src/HOL/Tools/Meson/meson.ML
author wenzelm
Tue Mar 13 16:40:06 2012 +0100 (2012-03-13)
changeset 46904 f30e941b4512
parent 46818 2a28e66e2e4c
child 47022 8eac39af4ec0
permissions -rw-r--r--
prefer abs_def over def_raw;
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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 first_order_resolve : thm -> 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:
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    thm list -> thm -> Proof.context
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    -> Proof.context -> thm list * Proof.context
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  val finish_cnf: thm list -> thm list
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  val presimplified_consts : string 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 extensionalize_conv : Proof.context -> conv
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  val extensionalize_theorem : Proof.context -> thm -> thm
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  val make_clauses_unsorted: Proof.context -> thm list -> thm list
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  val make_clauses: Proof.context -> 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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end
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structure Meson : MESON =
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struct
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val trace = Attrib.setup_config_bool @{binding meson_trace} (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 = Attrib.setup_config_int @{binding meson_max_clauses} (K 60)
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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) (@{term False} :: 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
paulson@24937
   292
    else th;
paulson@24937
   293
paulson@24937
   294
paulson@18389
   295
(*** The basic CNF transformation ***)
paulson@18389
   296
blanchet@39328
   297
fun estimated_num_clauses bound t =
paulson@26562
   298
 let
blanchet@39269
   299
  fun sum x y = if x < bound andalso y < bound then x+y else bound
blanchet@39269
   300
  fun prod x y = if x < bound andalso y < bound then x*y else bound
paulson@26562
   301
  
paulson@26562
   302
  (*Estimate the number of clauses in order to detect infeasible theorems*)
haftmann@38557
   303
  fun signed_nclauses b (Const(@{const_name Trueprop},_) $ t) = signed_nclauses b t
haftmann@38557
   304
    | signed_nclauses b (Const(@{const_name Not},_) $ t) = signed_nclauses (not b) t
haftmann@38795
   305
    | signed_nclauses b (Const(@{const_name HOL.conj},_) $ t $ u) =
wenzelm@32960
   306
        if b then sum (signed_nclauses b t) (signed_nclauses b u)
wenzelm@32960
   307
             else prod (signed_nclauses b t) (signed_nclauses b u)
haftmann@38795
   308
    | signed_nclauses b (Const(@{const_name HOL.disj},_) $ t $ u) =
wenzelm@32960
   309
        if b then prod (signed_nclauses b t) (signed_nclauses b u)
wenzelm@32960
   310
             else sum (signed_nclauses b t) (signed_nclauses b u)
haftmann@38786
   311
    | signed_nclauses b (Const(@{const_name HOL.implies},_) $ t $ u) =
wenzelm@32960
   312
        if b then prod (signed_nclauses (not b) t) (signed_nclauses b u)
wenzelm@32960
   313
             else sum (signed_nclauses (not b) t) (signed_nclauses b u)
haftmann@38864
   314
    | signed_nclauses b (Const(@{const_name HOL.eq}, Type ("fun", [T, _])) $ t $ u) =
wenzelm@32960
   315
        if T = HOLogic.boolT then (*Boolean equality is if-and-only-if*)
wenzelm@32960
   316
            if b then sum (prod (signed_nclauses (not b) t) (signed_nclauses b u))
wenzelm@32960
   317
                          (prod (signed_nclauses (not b) u) (signed_nclauses b t))
wenzelm@32960
   318
                 else sum (prod (signed_nclauses b t) (signed_nclauses b u))
wenzelm@32960
   319
                          (prod (signed_nclauses (not b) t) (signed_nclauses (not b) u))
