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(* Title: HOL/Tools/Metis/metis_reconstruct.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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Proof reconstruction for Metis.
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*)
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signature METIS_RECONSTRUCT =
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sig
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type mode = Metis_Translate.mode
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val trace : bool Config.T
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val trace_msg : Proof.context -> (unit -> string) -> unit
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val verbose : bool Config.T
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val verbose_warning : Proof.context -> string -> unit
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val lookth : (Metis_Thm.thm * 'a) list -> Metis_Thm.thm -> 'a
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val untyped_aconv : term -> term -> bool
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val replay_one_inference :
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Proof.context -> mode -> (string * term) list
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-> Metis_Thm.thm * Metis_Proof.inference -> (Metis_Thm.thm * thm) list
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-> (Metis_Thm.thm * thm) list
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val discharge_skolem_premises :
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Proof.context -> (thm * term) option list -> thm -> thm
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val setup : theory -> theory
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end;
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structure Metis_Reconstruct : METIS_RECONSTRUCT =
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struct
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open Metis_Translate
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val (trace, trace_setup) = Attrib.config_bool "metis_trace" (K false)
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val (verbose, verbose_setup) = Attrib.config_bool "metis_verbose" (K true)
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fun trace_msg ctxt msg = if Config.get ctxt trace then tracing (msg ()) else ()
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fun verbose_warning ctxt msg =
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if Config.get ctxt verbose then warning msg else ()
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datatype term_or_type = SomeTerm of term | SomeType of typ
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fun terms_of [] = []
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| terms_of (SomeTerm t :: tts) = t :: terms_of tts
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| terms_of (SomeType _ :: tts) = terms_of tts;
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fun types_of [] = []
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| types_of (SomeTerm (Var ((a,idx), _)) :: tts) =
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if String.isPrefix metis_generated_var_prefix 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 (SomeTerm _ :: tts) = types_of tts
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| types_of (SomeType 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 SomeTerm (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 " ^ string_of_int 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) = 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 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 => Type (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 ctxt (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 => SomeType (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 => SomeTerm (mk_var (w, HOLogic.typeT))
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| NONE => SomeTerm (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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SomeTerm t => SomeTerm (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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SomeTerm (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
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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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val t =
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if String.isPrefix new_skolem_const_prefix c then
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Var ((new_skolem_var_name_from_const c, 1),
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Type_Infer.paramify_vars (tl tys ---> hd tys))
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else
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Const (c, dummyT)
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in if length tys = ntypes then
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apply_list t nterms (List.drop(tts,ntypes))
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else
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raise Fail ("Constant " ^ c ^ " expects " ^ string_of_int ntypes ^
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" but gets " ^ string_of_int (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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case strip_prefix_and_unascii type_const_prefix a of
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SOME b =>
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SomeType (Type (invert_const b, types_of (map tm_to_tt ts)))
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| NONE => (*Maybe a TFree. Should then check that ts=[].*)
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case strip_prefix_and_unascii tfree_prefix a of
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SOME b => SomeType (mk_tfree ctxt b)
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| NONE => (*a fixed variable? They are Skolem functions.*)
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case strip_prefix_and_unascii fixed_var_prefix a of
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SOME b =>
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let val opr = Free (b, HOLogic.typeT)
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in apply_list opr (length ts) (map tm_to_tt ts) end
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| NONE => raise Fail ("unexpected metis function: " ^ a)
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in
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case tm_to_tt fol_tm of
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SomeTerm t => t
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| SomeType T => raise TYPE ("fol_tm_to_tt: Term expected", [T], [])
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end
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(*Maps fully-typed metis terms to isabelle terms*)
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fun hol_term_from_metis_FT ctxt fol_tm =
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let val _ = trace_msg ctxt (fn () => "hol_term_from_metis_FT: " ^
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Metis_Term.toString fol_tm)
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fun do_const c =
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let val c = c |> invert_const in
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if String.isPrefix new_skolem_const_prefix c then
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Var ((new_skolem_var_name_from_const c, 1), dummyT)
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else
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Const (c, dummyT)
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end
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fun cvt (Metis_Term.Fn ("ti", [Metis_Term.Var v, _])) =
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(case strip_prefix_and_unascii schematic_var_prefix v of
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SOME w => mk_var(w, dummyT)
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| NONE => mk_var(v, dummyT))
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| cvt (Metis_Term.Fn ("ti", [Metis_Term.Fn ("=",[]), _])) =
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Const (@{const_name HOL.eq}, HOLogic.typeT)
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| cvt (Metis_Term.Fn ("ti", [Metis_Term.Fn (x,[]), ty])) =
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(case strip_prefix_and_unascii const_prefix x of
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SOME c => do_const c
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| NONE => (*Not a constant. Is it a fixed variable??*)
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case strip_prefix_and_unascii fixed_var_prefix x of
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SOME v => Free (v, hol_type_from_metis_term ctxt ty)
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| NONE => raise Fail ("hol_term_from_metis_FT bad constant: " ^ x))
