src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Thu Dec 16 15:46:54 2010 +0100 (2010-12-16)
changeset 41211 1e2e16bc0077
parent 41199 4698d12dd860
child 41313 a96ac4d180b7
permissions -rw-r--r--
no need to do a super-duper atomization if Metis fails afterwards anyway
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(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
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    Author:     Fabian Immler, TU Muenchen
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    Author:     Makarius
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    Author:     Jasmin Blanchette, TU Muenchen
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Translation of HOL to FOL for Sledgehammer.
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*)
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signature SLEDGEHAMMER_ATP_TRANSLATE =
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sig
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  type 'a problem = 'a ATP_Problem.problem
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  type translated_formula
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  datatype type_system =
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    Tags of bool |
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    Preds of bool |
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    Const_Args |
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    No_Types
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  val precise_overloaded_args : bool Unsynchronized.ref
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  val fact_prefix : string
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  val conjecture_prefix : string
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  val types_dangerous_types : type_system -> bool
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  val num_atp_type_args : theory -> type_system -> string -> int
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  val translate_atp_fact :
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    Proof.context -> (string * 'a) * thm
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    -> translated_formula option * ((string * 'a) * thm)
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  val prepare_atp_problem :
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    Proof.context -> bool -> bool -> type_system -> bool -> term list -> term
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    -> (translated_formula option * ((string * 'a) * thm)) list
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    -> string problem * string Symtab.table * int * (string * 'a) list vector
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end;
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structure Sledgehammer_ATP_Translate : SLEDGEHAMMER_ATP_TRANSLATE =
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struct
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open ATP_Problem
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open Metis_Translate
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open Sledgehammer_Util
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(* FIXME: Remove references once appropriate defaults have been determined
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   empirically. *)
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val precise_overloaded_args = Unsynchronized.ref false
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val fact_prefix = "fact_"
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val conjecture_prefix = "conj_"
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val helper_prefix = "help_"
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val class_rel_clause_prefix = "clrel_";
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val arity_clause_prefix = "arity_"
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val tfree_prefix = "tfree_"
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(* Freshness almost guaranteed! *)
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val sledgehammer_weak_prefix = "Sledgehammer:"
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type translated_formula =
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  {name: string,
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   kind: kind,
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   combformula: (name, combterm) formula,
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   ctypes_sorts: typ list}
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datatype type_system =
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  Tags of bool |
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  Preds of bool |
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  Const_Args |
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  No_Types
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fun types_dangerous_types (Tags _) = true
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  | types_dangerous_types (Preds _) = true
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  | types_dangerous_types _ = false
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(* This is an approximation. If it returns "true" for a constant that isn't
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   overloaded (i.e., that has one uniform definition), needless clutter is
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   generated; if it returns "false" for an overloaded constant, the ATP gets a
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   license to do unsound reasoning if the type system is "overloaded_args". *)
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fun is_overloaded thy s =
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  not (!precise_overloaded_args) orelse
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  s = @{const_name finite} orelse