wenzelm@32960
   320
        else 1
haftmann@38557
   321
    | signed_nclauses b (Const(@{const_name Ex}, _) $ Abs (_,_,t)) = signed_nclauses b t
haftmann@38557
   322
    | signed_nclauses b (Const(@{const_name All},_) $ Abs (_,_,t)) = signed_nclauses b t
paulson@26562
   323
    | signed_nclauses _ _ = 1; (* literal *)
blanchet@39269
   324
 in signed_nclauses true t end
blanchet@39269
   325
blanchet@39269
   326
fun has_too_many_clauses ctxt t =
blanchet@39269
   327
  let val max_cl = Config.get ctxt max_clauses in
blanchet@39328
   328
    estimated_num_clauses (max_cl + 1) t > max_cl
blanchet@39269
   329
  end
paulson@19894
   330
paulson@15579
   331
(*Replaces universally quantified variables by FREE variables -- because
paulson@24937
   332
  assumptions may not contain scheme variables.  Later, generalize using Variable.export. *)
paulson@24937
   333
local  
paulson@24937
   334
  val spec_var = Thm.dest_arg (Thm.dest_arg (#2 (Thm.dest_implies (Thm.cprop_of spec))));
paulson@24937
   335
  val spec_varT = #T (Thm.rep_cterm spec_var);
haftmann@38557
   336
  fun name_of (Const (@{const_name All}, _) $ Abs(x,_,_)) = x | name_of _ = Name.uu;
paulson@24937
   337
in  
paulson@24937
   338
  fun freeze_spec th ctxt =
paulson@24937
   339
    let
wenzelm@42361
   340
      val cert = Thm.cterm_of (Proof_Context.theory_of ctxt);
paulson@24937
   341
      val ([x], ctxt') = Variable.variant_fixes [name_of (HOLogic.dest_Trueprop (concl_of th))] ctxt;
paulson@24937
   342
      val spec' = Thm.instantiate ([], [(spec_var, cert (Free (x, spec_varT)))]) spec;
paulson@24937
   343
    in (th RS spec', ctxt') end
paulson@24937
   344
end;
paulson@9840
   345
paulson@15998
   346
(*Used with METAHYPS below. There is one assumption, which gets bound to prem
paulson@15998
   347
  and then normalized via function nf. The normal form is given to resolve_tac,
paulson@22515
   348
  instantiate a Boolean variable created by resolution with disj_forward. Since
paulson@22515
   349
  (nf prem) returns a LIST of theorems, we can backtrack to get all combinations.*)
paulson@15579
   350
fun resop nf [prem] = resolve_tac (nf prem) 1;
paulson@9840
   351
blanchet@39037
   352
(* Any need to extend this list with "HOL.type_class", "HOL.eq_class",
blanchet@39037
   353
   and "Pure.term"? *)
haftmann@38557
   354
val has_meta_conn = exists_Const (member (op =) ["==", "==>", "=simp=>", "all", "prop"] o #1);
paulson@20417
   355
blanchet@37410
   356
fun apply_skolem_theorem (th, rls) =
blanchet@37398
   357
  let
blanchet@37410
   358
    fun tryall [] = raise THM ("apply_skolem_theorem", 0, th::rls)
blanchet@37398
   359
      | tryall (rl :: rls) =
blanchet@37398
   360
        first_order_resolve th rl handle THM _ => tryall rls
blanchet@37398
   361
  in tryall rls end
paulson@22515
   362
blanchet@37410
   363
(* Conjunctive normal form, adding clauses from th in front of ths (for foldr).
blanchet@37410
   364
   Strips universal quantifiers and breaks up conjunctions.
blanchet@37410
   365
   Eliminates existential quantifiers using Skolemization theorems. *)
blanchet@43964
   366
fun cnf old_skolem_ths ctxt ctxt0 (th, ths) =
blanchet@43964
   367
  let val ctxt0r = Unsynchronized.ref ctxt0   (* FIXME ??? *)
paulson@24937
   368
      fun cnf_aux (th,ths) =
wenzelm@24300
   369
        if not (can HOLogic.dest_Trueprop (prop_of th)) then ths (*meta-level: ignore*)
haftmann@38795
   370
        else if not (has_conns [@{const_name All}, @{const_name Ex}, @{const_name HOL.conj}] (prop_of th))
blanchet@43964
   371
        then nodups ctxt0 th :: ths (*no work to do, terminate*)
wenzelm@24300
   372
        else case head_of (HOLogic.dest_Trueprop (concl_of th)) of
haftmann@38795
   373
            Const (@{const_name HOL.conj}, _) => (*conjunction*)
wenzelm@24300
   374
                cnf_aux (th RS conjunct1, cnf_aux (th RS conjunct2, ths))
haftmann@38557
   375
          | Const (@{const_name All}, _) => (*universal quantifier*)
blanchet@43964
   376
