--- a/src/HOL/Tools/Sledgehammer/metis_reconstruct.ML Mon Oct 04 22:01:34 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,557 +0,0 @@
-(* Title: HOL/Tools/Sledgehammer/metis_reconstruct.ML
- Author: Kong W. Susanto, Cambridge University Computer Laboratory
- Author: Lawrence C. Paulson, Cambridge University Computer Laboratory
- Author: Jasmin Blanchette, TU Muenchen
- Copyright Cambridge University 2007
-
-Proof reconstruction for Metis.
-*)
-
-signature METIS_RECONSTRUCT =
-sig
- type mode = Metis_Translate.mode
-
- val trace : bool Unsynchronized.ref
- val lookth : (Metis_Thm.thm * 'a) list -> Metis_Thm.thm -> 'a
- val untyped_aconv : term -> term -> bool
- val replay_one_inference :
- Proof.context -> mode -> (string * term) list
- -> Metis_Thm.thm * Metis_Proof.inference -> (Metis_Thm.thm * thm) list
- -> (Metis_Thm.thm * thm) list
-end;
-
-structure Metis_Reconstruct : METIS_RECONSTRUCT =
-struct
-
-open Metis_Translate
-
-val trace = Unsynchronized.ref false
-fun trace_msg msg = if !trace then tracing (msg ()) else ()
-
-datatype term_or_type = SomeTerm of term | SomeType of typ
-
-fun terms_of [] = []
- | terms_of (SomeTerm t :: tts) = t :: terms_of tts
- | terms_of (SomeType _ :: tts) = terms_of tts;
-
-fun types_of [] = []
- | types_of (SomeTerm (Var ((a,idx), _)) :: tts) =
- if String.isPrefix "_" a then
- (*Variable generated by Metis, which might have been a type variable.*)
- TVar (("'" ^ a, idx), HOLogic.typeS) :: types_of tts
- else types_of tts
- | types_of (SomeTerm _ :: tts) = types_of tts
- | types_of (SomeType T :: tts) = T :: types_of tts;
-
-fun apply_list rator nargs rands =
- let val trands = terms_of rands
- in if length trands = nargs then SomeTerm (list_comb(rator, trands))
- else raise Fail
- ("apply_list: wrong number of arguments: " ^ Syntax.string_of_term_global Pure.thy rator ^
- " expected " ^ Int.toString nargs ^
- " received " ^ commas (map (Syntax.string_of_term_global Pure.thy) trands))
- end;
-
-fun infer_types ctxt =
- Syntax.check_terms (ProofContext.set_mode ProofContext.mode_pattern ctxt);
-
-(*We use 1 rather than 0 because variable references in clauses may otherwise conflict
- with variable constraints in the goal...at least, type inference often fails otherwise.