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  (s <> @{const_name HOL.eq} andalso
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   length (Defs.specifications_of (Theory.defs_of thy) s) > 1)
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fun needs_type_args thy type_sys s =
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  case type_sys of
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    Tags full_types => not full_types andalso is_overloaded thy s
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  | Preds _ => is_overloaded thy s (* FIXME: could be more precise *)
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  | Const_Args => is_overloaded thy s
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  | No_Types => false
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fun num_atp_type_args thy type_sys s =
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  if needs_type_args thy type_sys s then num_type_args thy s else 0
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fun atp_type_literals_for_types type_sys Ts =
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  if type_sys = No_Types then [] else type_literals_for_types Ts
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fun mk_anot phi = AConn (ANot, [phi])
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fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
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fun mk_ahorn [] phi = phi
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  | mk_ahorn (phi :: phis) psi =
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    AConn (AImplies, [fold (mk_aconn AAnd) phis phi, psi])
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fun close_universally phi =
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  let
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    fun term_vars bounds (ATerm (name as (s, _), tms)) =
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        (is_atp_variable s andalso not (member (op =) bounds name))
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          ? insert (op =) name
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        #> fold (term_vars bounds) tms
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    fun formula_vars bounds (AQuant (_, xs, phi)) =
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        formula_vars (xs @ bounds) phi
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      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
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      | formula_vars bounds (AAtom tm) = term_vars bounds tm
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  in
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    case formula_vars [] phi [] of [] => phi | xs => AQuant (AForall, xs, phi)
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  end
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fun combformula_for_prop thy eq_as_iff =
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  let
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    fun do_term bs t ts =
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      combterm_from_term thy bs (Envir.eta_contract t)
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      |>> AAtom ||> union (op =) ts
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    fun do_quant bs q s T t' =
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      let val s = Name.variant (map fst bs) s in
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        do_formula ((s, T) :: bs) t'
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        #>> (fn phi => AQuant (q, [`make_bound_var s], phi))
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      end
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    and do_conn bs c t1 t2 =
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      do_formula bs t1 ##>> do_formula bs t2
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      #>> (fn (phi1, phi2) => AConn (c, [phi1, phi2]))
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    and do_formula bs t =
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      case t of
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        @{const Not} $ t1 =>
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        do_formula bs t1 #>> (fn phi => AConn (ANot, [phi]))
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      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
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        do_quant bs AForall s T t'
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      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
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        do_quant bs AExists s T t'
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      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
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      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
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      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
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      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
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        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
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      | _ => do_term bs t
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  in do_formula [] end
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val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
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fun concealed_bound_name j = sledgehammer_weak_prefix ^ Int.toString j
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fun conceal_bounds Ts t =
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  subst_bounds (map (Free o apfst concealed_bound_name)
