringtree detects repeated assumptions.*)
16801
4bb13fa6ae72 tuned concat_with_and;
wenzelm
parents: 16588
diff changeset
   465
fun ins_term (net,t) = Net.insert_term (op aconv) (t,t) net;
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   466
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   467
(*detects repetitions in a list of terms*)
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   468
fun has_reps [] = false
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   469
  | has_reps [_] = false
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   470
  | has_reps [t,u] = (t aconv u)
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   471
  | has_reps ts = (Library.foldl ins_term (Net.empty, ts);  false)
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   472
                  handle Net.INSERT => true;
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   473
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   474
(*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*)
18508
paulson
parents: 18405
diff changeset
   475
fun TRYING_eq_assume_tac 0 st = Seq.single st
paulson
parents: 18405
diff changeset
   476
  | TRYING_eq_assume_tac i st =
31945
d5f186aa0bed structure Thm: less pervasive names;
wenzelm
parents: 31454
diff changeset
   477
       TRYING_eq_assume_tac (i-1) (Thm.eq_assumption i st)
18508
paulson
parents: 18405
diff changeset
   478
       handle THM _ => TRYING_eq_assume_tac (i-1) st;
paulson
parents: 18405
diff changeset
   479
paulson
parents: 18405
diff changeset
   480
fun TRYALL_eq_assume_tac st = TRYING_eq_assume_tac (nprems_of st) st;
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   481
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   482
(*Loop checking: FAIL if trying to prove the same thing twice
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   483
  -- if *ANY* subgoal has repeated literals*)
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   484
fun check_tac st =
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   485
  if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st)
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   486
  then  Seq.empty  else  Seq.single st;
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   487
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   488
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   489
(* net_resolve_tac actually made it slower... *)
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   490
fun prolog_step_tac horns i =
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   491
    (assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
18508
paulson
parents: 18405
diff changeset
   492
    TRYALL_eq_assume_tac;
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   493
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   494
(*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*)
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   495
fun addconcl(prem,sz) = size_of_term(Logic.strip_assums_concl prem) + sz
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   496
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29684
diff changeset
   497
fun size_of_subgoals st = List.foldr addconcl 0 (prems_of st);
15579
32bee18c675f Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents: 15574
diff changeset
   498
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   499
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   500
(*Negation Normal Form*)
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   501
val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD,
9869
95dca9f991f2 improved meson setup;
wenzelm
parents: 9840
diff changeset
   502
               not_impD, not_iffD, not_allD, not_exD, not_notD];
15581
f07e865d9d40 now checks for higher-order vars
paulson
parents: 15579
diff changeset
   503
21102
7f2ebe5c5b72 Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents: 21095
diff changeset
   504
fun ok4nnf (Const ("Trueprop",_) $ (Const ("Not", _) $ t)) = rigid t
7f2ebe5c5b72 Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents: 21095
diff changeset
   505
  | ok4nnf (Const ("Trueprop",_) $ t) = rigid t
7f2ebe5c5b72 Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents: 21095
diff changeset
   506
  | ok4nnf _ = false;
7f2ebe5c5b72 Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents: 21095
diff changeset
   507
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   508
fun make_nnf1 ctxt th =
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   509
  if ok4nnf (concl_of th)
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   510
  then make_nnf1 ctxt (tryres(th, nnf_rls))
28174
626f0a79a4b9 more careful exception handling in order to prevent backtracking; miscellaneous tidying up.
paulson
parents: 27865
diff changeset
   511
    handle THM ("tryres", _, _) =>
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   512
        forward_res ctxt (make_nnf1 ctxt)
9869
95dca9f991f2 improved meson setup;
wenzelm
parents: 9840
diff changeset
   513
           (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
28174
626f0a79a4b9 more careful exception handling in order to prevent backtracking; miscellaneous tidying up.
paulson
parents: 27865
diff changeset
   514
    handle THM ("tryres", _, _) => th
21102
7f2ebe5c5b72 Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents: 21095
diff changeset
   515
  else th;
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   516
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   517
(*The simplification removes defined quantifiers and occurrences of True and False.
