src/HOL/Tools/meson.ML
author blanchet
Wed Sep 29 22:23:27 2010 +0200 (2010-09-29)
changeset 39886 8a9f0c97d550
parent 39328 268cd501bdc1
child 39893 25a339e1ff9b
permissions -rw-r--r--
first step towards a new skolemizer that doesn't require "Eps"
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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 flexflex_first_order: thm -> thm
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  val size_of_subgoals: thm -> int
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  val has_too_many_clauses: Proof.context -> 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 presimplify: thm -> thm
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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_unsorted: thm list -> thm list
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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:
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    tactic -> (thm list -> thm list) -> (thm list -> tactic) -> Proof.context
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    -> 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 "meson_max_clauses" (K max_clauses_default);
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(*No known example (on 1-5-2007) needs even thirty*)
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val iter_deepen_limit = 50;
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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 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 tenv =
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            Pattern.first_order_match thy (tmB, tmA)
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                                          (Vartab.empty, Vartab.empty) |> snd
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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 Thm.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 (_, 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 (Misc_Legacy.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 _) = false
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        | has (Const(@{const_name Trueprop},_) $ p) = has p
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        | has (Const(@{const_name Not},_) $ p) = has p
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        | has (Const(@{const_name HOL.disj},_) $ p $ q) = member (op =) bs @{const_name HOL.disj} orelse has p orelse has q
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        | has (Const(@{const_name HOL.conj},_) $ p $ q) = member (op =) bs @{const_name HOL.conj} orelse has p orelse has q
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        | has (Const(@{const_name All},_) $ Abs(_,_,p)) = member (op =) bs @{const_name All} orelse has p
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        | has (Const(@{const_name Ex},_) $ Abs(_,_,p)) = member (op =) bs @{const_name 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(@{const_name Trueprop},_) $ P) = literals P
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  | literals (Const(@{const_name HOL.disj},_) $ P $ Q) = literals P @ literals Q
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  | literals (Const(@{const_name 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 (@{const_name HOL.disj}, _) $ 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(@{const_name 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(@{const_name HOL.eq},_) $ t $ u) = t aconv u
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  | taut_poslit (Const(@{const_name 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 (@{const_name HOL.disj}, _) $ (Const (@{const_name HOL.disj}, _) $ _ $ _) $ _) =>
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            refl_clause_aux n (th RS disj_assoc)    (*isolate an atom as first disjunct*)
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        | (Const (@{const_name HOL.disj}, _) $ (Const(@{const_name Not},_) $ (Const(@{const_name HOL.eq},_) $ 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 (@{const_name HOL.disj}, _) $ _ $ _) => 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 (@{const_name HOL.disj}, _) $ P $ Q) =
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      notequal_lits_count P + notequal_lits_count Q
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  | notequal_lits_count (Const(@{const_name Not},_) $ (Const(@{const_name HOL.eq},_) $ _ $ _)) = 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 nf hyps st =
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  case Seq.pull
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        (REPEAT
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         (Misc_Legacy.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 (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 estimated_num_clauses bound t =
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 let
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  fun sum x y = if x < bound andalso y < bound then x+y else bound