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| cvt (Metis_Term.Fn ("ti", [Metis_Term.Fn (".",[tm1,tm2]), _])) =
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cvt tm1 $ cvt tm2
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| cvt (Metis_Term.Fn (".",[tm1,tm2])) = (*untyped application*)
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cvt tm1 $ cvt tm2
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| cvt (Metis_Term.Fn ("{}", [arg])) = cvt arg (*hBOOL*)
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| cvt (Metis_Term.Fn ("=", [tm1,tm2])) =
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list_comb(Const (@{const_name HOL.eq}, HOLogic.typeT), map cvt [tm1,tm2])
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| cvt (t as Metis_Term.Fn (x, [])) =
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(case strip_prefix_and_unascii const_prefix x of
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SOME c => do_const c
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| NONE => (*Not a constant. Is it a fixed variable??*)
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case strip_prefix_and_unascii fixed_var_prefix x of
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SOME v => Free (v, dummyT)
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| NONE => (trace_msg ctxt (fn () =>
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"hol_term_from_metis_FT bad const: " ^ x);
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hol_term_from_metis_PT ctxt t))
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| cvt t = (trace_msg ctxt (fn () =>
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"hol_term_from_metis_FT bad term: " ^ Metis_Term.toString t);
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hol_term_from_metis_PT ctxt t)
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in fol_tm |> cvt end
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fun hol_term_from_metis FT = hol_term_from_metis_FT
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| hol_term_from_metis _ = hol_term_from_metis_PT
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fun hol_terms_from_metis ctxt mode old_skolems fol_tms =
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let val ts = map (hol_term_from_metis mode ctxt) fol_tms
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val _ = trace_msg ctxt (fn () => " calling type inference:")
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val _ = app (fn t => trace_msg ctxt
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(fn () => Syntax.string_of_term ctxt t)) ts
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val ts' = ts |> map (reveal_old_skolem_terms old_skolems)
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|> infer_types ctxt
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val _ = app (fn t => trace_msg ctxt
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(fn () => " final term: " ^ Syntax.string_of_term ctxt t ^
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" of type " ^ Syntax.string_of_typ ctxt (type_of t)))
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ts'
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in ts' end;
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(* ------------------------------------------------------------------------- *)
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(* FOL step Inference Rules *)
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(* ------------------------------------------------------------------------- *)
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(*for debugging only*)
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(*
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fun print_thpair ctxt (fth,th) =
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(trace_msg ctxt (fn () => "=============================================");
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trace_msg ctxt (fn () => "Metis: " ^ Metis_Thm.toString fth);
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trace_msg ctxt (fn () => "Isabelle: " ^ Display.string_of_thm_without_context th));
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*)
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fun lookth thpairs (fth : Metis_Thm.thm) =
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the (AList.lookup (uncurry Metis_Thm.equal) thpairs fth)
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handle Option.Option =>
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raise Fail ("Failed to find Metis theorem " ^ Metis_Thm.toString fth)
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fun cterm_incr_types thy idx = cterm_of thy o (map_types (Logic.incr_tvar idx));
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(* INFERENCE RULE: AXIOM *)
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fun axiom_inf thpairs th = Thm.incr_indexes 1 (lookth thpairs th);
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(*This causes variables to have an index of 1 by default. SEE ALSO mk_var above.*)
|
blanchet@39737
|
250 |
|
blanchet@39737
|
251 |
(* INFERENCE RULE: ASSUME *)
|
blanchet@39737
|
252 |
|
blanchet@39737
|
253 |
val EXCLUDED_MIDDLE = @{lemma "P ==> ~ P ==> False" by (rule notE)}
|
blanchet@39737
|
254 |
|
blanchet@39737
|
255 |
fun inst_excluded_middle thy i_atm =
|
blanchet@39737
|
256 |
let val th = EXCLUDED_MIDDLE
|
blanchet@39737
|
257 |
val [vx] = Term.add_vars (prop_of th) []
|
blanchet@39737
|
258 |
val substs = [(cterm_of thy (Var vx), cterm_of thy i_atm)]
|
blanchet@39737
|
259 |
in cterm_instantiate substs th end;
|
blanchet@39737
|
260 |
|
blanchet@40502
|
261 |
fun assume_inf ctxt mode skolem_params atm =
|
blanchet@39737
|
262 |
inst_excluded_middle
|
blanchet@39737
|
263 |
(ProofContext.theory_of ctxt)
|
blanchet@40502
|
264 |
(singleton (hol_terms_from_metis ctxt mode skolem_params)
|
blanchet@40502
|
265 |
(Metis_Term.Fn atm))
|
blanchet@39737
|
266 |
|
blanchet@39738
|
267 |
(* INFERENCE RULE: INSTANTIATE (SUBST). Type instantiations are ignored. Trying
|
blanchet@39737
|
268 |
to reconstruct them admits new possibilities of errors, e.g. concerning
|
blanchet@39737
|
269 |
sorts. Instead we try to arrange that new TVars are distinct and that types
|
blanchet@39738
|
270 |
can be inferred from terms. *)
|
blanchet@39737
|
271 |
|
blanchet@43212
|
272 |
fun inst_inf ctxt mode old_skolems thpairs fsubst th =
|
blanchet@39737
|
273 |
let val thy = ProofContext.theory_of ctxt
|
blanchet@39738
|
274 |
val i_th = lookth thpairs th
|
blanchet@39737
|
275 |
val i_th_vars = Term.add_vars (prop_of i_th) []
|
blanchet@39737
|
276 |
fun find_var x = the (List.find (fn ((a,_),_) => a=x) i_th_vars)
|
blanchet@39737
|
277 |
fun subst_translation (x,y) =
|
blanchet@39738
|
278 |
let val v = find_var x
|
blanchet@40067
|
279 |
(* We call "reveal_old_skolem_terms" and "infer_types" below. *)
|
blanchet@43212
|
280 |
val t = hol_term_from_metis mode ctxt y
|
blanchet@39738
|
281 |
in SOME (cterm_of thy (Var v), t) end
|
blanchet@39738
|
282 |
handle Option.Option =>
|
blanchet@40159
|
283 |
(trace_msg ctxt (fn () => "\"find_var\" failed for " ^ x ^
|
blanchet@40159
|
284 |
" in " ^ Display.string_of_thm ctxt i_th);
|
blanchet@39738
|
285 |
NONE)
|
blanchet@39738
|
286 |
| TYPE _ =>
|
blanchet@40159
|
287 |
(trace_msg ctxt (fn () => "\"hol_term_from_metis\" failed for " ^ x ^
|
blanchet@40159
|
288 |
" in " ^ Display.string_of_thm ctxt i_th);
|
blanchet@39738
|
289 |
NONE)
|
blanchet@39737
|
290 |
fun remove_typeinst (a, t) =
|
blanchet@39737
|
291 |
case strip_prefix_and_unascii schematic_var_prefix a of
|
blanchet@39737
|
292 |
SOME b => SOME (b, t)
|
blanchet@39737
|
293 |
| NONE => case strip_prefix_and_unascii tvar_prefix a of
|
blanchet@39737
|
294 |
SOME _ => NONE (*type instantiations are forbidden!*)
|
blanchet@39737
|
295 |
| NONE => SOME (a,t) (*internal Metis var?*)
|
blanchet@40159
|
296 |
val _ = trace_msg ctxt (fn () => " isa th: " ^ Display.string_of_thm ctxt i_th)
|
blanchet@39737
|
297 |
val substs = map_filter remove_typeinst (Metis_Subst.toList fsubst)
|
blanchet@39737
|
298 |
val (vars,rawtms) = ListPair.unzip (map_filter subst_translation substs)
|
blanchet@40067
|
299 |
val tms = rawtms |> map (reveal_old_skolem_terms old_skolems)
|
blanchet@40067
|
300 |
|> infer_types ctxt
|
blanchet@39737
|
301 |
val ctm_of = cterm_incr_types thy (1 + Thm.maxidx_of i_th)
|
blanchet@39737
|
302 |
val substs' = ListPair.zip (vars, map ctm_of tms)
|
blanchet@40159
|
303 |
val _ = trace_msg ctxt (fn () =>
|
blanchet@39737
|
304 |
cat_lines ("subst_translations:" ::
|
blanchet@39737
|
305 |
(substs' |> map (fn (x, y) =>
|
blanchet@39737
|
306 |
Syntax.string_of_term ctxt (term_of x) ^ " |-> " ^
|
blanchet@39737
|
307 |
Syntax.string_of_term ctxt (term_of y)))));
|
blanchet@39737
|
308 |
in cterm_instantiate substs' i_th end
|
blanchet@39737
|
309 |
handle THM (msg, _, _) =>
|
blanchet@39737
|
310 |
error ("Cannot replay Metis proof in Isabelle:\n" ^ msg)
|
blanchet@39737
|
311 |
|
blanchet@39737
|
312 |
(* INFERENCE RULE: RESOLVE *)
|
blanchet@39737
|
313 |
|
blanchet@39737
|
314 |
(* Like RSN, but we rename apart only the type variables. Vars here typically
|
blanchet@39737
|
315 |
have an index of 1, and the use of RSN would increase this typically to 3.
