src/HOL/Tools/meson.ML
author wenzelm
Wed Jul 29 19:35:10 2009 +0200 (2009-07-29)
changeset 32262 73cd8f74cf2a
parent 32231 95b8afcbb0ed
child 32283 3bebc195c124
permissions -rw-r--r--
Meson.first_order_resolve: avoid handle _;
proper context for various Meson and Metis rules and tactics
unified meson_tac/meson_claset_tac;
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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 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 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. *)
paulson@24937
   289
local  
paulson@24937
   290
  val spec_var = Thm.dest_arg (Thm.dest_arg (#2 (Thm.dest_implies (Thm.cprop_of spec))));
paulson@24937
   291
  val spec_varT = #T (Thm.rep_cterm spec_var);
paulson@24937
   292
  fun name_of (Const ("All", _) $ Abs(x,_,_)) = x | name_of _ = Name.uu;
paulson@24937
   293
in  
paulson@24937
   294
  fun freeze_spec th ctxt =
paulson@24937
   295
    let
paulson@24937
   296
      val cert = Thm.cterm_of (ProofContext.theory_of ctxt);
paulson@24937
   297
      val ([x], ctxt') = Variable.variant_fixes [name_of (HOLogic.dest_Trueprop (concl_of th))] ctxt;
paulson@24937
   298
      val spec' = Thm.instantiate ([], [(spec_var, cert (Free (x, spec_varT)))]) spec;
paulson@24937
   299
    in (th RS spec', ctxt') end
paulson@24937
   300
end;
paulson@9840
   301
paulson@15998
   302
(*Used with METAHYPS below. There is one assumption, which gets bound to prem
paulson@15998
   303
  and then normalized via function nf. The normal form is given to resolve_tac,
paulson@22515
   304
  instantiate a Boolean variable created by resolution with disj_forward. Since
paulson@22515
   305
  (nf prem) returns a LIST of theorems, we can backtrack to get all combinations.*)
paulson@15579
   306
fun resop nf [prem] = resolve_tac (nf prem) 1;
paulson@9840
   307
wenzelm@24300
   308
(*Any need to extend this list with
wenzelm@26424
   309
  "HOL.type_class","HOL.eq_class","Pure.term"?*)
wenzelm@24300
   310
val has_meta_conn =
paulson@29684
   311
    exists_Const (member (op =) ["==", "==>", "=simp=>", "all", "prop"] o #1);
paulson@20417
   312
wenzelm@24300
   313
fun apply_skolem_ths (th, rls) =
paulson@20417
   314
  let fun tryall [] = raise THM("apply_skolem_ths", 0, th::rls)
paulson@20417
   315
        | tryall (rl::rls) = (first_order_resolve th rl handle THM _ => tryall rls)
paulson@20417
   316
  in  tryall rls  end;
paulson@22515
   317
paulson@15998
   318
(*Conjunctive normal form, adding clauses from th in front of ths (for foldr).
paulson@15998
   319
  Strips universal quantifiers and breaks up conjunctions.
paulson@15998
   320
  Eliminates existential quantifiers using skoths: Skolemization theorems.*)
paulson@24937
   321
fun cnf skoths ctxt (th,ths) =
paulson@24937
   322
  let val ctxtr = ref ctxt
paulson@24937
   323
      fun cnf_aux (th,ths) =
wenzelm@24300
   324
        if not (can HOLogic.dest_Trueprop (prop_of th)) then ths (*meta-level: ignore*)
wenzelm@24300
   325
        else if not (has_conns ["All","Ex","op &"] (prop_of th))
wenzelm@32262
   326
        then nodups ctxt th :: ths (*no work to do, terminate*)
wenzelm@24300
   327
        else case head_of (HOLogic.dest_Trueprop (concl_of th)) of
wenzelm@24300
   328
            Const ("op &", _) => (*conjunction*)
wenzelm@24300
   329
                cnf_aux (th RS conjunct1, cnf_aux (th RS conjunct2, ths))
wenzelm@24300
   330
          | Const ("All", _) => (*universal quantifier*)
paulson@24937
   331
                let val (th',ctxt') = freeze_spec th (!ctxtr)
paulson@24937
   332
                in  ctxtr := ctxt'; cnf_aux (th', ths) end
wenzelm@24300
   333
          | Const ("Ex", _) =>
wenzelm@24300
   334
              (*existential quantifier: Insert Skolem functions*)
wenzelm@24300
   335
              cnf_aux (apply_skolem_ths (th,skoths), ths)
wenzelm@24300
   336
          | Const ("op |", _) =>
wenzelm@24300
   337
              (*Disjunction of P, Q: Create new goal of proving ?P | ?Q and solve it using
wenzelm@24300
   338
                all combinations of converting P, Q to CNF.*)
