src/HOL/Tools/Metis/metis_translate.ML

+(*  Title:      HOL/Tools/Sledgehammer/metis_translate.ML
+    Author:     Jia Meng, Cambridge University Computer Laboratory and NICTA
+    Author:     Kong W. Susanto, Cambridge University Computer Laboratory
+    Author:     Lawrence C. Paulson, Cambridge University Computer Laboratory
+    Author:     Jasmin Blanchette, TU Muenchen
+
+Translation of HOL to FOL for Metis.
+*)
+
+signature METIS_TRANSLATE =
+sig
+  type name = string * string
+  datatype type_literal =
+    TyLitVar of name * name |
+    TyLitFree of name * name
+  datatype arLit =
+    TConsLit of name * name * name list |
+    TVarLit of name * name
+  datatype arity_clause =
+    ArityClause of {name: string, conclLit: arLit, premLits: arLit list}
+  datatype class_rel_clause =
+    ClassRelClause of {name: string, subclass: name, superclass: name}
+  datatype combtyp =
+    CombTVar of name |
+    CombTFree of name |
+    CombType of name * combtyp list
+  datatype combterm =
+    CombConst of name * combtyp * combtyp list (* Const and Free *) |
+    CombVar of name * combtyp |
+    CombApp of combterm * combterm
+  datatype fol_literal = FOLLiteral of bool * combterm
+
+  datatype mode = FO | HO | FT
+  type logic_map =
+    {axioms: (Metis_Thm.thm * thm) list,
+     tfrees: type_literal list,
+     old_skolems: (string * term) list}
+
+  val type_wrapper_name : string
+  val bound_var_prefix : string
+  val schematic_var_prefix: string
+  val fixed_var_prefix: string
+  val tvar_prefix: string
+  val tfree_prefix: string
+  val const_prefix: string
+  val type_const_prefix: string
+  val class_prefix: string
+  val new_skolem_const_prefix : string
+  val invert_const: string -> string
+  val ascii_of: string -> string
+  val unascii_of: string -> string
+  val strip_prefix_and_unascii: string -> string -> string option
+  val make_bound_var : string -> string
+  val make_schematic_var : string * int -> string
+  val make_fixed_var : string -> string
+  val make_schematic_type_var : string * int -> string
+  val make_fixed_type_var : string -> string
+  val make_fixed_const : string -> string
+  val make_fixed_type_const : string -> string
+  val make_type_class : string -> string
+  val num_type_args: theory -> string -> int
+  val new_skolem_var_from_const: string -> indexname
+  val type_literals_for_types : typ list -> type_literal list
+  val make_class_rel_clauses :
+    theory -> class list -> class list -> class_rel_clause list
+  val make_arity_clauses :
+    theory -> string list -> class list -> class list * arity_clause list
+  val combtyp_of : combterm -> combtyp
+  val strip_combterm_comb : combterm -> combterm * combterm list
+  val combterm_from_term :
+    theory -> int -> (string * typ) list -> term -> combterm * typ list
+  val reveal_old_skolem_terms : (string * term) list -> term -> term
+  val tfree_classes_of_terms : term list -> string list
+  val tvar_classes_of_terms : term list -> string list
+  val type_consts_of_terms : theory -> term list -> string list
+  val string_of_mode : mode -> string
+  val build_logic_map :
+    mode -> Proof.context -> bool -> thm list -> thm list list
+    -> mode * logic_map
+end
+
+structure Metis_Translate : METIS_TRANSLATE =
+struct
+
+val type_wrapper_name = "ti"
+
+val bound_var_prefix = "B_"
+val schematic_var_prefix = "V_"
+val fixed_var_prefix = "v_"
+
+val tvar_prefix = "T_";
+val tfree_prefix = "t_";
+
+val const_prefix = "c_";
+val type_const_prefix = "tc_";
+val class_prefix = "class_";
+
+val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
+val old_skolem_const_prefix = skolem_const_prefix ^ "o"
+val new_skolem_const_prefix = skolem_const_prefix ^ "n"
+
+fun union_all xss = fold (union (op =)) xss []
+
+(* Readable names for the more common symbolic functions. Do not mess with the
+   last nine entries of the table unless you know what you are doing. *)
+val const_trans_table =
+  Symtab.make [(@{type_name Product_Type.prod}, "prod"),
+               (@{type_name Sum_Type.sum}, "sum"),
+               (@{const_name HOL.eq}, "equal"),
+               (@{const_name HOL.conj}, "and"),
+               (@{const_name HOL.disj}, "or"),
+               (@{const_name HOL.implies}, "implies"),
+               (@{const_name Set.member}, "member"),
+               (@{const_name fequal}, "fequal"),
+               (@{const_name COMBI}, "COMBI"),
+               (@{const_name COMBK}, "COMBK"),
+               (@{const_name COMBB}, "COMBB"),
+               (@{const_name COMBC}, "COMBC"),
+               (@{const_name COMBS}, "COMBS"),
+               (@{const_name True}, "True"),
+               (@{const_name False}, "False"),
+               (@{const_name If}, "If")]
+
+(* Invert the table of translations between Isabelle and ATPs. *)
+val const_trans_table_inv =
+  Symtab.update ("fequal", @{const_name HOL.eq})
+                (Symtab.make (map swap (Symtab.dest const_trans_table)))
+
+val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
+
+(*Escaping of special characters.