|
blanchet@39737
|
316 |
Instantiations of those Vars could then fail. See comment on "mk_var". *)
|
blanchet@39737
|
317 |
fun resolve_inc_tyvars thy tha i thb =
|
blanchet@39737
|
318 |
let
|
blanchet@39737
|
319 |
val tha = Drule.incr_type_indexes (1 + Thm.maxidx_of thb) tha
|
blanchet@39737
|
320 |
fun aux tha thb =
|
blanchet@39737
|
321 |
case Thm.bicompose false (false, tha, nprems_of tha) i thb
|
blanchet@39737
|
322 |
|> Seq.list_of |> distinct Thm.eq_thm of
|
blanchet@39737
|
323 |
[th] => th
|
blanchet@39737
|
324 |
| _ => raise THM ("resolve_inc_tyvars: unique result expected", i,
|
blanchet@39737
|
325 |
[tha, thb])
|
blanchet@39737
|
326 |
in
|
blanchet@39737
|
327 |
aux tha thb
|
blanchet@39737
|
328 |
handle TERM z =>
|
blanchet@39737
|
329 |
(* The unifier, which is invoked from "Thm.bicompose", will sometimes
|
blanchet@39737
|
330 |
refuse to unify "?a::?'a" with "?a::?'b" or "?a::nat" and throw a
|
blanchet@39737
|
331 |
"TERM" exception (with "add_ffpair" as first argument). We then
|
blanchet@39737
|
332 |
perform unification of the types of variables by hand and try
|
blanchet@39737
|
333 |
again. We could do this the first time around but this error
|
blanchet@39737
|
334 |
occurs seldom and we don't want to break existing proofs in subtle
|
blanchet@39737
|
335 |
ways or slow them down needlessly. *)
|
blanchet@39737
|
336 |
case [] |> fold (Term.add_vars o prop_of) [tha, thb]
|
blanchet@39737
|
337 |
|> AList.group (op =)
|
blanchet@39737
|
338 |
|> maps (fn ((s, _), T :: Ts) =>
|
blanchet@39737
|
339 |
map (fn T' => (Free (s, T), Free (s, T'))) Ts)
|
blanchet@39737
|
340 |
|> rpair (Envir.empty ~1)
|
blanchet@39737
|
341 |
|-> fold (Pattern.unify thy)
|
blanchet@39737
|
342 |
|> Envir.type_env |> Vartab.dest
|
blanchet@39737
|
343 |
|> map (fn (x, (S, T)) =>
|
blanchet@39737
|
344 |
pairself (ctyp_of thy) (TVar (x, S), T)) of
|
blanchet@39737
|
345 |
[] => raise TERM z
|
blanchet@39737
|
346 |
| ps => aux (instantiate (ps, []) tha) (instantiate (ps, []) thb)
|
blanchet@39737
|
347 |
end
|
blanchet@39737
|
348 |
|
blanchet@40462
|
349 |
fun s_not (@{const Not} $ t) = t
|
blanchet@40462
|
350 |
| s_not t = HOLogic.mk_not t
|
blanchet@40462
|
351 |
fun simp_not_not (@{const Not} $ t) = s_not (simp_not_not t)
|
blanchet@40462
|
352 |
| simp_not_not t = t
|
blanchet@39737
|
353 |
|
blanchet@39737
|
354 |
(* Match untyped terms. *)
|
blanchet@39737
|
355 |
fun untyped_aconv (Const (a, _)) (Const(b, _)) = (a = b)
|
blanchet@39737
|
356 |
| untyped_aconv (Free (a, _)) (Free (b, _)) = (a = b)
|
blanchet@39737
|
357 |
| untyped_aconv (Var ((a, _), _)) (Var ((b, _), _)) =
|
blanchet@39737
|
358 |
(a = b) (* The index is ignored, for some reason. *)
|
blanchet@39737
|
359 |
| untyped_aconv (Bound i) (Bound j) = (i = j)
|
blanchet@39737
|
360 |
| untyped_aconv (Abs (_, _, t)) (Abs (_, _, u)) = untyped_aconv t u
|
blanchet@39737
|
361 |
| untyped_aconv (t1 $ t2) (u1 $ u2) =
|
blanchet@39737
|
362 |
untyped_aconv t1 u1 andalso untyped_aconv t2 u2
|
blanchet@39737
|
363 |
| untyped_aconv _ _ = false
|
blanchet@39737
|
364 |
|
blanchet@39737
|
365 |
(* Finding the relative location of an untyped term within a list of terms *)
|
blanchet@40462
|
366 |
fun index_of_literal lit haystack =
|
blanchet@39737
|
367 |
let
|
blanchet@40462
|
368 |
val normalize = simp_not_not o Envir.eta_contract
|
blanchet@40462
|
369 |
val match_lit =
|
blanchet@40462
|
370 |
HOLogic.dest_Trueprop #> normalize #> untyped_aconv (lit |> normalize)
|
blanchet@40462
|
371 |
in case find_index match_lit haystack of ~1 => raise Empty | n => n + 1 end
|
blanchet@39737
|
372 |
|
blanchet@40074
|
373 |
(* Permute a rule's premises to move the i-th premise to the last position. *)
|
blanchet@40074
|
374 |
fun make_last i th =
|
blanchet@40074
|
375 |
let val n = nprems_of th
|
blanchet@40074
|
376 |
in if 1 <= i andalso i <= n
|
blanchet@40074
|
377 |
then Thm.permute_prems (i-1) 1 th
|
blanchet@40074
|
378 |
else raise THM("select_literal", i, [th])
|
blanchet@40074
|
379 |
end;
|
blanchet@40074
|
380 |
|
blanchet@41391
|
381 |
val neg_neg_imp = @{lemma "~ ~ Q ==> Q" by blast}
|
blanchet@41391
|
382 |
|
blanchet@40074
|
383 |
(* Maps a rule that ends "... ==> P ==> False" to "... ==> ~P" while suppressing
|
blanchet@40074
|
384 |
double-negations. *)
|
blanchet@41391
|
385 |
fun negate_head thy =
|
blanchet@41391
|
386 |
rewrite_rule @{thms atomize_not}
|
blanchet@41391
|
387 |
#> perhaps (try (fn th => resolve_inc_tyvars thy th 1 neg_neg_imp))
|
blanchet@40074
|
388 |
|
blanchet@40074
|
389 |
(* Maps the clause [P1,...Pn]==>False to [P1,...,P(i-1),P(i+1),...Pn] ==> ~P *)
|
blanchet@41391
|
390 |
fun select_literal thy = negate_head thy oo make_last
|
blanchet@40074
|
391 |
|
blanchet@40502
|
392 |
fun resolve_inf ctxt mode skolem_params thpairs atm th1 th2 =
|
blanchet@39737
|
393 |
let
|
blanchet@39737
|
394 |
val thy = ProofContext.theory_of ctxt
|
blanchet@39737
|
395 |
val i_th1 = lookth thpairs th1 and i_th2 = lookth thpairs th2
|
blanchet@40159
|
396 |
val _ = trace_msg ctxt (fn () => " isa th1 (pos): " ^ Display.string_of_thm ctxt i_th1)
|
blanchet@40159
|
397 |
val _ = trace_msg ctxt (fn () => " isa th2 (neg): " ^ Display.string_of_thm ctxt i_th2)
|
blanchet@39737
|
398 |
in
|
blanchet@39737
|
399 |
(* Trivial cases where one operand is type info *)
|
blanchet@39737
|
400 |
if Thm.eq_thm (TrueI, i_th1) then
|
blanchet@39737
|
401 |
i_th2
|
blanchet@39737
|
402 |
else if Thm.eq_thm (TrueI, i_th2) then
|
blanchet@39737
|
403 |
i_th1
|
blanchet@39737
|
404 |
else
|
blanchet@39737
|
405 |
let
|
blanchet@40462
|
406 |
val i_atm =
|
blanchet@40502
|
407 |
singleton (hol_terms_from_metis ctxt mode skolem_params)
|
blanchet@40462
|
408 |
(Metis_Term.Fn atm)
|
blanchet@40159
|
409 |
val _ = trace_msg ctxt (fn () => " atom: " ^ Syntax.string_of_term ctxt i_atm)
|
blanchet@39737
|
410 |
val prems_th1 = prems_of i_th1
|
blanchet@39737