20018
5419a71d0baa removed the "tagging" feature
paulson
parents: 19894
diff changeset
   518
  nnf_ss also includes the one-point simprocs,
18405
afb1a52a7011 removal of some redundancies (e.g. one-point-rules) in clause production
paulson
parents: 18389
diff changeset
   519
  which are needed to avoid the various one-point theorems from generating junk clauses.*)
19894
7c7e15b27145 the "all_theorems" option and some fixes
paulson
parents: 19875
diff changeset
   520
val nnf_simps =
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   521
     [simp_implies_def, Ex1_def, Ball_def, Bex_def, if_True,
19894
7c7e15b27145 the "all_theorems" option and some fixes
paulson
parents: 19875
diff changeset
   522
      if_False, if_cancel, if_eq_cancel, cases_simp];
7c7e15b27145 the "all_theorems" option and some fixes
paulson
parents: 19875
diff changeset
   523
val nnf_extra_simps =
7c7e15b27145 the "all_theorems" option and some fixes
paulson
parents: 19875
diff changeset
   524
      thms"split_ifs" @ ex_simps @ all_simps @ simp_thms;
18405
afb1a52a7011 removal of some redundancies (e.g. one-point-rules) in clause production
paulson
parents: 18389
diff changeset
   525
afb1a52a7011 removal of some redundancies (e.g. one-point-rules) in clause production
paulson
parents: 18389
diff changeset
   526
val nnf_ss =
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   527
  HOL_basic_ss addsimps nnf_extra_simps
24040
0d5cf52ebf87 proper simproc_setup for "neq", "let_simp";
wenzelm
parents: 23894
diff changeset
   528
    addsimprocs [defALL_regroup,defEX_regroup, @{simproc neq}, @{simproc let_simp}];
15872
8336ff711d80 fixed treatment of higher-order simprules
paulson
parents: 15862
diff changeset
   529
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   530
fun make_nnf ctxt th = case prems_of th of
21050
d0447a511edb More robust error handling in make_nnf and forward_res
paulson
parents: 21046
diff changeset
   531
    [] => th |> rewrite_rule (map safe_mk_meta_eq nnf_simps)
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   532
             |> simplify nnf_ss
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   533
             |> make_nnf1 ctxt
21050
d0447a511edb More robust error handling in make_nnf and forward_res
paulson
parents: 21046
diff changeset
   534
  | _ => raise THM ("make_nnf: premises in argument", 0, [th]);
15581
f07e865d9d40 now checks for higher-order vars
paulson
parents: 15579
diff changeset
   535
15965
f422f8283491 Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents: 15946
diff changeset
   536
(*Pull existential quantifiers to front. This accomplishes Skolemization for
f422f8283491 Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents: 15946
diff changeset
   537
  clauses that arise from a subgoal.*)
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   538
fun skolemize1 ctxt th =
20134
73cb53843190 has_consts renamed to has_conn, now actually parses the first-order formula
paulson
parents: 20119
diff changeset
   539
  if not (has_conns ["Ex"] (prop_of th)) then th
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   540
  else (skolemize1 ctxt (tryres(th, [choice, conj_exD1, conj_exD2,
15679
28eb0fe50533 Integrating the reconstruction files into the building of HOL
quigley
parents: 15653
diff changeset
   541
                              disj_exD, disj_exD1, disj_exD2])))
28174
626f0a79a4b9 more careful exception handling in order to prevent backtracking; miscellaneous tidying up.
paulson
parents: 27865
diff changeset
   542
    handle THM ("tryres", _, _) =>
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   543
        skolemize1 ctxt (forward_res ctxt (skolemize1 ctxt)
9869
95dca9f991f2 improved meson setup;
wenzelm
parents: 9840
diff changeset
   544
                   (tryres (th, [conj_forward, disj_forward, all_forward])))
28174
626f0a79a4b9 more careful exception handling in order to prevent backtracking; miscellaneous tidying up.