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  fun prod x y = if x < bound andalso y < bound then x*y else bound
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  (*Estimate the number of clauses in order to detect infeasible theorems*)
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  fun signed_nclauses b (Const(@{const_name Trueprop},_) $ t) = signed_nclauses b t
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    | signed_nclauses b (Const(@{const_name Not},_) $ t) = signed_nclauses (not b) t
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    | signed_nclauses b (Const(@{const_name HOL.conj},_) $ 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(@{const_name HOL.disj},_) $ 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(@{const_name HOL.implies},_) $ 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(@{const_name HOL.eq}, 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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   287
        else 1
haftmann@38557
   288
    | signed_nclauses b (Const(@{const_name Ex}, _) $ Abs (_,_,t)) = signed_nclauses b t
haftmann@38557
   289
    | signed_nclauses b (Const(@{const_name All},_) $ Abs (_,_,t)) = signed_nclauses b t
paulson@26562
   290
    | signed_nclauses _ _ = 1; (* literal *)
blanchet@39269
   291
 in signed_nclauses true t end
blanchet@39269
   292
blanchet@39269
   293
fun has_too_many_clauses ctxt t =
blanchet@39269
   294
  let val max_cl = Config.get ctxt max_clauses in
blanchet@39328
   295
    estimated_num_clauses (max_cl + 1) t > max_cl
blanchet@39269
   296
  end
paulson@19894
   297
paulson@15579
   298
(*Replaces universally quantified variables by FREE variables -- because
paulson@24937
   299
  assumptions may not contain scheme variables.  Later, generalize using Variable.export. *)
paulson@24937
   300
local  
paulson@24937
   301
  val spec_var = Thm.dest_arg (Thm.dest_arg (#2 (Thm.dest_implies (Thm.cprop_of spec))));
paulson@24937
   302
  val spec_varT = #T (Thm.rep_cterm spec_var);
haftmann@38557
   303
  fun name_of (Const (@{const_name All}, _) $ Abs(x,_,_)) = x | name_of _ = Name.uu;
paulson@24937
   304
in  
paulson@24937
   305
  fun freeze_spec th ctxt =
paulson@24937
   306
    let
paulson@24937
   307
      val cert = Thm.cterm_of (ProofContext.theory_of ctxt);
paulson@24937
   308
      val ([x], ctxt') = Variable.variant_fixes [name_of (HOLogic.dest_Trueprop (concl_of th))] ctxt;
paulson@24937
   309
      val spec' = Thm.instantiate ([], [(spec_var, cert (Free (x, spec_varT)))]) spec;
paulson@24937
   310
    in (th RS spec', ctxt') end
paulson@24937
   311
end;
paulson@9840
   312
paulson@15998
   313
(*Used with METAHYPS below. There is one assumption, which gets bound to prem
paulson@15998
   314
  and then normalized via function nf. The normal form is given to resolve_tac,
paulson@22515
   315
  instantiate a Boolean variable created by resolution with disj_forward. Since
paulson@22515
   316
  (nf prem) returns a LIST of theorems, we can backtrack to get all combinations.*)
paulson@15579
   317
fun resop nf [prem] = resolve_tac (nf prem) 1;
paulson@9840
   318
blanchet@39037
   319
(* Any need to extend this list with "HOL.type_class", "HOL.eq_class",
blanchet@39037
   320
   and "Pure.term"? *)
haftmann@38557
   321
val has_meta_conn = exists_Const (member (op =) ["==", "==>", "=simp=>", "all", "prop"] o #1);
paulson@20417
   322
blanchet@37410
   323
fun apply_skolem_theorem (th, rls) =
blanchet@37398
   324
  let
blanchet@37410
   325
    fun tryall [] = raise THM ("apply_skolem_theorem", 0, th::rls)
blanchet@37398
   326
      | tryall (rl :: rls) =
blanchet@37398
   327
        first_order_resolve th rl handle THM _ => tryall rls
blanchet@37398
   328
  in tryall rls end
paulson@22515
   329
blanchet@37410
   330
(* Conjunctive normal form, adding clauses from th in front of ths (for foldr).
blanchet@37410
   331
   Strips universal quantifiers and breaks up conjunctions.
blanchet@37410
   332
   Eliminates existential quantifiers using Skolemization theorems. *)
blanchet@39886
   333
fun cnf old_skolem_ths ctxt (th, ths) =
wenzelm@33222
   334
  let val ctxtr = Unsynchronized.ref ctxt   (* FIXME ??? *)
paulson@24937
   335
      fun cnf_aux (th,ths) =
wenzelm@24300
   336
        if not (can HOLogic.dest_Trueprop (prop_of th)) then ths (*meta-level: ignore*)
haftmann@38795
   337
        else if not (has_conns [@{const_name All}, @{const_name Ex}, @{const_name HOL.conj}] (prop_of th))
wenzelm@32262
   338
        then nodups ctxt th :: ths (*no work to do, terminate*)
wenzelm@24300
   339
        else case head_of (HOLogic.dest_Trueprop (concl_of th)) of
haftmann@38795
   340
            Const (@{const_name HOL.conj}, _) => (*conjunction*)
wenzelm@24300
   341
                cnf_aux (th RS conjunct1, cnf_aux (th RS conjunct2, ths))
haftmann@38557
   342
          | Const (@{const_name All}, _) => (*universal quantifier*)
paulson@24937
   343
                let val (th',ctxt') = freeze_spec th (!ctxtr)
