src/HOL/Tools/Sledgehammer/sledgehammer_hol_clause.ML
author blanchet
Tue Jun 22 13:17:17 2010 +0200 (2010-06-22 ago)
changeset 37496 9ae78e12e126
parent 37479 f6b1ee5b420b
child 37498 b426cbdb5a23
permissions -rw-r--r--
reintroduce new Sledgehammer polymorphic handling code;
this time I tested the proper version of Isabelle
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(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_hol_clause.ML
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    Author:     Jia Meng, NICTA
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    Author:     Jasmin Blanchette, TU Muenchen
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FOL clauses translated from HOL formulae.
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*)
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signature SLEDGEHAMMER_HOL_CLAUSE =
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sig
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  type name = Sledgehammer_FOL_Clause.name
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  type name_pool = Sledgehammer_FOL_Clause.name_pool
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  type kind = Sledgehammer_FOL_Clause.kind
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  type fol_type = Sledgehammer_FOL_Clause.fol_type
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  type classrel_clause = Sledgehammer_FOL_Clause.classrel_clause
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  type arity_clause = Sledgehammer_FOL_Clause.arity_clause
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  type axiom_name = string
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  type polarity = bool
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  type hol_clause_id = int
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  datatype combterm =
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    CombConst of name * fol_type * fol_type list (* Const and Free *) |
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    CombVar of name * fol_type |
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    CombApp of combterm * combterm
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  datatype literal = Literal of polarity * combterm
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  datatype hol_clause =
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    HOLClause of {clause_id: hol_clause_id, axiom_name: axiom_name, th: thm,
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                  kind: kind, literals: literal list, ctypes_sorts: typ list}
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  val type_of_combterm : combterm -> fol_type
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  val strip_combterm_comb : combterm -> combterm * combterm list
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  val literals_of_term : theory -> term -> literal list * typ list
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  val conceal_skolem_somes :
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    int -> (string * term) list -> term -> (string * term) list * term
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  exception TRIVIAL
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  val make_conjecture_clauses : bool -> theory -> thm list -> hol_clause list
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  val make_axiom_clauses : bool -> theory ->
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       (thm * (axiom_name * hol_clause_id)) list -> (axiom_name * hol_clause) list
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  val type_wrapper_name : string
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  val get_helper_clauses :
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    bool -> theory -> bool -> bool -> hol_clause list
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      -> (thm * (axiom_name * hol_clause_id)) list -> hol_clause list
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  val write_tptp_file : bool -> bool -> bool -> Path.T ->
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    hol_clause list * hol_clause list * hol_clause list * hol_clause list *
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    classrel_clause list * arity_clause list -> name_pool option * int
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  val write_dfg_file : bool -> bool -> Path.T ->
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    hol_clause list * hol_clause list * hol_clause list * hol_clause list *
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    classrel_clause list * arity_clause list -> name_pool option * int
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end
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structure Sledgehammer_HOL_Clause : SLEDGEHAMMER_HOL_CLAUSE =
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struct
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open Sledgehammer_Util
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open Sledgehammer_FOL_Clause
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open Sledgehammer_Fact_Preprocessor
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fun min_arity_of const_min_arity c =
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  the_default 0 (Symtab.lookup const_min_arity c)
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(*True if the constant ever appears outside of the top-level position in literals.
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  If false, the constant always receives all of its arguments and is used as a predicate.*)
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fun needs_hBOOL explicit_apply const_needs_hBOOL c =