                let val (th',ctxt0') = freeze_spec th (!ctxt0r)
blanchet@43964
   377
                in  ctxt0r := ctxt0'; cnf_aux (th', ths) end
haftmann@38557
   378
          | Const (@{const_name Ex}, _) =>
wenzelm@24300
   379
              (*existential quantifier: Insert Skolem functions*)
blanchet@39886
   380
              cnf_aux (apply_skolem_theorem (th, old_skolem_ths), ths)
haftmann@38795
   381
          | Const (@{const_name HOL.disj}, _) =>
wenzelm@24300
   382
              (*Disjunction of P, Q: Create new goal of proving ?P | ?Q and solve it using
wenzelm@24300
   383
                all combinations of converting P, Q to CNF.*)
wenzelm@24300
   384
              let val tac =
wenzelm@37781
   385
                  Misc_Legacy.METAHYPS (resop cnf_nil) 1 THEN
wenzelm@37781
   386
                   (fn st' => st' |> Misc_Legacy.METAHYPS (resop cnf_nil) 1)
wenzelm@24300
   387
              in  Seq.list_of (tac (th RS disj_forward)) @ ths  end
blanchet@43964
   388
          | _ => nodups ctxt0 th :: ths  (*no work to do*)
paulson@19154
   389
      and cnf_nil th = cnf_aux (th,[])
blanchet@39269
   390
      val cls =
blanchet@43964
   391
        if has_too_many_clauses ctxt (concl_of th) then
blanchet@43964
   392
          (trace_msg ctxt (fn () =>
blanchet@43964
   393
               "cnf is ignoring: " ^ Display.string_of_thm ctxt0 th); ths)
blanchet@43964
   394
        else
blanchet@43964
   395
          cnf_aux (th, ths)
blanchet@43964
   396
  in (cls, !ctxt0r) end
blanchet@43964
   397
fun make_cnf old_skolem_ths th ctxt ctxt0 =
blanchet@43964
   398
  cnf old_skolem_ths ctxt ctxt0 (th, [])
paulson@20417
   399
paulson@20417
   400
(*Generalization, removal of redundant equalities, removal of tautologies.*)
paulson@24937
   401
fun finish_cnf ths = filter (not o is_taut) (map refl_clause ths);
paulson@9840
   402
paulson@9840
   403
paulson@15579
   404
(**** Generation of contrapositives ****)
paulson@9840
   405
haftmann@38557
   406
fun is_left (Const (@{const_name Trueprop}, _) $
haftmann@38795
   407
               (Const (@{const_name HOL.disj}, _) $ (Const (@{const_name HOL.disj}, _) $ _ $ _) $ _)) = true
paulson@21102
   408
  | is_left _ = false;
wenzelm@24300
   409
paulson@15579
   410
(*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
wenzelm@24300
   411
fun assoc_right th =
paulson@21102
   412
  if is_left (prop_of th) then assoc_right (th RS disj_assoc)
paulson@21102
   413
  else th;
paulson@9840
   414
paulson@15579
   415
(*Must check for negative literal first!*)
paulson@15579
   416
val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
paulson@9840
   417
paulson@15579
   418
(*For ordinary resolution. *)
paulson@15579
   419
val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule'];
paulson@9840
   420
paulson@15579
   421
(*Create a goal or support clause, conclusing False*)
paulson@15579
   422
fun make_goal th =   (*Must check for negative literal first!*)
paulson@15579
   423
    make_goal (tryres(th, clause_rules))
paulson@15579
   424
  handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
paulson@9840
   425
paulson@15579
   426
(*Sort clauses by number of literals*)
paulson@15579
   427
fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2);
paulson@9840
   428
paulson@18389
   429
fun sort_clauses ths = sort (make_ord fewerlits) ths;
paulson@9840
   430
blanchet@38099
   431
fun has_bool @{typ bool} = true
blanchet@38099
   432
  | has_bool (Type (_, Ts)) = exists has_bool Ts
blanchet@38099
   433
  | has_bool _ = false
blanchet@38099
   434
blanchet@38099
   435
fun has_fun (Type (@{type_name fun}, _)) = true
blanchet@38099
   436
  | has_fun (Type (_, Ts)) = exists has_fun Ts
blanchet@38099
   437
  | has_fun _ = false
wenzelm@24300
   438
wenzelm@24300
   439
(*Is the string the name of a connective? Really only | and Not can remain,
wenzelm@24300
   440
  since this code expects to be called on a clause form.*)
wenzelm@19875
   441
val is_conn = member (op =)
haftmann@38795
