src/HOL/Tools/Sledgehammer/metis_tactics.ML
author blanchet
Thu Sep 09 20:11:52 2010 +0200 (2010-09-09)
changeset 39269 c2795d8a2461
parent 39267 c663b0cdebc4
child 39352 7d850b17a7a6
permissions -rw-r--r--
use definitional CNF for the goal if at least one of the premisses would lead to too many clauses in Meson
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(*  Title:      HOL/Tools/Sledgehammer/metis_tactics.ML
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    Author:     Kong W. Susanto, Cambridge University Computer Laboratory
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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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    Copyright   Cambridge University 2007
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HOL setup for the Metis prover.
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*)
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signature METIS_TACTICS =
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sig
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  val trace: bool Unsynchronized.ref
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  val type_lits: bool Config.T
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  val metis_tac: Proof.context -> thm list -> int -> tactic
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  val metisF_tac: Proof.context -> thm list -> int -> tactic
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  val metisFT_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 Metis_Tactics : METIS_TACTICS =
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struct
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open Metis_Clauses
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val trace = Unsynchronized.ref false;
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fun trace_msg msg = if !trace then tracing (msg ()) else ();
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val (type_lits, type_lits_setup) = Attrib.config_bool "metis_type_lits" (K true);
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datatype mode = FO | HO | FT  (* first-order, higher-order, fully-typed *)
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(* ------------------------------------------------------------------------- *)
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(* Useful Theorems                                                           *)
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(* ------------------------------------------------------------------------- *)
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val EXCLUDED_MIDDLE = @{lemma "P ==> ~ P ==> False" by (rule notE)}
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val REFL_THM = Thm.incr_indexes 2 @{lemma "t ~= t ==> False" by simp}
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val subst_em = @{lemma "s = t ==> P s ==> ~ P t ==> False" by simp}
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val ssubst_em = @{lemma "s = t ==> P t ==> ~ P s ==> False" by simp}
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(* ------------------------------------------------------------------------- *)
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(* Useful Functions                                                          *)
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(* ------------------------------------------------------------------------- *)
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(* Match untyped terms. *)
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fun untyped_aconv (Const (a, _)) (Const(b, _)) = (a = b)
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  | untyped_aconv (Free (a, _)) (Free (b, _)) = (a = b)
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  | untyped_aconv (Var ((a, _), _)) (Var ((b, _), _)) =
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    (a = b) (* The index is ignored, for some reason. *)
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  | untyped_aconv (Bound i) (Bound j) = (i = j)
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  | untyped_aconv (Abs (_, _, t)) (Abs (_, _, u)) = untyped_aconv t u
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  | untyped_aconv (t1 $ t2) (u1 $ u2) =
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    untyped_aconv t1 u1 andalso untyped_aconv t2 u2
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  | untyped_aconv _ _ = false
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(* Finding the relative location of an untyped term within a list of terms *)
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fun get_index lit =
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  let val lit = Envir.eta_contract lit
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      fun get _ [] = raise Empty
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        | get n (x::xs) = if untyped_aconv lit (Envir.eta_contract (HOLogic.dest_Trueprop x))
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                          then n  else get (n+1) xs
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  in get 1 end;
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(* ------------------------------------------------------------------------- *)
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(* HOL to FOL  (Isabelle to Metis)                                           *)
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(* ------------------------------------------------------------------------- *)
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fun fn_isa_to_met_sublevel "equal" = "=" (* FIXME: "c_fequal" *)
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  | fn_isa_to_met_sublevel x = x
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fun fn_isa_to_met_toplevel "equal" = "="
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  | fn_isa_to_met_toplevel x = x
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fun metis_lit b c args = (b, (c, args));
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fun metis_term_from_combtyp (CombTVar (s, _)) = Metis.Term.Var s
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  | metis_term_from_combtyp (CombTFree (s, _)) = Metis.Term.Fn (s, [])
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  | metis_term_from_combtyp (CombType ((s, _), tps)) =
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    Metis.Term.Fn (s, map metis_term_from_combtyp tps);
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(*These two functions insert type literals before the real literals. That is the
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  opposite order from TPTP linkup, but maybe OK.*)
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fun hol_term_to_fol_FO tm =
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  case strip_combterm_comb tm of
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      (CombConst ((c, _), _, tys), tms) =>
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        let val tyargs = map metis_term_from_combtyp tys
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            val args   = map hol_term_to_fol_FO tms
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        in Metis.Term.Fn (c, tyargs @ args) end
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    | (CombVar ((v, _), _), []) => Metis.Term.Var v
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    | _ => raise Fail "non-first-order combterm"
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fun hol_term_to_fol_HO (CombConst ((a, _), _, tylist)) =
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      Metis.Term.Fn (fn_isa_to_met_sublevel a, map metis_term_from_combtyp tylist)
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  | hol_term_to_fol_HO (CombVar ((s, _), _)) = Metis.Term.Var s
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  | hol_term_to_fol_HO (CombApp (tm1, tm2)) =
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       Metis.Term.Fn (".", map hol_term_to_fol_HO [tm1, tm2]);
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(*The fully-typed translation, to avoid type errors*)
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fun wrap_type (tm, ty) = Metis.Term.Fn("ti", [tm, metis_term_from_combtyp ty]);
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fun hol_term_to_fol_FT (CombVar ((s, _), ty)) = wrap_type (Metis.Term.Var s, ty)
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  | hol_term_to_fol_FT (CombConst((a, _), ty, _)) =
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      wrap_type (Metis.Term.Fn(fn_isa_to_met_sublevel a, []), ty)
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  | hol_term_to_fol_FT (tm as CombApp(tm1,tm2)) =