paulson@24937
   344
                in  ctxtr := ctxt'; cnf_aux (th', ths) end
haftmann@38557
   345
          | Const (@{const_name Ex}, _) =>
wenzelm@24300
   346
              (*existential quantifier: Insert Skolem functions*)
blanchet@39886
   347
              cnf_aux (apply_skolem_theorem (th, old_skolem_ths), ths)
haftmann@38795
   348
          | Const (@{const_name HOL.disj}, _) =>
wenzelm@24300
   349
              (*Disjunction of P, Q: Create new goal of proving ?P | ?Q and solve it using
wenzelm@24300
   350
                all combinations of converting P, Q to CNF.*)
wenzelm@24300
   351
              let val tac =
wenzelm@37781
   352
                  Misc_Legacy.METAHYPS (resop cnf_nil) 1 THEN
wenzelm@37781
   353
                   (fn st' => st' |> Misc_Legacy.METAHYPS (resop cnf_nil) 1)
wenzelm@24300
   354
              in  Seq.list_of (tac (th RS disj_forward)) @ ths  end
wenzelm@32262
   355
          | _ => nodups ctxt th :: ths  (*no work to do*)
paulson@19154
   356
      and cnf_nil th = cnf_aux (th,[])
blanchet@39269
   357
      val cls =
blanchet@39269
   358
            if has_too_many_clauses ctxt (concl_of th)
wenzelm@32960
   359
            then (trace_msg (fn () => "cnf is ignoring: " ^ Display.string_of_thm ctxt th); ths)
wenzelm@32960
   360
            else cnf_aux (th,ths)
paulson@24937
   361
  in  (cls, !ctxtr)  end;
paulson@22515
   362
blanchet@39886
   363
fun make_cnf old_skolem_ths th ctxt = cnf old_skolem_ths ctxt (th, [])
paulson@20417
   364
paulson@20417
   365
(*Generalization, removal of redundant equalities, removal of tautologies.*)
paulson@24937
   366
fun finish_cnf ths = filter (not o is_taut) (map refl_clause ths);
paulson@9840
   367
paulson@9840
   368
paulson@15579
   369
(**** Generation of contrapositives ****)
paulson@9840
   370
haftmann@38557
   371
fun is_left (Const (@{const_name Trueprop}, _) $
haftmann@38795
   372
               (Const (@{const_name HOL.disj}, _) $ (Const (@{const_name HOL.disj}, _) $ _ $ _) $ _)) = true
paulson@21102
   373
  | is_left _ = false;
wenzelm@24300
   374
paulson@15579
   375
(*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
wenzelm@24300
   376
fun assoc_right th =
paulson@21102
   377
  if is_left (prop_of th) then assoc_right (th RS disj_assoc)
paulson@21102
   378
  else th;
paulson@9840
   379
paulson@15579
   380
(*Must check for negative literal first!*)
paulson@15579
   381
val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
paulson@9840
   382
paulson@15579
   383
(*For ordinary resolution. *)
paulson@15579
   384
val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule'];
paulson@9840
   385
paulson@15579
   386
(*Create a goal or support clause, conclusing False*)
paulson@15579
   387
fun make_goal th =   (*Must check for negative literal first!*)
paulson@15579
   388
    make_goal (tryres(th, clause_rules))
paulson@15579
   389
  handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
paulson@9840
   390
paulson@15579
   391
(*Sort clauses by number of literals*)
paulson@15579
   392
fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2);
paulson@9840
   393
paulson@18389
   394
fun sort_clauses ths = sort (make_ord fewerlits) ths;
paulson@9840
   395
blanchet@38099
   396
fun has_bool @{typ bool} = true
blanchet@38099
   397
  | has_bool (Type (_, Ts)) = exists has_bool Ts
blanchet@38099
   398
  | has_bool _ = false
blanchet@38099
   399
blanchet@38099
   400
fun has_fun (Type (@{type_name fun}, _)) = true
blanchet@38099
   401
  | has_fun (Type (_, Ts)) = exists has_fun Ts
blanchet@38099
   402
  | has_fun _ = false
wenzelm@24300
   403
wenzelm@24300
   404
(*Is the string the name of a connective? Really only | and Not can remain,
wenzelm@24300
   405
  since this code expects to be called on a clause form.*)
wenzelm@19875
   406
val is_conn = member (op =)
haftmann@38795
   407
    [@{const_name Trueprop}, @{const_name HOL.conj}, @{const_name HOL.disj},
haftmann@38786
   408
     @{const_name HOL.implies}, @{const_name Not},
haftmann@38557
   409
     @{const_name All}, @{const_name Ex}, @{const_name Ball}, @{const_name Bex}];
paulson@15613
   410
wenzelm@24300
   411
(*True if the term contains a function--not a logical connective--where the type
paulson@20524
   412
  of any argument contains bool.*)
wenzelm@24300
   413
val has_bool_arg_const =
paulson@15613
   414
    exists_Const
blanchet@38099
   415
      (fn (c,T) => not(is_conn c) andalso exists has_bool (binder_types T));
paulson@22381
   416
wenzelm@24300
   417
(*A higher-order instance of a first-order constant? Example is the definition of
haftmann@38622
   418
  one, 1, at a function type in theory Function_Algebras.*)
wenzelm@24300
   419
fun higher_inst_const thy (c,T) =
paulson@22381
   420
  case binder_types T of
paulson@22381
   421
      [] => false (*not a function type, OK*)
paulson@22381
   422
    | Ts => length (binder_types (Sign.the_const_type thy c)) <> length Ts;
paulson@22381
   423
paulson@24742
   424
(*Returns false if any Vars in the theorem mention type bool.