   442
    [@{const_name Trueprop}, @{const_name HOL.conj}, @{const_name HOL.disj},
haftmann@38786
   443
     @{const_name HOL.implies}, @{const_name Not},
haftmann@38557
   444
     @{const_name All}, @{const_name Ex}, @{const_name Ball}, @{const_name Bex}];
paulson@15613
   445
wenzelm@24300
   446
(*True if the term contains a function--not a logical connective--where the type
paulson@20524
   447
  of any argument contains bool.*)
wenzelm@24300
   448
val has_bool_arg_const =
paulson@15613
   449
    exists_Const
blanchet@38099
   450
      (fn (c,T) => not(is_conn c) andalso exists has_bool (binder_types T));
paulson@22381
   451
wenzelm@24300
   452
(*A higher-order instance of a first-order constant? Example is the definition of
haftmann@38622
   453
  one, 1, at a function type in theory Function_Algebras.*)
wenzelm@24300
   454
fun higher_inst_const thy (c,T) =
paulson@22381
   455
  case binder_types T of
paulson@22381
   456
      [] => false (*not a function type, OK*)
paulson@22381
   457
    | Ts => length (binder_types (Sign.the_const_type thy c)) <> length Ts;
paulson@22381
   458
paulson@21102
   459
fun rigid t = not (is_Var (head_of t));
paulson@21102
   460
haftmann@38795
   461
fun ok4horn (Const (@{const_name Trueprop},_) $ (Const (@{const_name HOL.disj}, _) $ t $ _)) = rigid t
haftmann@38557
   462
  | ok4horn (Const (@{const_name Trueprop},_) $ t) = rigid t
paulson@21102
   463
  | ok4horn _ = false;
paulson@21102
   464
paulson@15579
   465
(*Create a meta-level Horn clause*)
wenzelm@24300
   466
fun make_horn crules th =
wenzelm@24300
   467
  if ok4horn (concl_of th)
paulson@21102
   468
  then make_horn crules (tryres(th,crules)) handle THM _ => th
paulson@21102
   469
  else th;
paulson@9840
   470
paulson@16563
   471
(*Generate Horn clauses for all contrapositives of a clause. The input, th,
paulson@16563
   472
  is a HOL disjunction.*)
wenzelm@33339
   473
fun add_contras crules th hcs =
blanchet@39328
   474
  let fun rots (0,_) = hcs
wenzelm@24300
   475
        | rots (k,th) = zero_var_indexes (make_horn crules th) ::
wenzelm@24300
   476
                        rots(k-1, assoc_right (th RS disj_comm))
paulson@15862
   477
  in case nliterals(prop_of th) of
wenzelm@24300
   478
        1 => th::hcs
paulson@15579
   479
      | n => rots(n, assoc_right th)
paulson@15579
   480
  end;
paulson@9840
   481
paulson@15579
   482
(*Use "theorem naming" to label the clauses*)
paulson@15579
   483
fun name_thms label =
wenzelm@33339
   484
    let fun name1 th (k, ths) =
wenzelm@27865
   485
          (k-1, Thm.put_name_hint (label ^ string_of_int k) th :: ths)
wenzelm@33339
   486
    in  fn ths => #2 (fold_rev name1 ths (length ths, []))  end;
paulson@9840
   487
paulson@16563
   488
(*Is the given disjunction an all-negative support clause?*)
paulson@15579
   489
fun is_negative th = forall (not o #1) (literals (prop_of th));
paulson@9840
   490
wenzelm@33317
   491
val neg_clauses = filter is_negative;
paulson@9840
   492
paulson@9840
   493
paulson@15579
   494
(***** MESON PROOF PROCEDURE *****)
paulson@9840
   495
haftmann@38557
   496
fun rhyps (Const("==>",_) $ (Const(@{const_name Trueprop},_) $ A) $ phi,
wenzelm@24300
   497
           As) = rhyps(phi, A::As)
paulson@15579
   498
  | rhyps (_, As) = As;
paulson@9840
   499
paulson@15579
   500
(** Detecting repeated assumptions in a subgoal **)
paulson@9840
   501
paulson@15579
   502
(*The stringtree detects repeated assumptions.*)
wenzelm@33245
   503
fun ins_term t net = Net.insert_term (op aconv) (t, t) net;
paulson@9840
   504
paulson@15579
   505
(*detects repetitions in a list of terms*)
paulson@15579
   506
fun has_reps [] = false
paulson@15579
   507
  | has_reps [_] = false
paulson@15579
   508
  | has_reps [t,u] = (t aconv u)
wenzelm@33245
   509
  | has_reps ts = (fold ins_term ts Net.empty; false) handle Net.INSERT => true;
paulson@9840
   510
paulson@15579
   511
(*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*)
paulson@18508
   512