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                    (0 upto length Ts - 1 ~~ Ts), t)
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fun reveal_bounds Ts =
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  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
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                    (0 upto length Ts - 1 ~~ Ts))
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(* Removes the lambdas from an equation of the form "t = (%x. u)".
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   (Cf. "extensionalize_theorem" in "Meson_Clausify".) *)
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fun extensionalize_term t =
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  let
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    fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t'
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      | aux j (t as Const (s, Type (_, [Type (_, [_, T']),
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                                        Type (_, [_, res_T])]))
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                    $ t2 $ Abs (var_s, var_T, t')) =
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        if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then
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          let val var_t = Var ((var_s, j), var_T) in
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            Const (s, T' --> T' --> res_T)
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              $ betapply (t2, var_t) $ subst_bound (var_t, t')
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            |> aux (j + 1)
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          end
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        else
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          t
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      | aux _ t = t
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  in aux (maxidx_of_term t + 1) t end
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fun introduce_combinators_in_term ctxt kind t =
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  let val thy = ProofContext.theory_of ctxt in
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    if Meson.is_fol_term thy t then
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      t
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    else
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      let
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        fun aux Ts t =
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          case t of
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            @{const Not} $ t1 => @{const Not} $ aux Ts t1
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          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
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            t0 $ Abs (s, T, aux (T :: Ts) t')
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          | (t0 as Const (@{const_name All}, _)) $ t1 =>
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            aux Ts (t0 $ eta_expand Ts t1 1)
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          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
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            t0 $ Abs (s, T, aux (T :: Ts) t')
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          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
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            aux Ts (t0 $ eta_expand Ts t1 1)
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          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
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          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
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          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
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          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
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              $ t1 $ t2 =>
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            t0 $ aux Ts t1 $ aux Ts t2
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          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
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                   t
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                 else
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                   t |> conceal_bounds Ts
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                     |> Envir.eta_contract
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                     |> cterm_of thy
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                     |> Meson_Clausify.introduce_combinators_in_cterm
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                     |> prop_of |> Logic.dest_equals |> snd
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                     |> reveal_bounds Ts
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        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
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      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
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      handle THM _ =>
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             (* A type variable of sort "{}" will make abstraction fail. *)
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             if kind = Conjecture then HOLogic.false_const
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             else HOLogic.true_const
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  end
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(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