paulson@21102
   425
  Also rejects functions whose arguments are Booleans or other functions.*)
paulson@22381
   426
fun is_fol_term thy t =
haftmann@38557
   427
    Term.is_first_order ["all", @{const_name All}, @{const_name Ex}] t andalso
blanchet@38099
   428
    not (exists_subterm (fn Var (_, T) => has_bool T orelse has_fun T
blanchet@38099
   429
                           | _ => false) t orelse
blanchet@38099
   430
         has_bool_arg_const t orelse
wenzelm@24300
   431
         exists_Const (higher_inst_const thy) t orelse
wenzelm@24300
   432
         has_meta_conn t);
paulson@19204
   433
paulson@21102
   434
fun rigid t = not (is_Var (head_of t));
paulson@21102
   435
haftmann@38795
   436
fun ok4horn (Const (@{const_name Trueprop},_) $ (Const (@{const_name HOL.disj}, _) $ t $ _)) = rigid t
haftmann@38557
   437
  | ok4horn (Const (@{const_name Trueprop},_) $ t) = rigid t
paulson@21102
   438
  | ok4horn _ = false;
paulson@21102
   439
paulson@15579
   440
(*Create a meta-level Horn clause*)
wenzelm@24300
   441
fun make_horn crules th =
wenzelm@24300
   442
  if ok4horn (concl_of th)
paulson@21102
   443
  then make_horn crules (tryres(th,crules)) handle THM _ => th
paulson@21102
   444
  else th;
paulson@9840
   445
paulson@16563
   446
(*Generate Horn clauses for all contrapositives of a clause. The input, th,
paulson@16563
   447
  is a HOL disjunction.*)
wenzelm@33339
   448
fun add_contras crules th hcs =
blanchet@39328
   449
  let fun rots (0,_) = hcs
wenzelm@24300
   450
        | rots (k,th) = zero_var_indexes (make_horn crules th) ::
wenzelm@24300
   451
                        rots(k-1, assoc_right (th RS disj_comm))
paulson@15862
   452
  in case nliterals(prop_of th) of
wenzelm@24300
   453
        1 => th::hcs
paulson@15579
   454
      | n => rots(n, assoc_right th)
paulson@15579
   455
  end;
paulson@9840
   456
paulson@15579
   457
(*Use "theorem naming" to label the clauses*)
paulson@15579
   458
fun name_thms label =
wenzelm@33339
   459
    let fun name1 th (k, ths) =
wenzelm@27865
   460
          (k-1, Thm.put_name_hint (label ^ string_of_int k) th :: ths)
wenzelm@33339
   461
    in  fn ths => #2 (fold_rev name1 ths (length ths, []))  end;
paulson@9840
   462
paulson@16563
   463
(*Is the given disjunction an all-negative support clause?*)
paulson@15579
   464
fun is_negative th = forall (not o #1) (literals (prop_of th));
paulson@9840
   465
wenzelm@33317
   466
val neg_clauses = filter is_negative;
paulson@9840
   467
paulson@9840
   468
paulson@15579
   469
(***** MESON PROOF PROCEDURE *****)
paulson@9840
   470
haftmann@38557
   471
fun rhyps (Const("==>",_) $ (Const(@{const_name Trueprop},_) $ A) $ phi,
wenzelm@24300
   472
           As) = rhyps(phi, A::As)
paulson@15579
   473
  | rhyps (_, As) = As;
paulson@9840
   474
paulson@15579
   475
(** Detecting repeated assumptions in a subgoal **)
paulson@9840
   476
paulson@15579
   477
(*The stringtree detects repeated assumptions.*)