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       wrap_type (Metis.Term.Fn(".", map hol_term_to_fol_FT [tm1,tm2]),
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                  combtyp_of tm)
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fun hol_literal_to_fol FO (FOLLiteral (pos, tm)) =
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      let val (CombConst((p, _), _, tys), tms) = strip_combterm_comb tm
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          val tylits = if p = "equal" then [] else map metis_term_from_combtyp tys
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          val lits = map hol_term_to_fol_FO tms
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      in metis_lit pos (fn_isa_to_met_toplevel p) (tylits @ lits) end
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  | hol_literal_to_fol HO (FOLLiteral (pos, tm)) =
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     (case strip_combterm_comb tm of
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          (CombConst(("equal", _), _, _), tms) =>
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            metis_lit pos "=" (map hol_term_to_fol_HO tms)
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        | _ => metis_lit pos "{}" [hol_term_to_fol_HO tm])   (*hBOOL*)
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  | hol_literal_to_fol FT (FOLLiteral (pos, tm)) =
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     (case strip_combterm_comb tm of
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          (CombConst(("equal", _), _, _), tms) =>
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            metis_lit pos "=" (map hol_term_to_fol_FT tms)
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        | _ => metis_lit pos "{}" [hol_term_to_fol_FT tm])   (*hBOOL*);
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fun literals_of_hol_term thy mode t =
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      let val (lits, types_sorts) = literals_of_term thy t
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      in  (map (hol_literal_to_fol mode) lits, types_sorts) end;
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(*Sign should be "true" for conjecture type constraints, "false" for type lits in clauses.*)
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fun metis_of_type_literals pos (TyLitVar ((s, _), (s', _))) =
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    metis_lit pos s [Metis.Term.Var s']
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  | metis_of_type_literals pos (TyLitFree ((s, _), (s', _))) =
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    metis_lit pos s [Metis.Term.Fn (s',[])]
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fun default_sort _ (TVar _) = false
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  | default_sort ctxt (TFree (x, s)) = (s = the_default [] (Variable.def_sort ctxt (x, ~1)));
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fun metis_of_tfree tf =
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  Metis.Thm.axiom (Metis.LiteralSet.singleton (metis_of_type_literals true tf));
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fun hol_thm_to_fol is_conjecture ctxt mode j skolems th =
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  let
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    val thy = ProofContext.theory_of ctxt
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    val (skolems, (mlits, types_sorts)) =
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     th |> prop_of |> conceal_skolem_terms j skolems
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        ||> (HOLogic.dest_Trueprop #> literals_of_hol_term thy mode)
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  in
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      if is_conjecture then
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          (Metis.Thm.axiom (Metis.LiteralSet.fromList mlits),
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           type_literals_for_types types_sorts, skolems)
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      else
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        let val tylits = filter_out (default_sort ctxt) types_sorts
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                         |> type_literals_for_types
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            val mtylits = if Config.get ctxt type_lits
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                          then map (metis_of_type_literals false) tylits else []
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        in
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          (Metis.Thm.axiom (Metis.LiteralSet.fromList(mtylits @ mlits)), [],
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           skolems)
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        end
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  end;
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(* ARITY CLAUSE *)
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fun m_arity_cls (TConsLit ((c, _), (t, _), args)) =
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    metis_lit true c [Metis.Term.Fn(t, map (Metis.Term.Var o fst) args)]
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  | m_arity_cls (TVarLit ((c, _), (s, _))) =
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    metis_lit false c [Metis.Term.Var s]
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(*TrueI is returned as the Isabelle counterpart because there isn't any.*)
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fun arity_cls (ArityClause {conclLit, premLits, ...}) =
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  (TrueI,
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   Metis.Thm.axiom (Metis.LiteralSet.fromList (map m_arity_cls (conclLit :: premLits))));
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(* CLASSREL CLAUSE *)
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fun m_class_rel_cls (subclass, _) (superclass, _) =
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  [metis_lit false subclass [Metis.Term.Var "T"], metis_lit true superclass [Metis.Term.Var "T"]];
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fun class_rel_cls (ClassRelClause {subclass, superclass, ...}) =
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  (TrueI, Metis.Thm.axiom (Metis.LiteralSet.fromList (m_class_rel_cls subclass superclass)));
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(* ------------------------------------------------------------------------- *)
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(* FOL to HOL  (Metis to Isabelle)                                           *)
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(* ------------------------------------------------------------------------- *)
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datatype term_or_type = Term of Term.term | Type of Term.typ;
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fun terms_of [] = []
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  | terms_of (Term t :: tts) = t :: terms_of tts
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  | terms_of (Type _ :: tts) = terms_of tts;
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fun types_of [] = []
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  | types_of (Term (Term.Var ((a,idx), _)) :: tts) =
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      if String.isPrefix "_" a then
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          (*Variable generated by Metis, which might have been a type variable.*)
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          TVar (("'" ^ a, idx), HOLogic.typeS) :: types_of tts
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      else types_of tts
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  | types_of (Term _ :: tts) = types_of tts
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  | types_of (Type T :: tts) = T :: types_of tts;
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fun apply_list rator nargs rands =
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  let val trands = terms_of rands
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  in  if length trands = nargs then Term (list_comb(rator, trands))
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      else raise Fail
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        ("apply_list: wrong number of arguments: " ^ Syntax.string_of_term_global Pure.thy rator ^