|
411 |
val prems_th2 = prems_of i_th2
|
blanchet@40462
|
412 |
val index_th1 =
|
blanchet@40462
|
413 |
index_of_literal (s_not i_atm) prems_th1
|
blanchet@40462
|
414 |
handle Empty => raise Fail "Failed to find literal in th1"
|
wenzelm@41739
|
415 |
val _ = trace_msg ctxt (fn () => " index_th1: " ^ string_of_int index_th1)
|
blanchet@40462
|
416 |
val index_th2 =
|
blanchet@40462
|
417 |
index_of_literal i_atm prems_th2
|
blanchet@40462
|
418 |
handle Empty => raise Fail "Failed to find literal in th2"
|
wenzelm@41739
|
419 |
val _ = trace_msg ctxt (fn () => " index_th2: " ^ string_of_int index_th2)
|
blanchet@39737
|
420 |
in
|
blanchet@41391
|
421 |
resolve_inc_tyvars thy (select_literal thy index_th1 i_th1) index_th2
|
blanchet@41391
|
422 |
i_th2
|
blanchet@39737
|
423 |
end
|
blanchet@39737
|
424 |
end;
|
blanchet@39737
|
425 |
|
blanchet@39737
|
426 |
(* INFERENCE RULE: REFL *)
|
blanchet@39737
|
427 |
|
blanchet@39737
|
428 |
val REFL_THM = Thm.incr_indexes 2 @{lemma "t ~= t ==> False" by simp}
|
blanchet@39737
|
429 |
|
blanchet@39737
|
430 |
val refl_x = cterm_of @{theory} (Var (hd (Term.add_vars (prop_of REFL_THM) [])));
|
blanchet@39737
|
431 |
val refl_idx = 1 + Thm.maxidx_of REFL_THM;
|
blanchet@39737
|
432 |
|
blanchet@40502
|
433 |
fun refl_inf ctxt mode skolem_params t =
|
blanchet@39737
|
434 |
let val thy = ProofContext.theory_of ctxt
|
blanchet@40502
|
435 |
val i_t = singleton (hol_terms_from_metis ctxt mode skolem_params) t
|
blanchet@40159
|
436 |
val _ = trace_msg ctxt (fn () => " term: " ^ Syntax.string_of_term ctxt i_t)
|
blanchet@39737
|
437 |
val c_t = cterm_incr_types thy refl_idx i_t
|
blanchet@39737
|
438 |
in cterm_instantiate [(refl_x, c_t)] REFL_THM end;
|
blanchet@39737
|
439 |
|
blanchet@39737
|
440 |
(* INFERENCE RULE: EQUALITY *)
|
blanchet@39737
|
441 |
|
blanchet@39737
|
442 |
val subst_em = @{lemma "s = t ==> P s ==> ~ P t ==> False" by simp}
|
blanchet@39737
|
443 |
val ssubst_em = @{lemma "s = t ==> P t ==> ~ P s ==> False" by simp}
|
blanchet@39737
|
444 |
|
blanchet@39737
|
445 |
val metis_eq = Metis_Term.Fn ("=", []);
|
blanchet@39737
|
446 |
|
blanchet@39737
|
447 |
fun get_ty_arg_size _ (Const (@{const_name HOL.eq}, _)) = 0 (*equality has no type arguments*)
|
blanchet@39737
|
448 |
| get_ty_arg_size thy (Const (c, _)) = (num_type_args thy c handle TYPE _ => 0)
|
blanchet@39737
|
449 |
| get_ty_arg_size _ _ = 0;
|
blanchet@39737
|
450 |
|
blanchet@40502
|
451 |
fun equality_inf ctxt mode skolem_params (pos, atm) fp fr =
|
blanchet@39737
|
452 |
let val thy = ProofContext.theory_of ctxt
|
blanchet@39737
|
453 |
val m_tm = Metis_Term.Fn atm
|
blanchet@40502
|
454 |
val [i_atm,i_tm] = hol_terms_from_metis ctxt mode skolem_params [m_tm, fr]
|
blanchet@40159
|
455 |
val _ = trace_msg ctxt (fn () => "sign of the literal: " ^ Bool.toString pos)
|
blanchet@39737
|
456 |
fun replace_item_list lx 0 (_::ls) = lx::ls
|
blanchet@39737
|
457 |
| replace_item_list lx i (l::ls) = l :: replace_item_list lx (i-1) ls
|
blanchet@39738
|
458 |
fun path_finder_FO tm [] = (tm, Bound 0)
|
blanchet@39737
|
459 |
| path_finder_FO tm (p::ps) =
|
blanchet@39737
|
460 |
let val (tm1,args) = strip_comb tm
|
blanchet@39737
|
461 |
val adjustment = get_ty_arg_size thy tm1
|
blanchet@39737
|
462 |
val p' = if adjustment > p then p else p-adjustment
|
blanchet@39737
|
463 |
val tm_p = List.nth(args,p')
|
blanchet@39737
|
464 |
handle Subscript =>
|
blanchet@39737
|
465 |
error ("Cannot replay Metis proof in Isabelle:\n" ^
|
wenzelm@41739
|
466 |
"equality_inf: " ^ string_of_int p ^ " adj " ^
|
wenzelm@41739
|
467 |
string_of_int adjustment ^ " term " ^
|
blanchet@39737
|
468 |
Syntax.string_of_term ctxt tm)
|
wenzelm@41739
|
469 |
val _ = trace_msg ctxt (fn () => "path_finder: " ^ string_of_int p ^
|
blanchet@39737
|
470 |
" " ^ Syntax.string_of_term ctxt tm_p)
|
blanchet@39737
|
471 |
val (r,t) = path_finder_FO tm_p ps
|
blanchet@39737
|
472 |
in
|
blanchet@39737
|
473 |
(r, list_comb (tm1, replace_item_list t p' args))
|
blanchet@39737
|
474 |
end
|
blanchet@39738
|
475 |
fun path_finder_HO tm [] = (tm, Bound 0)
|
blanchet@39737
|
476 |
| path_finder_HO (t$u) (0::ps) = (fn(x,y) => (x, y$u)) (path_finder_HO t ps)
|
blanchet@39737
|
477 |
| path_finder_HO (t$u) (_::ps) = (fn(x,y) => (x, t$y)) (path_finder_HO u ps)
|
blanchet@39737
|
478 |
| path_finder_HO tm ps =
|
blanchet@39738
|
479 |
raise Fail ("Cannot replay Metis proof in Isabelle:\n" ^
|
blanchet@39738
|
480 |
"equality_inf, path_finder_HO: path = " ^
|
wenzelm@41739
|
481 |
space_implode " " (map string_of_int ps) ^
|
blanchet@39737
|
482 |
" isa-term: " ^ Syntax.string_of_term ctxt tm)
|
blanchet@39738
|
483 |
fun path_finder_FT tm [] _ = (tm, Bound 0)
|
blanchet@39737
|
484 |
| path_finder_FT tm (0::ps) (Metis_Term.Fn ("ti", [t1, _])) =
|
blanchet@39737
|
485 |
path_finder_FT tm ps t1
|
blanchet@39737
|
486 |
| path_finder_FT (t$u) (0::ps) (Metis_Term.Fn (".", [t1, _])) =
|
blanchet@39737
|
487 |
(fn(x,y) => (x, y$u)) (path_finder_FT t ps t1)
|
blanchet@39737
|
488 |
| path_finder_FT (t$u) (1::ps) (Metis_Term.Fn (".", [_, t2])) =
|
blanchet@39737
|
489 |
(fn(x,y) => (x, t$y)) (path_finder_FT u ps t2)
|
blanchet@39737
|
490 |
| path_finder_FT tm ps t =
|
blanchet@39738
|
491 |
raise Fail ("Cannot replay Metis proof in Isabelle:\n" ^
|
blanchet@39738
|
492 |
"equality_inf, path_finder_FT: path = " ^
|
wenzelm@41739
|
493 |
space_implode " " (map string_of_int ps) ^
|
blanchet@39737
|
494 |
" isa-term: " ^ Syntax.string_of_term ctxt tm ^
|
blanchet@39737
|
495 |
" fol-term: " ^ Metis_Term.toString t)
|
blanchet@39737
|
496 |
fun path_finder FO tm ps _ = path_finder_FO tm ps
|
blanchet@39737
|
497 |
| path_finder HO (tm as Const(@{const_name HOL.eq},_) $ _ $ _) (p::ps) _ =
|
blanchet@39737
|
498 |
(*equality: not curried, as other predicates are*)
|
blanchet@39737
|
499 |
if p=0 then path_finder_HO tm (0::1::ps) (*select first operand*)