wenzelm@33245
   478
fun ins_term t net = Net.insert_term (op aconv) (t, t) net;
paulson@9840
   479
paulson@15579
   480
(*detects repetitions in a list of terms*)
paulson@15579
   481
fun has_reps [] = false
paulson@15579
   482
  | has_reps [_] = false
paulson@15579
   483
  | has_reps [t,u] = (t aconv u)
wenzelm@33245
   484
  | has_reps ts = (fold ins_term ts Net.empty; false) handle Net.INSERT => true;
paulson@9840
   485
paulson@15579
   486
(*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*)
paulson@18508
   487
fun TRYING_eq_assume_tac 0 st = Seq.single st
paulson@18508
   488
  | TRYING_eq_assume_tac i st =
wenzelm@31945
   489
       TRYING_eq_assume_tac (i-1) (Thm.eq_assumption i st)
paulson@18508
   490
       handle THM _ => TRYING_eq_assume_tac (i-1) st;
paulson@18508
   491
paulson@18508
   492
fun TRYALL_eq_assume_tac st = TRYING_eq_assume_tac (nprems_of st) st;
paulson@9840
   493
paulson@15579
   494
(*Loop checking: FAIL if trying to prove the same thing twice
paulson@15579
   495
  -- if *ANY* subgoal has repeated literals*)
paulson@15579
   496
fun check_tac st =
paulson@15579
   497
  if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st)
paulson@15579
   498
  then  Seq.empty  else  Seq.single st;
paulson@9840
   499
paulson@9840
   500
paulson@15579
   501
(* net_resolve_tac actually made it slower... *)
paulson@15579
   502
fun prolog_step_tac horns i =
paulson@15579
   503
    (assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
paulson@18508
   504
    TRYALL_eq_assume_tac;
paulson@9840
   505
paulson@9840
   506
(*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*)
wenzelm@33339
   507
fun addconcl prem sz = size_of_term (Logic.strip_assums_concl prem) + sz;
paulson@15579
   508
wenzelm@33339
   509
fun size_of_subgoals st = fold_rev addconcl (prems_of st) 0;
paulson@15579
   510
paulson@9840
   511
paulson@9840
   512
(*Negation Normal Form*)
paulson@9840
   513
val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD,
wenzelm@9869
   514
               not_impD, not_iffD, not_allD, not_exD, not_notD];
paulson@15581
   515
haftmann@38557
   516
fun ok4nnf (Const (@{const_name Trueprop},_) $ (Const (@{const_name Not}, _) $ t)) = rigid t
haftmann@38557
   517
  | ok4nnf (Const (@{const_name Trueprop},_) $ t) = rigid t
paulson@21102
   518
  | ok4nnf _ = false;
paulson@21102
   519
wenzelm@32262
   520
fun make_nnf1 ctxt th =
wenzelm@24300
   521
  if ok4nnf (concl_of th)
wenzelm@32262
   522
  then make_nnf1 ctxt (tryres(th, nnf_rls))
paulson@28174
   523
    handle THM ("tryres", _, _) =>
wenzelm@32262
   524
        forward_res ctxt (make_nnf1 ctxt)
wenzelm@9869
   525
           (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
paulson@28174
   526
    handle THM ("tryres", _, _) => th
blanchet@38608
   527
  else th
paulson@9840
   528
wenzelm@24300
   529
(*The simplification removes defined quantifiers and occurrences of True and False.
