src/HOL/Tools/Meson/meson.ML
author blanchet
Fri Oct 29 12:49:05 2010 +0200 (2010-10-29)
changeset 40262 8403085384eb
parent 39979 b13515940b53
child 40724 d01a1b3ab23d
permissions -rw-r--r--
ensure that MESON correctly preserves the name of variables (needed by the new Skolemizer)
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(*  Title:      HOL/Tools/Meson/meson.ML
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Author:     Jasmin Blanchette, TU Muenchen
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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 Config.T
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  val max_clauses : int Config.T
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  val term_pair_of: indexname * (typ * 'a) -> term * 'a
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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 choice_theorems : theory -> thm list
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  val skolemize_with_choice_theorems : Proof.context -> thm list -> 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 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, trace_setup) = Attrib.config_bool "trace_meson" (K false)
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fun trace_msg ctxt msg = if Config.get ctxt trace then tracing (msg ()) else ()
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val max_clauses_default = 60
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val (max_clauses, max_clauses_setup) =
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  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 not_conjD = @{thm not_conjD};
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val not_disjD = @{thm not_disjD};
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val not_notD = @{thm not_notD};
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val not_allD = @{thm not_allD};
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val not_exD = @{thm not_exD};
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val imp_to_disjD = @{thm imp_to_disjD};
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val not_impD = @{thm not_impD};
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val iff_to_disjD = @{thm iff_to_disjD};
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val not_iffD = @{thm not_iffD};
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val conj_exD1 = @{thm conj_exD1};
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val conj_exD2 = @{thm conj_exD2};
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val disj_exD = @{thm disj_exD};
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val disj_exD1 = @{thm disj_exD1};
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val disj_exD2 = @{thm disj_exD2};
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val disj_assoc = @{thm disj_assoc};
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val disj_comm = @{thm disj_comm};
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val disj_FalseD1 = @{thm disj_FalseD1};
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val disj_FalseD2 = @{thm 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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(* Hack to make it less likely that we lose our precious bound variable names in
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   "rename_bound_vars_RS" below, because of a clash. *)
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val protect_prefix = "Meson_xyzzy"
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fun protect_bound_var_names (t $ u) =
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    protect_bound_var_names t $ protect_bound_var_names u
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  | protect_bound_var_names (Abs (s, T, t')) =
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    Abs (protect_prefix ^ s, T, protect_bound_var_names t')
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  | protect_bound_var_names t = t
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fun fix_bound_var_names old_t new_t =
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  let
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    fun quant_of @{const_name All} = SOME true
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      | quant_of @{const_name Ball} = SOME true
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      | quant_of @{const_name Ex} = SOME false
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      | quant_of @{const_name Bex} = SOME false
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      | quant_of _ = NONE
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    val flip_quant = Option.map not
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    fun some_eq (SOME x) (SOME y) = x = y
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      | some_eq _ _ = false
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    fun add_names quant (Const (quant_s, _) $ Abs (s, _, t')) =
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        add_names quant t' #> some_eq quant (quant_of quant_s) ? cons s
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      | add_names quant (@{const Not} $ t) = add_names (flip_quant quant) t
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      | add_names quant (@{const implies} $ t1 $ t2) =
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        add_names (flip_quant quant) t1 #> add_names quant t2
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      | add_names quant (t1 $ t2) = fold (add_names quant) [t1, t2]
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      | add_names _ _ = I
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    fun lost_names quant =
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      subtract (op =) (add_names quant new_t []) (add_names quant old_t [])
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    fun aux ((t1 as Const (quant_s, _)) $ (Abs (s, T, t'))) =
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      t1 $ Abs (s |> String.isPrefix protect_prefix s
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                   ? perhaps (try (fn _ => hd (lost_names (quant_of quant_s)))),
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                T, aux t')