paulson
parents: 27865
diff changeset
   545
    handle THM ("tryres", _, _) => 
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   546
        forward_res ctxt (skolemize1 ctxt) (rename_bvs_RS th ex_forward);
29684
40bf9f4e7a4e Minor reorganisation of the Skolemization code
paulson
parents: 29267
diff changeset
   547
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   548
fun skolemize ctxt th = skolemize1 ctxt (make_nnf ctxt th);
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   549
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   550
fun skolemize_nnf_list _ [] = []
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   551
  | skolemize_nnf_list ctxt (th::ths) =
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   552
      skolemize ctxt th :: skolemize_nnf_list ctxt ths
25710
4cdf7de81e1b Replaced refs by config params; finer critical section in mets method
paulson
parents: 25694
diff changeset
   553
      handle THM _ => (*RS can fail if Unify.search_bound is too small*)
32955
4a78daeb012b local channels for tracing/debugging;
wenzelm
parents: 32740
diff changeset
   554
       (trace_msg (fn () => "Failed to Skolemize " ^ Display.string_of_thm ctxt th);
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   555
        skolemize_nnf_list ctxt ths);
25694
cbb59ba6bf0c Skolemization now catches exception THM, which may be raised if unification fails.
paulson
parents: 24937
diff changeset
   556
24937
340523598914 context-based treatment of generalization; also handling TFrees in axiom clauses
paulson
parents: 24827
diff changeset
   557
fun add_clauses (th,cls) =
340523598914 context-based treatment of generalization; also handling TFrees in axiom clauses
paulson
parents: 24827
diff changeset
   558
  let val ctxt0 = Variable.thm_context th
340523598914 context-based treatment of generalization; also handling TFrees in axiom clauses
paulson
parents: 24827
diff changeset
   559
      val (cnfs,ctxt) = make_cnf [] th ctxt0
340523598914 context-based treatment of generalization; also handling TFrees in axiom clauses
paulson
parents: 24827
diff changeset
   560
  in Variable.export ctxt ctxt0 cnfs @ cls end;
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   561
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   562
(*Make clauses from a list of theorems, previously Skolemized and put into nnf.
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   563
  The resulting clauses are HOL disjunctions.*)
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29684
diff changeset
   564
fun make_clauses ths = sort_clauses (List.foldr add_clauses [] ths);
15773
f14ae2432710 Completed integration of reconstruction code. Now finds and displays proofs when used with modified version
quigley
parents: 15736
diff changeset
   565
16563
a92f96951355 meson method taking an argument list
paulson
parents: 16173
diff changeset
   566
(*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*)
9869
95dca9f991f2 improved meson setup;
wenzelm
parents: 9840
diff changeset
   567
fun make_horns ths =
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   568
    name_thms "Horn#"
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29684
diff changeset
   569
      (distinct Thm.eq_thm_prop (List.foldr (add_contras clause_rules) [] ths));
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   570
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   571
(*Could simply use nprems_of, which would count remaining subgoals -- no
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   572
  discrimination as to their size!  With BEST_FIRST, fails for problem 41.*)
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   573
9869
95dca9f991f2 improved meson setup;
wenzelm
parents: 9840
diff changeset
   574
fun best_prolog_tac sizef horns =
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   575
    BEST_FIRST (has_fewer_prems 1, sizef) (prolog_step_tac horns 1);
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   576
9869
95dca9f991f2 improved meson setup;
wenzelm
parents: 9840
diff changeset
   577
fun depth_prolog_tac horns =
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   578
    DEPTH_FIRST (has_fewer_prems 1) (prolog_step_tac horns 1);
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   579
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   580
(*Return all negative clauses, as possible goal clauses*)
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   581
fun gocls cls = name_thms "Goal#" (map make_goal (neg_clauses cls));
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   582
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   583
fun skolemize_prems_tac ctxt prems =
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   584
    cut_facts_tac (skolemize_nnf_list ctxt prems) THEN'
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   585
    REPEAT o (etac exE);
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   586
22546
c40d7ab8cbc5 MESON tactical takes an additional argument: the clausification function.
paulson
parents: 22515
diff changeset
   587
(*Basis of all meson-tactics.  Supplies cltac with clauses: HOL disjunctions.
c40d7ab8cbc5 MESON tactical takes an additional argument: the clausification function.