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  explicit_apply orelse the_default false (Symtab.lookup const_needs_hBOOL c)
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(******************************************************)
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(* data types for typed combinator expressions        *)
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(******************************************************)
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type axiom_name = string;
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type polarity = bool;
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type hol_clause_id = int;
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datatype combterm =
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  CombConst of name * fol_type * fol_type list (* Const and Free *) |
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  CombVar of name * fol_type |
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  CombApp of combterm * combterm
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datatype literal = Literal of polarity * combterm;
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datatype hol_clause =
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  HOLClause of {clause_id: hol_clause_id, axiom_name: axiom_name, th: thm,
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                kind: kind, literals: literal list, ctypes_sorts: typ list};
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(*********************************************************************)
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(* convert a clause with type Term.term to a clause with type clause *)
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(*********************************************************************)
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fun isFalse (Literal (pol, CombConst ((c, _), _, _))) =
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      (pol andalso c = "c_False") orelse (not pol andalso c = "c_True")
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  | isFalse _ = false;
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fun isTrue (Literal (pol, CombConst ((c, _), _, _))) =
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      (pol andalso c = "c_True") orelse
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      (not pol andalso c = "c_False")
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  | isTrue _ = false;
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fun isTaut (HOLClause {literals,...}) = exists isTrue literals;
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fun type_of dfg (Type (a, Ts)) =
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    let val (folTypes,ts) = types_of dfg Ts in
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      (TyConstr (`(make_fixed_type_const dfg) a, folTypes), ts)
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    end
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  | type_of _ (tp as TFree (a, _)) = (TyFree (`make_fixed_type_var a), [tp])
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  | type_of _ (tp as TVar (x, _)) =
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    (TyVar (make_schematic_type_var x, string_of_indexname x), [tp])
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and types_of dfg Ts =
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      let val (folTyps,ts) = ListPair.unzip (map (type_of dfg) Ts)
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      in  (folTyps, union_all ts)  end;
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(* same as above, but no gathering of sort information *)
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fun simp_type_of dfg (Type (a, Ts)) =
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      TyConstr (`(make_fixed_type_const dfg) a, map (simp_type_of dfg) Ts)
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  | simp_type_of _ (TFree (a, _)) = TyFree (`make_fixed_type_var a)
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  | simp_type_of _ (TVar (x, _)) =
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    TyVar (make_schematic_type_var x, string_of_indexname x);
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(* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)
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fun combterm_of dfg thy (Const (c, T)) =
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      let
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        val (tp, ts) = type_of dfg T
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        val tvar_list =
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          (if String.isPrefix skolem_theory_name c then
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             [] |> Term.add_tvarsT T |> map TVar
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           else
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             (c, T) |> Sign.const_typargs thy)
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          |> map (simp_type_of dfg)
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        val c' = CombConst (`(make_fixed_const dfg) c, tp, tvar_list)
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      in  (c',ts)  end
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  | combterm_of dfg _ (Free(v, T)) =
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      let val (tp,ts) = type_of dfg T
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          val v' = CombConst (`make_fixed_var v, tp, [])
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      in  (v',ts)  end
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  | combterm_of dfg _ (Var(v, T)) =