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   same in Sledgehammer to prevent the discovery of unreplable proofs. *)
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fun freeze_term t =
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  let
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    fun aux (t $ u) = aux t $ aux u
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      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
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      | aux (Var ((s, i), T)) =
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        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
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      | aux t = t
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  in t |> exists_subterm is_Var t ? aux end
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(* making fact and conjecture formulas *)
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fun make_formula ctxt eq_as_iff presimp name kind t =
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  let
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    val thy = ProofContext.theory_of ctxt
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    val t = t |> Envir.beta_eta_contract
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              |> transform_elim_term
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              |> Object_Logic.atomize_term thy
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    val need_trueprop = (fastype_of t = HOLogic.boolT)
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    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
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              |> extensionalize_term
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              |> presimp ? presimplify_term thy
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              |> perhaps (try (HOLogic.dest_Trueprop))
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              |> introduce_combinators_in_term ctxt kind
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              |> kind <> Axiom ? freeze_term
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    val (combformula, ctypes_sorts) = combformula_for_prop thy eq_as_iff t []
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  in
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    {name = name, combformula = combformula, kind = kind,
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     ctypes_sorts = ctypes_sorts}
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  end
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fun make_fact ctxt eq_as_iff presimp ((name, _), th) =
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  case make_formula ctxt eq_as_iff presimp name Axiom (prop_of th) of
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    {combformula = AAtom (CombConst (("c_True", _), _, _)), ...} => NONE
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  | formula => SOME formula
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fun make_conjecture ctxt ts =
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  let val last = length ts - 1 in
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    map2 (fn j => make_formula ctxt true true (Int.toString j)
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                               (if j = last then Conjecture else Hypothesis))
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         (0 upto last) ts
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  end
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(** Helper facts **)
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fun count_term (ATerm ((s, _), tms)) =
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  (if is_atp_variable s then I
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   else Symtab.map_entry s (Integer.add 1))
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  #> fold count_term tms
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fun count_formula (AQuant (_, _, phi)) = count_formula phi
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  | count_formula (AConn (_, phis)) = fold count_formula phis
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  | count_formula (AAtom tm) = count_term tm
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val init_counters =
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  metis_helpers |> map fst |> sort_distinct string_ord |> map (rpair 0)
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  |> Symtab.make
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fun get_helper_facts ctxt explicit_forall type_sys formulas =
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  let
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    val no_dangerous_types = types_dangerous_types type_sys
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    val ct = init_counters |> fold count_formula formulas
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    fun is_used s = the (Symtab.lookup ct s) > 0
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    fun dub c needs_full_types (th, j) =
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      ((c ^ "_" ^ string_of_int j ^ (if needs_full_types then "ft" else ""),
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        false), th)
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    fun make_facts eq_as_iff = map_filter (make_fact ctxt eq_as_iff false)
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  in
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    (metis_helpers
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     |> filter (is_used o fst)
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     |> maps (fn (c, (needs_full_types, ths)) =>
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                 if needs_full_types andalso not no_dangerous_types then