wenzelm@24300
   339
              let val tac =
wenzelm@32262
   340
                  OldGoals.METAHYPS (resop cnf_nil) 1 THEN
wenzelm@32231
   341
                   (fn st' => st' |> OldGoals.METAHYPS (resop cnf_nil) 1)
wenzelm@24300
   342
              in  Seq.list_of (tac (th RS disj_forward)) @ ths  end
wenzelm@32262
   343
          | _ => nodups ctxt th :: ths  (*no work to do*)
paulson@19154
   344
      and cnf_nil th = cnf_aux (th,[])
paulson@24937
   345
      val cls = 
paulson@26562
   346
	    if too_many_clauses (SOME ctxt) (concl_of th)
wenzelm@32091
   347
	    then (warning ("cnf is ignoring: " ^ Display.string_of_thm ctxt th); ths)
paulson@24937
   348
	    else cnf_aux (th,ths)
paulson@24937
   349
  in  (cls, !ctxtr)  end;
paulson@22515
   350
paulson@24937
   351
fun make_cnf skoths th ctxt = cnf skoths ctxt (th, []);
paulson@20417
   352
paulson@20417
   353
(*Generalization, removal of redundant equalities, removal of tautologies.*)
paulson@24937
   354
fun finish_cnf ths = filter (not o is_taut) (map refl_clause ths);
paulson@9840
   355
paulson@9840
   356
paulson@15579
   357
(**** Generation of contrapositives ****)
paulson@9840
   358
wenzelm@24300
   359
fun is_left (Const ("Trueprop", _) $
paulson@21102
   360
               (Const ("op |", _) $ (Const ("op |", _) $ _ $ _) $ _)) = true
paulson@21102
   361
  | is_left _ = false;
wenzelm@24300
   362
paulson@15579
   363
(*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
wenzelm@24300
   364
fun assoc_right th =
paulson@21102
   365
  if is_left (prop_of th) then assoc_right (th RS disj_assoc)
paulson@21102
   366
  else th;
paulson@9840
   367
paulson@15579
   368
(*Must check for negative literal first!*)
paulson@15579
   369
val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
paulson@9840
   370
paulson@15579
   371
(*For ordinary resolution. *)
paulson@15579
   372
val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule'];
paulson@9840
   373
paulson@15579
   374
(*Create a goal or support clause, conclusing False*)
paulson@15579
   375
fun make_goal th =   (*Must check for negative literal first!*)
paulson@15579
   376
    make_goal (tryres(th, clause_rules))
paulson@15579
   377
  handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
paulson@9840
   378
paulson@15579
   379
(*Sort clauses by number of literals*)
paulson@15579
   380
fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2);
paulson@9840
   381
paulson@18389
   382
fun sort_clauses ths = sort (make_ord fewerlits) ths;
paulson@9840
   383
paulson@15581
   384
(*True if the given type contains bool anywhere*)
paulson@15581
   385
fun has_bool (Type("bool",_)) = true
paulson@15581
   386
  | has_bool (Type(_, Ts)) = exists has_bool Ts
paulson@15581
   387
  | has_bool _ = false;
wenzelm@24300
   388
wenzelm@24300
   389
(*Is the string the name of a connective? Really only | and Not can remain,
wenzelm@24300
   390
  since this code expects to be called on a clause form.*)
wenzelm@19875
   391
val is_conn = member (op =)
wenzelm@24300
   392
    ["Trueprop", "op &", "op |", "op -->", "Not",
paulson@15613
   393
     "All", "Ex", "Ball", "Bex"];
paulson@15613
   394
wenzelm@24300
   395
(*True if the term contains a function--not a logical connective--where the type
paulson@20524
   396
  of any argument contains bool.*)
wenzelm@24300
   397
val has_bool_arg_const =
paulson@15613
   398
    exists_Const
paulson@15613
   399
      (fn (c,T) => not(is_conn c) andalso exists (has_bool) (binder_types T));
paulson@22381
   400
wenzelm@24300
   401
(*A higher-order instance of a first-order constant? Example is the definition of
paulson@22381
   402
  HOL.one, 1, at a function type in theory SetsAndFunctions.*)
wenzelm@24300
   403
fun higher_inst_const thy (c,T) =
paulson@22381
   404
  case binder_types T of
paulson@22381
   405
      [] => false (*not a function type, OK*)
paulson@22381
   406
    | Ts => length (binder_types (Sign.the_const_type thy c)) <> length Ts;
paulson@22381
   407
paulson@24742
   408
(*Returns false if any Vars in the theorem mention type bool.