- SEE ALSO axiom_inf below.*)
-fun mk_var (w, T) = Var ((w, 1), T)
-
-(*include the default sort, if available*)
-fun mk_tfree ctxt w =
- let val ww = "'" ^ w
- in TFree(ww, the_default HOLogic.typeS (Variable.def_sort ctxt (ww, ~1))) end;
-
-(*Remove the "apply" operator from an HO term*)
-fun strip_happ args (Metis_Term.Fn(".",[t,u])) = strip_happ (u::args) t
- | strip_happ args x = (x, args);
-
-fun make_tvar s = TVar (("'" ^ s, 0), HOLogic.typeS)
-
-fun smart_invert_const "fequal" = @{const_name HOL.eq}
- | smart_invert_const s = invert_const s
-
-fun hol_type_from_metis_term _ (Metis_Term.Var v) =
- (case strip_prefix_and_unascii tvar_prefix v of
- SOME w => make_tvar w
- | NONE => make_tvar v)
- | hol_type_from_metis_term ctxt (Metis_Term.Fn(x, tys)) =
- (case strip_prefix_and_unascii type_const_prefix x of
- SOME tc => Type (smart_invert_const tc,
- map (hol_type_from_metis_term ctxt) tys)
- | NONE =>
- case strip_prefix_and_unascii tfree_prefix x of
- SOME tf => mk_tfree ctxt tf
- | NONE => raise Fail ("hol_type_from_metis_term: " ^ x));
-
-(*Maps metis terms to isabelle terms*)
-fun hol_term_from_metis_PT ctxt fol_tm =
- let val thy = ProofContext.theory_of ctxt
- val _ = trace_msg (fn () => "hol_term_from_metis_PT: " ^
- Metis_Term.toString fol_tm)
- fun tm_to_tt (Metis_Term.Var v) =
- (case strip_prefix_and_unascii tvar_prefix v of
- SOME w => SomeType (make_tvar w)
- | NONE =>
- case strip_prefix_and_unascii schematic_var_prefix v of
- SOME w => SomeTerm (mk_var (w, HOLogic.typeT))
- | NONE => SomeTerm (mk_var (v, HOLogic.typeT)) )
- (*Var from Metis with a name like _nnn; possibly a type variable*)
- | tm_to_tt (Metis_Term.Fn ("{}", [arg])) = tm_to_tt arg (*hBOOL*)
- | tm_to_tt (t as Metis_Term.Fn (".",_)) =
- let val (rator,rands) = strip_happ [] t
- in case rator of
- Metis_Term.Fn(fname,ts) => applic_to_tt (fname, ts @ rands)
- | _ => case tm_to_tt rator of
- SomeTerm t => SomeTerm (list_comb(t, terms_of (map tm_to_tt rands)))
- | _ => raise Fail "tm_to_tt: HO application"
- end
- | tm_to_tt (Metis_Term.Fn (fname, args)) = applic_to_tt (fname,args)
- and applic_to_tt ("=",ts) =
- SomeTerm (list_comb(Const (@{const_name HOL.eq}, HOLogic.typeT), terms_of (map tm_to_tt ts)))
- | applic_to_tt (a,ts) =
- case strip_prefix_and_unascii const_prefix a of
- SOME b =>
- let
- val c = smart_invert_const b
- val ntypes = num_type_args thy c
- val nterms = length ts - ntypes
- val tts = map tm_to_tt ts
- val tys = types_of (List.take(tts,ntypes))
- val t =
- if String.isPrefix new_skolem_const_prefix c then
- Var (new_skolem_var_from_const c,
- Type_Infer.paramify_vars (tl tys ---> hd tys))
- else
- Const (c, dummyT)
- in if length tys = ntypes then
- apply_list t nterms (List.drop(tts,ntypes))
- else
- raise Fail ("Constant " ^ c ^ " expects " ^ Int.toString ntypes ^
- " but gets " ^ Int.toString (length tys) ^
- " type arguments\n" ^
- cat_lines (map (Syntax.string_of_typ ctxt) tys) ^
- " the terms are \n" ^
- cat_lines (map (Syntax.string_of_term ctxt) (terms_of tts)))
- end
- | NONE => (*Not a constant. Is it a type constructor?*)
- case strip_prefix_and_unascii type_const_prefix a of
- SOME b =>
- SomeType (Type (smart_invert_const b, types_of (map tm_to_tt ts)))
- | NONE => (*Maybe a TFree. Should then check that ts=[].*)