|
blanchet@39737
|
500 |
else path_finder_HO tm (p::ps) (*1 selects second operand*)
|
blanchet@39737
|
501 |
| path_finder HO tm (_ :: ps) (Metis_Term.Fn ("{}", [_])) =
|
blanchet@39737
|
502 |
path_finder_HO tm ps (*if not equality, ignore head to skip hBOOL*)
|
blanchet@39737
|
503 |
| path_finder FT (tm as Const(@{const_name HOL.eq}, _) $ _ $ _) (p::ps)
|
blanchet@39737
|
504 |
(Metis_Term.Fn ("=", [t1,t2])) =
|
blanchet@39737
|
505 |
(*equality: not curried, as other predicates are*)
|
blanchet@39737
|
506 |
if p=0 then path_finder_FT tm (0::1::ps)
|
blanchet@39737
|
507 |
(Metis_Term.Fn (".", [Metis_Term.Fn (".", [metis_eq,t1]), t2]))
|
blanchet@39737
|
508 |
(*select first operand*)
|
blanchet@39737
|
509 |
else path_finder_FT tm (p::ps)
|
blanchet@39737
|
510 |
(Metis_Term.Fn (".", [metis_eq,t2]))
|
blanchet@39737
|
511 |
(*1 selects second operand*)
|
blanchet@39737
|
512 |
| path_finder FT tm (_ :: ps) (Metis_Term.Fn ("{}", [t1])) = path_finder_FT tm ps t1
|
blanchet@39737
|
513 |
(*if not equality, ignore head to skip the hBOOL predicate*)
|
blanchet@39737
|
514 |
| path_finder FT tm ps t = path_finder_FT tm ps t (*really an error case!*)
|
blanchet@39737
|
515 |
fun path_finder_lit ((nt as Const (@{const_name Not}, _)) $ tm_a) idx =
|
blanchet@39737
|
516 |
let val (tm, tm_rslt) = path_finder mode tm_a idx m_tm
|
blanchet@39737
|
517 |
in (tm, nt $ tm_rslt) end
|
blanchet@39737
|
518 |
| path_finder_lit tm_a idx = path_finder mode tm_a idx m_tm
|
blanchet@39737
|
519 |
val (tm_subst, body) = path_finder_lit i_atm fp
|
blanchet@39738
|
520 |
val tm_abs = Abs ("x", type_of tm_subst, body)
|
blanchet@40159
|
521 |
val _ = trace_msg ctxt (fn () => "abstraction: " ^ Syntax.string_of_term ctxt tm_abs)
|
blanchet@40159
|
522 |
val _ = trace_msg ctxt (fn () => "i_tm: " ^ Syntax.string_of_term ctxt i_tm)
|
blanchet@40159
|
523 |
val _ = trace_msg ctxt (fn () => "located term: " ^ Syntax.string_of_term ctxt tm_subst)
|
blanchet@39737
|
524 |
val imax = maxidx_of_term (i_tm $ tm_abs $ tm_subst) (*ill typed but gives right max*)
|
blanchet@39737
|
525 |
val subst' = Thm.incr_indexes (imax+1) (if pos then subst_em else ssubst_em)
|
blanchet@40159
|
526 |
val _ = trace_msg ctxt (fn () => "subst' " ^ Display.string_of_thm ctxt subst')
|
blanchet@39737
|
527 |
val eq_terms = map (pairself (cterm_of thy))
|
blanchet@39737
|
528 |
(ListPair.zip (OldTerm.term_vars (prop_of subst'), [tm_abs, tm_subst, i_tm]))
|
blanchet@39737
|
529 |
in cterm_instantiate eq_terms subst' end;
|
blanchet@39737
|
530 |
|
blanchet@39737
|
531 |
val factor = Seq.hd o distinct_subgoals_tac;
|
blanchet@39737
|
532 |
|
blanchet@40502
|
533 |
fun step ctxt mode skolem_params thpairs p =
|
blanchet@39737
|
534 |
case p of
|
blanchet@39737
|
535 |
(fol_th, Metis_Proof.Axiom _) => factor (axiom_inf thpairs fol_th)
|
blanchet@40502
|
536 |
| (_, Metis_Proof.Assume f_atm) => assume_inf ctxt mode skolem_params f_atm
|
blanchet@39737
|
537 |
| (_, Metis_Proof.Metis_Subst (f_subst, f_th1)) =>
|
blanchet@40502
|
538 |
factor (inst_inf ctxt mode skolem_params thpairs f_subst f_th1)
|
blanchet@39737
|
539 |
| (_, Metis_Proof.Resolve(f_atm, f_th1, f_th2)) =>
|
blanchet@40502
|
540 |
factor (resolve_inf ctxt mode skolem_params thpairs f_atm f_th1 f_th2)
|
blanchet@40502
|
541 |
| (_, Metis_Proof.Refl f_tm) => refl_inf ctxt mode skolem_params f_tm
|
blanchet@39737
|
542 |
| (_, Metis_Proof.Equality (f_lit, f_p, f_r)) =>
|
blanchet@40502
|
543 |
equality_inf ctxt mode skolem_params f_lit f_p f_r
|
blanchet@39737
|
544 |
|
blanchet@40074
|
545 |
fun flexflex_first_order th =
|
blanchet@40074
|
546 |
case Thm.tpairs_of th of
|
blanchet@40074
|
547 |
[] => th
|
blanchet@40074
|
548 |
| pairs =>
|
blanchet@40074
|
549 |
let val thy = theory_of_thm th
|
blanchet@40074
|
550 |
val (_, tenv) =
|
blanchet@40074
|
551 |
fold (Pattern.first_order_match thy) pairs (Vartab.empty, Vartab.empty)
|
blanchet@40074
|
552 |
val t_pairs = map Meson.term_pair_of (Vartab.dest tenv)
|
blanchet@40074
|
553 |
val th' = Thm.instantiate ([], map (pairself (cterm_of thy)) t_pairs) th
|
blanchet@40074
|
554 |
in th' end
|
blanchet@40074
|
555 |
handle THM _ => th;
|
blanchet@39737
|
556 |
|
blanchet@40076
|
557 |
fun is_metis_literal_genuine (_, (s, _)) = not (String.isPrefix class_prefix s)
|
blanchet@40076
|
558 |
fun is_isabelle_literal_genuine t =
|
blanchet@40134
|
559 |
case t of _ $ (Const (@{const_name Meson.skolem}, _) $ _) => false | _ => true
|
blanchet@40076
|
560 |
|
blanchet@40076
|
561 |
fun count p xs = fold (fn x => if p x then Integer.add 1 else I) xs 0
|
blanchet@40076
|
562 |
|
blanchet@43204
|
563 |
(* Seldomly needed hack. A Metis clause is represented as a set, so duplicate
|
blanchet@43204
|
564 |
disjuncts are impossible. In the Isabelle proof, in spite of efforts to
|
blanchet@43204
|
565 |
eliminate them, duplicates sometimes appear with slightly different (but
|
blanchet@43204
|
566 |
unifiable) types. *)
|
blanchet@43204
|
567 |
fun resynchronize ctxt fol_th th =
|
blanchet@43204
|
568 |
let
|
blanchet@43204
|
569 |
val num_metis_lits =
|
blanchet@43204
|
570 |
count is_metis_literal_genuine
|
blanchet@43204
|
571 |
(Metis_LiteralSet.toList (Metis_Thm.clause fol_th))
|
blanchet@43204
|
572 |
val num_isabelle_lits = count is_isabelle_literal_genuine (prems_of th)
|
blanchet@43204
|
573 |
in
|
blanchet@43204
|
574 |
if num_metis_lits >= num_isabelle_lits then
|
blanchet@43204
|
575 |
th
|
blanchet@43204
|
576 |
else
|
blanchet@43204
|
577 |
let
|
blanchet@43204
|
578 |
val (prems0, concl) = th |> prop_of |> Logic.strip_horn
|
blanchet@43204
|
579 |
val prems = prems0 |> distinct (uncurry untyped_aconv)
|
blanchet@43204
|
580 |
val goal = Logic.list_implies (prems, concl)
|
blanchet@43204
|
581 |
in
|
blanchet@43204
|
582 |
if length prems = length prems0 then
|
blanchet@43204
|
583 |
error "Cannot replay Metis proof in Isabelle: Out of sync."