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          " expected " ^ Int.toString nargs ^
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          " received " ^ commas (map (Syntax.string_of_term_global Pure.thy) trands))
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  end;
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fun infer_types ctxt =
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  Syntax.check_terms (ProofContext.set_mode ProofContext.mode_pattern ctxt);
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(*We use 1 rather than 0 because variable references in clauses may otherwise conflict
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  with variable constraints in the goal...at least, type inference often fails otherwise.
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  SEE ALSO axiom_inf below.*)
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fun mk_var (w,T) = Term.Var((w,1), T);
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(*include the default sort, if available*)
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fun mk_tfree ctxt w =
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  let val ww = "'" ^ w
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  in  TFree(ww, the_default HOLogic.typeS (Variable.def_sort ctxt (ww, ~1)))  end;
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(*Remove the "apply" operator from an HO term*)
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fun strip_happ args (Metis.Term.Fn(".",[t,u])) = strip_happ (u::args) t
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  | strip_happ args x = (x, args);
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fun make_tvar s = TVar (("'" ^ s, 0), HOLogic.typeS)
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fun smart_invert_const "fequal" = @{const_name HOL.eq}
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  | smart_invert_const s = invert_const s
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fun hol_type_from_metis_term _ (Metis.Term.Var v) =
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     (case strip_prefix_and_unascii tvar_prefix v of
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          SOME w => make_tvar w
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        | NONE   => make_tvar v)
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  | hol_type_from_metis_term ctxt (Metis.Term.Fn(x, tys)) =
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     (case strip_prefix_and_unascii type_const_prefix x of
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          SOME tc => Term.Type (smart_invert_const tc,
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                                map (hol_type_from_metis_term ctxt) tys)
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        | NONE    =>
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      case strip_prefix_and_unascii tfree_prefix x of
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          SOME tf => mk_tfree ctxt tf
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        | NONE    => raise Fail ("hol_type_from_metis_term: " ^ x));
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(*Maps metis terms to isabelle terms*)
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fun hol_term_from_metis_PT ctxt fol_tm =
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  let val thy = ProofContext.theory_of ctxt
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      val _ = trace_msg (fn () => "hol_term_from_metis_PT: " ^
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                                  Metis.Term.toString fol_tm)
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      fun tm_to_tt (Metis.Term.Var v) =
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             (case strip_prefix_and_unascii tvar_prefix v of
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                  SOME w => Type (make_tvar w)
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                | NONE =>
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              case strip_prefix_and_unascii schematic_var_prefix v of
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                  SOME w => Term (mk_var (w, HOLogic.typeT))
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                | NONE   => Term (mk_var (v, HOLogic.typeT)) )
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                    (*Var from Metis with a name like _nnn; possibly a type variable*)
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        | tm_to_tt (Metis.Term.Fn ("{}", [arg])) = tm_to_tt arg   (*hBOOL*)
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        | tm_to_tt (t as Metis.Term.Fn (".",_)) =
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            let val (rator,rands) = strip_happ [] t
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            in  case rator of
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                    Metis.Term.Fn(fname,ts) => applic_to_tt (fname, ts @ rands)
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                  | _ => case tm_to_tt rator of
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                             Term t => Term (list_comb(t, terms_of (map tm_to_tt rands)))
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                           | _ => raise Fail "tm_to_tt: HO application"
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            end
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        | tm_to_tt (Metis.Term.Fn (fname, args)) = applic_to_tt (fname,args)
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      and applic_to_tt ("=",ts) =
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            Term (list_comb(Const (@{const_name HOL.eq}, HOLogic.typeT), terms_of (map tm_to_tt ts)))
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        | applic_to_tt (a,ts) =
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            case strip_prefix_and_unascii const_prefix a of
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                SOME b =>
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                  let val c = smart_invert_const b
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                      val ntypes = num_type_args thy c
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                      val nterms = length ts - ntypes
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                      val tts = map tm_to_tt ts
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                      val tys = types_of (List.take(tts,ntypes))
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                  in if length tys = ntypes then
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                         apply_list (Const (c, dummyT)) nterms (List.drop(tts,ntypes))
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                     else
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                       raise Fail ("Constant " ^ c ^ " expects " ^ Int.toString ntypes ^
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                                   " but gets " ^ Int.toString (length tys) ^
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                                   " type arguments\n" ^
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                                   cat_lines (map (Syntax.string_of_typ ctxt) tys) ^
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                                   " the terms are \n" ^
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                                   cat_lines (map (Syntax.string_of_term ctxt) (terms_of tts)))
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                     end
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              | NONE => (*Not a constant. Is it a type constructor?*)
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   287
            case strip_prefix_and_unascii type_const_prefix a of
wenzelm@33227
   288
                SOME b =>
blanchet@38606
   289
                  Type (Term.Type (smart_invert_const b, types_of (map tm_to_tt ts)))
wenzelm@32956
   290
              | NONE => (*Maybe a TFree. Should then check that ts=[].*)
blanchet@38748
   291
            case strip_prefix_and_unascii tfree_prefix a of
wenzelm@32956
   292
                SOME b => Type (mk_tfree ctxt b)
wenzelm@32956
   293
              | NONE => (*a fixed variable? They are Skolem functions.*)
blanchet@38748
   294
            case strip_prefix_and_unascii fixed_var_prefix a of
wenzelm@32956