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      let val (tp,ts) = type_of dfg T
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          val v' = CombVar ((make_schematic_var v, string_of_indexname v), tp)
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      in  (v',ts)  end
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  | combterm_of dfg thy (P $ Q) =
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      let val (P',tsP) = combterm_of dfg thy P
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          val (Q',tsQ) = combterm_of dfg thy Q
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      in  (CombApp(P',Q'), union (op =) tsP tsQ)  end
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  | combterm_of _ _ (t as Abs _) = raise CLAUSE ("HOL clause", t);
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fun predicate_of dfg thy ((@{const Not} $ P), polarity) = predicate_of dfg thy (P, not polarity)
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  | predicate_of dfg thy (t,polarity) = (combterm_of dfg thy (Envir.eta_contract t), polarity);
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fun literals_of_term1 dfg thy args (@{const Trueprop} $ P) = literals_of_term1 dfg thy args P
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  | literals_of_term1 dfg thy args (@{const "op |"} $ P $ Q) =
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      literals_of_term1 dfg thy (literals_of_term1 dfg thy args P) Q
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  | literals_of_term1 dfg thy (lits,ts) P =
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      let val ((pred,ts'),pol) = predicate_of dfg thy (P,true)
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      in
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          (Literal(pol,pred)::lits, union (op =) ts ts')
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      end;
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fun literals_of_term_dfg dfg thy P = literals_of_term1 dfg thy ([],[]) P;
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val literals_of_term = literals_of_term_dfg false;
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fun skolem_name i j num_T_args =
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  skolem_prefix ^ (space_implode "_" (map Int.toString [i, j, num_T_args])) ^
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  skolem_infix ^ "g"
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fun conceal_skolem_somes i skolem_somes t =
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  if exists_Const (curry (op =) @{const_name skolem_id} o fst) t then
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    let
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      fun aux skolem_somes
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              (t as (Const (@{const_name skolem_id}, Type (_, [_, T])) $ _)) =
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          let
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            val t = Envir.beta_eta_contract t
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            val (skolem_somes, s) =
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              if i = ~1 then
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                (skolem_somes, @{const_name undefined})
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              else case AList.find (op aconv) skolem_somes t of
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                s :: _ => (skolem_somes, s)
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              | [] =>
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                let
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                  val s = skolem_theory_name ^ "." ^
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                          skolem_name i (length skolem_somes)
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                                        (length (Term.add_tvarsT T []))
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                in ((s, t) :: skolem_somes, s) end
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          in (skolem_somes, Const (s, T)) end
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        | aux skolem_somes (t1 $ t2) =
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          let
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            val (skolem_somes, t1) = aux skolem_somes t1
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            val (skolem_somes, t2) = aux skolem_somes t2
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          in (skolem_somes, t1 $ t2) end
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        | aux skolem_somes (Abs (s, T, t')) =
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          let val (skolem_somes, t') = aux skolem_somes t' in
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            (skolem_somes, Abs (s, T, t'))
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          end
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        | aux skolem_somes t = (skolem_somes, t)
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    in aux skolem_somes t end
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  else
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    (skolem_somes, t)
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(* Trivial problem, which resolution cannot handle (empty clause) *)
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exception TRIVIAL;
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(* making axiom and conjecture clauses *)