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      | aux (t1 $ t2) = aux t1 $ aux t2
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      | aux t = t
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  in aux new_t end
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(* Forward proof while preserving bound variables names *)
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fun rename_bound_vars_RS th rl =
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  let
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    val t = concl_of th
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    val r = concl_of rl
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    val th' = th RS Thm.rename_boundvars r (protect_bound_var_names r) rl
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    val t' = concl_of th'
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  in Thm.rename_boundvars t' (fix_bound_var_names t t') 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) =
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          (rename_bound_vars_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 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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   293
(*** The basic CNF transformation ***)
paulson@18389
   294
blanchet@39328
   295
fun estimated_num_clauses bound t =
paulson@26562
   296
 let
blanchet@39269
   297
  fun sum x y = if x < bound andalso y < bound then x+y else bound
blanchet@39269
   298
  fun prod x y = if x < bound andalso y < bound then x*y else bound
paulson@26562
   299
  
paulson@26562
   300
  (*Estimate the number of clauses in order to detect infeasible theorems*)
haftmann@38557
   301
  fun signed_nclauses b (Const(@{const_name Trueprop},_) $ t) = signed_nclauses b t
haftmann@38557
   302
    | signed_nclauses b (Const(@{const_name Not},_) $ t) = signed_nclauses (not b) t
haftmann@38795
   303
    | signed_nclauses b (Const(@{const_name HOL.conj},_) $ t $ u) =
wenzelm@32960
   304
        if b then sum (signed_nclauses b t) (signed_nclauses b u)
wenzelm@32960
   305
             else prod (signed_nclauses b t) (signed_nclauses b u)
haftmann@38795
   306
    | signed_nclauses b (Const(@{const_name HOL.disj},_) $ t $ u) =
wenzelm@32960
   307
        if b then prod (signed_nclauses b t) (signed_nclauses b u)
wenzelm@32960
   308
             else sum (signed_nclauses b t) (signed_nclauses b u)
haftmann@38786
   309
    | signed_nclauses b (Const(@{const_name HOL.implies},_) $ t $ u) =
wenzelm@32960
   310
        if b then prod (signed_nclauses (not b) t) (signed_nclauses b u)
wenzelm@32960
   311
             else sum (signed_nclauses (not b) t) (signed_nclauses b u)
haftmann@38864
   312
    | signed_nclauses b (Const(@{const_name HOL.eq}, Type ("fun", [T, _])) $ t $ u) =
wenzelm@32960
   313
        if T = HOLogic.boolT then (*Boolean equality is if-and-only-if*)
wenzelm@32960
   314
            if b then sum (prod (signed_nclauses (not b) t) (signed_nclauses b u))
wenzelm@32960
   315
                          (prod (signed_nclauses (not b) u) (signed_nclauses b t))
wenzelm@32960
   316
                 else sum (prod (signed_nclauses b t) (signed_nclauses b u))
wenzelm@32960
   317
                          (prod (signed_nclauses (not b) t) (signed_nclauses (not b) u))
wenzelm@32960
   318
        else 1
haftmann@38557
   319
    | signed_nclauses b (Const(@{const_name Ex}, _) $ Abs (_,_,t)) = signed_nclauses b t
haftmann@38557
   320
    | signed_nclauses b (Const(@{const_name All},_) $ Abs (_,_,t)) = signed_nclauses b t
paulson@26562
   321
    | signed_nclauses _ _ = 1; (* literal *)
blanchet@39269
   322
 in signed_nclauses true t end
blanchet@39269
   323
blanchet@39269
   324
fun has_too_many_clauses ctxt t =
blanchet@39269
   325
  let val max_cl = Config.get ctxt max_clauses in
blanchet@39328
   326
    estimated_num_clauses (max_cl + 1) t > max_cl
blanchet@39269
   327
  end
paulson@19894
   328
paulson@15579
   329
(*Replaces universally quantified variables by FREE variables -- because
paulson@24937
   330
  assumptions may not contain scheme variables.  Later, generalize using Variable.export. *)
paulson@24937
   331
local  
paulson@24937
   332
  val spec_var = Thm.dest_arg (Thm.dest_arg (#2 (Thm.dest_implies (Thm.cprop_of spec))));
paulson@24937
   333
  val spec_varT = #T (Thm.rep_cterm spec_var);
haftmann@38557
   334
  fun name_of (Const (@{const_name All}, _) $ Abs(x,_,_)) = x | name_of _ = Name.uu;
paulson@24937
   335
in  
paulson@24937
   336
  fun freeze_spec th ctxt =
paulson@24937
   337
    let
paulson@24937
   338
      val cert = Thm.cterm_of (ProofContext.theory_of ctxt);
paulson@24937
   339
      val ([x], ctxt') = Variable.variant_fixes [name_of (HOLogic.dest_Trueprop (concl_of th))] ctxt;
paulson@24937
   340
      val spec' = Thm.instantiate ([], [(spec_var, cert (Free (x, spec_varT)))]) spec;
paulson@24937
   341
    in (th RS spec', ctxt') end
paulson@24937
   342
end;
paulson@9840
   343
paulson@15998
   344
(*Used with METAHYPS below. There is one assumption, which gets bound to prem
paulson@15998
   345
  and then normalized via function nf. The normal form is given to resolve_tac,
paulson@22515
   346
  instantiate a Boolean variable created by resolution with disj_forward. Since
paulson@22515
   347
  (nf prem) returns a LIST of theorems, we can backtrack to get all combinations.*)
paulson@15579
   348
fun resop nf [prem] = resolve_tac (nf prem) 1;
paulson@9840
   349
blanchet@39037
   350
(* Any need to extend this list with "HOL.type_class", "HOL.eq_class",
blanchet@39037
   351
   and "Pure.term"? *)
haftmann@38557
   352
val has_meta_conn = exists_Const (member (op =) ["==", "==>", "=simp=>", "all", "prop"] o #1);
paulson@20417
   353
blanchet@37410
   354
fun apply_skolem_theorem (th, rls) =
blanchet@37398
   355
  let
blanchet@37410
   356
    fun tryall [] = raise THM ("apply_skolem_theorem", 0, th::rls)
blanchet@37398
   357
      | tryall (rl :: rls) =
blanchet@37398
   358
        first_order_resolve th rl handle THM _ => tryall rls
blanchet@37398
   359
  in tryall rls end
paulson@22515
   360
blanchet@37410
   361
(* Conjunctive normal form, adding clauses from th in front of ths (for foldr).