fun TRYING_eq_assume_tac 0 st = Seq.single st
paulson@18508
   513
  | TRYING_eq_assume_tac i st =
wenzelm@31945
   514
       TRYING_eq_assume_tac (i-1) (Thm.eq_assumption i st)
paulson@18508
   515
       handle THM _ => TRYING_eq_assume_tac (i-1) st;
paulson@18508
   516
paulson@18508
   517
fun TRYALL_eq_assume_tac st = TRYING_eq_assume_tac (nprems_of st) st;
paulson@9840
   518
paulson@15579
   519
(*Loop checking: FAIL if trying to prove the same thing twice
paulson@15579
   520
  -- if *ANY* subgoal has repeated literals*)
paulson@15579
   521
fun check_tac st =
paulson@15579
   522
  if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st)
paulson@15579
   523
  then  Seq.empty  else  Seq.single st;
paulson@9840
   524
paulson@9840
   525
paulson@15579
   526
(* net_resolve_tac actually made it slower... *)
paulson@15579
   527
fun prolog_step_tac horns i =
paulson@15579
   528
    (assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
paulson@18508
   529
    TRYALL_eq_assume_tac;
paulson@9840
   530
paulson@9840
   531
(*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*)
wenzelm@33339
   532
fun addconcl prem sz = size_of_term (Logic.strip_assums_concl prem) + sz;
paulson@15579
   533
wenzelm@33339
   534
fun size_of_subgoals st = fold_rev addconcl (prems_of st) 0;
paulson@15579
   535
paulson@9840
   536
paulson@9840
   537
(*Negation Normal Form*)
paulson@9840
   538
val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD,
wenzelm@9869
   539
               not_impD, not_iffD, not_allD, not_exD, not_notD];
paulson@15581
   540
haftmann@38557
   541
fun ok4nnf (Const (@{const_name Trueprop},_) $ (Const (@{const_name Not}, _) $ t)) = rigid t
haftmann@38557
   542
  | ok4nnf (Const (@{const_name Trueprop},_) $ t) = rigid t
paulson@21102
   543
  | ok4nnf _ = false;
paulson@21102
   544
wenzelm@32262
   545
fun make_nnf1 ctxt th =
wenzelm@24300
   546
  if ok4nnf (concl_of th)
wenzelm@32262
   547
  then make_nnf1 ctxt (tryres(th, nnf_rls))
paulson@28174
   548
    handle THM ("tryres", _, _) =>
wenzelm@32262
   549
        forward_res ctxt (make_nnf1 ctxt)
wenzelm@9869
   550
           (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
paulson@28174
   551
    handle THM ("tryres", _, _) => th
blanchet@38608
   552
  else th
paulson@9840
   553
wenzelm@24300
   554
(*The simplification removes defined quantifiers and occurrences of True and False.
paulson@20018
   555
  nnf_ss also includes the one-point simprocs,
paulson@18405
   556
  which are needed to avoid the various one-point theorems from generating junk clauses.*)
paulson@19894
   557
val nnf_simps =
blanchet@37539
   558
  @{thms simp_implies_def Ex1_def Ball_def Bex_def if_True if_False if_cancel
blanchet@37539
   559
         if_eq_cancel cases_simp}
blanchet@37539
   560
val nnf_extra_simps = @{thms split_ifs ex_simps all_simps simp_thms}
paulson@18405
   561
blanchet@43821
   562
(* FIXME: "let_simp" is probably redundant now that we also rewrite with
wenzelm@46904
   563
  "Let_def [abs_def]". *)
paulson@18405
   564
val nnf_ss =
wenzelm@24300
   565
  HOL_basic_ss addsimps nnf_extra_simps
blanchet@43264
   566
    addsimprocs [@{simproc defined_All}, @{simproc defined_Ex}, @{simproc neq},
blanchet@43264
   567
                 @{simproc let_simp}]
blanchet@43264
   568
blanchet@46093
   569
val presimplified_consts =
blanchet@43264
   570
  [@{const_name simp_implies}, @{const_name False}, @{const_name True},
blanchet@43264
   571
   @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}, @{const_name If},
blanchet@43264
   572
   @{const_name Let}]
paulson@15872
   573
blanchet@46093
   574
val presimplify =
blanchet@42750
   575
  rewrite_rule (map safe_mk_meta_eq nnf_simps)
blanchet@42750
   576
  #> simplify nnf_ss
wenzelm@46904
   577
  #> Raw_Simplifier.rewrite_rule @{thms Let_def [abs_def]}
blanchet@38089
   578
wenzelm@32262
   579
fun make_nnf ctxt th = case prems_of th of
blanchet@46093
   580
    [] => th |> presimplify |> make_nnf1 ctxt
paulson@21050
   581