paulson@20018
   530
  nnf_ss also includes the one-point simprocs,
paulson@18405
   531
  which are needed to avoid the various one-point theorems from generating junk clauses.*)
paulson@19894
   532
val nnf_simps =
blanchet@37539
   533
  @{thms simp_implies_def Ex1_def Ball_def Bex_def if_True if_False if_cancel
blanchet@37539
   534
         if_eq_cancel cases_simp}
blanchet@37539
   535
val nnf_extra_simps = @{thms split_ifs ex_simps all_simps simp_thms}
paulson@18405
   536
paulson@18405
   537
val nnf_ss =
wenzelm@24300
   538
  HOL_basic_ss addsimps nnf_extra_simps
wenzelm@24040
   539
    addsimprocs [defALL_regroup,defEX_regroup, @{simproc neq}, @{simproc let_simp}];
paulson@15872
   540
blanchet@38089
   541
val presimplify =
blanchet@38089
   542
  rewrite_rule (map safe_mk_meta_eq nnf_simps)
blanchet@38089
   543
  #> simplify nnf_ss
blanchet@38089
   544
wenzelm@32262
   545
fun make_nnf ctxt th = case prems_of th of
blanchet@38606
   546
    [] => th |> presimplify |> make_nnf1 ctxt
paulson@21050
   547
  | _ => raise THM ("make_nnf: premises in argument", 0, [th]);
paulson@15581
   548
paulson@15965
   549
(*Pull existential quantifiers to front. This accomplishes Skolemization for
paulson@15965
   550
  clauses that arise from a subgoal.*)
wenzelm@32262
   551
fun skolemize1 ctxt th =
haftmann@38557
   552
  if not (has_conns [@{const_name Ex}] (prop_of th)) then th
wenzelm@32262
   553
  else (skolemize1 ctxt (tryres(th, [choice, conj_exD1, conj_exD2,
quigley@15679
   554
                              disj_exD, disj_exD1, disj_exD2])))
paulson@28174
   555
    handle THM ("tryres", _, _) =>
wenzelm@32262
   556
        skolemize1 ctxt (forward_res ctxt (skolemize1 ctxt)
wenzelm@9869
   557
                   (tryres (th, [conj_forward, disj_forward, all_forward])))
paulson@28174
   558
    handle THM ("tryres", _, _) => 
wenzelm@32262
   559
        forward_res ctxt (skolemize1 ctxt) (rename_bvs_RS th ex_forward);
paulson@29684
   560
wenzelm@32262
   561
fun skolemize ctxt th = skolemize1 ctxt (make_nnf ctxt th);
paulson@9840
   562
wenzelm@32262
   563
fun skolemize_nnf_list _ [] = []
wenzelm@32262
   564
  | skolemize_nnf_list ctxt (th::ths) =
wenzelm@32262
   565
      skolemize ctxt th :: skolemize_nnf_list ctxt ths
paulson@25710
   566
      handle THM _ => (*RS can fail if Unify.search_bound is too small*)
wenzelm@32955
   567
       (trace_msg (fn () => "Failed to Skolemize " ^ Display.string_of_thm ctxt th);
wenzelm@32262
   568
        skolemize_nnf_list ctxt ths);
paulson@25694
   569
wenzelm@33339
   570
fun add_clauses th cls =
wenzelm@36603
   571
  let val ctxt0 = Variable.global_thm_context th
wenzelm@33339
   572
      val (cnfs, ctxt) = make_cnf [] th ctxt0
paulson@24937
   573
  in Variable.export ctxt ctxt0 cnfs @ cls end;
paulson@9840
   574
paulson@9840
   575
(*Make clauses from a list of theorems, previously Skolemized and put into nnf.
paulson@9840
   576
  The resulting clauses are HOL disjunctions.*)
wenzelm@39235
   577
fun make_clauses_unsorted ths = fold_rev add_clauses ths [];
blanchet@35869
   578
val make_clauses = sort_clauses o make_clauses_unsorted;
quigley@15773
   579
paulson@16563
   580
(*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*)
wenzelm@9869
   581
fun make_horns ths =
paulson@9840
   582
    name_thms "Horn#"
wenzelm@33339
   583
      (distinct Thm.eq_thm_prop (fold_rev (add_contras clause_rules) ths []));
paulson@9840
   584
paulson@9840
   585
(*Could simply use nprems_of, which would count remaining subgoals -- no
paulson@9840
   586
  discrimination as to their size!  With BEST_FIRST, fails for problem 41.*)
paulson@9840
   587
wenzelm@9869
   588
fun best_prolog_tac sizef horns =
paulson@9840
   589
    BEST_FIRST (has_fewer_prems 1, sizef) (prolog_step_tac horns 1);
paulson@9840
   590
wenzelm@9869
   591
fun depth_prolog_tac horns =
paulson@9840
   592
    DEPTH_FIRST (has_fewer_prems 1) (prolog_step_tac horns 1);
paulson@9840
   593
paulson@9840
   594
(*Return all negative clauses, as possible goal clauses*)
paulson@9840
   595
fun gocls cls = name_thms "Goal#" (map make_goal (neg_clauses cls));
paulson@9840
   596
wenzelm@32262
   597
fun skolemize_prems_tac ctxt prems =
blanchet@37926
   598
  cut_facts_tac (skolemize_nnf_list ctxt prems) THEN' REPEAT o etac exE
paulson@9840
   599
paulson@22546
   600
(*Basis of all meson-tactics.  Supplies cltac with clauses: HOL disjunctions.