blanchet@37410
   362
   Strips universal quantifiers and breaks up conjunctions.
blanchet@37410
   363
   Eliminates existential quantifiers using Skolemization theorems. *)
blanchet@39886
   364
fun cnf old_skolem_ths ctxt (th, ths) =
wenzelm@33222
   365
  let val ctxtr = Unsynchronized.ref ctxt   (* FIXME ??? *)
paulson@24937
   366
      fun cnf_aux (th,ths) =
wenzelm@24300
   367
        if not (can HOLogic.dest_Trueprop (prop_of th)) then ths (*meta-level: ignore*)
haftmann@38795
   368
        else if not (has_conns [@{const_name All}, @{const_name Ex}, @{const_name HOL.conj}] (prop_of th))
wenzelm@32262
   369
        then nodups ctxt th :: ths (*no work to do, terminate*)
wenzelm@24300
   370
        else case head_of (HOLogic.dest_Trueprop (concl_of th)) of
haftmann@38795
   371
            Const (@{const_name HOL.conj}, _) => (*conjunction*)
wenzelm@24300
   372
                cnf_aux (th RS conjunct1, cnf_aux (th RS conjunct2, ths))
haftmann@38557
   373
          | Const (@{const_name All}, _) => (*universal quantifier*)
paulson@24937
   374
                let val (th',ctxt') = freeze_spec th (!ctxtr)
paulson@24937
   375
                in  ctxtr := ctxt'; cnf_aux (th', ths) end
haftmann@38557
   376
          | Const (@{const_name Ex}, _) =>
wenzelm@24300
   377
              (*existential quantifier: Insert Skolem functions*)
blanchet@39886
   378
              cnf_aux (apply_skolem_theorem (th, old_skolem_ths), ths)
haftmann@38795
   379
          | Const (@{const_name HOL.disj}, _) =>
wenzelm@24300
   380
              (*Disjunction of P, Q: Create new goal of proving ?P | ?Q and solve it using
wenzelm@24300
   381
                all combinations of converting P, Q to CNF.*)
wenzelm@24300
   382
              let val tac =
wenzelm@37781
   383
                  Misc_Legacy.METAHYPS (resop cnf_nil) 1 THEN
wenzelm@37781
   384
                   (fn st' => st' |> Misc_Legacy.METAHYPS (resop cnf_nil) 1)
wenzelm@24300
   385
              in  Seq.list_of (tac (th RS disj_forward)) @ ths  end
wenzelm@32262
   386
          | _ => nodups ctxt th :: ths  (*no work to do*)
paulson@19154
   387
      and cnf_nil th = cnf_aux (th,[])
blanchet@39269
   388
      val cls =
blanchet@39269
   389
            if has_too_many_clauses ctxt (concl_of th)
blanchet@39979
   390
            then (trace_msg ctxt (fn () => "cnf is ignoring: " ^ Display.string_of_thm ctxt th); ths)
wenzelm@32960
   391
            else cnf_aux (th,ths)
paulson@24937
   392
  in  (cls, !ctxtr)  end;
paulson@22515
   393
blanchet@39886
   394
fun make_cnf old_skolem_ths th ctxt = cnf old_skolem_ths ctxt (th, [])
paulson@20417
   395
paulson@20417
   396
(*Generalization, removal of redundant equalities, removal of tautologies.*)
paulson@24937
   397
fun finish_cnf ths = filter (not o is_taut) (map refl_clause ths);
paulson@9840
   398
paulson@9840
   399
paulson@15579
   400
(**** Generation of contrapositives ****)
paulson@9840
   401
haftmann@38557
   402
fun is_left (Const (@{const_name Trueprop}, _) $
haftmann@38795
   403
