src/HOL/Tools/Sledgehammer/sledgehammer_fact_preprocessor.ML
author blanchet
Mon Jun 14 10:36:01 2010 +0200 (2010-06-14)
changeset 37410 2bf7e6136047
parent 37403 7e3d7af86215
child 37416 d5ac8280497e
permissions -rw-r--r--
adjusted the polymorphism handling of Skolem constants so that proof reconstruction doesn't fail in "equality_inf"
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(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_fact_preprocessor.ML
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    Author:     Jia Meng, Cambridge University Computer Laboratory
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    Author:     Jasmin Blanchette, TU Muenchen
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Transformation of axiom rules (elim/intro/etc) into CNF forms.
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*)
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signature SLEDGEHAMMER_FACT_PREPROCESSOR =
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sig
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  val chained_prefix: string
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  val trace: bool Unsynchronized.ref
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  val trace_msg: (unit -> string) -> unit
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  val skolem_theory_name: string
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  val skolem_prefix: string
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  val skolem_infix: string
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  val is_skolem_const_name: string -> bool
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  val cnf_axiom: theory -> thm -> thm list
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  val multi_base_blacklist: string list
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  val is_theorem_bad_for_atps: thm -> bool
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  val type_has_topsort: typ -> bool
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  val cnf_rules_pairs:
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    theory -> (string * thm) list -> (thm * (string * int)) list
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  val use_skolem_cache: bool Unsynchronized.ref
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    (* for emergency use where the Skolem cache causes problems *)
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  val strip_subgoal : thm -> int -> (string * typ) list * term list * term
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  val neg_clausify: thm -> thm list
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  val neg_conjecture_clauses:
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    Proof.context -> thm -> int -> thm list list * (string * typ) list
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  val neg_clausify_tac: Proof.context -> int -> tactic
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  val setup: theory -> theory
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end;
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structure Sledgehammer_Fact_Preprocessor : SLEDGEHAMMER_FACT_PREPROCESSOR =
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struct
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open Sledgehammer_FOL_Clause
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(* Used to label theorems chained into the goal. *)
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val chained_prefix = "Sledgehammer.chained_"
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val trace = Unsynchronized.ref false;
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fun trace_msg msg = if !trace then tracing (msg ()) else ();
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val skolem_theory_name = "Sledgehammer.Sko"
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val skolem_prefix = "sko_"
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val skolem_infix = "$"
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fun freeze_thm th = #1 (Drule.legacy_freeze_thaw th);
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val type_has_topsort = Term.exists_subtype
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  (fn TFree (_, []) => true
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    | TVar (_, []) => true
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    | _ => false);
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(**** Transformation of Elimination Rules into First-Order Formulas****)
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val cfalse = cterm_of @{theory HOL} HOLogic.false_const;
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val ctp_false = cterm_of @{theory HOL} (HOLogic.mk_Trueprop HOLogic.false_const);
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(*Converts an elim-rule into an equivalent theorem that does not have the
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  predicate variable.  Leaves other theorems unchanged.  We simply instantiate the
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  conclusion variable to False.*)
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fun transform_elim th =
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  case concl_of th of    (*conclusion variable*)
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       @{const Trueprop} $ (v as Var (_, @{typ bool})) =>
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           Thm.instantiate ([], [(cterm_of @{theory HOL} v, cfalse)]) th
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    | v as Var(_, @{typ prop}) =>
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           Thm.instantiate ([], [(cterm_of @{theory HOL} v, ctp_false)]) th
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    | _ => th;
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(*To enforce single-threading*)
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exception Clausify_failure of theory;
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(**** SKOLEMIZATION BY INFERENCE (lcp) ****)
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(*Keep the full complexity of the original name*)
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fun flatten_name s = space_implode "_X" (Long_Name.explode s);
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fun skolem_name thm_name j var_name =
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  skolem_prefix ^ thm_name ^ "_" ^ Int.toString j ^