   295
                SOME b =>
wenzelm@32956
   296
                  let val opr = Term.Free(b, HOLogic.typeT)
wenzelm@32956
   297
                  in  apply_list opr (length ts) (map tm_to_tt ts)  end
blanchet@37402
   298
              | NONE => raise Fail ("unexpected metis function: " ^ a)
blanchet@37399
   299
  in
blanchet@37399
   300
    case tm_to_tt fol_tm of
blanchet@37399
   301
      Term t => t
blanchet@37402
   302
    | _ => raise Fail "fol_tm_to_tt: Term expected"
blanchet@37399
   303
  end
wenzelm@23442
   304
wenzelm@32956
   305
(*Maps fully-typed metis terms to isabelle terms*)
blanchet@37926
   306
fun hol_term_from_metis_FT ctxt fol_tm =
blanchet@37926
   307
  let val _ = trace_msg (fn () => "hol_term_from_metis_FT: " ^
blanchet@37399
   308
                                  Metis.Term.toString fol_tm)
wenzelm@32994
   309
      fun cvt (Metis.Term.Fn ("ti", [Metis.Term.Var v, _])) =
blanchet@38748
   310
             (case strip_prefix_and_unascii schematic_var_prefix v of
wenzelm@32956
   311
                  SOME w =>  mk_var(w, dummyT)
wenzelm@32956
   312
                | NONE   => mk_var(v, dummyT))
wenzelm@32994
   313
        | cvt (Metis.Term.Fn ("ti", [Metis.Term.Fn ("=",[]), _])) =
haftmann@38864
   314
            Const (@{const_name HOL.eq}, HOLogic.typeT)
wenzelm@32956
   315
        | cvt (Metis.Term.Fn ("ti", [Metis.Term.Fn (x,[]), ty])) =
blanchet@38748
   316
           (case strip_prefix_and_unascii const_prefix x of
blanchet@38606
   317
                SOME c => Const (smart_invert_const c, dummyT)
wenzelm@32956
   318
              | NONE => (*Not a constant. Is it a fixed variable??*)
blanchet@38748
   319
            case strip_prefix_and_unascii fixed_var_prefix x of
blanchet@37926
   320
                SOME v => Free (v, hol_type_from_metis_term ctxt ty)
blanchet@37926
   321
              | NONE => raise Fail ("hol_term_from_metis_FT bad constant: " ^ x))
wenzelm@32956
   322
        | cvt (Metis.Term.Fn ("ti", [Metis.Term.Fn (".",[tm1,tm2]), _])) =
wenzelm@32956
   323
            cvt tm1 $ cvt tm2
wenzelm@32956
   324
        | cvt (Metis.Term.Fn (".",[tm1,tm2])) = (*untyped application*)
wenzelm@32956
   325
            cvt tm1 $ cvt tm2
wenzelm@32956
   326
        | cvt (Metis.Term.Fn ("{}", [arg])) = cvt arg   (*hBOOL*)
wenzelm@32956
   327
        | cvt (Metis.Term.Fn ("=", [tm1,tm2])) =
haftmann@38864
   328
            list_comb(Const (@{const_name HOL.eq}, HOLogic.typeT), map cvt [tm1,tm2])
wenzelm@32956
   329
        | cvt (t as Metis.Term.Fn (x, [])) =
blanchet@38748
   330
           (case strip_prefix_and_unascii const_prefix x of
blanchet@38606
   331
                SOME c => Const (smart_invert_const c, dummyT)
wenzelm@32956
   332
              | NONE => (*Not a constant. Is it a fixed variable??*)
blanchet@38748
   333
            case strip_prefix_and_unascii fixed_var_prefix x of
wenzelm@32956
   334
                SOME v => Free (v, dummyT)
blanchet@37926
   335
              | NONE => (trace_msg (fn () => "hol_term_from_metis_FT bad const: " ^ x);
blanchet@37926
   336
                  hol_term_from_metis_PT ctxt t))
blanchet@37926
   337
        | cvt t = (trace_msg (fn () => "hol_term_from_metis_FT bad term: " ^ Metis.Term.toString t);
blanchet@37926
   338
            hol_term_from_metis_PT ctxt t)
blanchet@37399
   339
  in fol_tm |> cvt end
paulson@32532
   340
blanchet@37926
   341
fun hol_term_from_metis FT = hol_term_from_metis_FT
blanchet@37926
   342
  | hol_term_from_metis _ = hol_term_from_metis_PT
paulson@32532
   343
blanchet@37625
   344
fun hol_terms_from_fol ctxt mode skolems fol_tms =
blanchet@37926
   345
  let val ts = map (hol_term_from_metis mode ctxt) fol_tms
wenzelm@32956
   346
      val _ = trace_msg (fn () => "  calling type inference:")
wenzelm@32956
   347
      val _ = app (fn t => trace_msg (fn () => Syntax.string_of_term ctxt t)) ts
blanchet@37625
   348
      val ts' = ts |> map (reveal_skolem_terms skolems) |> infer_types ctxt
wenzelm@32956
   349
      val _ = app (fn t => trace_msg
wenzelm@32956
   350
                    (fn () => "  final term: " ^ Syntax.string_of_term ctxt t ^
wenzelm@32956
   351
                              "  of type  " ^ Syntax.string_of_typ ctxt (type_of t)))
wenzelm@32956
   352
                  ts'
wenzelm@32956
   353
  in  ts'  end;
wenzelm@23442
   354
blanchet@35865
   355
fun mk_not (Const (@{const_name Not}, _) $ b) = b
wenzelm@32956
   356
  | mk_not b = HOLogic.mk_not b;
wenzelm@23442
   357
wenzelm@32956
   358
val metis_eq = Metis.Term.Fn ("=", []);
paulson@32532
   359
wenzelm@32956
   360
(* ------------------------------------------------------------------------- *)
wenzelm@32956
   361
(* FOL step Inference Rules                                                  *)
wenzelm@32956
   362
(* ------------------------------------------------------------------------- *)
wenzelm@23442
   363
wenzelm@32956
   364
(*for debugging only*)
wenzelm@32956
   365
fun print_thpair (fth,th) =
wenzelm@32956
   366
  (trace_msg (fn () => "=============================================");
wenzelm@32956
   367
   trace_msg (fn () => "Metis: " ^ Metis.Thm.toString fth);
wenzelm@32956
   368
   trace_msg (fn () => "Isabelle: " ^ Display.string_of_thm_without_context th));
wenzelm@23442
   369
wenzelm@32956
   370
fun lookth thpairs (fth : Metis.Thm.thm) =
wenzelm@33035
   371
  the (AList.lookup (uncurry Metis.Thm.equal) thpairs fth)
blanchet@37402
   372
  handle Option =>
blanchet@37402
   373
         raise Fail ("Failed to find a Metis theorem " ^ Metis.Thm.toString fth);
wenzelm@23442
   374
wenzelm@32956
   375
fun is_TrueI th = Thm.eq_thm(TrueI,th);
wenzelm@23442
   376
wenzelm@32956
   377
fun cterm_incr_types thy idx = cterm_of thy o (map_types (Logic.incr_tvar idx));
paulson@24974
   378
wenzelm@32956
   379
fun inst_excluded_middle thy i_atm =
wenzelm@32956
   380
  let val th = EXCLUDED_MIDDLE
wenzelm@32956
   381
      val [vx] = Term.add_vars (prop_of th) []
wenzelm@32956
   382
      val substs = [(cterm_of thy (Var vx), cterm_of thy i_atm)]
wenzelm@32956
   383
  in  cterm_instantiate substs th  end;
wenzelm@23442
   384
wenzelm@32956
   385
(* INFERENCE RULE: AXIOM *)
wenzelm@36945
   386
fun axiom_inf thpairs th = Thm.incr_indexes 1 (lookth thpairs th);
wenzelm@32956
   387
    (*This causes variables to have an index of 1 by default. SEE ALSO mk_var above.*)
wenzelm@23442
   388
wenzelm@32956
   389
(* INFERENCE RULE: ASSUME *)
blanchet@37625
   390
fun assume_inf ctxt mode skolems atm =
wenzelm@32956
   391
  inst_excluded_middle
blanchet@37625
   392
      (ProofContext.theory_of ctxt)
blanchet@37625
   393
      (singleton (hol_terms_from_fol ctxt mode skolems) (Metis.Term.Fn atm))
wenzelm@23442
   394
wenzelm@32956
   395
(* INFERENCE RULE: INSTANTIATE (Subst). Type instantiations are ignored. Trying to reconstruct
wenzelm@32956
   396
   them admits new possibilities of errors, e.g. concerning sorts. Instead we try to arrange
wenzelm@32956
   397
   that new TVars are distinct and that types can be inferred from terms.*)
blanchet@37625
   398
fun inst_inf ctxt mode skolems thpairs fsubst th =
wenzelm@32956
   399
  let val thy = ProofContext.theory_of ctxt
wenzelm@32956
   400
      val i_th   = lookth thpairs th
wenzelm@32956
   401
      val i_th_vars = Term.add_vars (prop_of i_th) []
wenzelm@33035
   402
      fun find_var x = the (List.find (fn ((a,_),_) => a=x) i_th_vars)
wenzelm@32956
   403
      fun subst_translation (x,y) =
wenzelm@32956
   404
            let val v = find_var x
blanchet@37625
   405
                (* We call "reveal_skolem_terms" and "infer_types" below. *)
blanchet@37926
   406
                val t = hol_term_from_metis mode ctxt y
wenzelm@32956
   407
            in  SOME (cterm_of thy (Var v), t)  end
wenzelm@32956
   408
            handle Option =>
wenzelm@32956
   409
                (trace_msg (fn() => "List.find failed for the variable " ^ x ^
wenzelm@32956
   410
                                       " in " ^ Display.string_of_thm ctxt i_th);
wenzelm@32956
   411
                 NONE)
wenzelm@32956
   412
      fun remove_typeinst (a, t) =
blanchet@38748
   413
            case strip_prefix_and_unascii schematic_var_prefix a of
wenzelm@32956
   414
                SOME b => SOME (b, t)
blanchet@38748
   415
              | NONE => case strip_prefix_and_unascii tvar_prefix a of
wenzelm@32956
   416
                SOME _ => NONE          (*type instantiations are forbidden!*)
blanchet@38748
   417
              | NONE => SOME (a,t)    (*internal Metis var?*)
wenzelm@32956
   418
      val _ = trace_msg (fn () => "  isa th: " ^ Display.string_of_thm ctxt i_th)
wenzelm@32956
   419
      val substs = map_filter remove_typeinst (Metis.Subst.toList fsubst)