               (Const (@{const_name HOL.disj}, _) $ (Const (@{const_name HOL.disj}, _) $ _ $ _) $ _)) = true
paulson@21102
   404
  | is_left _ = false;
wenzelm@24300
   405
paulson@15579
   406
(*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
wenzelm@24300
   407
fun assoc_right th =
paulson@21102
   408
  if is_left (prop_of th) then assoc_right (th RS disj_assoc)
paulson@21102
   409
  else th;
paulson@9840
   410
paulson@15579
   411
(*Must check for negative literal first!*)
paulson@15579
   412
val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
paulson@9840
   413
paulson@15579
   414
(*For ordinary resolution. *)
paulson@15579
   415
val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule'];
paulson@9840
   416
paulson@15579
   417
(*Create a goal or support clause, conclusing False*)
paulson@15579
   418
fun make_goal th =   (*Must check for negative literal first!*)
paulson@15579
   419
    make_goal (tryres(th, clause_rules))
paulson@15579
   420
  handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
paulson@9840
   421
paulson@15579
   422
(*Sort clauses by number of literals*)
paulson@15579
   423
fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2);
paulson@9840
   424
paulson@18389
   425
fun sort_clauses ths = sort (make_ord fewerlits) ths;
paulson@9840
   426
blanchet@38099
   427
fun has_bool @{typ bool} = true
blanchet@38099
   428
  | has_bool (Type (_, Ts)) = exists has_bool Ts
blanchet@38099
   429
  | has_bool _ = false
blanchet@38099
   430
blanchet@38099
   431
fun has_fun (Type (@{type_name fun}, _)) = true
blanchet@38099
   432
  | has_fun (Type (_, Ts)) = exists has_fun Ts
blanchet@38099
   433
  | has_fun _ = false
wenzelm@24300
   434
wenzelm@24300
   435
(*Is the string the name of a connective? Really only | and Not can remain,
wenzelm@24300
   436
  since this code expects to be called on a clause form.*)
wenzelm@19875
   437
val is_conn = member (op =)
haftmann@38795
   438
    [@{const_name Trueprop}, @{const_name HOL.conj}, @{const_name HOL.disj},
haftmann@38786
   439
     @{const_name HOL.implies}, @{const_name Not},
haftmann@38557
   440
     @{const_name All}, @{const_name Ex}, @{const_name Ball}, @{const_name Bex}];
paulson@15613
   441
wenzelm@24300
   442
(*True if the term contains a function--not a logical connective--where the type
paulson@20524
   443
  of any argument contains bool.*)
wenzelm@24300
   444
val has_bool_arg_const =
paulson@15613
   445
    exists_Const
blanchet@38099
   446
      (fn (c,T) => not(is_conn c) andalso exists has_bool (binder_types T));
paulson@22381
   447
wenzelm@24300
   448
(*A higher-order instance of a first-order constant? Example is the definition of
haftmann@38622
   449
  one, 1, at a function type in theory Function_Algebras.*)
wenzelm@24300
   450
fun higher_inst_const thy (c,T) =
paulson@22381
   451
  case binder_types T of
paulson@22381
   452
      [] => false (*not a function type, OK*)
paulson@22381
   453
    | Ts => length (binder_types (Sign.the_const_type thy c)) <> length Ts;
paulson@22381
   454
paulson@24742
   455
(*Returns false if any Vars in the theorem mention type bool.