+  Alphanumeric characters are left unchanged.
+  The character _ goes to __
+  Characters in the range ASCII space to / go to _A to _P, respectively.
+  Other characters go to _nnn where nnn is the decimal ASCII code.*)
+val A_minus_space = Char.ord #"A" - Char.ord #" ";
+
+fun stringN_of_int 0 _ = ""
+  | stringN_of_int k n = stringN_of_int (k-1) (n div 10) ^ Int.toString (n mod 10);
+
+fun ascii_of_c c =
+  if Char.isAlphaNum c then String.str c
+  else if c = #"_" then "__"
+  else if #" " <= c andalso c <= #"/"
+       then "_" ^ String.str (Char.chr (Char.ord c + A_minus_space))
+  else ("_" ^ stringN_of_int 3 (Char.ord c))  (*fixed width, in case more digits follow*)
+
+val ascii_of = String.translate ascii_of_c;
+
+(** Remove ASCII armouring from names in proof files **)
+
+(*We don't raise error exceptions because this code can run inside the watcher.
+  Also, the errors are "impossible" (hah!)*)
+fun unascii_aux rcs [] = String.implode(rev rcs)
+  | unascii_aux rcs [#"_"] = unascii_aux (#"_"::rcs) []  (*ERROR*)
+      (*Three types of _ escapes: __, _A to _P, _nnn*)
+  | unascii_aux rcs (#"_" :: #"_" :: cs) = unascii_aux (#"_"::rcs) cs
+  | unascii_aux rcs (#"_" :: c :: cs) =
+      if #"A" <= c andalso c<= #"P"  (*translation of #" " to #"/"*)
+      then unascii_aux (Char.chr(Char.ord c - A_minus_space) :: rcs) cs
+      else
+        let val digits = List.take (c::cs, 3) handle Subscript => []
+        in
+            case Int.fromString (String.implode digits) of
+                NONE => unascii_aux (c:: #"_"::rcs) cs  (*ERROR*)
+              | SOME n => unascii_aux (Char.chr n :: rcs) (List.drop (cs, 2))
+        end
+  | unascii_aux rcs (c::cs) = unascii_aux (c::rcs) cs
+val unascii_of = unascii_aux [] o String.explode
+
+(* If string s has the prefix s1, return the result of deleting it,
+   un-ASCII'd. *)
+fun strip_prefix_and_unascii s1 s =
+  if String.isPrefix s1 s then
+    SOME (unascii_of (String.extract (s, size s1, NONE)))
+  else
+    NONE
+
+(*Remove the initial ' character from a type variable, if it is present*)
+fun trim_type_var s =
+  if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
+  else error ("trim_type: Malformed type variable encountered: " ^ s);
+
+fun ascii_of_indexname (v,0) = ascii_of v
+  | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ Int.toString i;
+
+fun make_bound_var x = bound_var_prefix ^ ascii_of x
+fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
+fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
+
+fun make_schematic_type_var (x,i) =
+      tvar_prefix ^ (ascii_of_indexname (trim_type_var x,i));
+fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x));
+
+fun lookup_const c =
+  case Symtab.lookup const_trans_table c of
+    SOME c' => c'
+  | NONE => ascii_of c
+
+(* HOL.eq MUST BE "equal" because it's built into ATPs. *)
+fun make_fixed_const @{const_name HOL.eq} = "equal"
+  | make_fixed_const c = const_prefix ^ lookup_const c
+
+fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
+
+fun make_type_class clas = class_prefix ^ ascii_of clas;
+
+(* The number of type arguments of a constant, zero if it's monomorphic. For
+   (instances of) Skolem pseudoconstants, this information is encoded in the
+   constant name. *)
+fun num_type_args thy s =
+  if String.isPrefix skolem_const_prefix s then
+    s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
+  else
+    (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
+
+fun new_skolem_var_from_const s =
+  let
+    val ss = s |> space_explode Long_Name.separator
+    val n = length ss
+  in (nth ss (n - 2), nth ss (n - 3) |> Int.fromString |> the) end
+
+
+(**** Definitions and functions for FOL clauses for TPTP format output ****)
+
+type name = string * string
+
+(**** Isabelle FOL clauses ****)