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fun make_clause dfg thy (clause_id, axiom_name, kind, th) skolem_somes =
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  let
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    val (skolem_somes, t) =
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      th |> prop_of |> conceal_skolem_somes clause_id skolem_somes
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    val (lits, ctypes_sorts) = literals_of_term_dfg dfg thy t
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  in
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    if forall isFalse lits then
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      raise TRIVIAL
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    else
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      (skolem_somes,
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       HOLClause {clause_id = clause_id, axiom_name = axiom_name, th = th,
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                  kind = kind, literals = lits, ctypes_sorts = ctypes_sorts})
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  end
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fun add_axiom_clause dfg thy (th, (name, id)) (skolem_somes, clss) =
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  let
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    val (skolem_somes, cls) =
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      make_clause dfg thy (id, name, Axiom, th) skolem_somes
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  in (skolem_somes, clss |> not (isTaut cls) ? cons (name, cls)) end
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fun make_axiom_clauses dfg thy clauses =
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  ([], []) |> fold (add_axiom_clause dfg thy) clauses |> snd
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fun make_conjecture_clauses dfg thy =
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  let
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    fun aux _ _ [] = []
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      | aux n skolem_somes (th :: ths) =
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        let
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          val (skolem_somes, cls) =
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            make_clause dfg thy (n, "conjecture", Conjecture, th) skolem_somes
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        in cls :: aux (n + 1) skolem_somes ths end
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  in aux 0 [] end
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(**********************************************************************)
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(* convert clause into ATP specific formats:                          *)
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(* TPTP used by Vampire and E                                         *)
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(* DFG used by SPASS                                                  *)
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(**********************************************************************)
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(*Result of a function type; no need to check that the argument type matches.*)
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fun result_type (TyConstr (_, [_, tp2])) = tp2
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  | result_type _ = raise Fail "non-function type"
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fun type_of_combterm (CombConst (_, tp, _)) = tp
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  | type_of_combterm (CombVar (_, tp)) = tp
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  | type_of_combterm (CombApp (t1, _)) = result_type (type_of_combterm t1);
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(*gets the head of a combinator application, along with the list of arguments*)
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fun strip_combterm_comb u =
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    let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
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        |   stripc  x =  x
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    in  stripc(u,[])  end;
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val type_wrapper_name = "ti"
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fun head_needs_hBOOL explicit_apply const_needs_hBOOL
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                     (CombConst ((c, _), _, _)) =
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    needs_hBOOL explicit_apply const_needs_hBOOL c
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  | head_needs_hBOOL _ _ _ = true
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fun wrap_type full_types (s, ty) pool =
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  if full_types then
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    let val (s', pool) = string_of_fol_type ty pool in
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      (type_wrapper_name ^ paren_pack [s, s'], pool)
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    end
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  else
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    (s, pool)
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fun wrap_type_if full_types explicit_apply cnh (head, s, tp) =
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  if head_needs_hBOOL explicit_apply cnh head then
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    wrap_type full_types (s, tp)
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  else