paulson@21102
   456
  Also rejects functions whose arguments are Booleans or other functions.*)
paulson@22381
   457
fun is_fol_term thy t =
haftmann@38557
   458
    Term.is_first_order ["all", @{const_name All}, @{const_name Ex}] t andalso
blanchet@38099
   459
    not (exists_subterm (fn Var (_, T) => has_bool T orelse has_fun T
blanchet@38099
   460
                           | _ => false) t orelse
blanchet@38099
   461
         has_bool_arg_const t orelse
wenzelm@24300
   462
         exists_Const (higher_inst_const thy) t orelse
wenzelm@24300
   463
         has_meta_conn t);
paulson@19204
   464
paulson@21102
   465
fun rigid t = not (is_Var (head_of t));
paulson@21102
   466
haftmann@38795
   467
fun ok4horn (Const (@{const_name Trueprop},_) $ (Const (@{const_name HOL.disj}, _) $ t $ _)) = rigid t
haftmann@38557
   468
  | ok4horn (Const (@{const_name Trueprop},_) $ t) = rigid t
paulson@21102
   469
  | ok4horn _ = false;
paulson@21102
   470
paulson@15579
   471
(*Create a meta-level Horn clause*)
wenzelm@24300
   472
fun make_horn crules th =
wenzelm@24300
   473
  if ok4horn (concl_of th)
paulson@21102
   474
  then make_horn crules (tryres(th,crules)) handle THM _ => th
paulson@21102
   475
  else th;
paulson@9840
   476
paulson@16563
   477
(*Generate Horn clauses for all contrapositives of a clause. The input, th,
paulson@16563
   478
  is a HOL disjunction.*)
wenzelm@33339
   479
fun add_contras crules th hcs =
blanchet@39328
   480
  let fun rots (0,_) = hcs
wenzelm@24300
   481
        | rots (k,th) = zero_var_indexes (make_horn crules th) ::
wenzelm@24300
   482
                        rots(k-1, assoc_right (th RS disj_comm))
paulson@15862
   483
  in case nliterals(prop_of th) of
wenzelm@24300
   484
        1 => th::hcs
paulson@15579
   485
      | n => rots(n, assoc_right th)
paulson@15579
   486
  end;
paulson@9840
   487
paulson@15579
   488
(*Use "theorem naming" to label the clauses*)
paulson@15579
   489
fun name_thms label =
wenzelm@33339
   490
    let fun name1 th (k, ths) =
wenzelm@27865
   491
          (k-1, Thm.put_name_hint (label ^ string_of_int k) th :: ths)
wenzelm@33339
   492
    in  fn ths => #2 (fold_rev name1 ths (length ths, []))  end;
paulson@9840
   493
paulson@16563
   494
(*Is the given disjunction an all-negative support clause?*)
paulson@15579
   495
fun is_negative th = forall (not o #1) (literals (prop_of th));
paulson@9840
   496
wenzelm@33317
   497
val neg_clauses = filter is_negative;
paulson@9840
   498
paulson@9840
   499
paulson@15579
   500
(***** MESON PROOF PROCEDURE *****)
paulson@9840
   501
haftmann@38557
   502
fun rhyps (Const("==>",_) $ (Const(@{const_name Trueprop},_) $ A) $ phi,
wenzelm@24300
   503
           As) = rhyps(phi, A::As)
paulson@15579
   504
  | rhyps (_, As) = As;
paulson@9840
   505
paulson@15579
   506
(** Detecting repeated assumptions in a subgoal **)
paulson@9840
   507
paulson@15579
   508
(*The stringtree detects repeated assumptions.*)
wenzelm@33245
   509
fun ins_term t net = Net.insert_term (op aconv) (t, t) net;
paulson@9840
   510
paulson@15579
   511
(*detects repetitions in a list of terms*)
paulson@15579
   512
fun has_reps [] = false
paulson@15579
   513
  | has_reps [_] = false
paulson@15579
   514
  | has_reps [t,u] = (t aconv u)
wenzelm@33245
   515
  | has_reps ts = (fold ins_term ts Net.empty; false) handle Net.INSERT => true;
paulson@9840
   516
paulson@15579
   517
(*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*)
paulson@18508
   518
fun TRYING_eq_assume_tac 0 st = Seq.single st
paulson@18508
   519
  | TRYING_eq_assume_tac i st =
wenzelm@31945
   520
       TRYING_eq_assume_tac (i-1) (Thm.eq_assumption i st)
paulson@18508
   521
       handle THM _ => TRYING_eq_assume_tac (i-1) st;
paulson@18508
   522
paulson@18508
   523
fun TRYALL_eq_assume_tac st = TRYING_eq_assume_tac (nprems_of st) st;
paulson@9840
   524
paulson@15579
   525
(*Loop checking: FAIL if trying to prove the same thing twice
paulson@15579
   526
  -- if *ANY* subgoal has repeated literals*)
paulson@15579
   527
fun check_tac st =
paulson@15579
   528
  if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st)
paulson@15579
   529
  then  Seq.empty  else  Seq.single st;
paulson@9840
   530
paulson@9840
   531
paulson@15579
   532
(* net_resolve_tac actually made it slower... *)
paulson@15579
   533
fun prolog_step_tac horns i =
paulson@15579
   534
    (assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
paulson@18508
   535
    TRYALL_eq_assume_tac;
paulson@9840
   536
paulson@9840
   537
(*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*)
wenzelm@33339
   538
fun addconcl prem sz = size_of_term (Logic.strip_assums_concl prem) + sz;
paulson@15579
   539
wenzelm@33339
   540
fun size_of_subgoals st = fold_rev addconcl (prems_of st) 0;
paulson@15579
   541
paulson@9840
   542
paulson@9840
   543
(*Negation Normal Form*)
paulson@9840
   544
val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD,
wenzelm@9869
   545
               not_impD, not_iffD, not_allD, not_exD, not_notD];
paulson@15581
   546
haftmann@38557
   547
fun ok4nnf (Const (@{const_name Trueprop},_) $ (Const (@{const_name Not}, _) $ t)) = rigid t
haftmann@38557
   548
  | ok4nnf (Const (@{const_name Trueprop},_) $ t) = rigid t
paulson@21102
   549
  | ok4nnf _ = false;
paulson@21102
   550
wenzelm@32262
   551
fun make_nnf1 ctxt th =
wenzelm@24300
   552
  if ok4nnf (concl_of th)
wenzelm@32262
   553
  then make_nnf1 ctxt (tryres(th, nnf_rls))
paulson@28174
   554
    handle THM ("tryres", _, _) =>
wenzelm@32262
   555
        forward_res ctxt (make_nnf1 ctxt)
wenzelm@9869
   556
           (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
paulson@28174
   557
    handle THM ("tryres", _, _) => th
blanchet@38608
   558
  else th
paulson@9840
   559
wenzelm@24300
   560
(*The simplification removes defined quantifiers and occurrences of True and False.