|
blanchet@43204
|
584 |
else
|
blanchet@43204
|
585 |
Goal.prove ctxt [] [] goal (K (cut_rules_tac [th] 1
|
blanchet@43204
|
586 |
THEN ALLGOALS assume_tac))
|
blanchet@43204
|
587 |
|> resynchronize ctxt fol_th
|
blanchet@43204
|
588 |
end
|
blanchet@43204
|
589 |
end
|
blanchet@43204
|
590 |
|
blanchet@40502
|
591 |
fun replay_one_inference ctxt mode skolem_params (fol_th, inf) thpairs =
|
blanchet@41110
|
592 |
if not (null thpairs) andalso prop_of (snd (hd thpairs)) aconv @{prop False} then
|
blanchet@41110
|
593 |
(* Isabelle sometimes identifies literals (premises) that are distinct in
|
blanchet@41110
|
594 |
Metis (e.g., because of type variables). We give the Isabelle proof the
|
blanchet@41110
|
595 |
benefice of the doubt. *)
|
blanchet@41110
|
596 |
thpairs
|
blanchet@41110
|
597 |
else
|
blanchet@41110
|
598 |
let
|
blanchet@41110
|
599 |
val _ = trace_msg ctxt
|
blanchet@41110
|
600 |
(fn () => "=============================================")
|
blanchet@41110
|
601 |
val _ = trace_msg ctxt
|
blanchet@41110
|
602 |
(fn () => "METIS THM: " ^ Metis_Thm.toString fol_th)
|
blanchet@41110
|
603 |
val _ = trace_msg ctxt
|
blanchet@41110
|
604 |
(fn () => "INFERENCE: " ^ Metis_Proof.inferenceToString inf)
|
blanchet@41110
|
605 |
val th = step ctxt mode skolem_params thpairs (fol_th, inf)
|
blanchet@41110
|
606 |
|> flexflex_first_order
|
blanchet@43204
|
607 |
|> resynchronize ctxt fol_th
|
blanchet@41110
|
608 |
val _ = trace_msg ctxt
|
blanchet@41110
|
609 |
(fn () => "ISABELLE THM: " ^ Display.string_of_thm ctxt th)
|
blanchet@41110
|
610 |
val _ = trace_msg ctxt
|
blanchet@41110
|
611 |
(fn () => "=============================================")
|
blanchet@41110
|
612 |
in (fol_th, th) :: thpairs end
|
blanchet@39737
|
613 |
|
blanchet@43213
|
614 |
(* It is normally sufficient to apply "assume_tac" to unify the conclusion with
|
blanchet@43213
|
615 |
one of the premises. Unfortunately, this sometimes yields "Variable
|
blanchet@43213
|
616 |
?SK_a_b_c_x has two distinct types" errors. To avoid this, we instantiate the
|
blanchet@43213
|
617 |
variables before applying "assume_tac". Typical constraints are of the form
|
blanchet@43213
|
618 |
?SK_a_b_c_x SK_d_e_f_y ... SK_a_b_c_x ... SK_g_h_i_z =?= SK_a_b_c_x,
|
blanchet@43213
|
619 |
where the nonvariables are goal parameters. *)
|
blanchet@43213
|
620 |
fun unify_first_prem_with_concl thy i th =
|
blanchet@43213
|
621 |
let
|
blanchet@43213
|
622 |
val goal = Logic.get_goal (prop_of th) i |> Envir.beta_eta_contract
|
blanchet@43213
|
623 |
val prem = goal |> Logic.strip_assums_hyp |> hd
|
blanchet@43213
|
624 |
val concl = goal |> Logic.strip_assums_concl
|
blanchet@43213
|
625 |
fun pair_untyped_aconv (t1, t2) (u1, u2) =
|
blanchet@43213
|
626 |
untyped_aconv t1 u1 andalso untyped_aconv t2 u2
|
blanchet@43213
|
627 |
fun add_terms tp inst =
|
blanchet@43213
|
628 |
if exists (pair_untyped_aconv tp) inst then inst
|
blanchet@43213
|
629 |
else tp :: map (apsnd (subst_atomic [tp])) inst
|
blanchet@43213
|
630 |
fun is_flex t =
|
blanchet@43213
|
631 |
case strip_comb t of
|
blanchet@43213
|
632 |
(Var _, args) => forall is_Bound args
|
blanchet@43213
|
633 |
| _ => false
|
blanchet@43213
|
634 |
fun unify_flex flex rigid =
|
blanchet@43213
|
635 |
case strip_comb flex of
|
blanchet@43213
|
636 |
(Var (z as (_, T)), args) =>
|
blanchet@43213
|
637 |
add_terms (Var z,
|
blanchet@43213
|
638 |
fold_rev (curry absdummy) (take (length args) (binder_types T)) rigid)
|
blanchet@43213
|
639 |
| _ => I
|
blanchet@43213
|
640 |
fun unify_potential_flex comb atom =
|
blanchet@43213
|
641 |
if is_flex comb then unify_flex comb atom
|
blanchet@43213
|
642 |
else if is_Var atom then add_terms (atom, comb)
|
blanchet@43213
|
643 |
else I
|
blanchet@43213
|
644 |
fun unify_terms (t, u) =
|
blanchet@43213
|
645 |
case (t, u) of
|
blanchet@43213
|
646 |
(t1 $ t2, u1 $ u2) =>
|
blanchet@43213
|
647 |
if is_flex t then unify_flex t u
|
blanchet@43213
|
648 |
else if is_flex u then unify_flex u t
|
blanchet@43213
|
649 |
else fold unify_terms [(t1, u1), (t2, u2)]
|
blanchet@43213
|
650 |
| (_ $ _, _) => unify_potential_flex t u
|
blanchet@43213
|
651 |
| (_, _ $ _) => unify_potential_flex u t
|
blanchet@43213
|
652 |
| (Var _, _) => add_terms (t, u)
|
blanchet@43213
|
653 |
| (_, Var _) => add_terms (u, t)
|
blanchet@43213
|
654 |
| _ => I
|
blanchet@43215
|
655 |
val t_inst =
|
blanchet@43215
|
656 |
[] |> try (unify_terms (prem, concl) #> map (pairself (cterm_of thy)))
|
blanchet@43215
|
657 |
|> the_default [] (* FIXME *)
|
blanchet@43213
|
658 |
in th |> cterm_instantiate t_inst end
|
blanchet@40145
|
659 |
|
blanchet@40145
|
660 |
val copy_prem = @{lemma "P ==> (P ==> P ==> Q) ==> Q" by fast}
|
blanchet@40145
|
661 |
|
blanchet@40145
|
662 |
fun copy_prems_tac [] ns i =
|
blanchet@40145
|
663 |
if forall (curry (op =) 1) ns then all_tac else copy_prems_tac (rev ns) [] i
|
blanchet@40145
|
664 |
| copy_prems_tac (1 :: ms) ns i =
|
blanchet@40145
|
665 |
rotate_tac 1 i THEN copy_prems_tac ms (1 :: ns) i
|
blanchet@40145
|
666 |
| copy_prems_tac (m :: ms) ns i =
|
blanchet@40145
|
667 |
etac copy_prem i THEN copy_prems_tac ms (m div 2 :: (m + 1) div 2 :: ns) i
|
blanchet@40145
|
668 |
|
blanchet@43135
|
669 |
(* Metis generates variables of the form _nnn. *)
|
blanchet@43135
|
670 |
val is_metis_fresh_variable = String.isPrefix "_"
|
blanchet@43135
|
671 |
|
blanchet@40501
|
672 |
fun instantiate_forall_tac thy t i st =
|
blanchet@40145
|
673 |
let
|
blanchet@40501
|
674 |
val params = Logic.strip_params (Logic.get_goal (prop_of st) i) |> rev
|
blanchet@40145
|
675 |
fun repair (t as (Var ((s, _), _))) =
|
blanchet@40501
|
676 |
(case find_index (fn (s', _) => s' = s) params of
|
blanchet@40145
|
677 |
~1 => t
|
blanchet@40145
|
678 |
| j => Bound j)
|
blanchet@40504
|
679 |
| repair (t $ u) =
|
blanchet@40504
|
680 |
(case (repair t, repair u) of
|
blanchet@40504
|
681 |
(t as Bound j, u as Bound k) =>
|
blanchet@40504
|
682 |
(* This is a rather subtle trick to repair the discrepancy between
|
blanchet@40504
|
683 |
the fully skolemized term that MESON gives us (where existentials
|
blanchet@40504
|
684 |
were pulled out) and the reality. *)
|
blanchet@40504
|
685 |
if k > j then t else t $ u
|
blanchet@40504
|
686 |