- case strip_prefix_and_unascii tfree_prefix a of
- SOME b => SomeType (mk_tfree ctxt b)
- | NONE => (*a fixed variable? They are Skolem functions.*)
- case strip_prefix_and_unascii fixed_var_prefix a of
- SOME b =>
- let val opr = Free (b, HOLogic.typeT)
- in apply_list opr (length ts) (map tm_to_tt ts) end
- | NONE => raise Fail ("unexpected metis function: " ^ a)
- in
- case tm_to_tt fol_tm of
- SomeTerm t => t
- | SomeType T => raise TYPE ("fol_tm_to_tt: Term expected", [T], [])
- end
-
-(*Maps fully-typed metis terms to isabelle terms*)
-fun hol_term_from_metis_FT ctxt fol_tm =
- let val _ = trace_msg (fn () => "hol_term_from_metis_FT: " ^
- Metis_Term.toString fol_tm)
- fun cvt (Metis_Term.Fn ("ti", [Metis_Term.Var v, _])) =
- (case strip_prefix_and_unascii schematic_var_prefix v of
- SOME w => mk_var(w, dummyT)
- | NONE => mk_var(v, dummyT))
- | cvt (Metis_Term.Fn ("ti", [Metis_Term.Fn ("=",[]), _])) =
- Const (@{const_name HOL.eq}, HOLogic.typeT)
- | cvt (Metis_Term.Fn ("ti", [Metis_Term.Fn (x,[]), ty])) =
- (case strip_prefix_and_unascii const_prefix x of
- SOME c => Const (smart_invert_const c, dummyT)
- | NONE => (*Not a constant. Is it a fixed variable??*)
- case strip_prefix_and_unascii fixed_var_prefix x of
- SOME v => Free (v, hol_type_from_metis_term ctxt ty)
- | NONE => raise Fail ("hol_term_from_metis_FT bad constant: " ^ x))
- | cvt (Metis_Term.Fn ("ti", [Metis_Term.Fn (".",[tm1,tm2]), _])) =
- cvt tm1 $ cvt tm2
- | cvt (Metis_Term.Fn (".",[tm1,tm2])) = (*untyped application*)
- cvt tm1 $ cvt tm2
- | cvt (Metis_Term.Fn ("{}", [arg])) = cvt arg (*hBOOL*)
- | cvt (Metis_Term.Fn ("=", [tm1,tm2])) =
- list_comb(Const (@{const_name HOL.eq}, HOLogic.typeT), map cvt [tm1,tm2])
- | cvt (t as Metis_Term.Fn (x, [])) =
- (case strip_prefix_and_unascii const_prefix x of
- SOME c => Const (smart_invert_const c, dummyT)
- | NONE => (*Not a constant. Is it a fixed variable??*)
- case strip_prefix_and_unascii fixed_var_prefix x of
- SOME v => Free (v, dummyT)
- | NONE => (trace_msg (fn () => "hol_term_from_metis_FT bad const: " ^ x);
- hol_term_from_metis_PT ctxt t))
- | cvt t = (trace_msg (fn () => "hol_term_from_metis_FT bad term: " ^ Metis_Term.toString t);
- hol_term_from_metis_PT ctxt t)
- in fol_tm |> cvt end
-
-fun hol_term_from_metis FT = hol_term_from_metis_FT
- | hol_term_from_metis _ = hol_term_from_metis_PT
-
-fun hol_terms_from_fol ctxt mode old_skolems fol_tms =
- let val ts = map (hol_term_from_metis mode ctxt) fol_tms
- val _ = trace_msg (fn () => " calling type inference:")
- val _ = app (fn t => trace_msg (fn () => Syntax.string_of_term ctxt t)) ts
- val ts' = ts |> map (reveal_old_skolem_terms old_skolems)
- |> infer_types ctxt
- val _ = app (fn t => trace_msg
- (fn () => " final term: " ^ Syntax.string_of_term ctxt t ^
- " of type " ^ Syntax.string_of_typ ctxt (type_of t)))
- ts'
- in ts' end;
-
-(* ------------------------------------------------------------------------- *)
-(* FOL step Inference Rules *)
-(* ------------------------------------------------------------------------- *)
-
-(*for debugging only*)
-(*
-fun print_thpair (fth,th) =
- (trace_msg (fn () => "=============================================");
- trace_msg (fn () => "Metis: " ^ Metis_Thm.toString fth);