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                   []
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                 else
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                   ths ~~ (1 upto length ths)
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                   |> map (dub c needs_full_types)
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                   |> make_facts (not needs_full_types)),
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     if type_sys = Tags false then
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       let
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         fun var s = ATerm (`I s, [])
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         fun tag tm = ATerm (`I type_tag_name, [var "X", tm])
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       in
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         [Fof (helper_prefix ^ ascii_of "ti_ti", Axiom,
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               AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
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               |> explicit_forall ? close_universally)]
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       end
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     else
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       [])
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  end
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fun translate_atp_fact ctxt = `(make_fact ctxt true true)
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fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts =
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  let
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    val thy = ProofContext.theory_of ctxt
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    val fact_ts = map (prop_of o snd o snd) rich_facts
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    val (facts, fact_names) =
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      rich_facts
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      |> map_filter (fn (NONE, _) => NONE
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                      | (SOME fact, (name, _)) => SOME (fact, name))
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      |> ListPair.unzip
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    (* Remove existing facts from the conjecture, as this can dramatically
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       boost an ATP's performance (for some reason). *)
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    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
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   314
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@38282
   315
    val subs = tfree_classes_of_terms [goal_t]
blanchet@40204
   316
    val supers = tvar_classes_of_terms fact_ts
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   317
    val tycons = type_consts_of_terms thy (goal_t :: fact_ts)
blanchet@40204
   318
    (* TFrees in the conjecture; TVars in the facts *)
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   319
    val conjectures = make_conjecture ctxt (hyp_ts @ [concl_t])
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   320
    val (supers', arity_clauses) =
blanchet@41137
   321
      if type_sys = No_Types then ([], [])
blanchet@41137
   322
      else make_arity_clauses thy tycons supers
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   323
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@38282
   324
  in
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   325
    (fact_names |> map single,
blanchet@41140
   326
     (conjectures, facts, class_rel_clauses, arity_clauses))
blanchet@38282
   327
  end
blanchet@38282
   328
blanchet@41138
   329
fun tag_with_type ty t = ATerm (`I type_tag_name, [ty, t])
blanchet@38282
   330
blanchet@38282
   331
fun fo_term_for_combtyp (CombTVar name) = ATerm (name, [])
blanchet@38282
   332
  | fo_term_for_combtyp (CombTFree name) = ATerm (name, [])
blanchet@38282
   333
  | fo_term_for_combtyp (CombType (name, tys)) =
blanchet@38282
   334
    ATerm (name, map fo_term_for_combtyp tys)
blanchet@38282
   335
blanchet@38282
   336
fun fo_literal_for_type_literal (TyLitVar (class, name)) =
blanchet@38282
   337
    (true, ATerm (class, [ATerm (name, [])]))
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   338
  | fo_literal_for_type_literal (TyLitFree (class, name)) =
blanchet@38282
   339
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@38282
   340
blanchet@38282
   341
fun formula_for_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@38282
   342
blanchet@41138
   343
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
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   344
   considered dangerous because their "exhaust" properties can easily lead to
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   345
   unsound ATP proofs. The checks below are an (unsound) approximation of
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   346
   finiteness. *)
blanchet@41138
   347
blanchet@41138
   348
fun is_dtyp_dangerous _ (Datatype_Aux.DtTFree _) = true
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   349
  | is_dtyp_dangerous ctxt (Datatype_Aux.DtType (s, Us)) =
blanchet@41138
   350
    is_type_constr_dangerous ctxt s andalso forall (is_dtyp_dangerous ctxt) Us
blanchet@41138
   351
  | is_dtyp_dangerous _ (Datatype_Aux.DtRec _) = false
blanchet@41138
   352
and is_type_dangerous ctxt (Type (s, Ts)) =
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   353
    is_type_constr_dangerous ctxt s andalso forall (is_type_dangerous ctxt) Ts
blanchet@41140
   354
  | is_type_dangerous _ _ = false
blanchet@41138
   355
and is_type_constr_dangerous ctxt s =
blanchet@41138
   356
  let val thy = ProofContext.theory_of ctxt in