paulson@21102
   409
  Also rejects functions whose arguments are Booleans or other functions.*)
paulson@22381
   410
fun is_fol_term thy t =
paulson@22381
   411
    Term.is_first_order ["all","All","Ex"] t andalso
wenzelm@29267
   412
    not (exists_subterm (fn Var (_, T) => has_bool T | _ => false) t  orelse
wenzelm@24300
   413
         has_bool_arg_const t  orelse
wenzelm@24300
   414
         exists_Const (higher_inst_const thy) t orelse
wenzelm@24300
   415
         has_meta_conn t);
paulson@19204
   416
paulson@21102
   417
fun rigid t = not (is_Var (head_of t));
paulson@21102
   418
paulson@21102
   419
fun ok4horn (Const ("Trueprop",_) $ (Const ("op |", _) $ t $ _)) = rigid t
paulson@21102
   420
  | ok4horn (Const ("Trueprop",_) $ t) = rigid t
paulson@21102
   421
  | ok4horn _ = false;
paulson@21102
   422
paulson@15579
   423
(*Create a meta-level Horn clause*)
wenzelm@24300
   424
fun make_horn crules th =
wenzelm@24300
   425
  if ok4horn (concl_of th)
paulson@21102
   426
  then make_horn crules (tryres(th,crules)) handle THM _ => th
paulson@21102
   427
  else th;
paulson@9840
   428
paulson@16563
   429
(*Generate Horn clauses for all contrapositives of a clause. The input, th,
paulson@16563
   430
  is a HOL disjunction.*)
paulson@15579
   431
fun add_contras crules (th,hcs) =
paulson@15579
   432
  let fun rots (0,th) = hcs
wenzelm@24300
   433
        | rots (k,th) = zero_var_indexes (make_horn crules th) ::
wenzelm@24300
   434
                        rots(k-1, assoc_right (th RS disj_comm))
paulson@15862
   435
  in case nliterals(prop_of th) of
wenzelm@24300
   436
        1 => th::hcs
paulson@15579
   437
      | n => rots(n, assoc_right th)
paulson@15579
   438
  end;
paulson@9840
   439
paulson@15579
   440
(*Use "theorem naming" to label the clauses*)
paulson@15579
   441
fun name_thms label =
paulson@15579
   442
    let fun name1 (th, (k,ths)) =
wenzelm@27865
   443
          (k-1, Thm.put_name_hint (label ^ string_of_int k) th :: ths)
wenzelm@30190
   444
    in  fn ths => #2 (List.foldr name1 (length ths, []) ths)  end;
paulson@9840
   445
paulson@16563
   446
(*Is the given disjunction an all-negative support clause?*)
paulson@15579
   447
fun is_negative th = forall (not o #1) (literals (prop_of th));
paulson@9840
   448
paulson@15579
   449
val neg_clauses = List.filter is_negative;
paulson@9840
   450
paulson@9840
   451
paulson@15579
   452
(***** MESON PROOF PROCEDURE *****)
paulson@9840
   453
paulson@15579
   454
fun rhyps (Const("==>",_) $ (Const("Trueprop",_) $ A) $ phi,
wenzelm@24300
   455
           As) = rhyps(phi, A::As)
paulson@15579
   456
  | rhyps (_, As) = As;
paulson@9840
   457
paulson@15579
   458
(** Detecting repeated assumptions in a subgoal **)
paulson@9840
   459
paulson@15579
   460
(*The stringtree detects repeated assumptions.*)
wenzelm@16801
   461
fun ins_term (net,t) = Net.insert_term (op aconv) (t,t) net;