| (t, u) => t $ u)
|
blanchet@40145
|
687 |
| repair t = t
|
blanchet@40145
|
688 |
val t' = t |> repair |> fold (curry absdummy) (map snd params)
|
blanchet@40145
|
689 |
fun do_instantiate th =
|
blanchet@43134
|
690 |
case Term.add_vars (prop_of th) []
|
blanchet@43135
|
691 |
|> filter_out ((Meson_Clausify.is_zapped_var_name orf
|
blanchet@43135
|
692 |
is_metis_fresh_variable) o fst o fst) of
|
blanchet@43134
|
693 |
[] => th
|
blanchet@43135
|
694 |
| [var as (_, T)] =>
|
blanchet@43135
|
695 |
let
|
blanchet@43135
|
696 |
val var_binder_Ts = T |> binder_types |> take (length params) |> rev
|
blanchet@43135
|
697 |
val var_body_T = T |> funpow (length params) range_type
|
blanchet@43135
|
698 |
val tyenv =
|
blanchet@43135
|
699 |
Vartab.empty |> Type.raw_unifys (fastype_of t :: map snd params,
|
blanchet@43135
|
700 |
var_body_T :: var_binder_Ts)
|
blanchet@43135
|
701 |
val env =
|
blanchet@43135
|
702 |
Envir.Envir {maxidx = Vartab.fold (Integer.max o snd o fst) tyenv 0,
|
blanchet@43135
|
703 |
tenv = Vartab.empty, tyenv = tyenv}
|
blanchet@43135
|
704 |
val ty_inst =
|
blanchet@43135
|
705 |
Vartab.fold (fn (x, (S, T)) =>
|
blanchet@43135
|
706 |
cons (pairself (ctyp_of thy) (TVar (x, S), T)))
|
blanchet@43135
|
707 |
tyenv []
|
blanchet@43135
|
708 |
val t_inst =
|
blanchet@43135
|
709 |
[pairself (cterm_of thy o Envir.norm_term env) (Var var, t')]
|
blanchet@43213
|
710 |
in th |> instantiate (ty_inst, t_inst) end
|
blanchet@43135
|
711 |
| _ => raise Fail "expected a single non-zapped, non-Metis Var"
|
blanchet@40145
|
712 |
in
|
blanchet@43135
|
713 |
(DETERM (etac @{thm allE} i THEN rotate_tac ~1 i)
|
blanchet@40501
|
714 |
THEN PRIMITIVE do_instantiate) st
|
blanchet@40145
|
715 |
end
|
blanchet@40145
|
716 |
|
blanchet@41383
|
717 |
fun fix_exists_tac t =
|
blanchet@40504
|
718 |
etac @{thm exE}
|
blanchet@40504
|
719 |
THEN' rename_tac [t |> dest_Var |> fst |> fst]
|
blanchet@40504
|
720 |
|
blanchet@40504
|
721 |
fun release_quantifier_tac thy (skolem, t) =
|
blanchet@41383
|
722 |
(if skolem then fix_exists_tac else instantiate_forall_tac thy) t
|
blanchet@40504
|
723 |
|
blanchet@40501
|
724 |
fun release_clusters_tac _ _ _ [] = K all_tac
|
blanchet@40501
|
725 |
| release_clusters_tac thy ax_counts substs
|
blanchet@40145
|
726 |
((ax_no, cluster_no) :: clusters) =
|
blanchet@40145
|
727 |
let
|
blanchet@40504
|
728 |
val cluster_of_var =
|
blanchet@40504
|
729 |
Meson_Clausify.cluster_of_zapped_var_name o fst o fst o dest_Var
|
blanchet@40504
|
730 |
fun in_right_cluster ((_, (cluster_no', _)), _) = cluster_no' = cluster_no
|
blanchet@40145
|
731 |
val cluster_substs =
|
blanchet@40145
|
732 |
substs
|
blanchet@40145
|
733 |
|> map_filter (fn (ax_no', (_, (_, tsubst))) =>
|
blanchet@40145
|
734 |
if ax_no' = ax_no then
|
blanchet@40504
|
735 |
tsubst |> map (apfst cluster_of_var)
|
blanchet@40504
|
736 |
|> filter (in_right_cluster o fst)
|
blanchet@40504
|
737 |
|> map (apfst snd)
|
blanchet@40504
|
738 |
|> SOME
|
blanchet@40504
|
739 |
else
|
blanchet@40504
|
740 |
NONE)
|
blanchet@40145
|
741 |
fun do_cluster_subst cluster_subst =
|
blanchet@40504
|
742 |
map (release_quantifier_tac thy) cluster_subst @ [rotate_tac 1]
|
blanchet@40145
|
743 |
val first_prem = find_index (fn (ax_no', _) => ax_no' = ax_no) substs
|
blanchet@40145
|
744 |
in
|
blanchet@40145
|
745 |
rotate_tac first_prem
|
blanchet@40145
|
746 |
THEN' (EVERY' (maps do_cluster_subst cluster_substs))
|
blanchet@40145
|
747 |
THEN' rotate_tac (~ first_prem - length cluster_substs)
|
blanchet@40501
|
748 |
THEN' release_clusters_tac thy ax_counts substs clusters
|
blanchet@40145
|
749 |
end
|
blanchet@40145
|
750 |
|
blanchet@40507
|
751 |
fun cluster_key ((ax_no, (cluster_no, index_no)), skolem) =
|
blanchet@40507
|
752 |
(ax_no, (cluster_no, (skolem, index_no)))
|
blanchet@40507
|
753 |
fun cluster_ord p =
|
blanchet@40507
|
754 |
prod_ord int_ord (prod_ord int_ord (prod_ord bool_ord int_ord))
|
blanchet@40507
|
755 |
(pairself cluster_key p)
|
blanchet@40145
|
756 |
|
blanchet@40145
|
757 |
val tysubst_ord =
|
blanchet@40145
|
758 |
list_ord (prod_ord Term_Ord.fast_indexname_ord
|
blanchet@40145
|
759 |
(prod_ord Term_Ord.sort_ord Term_Ord.typ_ord))
|
blanchet@40145
|
760 |
|
blanchet@40145
|
761 |
structure Int_Tysubst_Table =
|
blanchet@40145
|
762 |
Table(type key = int * (indexname * (sort * typ)) list
|
blanchet@40145
|
763 |
val ord = prod_ord int_ord tysubst_ord)
|
blanchet@40145
|
764 |
|
blanchet@40145
|
765 |
structure Int_Pair_Graph =
|
blanchet@40145
|
766 |
Graph(type key = int * int val ord = prod_ord int_ord int_ord)
|
blanchet@40145
|
767 |
|
blanchet@43135
|
768 |
fun shuffle_key (((axiom_no, (_, index_no)), _), _) = (axiom_no, index_no)
|
blanchet@40501
|
769 |
fun shuffle_ord p = prod_ord int_ord int_ord (pairself shuffle_key p)
|
blanchet@40501
|
770 |
|
blanchet@40145
|
771 |
(* Attempts to derive the theorem "False" from a theorem of the form
|
blanchet@40145
|
772 |
"P1 ==> ... ==> Pn ==> False", where the "Pi"s are to be discharged using the
|
blanchet@40145
|
773 |
specified axioms. The axioms have leading "All" and "Ex" quantifiers, which
|
blanchet@40145
|
774 |
must be eliminated first. *)
|
blanchet@40145
|
775 |
fun discharge_skolem_premises ctxt axioms prems_imp_false =
|
blanchet@40145
|
776 |
if prop_of prems_imp_false aconv @{prop False} then
|
blanchet@40145
|
777 |
prems_imp_false
|
blanchet@40145
|
778 |
else
|
blanchet@40145
|
779 |
let
|
blanchet@40145
|
780 |
val thy = ProofContext.theory_of ctxt
|
blanchet@40145
|
781 |
fun match_term p =
|
blanchet@40145
|
782 |
let
|
blanchet@40145
|
783 |
val (tyenv, tenv) =
|
blanchet@40145
|
784 |
Pattern.first_order_match thy p (Vartab.empty, Vartab.empty)
|
blanchet@40145
|
785 |
val tsubst =
|
blanchet@40145
|
786 |
tenv |> Vartab.dest
|
blanchet@42963
|
787 |
|> filter (Meson_Clausify.is_zapped_var_name o fst o fst)
|
blanchet@40145
|
788 |
|> sort (cluster_ord
|
blanchet@40145
|
789 |
o pairself (Meson_Clausify.cluster_of_zapped_var_name
|
blanchet@40145
|
790 |
o fst o fst))
|
blanchet@40145
|
791 |
|> map (Meson.term_pair_of
|
blanchet@40145
|
792 |
#> pairself (Envir.subst_term_types tyenv))
|
blanchet@40145
|
793 |
val tysubst = tyenv |> Vartab.dest
|
blanchet@40145
|
794 |
