src/HOL/Tools/Sledgehammer/metis_tactics.ML
author blanchet
Mon Jun 14 10:36:01 2010 +0200 (2010-06-14)
changeset 37410 2bf7e6136047
parent 37402 12cb33916e37
child 37417 0714ece49081
permissions -rw-r--r--
adjusted the polymorphism handling of Skolem constants so that proof reconstruction doesn't fail in "equality_inf"
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(*  Title:      HOL/Tools/Sledgehammer/metis_tactics.ML
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    Author:     Kong W. Susanto and Lawrence C. Paulson, CU Computer Laboratory
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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 Sledgehammer_Util
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open Sledgehammer_FOL_Clause
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open Sledgehammer_Fact_Preprocessor
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open Sledgehammer_HOL_Clause
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open Sledgehammer_Proof_Reconstruct
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open Sledgehammer_Fact_Filter
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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,_),_)) = (a=b)   (*the index is ignored!*)
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  | untyped_aconv (Bound i)      (Bound j)      = (i=j)
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  | untyped_aconv (Abs(a,_,t))  (Abs(b,_,u))    = (a=b) andalso untyped_aconv t u
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  | untyped_aconv (t1$t2) (u1$u2)  = 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 n [] = 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 "equal" = "="
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  | fn_isa_to_met x       = x;
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fun metis_lit b c args = (b, (c, args));
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fun hol_type_to_fol (TyVar (x, _)) = Metis.Term.Var x
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  | hol_type_to_fol (TyFree (s, _)) = Metis.Term.Fn (s, [])
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  | hol_type_to_fol (TyConstr ((s, _), tps)) =
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    Metis.Term.Fn (s, map hol_type_to_fol 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 hol_type_to_fol 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 "hol_term_to_fol_FO";
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fun hol_term_to_fol_HO (CombVar ((s, _), _)) = Metis.Term.Var s
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  | hol_term_to_fol_HO (CombConst ((a, _), _, tylist)) =
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      Metis.Term.Fn (fn_isa_to_met a, map hol_type_to_fol tylist)
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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, hol_type_to_fol 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 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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                  type_of_combterm tm);
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fun hol_literal_to_fol FO (Literal (pol, 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 hol_type_to_fol tys
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          val lits = map hol_term_to_fol_FO tms
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      in metis_lit pol (fn_isa_to_met p) (tylits @ lits) end
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  | hol_literal_to_fol HO (Literal (pol, tm)) =
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     (case strip_combterm_comb tm of
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          (CombConst(("equal", _), _, _), tms) =>
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            metis_lit pol "=" (map hol_term_to_fol_HO tms)
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        | _ => metis_lit pol "{}" [hol_term_to_fol_HO tm])   (*hBOOL*)
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  | hol_literal_to_fol FT (Literal (pol, tm)) =
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     (case strip_combterm_comb tm of
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          (CombConst(("equal", _), _, _), tms) =>
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            metis_lit pol "=" (map hol_term_to_fol_FT tms)
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        | _ => metis_lit pol "{}" [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 skolem_somes th =
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  let
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    val thy = ProofContext.theory_of ctxt
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    val (skolem_somes, (mlits, types_sorts)) =
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     th |> prop_of |> conceal_skolem_somes j skolem_somes
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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, skolem_somes)
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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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           skolem_somes)
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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 (make_type_class c) [Metis.Term.Fn(t, map Metis.Term.Var args)]
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  | m_arity_cls (TVarLit (c,str))     =
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      metis_lit false (make_type_class c) [Metis.Term.Var str];
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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_classrel_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 classrel_cls (ClassrelClause {subclass, superclass, ...}) =
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  (TrueI, Metis.Thm.axiom (Metis.LiteralSet.fromList (m_classrel_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 fol_type_to_isa _ (Metis.Term.Var v) =
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     (case strip_prefix 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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  | fol_type_to_isa ctxt (Metis.Term.Fn(x, tys)) =
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     (case strip_prefix tconst_prefix x of
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          SOME tc => Term.Type (invert_type_const tc, map (fol_type_to_isa ctxt) tys)
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        | NONE    =>
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      case strip_prefix tfree_prefix x of
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          SOME tf => mk_tfree ctxt tf