+
+(* The first component is the type class; the second is a TVar or TFree. *)
+datatype type_literal =
+  TyLitVar of name * name |
+  TyLitFree of name * name
+
+(*Make literals for sorted type variables*)
+fun sorts_on_typs_aux (_, [])   = []
+  | sorts_on_typs_aux ((x,i),  s::ss) =
+      let val sorts = sorts_on_typs_aux ((x,i), ss)
+      in
+          if s = "HOL.type" then sorts
+          else if i = ~1 then TyLitFree (`make_type_class s, `make_fixed_type_var x) :: sorts
+          else TyLitVar (`make_type_class s, (make_schematic_type_var (x,i), x)) :: sorts
+      end;
+
+fun sorts_on_typs (TFree (a,s)) = sorts_on_typs_aux ((a,~1),s)
+  | sorts_on_typs (TVar (v,s))  = sorts_on_typs_aux (v,s);
+
+(*Given a list of sorted type variables, return a list of type literals.*)
+fun type_literals_for_types Ts =
+  fold (union (op =)) (map sorts_on_typs Ts) []
+
+(** make axiom and conjecture clauses. **)
+
+(**** Isabelle arities ****)
+
+datatype arLit =
+  TConsLit of name * name * name list |
+  TVarLit of name * name
+
+datatype arity_clause =
+  ArityClause of {name: string, conclLit: arLit, premLits: arLit list}
+
+
+fun gen_TVars 0 = []
+  | gen_TVars n = ("T_" ^ Int.toString n) :: gen_TVars (n-1);
+
+fun pack_sort(_,[])  = []
+  | pack_sort(tvar, "HOL.type"::srt) = pack_sort (tvar, srt)   (*IGNORE sort "type"*)
+  | pack_sort(tvar, cls::srt) =
+    (`make_type_class cls, (tvar, tvar)) :: pack_sort (tvar, srt)
+
+(*Arity of type constructor tcon :: (arg1,...,argN)res*)
+fun make_axiom_arity_clause (tcons, name, (cls,args)) =
+  let
+    val tvars = gen_TVars (length args)
+    val tvars_srts = ListPair.zip (tvars, args)
+  in
+    ArityClause {name = name,
+                 conclLit = TConsLit (`make_type_class cls,
+                                      `make_fixed_type_const tcons,
+                                      tvars ~~ tvars),
+                 premLits = map TVarLit (union_all (map pack_sort tvars_srts))}
+  end
+
+
+(**** Isabelle class relations ****)
+
+datatype class_rel_clause =
+  ClassRelClause of {name: string, subclass: name, superclass: name}
+
+(*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
+fun class_pairs _ [] _ = []
+  | class_pairs thy subs supers =
+      let
+        val class_less = Sorts.class_less (Sign.classes_of thy)
+        fun add_super sub super = class_less (sub, super) ? cons (sub, super)
+        fun add_supers sub = fold (add_super sub) supers
+      in fold add_supers subs [] end
+
+fun make_class_rel_clause (sub,super) =
+  ClassRelClause {name = sub ^ "_" ^ super,
+                  subclass = `make_type_class sub,
+                  superclass = `make_type_class super}
+
+fun make_class_rel_clauses thy subs supers =
+  map make_class_rel_clause (class_pairs thy subs supers);
+
+
+(** Isabelle arities **)
+
+fun arity_clause _ _ (_, []) = []
+  | arity_clause seen n (tcons, ("HOL.type",_)::ars) =  (*ignore*)
+      arity_clause seen n (tcons,ars)
+  | arity_clause seen n (tcons, (ar as (class,_)) :: ars) =
+      if member (op =) seen class then (*multiple arities for the same tycon, class pair*)
+          make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class ^ "_" ^ Int.toString n, ar) ::
+          arity_clause seen (n+1) (tcons,ars)
+      else
+          make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class, ar) ::
+          arity_clause (class::seen) n (tcons,ars)
+
+fun multi_arity_clause [] = []
+  | multi_arity_clause ((tcons, ars) :: tc_arlists) =
+      arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
+
+(*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
+  provided its arguments have the corresponding sorts.*)
+fun type_class_pairs thy tycons classes =
+  let val alg = Sign.classes_of thy