blanchet@41138
   357
    case Datatype_Data.get_info thy s of
blanchet@41138
   358
      SOME {descr, ...} =>
blanchet@41138
   359
      forall (fn (_, (_, _, constrs)) =>
blanchet@41138
   360
                 forall (forall (is_dtyp_dangerous ctxt) o snd) constrs) descr
blanchet@41138
   361
    | NONE =>
blanchet@41138
   362
      case Typedef.get_info ctxt s of
blanchet@41138
   363
        ({rep_type, ...}, _) :: _ => is_type_dangerous ctxt rep_type
blanchet@41138
   364
      | [] => true
blanchet@41138
   365
  end
blanchet@41138
   366
blanchet@41138
   367
fun is_combtyp_dangerous ctxt (CombType ((s, _), tys)) =
blanchet@41138
   368
    (case strip_prefix_and_unascii type_const_prefix s of
blanchet@41138
   369
       SOME s' => forall (is_combtyp_dangerous ctxt) tys andalso
blanchet@41138
   370
                  is_type_constr_dangerous ctxt (invert_const s')
blanchet@41138
   371
     | NONE => false)
blanchet@41138
   372
  | is_combtyp_dangerous _ _ = false
blanchet@41138
   373
blanchet@41138
   374
fun should_tag_with_type ctxt (Tags full_types) ty =
blanchet@41138
   375
    full_types orelse is_combtyp_dangerous ctxt ty
blanchet@41138
   376
  | should_tag_with_type _ _ _ = false
blanchet@41138
   377
blanchet@41140
   378
val fname_table =
blanchet@41140
   379
  [("c_False", (0, ("c_fFalse", @{const_name Metis.fFalse}))),
blanchet@41140
   380
   ("c_True", (0, ("c_fTrue", @{const_name Metis.fTrue}))),
blanchet@41140
   381
   ("c_Not", (1, ("c_fNot", @{const_name Metis.fNot}))),
blanchet@41140
   382
   ("c_conj", (2, ("c_fconj", @{const_name Metis.fconj}))),
blanchet@41140
   383
   ("c_disj", (2, ("c_fdisj", @{const_name Metis.fdisj}))),
blanchet@41140
   384
   ("c_implies", (2, ("c_fimplies", @{const_name Metis.fimplies}))),
blanchet@41140
   385
   ("equal", (2, ("c_fequal", @{const_name Metis.fequal})))]
blanchet@41140
   386
blanchet@41138
   387
fun fo_term_for_combterm ctxt type_sys =
blanchet@38282
   388
  let
blanchet@41138
   389
    val thy = ProofContext.theory_of ctxt
blanchet@38282
   390
    fun aux top_level u =
blanchet@38282
   391
      let
blanchet@38282
   392
        val (head, args) = strip_combterm_comb u
blanchet@38282
   393
        val (x, ty_args) =
blanchet@38282
   394
          case head of
blanchet@38282
   395
            CombConst (name as (s, s'), _, ty_args) =>
blanchet@41140
   396
            (case AList.lookup (op =) fname_table s of
blanchet@41140
   397
               SOME (n, fname) =>
blanchet@41150
   398
               (if top_level andalso length args = n then
blanchet@41150
   399
                  case s of
blanchet@41150
   400
                    "c_False" => ("$false", s')
blanchet@41150
   401
                  | "c_True" => ("$true", s')
blanchet@41150
   402
                  | _ => name
blanchet@41150
   403
                else
blanchet@41150
   404
                  fname, [])
blanchet@41140
   405
             | NONE =>
blanchet@41140
   406
               case strip_prefix_and_unascii const_prefix s of
blanchet@41140
   407
                 NONE => (name, ty_args)
blanchet@41140
   408
               | SOME s'' =>
blanchet@41140
   409
                 let
blanchet@41140
   410
                   val s'' = invert_const s''
blanchet@41140
   411
                   val ty_args =
blanchet@41140
   412
                     if needs_type_args thy type_sys s'' then ty_args else []
blanchet@41150
   413
                  in (name, ty_args) end)
blanchet@38282
   414
          | CombVar (name, _) => (name, [])
blanchet@38282
   415
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@41138
   416
        val t =
blanchet@41138
   417
          ATerm (x, map fo_term_for_combtyp ty_args @ map (aux false) args)
blanchet@41138
   418
        val ty = combtyp_of u
blanchet@38282
   419
    in
blanchet@41138
   420
      t |> (if should_tag_with_type ctxt type_sys ty then
blanchet@41138
   421
              tag_with_type (fo_term_for_combtyp ty)
blanchet@41134
   422
            else
blanchet@41134
   423
              I)
blanchet@38282
   424
    end
blanchet@38282
   425
  in aux true end
blanchet@38282
   426
blanchet@41138
   427
fun formula_for_combformula ctxt type_sys =
blanchet@38282
   428
  let
blanchet@38282
   429
    fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi)
blanchet@38282
   430
      | aux (AConn (c, phis)) = AConn (c, map aux phis)
blanchet@41138
   431
      | aux (AAtom tm) = AAtom (fo_term_for_combterm ctxt type_sys tm)
blanchet@38282
   432
  in aux end
blanchet@38282
   433
blanchet@41138
   434
fun formula_for_fact ctxt type_sys
blanchet@40204
   435
                     ({combformula, ctypes_sorts, ...} : translated_formula) =
blanchet@38282
   436
  mk_ahorn (map (formula_for_fo_literal o fo_literal_for_type_literal)
blanchet@41137
   437
                (atp_type_literals_for_types type_sys ctypes_sorts))
blanchet@41138
   438
           (formula_for_combformula ctxt type_sys combformula)
blanchet@38282
   439
blanchet@41138
   440
fun problem_line_for_fact ctxt prefix type_sys (formula as {name, kind, ...}) =
blanchet@41138
   441
  Fof (prefix ^ ascii_of name, kind, formula_for_fact ctxt type_sys formula)
blanchet@38282
   442
blanchet@38282
   443
fun problem_line_for_class_rel_clause (ClassRelClause {name, subclass,
blanchet@38282
   444
                                                       superclass, ...}) =
blanchet@38282
   445
  let val ty_arg = ATerm (("T", "T"), []) in
blanchet@38282
   446
    Fof (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@38282
   447
         AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@38282
   448
                           AAtom (ATerm (superclass, [ty_arg]))]))
blanchet@38282
   449
  end
blanchet@38282
   450
blanchet@38282
   451
fun fo_literal_for_arity_literal (TConsLit (c, t, args)) =
blanchet@38282
   452
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@38282
   453