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        | NONE    => raise Fail ("fol_type_to_isa: " ^ x));
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fun reveal_skolem_somes skolem_somes =
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  map_aterms (fn t as Const (s, T) =>
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                 if String.isPrefix skolem_theory_name s then
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                   AList.lookup (op =) skolem_somes s
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                   |> the |> map_types Type_Infer.paramify_vars
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                 else
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                   t
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               | t => t)
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(*Maps metis terms to isabelle terms*)
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fun hol_term_from_fol_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_fol_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 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 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 "op ="}, 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 const_prefix a of
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                SOME b =>
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                  let val c = 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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   291
            case strip_prefix tconst_prefix a of
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   292
                SOME b =>
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   293
                  Type (Term.Type (invert_type_const b, types_of (map tm_to_tt ts)))
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   294
              | NONE => (*Maybe a TFree. Should then check that ts=[].*)
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   295
            case strip_prefix tfree_prefix a of
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   296
                SOME b => Type (mk_tfree ctxt b)
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   297
              | NONE => (*a fixed variable? They are Skolem functions.*)
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   298
            case strip_prefix fixed_var_prefix a of
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   299
                SOME b =>
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   300
                  let val opr = Term.Free(b, HOLogic.typeT)
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   301
                  in  apply_list opr (length ts) (map tm_to_tt ts)  end
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   302
              | NONE => raise Fail ("unexpected metis function: " ^ a)
blanchet@37399
   303
  in
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   304
    case tm_to_tt fol_tm of
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   305
      Term t => t
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   306
    | _ => raise Fail "fol_tm_to_tt: Term expected"
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   307
  end
wenzelm@23442
   308
wenzelm@32956
   309
(*Maps fully-typed metis terms to isabelle terms*)
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   310
fun hol_term_from_fol_FT ctxt fol_tm =
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   311
  let val _ = trace_msg (fn () => "hol_term_from_fol_FT: " ^
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   312
                                  Metis.Term.toString fol_tm)
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   313
      fun cvt (Metis.Term.Fn ("ti", [Metis.Term.Var v, _])) =
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   314
             (case strip_prefix schematic_var_prefix v of
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   315
                  SOME w =>  mk_var(w, dummyT)
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   316
                | NONE   => mk_var(v, dummyT))
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   317
        | cvt (Metis.Term.Fn ("ti", [Metis.Term.Fn ("=",[]), _])) =
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   318
            Const ("op =", HOLogic.typeT)
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   319
        | cvt (Metis.Term.Fn ("ti", [Metis.Term.Fn (x,[]), ty])) =
blanchet@35865
   320
           (case strip_prefix const_prefix x of
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   321
                SOME c => Const (invert_const c, dummyT)
wenzelm@32956
   322
              | NONE => (*Not a constant. Is it a fixed variable??*)
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   323
            case strip_prefix fixed_var_prefix x of
wenzelm@32956
   324
                SOME v => Free (v, fol_type_to_isa ctxt ty)
blanchet@37402
   325
              | NONE => raise Fail ("hol_term_from_fol_FT bad constant: " ^ x))
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   326
        | cvt (Metis.Term.Fn ("ti", [Metis.Term.Fn (".",[tm1,tm2]), _])) =
wenzelm@32956
   327
            cvt tm1 $ cvt tm2
wenzelm@32956
   328
        | cvt (Metis.Term.Fn (".",[tm1,tm2])) = (*untyped application*)
wenzelm@32956
   329
            cvt tm1 $ cvt tm2
wenzelm@32956
   330
        | cvt (Metis.Term.Fn ("{}", [arg])) = cvt arg   (*hBOOL*)
wenzelm@32956
   331
        | cvt (Metis.Term.Fn ("=", [tm1,tm2])) =
blanchet@35865
   332
            list_comb(Const (@{const_name "op ="}, HOLogic.typeT), map cvt [tm1,tm2])
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   333
        | cvt (t as Metis.Term.Fn (x, [])) =
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   334
           (case strip_prefix const_prefix x of
blanchet@35865
   335
                SOME c => Const (invert_const c, dummyT)
wenzelm@32956
   336
              | NONE => (*Not a constant. Is it a fixed variable??*)
blanchet@35865
   337
            case strip_prefix fixed_var_prefix x of
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   338
                SOME v => Free (v, dummyT)
blanchet@37399
   339
              | NONE => (trace_msg (fn () => "hol_term_from_fol_FT bad const: " ^ x);
blanchet@37399
   340
                  hol_term_from_fol_PT ctxt t))
blanchet@37399
   341
        | cvt t = (trace_msg (fn () => "hol_term_from_fol_FT bad term: " ^ Metis.Term.toString t);
blanchet@37399
   342
            hol_term_from_fol_PT ctxt t)
blanchet@37399
   343
  in fol_tm |> cvt end
paulson@32532
   344
blanchet@37399
   345
fun hol_term_from_fol FT = hol_term_from_fol_FT
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   346