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  skolem_infix ^ (if var_name = "" then "g" else flatten_name var_name)
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(* Hack: Could return false positives (e.g., a user happens to declare a
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   constant called "SomeTheory.sko_means_shoe_in_$wedish". *)
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val is_skolem_const_name =
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  Long_Name.base_name
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  #> String.isPrefix skolem_prefix andf String.isSubstring skolem_infix
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fun rhs_extra_types lhsT rhs =
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  let val lhs_vars = Term.add_tfreesT lhsT []
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      fun add_new_TFrees (TFree v) =
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            if member (op =) lhs_vars v then I else insert (op =) (TFree v)
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        | add_new_TFrees _ = I
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      val rhs_consts = fold_aterms (fn Const c => insert (op =) c | _ => I) rhs []
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  in fold (#2 #> Term.fold_atyps add_new_TFrees) rhs_consts [] end;
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fun skolem_type_and_args bound_T body =
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  let
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    val args1 = OldTerm.term_frees body
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    val Ts1 = map type_of args1
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    val Ts2 = rhs_extra_types (Ts1 ---> bound_T) body
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    val args2 = map (fn T => Free (gensym "vsk", T)) Ts2
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  in (Ts2 ---> Ts1 ---> bound_T, args2 @ args1) end
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(* Traverse a theorem, declaring Skolem function definitions. String "s" is the
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   suggested prefix for the Skolem constants. *)
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fun declare_skolem_funs s th thy =
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  let
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    val skolem_count = Unsynchronized.ref 0    (* FIXME ??? *)
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    fun dec_sko (Const (@{const_name Ex}, _) $ (body as Abs (s', T, p)))
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                (axs, thy) =
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        (*Existential: declare a Skolem function, then insert into body and continue*)
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        let
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          val id = skolem_name s (Unsynchronized.inc skolem_count) s'
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          val (cT, args) = skolem_type_and_args T body
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          val rhs = list_abs_free (map dest_Free args,
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                                   HOLogic.choice_const T $ body)
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                  (*Forms a lambda-abstraction over the formal parameters*)
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          val (c, thy) =
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            Sign.declare_const ((Binding.conceal (Binding.name id), cT), NoSyn) thy
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          val cdef = id ^ "_def"
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          val ((_, ax), thy) =
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            Thm.add_def true false (Binding.name cdef, Logic.mk_equals (c, rhs)) thy
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          val ax' = Drule.export_without_context ax
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        in dec_sko (subst_bound (list_comb (c, args), p)) (ax' :: axs, thy) end
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      | dec_sko (Const (@{const_name All}, _) $ (Abs (a, T, p))) thx =
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        (*Universal quant: insert a free variable into body and continue*)
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        let val fname = Name.variant (OldTerm.add_term_names (p, [])) a
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        in dec_sko (subst_bound (Free (fname, T), p)) thx end
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      | dec_sko (@{const "op &"} $ p $ q) thx = dec_sko q (dec_sko p thx)
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      | dec_sko (@{const "op |"} $ p $ q) thx = dec_sko q (dec_sko p thx)
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      | dec_sko (@{const Trueprop} $ p) thx = dec_sko p thx
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      | dec_sko t thx = thx
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  in dec_sko (prop_of th) ([], thy) end
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fun mk_skolem_id t =
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  let val T = fastype_of t in Const (@{const_name skolem_id}, T --> T) $ t end
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(*Traverse a theorem, accumulating Skolem function definitions.*)
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fun assume_skolem_funs inline s th =
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  let
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    val skolem_count = Unsynchronized.ref 0   (* FIXME ??? *)
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    fun dec_sko (Const (@{const_name Ex}, _) $ (body as Abs (s', T, p))) defs =
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        (*Existential: declare a Skolem function, then insert into body and continue*)
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        let
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          val skos = map (#1 o Logic.dest_equals) defs  (*existing sko fns*)
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          val args = subtract (op =) skos (OldTerm.term_frees body) (*the formal parameters*)
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          val Ts = map type_of args