paulson@9840
   462
paulson@15579
   463
(*detects repetitions in a list of terms*)
paulson@15579
   464
fun has_reps [] = false
paulson@15579
   465
  | has_reps [_] = false
paulson@15579
   466
  | has_reps [t,u] = (t aconv u)
paulson@15579
   467
  | has_reps ts = (Library.foldl ins_term (Net.empty, ts);  false)
wenzelm@24300
   468
                  handle Net.INSERT => true;
paulson@9840
   469
paulson@15579
   470
(*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*)
paulson@18508
   471
fun TRYING_eq_assume_tac 0 st = Seq.single st
paulson@18508
   472
  | TRYING_eq_assume_tac i st =
wenzelm@31945
   473
       TRYING_eq_assume_tac (i-1) (Thm.eq_assumption i st)
paulson@18508
   474
       handle THM _ => TRYING_eq_assume_tac (i-1) st;
paulson@18508
   475
paulson@18508
   476
fun TRYALL_eq_assume_tac st = TRYING_eq_assume_tac (nprems_of st) st;
paulson@9840
   477
paulson@15579
   478
(*Loop checking: FAIL if trying to prove the same thing twice
paulson@15579
   479
  -- if *ANY* subgoal has repeated literals*)
paulson@15579
   480
fun check_tac st =
paulson@15579
   481
  if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st)
paulson@15579
   482
  then  Seq.empty  else  Seq.single st;
paulson@9840
   483
paulson@9840
   484
paulson@15579
   485
(* net_resolve_tac actually made it slower... *)
paulson@15579
   486
fun prolog_step_tac horns i =
paulson@15579
   487
    (assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
paulson@18508
   488
    TRYALL_eq_assume_tac;
paulson@9840
   489
paulson@9840
   490
(*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*)
paulson@15579
   491
fun addconcl(prem,sz) = size_of_term(Logic.strip_assums_concl prem) + sz
paulson@15579
   492
wenzelm@30190
   493
fun size_of_subgoals st = List.foldr addconcl 0 (prems_of st);
paulson@15579
   494
paulson@9840
   495
paulson@9840
   496
(*Negation Normal Form*)
paulson@9840
   497
val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD,
wenzelm@9869
   498
               not_impD, not_iffD, not_allD, not_exD, not_notD];
paulson@15581
   499
paulson@21102
   500
fun ok4nnf (Const ("Trueprop",_) $ (Const ("Not", _) $ t)) = rigid t
paulson@21102
   501
  | ok4nnf (Const ("Trueprop",_) $ t) = rigid t
paulson@21102
   502
  | ok4nnf _ = false;
paulson@21102
   503
wenzelm@32262
   504
fun make_nnf1 ctxt th =
wenzelm@24300
   505
  if ok4nnf (concl_of th)
wenzelm@32262
   506
  then make_nnf1 ctxt (tryres(th, nnf_rls))
paulson@28174
   507
    handle THM ("tryres", _, _) =>
wenzelm@32262
   508
        forward_res ctxt (make_nnf1 ctxt)
wenzelm@9869
   509
           (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
paulson@28174
   510
    handle THM ("tryres", _, _) => th
paulson@21102
   511
  else th;
paulson@9840
   512
wenzelm@24300
   513
(*The simplification removes defined quantifiers and occurrences of True and False.