- trace_msg (fn () => "Isabelle: " ^ Display.string_of_thm_without_context th));
-*)
-
-fun lookth thpairs (fth : Metis_Thm.thm) =
- the (AList.lookup (uncurry Metis_Thm.equal) thpairs fth)
- handle Option.Option =>
- raise Fail ("Failed to find Metis theorem " ^ Metis_Thm.toString fth)
-
-fun cterm_incr_types thy idx = cterm_of thy o (map_types (Logic.incr_tvar idx));
-
-(* INFERENCE RULE: AXIOM *)
-
-fun axiom_inf thpairs th = Thm.incr_indexes 1 (lookth thpairs th);
- (*This causes variables to have an index of 1 by default. SEE ALSO mk_var above.*)
-
-(* INFERENCE RULE: ASSUME *)
-
-val EXCLUDED_MIDDLE = @{lemma "P ==> ~ P ==> False" by (rule notE)}
-
-fun inst_excluded_middle thy i_atm =
- let val th = EXCLUDED_MIDDLE
- val [vx] = Term.add_vars (prop_of th) []
- val substs = [(cterm_of thy (Var vx), cterm_of thy i_atm)]
- in cterm_instantiate substs th end;
-
-fun assume_inf ctxt mode old_skolems atm =
- inst_excluded_middle
- (ProofContext.theory_of ctxt)
- (singleton (hol_terms_from_fol ctxt mode old_skolems) (Metis_Term.Fn atm))
-
-(* INFERENCE RULE: INSTANTIATE (SUBST). Type instantiations are ignored. Trying
- to reconstruct them admits new possibilities of errors, e.g. concerning
- sorts. Instead we try to arrange that new TVars are distinct and that types
- can be inferred from terms. *)
-
-fun inst_inf ctxt mode old_skolems thpairs fsubst th =
- let val thy = ProofContext.theory_of ctxt
- val i_th = lookth thpairs th
- val i_th_vars = Term.add_vars (prop_of i_th) []
- fun find_var x = the (List.find (fn ((a,_),_) => a=x) i_th_vars)
- fun subst_translation (x,y) =
- let val v = find_var x
- (* We call "reveal_old_skolem_terms" and "infer_types" below. *)
- val t = hol_term_from_metis mode ctxt y
- in SOME (cterm_of thy (Var v), t) end
- handle Option.Option =>
- (trace_msg (fn () => "\"find_var\" failed for " ^ x ^
- " in " ^ Display.string_of_thm ctxt i_th);
- NONE)
- | TYPE _ =>
- (trace_msg (fn () => "\"hol_term_from_metis\" failed for " ^ x ^
- " in " ^ Display.string_of_thm ctxt i_th);
- NONE)
- fun remove_typeinst (a, t) =
- case strip_prefix_and_unascii schematic_var_prefix a of
- SOME b => SOME (b, t)
- | NONE => case strip_prefix_and_unascii tvar_prefix a of
- SOME _ => NONE (*type instantiations are forbidden!*)
- | NONE => SOME (a,t) (*internal Metis var?*)
- val _ = trace_msg (fn () => " isa th: " ^ Display.string_of_thm ctxt i_th)
- val substs = map_filter remove_typeinst (Metis_Subst.toList fsubst)
- val (vars,rawtms) = ListPair.unzip (map_filter subst_translation substs)
- val tms = rawtms |> map (reveal_old_skolem_terms old_skolems)
- |> infer_types ctxt
- val ctm_of = cterm_incr_types thy (1 + Thm.maxidx_of i_th)
- val substs' = ListPair.zip (vars, map ctm_of tms)
- val _ = trace_msg (fn () =>
- cat_lines ("subst_translations:" ::
- (substs' |> map (fn (x, y) =>
- Syntax.string_of_term ctxt (term_of x) ^ " |-> " ^
- Syntax.string_of_term ctxt (term_of y)))));
- in cterm_instantiate substs' i_th end
- handle THM (msg, _, _) =>
- error ("Cannot replay Metis proof in Isabelle:\n" ^ msg)
-
-(* INFERENCE RULE: RESOLVE *)
-
-(* Like RSN, but we rename apart only the type variables. Vars here typically
- have an index of 1, and the use of RSN would increase this typically to 3.