paulson@22546
   601
  Function mkcl converts theorems to clauses.*)
blanchet@39037
   602
fun MESON preskolem_tac mkcl cltac ctxt i st =
paulson@16588
   603
  SELECT_GOAL
wenzelm@35625
   604
    (EVERY [Object_Logic.atomize_prems_tac 1,
paulson@23552
   605
            rtac ccontr 1,
blanchet@39269
   606
            preskolem_tac,
wenzelm@32283
   607
            Subgoal.FOCUS (fn {context = ctxt', prems = negs, ...} =>
blanchet@39269
   608
                      EVERY1 [skolemize_prems_tac ctxt negs,
wenzelm@32283
   609
                              Subgoal.FOCUS (cltac o mkcl o #prems) ctxt']) ctxt 1]) i st
wenzelm@24300
   610
  handle THM _ => no_tac st;    (*probably from make_meta_clause, not first-order*)
paulson@9840
   611
blanchet@39037
   612
paulson@9840
   613
(** Best-first search versions **)
paulson@9840
   614
paulson@16563
   615
(*ths is a list of additional clauses (HOL disjunctions) to use.*)
wenzelm@9869
   616
fun best_meson_tac sizef =
blanchet@39269
   617
  MESON all_tac make_clauses
paulson@22546
   618
    (fn cls =>
paulson@9840
   619
         THEN_BEST_FIRST (resolve_tac (gocls cls) 1)
paulson@9840
   620
                         (has_fewer_prems 1, sizef)
paulson@9840
   621
                         (prolog_step_tac (make_horns cls) 1));
paulson@9840
   622
paulson@9840
   623
(*First, breaks the goal into independent units*)
wenzelm@32262
   624
fun safe_best_meson_tac ctxt =
wenzelm@32262
   625
     SELECT_GOAL (TRY (safe_tac (claset_of ctxt)) THEN
wenzelm@32262
   626
                  TRYALL (best_meson_tac size_of_subgoals ctxt));
paulson@9840
   627
paulson@9840
   628
(** Depth-first search version **)
paulson@9840
   629
paulson@9840
   630
val depth_meson_tac =
blanchet@39269
   631
  MESON all_tac make_clauses
paulson@22546
   632
    (fn cls => EVERY [resolve_tac (gocls cls) 1, depth_prolog_tac (make_horns cls)]);
paulson@9840
   633
paulson@9840
   634
paulson@9840
   635
(** Iterative deepening version **)
paulson@9840
   636
paulson@9840
   637
(*This version does only one inference per call;
paulson@9840
   638
  having only one eq_assume_tac speeds it up!*)
wenzelm@9869
   639
fun prolog_step_tac' horns =
blanchet@39328
   640
    let val (horn0s, _) = (*0 subgoals vs 1 or more*)
paulson@9840
   641
            take_prefix Thm.no_prems horns
paulson@9840
   642
        val nrtac = net_resolve_tac horns
paulson@9840
   643
    in  fn i => eq_assume_tac i ORELSE
paulson@9840
   644
                match_tac horn0s i ORELSE  (*no backtracking if unit MATCHES*)
paulson@9840
   645
                ((assume_tac i APPEND nrtac i) THEN check_tac)
paulson@9840
   646
    end;
paulson@9840
   647
wenzelm@9869
   648
fun iter_deepen_prolog_tac horns =
wenzelm@38802
   649
    ITER_DEEPEN iter_deepen_limit (has_fewer_prems 1) (prolog_step_tac' horns);
paulson@9840
   650
blanchet@39269
   651
fun iter_deepen_meson_tac ctxt ths = ctxt |> MESON all_tac make_clauses
wenzelm@32091
   652
  (fn cls =>
wenzelm@32091
   653
    (case (gocls (cls @ ths)) of
wenzelm@32091
   654
      [] => no_tac  (*no goal clauses*)
wenzelm@32091
   655
    | goes =>
wenzelm@32091
   656
        let
wenzelm@32091
   657
          val horns = make_horns (cls @ ths)
wenzelm@32955
   658
          val _ = trace_msg (fn () =>
wenzelm@32091
   659
            cat_lines ("meson method called:" ::
wenzelm@32262
   660
              map (Display.string_of_thm ctxt) (cls @ ths) @
wenzelm@32262
   661
              ["clauses:"] @ map (Display.string_of_thm ctxt) horns))
wenzelm@38802
   662
        in
wenzelm@38802
   663
          THEN_ITER_DEEPEN iter_deepen_limit
wenzelm@38802
   664
            (resolve_tac goes 1) (has_fewer_prems 1) (prolog_step_tac' horns)
wenzelm@38802
   665