+      fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
+      fun add_class tycon class =
+        cons (class, domain_sorts tycon class)
+        handle Sorts.CLASS_ERROR _ => I
+      fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
+  in  map try_classes tycons  end;
+
+(*Proving one (tycon, class) membership may require proving others, so iterate.*)
+fun iter_type_class_pairs _ _ [] = ([], [])
+  | iter_type_class_pairs thy tycons classes =
+      let val cpairs = type_class_pairs thy tycons classes
+          val newclasses = union_all (union_all (union_all (map (map #2 o #2) cpairs)))
+            |> subtract (op =) classes |> subtract (op =) HOLogic.typeS
+          val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
+      in (union (op =) classes' classes, union (op =) cpairs' cpairs) end;
+
+fun make_arity_clauses thy tycons classes =
+  let val (classes', cpairs) = iter_type_class_pairs thy tycons classes
+  in  (classes', multi_arity_clause cpairs)  end;
+
+datatype combtyp =
+  CombTVar of name |
+  CombTFree of name |
+  CombType of name * combtyp list
+
+datatype combterm =
+  CombConst of name * combtyp * combtyp list (* Const and Free *) |
+  CombVar of name * combtyp |
+  CombApp of combterm * combterm
+
+datatype fol_literal = FOLLiteral of bool * combterm
+
+(*********************************************************************)
+(* convert a clause with type Term.term to a clause with type clause *)
+(*********************************************************************)
+
+(*Result of a function type; no need to check that the argument type matches.*)
+fun result_type (CombType (_, [_, tp2])) = tp2
+  | result_type _ = raise Fail "non-function type"
+
+fun combtyp_of (CombConst (_, tp, _)) = tp
+  | combtyp_of (CombVar (_, tp)) = tp
+  | combtyp_of (CombApp (t1, _)) = result_type (combtyp_of t1)
+
+(*gets the head of a combinator application, along with the list of arguments*)
+fun strip_combterm_comb u =
+    let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
+        |   stripc  x =  x
+    in stripc(u,[]) end
+
+fun combtype_of (Type (a, Ts)) =
+    let val (folTypes, ts) = combtypes_of Ts in
+      (CombType (`make_fixed_type_const a, folTypes), ts)
+    end
+  | combtype_of (tp as TFree (a, _)) = (CombTFree (`make_fixed_type_var a), [tp])
+  | combtype_of (tp as TVar (x, _)) =
+    (CombTVar (make_schematic_type_var x, string_of_indexname x), [tp])
+and combtypes_of Ts =
+  let val (folTyps, ts) = ListPair.unzip (map combtype_of Ts) in
+    (folTyps, union_all ts)
+  end
+
+(* same as above, but no gathering of sort information *)
+fun simple_combtype_of (Type (a, Ts)) =
+    CombType (`make_fixed_type_const a, map simple_combtype_of Ts)
+  | simple_combtype_of (TFree (a, _)) = CombTFree (`make_fixed_type_var a)
+  | simple_combtype_of (TVar (x, _)) =
+    CombTVar (make_schematic_type_var x, string_of_indexname x)
+
+fun new_skolem_const_name th_no s num_T_args =
+  [new_skolem_const_prefix, string_of_int th_no, s, string_of_int num_T_args]
+  |> space_implode Long_Name.separator
+
+(* Converts a term (with combinators) into a combterm. Also accummulates sort
+   infomation. *)
+fun combterm_from_term thy th_no bs (P $ Q) =
+      let val (P', tsP) = combterm_from_term thy th_no bs P
+          val (Q', tsQ) = combterm_from_term thy th_no bs Q
+      in  (CombApp (P', Q'), union (op =) tsP tsQ)  end
+  | combterm_from_term thy _ _ (Const (c, T)) =
+      let
+        val (tp, ts) = combtype_of T
+        val tvar_list =
+          (if String.isPrefix old_skolem_const_prefix c then
+             [] |> Term.add_tvarsT T |> map TVar
+           else
+             (c, T) |> Sign.const_typargs thy)
+          |> map simple_combtype_of
+        val c' = CombConst (`make_fixed_const c, tp, tvar_list)