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          val cT = Ts ---> T (* FIXME: use "skolem_type_and_args" *)
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          val id = skolem_name s (Unsynchronized.inc skolem_count) s'
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          val c = Free (id, cT)
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          val rhs = list_abs_free (map dest_Free args,
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                                   HOLogic.choice_const T $ body)
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                    |> inline ? mk_skolem_id
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                (*Forms a lambda-abstraction over the formal parameters*)
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          val def = Logic.mk_equals (c, rhs)
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          val comb = list_comb (if inline then rhs else c, args)
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        in dec_sko (subst_bound (comb, p)) (def :: defs) end
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      | dec_sko (Const (@{const_name All},_) $ Abs (a, T, p)) defs =
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        (*Universal quant: insert a free variable into body and continue*)
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        let val fname = Name.variant (OldTerm.add_term_names (p,[])) a
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        in dec_sko (subst_bound (Free(fname,T), p)) defs end
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      | dec_sko (@{const "op &"} $ p $ q) defs = dec_sko q (dec_sko p defs)
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      | dec_sko (@{const "op |"} $ p $ q) defs = dec_sko q (dec_sko p defs)
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      | dec_sko (@{const Trueprop} $ p) defs = dec_sko p defs
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      | dec_sko t defs = defs (*Do nothing otherwise*)
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  in  dec_sko (prop_of th) []  end;
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(**** REPLACING ABSTRACTIONS BY COMBINATORS ****)
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(*Returns the vars of a theorem*)
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fun vars_of_thm th =
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  map (Thm.cterm_of (theory_of_thm th) o Var) (Thm.fold_terms Term.add_vars th []);
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(*Make a version of fun_cong with a given variable name*)
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local
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    val fun_cong' = fun_cong RS asm_rl; (*renumber f, g to prevent clashes with (a,0)*)
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    val cx = hd (vars_of_thm fun_cong');
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    val ty = typ_of (ctyp_of_term cx);
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    val thy = theory_of_thm fun_cong;
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    fun mkvar a = cterm_of thy (Var((a,0),ty));
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in
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fun xfun_cong x = Thm.instantiate ([], [(cx, mkvar x)]) fun_cong'
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end;
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(*Removes the lambdas from an equation of the form t = (%x. u).  A non-negative n,
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  serves as an upper bound on how many to remove.*)
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fun strip_lambdas 0 th = th
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  | strip_lambdas n th =
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      case prop_of th of
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          _ $ (Const (@{const_name "op ="}, _) $ _ $ Abs (x, _, _)) =>
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              strip_lambdas (n-1) (freeze_thm (th RS xfun_cong x))
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        | _ => th;
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val lambda_free = not o Term.has_abs;
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val [f_B,g_B] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_B}));
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val [g_C,f_C] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_C}));
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val [f_S,g_S] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_S}));
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(*FIXME: requires more use of cterm constructors*)
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fun abstract ct =
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  let
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      val thy = theory_of_cterm ct
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      val Abs(x,_,body) = term_of ct
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      val Type(@{type_name fun}, [xT,bodyT]) = typ_of (ctyp_of_term ct)
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      val cxT = ctyp_of thy xT and cbodyT = ctyp_of thy bodyT
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      fun makeK() = instantiate' [SOME cxT, SOME cbodyT] [SOME (cterm_of thy body)] @{thm abs_K}
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  in
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      case body of
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          Const _ => makeK()
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        | Free _ => makeK()
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        | Var _ => makeK()  (*though Var isn't expected*)
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        | Bound 0 => instantiate' [SOME cxT] [] @{thm abs_I} (*identity: I*)
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        | rator$rand =>
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            if loose_bvar1 (rator,0) then (*C or S*)
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               if loose_bvar1 (rand,0) then (*S*)
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                 let val crator = cterm_of thy (Abs(x,xT,rator))
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                     val crand = cterm_of thy (Abs(x,xT,rand))