paulson@20018
   514
  nnf_ss also includes the one-point simprocs,
paulson@18405
   515
  which are needed to avoid the various one-point theorems from generating junk clauses.*)
paulson@19894
   516
val nnf_simps =
wenzelm@24300
   517
     [simp_implies_def, Ex1_def, Ball_def, Bex_def, if_True,
paulson@19894
   518
      if_False, if_cancel, if_eq_cancel, cases_simp];
paulson@19894
   519
val nnf_extra_simps =
paulson@19894
   520
      thms"split_ifs" @ ex_simps @ all_simps @ simp_thms;
paulson@18405
   521
paulson@18405
   522
val nnf_ss =
wenzelm@24300
   523
  HOL_basic_ss addsimps nnf_extra_simps
wenzelm@24040
   524
    addsimprocs [defALL_regroup,defEX_regroup, @{simproc neq}, @{simproc let_simp}];
paulson@15872
   525
wenzelm@32262
   526
fun make_nnf ctxt th = case prems_of th of
paulson@21050
   527
    [] => th |> rewrite_rule (map safe_mk_meta_eq nnf_simps)
wenzelm@24300
   528
             |> simplify nnf_ss
wenzelm@32262
   529
             |> make_nnf1 ctxt
paulson@21050
   530
  | _ => raise THM ("make_nnf: premises in argument", 0, [th]);
paulson@15581
   531
paulson@15965
   532
(*Pull existential quantifiers to front. This accomplishes Skolemization for
paulson@15965
   533
  clauses that arise from a subgoal.*)
wenzelm@32262
   534
fun skolemize1 ctxt th =
paulson@20134
   535
  if not (has_conns ["Ex"] (prop_of th)) then th
wenzelm@32262
   536
  else (skolemize1 ctxt (tryres(th, [choice, conj_exD1, conj_exD2,
quigley@15679
   537
                              disj_exD, disj_exD1, disj_exD2])))
paulson@28174
   538
    handle THM ("tryres", _, _) =>
wenzelm@32262
   539
        skolemize1 ctxt (forward_res ctxt (skolemize1 ctxt)
wenzelm@9869
   540
                   (tryres (th, [conj_forward, disj_forward, all_forward])))
paulson@28174
   541
    handle THM ("tryres", _, _) => 
wenzelm@32262
   542
        forward_res ctxt (skolemize1 ctxt) (rename_bvs_RS th ex_forward);
paulson@29684
   543
wenzelm@32262
   544
fun skolemize ctxt th = skolemize1 ctxt (make_nnf ctxt th);
paulson@9840
   545
wenzelm@32262
   546
fun skolemize_nnf_list _ [] = []
wenzelm@32262
   547
  | skolemize_nnf_list ctxt (th::ths) =
wenzelm@32262
   548
      skolemize ctxt th :: skolemize_nnf_list ctxt ths
paulson@25710
   549
      handle THM _ => (*RS can fail if Unify.search_bound is too small*)
wenzelm@32262
   550
       (warning ("Failed to Skolemize " ^ Display.string_of_thm ctxt th);
wenzelm@32262
   551
        skolemize_nnf_list ctxt ths);
paulson@25694
   552
paulson@24937
   553
fun add_clauses (th,cls) =
paulson@24937
   554
  let val ctxt0 = Variable.thm_context th
paulson@24937
   555
      val (cnfs,ctxt) = make_cnf [] th ctxt0
paulson@24937
   556
  in Variable.export ctxt ctxt0 cnfs @ cls end;
paulson@9840
   557
paulson@9840
   558
(*Make clauses from a list of theorems, previously Skolemized and put into nnf.
paulson@9840
   559
  The resulting clauses are HOL disjunctions.*)
wenzelm@30190
   560
fun make_clauses ths = sort_clauses (List.foldr add_clauses [] ths);
quigley@15773
   561
paulson@16563
   562
(*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*)
wenzelm@9869
   563
fun make_horns ths =
paulson@9840
   564
    name_thms "Horn#"
wenzelm@30190
   565
      (distinct Thm.eq_thm_prop (List.foldr (add_contras clause_rules) [] ths));
paulson@9840
   566
paulson@9840
   567
(*Could simply use nprems_of, which would count remaining subgoals -- no
paulson@9840
   568
  discrimination as to their size!  With BEST_FIRST, fails for problem 41.*)
paulson@9840
   569
wenzelm@9869
   570
fun best_prolog_tac sizef horns =
paulson@9840
   571
    BEST_FIRST (has_fewer_prems 1, sizef) (prolog_step_tac horns 1);
paulson@9840
   572
wenzelm@9869
   573
fun depth_prolog_tac horns =
paulson@9840
   574
    DEPTH_FIRST (has_fewer_prems 1) (prolog_step_tac horns 1);
paulson@9840
   575
paulson@9840
   576
(*Return all negative clauses, as possible goal clauses*)
paulson@9840
   577
fun gocls cls = name_thms "Goal#" (map make_goal (neg_clauses cls));
paulson@9840
   578
wenzelm@32262
   579
fun skolemize_prems_tac ctxt prems =
wenzelm@32262
   580
    cut_facts_tac (skolemize_nnf_list ctxt prems) THEN'
paulson@9840
   581
    REPEAT o (etac exE);
paulson@9840
   582
paulson@22546
   583
(*Basis of all meson-tactics.  Supplies cltac with clauses: HOL disjunctions.