  | hol_term_from_fol _ = hol_term_from_fol_PT
paulson@32532
   347
blanchet@37399
   348
fun hol_terms_from_fol ctxt mode skolem_somes fol_tms =
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   349
  let val thy = ProofContext.theory_of ctxt
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   350
      val ts = map (hol_term_from_fol mode ctxt) fol_tms
wenzelm@32956
   351
      val _ = trace_msg (fn () => "  calling type inference:")
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   352
      val _ = app (fn t => trace_msg (fn () => Syntax.string_of_term ctxt t)) ts
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   353
      val ts' = ts |> map (reveal_skolem_somes skolem_somes) |> infer_types ctxt
wenzelm@32956
   354
      val _ = app (fn t => trace_msg
wenzelm@32956
   355
                    (fn () => "  final term: " ^ Syntax.string_of_term ctxt t ^
wenzelm@32956
   356
                              "  of type  " ^ Syntax.string_of_typ ctxt (type_of t)))
wenzelm@32956
   357
                  ts'
wenzelm@32956
   358
  in  ts'  end;
wenzelm@23442
   359
blanchet@35865
   360
fun mk_not (Const (@{const_name Not}, _) $ b) = b
wenzelm@32956
   361
  | mk_not b = HOLogic.mk_not b;
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   362
wenzelm@32956
   363
val metis_eq = Metis.Term.Fn ("=", []);
paulson@32532
   364
wenzelm@32956
   365
(* ------------------------------------------------------------------------- *)
wenzelm@32956
   366
(* FOL step Inference Rules                                                  *)
wenzelm@32956
   367
(* ------------------------------------------------------------------------- *)
wenzelm@23442
   368
wenzelm@32956
   369
(*for debugging only*)
wenzelm@32956
   370
fun print_thpair (fth,th) =
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   371
  (trace_msg (fn () => "=============================================");
wenzelm@32956
   372
   trace_msg (fn () => "Metis: " ^ Metis.Thm.toString fth);
wenzelm@32956
   373
   trace_msg (fn () => "Isabelle: " ^ Display.string_of_thm_without_context th));
wenzelm@23442
   374
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   375
fun lookth thpairs (fth : Metis.Thm.thm) =
wenzelm@33035
   376
  the (AList.lookup (uncurry Metis.Thm.equal) thpairs fth)
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   377
  handle Option =>
blanchet@37402
   378
         raise Fail ("Failed to find a Metis theorem " ^ Metis.Thm.toString fth);
wenzelm@23442
   379
wenzelm@32956
   380
fun is_TrueI th = Thm.eq_thm(TrueI,th);
wenzelm@23442
   381
wenzelm@32956
   382
fun cterm_incr_types thy idx = cterm_of thy o (map_types (Logic.incr_tvar idx));
paulson@24974
   383
wenzelm@32956
   384
fun inst_excluded_middle thy i_atm =
wenzelm@32956
   385
  let val th = EXCLUDED_MIDDLE
wenzelm@32956
   386
      val [vx] = Term.add_vars (prop_of th) []
wenzelm@32956
   387
      val substs = [(cterm_of thy (Var vx), cterm_of thy i_atm)]
wenzelm@32956
   388
  in  cterm_instantiate substs th  end;
wenzelm@23442
   389
wenzelm@32956
   390
(* INFERENCE RULE: AXIOM *)
wenzelm@36945
   391
fun axiom_inf thpairs th = Thm.incr_indexes 1 (lookth thpairs th);
wenzelm@32956
   392
    (*This causes variables to have an index of 1 by default. SEE ALSO mk_var above.*)
wenzelm@23442
   393
wenzelm@32956
   394
(* INFERENCE RULE: ASSUME *)
blanchet@37399
   395
fun assume_inf ctxt mode skolem_somes atm =
wenzelm@32956
   396
  inst_excluded_middle
wenzelm@32956
   397
    (ProofContext.theory_of ctxt)
blanchet@37399
   398
    (singleton (hol_terms_from_fol ctxt mode skolem_somes) (Metis.Term.Fn atm))
wenzelm@23442
   399
wenzelm@32956
   400
(* INFERENCE RULE: INSTANTIATE (Subst). Type instantiations are ignored. Trying to reconstruct
wenzelm@32956
   401
   them admits new possibilities of errors, e.g. concerning sorts. Instead we try to arrange
wenzelm@32956
   402
   that new TVars are distinct and that types can be inferred from terms.*)
blanchet@37399
   403
fun inst_inf ctxt mode skolem_somes thpairs fsubst th =
wenzelm@32956
   404
  let val thy = ProofContext.theory_of ctxt
wenzelm@32956
   405
      val i_th   = lookth thpairs th
wenzelm@32956
   406
      val i_th_vars = Term.add_vars (prop_of i_th) []
wenzelm@33035
   407
      fun find_var x = the (List.find (fn ((a,_),_) => a=x) i_th_vars)
wenzelm@32956
   408
      fun subst_translation (x,y) =
wenzelm@32956
   409
            let val v = find_var x
blanchet@37410
   410
                (* We call "reveal_skolem_somes" and "infer_types" below. *)
blanchet@37399
   411
                val t = hol_term_from_fol mode ctxt y
wenzelm@32956
   412
            in  SOME (cterm_of thy (Var v), t)  end
wenzelm@32956
   413
            handle Option =>
wenzelm@32956
   414
                (trace_msg (fn() => "List.find failed for the variable " ^ x ^
wenzelm@32956
   415
                                       " in " ^ Display.string_of_thm ctxt i_th);
wenzelm@32956
   416
                 NONE)
wenzelm@32956
   417
      fun remove_typeinst (a, t) =
blanchet@35865
   418
            case strip_prefix schematic_var_prefix a of
wenzelm@32956
   419
                SOME b => SOME (b, t)
blanchet@35865
   420
              | NONE   => case strip_prefix tvar_prefix a of
wenzelm@32956
   421
                SOME _ => NONE          (*type instantiations are forbidden!*)
wenzelm@32956
   422
              | NONE   => SOME (a,t)    (*internal Metis var?*)
wenzelm@32956
   423
      val _ = trace_msg (fn () => "  isa th: " ^ Display.string_of_thm ctxt i_th)
wenzelm@32956
   424
      val substs = map_filter remove_typeinst (Metis.Subst.toList fsubst)
wenzelm@32956
   425
      val (vars,rawtms) = ListPair.unzip (map_filter subst_translation substs)
blanchet@37410
   426
      val tms = rawtms |> map (reveal_skolem_somes skolem_somes)
blanchet@37399
   427
                       |> infer_types ctxt
wenzelm@32956
   428
      val ctm_of = cterm_incr_types thy (1 + Thm.maxidx_of i_th)
wenzelm@32956
   429
      val substs' = ListPair.zip (vars, map ctm_of tms)
wenzelm@32956
   430
      val _ = trace_msg (fn () =>
wenzelm@32956
   431
        cat_lines ("subst_translations:" ::
wenzelm@32956
   432
          (substs' |> map (fn (x, y) =>
wenzelm@32956
   433
            Syntax.string_of_term ctxt (term_of x) ^ " |-> " ^
wenzelm@32956
   434
            Syntax.string_of_term ctxt (term_of y)))));
blanchet@37399
   435
  in cterm_instantiate substs' i_th end
blanchet@37318
   436
  handle THM (msg, _, _) => error ("metis error (inst_inf):\n" ^ msg)
blanchet@37318
   437
       | ERROR msg => error ("metis error (inst_inf):\n" ^ msg ^
blanchet@37399
   438
                             "\n(Perhaps you want to try \"metisFT\" if you \
blanchet@37399
   439
                             \haven't done so already.)")