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    pair s
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fun apply ss = "hAPP" ^ paren_pack ss;
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fun rev_apply (v, []) = v
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  | rev_apply (v, arg::args) = apply [rev_apply (v, args), arg];
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fun string_apply (v, args) = rev_apply (v, rev args);
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(* Apply an operator to the argument strings, using either the "apply" operator
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   or direct function application. *)
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fun string_of_application full_types cma (CombConst ((s, s'), _, tvars), args)
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                          pool =
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    let
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      val s = if s = "equal" then "c_fequal" else s
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      val nargs = min_arity_of cma s
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      val args1 = List.take (args, nargs)
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        handle Subscript =>
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               raise Fail (quote s ^ " has arity " ^ Int.toString nargs ^
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                           " but is applied to " ^ commas (map quote args))
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      val args2 = List.drop (args, nargs)
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      val (targs, pool) = if full_types then ([], pool)
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                          else pool_map string_of_fol_type tvars pool
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      val (s, pool) = nice_name (s, s') pool
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    in (string_apply (s ^ paren_pack (args1 @ targs), args2), pool) end
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  | string_of_application _ _ (CombVar (name, _), args) pool =
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    nice_name name pool |>> (fn s => string_apply (s, args))
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fun string_of_combterm (params as (full_types, explicit_apply, cma, cnh)) t
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                       pool =
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  let
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    val (head, args) = strip_combterm_comb t
blanchet@36170
   306
    val (ss, pool) = pool_map (string_of_combterm params) args pool
blanchet@36170
   307
    val (s, pool) = string_of_application full_types cma (head, ss) pool
blanchet@36235
   308
  in
blanchet@36235
   309
    wrap_type_if full_types explicit_apply cnh (head, s, type_of_combterm t)
blanchet@36235
   310
                 pool
blanchet@36235
   311
  end
mengj@18356
   312
paulson@22064
   313
(*Boolean-valued terms are here converted to literals.*)
blanchet@36170
   314
fun boolify params c =
blanchet@36170
   315
  string_of_combterm params c #>> prefix "hBOOL" o paren_pack o single
paulson@22064
   316
blanchet@36235
   317
fun string_of_predicate (params as (_, explicit_apply, _, cnh)) t =
paulson@22064
   318
  case t of
blanchet@36170
   319
    (CombApp (CombApp (CombConst (("equal", _), _, _), t1), t2)) =>
blanchet@36170
   320
    (* DFG only: new TPTP prefers infix equality *)
blanchet@36170
   321
    pool_map (string_of_combterm params) [t1, t2]
blanchet@36170
   322
    #>> prefix "equal" o paren_pack
blanchet@36170
   323
  | _ =>
blanchet@36170
   324
    case #1 (strip_combterm_comb t) of
blanchet@36170
   325
      CombConst ((s, _), _, _) =>
blanchet@36235
   326
      (if needs_hBOOL explicit_apply cnh s then boolify else string_of_combterm)
blanchet@36235
   327
          params t
blanchet@36170
   328
    | _ => boolify params t
mengj@18356
   329
mengj@17998
   330
blanchet@36170
   331
(*** TPTP format ***)
mengj@19720
   332
blanchet@36170
   333
fun tptp_of_equality params pos (t1, t2) =
blanchet@36170
   334
  pool_map (string_of_combterm params) [t1, t2]
blanchet@36170
   335
  #>> space_implode (if pos then " = " else " != ")
wenzelm@24311
   336
blanchet@36170
   337
fun tptp_literal params
blanchet@36170
   338
        (Literal (pos, CombApp (CombApp (CombConst (("equal", _), _, _), t1),
blanchet@36170
   339
                                         t2))) =
blanchet@36170
   340
    tptp_of_equality params pos (t1, t2)
blanchet@36170
   341
  | tptp_literal params (Literal (pos, pred)) =
blanchet@36170
   342
    string_of_predicate params pred #>> tptp_sign pos
blanchet@36170
   343
 
blanchet@36170
   344
(* Given a clause, returns its literals paired with a list of literals
blanchet@36170
   345
   concerning TFrees; the latter should only occur in conjecture clauses. *)
blanchet@36556
   346
fun tptp_type_literals params pos (HOLClause {literals, ctypes_sorts, ...})
blanchet@36556
   347
                       pool =
blanchet@36556
   348
  let
blanchet@36556
   349
    val (lits, pool) = pool_map (tptp_literal params) literals pool
blanchet@36556
   350
    val (tylits, pool) = pool_map (tptp_of_type_literal pos)
blanchet@36966
   351
                                  (type_literals_for_types ctypes_sorts) pool
blanchet@36556
   352
  in ((lits, tylits), pool) end
wenzelm@24311
   353
blanchet@36170
   354
fun tptp_clause params (cls as HOLClause {axiom_name, clause_id, kind, ...})
blanchet@36170
   355
                pool =
blanchet@36170