paulson@22546
   584
  Function mkcl converts theorems to clauses.*)
wenzelm@32262
   585
fun MESON mkcl cltac ctxt i st =
paulson@16588
   586
  SELECT_GOAL
wenzelm@23590
   587
    (EVERY [ObjectLogic.atomize_prems_tac 1,
paulson@23552
   588
            rtac ccontr 1,
wenzelm@32262
   589
            FOCUS (fn {context = ctxt', prems = negs, ...} =>
wenzelm@32262
   590
                      EVERY1 [skolemize_prems_tac ctxt negs,
wenzelm@32262
   591
                              FOCUS (cltac o mkcl o #prems) ctxt']) ctxt 1]) i st
wenzelm@24300
   592
  handle THM _ => no_tac st;    (*probably from make_meta_clause, not first-order*)
paulson@9840
   593
paulson@9840
   594
(** Best-first search versions **)
paulson@9840
   595
paulson@16563
   596
(*ths is a list of additional clauses (HOL disjunctions) to use.*)
wenzelm@9869
   597
fun best_meson_tac sizef =
wenzelm@24300
   598
  MESON make_clauses
paulson@22546
   599
    (fn cls =>
paulson@9840
   600
         THEN_BEST_FIRST (resolve_tac (gocls cls) 1)
paulson@9840
   601
                         (has_fewer_prems 1, sizef)
paulson@9840
   602
                         (prolog_step_tac (make_horns cls) 1));
paulson@9840
   603
paulson@9840
   604
(*First, breaks the goal into independent units*)
wenzelm@32262
   605
fun safe_best_meson_tac ctxt =
wenzelm@32262
   606
     SELECT_GOAL (TRY (safe_tac (claset_of ctxt)) THEN
wenzelm@32262
   607
                  TRYALL (best_meson_tac size_of_subgoals ctxt));
paulson@9840
   608
paulson@9840
   609
(** Depth-first search version **)
paulson@9840
   610
paulson@9840
   611
val depth_meson_tac =
paulson@22546
   612
  MESON make_clauses
paulson@22546
   613
    (fn cls => EVERY [resolve_tac (gocls cls) 1, depth_prolog_tac (make_horns cls)]);
paulson@9840
   614
paulson@9840
   615
paulson@9840
   616
(** Iterative deepening version **)
paulson@9840
   617
paulson@9840
   618
(*This version does only one inference per call;
paulson@9840
   619
  having only one eq_assume_tac speeds it up!*)
wenzelm@9869
   620
fun prolog_step_tac' horns =
paulson@9840
   621
    let val (horn0s, hornps) = (*0 subgoals vs 1 or more*)
paulson@9840
   622
            take_prefix Thm.no_prems horns
paulson@9840
   623
        val nrtac = net_resolve_tac horns
paulson@9840
   624
    in  fn i => eq_assume_tac i ORELSE
paulson@9840
   625
                match_tac horn0s i ORELSE  (*no backtracking if unit MATCHES*)
paulson@9840
   626
                ((assume_tac i APPEND nrtac i) THEN check_tac)
paulson@9840
   627
    end;
paulson@9840
   628
wenzelm@9869
   629
fun iter_deepen_prolog_tac horns =
paulson@9840
   630
    ITER_DEEPEN (has_fewer_prems 1) (prolog_step_tac' horns);
paulson@9840
   631
wenzelm@32262
   632
fun iter_deepen_meson_tac ctxt ths = ctxt |> MESON make_clauses
wenzelm@32091
   633
  (fn cls =>
wenzelm@32091
   634
    (case (gocls (cls @ ths)) of
wenzelm@32091
   635
      [] => no_tac  (*no goal clauses*)
wenzelm@32091
   636
    | goes =>
wenzelm@32091
   637
        let
wenzelm@32091
   638
          val horns = make_horns (cls @ ths)
wenzelm@32091
   639
          val _ = Output.debug (fn () =>
wenzelm@32091
   640
            cat_lines ("meson method called:" ::
wenzelm@32262
   641
              map (Display.string_of_thm ctxt) (cls @ ths) @
wenzelm@32262
   642
              ["clauses:"] @ map (Display.string_of_thm ctxt) horns))
wenzelm@32091
   643
        in THEN_ITER_DEEPEN (resolve_tac goes 1) (has_fewer_prems 1) (prolog_step_tac' horns) end));
paulson@9840
   644
wenzelm@32262
   645
fun meson_tac ctxt ths =
wenzelm@32262
   646