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                     val abs_S' = cterm_instantiate [(f_S,crator),(g_S,crand)] @{thm abs_S}
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                     val (_,rhs) = Thm.dest_equals (cprop_of abs_S')
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                 in
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                   Thm.transitive abs_S' (Conv.binop_conv abstract rhs)
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                 end
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               else (*C*)
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                 let val crator = cterm_of thy (Abs(x,xT,rator))
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                     val abs_C' = cterm_instantiate [(f_C,crator),(g_C,cterm_of thy rand)] @{thm abs_C}
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                     val (_,rhs) = Thm.dest_equals (cprop_of abs_C')
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                 in
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                   Thm.transitive abs_C' (Conv.fun_conv (Conv.arg_conv abstract) rhs)
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                 end
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            else if loose_bvar1 (rand,0) then (*B or eta*)
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               if rand = Bound 0 then Thm.eta_conversion ct
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               else (*B*)
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                 let val crand = cterm_of thy (Abs(x,xT,rand))
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                     val crator = cterm_of thy rator
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                     val abs_B' = cterm_instantiate [(f_B,crator),(g_B,crand)] @{thm abs_B}
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                     val (_,rhs) = Thm.dest_equals (cprop_of abs_B')
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                 in Thm.transitive abs_B' (Conv.arg_conv abstract rhs) end
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            else makeK()
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        | _ => raise Fail "abstract: Bad term"
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  end;
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(* Traverse a theorem, remplacing lambda-abstractions with combinators. *)
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fun do_introduce_combinators ct =
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  if lambda_free (term_of ct) then
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    Thm.reflexive ct
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  else case term_of ct of
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    Abs _ =>
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    let
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      val (cv, cta) = Thm.dest_abs NONE ct
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      val (v, _) = dest_Free (term_of cv)
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      val u_th = do_introduce_combinators cta
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      val cu = Thm.rhs_of u_th
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      val comb_eq = abstract (Thm.cabs cv cu)
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    in Thm.transitive (Thm.abstract_rule v cv u_th) comb_eq end
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  | _ $ _ =>
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    let val (ct1, ct2) = Thm.dest_comb ct in
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        Thm.combination (do_introduce_combinators ct1)
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                        (do_introduce_combinators ct2)
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    end
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fun introduce_combinators th =
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  if lambda_free (prop_of th) then
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    th
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  else
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    let
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      val th = Drule.eta_contraction_rule th
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      val eqth = do_introduce_combinators (cprop_of th)
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    in Thm.equal_elim eqth th end
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    handle THM (msg, _, _) =>
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           (warning ("Error in the combinator translation of " ^
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                     Display.string_of_thm_without_context th ^
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                     "\nException message: " ^ msg ^ ".");
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            (* A type variable of sort "{}" will make abstraction fail. *)
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            TrueI)
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(*cterms are used throughout for efficiency*)
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val cTrueprop = Thm.cterm_of @{theory HOL} HOLogic.Trueprop;
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(*cterm version of mk_cTrueprop*)
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fun c_mkTrueprop A = Thm.capply cTrueprop A;
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(*Given an abstraction over n variables, replace the bound variables by free
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  ones. Return the body, along with the list of free variables.*)
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fun c_variant_abs_multi (ct0, vars) =
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      let val (cv,ct) = Thm.dest_abs NONE ct0
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      in  c_variant_abs_multi (ct, cv::vars)  end
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      handle CTERM _ => (ct0, rev vars);
paulson@16009
   293
wenzelm@20461
   294
(*Given the definition of a Skolem function, return a theorem to replace
wenzelm@20461
   295
  an existential formula by a use of that function.