paulson@20018
   561
  nnf_ss also includes the one-point simprocs,
paulson@18405
   562
  which are needed to avoid the various one-point theorems from generating junk clauses.*)
paulson@19894
   563
val nnf_simps =
blanchet@37539
   564
  @{thms simp_implies_def Ex1_def Ball_def Bex_def if_True if_False if_cancel
blanchet@37539
   565
         if_eq_cancel cases_simp}
blanchet@37539
   566
val nnf_extra_simps = @{thms split_ifs ex_simps all_simps simp_thms}
paulson@18405
   567
paulson@18405
   568
val nnf_ss =
wenzelm@24300
   569
  HOL_basic_ss addsimps nnf_extra_simps
wenzelm@24040
   570
    addsimprocs [defALL_regroup,defEX_regroup, @{simproc neq}, @{simproc let_simp}];
paulson@15872
   571
blanchet@38089
   572
val presimplify =
blanchet@39900
   573
  rewrite_rule (map safe_mk_meta_eq nnf_simps) #> simplify nnf_ss
blanchet@38089
   574
wenzelm@32262
   575
fun make_nnf ctxt th = case prems_of th of
blanchet@38606
   576
    [] => th |> presimplify |> make_nnf1 ctxt
paulson@21050
   577
  | _ => raise THM ("make_nnf: premises in argument", 0, [th]);
paulson@15581
   578
blanchet@39950
   579
fun choice_theorems thy =
blanchet@39950
   580
  try (Global_Theory.get_thm thy) "Hilbert_Choice.choice" |> the_list
blanchet@39950
   581
blanchet@39900
   582
(* Pull existential quantifiers to front. This accomplishes Skolemization for
blanchet@39900
   583
   clauses that arise from a subgoal. *)
blanchet@39950
   584
fun skolemize_with_choice_theorems ctxt choice_ths =
blanchet@39900
   585
  let
blanchet@39900
   586
    fun aux th =
blanchet@39900
   587
      if not (has_conns [@{const_name Ex}] (prop_of th)) then
blanchet@39900
   588
        th
blanchet@39900
   589
      else
blanchet@39901
   590
        tryres (th, choice_ths @
blanchet@39900
   591
                    [conj_exD1, conj_exD2, disj_exD, disj_exD1, disj_exD2])
blanchet@39900
   592
        |> aux
blanchet@39900
   593
        handle THM ("tryres", _, _) =>
blanchet@39900
   594
               tryres (th, [conj_forward, disj_forward, all_forward])
blanchet@39900
   595
               |> forward_res ctxt aux
blanchet@39900
   596
               |> aux
blanchet@39900
   597
               handle THM ("tryres", _, _) =>
blanchet@40262
   598
                      rename_bound_vars_RS th ex_forward
blanchet@39900
   599
                      |> forward_res ctxt aux
blanchet@39900
   600
  in aux o make_nnf ctxt end
paulson@29684
   601
blanchet@39950
   602
fun skolemize ctxt =
blanchet@39950
   603
  let val thy = ProofContext.theory_of ctxt in
blanchet@39950
   604
    skolemize_with_choice_theorems ctxt (choice_theorems thy)
blanchet@39950
   605
  end
blanchet@39904
   606
blanchet@39900
   607
(* "RS" can fail if "unify_search_bound" is too small. *)
blanchet@39900
   608
fun try_skolemize ctxt th =
blanchet@39904
   609
  try (skolemize ctxt) th
blanchet@39979
   610
  |> tap (fn NONE => trace_msg ctxt (fn () => "Failed to skolemize " ^
blanchet@39979
   611
                                              Display.string_of_thm ctxt th)
blanchet@39900
   612
           | _ => ())
paulson@25694
   613
wenzelm@33339
   614
fun add_clauses th cls =
wenzelm@36603
   615
  let val ctxt0 = Variable.global_thm_context th
wenzelm@33339
   616
      val (cnfs, ctxt) = make_cnf [] th ctxt0
paulson@24937
   617
  in Variable.export ctxt ctxt0 cnfs @ cls end;
paulson@9840
   618
paulson@9840
   619
(*Make clauses from a list of theorems, previously Skolemized and put into nnf.