  SELECT_GOAL (TRY (safe_tac (claset_of ctxt)) THEN TRYALL (iter_deepen_meson_tac ctxt ths));
wenzelm@9869
   647
wenzelm@9869
   648
paulson@14813
   649
(**** Code to support ordinary resolution, rather than Model Elimination ****)
paulson@14744
   650
wenzelm@24300
   651
(*Convert a list of clauses (disjunctions) to meta-level clauses (==>),
paulson@15008
   652
  with no contrapositives, for ordinary resolution.*)
paulson@14744
   653
paulson@14744
   654
(*Rules to convert the head literal into a negated assumption. If the head
paulson@14744
   655
  literal is already negated, then using notEfalse instead of notEfalse'
paulson@14744
   656
  prevents a double negation.*)
wenzelm@27239
   657
val notEfalse = read_instantiate @{context} [(("R", 0), "False")] notE;
paulson@14744
   658
val notEfalse' = rotate_prems 1 notEfalse;
paulson@14744
   659
wenzelm@24300
   660
fun negated_asm_of_head th =
paulson@14744
   661
    th RS notEfalse handle THM _ => th RS notEfalse';
paulson@14744
   662
paulson@26066
   663
(*Converting one theorem from a disjunction to a meta-level clause*)
paulson@26066
   664
fun make_meta_clause th =
paulson@26066
   665
  let val (fth,thaw) = Drule.freeze_thaw_robust th
paulson@26066
   666
  in  
paulson@26066
   667
      (zero_var_indexes o Thm.varifyT o thaw 0 o 
paulson@26066
   668
       negated_asm_of_head o make_horn resolution_clause_rules) fth
paulson@26066
   669
  end;
wenzelm@24300
   670
paulson@14744
   671
fun make_meta_clauses ths =
paulson@14744
   672
    name_thms "MClause#"
wenzelm@22360
   673
      (distinct Thm.eq_thm_prop (map make_meta_clause ths));
paulson@14744
   674
paulson@14744
   675
(*Permute a rule's premises to move the i-th premise to the last position.*)
paulson@14744
   676
fun make_last i th =
wenzelm@24300
   677
  let val n = nprems_of th
wenzelm@24300
   678
  in  if 1 <= i andalso i <= n
paulson@14744
   679
      then Thm.permute_prems (i-1) 1 th
paulson@15118
   680
      else raise THM("select_literal", i, [th])
paulson@14744
   681
  end;
paulson@14744
   682
paulson@14744
   683
(*Maps a rule that ends "... ==> P ==> False" to "... ==> ~P" while suppressing
paulson@14744
   684
  double-negations.*)
paulson@14744
   685
val negate_head = rewrite_rule [atomize_not, not_not RS eq_reflection];
paulson@14744
   686
paulson@14744
   687
(*Maps the clause  [P1,...Pn]==>False to [P1,...,P(i-1),P(i+1),...Pn] ==> ~P*)
paulson@14744
   688
fun select_literal i cl = negate_head (make_last i cl);
paulson@14744
   689
paulson@18508
   690
paulson@14813
   691
(*Top-level Skolemization. Allows part of the conversion to clauses to be
wenzelm@24300
   692
  expressed as a tactic (or Isar method).  Each assumption of the selected
paulson@14813
   693
  goal is converted to NNF and then its existential quantifiers are pulled
wenzelm@24300
   694
  to the front. Finally, all existential quantifiers are eliminated,
paulson@14813
   695
  leaving !!-quantified variables. Perhaps Safe_tac should follow, but it
paulson@14813
   696
  might generate many subgoals.*)
mengj@18194
   697
wenzelm@32262
   698
fun skolemize_tac ctxt = SUBGOAL (fn (goal, i) =>
wenzelm@32262
   699
  let val ts = Logic.strip_assums_hyp goal
wenzelm@24300
   700
  in
wenzelm@32262
   701
    EVERY'
wenzelm@32262
   702
     [OldGoals.METAHYPS (fn hyps =>
wenzelm@32262
   703
        (cut_facts_tac (skolemize_nnf_list ctxt hyps) 1
wenzelm@32262
   704
          THEN REPEAT (etac exE 1))),
wenzelm@32262
   705
      REPEAT_DETERM_N (length ts) o (etac thin_rl)] i
wenzelm@32262
   706
  end);
mengj@18194
   707
paulson@9840
   708
end;