  | fo_literal_for_arity_literal (TVarLit (c, sort)) =
blanchet@38282
   454
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@38282
   455
blanchet@38282
   456
fun problem_line_for_arity_clause (ArityClause {name, conclLit, premLits,
blanchet@38282
   457
                                                ...}) =
blanchet@38282
   458
  Fof (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@38282
   459
       mk_ahorn (map (formula_for_fo_literal o apfst not
blanchet@38282
   460
                      o fo_literal_for_arity_literal) premLits)
blanchet@38282
   461
                (formula_for_fo_literal
blanchet@38282
   462
                     (fo_literal_for_arity_literal conclLit)))
blanchet@38282
   463
blanchet@41138
   464
fun problem_line_for_conjecture ctxt type_sys
blanchet@40114
   465
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@38282
   466
  Fof (conjecture_prefix ^ name, kind,
blanchet@41138
   467
       formula_for_combformula ctxt type_sys combformula)
blanchet@38282
   468
blanchet@41137
   469
fun free_type_literals_for_conjecture type_sys
blanchet@40114
   470
        ({ctypes_sorts, ...} : translated_formula) =
blanchet@41137
   471
  ctypes_sorts |> atp_type_literals_for_types type_sys
blanchet@41137
   472
               |> map fo_literal_for_type_literal
blanchet@38282
   473
blanchet@39975
   474
fun problem_line_for_free_type j lit =
blanchet@39975
   475
  Fof (tfree_prefix ^ string_of_int j, Hypothesis, formula_for_fo_literal lit)
blanchet@41137
   476
fun problem_lines_for_free_types type_sys conjectures =
blanchet@38282
   477
  let
blanchet@41137
   478
    val litss = map (free_type_literals_for_conjecture type_sys) conjectures
blanchet@38282
   479
    val lits = fold (union (op =)) litss []
blanchet@39975
   480
  in map2 problem_line_for_free_type (0 upto length lits - 1) lits end
blanchet@38282
   481
blanchet@38282
   482
(** "hBOOL" and "hAPP" **)
blanchet@38282
   483
blanchet@38282
   484
type const_info = {min_arity: int, max_arity: int, sub_level: bool}
blanchet@38282
   485
blanchet@38282
   486
fun consider_term top_level (ATerm ((s, _), ts)) =
blanchet@39452
   487
  (if is_atp_variable s then
blanchet@38282
   488
     I
blanchet@38282
   489
   else
blanchet@38282
   490
     let val n = length ts in
blanchet@38282
   491
       Symtab.map_default
blanchet@38282
   492
           (s, {min_arity = n, max_arity = 0, sub_level = false})
blanchet@38282
   493
           (fn {min_arity, max_arity, sub_level} =>
blanchet@38282
   494
               {min_arity = Int.min (n, min_arity),
blanchet@38282
   495
                max_arity = Int.max (n, max_arity),
blanchet@38282
   496
                sub_level = sub_level orelse not top_level})
blanchet@38282
   497
     end)
blanchet@41138
   498
  #> fold (consider_term (top_level andalso s = type_tag_name)) ts
blanchet@38282
   499
fun consider_formula (AQuant (_, _, phi)) = consider_formula phi
blanchet@38282
   500
  | consider_formula (AConn (_, phis)) = fold consider_formula phis
blanchet@38282
   501
  | consider_formula (AAtom tm) = consider_term true tm
blanchet@38282
   502
blanchet@38282
   503
fun consider_problem_line (Fof (_, _, phi)) = consider_formula phi
blanchet@38282
   504
fun consider_problem problem = fold (fold consider_problem_line o snd) problem
blanchet@38282
   505
blanchet@41140
   506
(* needed for helper facts if the problem otherwise does not involve equality *)
blanchet@41140
   507
val equal_entry = ("equal", {min_arity = 2, max_arity = 2, sub_level = false})
blanchet@41140
   508
blanchet@38282
   509
fun const_table_for_problem explicit_apply problem =
blanchet@41140
   510
  if explicit_apply then
blanchet@41140
   511
    NONE
blanchet@41140
   512
  else
blanchet@41147
   513
    SOME (Symtab.empty |> Symtab.default equal_entry |> consider_problem problem)
blanchet@38282
   514
blanchet@41134
   515
fun min_arity_of thy type_sys NONE s =
blanchet@41138
   516
    (if s = "equal" orelse s = type_tag_name orelse
blanchet@38282
   517
        String.isPrefix type_const_prefix s orelse
blanchet@38282
   518
        String.isPrefix class_prefix s then
blanchet@38282
   519
       16383 (* large number *)
blanchet@38748
   520
     else case strip_prefix_and_unascii const_prefix s of
blanchet@41136
   521
       SOME s' => num_atp_type_args thy type_sys (invert_const s')
blanchet@38282
   522
     | NONE => 0)
blanchet@38282
   523
  | min_arity_of _ _ (SOME the_const_tab) s =
blanchet@38282
   524
    case Symtab.lookup the_const_tab s of
blanchet@38282
   525
      SOME ({min_arity, ...} : const_info) => min_arity
blanchet@38282
   526
    | NONE => 0
blanchet@38282
   527
blanchet@38282
   528
fun full_type_of (ATerm ((s, _), [ty, _])) =
blanchet@41138
   529
    if s = type_tag_name then SOME ty else NONE
blanchet@41138
   530
  | full_type_of _ = NONE
blanchet@38282
   531
blanchet@38282
   532
fun list_hAPP_rev _ t1 [] = t1
blanchet@38282
   533
  | list_hAPP_rev NONE t1 (t2 :: ts2) =
blanchet@38282
   534
    ATerm (`I "hAPP", [list_hAPP_rev NONE t1 ts2, t2])
blanchet@38282
   535
  | list_hAPP_rev (SOME ty) t1 (t2 :: ts2) =
blanchet@41138
   536
    case full_type_of t2 of
blanchet@41138
   537
      SOME ty2 =>
blanchet@41138
   538
      let val ty' = ATerm (`make_fixed_type_const @{type_name fun},
blanchet@41138
   539
                           [ty2, ty]) in
blanchet@41138
   540
        ATerm (`I "hAPP",
blanchet@41138
   541
               [tag_with_type ty' (list_hAPP_rev (SOME ty') t1 ts2), t2])
blanchet@41138
   542
      end
blanchet@41138
   543
    | NONE => list_hAPP_rev NONE t1 (t2 :: ts2)
blanchet@38282
   544
blanchet@41134
   545
fun repair_applications_in_term thy type_sys const_tab =
blanchet@38282
   546
  let
blanchet@38282
   547
    fun aux opt_ty (ATerm (name as (s, _), ts)) =
blanchet@41138
   548
      if s = type_tag_name then
blanchet@38282
   549
        case ts of
blanchet@38282
   550
          [t1, t2] => ATerm (name, [aux NONE t1, aux (SOME t1) t2])