wenzelm@32956
   420
      val (vars,rawtms) = ListPair.unzip (map_filter subst_translation substs)
blanchet@37625
   421
      val tms = rawtms |> map (reveal_skolem_terms skolems) |> infer_types ctxt
wenzelm@32956
   422
      val ctm_of = cterm_incr_types thy (1 + Thm.maxidx_of i_th)
wenzelm@32956
   423
      val substs' = ListPair.zip (vars, map ctm_of tms)
wenzelm@32956
   424
      val _ = trace_msg (fn () =>
wenzelm@32956
   425
        cat_lines ("subst_translations:" ::
wenzelm@32956
   426
          (substs' |> map (fn (x, y) =>
wenzelm@32956
   427
            Syntax.string_of_term ctxt (term_of x) ^ " |-> " ^
wenzelm@32956
   428
            Syntax.string_of_term ctxt (term_of y)))));
blanchet@37399
   429
  in cterm_instantiate substs' i_th end
blanchet@38695
   430
  handle THM (msg, _, _) =>
blanchet@38695
   431
         error ("Cannot replay Metis proof in Isabelle:\n" ^ msg)
wenzelm@23442
   432
wenzelm@32956
   433
(* INFERENCE RULE: RESOLVE *)
wenzelm@25713
   434
blanchet@39267
   435
(* Like RSN, but we rename apart only the type variables. Vars here typically
blanchet@39267
   436
   have an index of 1, and the use of RSN would increase this typically to 3.
blanchet@39267
   437
   Instantiations of those Vars could then fail. See comment on "mk_var". *)
blanchet@39258
   438
fun resolve_inc_tyvars thy tha i thb =
blanchet@37548
   439
  let
blanchet@39266
   440
    val tha = Drule.incr_type_indexes (1 + Thm.maxidx_of thb) tha
blanchet@39258
   441
    fun aux tha thb =
blanchet@39266
   442
      case Thm.bicompose false (false, tha, nprems_of tha) i thb
blanchet@39266
   443
           |> Seq.list_of |> distinct Thm.eq_thm of
blanchet@39266
   444
        [th] => th
blanchet@39266
   445
      | _ => raise THM ("resolve_inc_tyvars: unique result expected", i,
blanchet@39266
   446
                        [tha, thb])
wenzelm@32956
   447
  in
blanchet@39258
   448
    aux tha thb
blanchet@39266
   449
    handle TERM z =>
blanchet@39267
   450
           (* The unifier, which is invoked from "Thm.bicompose", will sometimes
blanchet@39267
   451
              refuse to unify "?a::?'a" with "?a::?'b" or "?a::nat" and throw a
blanchet@39267
   452
              "TERM" exception (with "add_ffpair" as first argument). We then
blanchet@39267
   453
              perform unification of the types of variables by hand and try
blanchet@39267
   454
              again. We could do this the first time around but this error
blanchet@39267
   455
              occurs seldom and we don't want to break existing proofs in subtle
blanchet@39267
   456
              ways or slow them down needlessly. *)
blanchet@39266
   457
           case [] |> fold (Term.add_vars o prop_of) [tha, thb]
blanchet@39266
   458
                   |> AList.group (op =)
blanchet@39266
   459
                   |> maps (fn ((s, _), T :: Ts) =>
blanchet@39266
   460
                               map (fn T' => (Free (s, T), Free (s, T'))) Ts)
blanchet@39266
   461
                   |> rpair (Envir.empty ~1)
blanchet@39266
   462
                   |-> fold (Pattern.unify thy)
blanchet@39266
   463
                   |> Envir.type_env |> Vartab.dest
blanchet@39266
   464
                   |> map (fn (x, (S, T)) =>
blanchet@39266
   465
                              pairself (ctyp_of thy) (TVar (x, S), T)) of
blanchet@39266
   466
             [] => raise TERM z
blanchet@39266
   467
           | ps => aux (instantiate (ps, []) tha) (instantiate (ps, []) thb)
blanchet@37548
   468
  end
wenzelm@23442
   469
blanchet@37625
   470
fun resolve_inf ctxt mode skolems thpairs atm th1 th2 =
wenzelm@32956
   471
  let
blanchet@39258
   472
    val thy = ProofContext.theory_of ctxt
wenzelm@32956
   473
    val i_th1 = lookth thpairs th1 and i_th2 = lookth thpairs th2
wenzelm@32956
   474
    val _ = trace_msg (fn () => "  isa th1 (pos): " ^ Display.string_of_thm ctxt i_th1)
wenzelm@32956
   475
    val _ = trace_msg (fn () => "  isa th2 (neg): " ^ Display.string_of_thm ctxt i_th2)
wenzelm@32956
   476
  in
wenzelm@32956
   477
    if is_TrueI i_th1 then i_th2 (*Trivial cases where one operand is type info*)
wenzelm@32956
   478
    else if is_TrueI i_th2 then i_th1
wenzelm@32956
   479
    else
wenzelm@32956
   480
      let
blanchet@37625
   481
        val i_atm = singleton (hol_terms_from_fol ctxt mode skolems)
blanchet@37399
   482
                              (Metis.Term.Fn atm)
wenzelm@32956
   483
        val _ = trace_msg (fn () => "  atom: " ^ Syntax.string_of_term ctxt i_atm)
wenzelm@32956
   484
        val prems_th1 = prems_of i_th1
wenzelm@32956
   485
        val prems_th2 = prems_of i_th2
wenzelm@32956
   486
        val index_th1 = get_index (mk_not i_atm) prems_th1
blanchet@37402
   487
              handle Empty => raise Fail "Failed to find literal in th1"
wenzelm@32956
   488
        val _ = trace_msg (fn () => "  index_th1: " ^ Int.toString index_th1)
wenzelm@32956
   489
        val index_th2 = get_index i_atm prems_th2
blanchet@37402
   490
              handle Empty => raise Fail "Failed to find literal in th2"
wenzelm@32956
   491
        val _ = trace_msg (fn () => "  index_th2: " ^ Int.toString index_th2)
blanchet@39258
   492
    in
blanchet@39258
   493
      resolve_inc_tyvars thy (Meson.select_literal index_th1 i_th1) index_th2
blanchet@39258
   494
                         i_th2
blanchet@39258
   495
    end
wenzelm@32956
   496
  end;
wenzelm@23442
   497
wenzelm@32956
   498
(* INFERENCE RULE: REFL *)
wenzelm@32956
   499
val refl_x = cterm_of @{theory} (Var (hd (Term.add_vars (prop_of REFL_THM) [])));
wenzelm@32956
   500
val refl_idx = 1 + Thm.maxidx_of REFL_THM;
wenzelm@25713
   501
blanchet@37625
   502
fun refl_inf ctxt mode skolems t =
wenzelm@32956
   503
  let val thy = ProofContext.theory_of ctxt
blanchet@37625
   504
      val i_t = singleton (hol_terms_from_fol ctxt mode skolems) t
wenzelm@32956
   505
      val _ = trace_msg (fn () => "  term: " ^ Syntax.string_of_term ctxt i_t)
wenzelm@32956
   506
      val c_t = cterm_incr_types thy refl_idx i_t
wenzelm@32956
   507
  in  cterm_instantiate [(refl_x, c_t)] REFL_THM  end;
wenzelm@23442
   508
haftmann@38864
   509
fun get_ty_arg_size _ (Const (@{const_name HOL.eq}, _)) = 0  (*equality has no type arguments*)
blanchet@36909
   510
  | get_ty_arg_size thy (Const (c, _)) = (num_type_args thy c handle TYPE _ => 0)
wenzelm@32994
   511
  | get_ty_arg_size _ _ = 0;
wenzelm@23442
   512
wenzelm@32956
   513
(* INFERENCE RULE: EQUALITY *)
blanchet@37625
   514
fun equality_inf ctxt mode skolems (pos, atm) fp fr =
wenzelm@32956
   515
  let val thy = ProofContext.theory_of ctxt
wenzelm@32956
   516
      val m_tm = Metis.Term.Fn atm
blanchet@37625
   517
      val [i_atm,i_tm] = hol_terms_from_fol ctxt mode skolems [m_tm, fr]
wenzelm@32956
   518
      val _ = trace_msg (fn () => "sign of the literal: " ^ Bool.toString pos)
wenzelm@32994
   519
      fun replace_item_list lx 0 (_::ls) = lx::ls
wenzelm@32956
   520
        | replace_item_list lx i (l::ls) = l :: replace_item_list lx (i-1) ls
wenzelm@32956
   521
      fun path_finder_FO tm [] = (tm, Term.Bound 0)
wenzelm@32956
   522
        | path_finder_FO tm (p::ps) =
blanchet@35865
   523
            let val (tm1,args) = strip_comb tm
wenzelm@32956
   524
                val adjustment = get_ty_arg_size thy tm1
wenzelm@32956
   525
                val p' = if adjustment > p then p else p-adjustment
wenzelm@32956
   526
                val tm_p = List.nth(args,p')
blanchet@38695
   527
                  handle Subscript =>
blanchet@38695
   528
                         error ("Cannot replay Metis proof in Isabelle:\n" ^
blanchet@38695
   529
                                "equality_inf: " ^ Int.toString p ^ " adj " ^
blanchet@38695
   530
                                Int.toString adjustment ^ " term " ^
blanchet@38695
   531
                                Syntax.string_of_term ctxt tm)
wenzelm@32956
   532
                val _ = trace_msg (fn () => "path_finder: " ^ Int.toString p ^
wenzelm@32956
   533
                                      "  " ^ Syntax.string_of_term ctxt tm_p)
wenzelm@32956
   534
                val (r,t) = path_finder_FO tm_p ps
wenzelm@32956
   535
            in
wenzelm@32956
   536
                (r, list_comb (tm1, replace_item_list t p' args))
wenzelm@32956
   537
            end
wenzelm@32956
   538
      fun path_finder_HO tm [] = (tm, Term.Bound 0)
wenzelm@32956
   539
        | path_finder_HO (t$u) (0::ps) = (fn(x,y) => (x, y$u)) (path_finder_HO t ps)
wenzelm@32994
   540
        | path_finder_HO (t$u) (_::ps) = (fn(x,y) => (x, t$y)) (path_finder_HO u ps)
blanchet@37402
   541
        | path_finder_HO tm ps =
blanchet@37402