   356
let
blanchet@36170
   357
    val ((lits, tylits), pool) =
blanchet@36170
   358
      tptp_type_literals params (kind = Conjecture) cls pool
paulson@24937
   359
  in
blanchet@36170
   360
    ((gen_tptp_cls (clause_id, axiom_name, kind, lits, tylits), tylits), pool)
blanchet@36170
   361
  end
mengj@17998
   362
mengj@17998
   363
blanchet@36170
   364
(*** DFG format ***)
paulson@21561
   365
blanchet@36170
   366
fun dfg_literal params (Literal (pos, pred)) =
blanchet@36170
   367
  string_of_predicate params pred #>> dfg_sign pos
mengj@19720
   368
blanchet@36170
   369
fun dfg_type_literals params pos (HOLClause {literals, ctypes_sorts, ...}) =
blanchet@36170
   370
  pool_map (dfg_literal params) literals
blanchet@36966
   371
  #>> rpair (map (dfg_of_type_literal pos)
blanchet@36966
   372
                 (type_literals_for_types ctypes_sorts))
mengj@19720
   373
blanchet@36170
   374
fun get_uvars (CombConst _) vars pool = (vars, pool)
blanchet@36170
   375
  | get_uvars (CombVar (name, _)) vars pool =
blanchet@36170
   376
    nice_name name pool |>> (fn var => var :: vars)
blanchet@36170
   377
  | get_uvars (CombApp (P, Q)) vars pool =
blanchet@36170
   378
    let val (vars, pool) = get_uvars P vars pool in get_uvars Q vars pool end
mengj@19720
   379
blanchet@36170
   380
fun get_uvars_l (Literal (_, c)) = get_uvars c [];
mengj@19720
   381
blanchet@36170
   382
fun dfg_vars (HOLClause {literals, ...}) =
blanchet@36170
   383
  pool_map get_uvars_l literals #>> union_all
wenzelm@24311
   384
blanchet@36170
   385
fun dfg_clause params (cls as HOLClause {axiom_name, clause_id, kind,
blanchet@36170
   386
                                         ctypes_sorts, ...}) pool =
blanchet@36170
   387
  let
blanchet@36170
   388
    val ((lits, tylits), pool) =
blanchet@36170
   389
      dfg_type_literals params (kind = Conjecture) cls pool
blanchet@36170
   390
    val (vars, pool) = dfg_vars cls pool
blanchet@36170
   391
    val tvars = get_tvar_strs ctypes_sorts
paulson@24937
   392
  in
blanchet@36170
   393
    ((gen_dfg_cls (clause_id, axiom_name, kind, lits, tylits, tvars @ vars),
blanchet@36170
   394
      tylits), pool)
blanchet@36170
   395
  end
paulson@24937
   396
mengj@19720
   397
paulson@22064
   398
(** For DFG format: accumulate function and predicate declarations **)
mengj@19720
   399
blanchet@36218
   400
fun add_types tvars = fold add_fol_type_funcs tvars
mengj@19720
   401
blanchet@36235
   402
fun add_decls (full_types, explicit_apply, cma, cnh)
blanchet@36565
   403
              (CombConst ((c, _), ctp, tvars)) (funcs, preds) =
blanchet@36565
   404
      (if c = "equal" then
blanchet@36565
   405
         (add_types tvars funcs, preds)
blanchet@36565
   406
       else
blanchet@36565
   407
         let val arity = min_arity_of cma c
blanchet@36565
   408
             val ntys = if not full_types then length tvars else 0
blanchet@36565
   409
             val addit = Symtab.update(c, arity + ntys)
blanchet@36565
   410
         in
blanchet@36565
   411
             if needs_hBOOL explicit_apply cnh c then
blanchet@36565
   412
               (add_types tvars (addit funcs), preds)
blanchet@36565
   413
             else
blanchet@36565
   414
               (add_types tvars funcs, addit preds)
blanchet@36565
   415
         end) |>> full_types ? add_fol_type_funcs ctp
blanchet@36218
   416
  | add_decls _ (CombVar (_, ctp)) (funcs, preds) =
blanchet@36218
   417
      (add_fol_type_funcs ctp funcs, preds)
blanchet@36218
   418
  | add_decls params (CombApp (P, Q)) decls =
blanchet@36218
   419
      decls |> add_decls params P |> add_decls params Q
mengj@19720
   420
blanchet@36218
   421
fun add_literal_decls params (Literal (_, c)) = add_decls params c
mengj@19720
   422
blanchet@36218
   423
fun add_clause_decls params (HOLClause {literals, ...}) decls =
blanchet@36218
   424
    fold (add_literal_decls params) literals decls
wenzelm@27187
   425
    handle Symtab.DUP a => error ("function " ^ a ^ " has multiple arities")
mengj@19720
   426
blanchet@37414
   427
fun decls_of_clauses (params as (full_types, explicit_apply, _, _)) clauses
blanchet@37414
   428
                     arity_clauses =
blanchet@37414
   429
  let
blanchet@37414
   430
    val functab =
blanchet@37414
   431
      init_functab
blanchet@37414
   432
      |> fold Symtab.update [(type_wrapper_name, 2), ("hAPP", 2),
blanchet@37414
   433
                             ("tc_bool", 0)]
blanchet@36218
   434
      val predtab = Symtab.empty |> Symtab.update ("hBOOL", 1)
blanchet@36218
   435
      val (functab, predtab) =
blanchet@36218
   436
        (functab, predtab) |> fold (add_clause_decls params) clauses
blanchet@36218
   437
                           |>> fold add_arity_clause_funcs arity_clauses
blanchet@36218
   438
  in (Symtab.dest functab, Symtab.dest predtab) end
mengj@19720
   439
blanchet@36218
   440
fun add_clause_preds (HOLClause {ctypes_sorts, ...}) preds =
blanchet@36218
   441
  fold add_type_sort_preds ctypes_sorts preds
wenzelm@27187
   442
  handle Symtab.DUP a => error ("predicate " ^ a ^ " has multiple arities")
paulson@21398
   443
paulson@21398
   444
(*Higher-order clauses have only the predicates hBOOL and type classes.*)
wenzelm@24311
   445
fun preds_of_clauses clauses clsrel_clauses arity_clauses =
blanchet@36218
   446
  Symtab.empty
blanchet@36218
   447
  |> fold add_clause_preds clauses
blanchet@36218
   448
  |> fold add_arity_clause_preds arity_clauses
blanchet@36218
   449
  |> fold add_classrel_clause_preds clsrel_clauses
blanchet@36218
   450
  |> Symtab.dest
mengj@18440
   451
mengj@18440
   452
(**********************************************************************)
mengj@19198
   453
(* write clauses to files                                             *)