        end));
paulson@9840
   666
wenzelm@32262
   667
fun meson_tac ctxt ths =
wenzelm@32262
   668
  SELECT_GOAL (TRY (safe_tac (claset_of ctxt)) THEN TRYALL (iter_deepen_meson_tac ctxt ths));
wenzelm@9869
   669
wenzelm@9869
   670
paulson@14813
   671
(**** Code to support ordinary resolution, rather than Model Elimination ****)
paulson@14744
   672
wenzelm@24300
   673
(*Convert a list of clauses (disjunctions) to meta-level clauses (==>),
paulson@15008
   674
  with no contrapositives, for ordinary resolution.*)
paulson@14744
   675
paulson@14744
   676
(*Rules to convert the head literal into a negated assumption. If the head
paulson@14744
   677
  literal is already negated, then using notEfalse instead of notEfalse'
paulson@14744
   678
  prevents a double negation.*)
wenzelm@27239
   679
val notEfalse = read_instantiate @{context} [(("R", 0), "False")] notE;
paulson@14744
   680
val notEfalse' = rotate_prems 1 notEfalse;
paulson@14744
   681
wenzelm@24300
   682
fun negated_asm_of_head th =
paulson@14744
   683
    th RS notEfalse handle THM _ => th RS notEfalse';
paulson@14744
   684
paulson@26066
   685
(*Converting one theorem from a disjunction to a meta-level clause*)
paulson@26066
   686
fun make_meta_clause th =
wenzelm@33832
   687
  let val (fth,thaw) = Drule.legacy_freeze_thaw_robust th
paulson@26066
   688
  in  
wenzelm@35845
   689
      (zero_var_indexes o Thm.varifyT_global o thaw 0 o 
paulson@26066
   690
       negated_asm_of_head o make_horn resolution_clause_rules) fth
paulson@26066
   691
  end;
wenzelm@24300
   692
paulson@14744
   693
fun make_meta_clauses ths =
paulson@14744
   694
    name_thms "MClause#"
wenzelm@22360
   695
      (distinct Thm.eq_thm_prop (map make_meta_clause ths));
paulson@14744
   696
paulson@14744
   697
(*Permute a rule's premises to move the i-th premise to the last position.*)
paulson@14744
   698
fun make_last i th =
wenzelm@24300
   699
  let val n = nprems_of th
wenzelm@24300
   700
  in  if 1 <= i andalso i <= n
paulson@14744
   701
      then Thm.permute_prems (i-1) 1 th
paulson@15118
   702
      else raise THM("select_literal", i, [th])
paulson@14744
   703
  end;
paulson@14744
   704
paulson@14744
   705
(*Maps a rule that ends "... ==> P ==> False" to "... ==> ~P" while suppressing
paulson@14744
   706
  double-negations.*)
wenzelm@35410
   707
val negate_head = rewrite_rule [@{thm atomize_not}, not_not RS eq_reflection];
paulson@14744
   708
paulson@14744
   709
(*Maps the clause  [P1,...Pn]==>False to [P1,...,P(i-1),P(i+1),...Pn] ==> ~P*)
paulson@14744
   710
fun select_literal i cl = negate_head (make_last i cl);
paulson@14744
   711
paulson@18508
   712
paulson@14813
   713
(*Top-level Skolemization. Allows part of the conversion to clauses to be
wenzelm@24300
   714
  expressed as a tactic (or Isar method).  Each assumption of the selected
paulson@14813
   715
  goal is converted to NNF and then its existential quantifiers are pulled
wenzelm@24300
   716
  to the front. Finally, all existential quantifiers are eliminated,
paulson@14813
   717
  leaving !!-quantified variables. Perhaps Safe_tac should follow, but it
paulson@14813
   718
  might generate many subgoals.*)
mengj@18194
   719
wenzelm@32262
   720
fun skolemize_tac ctxt = SUBGOAL (fn (goal, i) =>
wenzelm@32262
   721
  let val ts = Logic.strip_assums_hyp goal
wenzelm@24300
   722
  in
wenzelm@32262
   723
    EVERY'
wenzelm@37781
   724
     [Misc_Legacy.METAHYPS (fn hyps =>
wenzelm@32262
   725
        (cut_facts_tac (skolemize_nnf_list ctxt hyps) 1
wenzelm@32262
   726
          THEN REPEAT (etac exE 1))),
wenzelm@32262
   727
      REPEAT_DETERM_N (length ts) o (etac thin_rl)] i
wenzelm@32262
   728
  end);
mengj@18194
   729
paulson@9840
   730
end;