   542
          raise Fail ("equality_inf, path_finder_HO: path = " ^
blanchet@37402
   543
                      space_implode " " (map Int.toString ps) ^
blanchet@37402
   544
                      " isa-term: " ^  Syntax.string_of_term ctxt tm)
wenzelm@32956
   545
      fun path_finder_FT tm [] _ = (tm, Term.Bound 0)
wenzelm@32994
   546
        | path_finder_FT tm (0::ps) (Metis.Term.Fn ("ti", [t1, _])) =
wenzelm@32956
   547
            path_finder_FT tm ps t1
wenzelm@32994
   548
        | path_finder_FT (t$u) (0::ps) (Metis.Term.Fn (".", [t1, _])) =
wenzelm@32956
   549
            (fn(x,y) => (x, y$u)) (path_finder_FT t ps t1)
wenzelm@32994
   550
        | path_finder_FT (t$u) (1::ps) (Metis.Term.Fn (".", [_, t2])) =
wenzelm@32956
   551
            (fn(x,y) => (x, t$y)) (path_finder_FT u ps t2)
blanchet@37402
   552
        | path_finder_FT tm ps t =
blanchet@37402
   553
          raise Fail ("equality_inf, path_finder_FT: path = " ^
blanchet@37402
   554
                      space_implode " " (map Int.toString ps) ^
blanchet@37402
   555
                      " isa-term: " ^  Syntax.string_of_term ctxt tm ^
blanchet@37402
   556
                      " fol-term: " ^ Metis.Term.toString t)
wenzelm@32956
   557
      fun path_finder FO tm ps _ = path_finder_FO tm ps
haftmann@38864
   558
        | path_finder HO (tm as Const(@{const_name HOL.eq},_) $ _ $ _) (p::ps) _ =
wenzelm@32956
   559
             (*equality: not curried, as other predicates are*)
wenzelm@32956
   560
             if p=0 then path_finder_HO tm (0::1::ps)  (*select first operand*)
wenzelm@32956
   561
             else path_finder_HO tm (p::ps)        (*1 selects second operand*)
wenzelm@32994
   562
        | path_finder HO tm (_ :: ps) (Metis.Term.Fn ("{}", [_])) =
wenzelm@32956
   563
             path_finder_HO tm ps      (*if not equality, ignore head to skip hBOOL*)
haftmann@38864
   564
        | path_finder FT (tm as Const(@{const_name HOL.eq}, _) $ _ $ _) (p::ps)
wenzelm@32956
   565
                            (Metis.Term.Fn ("=", [t1,t2])) =
wenzelm@32956
   566
             (*equality: not curried, as other predicates are*)
wenzelm@32956
   567
             if p=0 then path_finder_FT tm (0::1::ps)
wenzelm@32956
   568
                          (Metis.Term.Fn (".", [Metis.Term.Fn (".", [metis_eq,t1]), t2]))
wenzelm@32956
   569
                          (*select first operand*)
wenzelm@32956
   570
             else path_finder_FT tm (p::ps)
wenzelm@32956
   571
                   (Metis.Term.Fn (".", [metis_eq,t2]))
wenzelm@32956
   572
                   (*1 selects second operand*)
wenzelm@32994
   573
        | path_finder FT tm (_ :: ps) (Metis.Term.Fn ("{}", [t1])) = path_finder_FT tm ps t1
wenzelm@32956
   574
             (*if not equality, ignore head to skip the hBOOL predicate*)
wenzelm@32956
   575
        | path_finder FT tm ps t = path_finder_FT tm ps t  (*really an error case!*)
blanchet@35865
   576
      fun path_finder_lit ((nt as Const (@{const_name Not}, _)) $ tm_a) idx =
wenzelm@32956
   577
            let val (tm, tm_rslt) = path_finder mode tm_a idx m_tm
wenzelm@32956
   578
            in (tm, nt $ tm_rslt) end
wenzelm@32956
   579
        | path_finder_lit tm_a idx = path_finder mode tm_a idx m_tm
wenzelm@32956
   580
      val (tm_subst, body) = path_finder_lit i_atm fp
wenzelm@32956
   581
      val tm_abs = Term.Abs("x", Term.type_of tm_subst, body)
wenzelm@32956
   582
      val _ = trace_msg (fn () => "abstraction: " ^ Syntax.string_of_term ctxt tm_abs)
wenzelm@32956
   583
      val _ = trace_msg (fn () => "i_tm: " ^ Syntax.string_of_term ctxt i_tm)
wenzelm@32956
   584
      val _ = trace_msg (fn () => "located term: " ^ Syntax.string_of_term ctxt tm_subst)
wenzelm@32956
   585
      val imax = maxidx_of_term (i_tm $ tm_abs $ tm_subst)  (*ill typed but gives right max*)
wenzelm@36945
   586
      val subst' = Thm.incr_indexes (imax+1) (if pos then subst_em else ssubst_em)
wenzelm@32956
   587
      val _ = trace_msg (fn () => "subst' " ^ Display.string_of_thm ctxt subst')
wenzelm@32956
   588
      val eq_terms = map (pairself (cterm_of thy))
wenzelm@33227
   589
        (ListPair.zip (OldTerm.term_vars (prop_of subst'), [tm_abs, tm_subst, i_tm]))
wenzelm@32956
   590
  in  cterm_instantiate eq_terms subst'  end;
wenzelm@23442
   591
wenzelm@32956
   592
val factor = Seq.hd o distinct_subgoals_tac;
paulson@28528
   593
blanchet@37625
   594
fun step ctxt mode skolems thpairs p =
blanchet@37399
   595
  case p of
blanchet@37399
   596
    (fol_th, Metis.Proof.Axiom _) => factor (axiom_inf thpairs fol_th)
blanchet@37625
   597
  | (_, Metis.Proof.Assume f_atm) => assume_inf ctxt mode skolems f_atm
blanchet@37399
   598
  | (_, Metis.Proof.Subst (f_subst, f_th1)) =>
blanchet@37625
   599
    factor (inst_inf ctxt mode skolems thpairs f_subst f_th1)
blanchet@37399
   600
  | (_, Metis.Proof.Resolve(f_atm, f_th1, f_th2)) =>
blanchet@37625
   601
    factor (resolve_inf ctxt mode skolems thpairs f_atm f_th1 f_th2)
blanchet@37625
   602
  | (_, Metis.Proof.Refl f_tm) => refl_inf ctxt mode skolems f_tm
blanchet@37399
   603
  | (_, Metis.Proof.Equality (f_lit, f_p, f_r)) =>
blanchet@37625
   604
    equality_inf ctxt mode skolems f_lit f_p f_r
wenzelm@23442
   605
blanchet@35865
   606
fun real_literal (_, (c, _)) = not (String.isPrefix class_prefix c);
wenzelm@23442
   607
blanchet@38280
   608
fun translate_one ctxt mode skolems (fol_th, inf) thpairs =
blanchet@38280
   609
  let
blanchet@38280
   610
    val _ = trace_msg (fn () => "=============================================")
blanchet@38280
   611
    val _ = trace_msg (fn () => "METIS THM: " ^ Metis.Thm.toString fol_th)
blanchet@38280
   612
    val _ = trace_msg (fn () => "INFERENCE: " ^ Metis.Proof.inferenceToString inf)
blanchet@38280
   613
    val th = Meson.flexflex_first_order (step ctxt mode skolems
blanchet@38280
   614
                                              thpairs (fol_th, inf))
blanchet@38280
   615
    val _ = trace_msg (fn () => "ISABELLE THM: " ^ Display.string_of_thm ctxt th)
blanchet@38280
   616
    val _ = trace_msg (fn () => "=============================================")
blanchet@38280
   617
    val n_metis_lits =
blanchet@38280
   618
      length (filter real_literal (Metis.LiteralSet.toList (Metis.Thm.clause fol_th)))
blanchet@38695
   619
    val _ = if nprems_of th = n_metis_lits then ()
blanchet@38695
   620
            else error "Cannot replay Metis proof in Isabelle."
blanchet@38280
   621
  in (fol_th, th) :: thpairs end
wenzelm@23442
   622
wenzelm@32956
   623
(*Determining which axiom clauses are actually used*)
wenzelm@32956
   624
fun used_axioms axioms (th, Metis.Proof.Axiom _) = SOME (lookth axioms th)
wenzelm@32994
   625
  | used_axioms _ _ = NONE;
paulson@24855
   626
wenzelm@32956
   627
(* ------------------------------------------------------------------------- *)
wenzelm@32956
   628
(* Translation of HO Clauses                                                 *)
wenzelm@32956
   629
(* ------------------------------------------------------------------------- *)
wenzelm@23442
   630
wenzelm@32956
   631
fun type_ext thy tms =
blanchet@35865
   632
  let val subs = tfree_classes_of_terms tms
blanchet@35865
   633
      val supers = tvar_classes_of_terms tms
blanchet@35865
   634
      and tycons = type_consts_of_terms thy tms
blanchet@35865
   635
      val (supers', arity_clauses) = make_arity_clauses thy tycons supers
blanchet@37925
   636
      val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@37925
   637
  in  map class_rel_cls class_rel_clauses @ map arity_cls arity_clauses
wenzelm@32956
   638
  end;
wenzelm@23442
   639
wenzelm@32956
   640
(* ------------------------------------------------------------------------- *)
wenzelm@32956
   641
(* Logic maps manage the interface between HOL and first-order logic.        *)
wenzelm@32956
   642
(* ------------------------------------------------------------------------- *)
wenzelm@23442
   643
wenzelm@32956
   644
type logic_map =
blanchet@35865
   645
  {axioms: (Metis.Thm.thm * thm) list,
blanchet@37399
   646
   tfrees: type_literal list,
blanchet@37625
   647
   skolems: (string * term) list}
wenzelm@23442
   648
wenzelm@32994
   649
fun const_in_metis c (pred, tm_list) =
wenzelm@32956
   650
  let
wenzelm@32994
   651
    fun in_mterm (Metis.Term.Var _) = false
wenzelm@32956
   652
      | in_mterm (Metis.Term.Fn (".", tm_list)) = exists in_mterm tm_list
wenzelm@32956
   653
      | in_mterm (Metis.Term.Fn (nm, tm_list)) = c=nm orelse exists in_mterm tm_list
wenzelm@32994
   654
  in  c = pred orelse exists in_mterm tm_list  end;
wenzelm@23442
   655
wenzelm@32956
   656
(*Extract TFree constraints from context to include as conjecture clauses*)