  | _ => raise THM ("make_nnf: premises in argument", 0, [th]);
paulson@15581
   582
blanchet@39950
   583
fun choice_theorems thy =
blanchet@39950
   584
  try (Global_Theory.get_thm thy) "Hilbert_Choice.choice" |> the_list
blanchet@39950
   585
blanchet@39900
   586
(* Pull existential quantifiers to front. This accomplishes Skolemization for
blanchet@39900
   587
   clauses that arise from a subgoal. *)
blanchet@39950
   588
fun skolemize_with_choice_theorems ctxt choice_ths =
blanchet@39900
   589
  let
blanchet@39900
   590
    fun aux th =
blanchet@39900
   591
      if not (has_conns [@{const_name Ex}] (prop_of th)) then
blanchet@39900
   592
        th
blanchet@39900
   593
      else
blanchet@39901
   594
        tryres (th, choice_ths @
blanchet@39900
   595
                    [conj_exD1, conj_exD2, disj_exD, disj_exD1, disj_exD2])
blanchet@39900
   596
        |> aux
blanchet@39900
   597
        handle THM ("tryres", _, _) =>
blanchet@39900
   598
               tryres (th, [conj_forward, disj_forward, all_forward])
blanchet@39900
   599
               |> forward_res ctxt aux
blanchet@39900
   600
               |> aux
blanchet@39900
   601
               handle THM ("tryres", _, _) =>
blanchet@40262
   602
                      rename_bound_vars_RS th ex_forward
blanchet@39900
   603
                      |> forward_res ctxt aux
blanchet@39900
   604
  in aux o make_nnf ctxt end
paulson@29684
   605
blanchet@39950
   606
fun skolemize ctxt =
wenzelm@42361
   607
  let val thy = Proof_Context.theory_of ctxt in
blanchet@39950
   608
    skolemize_with_choice_theorems ctxt (choice_theorems thy)
blanchet@39950
   609
  end
blanchet@39904
   610
blanchet@42760
   611
(* Removes the lambdas from an equation of the form "t = (%x1 ... xn. u)". It
blanchet@42760
   612
   would be desirable to do this symmetrically but there's at least one existing
blanchet@42760
   613
   proof in "Tarski" that relies on the current behavior. *)
blanchet@42747
   614
fun extensionalize_conv ctxt ct =
blanchet@42747
   615
  case term_of ct of
blanchet@42760
   616
    Const (@{const_name HOL.eq}, _) $ _ $ Abs _ =>
blanchet@42760
   617
    ct |> (Conv.rewr_conv @{thm fun_eq_iff [THEN eq_reflection]}
blanchet@42760
   618
           then_conv extensionalize_conv ctxt)
blanchet@42747
   619
  | _ $ _ => Conv.comb_conv (extensionalize_conv ctxt) ct
blanchet@42747
   620
  | Abs _ => Conv.abs_conv (extensionalize_conv o snd) ctxt ct
blanchet@42747
   621
  | _ => Conv.all_conv ct
blanchet@42747
   622
blanchet@42747
   623
val extensionalize_theorem = Conv.fconv_rule o extensionalize_conv
blanchet@42747
   624
blanchet@39900
   625
(* "RS" can fail if "unify_search_bound" is too small. *)
blanchet@46071
   626
fun try_skolemize_etc ctxt th =
blanchet@42747
   627
  (* Extensionalize "th", because that makes sense and that's what Sledgehammer
blanchet@42747
   628
     does, but also keep an unextensionalized version of "th" for backward
blanchet@42747
   629
     compatibility. *)
blanchet@46071
   630
  [th] |> insert Thm.eq_thm_prop (extensionalize_theorem ctxt th)
blanchet@46071
   631
       |> map_filter (fn th => th |> try (skolemize ctxt)
blanchet@46071
   632
                                  |> tap (fn NONE =>
blanchet@46071
   633
                                             trace_msg ctxt (fn () =>
blanchet@46071
   634
                                                 "Failed to skolemize " ^
blanchet@46071
   635
                                                  Display.string_of_thm ctxt th)
blanchet@46071
   636
                                           | _ => ()))
paulson@25694
   637
blanchet@43964
   638
fun add_clauses ctxt th cls =
wenzelm@36603
   639
  let val ctxt0 = Variable.global_thm_context th
blanchet@43964
   640
      val (cnfs, ctxt) = make_cnf [] th ctxt ctxt0
paulson@24937
   641
  in Variable.export ctxt ctxt0 cnfs @ cls end;
paulson@9840
   642
paulson@9840
   643
(*Make clauses from a list of theorems, previously Skolemized and put into nnf.