wenzelm@23442
   440
wenzelm@32956
   441
(* INFERENCE RULE: RESOLVE *)
wenzelm@25713
   442
wenzelm@32956
   443
(*Like RSN, but we rename apart only the type variables. Vars here typically have an index
wenzelm@32956
   444
  of 1, and the use of RSN would increase this typically to 3. Instantiations of those Vars
wenzelm@32956
   445
  could then fail. See comment on mk_var.*)
wenzelm@32956
   446
fun resolve_inc_tyvars(tha,i,thb) =
wenzelm@32956
   447
  let val tha = Drule.incr_type_indexes (1 + Thm.maxidx_of thb) tha
wenzelm@32956
   448
      val ths = Seq.list_of (Thm.bicompose false (false,tha,nprems_of tha) i thb)
wenzelm@32956
   449
  in
wenzelm@32956
   450
      case distinct Thm.eq_thm ths of
wenzelm@32956
   451
        [th] => th
wenzelm@32956
   452
      | _ => raise THM ("resolve_inc_tyvars: unique result expected", i, [tha,thb])
wenzelm@32956
   453
  end;
wenzelm@23442
   454
blanchet@37399
   455
fun resolve_inf ctxt mode skolem_somes thpairs atm th1 th2 =
wenzelm@32956
   456
  let
wenzelm@32956
   457
    val i_th1 = lookth thpairs th1 and i_th2 = lookth thpairs th2
wenzelm@32956
   458
    val _ = trace_msg (fn () => "  isa th1 (pos): " ^ Display.string_of_thm ctxt i_th1)
wenzelm@32956
   459
    val _ = trace_msg (fn () => "  isa th2 (neg): " ^ Display.string_of_thm ctxt i_th2)
wenzelm@32956
   460
  in
wenzelm@32956
   461
    if is_TrueI i_th1 then i_th2 (*Trivial cases where one operand is type info*)
wenzelm@32956
   462
    else if is_TrueI i_th2 then i_th1
wenzelm@32956
   463
    else
wenzelm@32956
   464
      let
blanchet@37399
   465
        val i_atm = singleton (hol_terms_from_fol ctxt mode skolem_somes)
blanchet@37399
   466
                              (Metis.Term.Fn atm)
wenzelm@32956
   467
        val _ = trace_msg (fn () => "  atom: " ^ Syntax.string_of_term ctxt i_atm)
wenzelm@32956
   468
        val prems_th1 = prems_of i_th1
wenzelm@32956
   469
        val prems_th2 = prems_of i_th2
wenzelm@32956
   470
        val index_th1 = get_index (mk_not i_atm) prems_th1
blanchet@37402
   471
              handle Empty => raise Fail "Failed to find literal in th1"
wenzelm@32956
   472
        val _ = trace_msg (fn () => "  index_th1: " ^ Int.toString index_th1)
wenzelm@32956
   473
        val index_th2 = get_index i_atm prems_th2
blanchet@37402
   474
              handle Empty => raise Fail "Failed to find literal in th2"
wenzelm@32956
   475
        val _ = trace_msg (fn () => "  index_th2: " ^ Int.toString index_th2)
wenzelm@32956
   476
    in  resolve_inc_tyvars (Meson.select_literal index_th1 i_th1, index_th2, i_th2)  end
wenzelm@32956
   477
  end;
wenzelm@23442
   478
wenzelm@32956
   479
(* INFERENCE RULE: REFL *)
wenzelm@32956
   480
val refl_x = cterm_of @{theory} (Var (hd (Term.add_vars (prop_of REFL_THM) [])));
wenzelm@32956
   481
val refl_idx = 1 + Thm.maxidx_of REFL_THM;
wenzelm@25713
   482
blanchet@37399
   483
fun refl_inf ctxt mode skolem_somes t =
wenzelm@32956
   484
  let val thy = ProofContext.theory_of ctxt
blanchet@37399
   485
      val i_t = singleton (hol_terms_from_fol ctxt mode skolem_somes) t
wenzelm@32956
   486
      val _ = trace_msg (fn () => "  term: " ^ Syntax.string_of_term ctxt i_t)
wenzelm@32956
   487
      val c_t = cterm_incr_types thy refl_idx i_t
wenzelm@32956
   488
  in  cterm_instantiate [(refl_x, c_t)] REFL_THM  end;
wenzelm@23442
   489
blanchet@35865
   490
fun get_ty_arg_size _ (Const (@{const_name "op ="}, _)) = 0  (*equality has no type arguments*)
blanchet@36909
   491
  | get_ty_arg_size thy (Const (c, _)) = (num_type_args thy c handle TYPE _ => 0)
wenzelm@32994
   492
  | get_ty_arg_size _ _ = 0;
wenzelm@23442
   493
wenzelm@32956
   494
(* INFERENCE RULE: EQUALITY *)
blanchet@37399
   495
fun equality_inf ctxt mode skolem_somes (pos, atm) fp fr =
wenzelm@32956
   496
  let val thy = ProofContext.theory_of ctxt
wenzelm@32956
   497
      val m_tm = Metis.Term.Fn atm
blanchet@37399
   498
      val [i_atm,i_tm] = hol_terms_from_fol ctxt mode skolem_somes [m_tm, fr]
wenzelm@32956
   499
      val _ = trace_msg (fn () => "sign of the literal: " ^ Bool.toString pos)
wenzelm@32994
   500
      fun replace_item_list lx 0 (_::ls) = lx::ls
wenzelm@32956
   501
        | replace_item_list lx i (l::ls) = l :: replace_item_list lx (i-1) ls
wenzelm@32956
   502
      fun path_finder_FO tm [] = (tm, Term.Bound 0)
wenzelm@32956
   503
        | path_finder_FO tm (p::ps) =
blanchet@35865
   504
            let val (tm1,args) = strip_comb tm
wenzelm@32956
   505
                val adjustment = get_ty_arg_size thy tm1
wenzelm@32956
   506
                val p' = if adjustment > p then p else p-adjustment
wenzelm@32956
   507
                val tm_p = List.nth(args,p')
wenzelm@32956
   508
                  handle Subscript => error ("equality_inf: " ^ Int.toString p ^ " adj " ^
wenzelm@32956
   509
                    Int.toString adjustment  ^ " term " ^  Syntax.string_of_term ctxt tm)
wenzelm@32956
   510
                val _ = trace_msg (fn () => "path_finder: " ^ Int.toString p ^
wenzelm@32956
   511
                                      "  " ^ Syntax.string_of_term ctxt tm_p)