- Instantiations of those Vars could then fail. See comment on "mk_var". *)
-fun resolve_inc_tyvars thy tha i thb =
- let
- val tha = Drule.incr_type_indexes (1 + Thm.maxidx_of thb) tha
- fun aux tha thb =
- case Thm.bicompose false (false, tha, nprems_of tha) i thb
- |> Seq.list_of |> distinct Thm.eq_thm of
- [th] => th
- | _ => raise THM ("resolve_inc_tyvars: unique result expected", i,
- [tha, thb])
- in
- aux tha thb
- handle TERM z =>
- (* The unifier, which is invoked from "Thm.bicompose", will sometimes
- refuse to unify "?a::?'a" with "?a::?'b" or "?a::nat" and throw a
- "TERM" exception (with "add_ffpair" as first argument). We then
- perform unification of the types of variables by hand and try
- again. We could do this the first time around but this error
- occurs seldom and we don't want to break existing proofs in subtle
- ways or slow them down needlessly. *)
- case [] |> fold (Term.add_vars o prop_of) [tha, thb]
- |> AList.group (op =)
- |> maps (fn ((s, _), T :: Ts) =>
- map (fn T' => (Free (s, T), Free (s, T'))) Ts)
- |> rpair (Envir.empty ~1)
- |-> fold (Pattern.unify thy)
- |> Envir.type_env |> Vartab.dest
- |> map (fn (x, (S, T)) =>
- pairself (ctyp_of thy) (TVar (x, S), T)) of
- [] => raise TERM z
- | ps => aux (instantiate (ps, []) tha) (instantiate (ps, []) thb)
- end
-
-fun mk_not (Const (@{const_name Not}, _) $ b) = b
- | mk_not b = HOLogic.mk_not b
-
-(* Match untyped terms. *)
-fun untyped_aconv (Const (a, _)) (Const(b, _)) = (a = b)
- | untyped_aconv (Free (a, _)) (Free (b, _)) = (a = b)
- | untyped_aconv (Var ((a, _), _)) (Var ((b, _), _)) =
- (a = b) (* The index is ignored, for some reason. *)
- | untyped_aconv (Bound i) (Bound j) = (i = j)
- | untyped_aconv (Abs (_, _, t)) (Abs (_, _, u)) = untyped_aconv t u
- | untyped_aconv (t1 $ t2) (u1 $ u2) =
- untyped_aconv t1 u1 andalso untyped_aconv t2 u2
- | untyped_aconv _ _ = false
-
-(* Finding the relative location of an untyped term within a list of terms *)
-fun literal_index lit =
- let
- val lit = Envir.eta_contract lit
- fun get _ [] = raise Empty
- | get n (x :: xs) =
- if untyped_aconv lit (Envir.eta_contract (HOLogic.dest_Trueprop x)) then
- n
- else
- get (n+1) xs
- in get 1 end
-
-(* Permute a rule's premises to move the i-th premise to the last position. *)
-fun make_last i th =
- let val n = nprems_of th
- in if 1 <= i andalso i <= n
- then Thm.permute_prems (i-1) 1 th
- else raise THM("select_literal", i, [th])
- end;
-
-(* Maps a rule that ends "... ==> P ==> False" to "... ==> ~P" while suppressing
- double-negations. *)
-val negate_head = rewrite_rule [@{thm atomize_not}, not_not RS eq_reflection]
-
-(* Maps the clause [P1,...Pn]==>False to [P1,...,P(i-1),P(i+1),...Pn] ==> ~P *)
-val select_literal = negate_head oo make_last
-
-fun resolve_inf ctxt mode old_skolems thpairs atm th1 th2 =