paulson@18141
   296
   Example: "EX x. x : A & x ~: B ==> sko A B : A & sko A B ~: B"  [.] *)
blanchet@37399
   297
fun skolem_theorem_of_def inline def =
blanchet@37399
   298
  let
blanchet@37410
   299
      val (c, rhs) = Thm.dest_equals (cprop_of (freeze_thm def))
blanchet@37410
   300
      val rhs' = rhs |> inline ? (snd o Thm.dest_comb)
blanchet@37410
   301
      val (ch, frees) = c_variant_abs_multi (rhs', [])
blanchet@37410
   302
      val (chilbert, cabs) = ch |> Thm.dest_comb
wenzelm@26627
   303
      val thy = Thm.theory_of_cterm chilbert
wenzelm@26627
   304
      val t = Thm.term_of chilbert
blanchet@37399
   305
      val T =
blanchet@37399
   306
        case t of
blanchet@37410
   307
          Const (@{const_name Eps}, Type (@{type_name fun}, [_, T])) => T
blanchet@37410
   308
        | _ => raise TERM ("skolem_theorem_of_def: expected \"Eps\"", [t])
wenzelm@22596
   309
      val cex = Thm.cterm_of thy (HOLogic.exists_const T)
paulson@16009
   310
      val ex_tm = c_mkTrueprop (Thm.capply cex cabs)
blanchet@37399
   311
      and conc =
blanchet@37399
   312
        Drule.list_comb (if inline then rhs else c, frees)
blanchet@37399
   313
        |> Drule.beta_conv cabs |> c_mkTrueprop
blanchet@37399
   314
      fun tacf [prem] =
blanchet@37410
   315
        (if inline then rewrite_goals_tac @{thms skolem_id_def_raw}
blanchet@37410
   316
         else rewrite_goals_tac [def])
blanchet@37410
   317
        THEN rtac ((prem |> inline ? rewrite_rule @{thms skolem_id_def_raw})
blanchet@37410
   318
                   RS @{thm someI_ex}) 1
wenzelm@23352
   319
  in  Goal.prove_internal [ex_tm] conc tacf
paulson@18141
   320
       |> forall_intr_list frees
wenzelm@26653
   321
       |> Thm.forall_elim_vars 0  (*Introduce Vars, but don't discharge defs.*)
wenzelm@35845
   322
       |> Thm.varifyT_global
paulson@18141
   323
  end;
paulson@16009
   324
paulson@24742
   325
paulson@20863
   326
(*Converts an Isabelle theorem (intro, elim or simp format, even higher-order) into NNF.*)
paulson@24937
   327
fun to_nnf th ctxt0 =
wenzelm@27179
   328
  let val th1 = th |> transform_elim |> zero_var_indexes
wenzelm@32262
   329
      val ((_, [th2]), ctxt) = Variable.import true [th1] ctxt0
wenzelm@32262
   330
      val th3 = th2
wenzelm@35625
   331
        |> Conv.fconv_rule Object_Logic.atomize
wenzelm@32262
   332
        |> Meson.make_nnf ctxt |> strip_lambdas ~1
paulson@24937
   333
  in  (th3, ctxt)  end;
paulson@16009
   334
paulson@18141
   335
(*Generate Skolem functions for a theorem supplied in nnf*)
blanchet@37399
   336
fun skolem_theorems_of_assume inline s th =
blanchet@37399
   337
  map (skolem_theorem_of_def inline o Thm.assume o cterm_of (theory_of_thm th))
blanchet@37399
   338
      (assume_skolem_funs inline s th)
paulson@18141
   339
paulson@25007
   340
blanchet@37349
   341
(*** Blacklisting (more in "Sledgehammer_Fact_Filter") ***)
paulson@25007
   342
blanchet@37348
   343
val max_lambda_nesting = 3
wenzelm@27184
   344
blanchet@37348
   345
fun term_has_too_many_lambdas max (t1 $ t2) =
blanchet@37348
   346
    exists (term_has_too_many_lambdas max) [t1, t2]
blanchet@37348
   347
  | term_has_too_many_lambdas max (Abs (_, _, t)) =
blanchet@37348
   348
    max = 0 orelse term_has_too_many_lambdas (max - 1) t
blanchet@37348
   349
  | term_has_too_many_lambdas _ _ = false
paulson@25007