+      in  (c',ts)  end
+  | combterm_from_term _ _ _ (Free (v, T)) =
+      let val (tp, ts) = combtype_of T
+          val v' = CombConst (`make_fixed_var v, tp, [])
+      in  (v',ts)  end
+  | combterm_from_term _ th_no _ (Var (v as (s, _), T)) =
+    let
+      val (tp, ts) = combtype_of T
+      val v' =
+        if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
+          let
+            val tys = T |> strip_type |> swap |> op ::
+            val s' = new_skolem_const_name th_no s (length tys)
+          in
+            CombConst (`make_fixed_const s', tp, map simple_combtype_of tys)
+          end
+        else
+          CombVar ((make_schematic_var v, string_of_indexname v), tp)
+    in (v', ts) end
+  | combterm_from_term _ _ bs (Bound j) =
+      let
+        val (s, T) = nth bs j
+        val (tp, ts) = combtype_of T
+        val v' = CombConst (`make_bound_var s, tp, [])
+      in (v', ts) end
+  | combterm_from_term _ _ _ (Abs _) = raise Fail "HOL clause: Abs"
+
+fun predicate_of thy th_no ((@{const Not} $ P), pos) =
+    predicate_of thy th_no (P, not pos)
+  | predicate_of thy th_no (t, pos) =
+    (combterm_from_term thy th_no [] (Envir.eta_contract t), pos)
+
+fun literals_of_term1 args thy th_no (@{const Trueprop} $ P) =
+    literals_of_term1 args thy th_no P
+  | literals_of_term1 args thy th_no (@{const HOL.disj} $ P $ Q) =
+    literals_of_term1 (literals_of_term1 args thy th_no P) thy th_no Q
+  | literals_of_term1 (lits, ts) thy th_no P =
+    let val ((pred, ts'), pol) = predicate_of thy th_no (P, true) in
+      (FOLLiteral (pol, pred) :: lits, union (op =) ts ts')
+    end
+val literals_of_term = literals_of_term1 ([], [])
+
+fun old_skolem_const_name i j num_T_args =
+  old_skolem_const_prefix ^ Long_Name.separator ^
+  (space_implode Long_Name.separator (map Int.toString [i, j, num_T_args]))
+
+fun conceal_old_skolem_terms i old_skolems t =
+  if exists_Const (curry (op =) @{const_name skolem} o fst) t then
+    let
+      fun aux old_skolems
+              (t as (Const (@{const_name skolem}, Type (_, [_, T])) $ _)) =
+          let
+            val (old_skolems, s) =
+              if i = ~1 then
+                (old_skolems, @{const_name undefined})
+              else case AList.find (op aconv) old_skolems t of
+                s :: _ => (old_skolems, s)
+              | [] =>
+                let
+                  val s = old_skolem_const_name i (length old_skolems)
+                                                (length (Term.add_tvarsT T []))
+                in ((s, t) :: old_skolems, s) end
+          in (old_skolems, Const (s, T)) end
+        | aux old_skolems (t1 $ t2) =
+          let
+            val (old_skolems, t1) = aux old_skolems t1
+            val (old_skolems, t2) = aux old_skolems t2
+          in (old_skolems, t1 $ t2) end
+        | aux old_skolems (Abs (s, T, t')) =
+          let val (old_skolems, t') = aux old_skolems t' in
+            (old_skolems, Abs (s, T, t'))
+          end
+        | aux old_skolems t = (old_skolems, t)
+    in aux old_skolems t end
+  else
+    (old_skolems, t)
+
+fun reveal_old_skolem_terms old_skolems =
+  map_aterms (fn t as Const (s, _) =>
+                 if String.isPrefix old_skolem_const_prefix s then
+                   AList.lookup (op =) old_skolems s |> the
+                   |> map_types Type_Infer.paramify_vars
+                 else
+                   t
+               | t => t)
+
+
+(***************************************************************)
+(* Type Classes Present in the Axiom or Conjecture Clauses     *)
+(***************************************************************)
+
+fun set_insert (x, s) = Symtab.update (x, ()) s
+
+fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
+
+(*Remove this trivial type class*)
+fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset;
+
+fun tfree_classes_of_terms ts =
+  let val sorts_list = map (map #2 o OldTerm.term_tfrees) ts
+  in  Symtab.keys (delete_type (List.foldl add_classes Symtab.empty sorts_list))  end;
+
+fun tvar_classes_of_terms ts =
+  let val sorts_list = map (map #2 o OldTerm.term_tvars) ts
+  in  Symtab.keys (delete_type (List.foldl add_classes Symtab.empty sorts_list))  end;
+
+(*fold type constructors*)
+fun fold_type_consts f (Type (a, Ts)) x = fold (fold_type_consts f) Ts (f (a,x))
+  | fold_type_consts _ _ x = x;
+
+(*Type constructors used to instantiate overloaded constants are the only ones needed.*)
+fun add_type_consts_in_term thy =
+  let
+    fun aux (Const x) =
+        fold (fold_type_consts set_insert) (Sign.const_typargs thy x)
+      | aux (Abs (_, _, u)) = aux u
+      | aux (Const (@{const_name skolem}, _) $ _) = I
+      | aux (t $ u) = aux t #> aux u
+      | aux _ = I
+  in aux end
+
+fun type_consts_of_terms thy ts =
+  Symtab.keys (fold (add_type_consts_in_term thy) ts Symtab.empty);
+
+(* ------------------------------------------------------------------------- *)
+(* HOL to FOL  (Isabelle to Metis)                                           *)
+(* ------------------------------------------------------------------------- *)
+
+datatype mode = FO | HO | FT  (* first-order, higher-order, fully-typed *)
+
+fun string_of_mode FO = "FO"
+  | string_of_mode HO = "HO"
+  | string_of_mode FT = "FT"
+
+fun fn_isa_to_met_sublevel "equal" = "=" (* FIXME: "c_fequal" *)
+  | fn_isa_to_met_sublevel x = x
+fun fn_isa_to_met_toplevel "equal" = "="
+  | fn_isa_to_met_toplevel x = x
+
+fun metis_lit b c args = (b, (c, args));
+
+fun metis_term_from_combtyp (CombTVar (s, _)) = Metis_Term.Var s
+  | metis_term_from_combtyp (CombTFree (s, _)) = Metis_Term.Fn (s, [])
+  | metis_term_from_combtyp (CombType ((s, _), tps)) =
+    Metis_Term.Fn (s, map metis_term_from_combtyp tps);
+
+(*These two functions insert type literals before the real literals. That is the
+  opposite order from TPTP linkup, but maybe OK.*)
+
+fun hol_term_to_fol_FO tm =
+  case strip_combterm_comb tm of
+      (CombConst ((c, _), _, tys), tms) =>
+        let val tyargs = map metis_term_from_combtyp tys
+            val args   = map hol_term_to_fol_FO tms
+        in Metis_Term.Fn (c, tyargs @ args) end
+    | (CombVar ((v, _), _), []) => Metis_Term.Var v
+    | _ => raise Fail "non-first-order combterm"
+
+fun hol_term_to_fol_HO (CombConst ((a, _), _, tylist)) =
+      Metis_Term.Fn (fn_isa_to_met_sublevel a, map metis_term_from_combtyp tylist)
+  | hol_term_to_fol_HO (CombVar ((s, _), _)) = Metis_Term.Var s
+  | hol_term_to_fol_HO (CombApp (tm1, tm2)) =
+       Metis_Term.Fn (".", map hol_term_to_fol_HO [tm1, tm2]);
+
+(*The fully-typed translation, to avoid type errors*)
+fun wrap_type (tm, ty) =
+  Metis_Term.Fn (type_wrapper_name, [tm, metis_term_from_combtyp ty])
+
+fun hol_term_to_fol_FT (CombVar ((s, _), ty)) = wrap_type (Metis_Term.Var s, ty)
+  | hol_term_to_fol_FT (CombConst((a, _), ty, _)) =
+      wrap_type (Metis_Term.Fn(fn_isa_to_met_sublevel a, []), ty)
+  | hol_term_to_fol_FT (tm as CombApp(tm1,tm2)) =
+       wrap_type (Metis_Term.Fn(".", map hol_term_to_fol_FT [tm1,tm2]),
+                  combtyp_of tm)
+
+fun hol_literal_to_fol FO (FOLLiteral (pos, tm)) =
+      let val (CombConst((p, _), _, tys), tms) = strip_combterm_comb tm
+          val tylits = if p = "equal" then [] else map metis_term_from_combtyp tys
+          val lits = map hol_term_to_fol_FO tms
+      in metis_lit pos (fn_isa_to_met_toplevel p) (tylits @ lits) end
+  | hol_literal_to_fol HO (FOLLiteral (pos, tm)) =
+     (case strip_combterm_comb tm of
+          (CombConst(("equal", _), _, _), tms) =>