mengj@19198
   454
(**********************************************************************)
mengj@19198
   455
blanchet@36218
   456
fun count_combterm (CombConst ((c, _), _, _)) =
blanchet@36218
   457
    Symtab.map_entry c (Integer.add 1)
blanchet@36218
   458
  | count_combterm (CombVar _) = I
blanchet@36218
   459
  | count_combterm (CombApp (t1, t2)) = count_combterm t1 #> count_combterm t2
paulson@21573
   460
blanchet@36218
   461
fun count_literal (Literal (_, t)) = count_combterm t
paulson@21573
   462
blanchet@36218
   463
fun count_clause (HOLClause {literals, ...}) = fold count_literal literals
paulson@21573
   464
blanchet@37479
   465
val raw_cnf_rules_pairs = map (fn (name, thm) => (thm, (name, 0)))
blanchet@37479
   466
fun cnf_helper_thms thy raw =
blanchet@37479
   467
  map (`Thm.get_name_hint)
blanchet@37479
   468
  #> (if raw then raw_cnf_rules_pairs else cnf_rules_pairs thy)
blanchet@37479
   469
blanchet@37479
   470
val optional_helpers =
blanchet@37479
   471
  [(["c_COMBI", "c_COMBK"], (false, @{thms COMBI_def COMBK_def})),
blanchet@37479
   472
   (["c_COMBB", "c_COMBC"], (false, @{thms COMBB_def COMBC_def})),
blanchet@37479
   473
   (["c_COMBS"], (false, @{thms COMBS_def}))]
blanchet@37479
   474
val optional_typed_helpers =
blanchet@37479
   475
  [(["c_True", "c_False"], (true, @{thms True_or_False})),
blanchet@37479
   476
   (["c_If"], (true, @{thms if_True if_False True_or_False}))]
blanchet@37479
   477
val mandatory_helpers = @{thms fequal_imp_equal equal_imp_fequal}
mengj@20644
   478
blanchet@37479
   479
val init_counters =
blanchet@37479
   480
  Symtab.make (maps (maps (map (rpair 0) o fst))
blanchet@37479
   481
                    [optional_helpers, optional_typed_helpers])
blanchet@37479
   482
blanchet@37479
   483
fun get_helper_clauses dfg thy is_FO full_types conjectures axcls =
blanchet@37479
   484
  let
blanchet@37479
   485
    val axclauses = map snd (make_axiom_clauses dfg thy axcls)
blanchet@37479
   486
    val ct = fold (fold count_clause) [conjectures, axclauses] init_counters
blanchet@37479
   487
    fun is_needed c = the (Symtab.lookup ct c) > 0
blanchet@37479
   488
    val cnfs =
blanchet@37479
   489
      (optional_helpers
blanchet@37479
   490
       |> full_types ? append optional_typed_helpers
blanchet@37479
   491
       |> maps (fn (ss, (raw, ths)) =>
blanchet@37479
   492
                   if exists is_needed ss then cnf_helper_thms thy raw ths
blanchet@37479
   493
                   else []))
blanchet@37479
   494
      @ (if is_FO then [] else cnf_helper_thms thy false mandatory_helpers)
blanchet@37479
   495
  in map snd (make_axiom_clauses dfg thy cnfs) end
mengj@20791
   496
paulson@22064
   497
(*Find the minimal arity of each function mentioned in the term. Also, note which uses
paulson@22064
   498
  are not at top level, to see if hBOOL is needed.*)
immler@30150
   499
fun count_constants_term toplev t (const_min_arity, const_needs_hBOOL) =
blanchet@35865
   500
  let val (head, args) = strip_combterm_comb t
paulson@22064
   501
      val n = length args
blanchet@36233
   502
      val (const_min_arity, const_needs_hBOOL) =
blanchet@36233
   503
        (const_min_arity, const_needs_hBOOL)
blanchet@36233
   504
        |> fold (count_constants_term false) args
paulson@22064
   505
  in
paulson@22064
   506
      case head of
blanchet@36170
   507
          CombConst ((a, _),_,_) => (*predicate or function version of "equal"?*)
wenzelm@24311
   508
            let val a = if a="equal" andalso not toplev then "c_fequal" else a
wenzelm@24311
   509
            in
blanchet@36233
   510
              (const_min_arity |> Symtab.map_default (a, n) (Integer.min n),
blanchet@36233
   511
               const_needs_hBOOL |> not toplev ? Symtab.update (a, true))
wenzelm@24311
   512
            end
wenzelm@32994
   513
        | _ => (const_min_arity, const_needs_hBOOL)
paulson@22064
   514
  end;
paulson@22064
   515
paulson@22064
   516
(*A literal is a top-level term*)
immler@30150
   517
fun count_constants_lit (Literal (_,t)) (const_min_arity, const_needs_hBOOL) =
immler@30150
   518
  count_constants_term true t (const_min_arity, const_needs_hBOOL);
paulson@22064
   519
blanchet@35865
   520
fun count_constants_clause (HOLClause {literals, ...})
blanchet@35865
   521
                           (const_min_arity, const_needs_hBOOL) =
immler@30150
   522
  fold count_constants_lit literals (const_min_arity, const_needs_hBOOL);
paulson@22064
   523
blanchet@36235
   524
fun display_arity explicit_apply const_needs_hBOOL (c,n) =
blanchet@35865
   525
  trace_msg (fn () => "Constant: " ^ c ^
blanchet@35826
   526
                " arity:\t" ^ Int.toString n ^
blanchet@36235
   527
                (if needs_hBOOL explicit_apply const_needs_hBOOL c then
blanchet@36235
   528
                   " needs hBOOL"
blanchet@36235
   529
                 else
blanchet@36235
   530
                   ""))
paulson@22064
   531
blanchet@36235
   532
fun count_constants explicit_apply
blanchet@36235
   533
                    (conjectures, _, extra_clauses, helper_clauses, _, _) =
blanchet@36235
   534
  if not explicit_apply then
immler@30150
   535
     let val (const_min_arity, const_needs_hBOOL) =
immler@30150
   536
          fold count_constants_clause conjectures (Symtab.empty, Symtab.empty)
immler@31865
   537
       |> fold count_constants_clause extra_clauses
immler@30149
   538
       |> fold count_constants_clause helper_clauses
blanchet@36481
   539
     val _ = app (display_arity explicit_apply const_needs_hBOOL)
blanchet@36481
   540
                 (Symtab.dest (const_min_arity))
immler@30150
   541
     in (const_min_arity, const_needs_hBOOL) end
immler@30150
   542
  else (Symtab.empty, Symtab.empty);
paulson@22064
   543