paulson
parents: 22515
diff changeset
   588
  Function mkcl converts theorems to clauses.*)
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   589
fun MESON mkcl cltac ctxt i st =
16588
8de758143786 stricter first-order check for meson
paulson
parents: 16563
diff changeset
   590
  SELECT_GOAL
23590
ad95084a5c63 renamed ObjectLogic.atomize_tac to ObjectLogic.atomize_prems_tac;
wenzelm
parents: 23552
diff changeset
   591
    (EVERY [ObjectLogic.atomize_prems_tac 1,
23552
6403d06abe25 to handle non-atomic assumptions
paulson
parents: 23440
diff changeset
   592
            rtac ccontr 1,
32283
3bebc195c124 qualified Subgoal.FOCUS;
wenzelm
parents: 32262
diff changeset
   593
            Subgoal.FOCUS (fn {context = ctxt', prems = negs, ...} =>
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   594
                      EVERY1 [skolemize_prems_tac ctxt negs,
32283
3bebc195c124 qualified Subgoal.FOCUS;
wenzelm
parents: 32262
diff changeset
   595
                              Subgoal.FOCUS (cltac o mkcl o #prems) ctxt']) ctxt 1]) i st
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   596
  handle THM _ => no_tac st;    (*probably from make_meta_clause, not first-order*)
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   597
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   598
(** Best-first search versions **)
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   599
16563
a92f96951355 meson method taking an argument list
paulson
parents: 16173
diff changeset
   600
(*ths is a list of additional clauses (HOL disjunctions) to use.*)
9869
95dca9f991f2 improved meson setup;
wenzelm
parents: 9840
diff changeset
   601
fun best_meson_tac sizef =
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   602
  MESON make_clauses
22546
c40d7ab8cbc5 MESON tactical takes an additional argument: the clausification function.
paulson
parents: 22515
diff changeset
   603
    (fn cls =>
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   604
         THEN_BEST_FIRST (resolve_tac (gocls cls) 1)
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   605
                         (has_fewer_prems 1, sizef)
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   606
                         (prolog_step_tac (make_horns cls) 1));
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   607
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   608
(*First, breaks the goal into independent units*)
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   609
fun safe_best_meson_tac ctxt =
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   610
     SELECT_GOAL (TRY (safe_tac (claset_of ctxt)) THEN
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   611
                  TRYALL (best_meson_tac size_of_subgoals ctxt));
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   612
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   613
(** Depth-first search version **)
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   614
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   615
val depth_meson_tac =
22546
c40d7ab8cbc5 MESON tactical takes an additional argument: the clausification function.
paulson
parents: 22515
diff changeset
   616
  MESON make_clauses
c40d7ab8cbc5 MESON tactical takes an additional argument: the clausification function.
paulson
parents: 22515
diff changeset
   617
    (fn cls => EVERY [resolve_tac (gocls cls) 1, depth_prolog_tac (make_horns cls)]);
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   618
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   619
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   620
(** Iterative deepening version **)
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   621
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   622
(*This version does only one inference per call;
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   623
  having only one eq_assume_tac speeds it up!*)
9869
95dca9f991f2 improved meson setup;
wenzelm
parents: 9840
diff changeset
   624
fun prolog_step_tac' horns =
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   625
    let val (horn0s, hornps) = (*0 subgoals vs 1 or more*)
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   626
            take_prefix Thm.no_prems horns
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   627
        val nrtac = net_resolve_tac horns
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   628
    in  fn i => eq_assume_tac i ORELSE
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   629
                match_tac horn0s i ORELSE  (*no backtracking if unit MATCHES*)
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   630
                ((assume_tac i APPEND nrtac i) THEN check_tac)
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   631
    end;
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   632
9869
95dca9f991f2 improved meson setup;
wenzelm
parents: 9840
diff changeset
   633
fun iter_deepen_prolog_tac horns =
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   634