- let
- val thy = ProofContext.theory_of ctxt
- val i_th1 = lookth thpairs th1 and i_th2 = lookth thpairs th2
- val _ = trace_msg (fn () => " isa th1 (pos): " ^ Display.string_of_thm ctxt i_th1)
- val _ = trace_msg (fn () => " isa th2 (neg): " ^ Display.string_of_thm ctxt i_th2)
- in
- (* Trivial cases where one operand is type info *)
- if Thm.eq_thm (TrueI, i_th1) then
- i_th2
- else if Thm.eq_thm (TrueI, i_th2) then
- i_th1
- else
- let
- val i_atm = singleton (hol_terms_from_fol ctxt mode old_skolems)
- (Metis_Term.Fn atm)
- val _ = trace_msg (fn () => " atom: " ^ Syntax.string_of_term ctxt i_atm)
- val prems_th1 = prems_of i_th1
- val prems_th2 = prems_of i_th2
- val index_th1 = literal_index (mk_not i_atm) prems_th1
- handle Empty => raise Fail "Failed to find literal in th1"
- val _ = trace_msg (fn () => " index_th1: " ^ Int.toString index_th1)
- val index_th2 = literal_index i_atm prems_th2
- handle Empty => raise Fail "Failed to find literal in th2"
- val _ = trace_msg (fn () => " index_th2: " ^ Int.toString index_th2)
- in
- resolve_inc_tyvars thy (select_literal index_th1 i_th1) index_th2 i_th2
- end
- end;
-
-(* INFERENCE RULE: REFL *)
-
-val REFL_THM = Thm.incr_indexes 2 @{lemma "t ~= t ==> False" by simp}
-
-val refl_x = cterm_of @{theory} (Var (hd (Term.add_vars (prop_of REFL_THM) [])));
-val refl_idx = 1 + Thm.maxidx_of REFL_THM;
-
-fun refl_inf ctxt mode old_skolems t =
- let val thy = ProofContext.theory_of ctxt
- val i_t = singleton (hol_terms_from_fol ctxt mode old_skolems) t
- val _ = trace_msg (fn () => " term: " ^ Syntax.string_of_term ctxt i_t)
- val c_t = cterm_incr_types thy refl_idx i_t
- in cterm_instantiate [(refl_x, c_t)] REFL_THM end;
-
-(* INFERENCE RULE: EQUALITY *)
-
-val subst_em = @{lemma "s = t ==> P s ==> ~ P t ==> False" by simp}
-val ssubst_em = @{lemma "s = t ==> P t ==> ~ P s ==> False" by simp}
-
-val metis_eq = Metis_Term.Fn ("=", []);
-
-fun get_ty_arg_size _ (Const (@{const_name HOL.eq}, _)) = 0 (*equality has no type arguments*)
- | get_ty_arg_size thy (Const (c, _)) = (num_type_args thy c handle TYPE _ => 0)
- | get_ty_arg_size _ _ = 0;
-
-fun equality_inf ctxt mode old_skolems (pos, atm) fp fr =
- let val thy = ProofContext.theory_of ctxt
- val m_tm = Metis_Term.Fn atm
- val [i_atm,i_tm] = hol_terms_from_fol ctxt mode old_skolems [m_tm, fr]
- val _ = trace_msg (fn () => "sign of the literal: " ^ Bool.toString pos)
- fun replace_item_list lx 0 (_::ls) = lx::ls
- | replace_item_list lx i (l::ls) = l :: replace_item_list lx (i-1) ls
- fun path_finder_FO tm [] = (tm, Bound 0)
- | path_finder_FO tm (p::ps) =
- let val (tm1,args) = strip_comb tm
- val adjustment = get_ty_arg_size thy tm1
- val p' = if adjustment > p then p else p-adjustment
- val tm_p = List.nth(args,p')
- handle Subscript =>
- error ("Cannot replay Metis proof in Isabelle:\n" ^