   350
blanchet@37348
   351
fun is_formula_type T = (T = HOLogic.boolT orelse T = propT)
paulson@25007
   352
blanchet@37348
   353
(* Don't count nested lambdas at the level of formulas, since they are
blanchet@37348
   354
   quantifiers. *)
blanchet@37348
   355
fun formula_has_too_many_lambdas Ts (Abs (_, T, t)) =
blanchet@37348
   356
    formula_has_too_many_lambdas (T :: Ts) t
blanchet@37348
   357
  | formula_has_too_many_lambdas Ts t =
blanchet@37348
   358
    if is_formula_type (fastype_of1 (Ts, t)) then
blanchet@37348
   359
      exists (formula_has_too_many_lambdas Ts) (#2 (strip_comb t))
blanchet@37348
   360
    else
blanchet@37348
   361
      term_has_too_many_lambdas max_lambda_nesting t
paulson@25007
   362
blanchet@37348
   363
(* The max apply depth of any "metis" call in "Metis_Examples" (on 31-10-2007)
blanchet@37348
   364
   was 11. *)
blanchet@37348
   365
val max_apply_depth = 15
wenzelm@27184
   366
blanchet@37348
   367
fun apply_depth (f $ t) = Int.max (apply_depth f, apply_depth t + 1)
blanchet@37348
   368
  | apply_depth (Abs (_, _, t)) = apply_depth t
blanchet@37348
   369
  | apply_depth _ = 0
paulson@25256
   370
blanchet@37348
   371
fun is_formula_too_complex t =
blanchet@37348
   372
  apply_depth t > max_apply_depth orelse Meson.too_many_clauses NONE t orelse
blanchet@37348
   373
  formula_has_too_many_lambdas [] t
wenzelm@27184
   374
paulson@25243
   375
fun is_strange_thm th =
paulson@25243
   376
  case head_of (concl_of th) of
blanchet@35963
   377
      Const (a, _) => (a <> @{const_name Trueprop} andalso
blanchet@35963
   378
                       a <> @{const_name "=="})
paulson@25243
   379
    | _ => false;
paulson@25243
   380
blanchet@37348
   381
fun is_theorem_bad_for_atps thm =
blanchet@37348
   382
  let val t = prop_of thm in
blanchet@37348
   383
    is_formula_too_complex t orelse exists_type type_has_topsort t orelse
blanchet@37348
   384
    is_strange_thm thm
blanchet@37348
   385
  end
paulson@25243
   386
blanchet@35963
   387
(* FIXME: put other record thms here, or declare as "no_atp" *)
paulson@25007
   388
val multi_base_blacklist =
blanchet@35963
   389
  ["defs", "select_defs", "update_defs", "induct", "inducts", "split", "splits",
blanchet@35963
   390
   "split_asm", "cases", "ext_cases"];
paulson@25007
   391
paulson@22731
   392
fun fake_name th =
wenzelm@27865
   393
  if Thm.has_name_hint th then flatten_name (Thm.get_name_hint th)
paulson@22731
   394
  else gensym "unknown_thm_";
paulson@22731
   395
wenzelm@27184
   396
(*Skolemize a named theorem, with Skolem functions as additional premises.*)
blanchet@37399
   397
fun skolemize_theorem s th =
blanchet@37345
   398
  if member (op =) multi_base_blacklist (Long_Name.base_name s) orelse
blanchet@37348
   399
     is_theorem_bad_for_atps th then
blanchet@37345
   400
    []
wenzelm@27184
   401
  else
wenzelm@27184
   402
    let
wenzelm@36603
   403
      val ctxt0 = Variable.global_thm_context th
blanchet@37349
   404
      val (nnfth, ctxt) = to_nnf th ctxt0
blanchet@37399
   405
      val inline = exists_type (exists_subtype (can dest_TFree)) (prop_of nnfth)
blanchet@37399
   406
      val defs = skolem_theorems_of_assume inline s nnfth
blanchet@37349
   407
      val (cnfs, ctxt) = Meson.make_cnf defs nnfth ctxt
blanchet@37349
   408
    in
blanchet@37349
   409
      cnfs |> map introduce_combinators