paulson@9840
   644
  The resulting clauses are HOL disjunctions.*)
blanchet@43964
   645
fun make_clauses_unsorted ctxt ths = fold_rev (add_clauses ctxt) ths [];
blanchet@43964
   646
val make_clauses = sort_clauses oo make_clauses_unsorted;
quigley@15773
   647
paulson@16563
   648
(*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*)
wenzelm@9869
   649
fun make_horns ths =
paulson@9840
   650
    name_thms "Horn#"
wenzelm@33339
   651
      (distinct Thm.eq_thm_prop (fold_rev (add_contras clause_rules) ths []));
paulson@9840
   652
paulson@9840
   653
(*Could simply use nprems_of, which would count remaining subgoals -- no
paulson@9840
   654
  discrimination as to their size!  With BEST_FIRST, fails for problem 41.*)
paulson@9840
   655
wenzelm@9869
   656
fun best_prolog_tac sizef horns =
paulson@9840
   657
    BEST_FIRST (has_fewer_prems 1, sizef) (prolog_step_tac horns 1);
paulson@9840
   658
wenzelm@9869
   659
fun depth_prolog_tac horns =
paulson@9840
   660
    DEPTH_FIRST (has_fewer_prems 1) (prolog_step_tac horns 1);
paulson@9840
   661
paulson@9840
   662
(*Return all negative clauses, as possible goal clauses*)
paulson@9840
   663
fun gocls cls = name_thms "Goal#" (map make_goal (neg_clauses cls));
paulson@9840
   664
wenzelm@32262
   665
fun skolemize_prems_tac ctxt prems =
blanchet@42747
   666
  cut_facts_tac (maps (try_skolemize_etc ctxt) prems) THEN' REPEAT o etac exE
paulson@9840
   667
paulson@22546
   668
(*Basis of all meson-tactics.  Supplies cltac with clauses: HOL disjunctions.
paulson@22546
   669
  Function mkcl converts theorems to clauses.*)
blanchet@39037
   670
fun MESON preskolem_tac mkcl cltac ctxt i st =
paulson@16588
   671
  SELECT_GOAL
wenzelm@35625
   672
    (EVERY [Object_Logic.atomize_prems_tac 1,
paulson@23552
   673
            rtac ccontr 1,
blanchet@39269
   674
            preskolem_tac,
wenzelm@32283
   675
            Subgoal.FOCUS (fn {context = ctxt', prems = negs, ...} =>
blanchet@39269
   676
                      EVERY1 [skolemize_prems_tac ctxt negs,
wenzelm@32283
   677
                              Subgoal.FOCUS (cltac o mkcl o #prems) ctxt']) ctxt 1]) i st
wenzelm@24300
   678
  handle THM _ => no_tac st;    (*probably from make_meta_clause, not first-order*)
paulson@9840
   679
blanchet@39037
   680
paulson@9840
   681
(** Best-first search versions **)
paulson@9840
   682
paulson@16563
   683
(*ths is a list of additional clauses (HOL disjunctions) to use.*)
blanchet@43964
   684
fun best_meson_tac sizef ctxt =
blanchet@43964
   685
  MESON all_tac (make_clauses ctxt)
paulson@22546
   686
    (fn cls =>
paulson@9840
   687
         THEN_BEST_FIRST (resolve_tac (gocls cls) 1)
paulson@9840
   688
                         (has_fewer_prems 1, sizef)
blanchet@43964
   689
                         (prolog_step_tac (make_horns cls) 1))
blanchet@43964
   690
    ctxt
paulson@9840
   691
paulson@9840
   692
(*First, breaks the goal into independent units*)
wenzelm@32262
   693
fun safe_best_meson_tac ctxt =
wenzelm@42793
   694
  SELECT_GOAL (TRY (safe_tac ctxt) THEN TRYALL (best_meson_tac size_of_subgoals ctxt));
paulson@9840
   695
paulson@9840
   696
(** Depth-first search version **)
paulson@9840
   697
blanchet@43964
   698
fun depth_meson_tac ctxt =
blanchet@43964
   699
  MESON all_tac (make_clauses ctxt)
blanchet@43964
   700
    (fn cls => EVERY [resolve_tac (gocls cls) 1, depth_prolog_tac (make_horns cls)])
blanchet@43964
   701
    ctxt
paulson@9840
   702
paulson@9840
   703
(** Iterative deepening version **)
paulson@9840
   704