paulson@9840
   620
  The resulting clauses are HOL disjunctions.*)
wenzelm@39235
   621
fun make_clauses_unsorted ths = fold_rev add_clauses ths [];
blanchet@35869
   622
val make_clauses = sort_clauses o make_clauses_unsorted;
quigley@15773
   623
paulson@16563
   624
(*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*)
wenzelm@9869
   625
fun make_horns ths =
paulson@9840
   626
    name_thms "Horn#"
wenzelm@33339
   627
      (distinct Thm.eq_thm_prop (fold_rev (add_contras clause_rules) ths []));
paulson@9840
   628
paulson@9840
   629
(*Could simply use nprems_of, which would count remaining subgoals -- no
paulson@9840
   630
  discrimination as to their size!  With BEST_FIRST, fails for problem 41.*)
paulson@9840
   631
wenzelm@9869
   632
fun best_prolog_tac sizef horns =
paulson@9840
   633
    BEST_FIRST (has_fewer_prems 1, sizef) (prolog_step_tac horns 1);
paulson@9840
   634
wenzelm@9869
   635
fun depth_prolog_tac horns =
paulson@9840
   636
    DEPTH_FIRST (has_fewer_prems 1) (prolog_step_tac horns 1);
paulson@9840
   637
paulson@9840
   638
(*Return all negative clauses, as possible goal clauses*)
paulson@9840
   639
fun gocls cls = name_thms "Goal#" (map make_goal (neg_clauses cls));
paulson@9840
   640
wenzelm@32262
   641
fun skolemize_prems_tac ctxt prems =
blanchet@39900
   642
  cut_facts_tac (map_filter (try_skolemize ctxt) prems) THEN' REPEAT o etac exE
paulson@9840
   643
paulson@22546
   644
(*Basis of all meson-tactics.  Supplies cltac with clauses: HOL disjunctions.
paulson@22546
   645
  Function mkcl converts theorems to clauses.*)
blanchet@39037
   646
fun MESON preskolem_tac mkcl cltac ctxt i st =
paulson@16588
   647
  SELECT_GOAL
wenzelm@35625
   648
    (EVERY [Object_Logic.atomize_prems_tac 1,
paulson@23552
   649
            rtac ccontr 1,
blanchet@39269
   650
            preskolem_tac,
wenzelm@32283
   651
            Subgoal.FOCUS (fn {context = ctxt', prems = negs, ...} =>
blanchet@39269
   652
                      EVERY1 [skolemize_prems_tac ctxt negs,
wenzelm@32283
   653
                              Subgoal.FOCUS (cltac o mkcl o #prems) ctxt']) ctxt 1]) i st
wenzelm@24300
   654
  handle THM _ => no_tac st;    (*probably from make_meta_clause, not first-order*)
paulson@9840
   655
blanchet@39037
   656
paulson@9840
   657
(** Best-first search versions **)
paulson@9840
   658
paulson@16563
   659
(*ths is a list of additional clauses (HOL disjunctions) to use.*)
wenzelm@9869
   660
fun best_meson_tac sizef =
blanchet@39269
   661
  MESON all_tac make_clauses
paulson@22546
   662
    (fn cls =>
paulson@9840
   663
         THEN_BEST_FIRST (resolve_tac (gocls cls) 1)
paulson@9840
   664
                         (has_fewer_prems 1, sizef)
paulson@9840
   665
                         (prolog_step_tac (make_horns cls) 1));
paulson@9840
   666
paulson@9840
   667
(*First, breaks the goal into independent units*)
wenzelm@32262
   668
fun safe_best_meson_tac ctxt =
wenzelm@32262
   669
     SELECT_GOAL (TRY (safe_tac (claset_of ctxt)) THEN
wenzelm@32262
   670
                  TRYALL (best_meson_tac size_of_subgoals ctxt));
paulson@9840
   671
paulson@9840
   672
(** Depth-first search version **)
paulson@9840
   673
paulson@9840
   674
val depth_meson_tac =
blanchet@39269
   675
  MESON all_tac make_clauses
paulson@22546
   676
    (fn cls => EVERY [resolve_tac (gocls cls) 1, depth_prolog_tac (make_horns cls)]);
paulson@9840
   677
paulson@9840
   678
paulson@9840
   679
(** Iterative deepening version **)
paulson@9840
   680
paulson@9840
   681
(*This version does only one inference per call;
paulson@9840