blanchet@37349
   410
           |> Variable.export ctxt ctxt0
blanchet@37349
   411
           |> Meson.finish_cnf
blanchet@37349
   412
    end
blanchet@37349
   413
    handle THM _ => []
wenzelm@27184
   414
paulson@24742
   415
(*The cache prevents repeated clausification of a theorem, and also repeated declaration of
paulson@24742
   416
  Skolem functions.*)
wenzelm@33522
   417
structure ThmCache = Theory_Data
wenzelm@22846
   418
(
wenzelm@28544
   419
  type T = thm list Thmtab.table * unit Symtab.table;
wenzelm@28544
   420
  val empty = (Thmtab.empty, Symtab.empty);
wenzelm@26618
   421
  val extend = I;
wenzelm@33522
   422
  fun merge ((cache1, seen1), (cache2, seen2)) : T =
wenzelm@27184
   423
    (Thmtab.merge (K true) (cache1, cache2), Symtab.merge (K true) (seen1, seen2));
wenzelm@22846
   424
);
paulson@22516
   425
wenzelm@27184
   426
val lookup_cache = Thmtab.lookup o #1 o ThmCache.get;
wenzelm@27184
   427
val already_seen = Symtab.defined o #2 o ThmCache.get;
wenzelm@20461
   428
wenzelm@27184
   429
val update_cache = ThmCache.map o apfst o Thmtab.update;
wenzelm@27184
   430
fun mark_seen name = ThmCache.map (apsnd (Symtab.update (name, ())));
paulson@25007
   431
blanchet@36228
   432
(* Convert Isabelle theorems into axiom clauses. *)
wenzelm@27179
   433
fun cnf_axiom thy th0 =
wenzelm@27184
   434
  let val th = Thm.transfer thy th0 in
wenzelm@27184
   435
    case lookup_cache thy th of
blanchet@37399
   436
      NONE => map Thm.close_derivation (skolemize_theorem (fake_name th) th)
wenzelm@27184
   437
    | SOME cls => cls
paulson@22516
   438
  end;
paulson@15347
   439
paulson@18141
   440
paulson@22471
   441
(**** Translate a set of theorems into CNF ****)
paulson@15347
   442
paulson@19894
   443
fun pair_name_cls k (n, []) = []
paulson@19894
   444
  | pair_name_cls k (n, cls::clss) = (cls, (n,k)) :: pair_name_cls (k+1) (n, clss)
wenzelm@20461
   445
wenzelm@27179
   446
fun cnf_rules_pairs_aux _ pairs [] = pairs
wenzelm@27179
   447
  | cnf_rules_pairs_aux thy pairs ((name,th)::ths) =
wenzelm@27179
   448
      let val pairs' = (pair_name_cls 0 (name, cnf_axiom thy th)) @ pairs
blanchet@35826
   449
                       handle THM _ => pairs |
blanchet@35865
   450
                              CLAUSE _ => pairs
wenzelm@27179
   451
      in  cnf_rules_pairs_aux thy pairs' ths  end;
wenzelm@20461
   452
paulson@21290
   453
(*The combination of rev and tail recursion preserves the original order*)
wenzelm@27179
   454
fun cnf_rules_pairs thy l = cnf_rules_pairs_aux thy [] (rev l);
mengj@19353
   455
mengj@19196
   456
blanchet@35865
   457
(**** Convert all facts of the theory into FOL or HOL clauses ****)
paulson@15347
   458
wenzelm@28544
   459
local
wenzelm@28544
   460
wenzelm@28544
   461
fun skolem_def (name, th) thy =
wenzelm@36603
   462
  let val ctxt0 = Variable.global_thm_context th in
blanchet@37348
   463
    case try (to_nnf th) ctxt0 of
wenzelm@28544
   464
      NONE => (NONE, thy)
blanchet@37349
   465
    | SOME (nnfth, ctxt) =>
blanchet@37348
   466
      let val (defs, thy') = declare_skolem_funs (flatten_name name) nnfth thy
blanchet@37349
   467
      in (SOME (th, ctxt0, ctxt, nnfth, defs), thy') end
wenzelm@28544
   468
  end;
paulson@24742
   469
blanchet@37349
   470
fun skolem_cnfs (th, ctxt0, ctxt, nnfth, defs) =
wenzelm@28544
   471