paulson@9840
   705
(*This version does only one inference per call;
paulson@9840
   706
  having only one eq_assume_tac speeds it up!*)
wenzelm@9869
   707
fun prolog_step_tac' horns =
blanchet@39328
   708
    let val (horn0s, _) = (*0 subgoals vs 1 or more*)
paulson@9840
   709
            take_prefix Thm.no_prems horns
paulson@9840
   710
        val nrtac = net_resolve_tac horns
paulson@9840
   711
    in  fn i => eq_assume_tac i ORELSE
paulson@9840
   712
                match_tac horn0s i ORELSE  (*no backtracking if unit MATCHES*)
paulson@9840
   713
                ((assume_tac i APPEND nrtac i) THEN check_tac)
paulson@9840
   714
    end;
paulson@9840
   715
wenzelm@9869
   716
fun iter_deepen_prolog_tac horns =
wenzelm@38802
   717
    ITER_DEEPEN iter_deepen_limit (has_fewer_prems 1) (prolog_step_tac' horns);
paulson@9840
   718
blanchet@43964
   719
fun iter_deepen_meson_tac ctxt ths = ctxt |> MESON all_tac (make_clauses ctxt)
wenzelm@32091
   720
  (fn cls =>
wenzelm@32091
   721
    (case (gocls (cls @ ths)) of
wenzelm@32091
   722
      [] => no_tac  (*no goal clauses*)
wenzelm@32091
   723
    | goes =>
wenzelm@32091
   724
        let
wenzelm@32091
   725
          val horns = make_horns (cls @ ths)
blanchet@39979
   726
          val _ = trace_msg ctxt (fn () =>
wenzelm@32091
   727
            cat_lines ("meson method called:" ::
wenzelm@32262
   728
              map (Display.string_of_thm ctxt) (cls @ ths) @
wenzelm@32262
   729
              ["clauses:"] @ map (Display.string_of_thm ctxt) horns))
wenzelm@38802
   730
        in
wenzelm@38802
   731
          THEN_ITER_DEEPEN iter_deepen_limit
wenzelm@38802
   732
            (resolve_tac goes 1) (has_fewer_prems 1) (prolog_step_tac' horns)
wenzelm@38802
   733
        end));
paulson@9840
   734
wenzelm@32262
   735
fun meson_tac ctxt ths =
wenzelm@42793
   736
  SELECT_GOAL (TRY (safe_tac ctxt) THEN TRYALL (iter_deepen_meson_tac ctxt ths));
wenzelm@9869
   737
wenzelm@9869
   738
paulson@14813
   739
(**** Code to support ordinary resolution, rather than Model Elimination ****)
paulson@14744
   740
wenzelm@24300
   741
(*Convert a list of clauses (disjunctions) to meta-level clauses (==>),
paulson@15008
   742
  with no contrapositives, for ordinary resolution.*)
paulson@14744
   743
paulson@14744
   744
(*Rules to convert the head literal into a negated assumption. If the head
paulson@14744
   745
  literal is already negated, then using notEfalse instead of notEfalse'
paulson@14744
   746
  prevents a double negation.*)
wenzelm@46503
   747
val notEfalse = @{lemma "~ P ==> P ==> False" by (rule notE)};
wenzelm@46503
   748
val notEfalse' = @{lemma "P ==> ~ P ==> False" by (rule notE)};
paulson@14744
   749
wenzelm@24300
   750
fun negated_asm_of_head th =
paulson@14744
   751
    th RS notEfalse handle THM _ => th RS notEfalse';
paulson@14744
   752
paulson@26066
   753
(*Converting one theorem from a disjunction to a meta-level clause*)
paulson@26066
   754
fun make_meta_clause th =
wenzelm@33832
   755
  let val (fth,thaw) = Drule.legacy_freeze_thaw_robust th
paulson@26066
   756
  in  
wenzelm@35845
   757
      (zero_var_indexes o Thm.varifyT_global o thaw 0 o 
paulson@26066
   758
       negated_asm_of_head o make_horn resolution_clause_rules) fth
paulson@26066
   759
  end;
wenzelm@24300
   760
paulson@14744
   761
fun make_meta_clauses ths =
paulson@14744
   762
    name_thms "MClause#"
wenzelm@22360
   763
      (distinct Thm.eq_thm_prop (map make_meta_clause ths));
paulson@14744
   764
paulson@9840
   765
end;