wenzelm@32956
   657
fun init_tfrees ctxt =
blanchet@36966
   658
  let fun add ((a,i),s) Ts = if i = ~1 then TFree(a,s) :: Ts else Ts in
blanchet@36966
   659
    Vartab.fold add (#2 (Variable.constraints_of ctxt)) []
blanchet@36966
   660
    |> type_literals_for_types
blanchet@36556
   661
  end;
paulson@24937
   662
wenzelm@32956
   663
(*transform isabelle type / arity clause to metis clause *)
wenzelm@32956
   664
fun add_type_thm [] lmap = lmap
blanchet@37625
   665
  | add_type_thm ((ith, mth) :: cls) {axioms, tfrees, skolems} =
blanchet@37399
   666
      add_type_thm cls {axioms = (mth, ith) :: axioms, tfrees = tfrees,
blanchet@37625
   667
                        skolems = skolems}
wenzelm@23442
   668
wenzelm@32956
   669
(*Insert non-logical axioms corresponding to all accumulated TFrees*)
blanchet@37625
   670
fun add_tfrees {axioms, tfrees, skolems} : logic_map =
blanchet@37399
   671
     {axioms = map (rpair TrueI o metis_of_tfree) (distinct (op =) tfrees) @
blanchet@37399
   672
               axioms,
blanchet@37625
   673
      tfrees = tfrees, skolems = skolems}
wenzelm@25713
   674
wenzelm@32956
   675
fun string_of_mode FO = "FO"
wenzelm@32956
   676
  | string_of_mode HO = "HO"
wenzelm@32956
   677
  | string_of_mode FT = "FT"
paulson@32532
   678
blanchet@37479
   679
val helpers =
blanchet@38606
   680
  [("c_COMBI", (false, map (`I) @{thms COMBI_def})),
blanchet@38606
   681
   ("c_COMBK", (false, map (`I) @{thms COMBK_def})),
blanchet@38606
   682
   ("c_COMBB", (false, map (`I) @{thms COMBB_def})),
blanchet@38606
   683
   ("c_COMBC", (false, map (`I) @{thms COMBC_def})),
blanchet@38606
   684
   ("c_COMBS", (false, map (`I) @{thms COMBS_def})),
blanchet@38606
   685
   ("c_fequal", (false, map (rpair @{thm equal_imp_equal})
blanchet@38606
   686
                            @{thms fequal_imp_equal equal_imp_fequal})),
blanchet@38606
   687
   ("c_True", (true, map (`I) @{thms True_or_False})),
blanchet@38606
   688
   ("c_False", (true, map (`I) @{thms True_or_False})),
blanchet@38606
   689
   ("c_If", (true, map (`I) @{thms if_True if_False True_or_False}))]
blanchet@37479
   690
blanchet@38100
   691
fun is_quasi_fol_clause thy =
blanchet@37625
   692
  Meson.is_fol_term thy o snd o conceal_skolem_terms ~1 [] o prop_of
blanchet@37623
   693
wenzelm@32956
   694
(* Function to generate metis clauses, including comb and type clauses *)
wenzelm@32956
   695
fun build_map mode0 ctxt cls ths =
wenzelm@32956
   696
  let val thy = ProofContext.theory_of ctxt
wenzelm@32956
   697
      (*The modes FO and FT are sticky. HO can be downgraded to FO.*)
wenzelm@32956
   698
      fun set_mode FO = FO
blanchet@37399
   699
        | set_mode HO =
blanchet@37623
   700
          if forall (is_quasi_fol_clause thy) (cls @ ths) then FO else HO
wenzelm@32956
   701
        | set_mode FT = FT
wenzelm@32956
   702
      val mode = set_mode mode0
wenzelm@32956
   703
      (*transform isabelle clause to metis clause *)
blanchet@38606
   704
      fun add_thm is_conjecture (metis_ith, isa_ith) {axioms, tfrees, skolems}
blanchet@38606
   705
                  : logic_map =
blanchet@37399
   706
        let
blanchet@37625
   707
          val (mth, tfree_lits, skolems) =
blanchet@38606
   708
            hol_thm_to_fol is_conjecture ctxt mode (length axioms) skolems
blanchet@38606
   709
                           metis_ith
wenzelm@32956
   710
        in
blanchet@38606
   711
           {axioms = (mth, Meson.make_meta_clause isa_ith) :: axioms,
blanchet@37625
   712
            tfrees = union (op =) tfree_lits tfrees, skolems = skolems}
wenzelm@32956
   713
        end;
blanchet@37625
   714
      val lmap = {axioms = [], tfrees = init_tfrees ctxt, skolems = []}
blanchet@38606
   715
                 |> fold (add_thm true o `I) cls
blanchet@37498
   716
                 |> add_tfrees
blanchet@38606
   717
                 |> fold (add_thm false o `I) ths
wenzelm@32956
   718
      val clause_lists = map (Metis.Thm.clause o #1) (#axioms lmap)
blanchet@37479
   719
      fun is_used c =
blanchet@37479
   720
        exists (Metis.LiteralSet.exists (const_in_metis c o #2)) clause_lists
blanchet@37399
   721
      val lmap =
blanchet@37479
   722
        if mode = FO then
blanchet@37479
   723
          lmap
blanchet@37479
   724
        else
blanchet@37479
   725
          let
blanchet@37479
   726
            val helper_ths =
blanchet@37479
   727
              helpers |> filter (is_used o fst)
blanchet@38606
   728
                      |> maps (fn (c, (needs_full_types, thms)) =>
blanchet@38606
   729
                                  if not (is_used c) orelse
blanchet@38606
   730
                                     needs_full_types andalso mode <> FT then
blanchet@38606
   731
                                    []
blanchet@37479
   732
                                  else
blanchet@38606
   733
                                    thms)
blanchet@37479
   734
          in lmap |> fold (add_thm false) helper_ths end
blanchet@37410
   735
  in (mode, add_type_thm (type_ext thy (map prop_of (cls @ ths))) lmap) end
wenzelm@23442
   736
wenzelm@32956
   737
fun refute cls =
wenzelm@32956
   738
    Metis.Resolution.loop (Metis.Resolution.new Metis.Resolution.default cls);
wenzelm@23442
   739
wenzelm@32956
   740
fun is_false t = t aconv (HOLogic.mk_Trueprop HOLogic.false_const);
wenzelm@23442
   741
wenzelm@32956
   742
fun common_thm ths1 ths2 = exists (member Thm.eq_thm ths1) (map Meson.make_meta_clause ths2);
paulson@24855
   743
blanchet@37573
   744
blanchet@37516
   745
(* Main function to start Metis proof and reconstruction *)
wenzelm@32956
   746
fun FOL_SOLVE mode ctxt cls ths0 =
wenzelm@32956
   747
  let val thy = ProofContext.theory_of ctxt
blanchet@35826
   748
      val th_cls_pairs =
blanchet@38016
   749
        map (fn th => (Thm.get_name_hint th, Clausifier.cnf_axiom thy th)) ths0
wenzelm@32956
   750
      val ths = maps #2 th_cls_pairs
wenzelm@32956
   751
      val _ = trace_msg (fn () => "FOL_SOLVE: CONJECTURE CLAUSES")
wenzelm@32956
   752
      val _ = app (fn th => trace_msg (fn () => Display.string_of_thm ctxt th)) cls
wenzelm@32956
   753
      val _ = trace_msg (fn () => "THEOREM CLAUSES")
wenzelm@32956
   754
      val _ = app (fn th => trace_msg (fn () => Display.string_of_thm ctxt th)) ths
blanchet@37625
   755
      val (mode, {axioms, tfrees, skolems}) = build_map mode ctxt cls ths
wenzelm@32956
   756
      val _ = if null tfrees then ()
wenzelm@32956
   757
              else (trace_msg (fn () => "TFREE CLAUSES");
blanchet@37643
   758
                    app (fn TyLitFree ((s, _), (s', _)) =>
blanchet@37573
   759
                            trace_msg (fn _ => s ^ "(" ^ s' ^ ")")) tfrees)
wenzelm@32956
   760
      val _ = trace_msg (fn () => "CLAUSES GIVEN TO METIS")
wenzelm@32956
   761
      val thms = map #1 axioms
wenzelm@32956
   762
      val _ = app (fn th => trace_msg (fn () => Metis.Thm.toString th)) thms
wenzelm@32956
   763
      val _ = trace_msg (fn () => "mode = " ^ string_of_mode mode)
wenzelm@32956
   764
      val _ = trace_msg (fn () => "START METIS PROVE PROCESS")
wenzelm@32956
   765
  in
wenzelm@33317
   766
      case filter (is_false o prop_of) cls of
wenzelm@32956
   767
          false_th::_ => [false_th RS @{thm FalseE}]
wenzelm@32956
   768
        | [] =>
wenzelm@32956
   769
      case refute thms of
wenzelm@32956
   770
          Metis.Resolution.Contradiction mth =>
wenzelm@32956
   771
            let val _ = trace_msg (fn () => "METIS RECONSTRUCTION START: " ^
wenzelm@32956
   772
                          Metis.Thm.toString mth)
wenzelm@32956
   773
                val ctxt' = fold Variable.declare_constraints (map prop_of cls) ctxt
wenzelm@32956
   774
                             (*add constraints arising from converting goal to clause form*)
wenzelm@32956
   775
                val proof = Metis.Proof.proof mth
blanchet@38280
   776
                val result = fold (translate_one ctxt' mode skolems) proof axioms
wenzelm@32956
   777
                and used = map_filter (used_axioms axioms) proof
wenzelm@32956
   778
                val _ = trace_msg (fn () => "METIS COMPLETED...clauses actually used:")
wenzelm@32956
   779
                val _ = app (fn th => trace_msg (fn () => Display.string_of_thm ctxt th)) used
wenzelm@33305
   780
                val unused = th_cls_pairs |> map_filter (fn (name, cls) =>
wenzelm@33305
   781
                  if common_thm used cls then NONE else SOME name)
wenzelm@32956
   782
            in
blanchet@36383
   783
                if not (null cls) andalso not (common_thm used cls) then
blanchet@36383
   784
                  warning "Metis: The assumptions are inconsistent."