- "equality_inf: " ^ Int.toString p ^ " adj " ^
- Int.toString adjustment ^ " term " ^
- Syntax.string_of_term ctxt tm)
- val _ = trace_msg (fn () => "path_finder: " ^ Int.toString p ^
- " " ^ Syntax.string_of_term ctxt tm_p)
- val (r,t) = path_finder_FO tm_p ps
- in
- (r, list_comb (tm1, replace_item_list t p' args))
- end
- fun path_finder_HO tm [] = (tm, Bound 0)
- | path_finder_HO (t$u) (0::ps) = (fn(x,y) => (x, y$u)) (path_finder_HO t ps)
- | path_finder_HO (t$u) (_::ps) = (fn(x,y) => (x, t$y)) (path_finder_HO u ps)
- | path_finder_HO tm ps =
- raise Fail ("Cannot replay Metis proof in Isabelle:\n" ^
- "equality_inf, path_finder_HO: path = " ^
- space_implode " " (map Int.toString ps) ^
- " isa-term: " ^ Syntax.string_of_term ctxt tm)
- fun path_finder_FT tm [] _ = (tm, Bound 0)
- | path_finder_FT tm (0::ps) (Metis_Term.Fn ("ti", [t1, _])) =
- path_finder_FT tm ps t1
- | path_finder_FT (t$u) (0::ps) (Metis_Term.Fn (".", [t1, _])) =
- (fn(x,y) => (x, y$u)) (path_finder_FT t ps t1)
- | path_finder_FT (t$u) (1::ps) (Metis_Term.Fn (".", [_, t2])) =
- (fn(x,y) => (x, t$y)) (path_finder_FT u ps t2)
- | path_finder_FT tm ps t =
- raise Fail ("Cannot replay Metis proof in Isabelle:\n" ^
- "equality_inf, path_finder_FT: path = " ^
- space_implode " " (map Int.toString ps) ^
- " isa-term: " ^ Syntax.string_of_term ctxt tm ^
- " fol-term: " ^ Metis_Term.toString t)
- fun path_finder FO tm ps _ = path_finder_FO tm ps
- | path_finder HO (tm as Const(@{const_name HOL.eq},_) $ _ $ _) (p::ps) _ =
- (*equality: not curried, as other predicates are*)
- if p=0 then path_finder_HO tm (0::1::ps) (*select first operand*)
- else path_finder_HO tm (p::ps) (*1 selects second operand*)
- | path_finder HO tm (_ :: ps) (Metis_Term.Fn ("{}", [_])) =
- path_finder_HO tm ps (*if not equality, ignore head to skip hBOOL*)
- | path_finder FT (tm as Const(@{const_name HOL.eq}, _) $ _ $ _) (p::ps)
- (Metis_Term.Fn ("=", [t1,t2])) =
- (*equality: not curried, as other predicates are*)
- if p=0 then path_finder_FT tm (0::1::ps)
- (Metis_Term.Fn (".", [Metis_Term.Fn (".", [metis_eq,t1]), t2]))
- (*select first operand*)
- else path_finder_FT tm (p::ps)
- (Metis_Term.Fn (".", [metis_eq,t2]))
- (*1 selects second operand*)
- | path_finder FT tm (_ :: ps) (Metis_Term.Fn ("{}", [t1])) = path_finder_FT tm ps t1
- (*if not equality, ignore head to skip the hBOOL predicate*)
- | path_finder FT tm ps t = path_finder_FT tm ps t (*really an error case!*)
- fun path_finder_lit ((nt as Const (@{const_name Not}, _)) $ tm_a) idx =
- let val (tm, tm_rslt) = path_finder mode tm_a idx m_tm
- in (tm, nt $ tm_rslt) end
- | path_finder_lit tm_a idx = path_finder mode tm_a idx m_tm
- val (tm_subst, body) = path_finder_lit i_atm fp
- val tm_abs = Abs ("x", type_of tm_subst, body)
- val _ = trace_msg (fn () => "abstraction: " ^ Syntax.string_of_term ctxt tm_abs)