   682
  having only one eq_assume_tac speeds it up!*)
wenzelm@9869
   683
fun prolog_step_tac' horns =
blanchet@39328
   684
    let val (horn0s, _) = (*0 subgoals vs 1 or more*)
paulson@9840
   685
            take_prefix Thm.no_prems horns
paulson@9840
   686
        val nrtac = net_resolve_tac horns
paulson@9840
   687
    in  fn i => eq_assume_tac i ORELSE
paulson@9840
   688
                match_tac horn0s i ORELSE  (*no backtracking if unit MATCHES*)
paulson@9840
   689
                ((assume_tac i APPEND nrtac i) THEN check_tac)
paulson@9840
   690
    end;
paulson@9840
   691
wenzelm@9869
   692
fun iter_deepen_prolog_tac horns =
wenzelm@38802
   693
    ITER_DEEPEN iter_deepen_limit (has_fewer_prems 1) (prolog_step_tac' horns);
paulson@9840
   694
blanchet@39269
   695
fun iter_deepen_meson_tac ctxt ths = ctxt |> MESON all_tac make_clauses
wenzelm@32091
   696
  (fn cls =>
wenzelm@32091
   697
    (case (gocls (cls @ ths)) of
wenzelm@32091
   698
      [] => no_tac  (*no goal clauses*)
wenzelm@32091
   699
    | goes =>
wenzelm@32091
   700
        let
wenzelm@32091
   701
          val horns = make_horns (cls @ ths)
blanchet@39979
   702
          val _ = trace_msg ctxt (fn () =>
wenzelm@32091
   703
            cat_lines ("meson method called:" ::
wenzelm@32262
   704
              map (Display.string_of_thm ctxt) (cls @ ths) @
wenzelm@32262
   705
              ["clauses:"] @ map (Display.string_of_thm ctxt) horns))
wenzelm@38802
   706
        in
wenzelm@38802
   707
          THEN_ITER_DEEPEN iter_deepen_limit
wenzelm@38802
   708
            (resolve_tac goes 1) (has_fewer_prems 1) (prolog_step_tac' horns)
wenzelm@38802
   709
        end));
paulson@9840
   710
wenzelm@32262
   711
fun meson_tac ctxt ths =
wenzelm@32262
   712
  SELECT_GOAL (TRY (safe_tac (claset_of ctxt)) THEN TRYALL (iter_deepen_meson_tac ctxt ths));
wenzelm@9869
   713
wenzelm@9869
   714
paulson@14813
   715
(**** Code to support ordinary resolution, rather than Model Elimination ****)
paulson@14744
   716
wenzelm@24300
   717
(*Convert a list of clauses (disjunctions) to meta-level clauses (==>),
paulson@15008
   718
  with no contrapositives, for ordinary resolution.*)
paulson@14744
   719
paulson@14744
   720
(*Rules to convert the head literal into a negated assumption. If the head
paulson@14744
   721
  literal is already negated, then using notEfalse instead of notEfalse'
paulson@14744
   722
  prevents a double negation.*)
wenzelm@27239
   723
val notEfalse = read_instantiate @{context} [(("R", 0), "False")] notE;
paulson@14744
   724
val notEfalse' = rotate_prems 1 notEfalse;
paulson@14744
   725
wenzelm@24300
   726
fun negated_asm_of_head th =
paulson@14744
   727
    th RS notEfalse handle THM _ => th RS notEfalse';
paulson@14744
   728
paulson@26066
   729
(*Converting one theorem from a disjunction to a meta-level clause*)
paulson@26066
   730
fun make_meta_clause th =
wenzelm@33832
   731
  let val (fth,thaw) = Drule.legacy_freeze_thaw_robust th
paulson@26066
   732
  in  
wenzelm@35845
   733
      (zero_var_indexes o Thm.varifyT_global o thaw 0 o 
paulson@26066
   734
       negated_asm_of_head o make_horn resolution_clause_rules) fth
paulson@26066
   735
  end;
wenzelm@24300
   736
paulson@14744
   737
fun make_meta_clauses ths =
paulson@14744
   738
    name_thms "MClause#"
wenzelm@22360
   739
      (distinct Thm.eq_thm_prop (map make_meta_clause ths));
paulson@14744
   740
blanchet@39979
   741
val setup =
blanchet@39979
   742
  trace_setup
blanchet@39979
   743
  #> max_clauses_setup
blanchet@39979
   744
paulson@9840
   745
end;