+            metis_lit pos "=" (map hol_term_to_fol_HO tms)
+        | _ => metis_lit pos "{}" [hol_term_to_fol_HO tm])   (*hBOOL*)
+  | hol_literal_to_fol FT (FOLLiteral (pos, tm)) =
+     (case strip_combterm_comb tm of
+          (CombConst(("equal", _), _, _), tms) =>
+            metis_lit pos "=" (map hol_term_to_fol_FT tms)
+        | _ => metis_lit pos "{}" [hol_term_to_fol_FT tm])   (*hBOOL*);
+
+fun literals_of_hol_term thy th_no mode t =
+      let val (lits, types_sorts) = literals_of_term thy th_no t
+      in  (map (hol_literal_to_fol mode) lits, types_sorts) end;
+
+(*Sign should be "true" for conjecture type constraints, "false" for type lits in clauses.*)
+fun metis_of_type_literals pos (TyLitVar ((s, _), (s', _))) =
+    metis_lit pos s [Metis_Term.Var s']
+  | metis_of_type_literals pos (TyLitFree ((s, _), (s', _))) =
+    metis_lit pos s [Metis_Term.Fn (s',[])]
+
+fun default_sort _ (TVar _) = false
+  | default_sort ctxt (TFree (x, s)) = (s = the_default [] (Variable.def_sort ctxt (x, ~1)));
+
+fun metis_of_tfree tf =
+  Metis_Thm.axiom (Metis_LiteralSet.singleton (metis_of_type_literals true tf));
+
+fun hol_thm_to_fol is_conjecture th_no ctxt type_lits mode j old_skolems th =
+  let
+    val thy = ProofContext.theory_of ctxt
+    val (old_skolems, (mlits, types_sorts)) =
+     th |> prop_of |> Logic.strip_imp_concl
+        |> conceal_old_skolem_terms j old_skolems
+        ||> (HOLogic.dest_Trueprop #> literals_of_hol_term thy th_no mode)
+  in
+    if is_conjecture then
+      (Metis_Thm.axiom (Metis_LiteralSet.fromList mlits),
+       type_literals_for_types types_sorts, old_skolems)
+    else
+      let
+        val tylits = filter_out (default_sort ctxt) types_sorts
+                     |> type_literals_for_types
+        val mtylits =
+          if type_lits then map (metis_of_type_literals false) tylits else []
+      in
+        (Metis_Thm.axiom (Metis_LiteralSet.fromList(mtylits @ mlits)), [],
+         old_skolems)
+      end
+  end;
+
+val helpers =
+  [("c_COMBI", (false, map (`I) @{thms COMBI_def})),
+   ("c_COMBK", (false, map (`I) @{thms COMBK_def})),
+   ("c_COMBB", (false, map (`I) @{thms COMBB_def})),
+   ("c_COMBC", (false, map (`I) @{thms COMBC_def})),
+   ("c_COMBS", (false, map (`I) @{thms COMBS_def})),
+   ("c_fequal", (false, map (rpair @{thm equal_imp_equal})
+                            @{thms fequal_imp_equal equal_imp_fequal})),
+   ("c_True", (true, map (`I) @{thms True_or_False})),
+   ("c_False", (true, map (`I) @{thms True_or_False})),
+   ("c_If", (true, map (`I) @{thms if_True if_False True_or_False}))]
+
+(* ------------------------------------------------------------------------- *)
+(* Logic maps manage the interface between HOL and first-order logic.        *)
+(* ------------------------------------------------------------------------- *)
+
+type logic_map =
+  {axioms: (Metis_Thm.thm * thm) list,
+   tfrees: type_literal list,
+   old_skolems: (string * term) list}
+
+fun is_quasi_fol_clause thy =
+  Meson.is_fol_term thy o snd o conceal_old_skolem_terms ~1 [] o prop_of
+
+(*Extract TFree constraints from context to include as conjecture clauses*)
+fun init_tfrees ctxt =
+  let fun add ((a,i),s) Ts = if i = ~1 then TFree(a,s) :: Ts else Ts in
+    Vartab.fold add (#2 (Variable.constraints_of ctxt)) []
+    |> type_literals_for_types
+  end;
+
+(*Insert non-logical axioms corresponding to all accumulated TFrees*)
+fun add_tfrees {axioms, tfrees, old_skolems} : logic_map =
+     {axioms = map (rpair TrueI o metis_of_tfree) (distinct (op =) tfrees) @
+               axioms,
+      tfrees = tfrees, old_skolems = old_skolems}
+
+(*transform isabelle type / arity clause to metis clause *)
+fun add_type_thm [] lmap = lmap
+  | add_type_thm ((ith, mth) :: cls) {axioms, tfrees, old_skolems} =