blanchet@41138
   551
        | _ => raise Fail "malformed type tag"
blanchet@38282
   552
      else
blanchet@38282
   553
        let
blanchet@38282
   554
          val ts = map (aux NONE) ts
blanchet@41134
   555
          val (ts1, ts2) = chop (min_arity_of thy type_sys const_tab s) ts
blanchet@38282
   556
        in list_hAPP_rev opt_ty (ATerm (name, ts1)) (rev ts2) end
blanchet@38282
   557
  in aux NONE end
blanchet@38282
   558
blanchet@38282
   559
fun boolify t = ATerm (`I "hBOOL", [t])
blanchet@38282
   560
blanchet@38282
   561
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   562
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   563
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   564
   arguments and is used as a predicate. *)
blanchet@38282
   565
fun is_predicate NONE s =
blanchet@38589
   566
    s = "equal" orelse s = "$false" orelse s = "$true" orelse
blanchet@38589
   567
    String.isPrefix type_const_prefix s orelse String.isPrefix class_prefix s
blanchet@38282
   568
  | is_predicate (SOME the_const_tab) s =
blanchet@38282
   569
    case Symtab.lookup the_const_tab s of
blanchet@38282
   570
      SOME {min_arity, max_arity, sub_level} =>
blanchet@38282
   571
      not sub_level andalso min_arity = max_arity
blanchet@38282
   572
    | NONE => false
blanchet@38282
   573
blanchet@41140
   574
fun repair_predicates_in_term pred_const_tab (t as ATerm ((s, _), ts)) =
blanchet@41138
   575
  if s = type_tag_name then
blanchet@38282
   576
    case ts of
blanchet@38282
   577
      [_, t' as ATerm ((s', _), _)] =>
blanchet@41140
   578
      if is_predicate pred_const_tab s' then t' else boolify t
blanchet@41138
   579
    | _ => raise Fail "malformed type tag"
blanchet@38282
   580
  else
blanchet@41140
   581
    t |> not (is_predicate pred_const_tab s) ? boolify
blanchet@38282
   582
blanchet@41134
   583
fun repair_formula thy explicit_forall type_sys const_tab =
blanchet@38282
   584
  let
blanchet@41140
   585
    val pred_const_tab = case type_sys of Tags _ => NONE | _ => const_tab
blanchet@38282
   586
    fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi)
blanchet@38282
   587
      | aux (AConn (c, phis)) = AConn (c, map aux phis)
blanchet@38282
   588
      | aux (AAtom tm) =
blanchet@41134
   589
        AAtom (tm |> repair_applications_in_term thy type_sys const_tab
blanchet@41140
   590
                  |> repair_predicates_in_term pred_const_tab)
blanchet@38282
   591
  in aux #> explicit_forall ? close_universally end
blanchet@38282
   592
blanchet@41134
   593
fun repair_problem_line thy explicit_forall type_sys const_tab
blanchet@38282
   594
                        (Fof (ident, kind, phi)) =
blanchet@41134
   595
  Fof (ident, kind, repair_formula thy explicit_forall type_sys const_tab phi)
blanchet@41140
   596
fun repair_problem thy = map o apsnd o map ooo repair_problem_line thy
blanchet@38282
   597
blanchet@41140
   598
fun dest_Fof (Fof z) = z
blanchet@38282
   599
blanchet@41157
   600
val factsN = "Relevant facts"
blanchet@41157
   601
val class_relsN = "Class relationships"
blanchet@41157
   602
val aritiesN = "Arity declarations"
blanchet@41157
   603
val helpersN = "Helper facts"
blanchet@41157
   604
val conjsN = "Conjectures"
blanchet@41157
   605
val tfreesN = "Type variables"
blanchet@41157
   606
blanchet@41157
   607
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
   608
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
   609
    if heading = needle then j
blanchet@41157
   610
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
   611
blanchet@41134
   612
fun prepare_atp_problem ctxt readable_names explicit_forall type_sys
blanchet@40204
   613
                        explicit_apply hyp_ts concl_t facts =
blanchet@38282
   614
  let
blanchet@38282
   615
    val thy = ProofContext.theory_of ctxt
blanchet@41140
   616
    val (fact_names, (conjectures, facts, class_rel_clauses, arity_clauses)) =
blanchet@41134
   617
      translate_formulas ctxt type_sys hyp_ts concl_t facts
blanchet@38282
   618
    (* Reordering these might or might not confuse the proof reconstruction
blanchet@38282
   619
       code or the SPASS Flotter hack. *)
blanchet@38282
   620
    val problem =
blanchet@41157
   621
      [(factsN, map (problem_line_for_fact ctxt fact_prefix type_sys) facts),
blanchet@41157
   622
       (class_relsN, map problem_line_for_class_rel_clause class_rel_clauses),
blanchet@41157
   623
       (aritiesN, map problem_line_for_arity_clause arity_clauses),
blanchet@41157
   624
       (helpersN, []),
blanchet@41157
   625
       (conjsN, map (problem_line_for_conjecture ctxt type_sys) conjectures),
blanchet@41157
   626
       (tfreesN, problem_lines_for_free_types type_sys conjectures)]
blanchet@41140
   627
    val const_tab = const_table_for_problem explicit_apply problem
blanchet@41140
   628
    val problem =
blanchet@41140
   629
      problem |> repair_problem thy explicit_forall type_sys const_tab
blanchet@41157
   630
    val helper_lines =
blanchet@41145
   631
      get_helper_facts ctxt explicit_forall type_sys
blanchet@41145
   632
                       (maps (map (#3 o dest_Fof) o snd) problem)
blanchet@41157
   633
      |>> map (problem_line_for_fact ctxt helper_prefix type_sys
blanchet@41157
   634
               #> repair_problem_line thy explicit_forall type_sys const_tab)
blanchet@41157
   635
      |> op @
blanchet@41140
   636
    val (problem, pool) =
blanchet@41157
   637
      problem |> AList.update (op =) (helpersN, helper_lines)
blanchet@41140
   638
              |> nice_atp_problem readable_names
blanchet@38282
   639
  in
blanchet@38282
   640
    (problem,
blanchet@38282
   641
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@41157
   642
     offset_of_heading_in_problem conjsN problem 0,
blanchet@41157
   643
     fact_names |> Vector.fromList)
blanchet@38282
   644
  end
blanchet@38282
   645
blanchet@38282
   646
end;