blanchet@36218
   544
fun header () =
blanchet@36218
   545
  "% This file was generated by Isabelle (most likely Sledgehammer)\n" ^
blanchet@36218
   546
  "% " ^ timestamp () ^ "\n"
blanchet@36218
   547
blanchet@35865
   548
(* TPTP format *)
immler@31749
   549
blanchet@36235
   550
fun write_tptp_file readable_names full_types explicit_apply file clauses =
immler@31409
   551
  let
blanchet@36167
   552
    fun section _ [] = []
blanchet@36393
   553
      | section name ss =
blanchet@36393
   554
        "\n% " ^ name ^ plural_s (length ss) ^ " (" ^ Int.toString (length ss) ^
blanchet@36393
   555
        ")\n" :: ss
blanchet@36222
   556
    val pool = empty_name_pool readable_names
immler@31865
   557
    val (conjectures, axclauses, _, helper_clauses,
immler@31865
   558
      classrel_clauses, arity_clauses) = clauses
blanchet@36235
   559
    val (cma, cnh) = count_constants explicit_apply clauses
blanchet@36235
   560
    val params = (full_types, explicit_apply, cma, cnh)
blanchet@36170
   561
    val ((conjecture_clss, tfree_litss), pool) =
blanchet@36170
   562
      pool_map (tptp_clause params) conjectures pool |>> ListPair.unzip
blanchet@36218
   563
    val tfree_clss = map tptp_tfree_clause (fold (union (op =)) tfree_litss [])
blanchet@36170
   564
    val (ax_clss, pool) = pool_map (apfst fst oo tptp_clause params) axclauses
blanchet@36170
   565
                                   pool
blanchet@36170
   566
    val classrel_clss = map tptp_classrel_clause classrel_clauses
blanchet@36170
   567
    val arity_clss = map tptp_arity_clause arity_clauses
blanchet@36170
   568
    val (helper_clss, pool) = pool_map (apfst fst oo tptp_clause params)
blanchet@36170
   569
                                       helper_clauses pool
blanchet@36402
   570
    val conjecture_offset =
blanchet@36402
   571
      length ax_clss + length classrel_clss + length arity_clss
blanchet@36402
   572
      + length helper_clss
blanchet@36393
   573
    val _ =
blanchet@36393
   574
      File.write_list file
blanchet@36393
   575
          (header () ::
blanchet@36393
   576
           section "Relevant fact" ax_clss @
blanchet@36402
   577
           section "Class relationship" classrel_clss @
blanchet@36402
   578
           section "Arity declaration" arity_clss @
blanchet@36393
   579
           section "Helper fact" helper_clss @
blanchet@36393
   580
           section "Conjecture" conjecture_clss @
blanchet@36402
   581
           section "Type variable" tfree_clss)
blanchet@36402
   582
  in (pool, conjecture_offset) end
mengj@19720
   583
blanchet@35865
   584
(* DFG format *)
mengj@19720
   585
blanchet@36966
   586
fun dfg_tfree_predicate s = (first_field "(" s |> the |> fst, 1)
blanchet@36966
   587
blanchet@36235
   588
fun write_dfg_file full_types explicit_apply file clauses =
immler@31409
   589
  let
blanchet@36219
   590
    (* Some of the helper functions below are not name-pool-aware. However,
blanchet@36219
   591
       there's no point in adding name pool support if the DFG format is on its
blanchet@36219
   592
       way out anyway. *)
blanchet@36219
   593
    val pool = NONE
immler@31865
   594
    val (conjectures, axclauses, _, helper_clauses,
immler@31865
   595
      classrel_clauses, arity_clauses) = clauses
blanchet@36235
   596
    val (cma, cnh) = count_constants explicit_apply clauses
blanchet@36235
   597
    val params = (full_types, explicit_apply, cma, cnh)
blanchet@36170
   598
    val ((conjecture_clss, tfree_litss), pool) =
blanchet@36170
   599
      pool_map (dfg_clause params) conjectures pool |>> ListPair.unzip
blanchet@36966
   600
    val tfree_lits = union_all tfree_litss
blanchet@36966
   601
    val problem_name = Path.implode (Path.base file)
blanchet@36170
   602
    val (axstrs, pool) = pool_map (apfst fst oo dfg_clause params) axclauses pool
blanchet@36966
   603
    val tfree_clss = map dfg_tfree_clause tfree_lits
blanchet@36966
   604
    val tfree_preds = map dfg_tfree_predicate tfree_lits
blanchet@36170
   605
    val (helper_clauses_strs, pool) =
blanchet@36170
   606
      pool_map (apfst fst oo dfg_clause params) helper_clauses pool
blanchet@37414
   607
    val (funcs, cl_preds) =
blanchet@37414
   608
      decls_of_clauses params (helper_clauses @ conjectures @ axclauses) arity_clauses
blanchet@36966
   609
    val ty_preds = preds_of_clauses axclauses classrel_clauses arity_clauses
blanchet@36966
   610
    val preds = tfree_preds @ cl_preds @ ty_preds
blanchet@36402
   611
    val conjecture_offset =
blanchet@36402
   612
      length axclauses + length classrel_clauses + length arity_clauses
blanchet@36402
   613
      + length helper_clauses
blanchet@36393
   614
    val _ =
blanchet@36393
   615
      File.write_list file
blanchet@36393
   616
          (header () ::
blanchet@36393
   617
           string_of_start problem_name ::
blanchet@36393
   618
           string_of_descrip problem_name ::
blanchet@36393
   619
           string_of_symbols (string_of_funcs funcs)
blanchet@36966
   620
                             (string_of_preds preds) ::
blanchet@36393
   621
           "list_of_clauses(axioms, cnf).\n" ::
blanchet@36393
   622
           axstrs @
blanchet@36393
   623
           map dfg_classrel_clause classrel_clauses @
blanchet@36393
   624
           map dfg_arity_clause arity_clauses @
blanchet@36393
   625
           helper_clauses_strs @
blanchet@36393
   626
           ["end_of_list.\n\nlist_of_clauses(conjectures, cnf).\n"] @
blanchet@36402
   627
           conjecture_clss @
blanchet@36393
   628
           tfree_clss @
blanchet@36393
   629
           ["end_of_list.\n\n",
blanchet@36393
   630
            "end_problem.\n"])
blanchet@36402
   631
  in (pool, conjecture_offset) end
mengj@19720
   632
wenzelm@33311
   633
end;