+      add_type_thm cls {axioms = (mth, ith) :: axioms, tfrees = tfrees,
+                        old_skolems = old_skolems}
+
+fun const_in_metis c (pred, tm_list) =
+  let
+    fun in_mterm (Metis_Term.Var _) = false
+      | in_mterm (Metis_Term.Fn (".", tm_list)) = exists in_mterm tm_list
+      | in_mterm (Metis_Term.Fn (nm, tm_list)) = c=nm orelse exists in_mterm tm_list
+  in  c = pred orelse exists in_mterm tm_list  end;
+
+(* ARITY CLAUSE *)
+fun m_arity_cls (TConsLit ((c, _), (t, _), args)) =
+    metis_lit true c [Metis_Term.Fn(t, map (Metis_Term.Var o fst) args)]
+  | m_arity_cls (TVarLit ((c, _), (s, _))) =
+    metis_lit false c [Metis_Term.Var s]
+(*TrueI is returned as the Isabelle counterpart because there isn't any.*)
+fun arity_cls (ArityClause {conclLit, premLits, ...}) =
+  (TrueI,
+   Metis_Thm.axiom (Metis_LiteralSet.fromList (map m_arity_cls (conclLit :: premLits))));
+
+(* CLASSREL CLAUSE *)
+fun m_class_rel_cls (subclass, _) (superclass, _) =
+  [metis_lit false subclass [Metis_Term.Var "T"], metis_lit true superclass [Metis_Term.Var "T"]];
+fun class_rel_cls (ClassRelClause {subclass, superclass, ...}) =
+  (TrueI, Metis_Thm.axiom (Metis_LiteralSet.fromList (m_class_rel_cls subclass superclass)));
+
+fun type_ext thy tms =
+  let val subs = tfree_classes_of_terms tms
+      val supers = tvar_classes_of_terms tms
+      and tycons = type_consts_of_terms thy tms
+      val (supers', arity_clauses) = make_arity_clauses thy tycons supers
+      val class_rel_clauses = make_class_rel_clauses thy subs supers'
+  in  map class_rel_cls class_rel_clauses @ map arity_cls arity_clauses
+  end;
+
+(* Function to generate metis clauses, including comb and type clauses *)
+fun build_logic_map mode0 ctxt type_lits cls thss =
+  let val thy = ProofContext.theory_of ctxt
+      (*The modes FO and FT are sticky. HO can be downgraded to FO.*)
+      fun set_mode FO = FO
+        | set_mode HO =
+          if forall (forall (is_quasi_fol_clause thy)) (cls :: thss) then FO
+          else HO
+        | set_mode FT = FT
+      val mode = set_mode mode0
+      (*transform isabelle clause to metis clause *)
+      fun add_thm th_no is_conjecture (metis_ith, isa_ith)
+                  {axioms, tfrees, old_skolems} : logic_map =
+        let
+          val (mth, tfree_lits, old_skolems) =
+            hol_thm_to_fol is_conjecture th_no ctxt type_lits mode (length axioms)
+                           old_skolems metis_ith
+        in
+           {axioms = (mth, Meson.make_meta_clause isa_ith) :: axioms,
+            tfrees = union (op =) tfree_lits tfrees, old_skolems = old_skolems}
+        end;
+      val lmap = {axioms = [], tfrees = init_tfrees ctxt, old_skolems = []}
+                 |> fold (add_thm 0 true o `I) cls
+                 |> add_tfrees
+                 |> fold (fn (th_no, ths) => fold (add_thm th_no false o `I) ths)
+                         (1 upto length thss ~~ thss)
+      val clause_lists = map (Metis_Thm.clause o #1) (#axioms lmap)
+      fun is_used c =
+        exists (Metis_LiteralSet.exists (const_in_metis c o #2)) clause_lists
+      val lmap =
+        if mode = FO then
+          lmap
+        else
+          let
+            val helper_ths =
+              helpers |> filter (is_used o fst)
+                      |> maps (fn (c, (needs_full_types, thms)) =>
+                                  if not (is_used c) orelse
+                                     needs_full_types andalso mode <> FT then
+                                    []
+                                  else
+                                    thms)
+          in lmap |> fold (add_thm ~1 false) helper_ths end
+  in
+    (mode, add_type_thm (type_ext thy (maps (map prop_of) (cls :: thss))) lmap)
+  end
+
+end;