wenzelm@32956
   512
                val (r,t) = path_finder_FO tm_p ps
wenzelm@32956
   513
            in
wenzelm@32956
   514
                (r, list_comb (tm1, replace_item_list t p' args))
wenzelm@32956
   515
            end
wenzelm@32956
   516
      fun path_finder_HO tm [] = (tm, Term.Bound 0)
wenzelm@32956
   517
        | path_finder_HO (t$u) (0::ps) = (fn(x,y) => (x, y$u)) (path_finder_HO t ps)
wenzelm@32994
   518
        | path_finder_HO (t$u) (_::ps) = (fn(x,y) => (x, t$y)) (path_finder_HO u ps)
blanchet@37402
   519
        | path_finder_HO tm ps =
blanchet@37402
   520
          raise Fail ("equality_inf, path_finder_HO: path = " ^
blanchet@37402
   521
                      space_implode " " (map Int.toString ps) ^
blanchet@37402
   522
                      " isa-term: " ^  Syntax.string_of_term ctxt tm)
wenzelm@32956
   523
      fun path_finder_FT tm [] _ = (tm, Term.Bound 0)
wenzelm@32994
   524
        | path_finder_FT tm (0::ps) (Metis.Term.Fn ("ti", [t1, _])) =
wenzelm@32956
   525
            path_finder_FT tm ps t1
wenzelm@32994
   526
        | path_finder_FT (t$u) (0::ps) (Metis.Term.Fn (".", [t1, _])) =
wenzelm@32956
   527
            (fn(x,y) => (x, y$u)) (path_finder_FT t ps t1)
wenzelm@32994
   528
        | path_finder_FT (t$u) (1::ps) (Metis.Term.Fn (".", [_, t2])) =
wenzelm@32956
   529
            (fn(x,y) => (x, t$y)) (path_finder_FT u ps t2)
blanchet@37402
   530
        | path_finder_FT tm ps t =
blanchet@37402
   531
          raise Fail ("equality_inf, path_finder_FT: path = " ^
blanchet@37402
   532
                      space_implode " " (map Int.toString ps) ^
blanchet@37402
   533
                      " isa-term: " ^  Syntax.string_of_term ctxt tm ^
blanchet@37402
   534
                      " fol-term: " ^ Metis.Term.toString t)
wenzelm@32956
   535
      fun path_finder FO tm ps _ = path_finder_FO tm ps
blanchet@35865
   536
        | path_finder HO (tm as Const(@{const_name "op ="},_) $ _ $ _) (p::ps) _ =
wenzelm@32956
   537
             (*equality: not curried, as other predicates are*)
wenzelm@32956
   538
             if p=0 then path_finder_HO tm (0::1::ps)  (*select first operand*)
wenzelm@32956
   539
             else path_finder_HO tm (p::ps)        (*1 selects second operand*)
wenzelm@32994
   540
        | path_finder HO tm (_ :: ps) (Metis.Term.Fn ("{}", [_])) =
wenzelm@32956
   541
             path_finder_HO tm ps      (*if not equality, ignore head to skip hBOOL*)
blanchet@35865
   542
        | path_finder FT (tm as Const(@{const_name "op ="}, _) $ _ $ _) (p::ps)
wenzelm@32956
   543
                            (Metis.Term.Fn ("=", [t1,t2])) =
wenzelm@32956
   544
             (*equality: not curried, as other predicates are*)
wenzelm@32956
   545
             if p=0 then path_finder_FT tm (0::1::ps)
wenzelm@32956
   546
                          (Metis.Term.Fn (".", [Metis.Term.Fn (".", [metis_eq,t1]), t2]))
wenzelm@32956
   547
                          (*select first operand*)
wenzelm@32956
   548
             else path_finder_FT tm (p::ps)
wenzelm@32956
   549
                   (Metis.Term.Fn (".", [metis_eq,t2]))
wenzelm@32956
   550
                   (*1 selects second operand*)
wenzelm@32994
   551
        | path_finder FT tm (_ :: ps) (Metis.Term.Fn ("{}", [t1])) = path_finder_FT tm ps t1
wenzelm@32956
   552
             (*if not equality, ignore head to skip the hBOOL predicate*)
wenzelm@32956
   553
        | path_finder FT tm ps t = path_finder_FT tm ps t  (*really an error case!*)
blanchet@35865
   554
      fun path_finder_lit ((nt as Const (@{const_name Not}, _)) $ tm_a) idx =
wenzelm@32956
   555
            let val (tm, tm_rslt) = path_finder mode tm_a idx m_tm
wenzelm@32956
   556
            in (tm, nt $ tm_rslt) end
wenzelm@32956
   557
        | path_finder_lit tm_a idx = path_finder mode tm_a idx m_tm
wenzelm@32956
   558
      val (tm_subst, body) = path_finder_lit i_atm fp
wenzelm@32956
   559
      val tm_abs = Term.Abs("x", Term.type_of tm_subst, body)
wenzelm@32956
   560
      val _ = trace_msg (fn () => "abstraction: " ^ Syntax.string_of_term ctxt tm_abs)
wenzelm@32956
   561
      val _ = trace_msg (fn () => "i_tm: " ^ Syntax.string_of_term ctxt i_tm)
wenzelm@32956
   562
      val _ = trace_msg (fn () => "located term: " ^ Syntax.string_of_term ctxt tm_subst)
wenzelm@32956
   563
      val imax = maxidx_of_term (i_tm $ tm_abs $ tm_subst)  (*ill typed but gives right max*)
wenzelm@36945
   564
      val subst' = Thm.incr_indexes (imax+1) (if pos then subst_em else ssubst_em)
wenzelm@32956
   565
      val _ = trace_msg (fn () => "subst' " ^ Display.string_of_thm ctxt subst')
wenzelm@32956
   566
      val eq_terms = map (pairself (cterm_of thy))
wenzelm@33227
   567
        (ListPair.zip (OldTerm.term_vars (prop_of subst'), [tm_abs, tm_subst, i_tm]))
wenzelm@32956
   568
  in  cterm_instantiate eq_terms subst'  end;
wenzelm@23442
   569
wenzelm@32956
   570
val factor = Seq.hd o distinct_subgoals_tac;
paulson@28528
   571
blanchet@37399
   572
fun step ctxt mode skolem_somes thpairs p =
blanchet@37399
   573
  case p of
blanchet@37399
   574