    ITER_DEEPEN (has_fewer_prems 1) (prolog_step_tac' horns);
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   635
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   636
fun iter_deepen_meson_tac ctxt ths = ctxt |> MESON make_clauses
32091
30e2ffbba718 proper context for Display.pretty_thm etc. or old-style versions Display.pretty_thm_global, Display.pretty_thm_without_context etc.;
wenzelm
parents: 32032
diff changeset
   637
  (fn cls =>
30e2ffbba718 proper context for Display.pretty_thm etc. or old-style versions Display.pretty_thm_global, Display.pretty_thm_without_context etc.;
wenzelm
parents: 32032
diff changeset
   638
    (case (gocls (cls @ ths)) of
30e2ffbba718 proper context for Display.pretty_thm etc. or old-style versions Display.pretty_thm_global, Display.pretty_thm_without_context etc.;
wenzelm
parents: 32032
diff changeset
   639
      [] => no_tac  (*no goal clauses*)
30e2ffbba718 proper context for Display.pretty_thm etc. or old-style versions Display.pretty_thm_global, Display.pretty_thm_without_context etc.;
wenzelm
parents: 32032
diff changeset
   640
    | goes =>
30e2ffbba718 proper context for Display.pretty_thm etc. or old-style versions Display.pretty_thm_global, Display.pretty_thm_without_context etc.;
wenzelm
parents: 32032
diff changeset
   641
        let
30e2ffbba718 proper context for Display.pretty_thm etc. or old-style versions Display.pretty_thm_global, Display.pretty_thm_without_context etc.;
wenzelm
parents: 32032
diff changeset
   642
          val horns = make_horns (cls @ ths)
32955
4a78daeb012b local channels for tracing/debugging;
wenzelm
parents: 32740
diff changeset
   643
          val _ = trace_msg (fn () =>
32091
30e2ffbba718 proper context for Display.pretty_thm etc. or old-style versions Display.pretty_thm_global, Display.pretty_thm_without_context etc.;
wenzelm
parents: 32032
diff changeset
   644
            cat_lines ("meson method called:" ::
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   645
              map (Display.string_of_thm ctxt) (cls @ ths) @
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   646
              ["clauses:"] @ map (Display.string_of_thm ctxt) horns))
32091
30e2ffbba718 proper context for Display.pretty_thm etc. or old-style versions Display.pretty_thm_global, Display.pretty_thm_without_context etc.;
wenzelm
parents: 32032
diff changeset
   647
        in THEN_ITER_DEEPEN (resolve_tac goes 1) (has_fewer_prems 1) (prolog_step_tac' horns) end));
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   648
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   649
fun meson_tac ctxt ths =
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   650
  SELECT_GOAL (TRY (safe_tac (claset_of ctxt)) THEN TRYALL (iter_deepen_meson_tac ctxt ths));
9869
95dca9f991f2 improved meson setup;
wenzelm
parents: 9840
diff changeset
   651
95dca9f991f2 improved meson setup;
wenzelm
parents: 9840
diff changeset
   652
14813
826edbc317e6 new skolemize_tac and skolemize method
paulson
parents: 14763
diff changeset
   653
(**** Code to support ordinary resolution, rather than Model Elimination ****)
14744
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   654
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   655
(*Convert a list of clauses (disjunctions) to meta-level clauses (==>),
15008
5abd18710a1f new method for explicit classical resolution
paulson
parents: 14890
diff changeset
   656
  with no contrapositives, for ordinary resolution.*)
14744
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   657
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   658
(*Rules to convert the head literal into a negated assumption. If the head
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   659
  literal is already negated, then using notEfalse instead of notEfalse'
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   660
  prevents a double negation.*)
27239
f2f42f9fa09d pervasive RuleInsts;
wenzelm
parents: 27230
diff changeset
   661
val notEfalse = read_instantiate @{context} [(("R", 0), "False")] notE;
14744
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   662
val notEfalse' = rotate_prems 1 notEfalse;
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   663
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   664
fun negated_asm_of_head th =
14744
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   665
    th RS notEfalse handle THM _ => th RS notEfalse';
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   666
26066
19df083a2bbf make_meta_clause bugfix: now works for higher-order clauses like LeastI_ex
paulson
parents: 25710
diff changeset
   667
(*Converting one theorem from a disjunction to a meta-level clause*)
19df083a2bbf make_meta_clause bugfix: now works for higher-order clauses like LeastI_ex
paulson
parents: 25710
diff changeset
   668
fun make_meta_clause th =
19df083a2bbf make_meta_clause bugfix: now works for higher-order clauses like LeastI_ex
paulson
parents: 25710
diff changeset
   669