in (tysubst, tsubst) end
|
blanchet@40145
|
795 |
fun subst_info_for_prem subgoal_no prem =
|
blanchet@40145
|
796 |
case prem of
|
blanchet@40145
|
797 |
_ $ (Const (@{const_name Meson.skolem}, _) $ (_ $ t $ num)) =>
|
blanchet@40145
|
798 |
let val ax_no = HOLogic.dest_nat num in
|
blanchet@40145
|
799 |
(ax_no, (subgoal_no,
|
blanchet@40145
|
800 |
match_term (nth axioms ax_no |> the |> snd, t)))
|
blanchet@40145
|
801 |
end
|
blanchet@40145
|
802 |
| _ => raise TERM ("discharge_skolem_premises: Malformed premise",
|
blanchet@40145
|
803 |
[prem])
|
blanchet@40145
|
804 |
fun cluster_of_var_name skolem s =
|
blanchet@42962
|
805 |
case try Meson_Clausify.cluster_of_zapped_var_name s of
|
blanchet@42962
|
806 |
NONE => NONE
|
blanchet@42962
|
807 |
| SOME ((ax_no, (cluster_no, _)), skolem') =>
|
blanchet@40145
|
808 |
if skolem' = skolem andalso cluster_no > 0 then
|
blanchet@40145
|
809 |
SOME (ax_no, cluster_no)
|
blanchet@40145
|
810 |
else
|
blanchet@40145
|
811 |
NONE
|
blanchet@40145
|
812 |
fun clusters_in_term skolem t =
|
blanchet@40145
|
813 |
Term.add_var_names t [] |> map_filter (cluster_of_var_name skolem o fst)
|
blanchet@40145
|
814 |
fun deps_for_term_subst (var, t) =
|
blanchet@40145
|
815 |
case clusters_in_term false var of
|
blanchet@40145
|
816 |
[] => NONE
|
blanchet@40145
|
817 |
| [(ax_no, cluster_no)] =>
|
blanchet@40145
|
818 |
SOME ((ax_no, cluster_no),
|
blanchet@40145
|
819 |
clusters_in_term true t
|
blanchet@40145
|
820 |
|> cluster_no > 1 ? cons (ax_no, cluster_no - 1))
|
blanchet@40145
|
821 |
| _ => raise TERM ("discharge_skolem_premises: Expected Var", [var])
|
blanchet@40145
|
822 |
val prems = Logic.strip_imp_prems (prop_of prems_imp_false)
|
blanchet@40145
|
823 |
val substs = prems |> map2 subst_info_for_prem (1 upto length prems)
|
blanchet@40145
|
824 |
|> sort (int_ord o pairself fst)
|
blanchet@40145
|
825 |
val depss = maps (map_filter deps_for_term_subst o snd o snd o snd) substs
|
blanchet@40145
|
826 |
val clusters = maps (op ::) depss
|
blanchet@40145
|
827 |
val ordered_clusters =
|
blanchet@40145
|
828 |
Int_Pair_Graph.empty
|
blanchet@40145
|
829 |
|> fold Int_Pair_Graph.default_node (map (rpair ()) clusters)
|
blanchet@40145
|
830 |
|> fold Int_Pair_Graph.add_deps_acyclic depss
|
blanchet@40145
|
831 |
|> Int_Pair_Graph.topological_order
|
blanchet@40145
|
832 |
handle Int_Pair_Graph.CYCLES _ =>
|
blanchet@40399
|
833 |
error "Cannot replay Metis proof in Isabelle without \
|
blanchet@40399
|
834 |
\\"Hilbert_Choice\"."
|
blanchet@40145
|
835 |
val ax_counts =
|
blanchet@40145
|
836 |
Int_Tysubst_Table.empty
|
blanchet@40145
|
837 |
|> fold (fn (ax_no, (_, (tysubst, _))) =>
|
blanchet@40145
|
838 |
Int_Tysubst_Table.map_default ((ax_no, tysubst), 0)
|
blanchet@40145
|
839 |
(Integer.add 1)) substs
|
blanchet@40145
|
840 |
|> Int_Tysubst_Table.dest
|
blanchet@43210
|
841 |
val needed_axiom_props =
|
blanchet@43210
|
842 |
0 upto length axioms - 1 ~~ axioms
|
blanchet@43210
|
843 |
|> map_filter (fn (_, NONE) => NONE
|
blanchet@43210
|
844 |
| (ax_no, SOME (_, t)) =>
|
blanchet@43210
|
845 |
if exists (fn ((ax_no', _), n) =>
|
blanchet@43210
|
846 |
ax_no' = ax_no andalso n > 0)
|
blanchet@43210
|
847 |
ax_counts then
|
blanchet@43210
|
848 |
SOME t
|
blanchet@43210
|
849 |
else
|
blanchet@43210
|
850 |
NONE)
|
blanchet@43210
|
851 |
val outer_param_names =
|
blanchet@43210
|
852 |
[] |> fold Term.add_var_names needed_axiom_props
|
blanchet@43210
|
853 |
|> filter (Meson_Clausify.is_zapped_var_name o fst)
|
blanchet@43210
|
854 |
|> map (`(Meson_Clausify.cluster_of_zapped_var_name o fst))
|
blanchet@43210
|
855 |
|> filter (fn (((_, (cluster_no, _)), skolem), _) =>
|
blanchet@43210
|
856 |
cluster_no = 0 andalso skolem)
|
blanchet@43210
|
857 |
|> sort shuffle_ord |> map (fst o snd)
|
blanchet@43134
|
858 |
(* for debugging only:
|
blanchet@40145
|
859 |
fun string_for_subst_info (ax_no, (subgoal_no, (tysubst, tsubst))) =
|
blanchet@40145
|
860 |
"ax: " ^ string_of_int ax_no ^ "; asm: " ^ string_of_int subgoal_no ^
|
blanchet@40145
|
861 |
"; tysubst: " ^ PolyML.makestring tysubst ^ "; tsubst: {" ^
|
blanchet@40145
|
862 |
commas (map ((fn (s, t) => s ^ " |-> " ^ t)
|
blanchet@40145
|
863 |
o pairself (Syntax.string_of_term ctxt)) tsubst) ^ "}"
|
blanchet@40507
|
864 |
val _ = tracing ("ORDERED CLUSTERS: " ^ PolyML.makestring ordered_clusters)
|
blanchet@40507
|
865 |
val _ = tracing ("AXIOM COUNTS: " ^ PolyML.makestring ax_counts)
|
blanchet@43210
|
866 |
val _ = tracing ("OUTER PARAMS: " ^ PolyML.makestring outer_param_names)
|
blanchet@40145
|
867 |
val _ = tracing ("SUBSTS (" ^ string_of_int (length substs) ^ "):\n" ^
|
blanchet@40145
|
868 |
cat_lines (map string_for_subst_info substs))
|
blanchet@40145
|
869 |
*)
|
blanchet@43135
|
870 |
fun cut_and_ex_tac axiom =
|
blanchet@43135
|
871 |
cut_rules_tac [axiom] 1
|
blanchet@43135
|
872 |
THEN TRY (REPEAT_ALL_NEW (etac @{thm exE}) 1)
|
blanchet@40145
|
873 |
fun rotation_for_subgoal i =
|
blanchet@40145
|
874 |
find_index (fn (_, (subgoal_no, _)) => subgoal_no = i) substs
|
blanchet@40145
|
875 |
in
|
blanchet@40145
|
876 |
Goal.prove ctxt [] [] @{prop False}
|
blanchet@43135
|
877 |
(K (DETERM (EVERY (map (cut_and_ex_tac o fst o the o nth axioms o fst
|
blanchet@43135
|
878 |
o fst) ax_counts)
|
blanchet@43135
|
879 |
THEN rename_tac outer_param_names 1
|
blanchet@43135
|
880 |
THEN copy_prems_tac (map snd ax_counts) [] 1)
|
blanchet@40501
|
881 |
THEN release_clusters_tac thy ax_counts substs ordered_clusters 1
|
blanchet@40145
|
882 |
THEN match_tac [prems_imp_false] 1
|
blanchet@40145
|
883 |
THEN ALLGOALS (fn i =>
|
blanchet@40145
|
884 |
rtac @{thm Meson.skolem_COMBK_I} i
|
blanchet@40145
|
885 |
THEN rotate_tac (rotation_for_subgoal i) i
|
blanchet@43213
|
886 |
THEN PRIMITIVE (unify_first_prem_with_concl thy i)
|
blanchet@43135
|
887 |
THEN assume_tac i
|
blanchet@43134
|
888 |
THEN flexflex_tac)))
|
blanchet@40399
|
889 |
handle ERROR _ =>
|
blanchet@40399
|
890 |
error ("Cannot replay Metis proof in Isabelle:\n\
|
blanchet@40399
|
891 |
\Error when discharging Skolem assumptions.")
|
blanchet@40145
|
892 |
end
|
blanchet@40145
|
893 |
|
blanchet@40913
|
894 |
val setup = trace_setup #> verbose_setup
|
blanchet@40159
|
895 |
|
blanchet@39735
|
896 |
end;
|