blanchet@36383
   785
                else
blanchet@36383
   786
                  ();
blanchet@36383
   787
                if not (null unused) then
blanchet@36230
   788
                  warning ("Metis: Unused theorems: " ^ commas_quote unused
blanchet@36230
   789
                           ^ ".")
blanchet@36230
   790
                else
blanchet@36230
   791
                  ();
wenzelm@32956
   792
                case result of
wenzelm@32956
   793
                    (_,ith)::_ =>
blanchet@36230
   794
                        (trace_msg (fn () => "Success: " ^ Display.string_of_thm ctxt ith);
wenzelm@32956
   795
                         [ith])
blanchet@38097
   796
                  | _ => (trace_msg (fn () => "Metis: No result"); [])
wenzelm@32956
   797
            end
wenzelm@32956
   798
        | Metis.Resolution.Satisfiable _ =>
wenzelm@32956
   799
            (trace_msg (fn () => "Metis: No first-order proof with the lemmas supplied");
blanchet@38097
   800
             [])
wenzelm@32956
   801
  end;
wenzelm@23442
   802
blanchet@38632
   803
(* Extensionalize "th", because that makes sense and that's what Sledgehammer
blanchet@38632
   804
   does, but also keep an unextensionalized version of "th" for backward
blanchet@38632
   805
   compatibility. *)
blanchet@38632
   806
fun also_extensionalize_theorem th =
blanchet@38632
   807
  let val th' = Clausifier.extensionalize_theorem th in
blanchet@38632
   808
    if Thm.eq_thm (th, th') then [th]
blanchet@38632
   809
    else th :: Meson.make_clauses_unsorted [th']
blanchet@38632
   810
  end
blanchet@38632
   811
blanchet@38028
   812
val neg_clausify =
blanchet@38028
   813
  single
blanchet@38028
   814
  #> Meson.make_clauses_unsorted
blanchet@38632
   815
  #> maps also_extensionalize_theorem
blanchet@38028
   816
  #> map Clausifier.introduce_combinators_in_theorem
blanchet@38028
   817
  #> Meson.finish_cnf
blanchet@38028
   818
blanchet@39269
   819
fun preskolem_tac ctxt st0 =
blanchet@39269
   820
  (if exists (Meson.has_too_many_clauses ctxt)
blanchet@39269
   821
             (Logic.prems_of_goal (prop_of st0) 1) then
blanchet@39269
   822
     cnf.cnfx_rewrite_tac ctxt 1
blanchet@39269
   823
   else
blanchet@39269
   824
     all_tac) st0
blanchet@39269
   825
blanchet@38652
   826
val type_has_top_sort =
blanchet@38652
   827
  exists_subtype (fn TFree (_, []) => true | TVar (_, []) => true | _ => false)
blanchet@38652
   828
blanchet@37516
   829
fun generic_metis_tac mode ctxt ths i st0 =
blanchet@37926
   830
  let
blanchet@39037
   831
    val thy = ProofContext.theory_of ctxt
blanchet@37926
   832
    val _ = trace_msg (fn () =>
wenzelm@32956
   833
        "Metis called with theorems " ^ cat_lines (map (Display.string_of_thm ctxt) ths))
wenzelm@32956
   834
  in
blanchet@37626
   835
    if exists_type type_has_top_sort (prop_of st0) then
blanchet@37516
   836
      (warning ("Metis: Proof state contains the universal sort {}"); Seq.empty)
wenzelm@35568
   837
    else
blanchet@39269
   838
      Meson.MESON (preskolem_tac ctxt) (maps neg_clausify)
blanchet@37926
   839
                  (fn cls => resolve_tac (FOL_SOLVE mode ctxt cls ths) 1)
blanchet@37926
   840
                  ctxt i st0
wenzelm@32956
   841
  end
wenzelm@23442
   842
blanchet@37516
   843
val metis_tac = generic_metis_tac HO
blanchet@37516
   844
val metisF_tac = generic_metis_tac FO
blanchet@37516
   845
val metisFT_tac = generic_metis_tac FT
wenzelm@23442
   846
blanchet@38632
   847
(* Whenever "X" has schematic type variables, we treat "using X by metis" as
blanchet@38632
   848
   "by (metis X)", to prevent "Subgoal.FOCUS" from freezing the type variables.
blanchet@38632
   849
   We don't do it for nonschematic facts "X" because this breaks a few proofs
blanchet@38632
   850
   (in the rare and subtle case where a proof relied on extensionality not being
blanchet@38994
   851
   applied) and brings few benefits. *)
blanchet@38632
   852
val has_tvar =
blanchet@38632
   853
  exists_type (exists_subtype (fn TVar _ => true | _ => false)) o prop_of
blanchet@37516
   854
fun method name mode =
blanchet@37516
   855
  Method.setup name (Attrib.thms >> (fn ths => fn ctxt =>
blanchet@38632
   856
    METHOD (fn facts =>
blanchet@38632
   857
               let
blanchet@38632
   858
                 val (schem_facts, nonschem_facts) =
blanchet@38632
   859
                   List.partition has_tvar facts
blanchet@38632
   860
               in
blanchet@38632
   861
                 HEADGOAL (Method.insert_tac nonschem_facts THEN'
blanchet@38632
   862
                           CHANGED_PROP
blanchet@38632
   863
                           o generic_metis_tac mode ctxt (schem_facts @ ths))
blanchet@38632
   864
               end)))
wenzelm@23442
   865
wenzelm@32956
   866
val setup =
blanchet@37516
   867
  type_lits_setup
blanchet@37516
   868
  #> method @{binding metis} HO "Metis for FOL/HOL problems"
blanchet@37516
   869
  #> method @{binding metisF} FO "Metis for FOL problems"
blanchet@37516
   870
  #> method @{binding metisFT} FT
blanchet@37516
   871
            "Metis for FOL/HOL problems with fully-typed translation"
wenzelm@23442
   872
wenzelm@23442
   873
end;