    (fol_th, Metis.Proof.Axiom _) => factor (axiom_inf thpairs fol_th)
blanchet@37399
   575
  | (_, Metis.Proof.Assume f_atm) => assume_inf ctxt mode skolem_somes f_atm
blanchet@37399
   576
  | (_, Metis.Proof.Subst (f_subst, f_th1)) =>
blanchet@37399
   577
    factor (inst_inf ctxt mode skolem_somes thpairs f_subst f_th1)
blanchet@37399
   578
  | (_, Metis.Proof.Resolve(f_atm, f_th1, f_th2)) =>
blanchet@37399
   579
    factor (resolve_inf ctxt mode skolem_somes thpairs f_atm f_th1 f_th2)
blanchet@37399
   580
  | (_, Metis.Proof.Refl f_tm) => refl_inf ctxt mode skolem_somes f_tm
blanchet@37399
   581
  | (_, Metis.Proof.Equality (f_lit, f_p, f_r)) =>
blanchet@37399
   582
    equality_inf ctxt mode skolem_somes f_lit f_p f_r
wenzelm@23442
   583
blanchet@35865
   584
fun real_literal (_, (c, _)) = not (String.isPrefix class_prefix c);
wenzelm@23442
   585
blanchet@37402
   586
(* FIXME: use "fold" instead *)
blanchet@37399
   587
fun translate _ _ _ thpairs [] = thpairs
blanchet@37399
   588
  | translate ctxt mode skolem_somes thpairs ((fol_th, inf) :: infpairs) =
wenzelm@32956
   589
      let val _ = trace_msg (fn () => "=============================================")
wenzelm@32956
   590
          val _ = trace_msg (fn () => "METIS THM: " ^ Metis.Thm.toString fol_th)
wenzelm@32956
   591
          val _ = trace_msg (fn () => "INFERENCE: " ^ Metis.Proof.inferenceToString inf)
blanchet@37399
   592
          val th = Meson.flexflex_first_order (step ctxt mode skolem_somes
blanchet@37399
   593
                                                    thpairs (fol_th, inf))
wenzelm@32956
   594
          val _ = trace_msg (fn () => "ISABELLE THM: " ^ Display.string_of_thm ctxt th)
wenzelm@32956
   595
          val _ = trace_msg (fn () => "=============================================")
wenzelm@32994
   596
          val n_metis_lits =
wenzelm@32994
   597
            length (filter real_literal (Metis.LiteralSet.toList (Metis.Thm.clause fol_th)))
wenzelm@32956
   598
      in
wenzelm@32956
   599
          if nprems_of th = n_metis_lits then ()
wenzelm@32956
   600
          else error "Metis: proof reconstruction has gone wrong";
blanchet@37399
   601
          translate ctxt mode skolem_somes ((fol_th, th) :: thpairs) infpairs
wenzelm@32956
   602
      end;
wenzelm@23442
   603
wenzelm@32956
   604
(*Determining which axiom clauses are actually used*)
wenzelm@32956
   605
fun used_axioms axioms (th, Metis.Proof.Axiom _) = SOME (lookth axioms th)
wenzelm@32994
   606
  | used_axioms _ _ = NONE;
paulson@24855
   607
wenzelm@32956
   608
(* ------------------------------------------------------------------------- *)
wenzelm@32956
   609
(* Translation of HO Clauses                                                 *)
wenzelm@32956
   610
(* ------------------------------------------------------------------------- *)
wenzelm@23442
   611
blanchet@35865
   612
fun cnf_th thy th = hd (cnf_axiom thy th);
wenzelm@23442
   613
wenzelm@32956
   614
fun type_ext thy tms =
blanchet@35865
   615
  let val subs = tfree_classes_of_terms tms
blanchet@35865
   616
      val supers = tvar_classes_of_terms tms
blanchet@35865
   617
      and tycons = type_consts_of_terms thy tms
blanchet@35865
   618
      val (supers', arity_clauses) = make_arity_clauses thy tycons supers
blanchet@35865
   619
      val classrel_clauses = make_classrel_clauses thy subs supers'
wenzelm@32956
   620
  in  map classrel_cls classrel_clauses @ map arity_cls arity_clauses
wenzelm@32956
   621
  end;
wenzelm@23442
   622
wenzelm@32956
   623
(* ------------------------------------------------------------------------- *)
wenzelm@32956
   624
(* Logic maps manage the interface between HOL and first-order logic.        *)
wenzelm@32956
   625
(* ------------------------------------------------------------------------- *)
wenzelm@23442
   626
wenzelm@32956
   627
type logic_map =
blanchet@35865
   628
  {axioms: (Metis.Thm.thm * thm) list,
blanchet@37399
   629
   tfrees: type_literal list,
blanchet@37410
   630
   skolem_somes: (string * term) list}
wenzelm@23442
   631
wenzelm@32994
   632
fun const_in_metis c (pred, tm_list) =
wenzelm@32956
   633
  let
wenzelm@32994
   634
    fun in_mterm (Metis.Term.Var _) = false
wenzelm@32956
   635
      | in_mterm (Metis.Term.Fn (".", tm_list)) = exists in_mterm tm_list
wenzelm@32956
   636
      | in_mterm (Metis.Term.Fn (nm, tm_list)) = c=nm orelse exists in_mterm tm_list
wenzelm@32994
   637
  in  c = pred orelse exists in_mterm tm_list  end;
wenzelm@23442
   638
wenzelm@32956
   639
(*Extract TFree constraints from context to include as conjecture clauses*)
wenzelm@32956
   640
fun init_tfrees ctxt =
blanchet@36966
   641
  let fun add ((a,i),s) Ts = if i = ~1 then TFree(a,s) :: Ts else Ts in
blanchet@36966
   642
    Vartab.fold add (#2 (Variable.constraints_of ctxt)) []
blanchet@36966
   643
    |> type_literals_for_types
blanchet@36556
   644
  end;
paulson@24937
   645
wenzelm@32956
   646
(*transform isabelle type / arity clause to metis clause *)
wenzelm@32956
   647
fun add_type_thm [] lmap = lmap
blanchet@37399
   648
  | add_type_thm ((ith, mth) :: cls) {axioms, tfrees, skolem_somes} =