- val _ = trace_msg (fn () => "i_tm: " ^ Syntax.string_of_term ctxt i_tm)
- val _ = trace_msg (fn () => "located term: " ^ Syntax.string_of_term ctxt tm_subst)
- val imax = maxidx_of_term (i_tm $ tm_abs $ tm_subst) (*ill typed but gives right max*)
- val subst' = Thm.incr_indexes (imax+1) (if pos then subst_em else ssubst_em)
- val _ = trace_msg (fn () => "subst' " ^ Display.string_of_thm ctxt subst')
- val eq_terms = map (pairself (cterm_of thy))
- (ListPair.zip (OldTerm.term_vars (prop_of subst'), [tm_abs, tm_subst, i_tm]))
- in cterm_instantiate eq_terms subst' end;
-
-val factor = Seq.hd o distinct_subgoals_tac;
-
-fun step ctxt mode old_skolems thpairs p =
- case p of
- (fol_th, Metis_Proof.Axiom _) => factor (axiom_inf thpairs fol_th)
- | (_, Metis_Proof.Assume f_atm) => assume_inf ctxt mode old_skolems f_atm
- | (_, Metis_Proof.Metis_Subst (f_subst, f_th1)) =>
- factor (inst_inf ctxt mode old_skolems thpairs f_subst f_th1)
- | (_, Metis_Proof.Resolve(f_atm, f_th1, f_th2)) =>
- factor (resolve_inf ctxt mode old_skolems thpairs f_atm f_th1 f_th2)
- | (_, Metis_Proof.Refl f_tm) => refl_inf ctxt mode old_skolems f_tm
- | (_, Metis_Proof.Equality (f_lit, f_p, f_r)) =>
- equality_inf ctxt mode old_skolems f_lit f_p f_r
-
-fun flexflex_first_order th =
- case Thm.tpairs_of th of
- [] => th
- | pairs =>
- let val thy = theory_of_thm th
- val (_, tenv) =
- fold (Pattern.first_order_match thy) pairs (Vartab.empty, Vartab.empty)
- val t_pairs = map Meson.term_pair_of (Vartab.dest tenv)
- val th' = Thm.instantiate ([], map (pairself (cterm_of thy)) t_pairs) th
- in th' end
- handle THM _ => th;
-
-fun is_metis_literal_genuine (_, (s, _)) = not (String.isPrefix class_prefix s)
-fun is_isabelle_literal_genuine t =
- case t of _ $ (Const (@{const_name skolem}, _) $ _) => false | _ => true
-
-fun count p xs = fold (fn x => if p x then Integer.add 1 else I) xs 0
-
-fun replay_one_inference ctxt mode old_skolems (fol_th, inf) thpairs =
- let
- val _ = trace_msg (fn () => "=============================================")
- val _ = trace_msg (fn () => "METIS THM: " ^ Metis_Thm.toString fol_th)
- val _ = trace_msg (fn () => "INFERENCE: " ^ Metis_Proof.inferenceToString inf)
- val th = step ctxt mode old_skolems thpairs (fol_th, inf)
- |> flexflex_first_order
- val _ = trace_msg (fn () => "ISABELLE THM: " ^ Display.string_of_thm ctxt th)
- val _ = trace_msg (fn () => "=============================================")
- val num_metis_lits =
- fol_th |> Metis_Thm.clause |> Metis_LiteralSet.toList
- |> count is_metis_literal_genuine
- val num_isabelle_lits =
- th |> prems_of |> count is_isabelle_literal_genuine
- val _ = if num_metis_lits = num_isabelle_lits then ()
- else error "Cannot replay Metis proof in Isabelle: Out of sync."
- in (fol_th, th) :: thpairs end
-
-end;