  let val (fth,thaw) = Drule.freeze_thaw_robust th
19df083a2bbf make_meta_clause bugfix: now works for higher-order clauses like LeastI_ex
paulson
parents: 25710
diff changeset
   670
  in  
19df083a2bbf make_meta_clause bugfix: now works for higher-order clauses like LeastI_ex
paulson
parents: 25710
diff changeset
   671
      (zero_var_indexes o Thm.varifyT o thaw 0 o 
19df083a2bbf make_meta_clause bugfix: now works for higher-order clauses like LeastI_ex
paulson
parents: 25710
diff changeset
   672
       negated_asm_of_head o make_horn resolution_clause_rules) fth
19df083a2bbf make_meta_clause bugfix: now works for higher-order clauses like LeastI_ex
paulson
parents: 25710
diff changeset
   673
  end;
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   674
14744
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   675
fun make_meta_clauses ths =
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   676
    name_thms "MClause#"
22360
26ead7ed4f4b moved eq_thm etc. to structure Thm in Pure/more_thm.ML;
wenzelm
parents: 22130
diff changeset
   677
      (distinct Thm.eq_thm_prop (map make_meta_clause ths));
14744
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   678
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   679
(*Permute a rule's premises to move the i-th premise to the last position.*)
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   680
fun make_last i th =
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   681
  let val n = nprems_of th
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   682
  in  if 1 <= i andalso i <= n
14744
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   683
      then Thm.permute_prems (i-1) 1 th
15118
e2bd080c7975 make_clauses now meta
paulson
parents: 15032
diff changeset
   684
      else raise THM("select_literal", i, [th])
14744
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   685
  end;
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   686
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   687
(*Maps a rule that ends "... ==> P ==> False" to "... ==> ~P" while suppressing
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   688
  double-negations.*)
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   689
val negate_head = rewrite_rule [atomize_not, not_not RS eq_reflection];
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   690
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   691
(*Maps the clause  [P1,...Pn]==>False to [P1,...,P(i-1),P(i+1),...Pn] ==> ~P*)
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   692
fun select_literal i cl = negate_head (make_last i cl);
7ccfc167e451 clauses for ordinary resolution
paulson
parents: 14733
diff changeset
   693
18508
paulson
parents: 18405
diff changeset
   694
14813
826edbc317e6 new skolemize_tac and skolemize method
paulson
parents: 14763
diff changeset
   695
(*Top-level Skolemization. Allows part of the conversion to clauses to be
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   696
  expressed as a tactic (or Isar method).  Each assumption of the selected
14813
826edbc317e6 new skolemize_tac and skolemize method
paulson
parents: 14763
diff changeset
   697
  goal is converted to NNF and then its existential quantifiers are pulled
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   698
  to the front. Finally, all existential quantifiers are eliminated,
14813
826edbc317e6 new skolemize_tac and skolemize method
paulson
parents: 14763
diff changeset
   699
  leaving !!-quantified variables. Perhaps Safe_tac should follow, but it
826edbc317e6 new skolemize_tac and skolemize method
paulson
parents: 14763
diff changeset
   700
  might generate many subgoals.*)
18194
940515d2fa26 -- removed "check_is_fol" from "make_nnf" so that the NNF procedure doesn't check whether a thm is FOL.
mengj
parents: 18175
diff changeset
   701
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   702
fun skolemize_tac ctxt = SUBGOAL (fn (goal, i) =>
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   703
  let val ts = Logic.strip_assums_hyp goal
24300
e170cee91c66 proper signature for Meson;
wenzelm
parents: 24040
diff changeset
   704
  in
32262
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   705
    EVERY'
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   706
     [OldGoals.METAHYPS (fn hyps =>
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   707
        (cut_facts_tac (skolemize_nnf_list ctxt hyps) 1
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   708
          THEN REPEAT (etac exE 1))),
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   709
      REPEAT_DETERM_N (length ts) o (etac thin_rl)] i
73cd8f74cf2a Meson.first_order_resolve: avoid handle _;
wenzelm
parents: 32231
diff changeset
   710
  end);
18194
940515d2fa26 -- removed "check_is_fol" from "make_nnf" so that the NNF procedure doesn't check whether a thm is FOL.
mengj
parents: 18175
diff changeset
   711
9840
9dfcb0224f8c meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff changeset
   712
end;