blanchet@37399
   649
      add_type_thm cls {axioms = (mth, ith) :: axioms, tfrees = tfrees,
blanchet@37399
   650
                        skolem_somes = skolem_somes}
wenzelm@23442
   651
wenzelm@32956
   652
(*Insert non-logical axioms corresponding to all accumulated TFrees*)
blanchet@37399
   653
fun add_tfrees {axioms, tfrees, skolem_somes} : logic_map =
blanchet@37399
   654
     {axioms = map (rpair TrueI o metis_of_tfree) (distinct (op =) tfrees) @
blanchet@37399
   655
               axioms,
blanchet@37399
   656
      tfrees = tfrees, skolem_somes = skolem_somes}
wenzelm@25713
   657
wenzelm@32956
   658
fun string_of_mode FO = "FO"
wenzelm@32956
   659
  | string_of_mode HO = "HO"
wenzelm@32956
   660
  | string_of_mode FT = "FT"
paulson@32532
   661
wenzelm@32956
   662
(* Function to generate metis clauses, including comb and type clauses *)
wenzelm@32956
   663
fun build_map mode0 ctxt cls ths =
wenzelm@32956
   664
  let val thy = ProofContext.theory_of ctxt
wenzelm@32956
   665
      (*The modes FO and FT are sticky. HO can be downgraded to FO.*)
wenzelm@32956
   666
      fun set_mode FO = FO
blanchet@37399
   667
        | set_mode HO =
blanchet@37399
   668
          if forall (is_quasi_fol_term thy o prop_of) (cls @ ths) then FO
blanchet@37399
   669
          else HO
wenzelm@32956
   670
        | set_mode FT = FT
wenzelm@32956
   671
      val mode = set_mode mode0
wenzelm@32956
   672
      (*transform isabelle clause to metis clause *)
blanchet@37399
   673
      fun add_thm is_conjecture ith {axioms, tfrees, skolem_somes} : logic_map =
blanchet@37399
   674
        let
blanchet@37399
   675
          val (mth, tfree_lits, skolem_somes) =
blanchet@37399
   676
            hol_thm_to_fol is_conjecture ctxt mode (length axioms) skolem_somes
blanchet@37399
   677
                           ith
wenzelm@32956
   678
        in
wenzelm@32956
   679
           {axioms = (mth, Meson.make_meta_clause ith) :: axioms,
blanchet@37399
   680
            tfrees = union (op =) tfree_lits tfrees,
blanchet@37399
   681
            skolem_somes = skolem_somes}
wenzelm@32956
   682
        end;
blanchet@37402
   683
      val lmap as {skolem_somes, ...} =
blanchet@37402
   684
        {axioms = [], tfrees = init_tfrees ctxt, skolem_somes = []}
blanchet@37402
   685
        |> fold (add_thm true) cls
blanchet@37402
   686
        |> add_tfrees
blanchet@37402
   687
        |> fold (add_thm false) ths
wenzelm@32956
   688
      val clause_lists = map (Metis.Thm.clause o #1) (#axioms lmap)
wenzelm@32994
   689
      fun used c = exists (Metis.LiteralSet.exists (const_in_metis c o #2)) clause_lists
wenzelm@32956
   690
      (*Now check for the existence of certain combinators*)
blanchet@35865
   691
      val thI  = if used "c_COMBI" then [cnf_th @{theory} @{thm COMBI_def}] else []
blanchet@35865
   692
      val thK  = if used "c_COMBK" then [cnf_th @{theory} @{thm COMBK_def}] else []
blanchet@35865
   693
      val thB   = if used "c_COMBB" then [cnf_th @{theory} @{thm COMBB_def}] else []
blanchet@35865
   694
      val thC   = if used "c_COMBC" then [cnf_th @{theory} @{thm COMBC_def}] else []
blanchet@35865
   695
      val thS   = if used "c_COMBS" then [cnf_th @{theory} @{thm COMBS_def}] else []
blanchet@35865
   696
      val thEQ  = if used "c_fequal" then [cnf_th @{theory} @{thm fequal_imp_equal}, cnf_th @{theory} @{thm equal_imp_fequal}] else []
blanchet@37399
   697
      val lmap =
blanchet@37399
   698
        lmap |> mode <> FO
blanchet@37399
   699
                ? fold (add_thm false) (thEQ @ thS @ thC @ thB @ thK @ thI)
blanchet@37410
   700
  in (mode, add_type_thm (type_ext thy (map prop_of (cls @ ths))) lmap) end
wenzelm@23442
   701
wenzelm@32956
   702
fun refute cls =
wenzelm@32956
   703
    Metis.Resolution.loop (Metis.Resolution.new Metis.Resolution.default cls);
wenzelm@23442
   704
wenzelm@32956
   705
fun is_false t = t aconv (HOLogic.mk_Trueprop HOLogic.false_const);
wenzelm@23442
   706
wenzelm@32956
   707
fun common_thm ths1 ths2 = exists (member Thm.eq_thm ths1) (map Meson.make_meta_clause ths2);
paulson@24855
   708
wenzelm@32956
   709
exception METIS of string;
paulson@28233
   710
blanchet@37399
   711
(* Main function to start metis proof and reconstruction *)
wenzelm@32956
   712
fun FOL_SOLVE mode ctxt cls ths0 =
wenzelm@32956
   713
  let val thy = ProofContext.theory_of ctxt
blanchet@35826
   714
      val th_cls_pairs =
blanchet@35865
   715
        map (fn th => (Thm.get_name_hint th, cnf_axiom thy th)) ths0
wenzelm@32956
   716
      val ths = maps #2 th_cls_pairs
wenzelm@32956
   717
      val _ = trace_msg (fn () => "FOL_SOLVE: CONJECTURE CLAUSES")
wenzelm@32956
   718
      val _ = app (fn th => trace_msg (fn () => Display.string_of_thm ctxt th)) cls
wenzelm@32956
   719
      val _ = trace_msg (fn () => "THEOREM CLAUSES")
wenzelm@32956
   720
      val _ = app (fn th => trace_msg (fn () => Display.string_of_thm ctxt th)) ths
blanchet@37399
   721
      val (mode, {axioms, tfrees, skolem_somes}) = build_map mode ctxt cls ths
wenzelm@32956
   722
      val _ = if null tfrees then ()
wenzelm@32956
   723
              else (trace_msg (fn () => "TFREE CLAUSES");
blanchet@36556
   724
                    app (fn tf => trace_msg (fn _ => tptp_of_type_literal true tf NONE |> fst)) tfrees)
wenzelm@32956
   725
      val _ = trace_msg (fn () => "CLAUSES GIVEN TO METIS")
wenzelm@32956
   726
      val thms = map #1 axioms
wenzelm@32956
   727
      val _ = app (fn th => trace_msg (fn () => Metis.Thm.toString th)) thms
wenzelm@32956
   728
      val _ = trace_msg (fn () => "mode = " ^ string_of_mode mode)
wenzelm@32956
   729
      val _ = trace_msg (fn () => "START METIS PROVE PROCESS")
wenzelm@32956
   730
  in
wenzelm@33317
   731
      case filter (is_false o prop_of) cls of
wenzelm@32956
   732
          false_th::_ => [false_th RS @{thm FalseE}]
wenzelm@32956
   733
        | [] =>
wenzelm@32956
   734
      case refute thms of
wenzelm@32956
   735
          Metis.Resolution.Contradiction mth =>
wenzelm@32956
   736
            let val _ = trace_msg (fn () => "METIS RECONSTRUCTION START: " ^
wenzelm@32956
   737
                          Metis.Thm.toString mth)
wenzelm@32956
   738
                val ctxt' = fold Variable.declare_constraints (map prop_of cls) ctxt
wenzelm@32956
   739
                             (*add constraints arising from converting goal to clause form*)
wenzelm@32956
   740
                val proof = Metis.Proof.proof mth
blanchet@37399
   741
                val result = translate ctxt' mode skolem_somes axioms proof
wenzelm@32956
   742
                and used = map_filter (used_axioms axioms) proof
wenzelm@32956
   743
                val _ = trace_msg (fn () => "METIS COMPLETED...clauses actually used:")
wenzelm@32956
   744
                val _ = app (fn th => trace_msg (fn () => Display.string_of_thm ctxt th)) used
wenzelm@33305
   745
                val unused = th_cls_pairs |> map_filter (fn (name, cls) =>
wenzelm@33305
   746
                  if common_thm used cls then NONE else SOME name)
wenzelm@32956
   747
            in
blanchet@36383
   748
                if not (null cls) andalso not (common_thm used cls) then
blanchet@36383
   749
                  warning "Metis: The assumptions are inconsistent."
blanchet@36383
   750
                else
blanchet@36383
   751
                  ();
blanchet@36383
   752
                if not (null unused) then
blanchet@36230
   753
                  warning ("Metis: Unused theorems: " ^ commas_quote unused
blanchet@36230
   754
                           ^ ".")
blanchet@36230
   755
                else
blanchet@36230
   756
                  ();
wenzelm@32956
   757
                case result of
wenzelm@32956
   758
                    (_,ith)::_ =>
blanchet@36230
   759
                        (trace_msg (fn () => "Success: " ^ Display.string_of_thm ctxt ith);
wenzelm@32956
   760
                         [ith])
blanchet@36230
   761
                  | _ => (trace_msg (fn () => "Metis: No result");
wenzelm@32956
   762
                          [])
wenzelm@32956
   763
            end
wenzelm@32956
   764
        | Metis.Resolution.Satisfiable _ =>
wenzelm@32956
   765
            (trace_msg (fn () => "Metis: No first-order proof with the lemmas supplied");
wenzelm@32956
   766
             [])
wenzelm@32956
   767
  end;
wenzelm@23442
   768
wenzelm@32956
   769
fun metis_general_tac mode ctxt ths i st0 =
wenzelm@32956
   770
  let val _ = trace_msg (fn () =>
wenzelm@32956
   771
        "Metis called with theorems " ^ cat_lines (map (Display.string_of_thm ctxt) ths))
wenzelm@32956
   772
  in
blanchet@35865
   773
    if exists_type type_has_topsort (prop_of st0)
wenzelm@35568
   774
    then raise METIS "Metis: Proof state contains the universal sort {}"
wenzelm@35568
   775
    else
blanchet@36401
   776
      (Meson.MESON (maps neg_clausify)
wenzelm@35568
   777
        (fn cls => resolve_tac (FOL_SOLVE mode ctxt cls ths) 1) ctxt i
blanchet@35865
   778
          THEN Meson_Tactic.expand_defs_tac st0) st0
wenzelm@32956
   779
  end
wenzelm@32956
   780
  handle METIS s => (warning ("Metis: " ^ s); Seq.empty);
wenzelm@23442
   781
wenzelm@32956
   782
val metis_tac = metis_general_tac HO;
wenzelm@32956
   783
val metisF_tac = metis_general_tac FO;
wenzelm@32956
   784
val metisFT_tac = metis_general_tac FT;
wenzelm@23442
   785
wenzelm@32956
   786
fun method name mode comment = Method.setup name (Attrib.thms >> (fn ths => fn ctxt =>
wenzelm@32956
   787
  SIMPLE_METHOD' (CHANGED_PROP o metis_general_tac mode ctxt ths))) comment;
wenzelm@23442
   788
wenzelm@32956
   789
val setup =
wenzelm@32956
   790
  type_lits_setup #>
blanchet@35865
   791
  method @{binding metis} HO "METIS for FOL and HOL problems" #>
wenzelm@32956
   792
  method @{binding metisF} FO "METIS for FOL problems" #>
wenzelm@35568
   793
  method @{binding metisFT} FT "METIS with fully-typed translation" #>
wenzelm@32956
   794
  Method.setup @{binding finish_clausify}
blanchet@35865
   795
    (Scan.succeed (K (SIMPLE_METHOD (Meson_Tactic.expand_defs_tac refl))))
wenzelm@32956
   796
    "cleanup after conversion to clauses";
wenzelm@23442
   797
wenzelm@23442
   798
end;