  let
blanchet@37399
   472
    val (cnfs, ctxt) =
blanchet@37399
   473
      Meson.make_cnf (map (skolem_theorem_of_def false) defs) nnfth ctxt
wenzelm@28544
   474
    val cnfs' = cnfs
blanchet@37349
   475
      |> map introduce_combinators
blanchet@37349
   476
      |> Variable.export ctxt ctxt0
wenzelm@28544
   477
      |> Meson.finish_cnf
wenzelm@28544
   478
      |> map Thm.close_derivation;
wenzelm@28544
   479
    in (th, cnfs') end;
wenzelm@28544
   480
wenzelm@28544
   481
in
paulson@24742
   482
wenzelm@27184
   483
fun saturate_skolem_cache thy =
wenzelm@28544
   484
  let
wenzelm@33306
   485
    val facts = PureThy.facts_of thy;
wenzelm@33306
   486
    val new_facts = (facts, []) |-> Facts.fold_static (fn (name, ths) =>
wenzelm@33306
   487
      if Facts.is_concealed facts name orelse already_seen thy name then I
wenzelm@33306
   488
      else cons (name, ths));
wenzelm@28544
   489
    val new_thms = (new_facts, []) |-> fold (fn (name, ths) =>
blanchet@37399
   490
      if member (op =) multi_base_blacklist (Long_Name.base_name name) then
blanchet@37399
   491
        I
blanchet@37399
   492
      else
blanchet@37399
   493
        fold_index (fn (i, th) =>
blanchet@37410
   494
          if is_theorem_bad_for_atps th orelse
blanchet@37410
   495
             is_some (lookup_cache thy th) then
blanchet@37399
   496
            I
blanchet@37399
   497
          else
blanchet@37399
   498
            cons (name ^ "_" ^ string_of_int (i + 1), Thm.transfer thy th)) ths)
wenzelm@28544
   499
  in
blanchet@37399
   500
    if null new_facts then
blanchet@37399
   501
      NONE
wenzelm@28544
   502
    else
wenzelm@28544
   503
      let
wenzelm@28544
   504
        val (defs, thy') = thy
wenzelm@28544
   505
          |> fold (mark_seen o #1) new_facts
wenzelm@28544
   506
          |> fold_map skolem_def (sort_distinct (Thm.thm_ord o pairself snd) new_thms)
wenzelm@28544
   507
          |>> map_filter I;
wenzelm@29368
   508
        val cache_entries = Par_List.map skolem_cnfs defs;
wenzelm@28544
   509
      in SOME (fold update_cache cache_entries thy') end
wenzelm@28544
   510
  end;
wenzelm@27184
   511
wenzelm@28544
   512
end;
paulson@24854
   513
blanchet@37348
   514
val use_skolem_cache = Unsynchronized.ref true
wenzelm@27184
   515
wenzelm@27184
   516
fun clause_cache_endtheory thy =
blanchet@37348
   517
  if !use_skolem_cache then saturate_skolem_cache thy else NONE
wenzelm@27184
   518
paulson@20457
   519
paulson@22516
   520
(*The cache can be kept smaller by inspecting the prop of each thm. Can ignore all that are
paulson@22516
   521
  lambda_free, but then the individual theory caches become much bigger.*)
paulson@21071
   522
wenzelm@27179
   523
blanchet@36398
   524
fun strip_subgoal goal i =
blanchet@36398
   525
  let
blanchet@36398
   526
    val (t, frees) = Logic.goal_params (prop_of goal) i
blanchet@36398
   527
    val hyp_ts = t |> Logic.strip_assums_hyp |> map (curry subst_bounds frees)
blanchet@36398
   528
    val concl_t = t |> Logic.strip_assums_concl |> curry subst_bounds frees
blanchet@36478
   529
  in (rev (map dest_Free frees), hyp_ts, concl_t) end
blanchet@36398
   530
paulson@21999
   531
(*** Converting a subgoal into negated conjecture clauses. ***)
paulson@21999
   532
wenzelm@32262
   533
fun neg_skolemize_tac ctxt =
blanchet@37332
   534
  EVERY' [rtac ccontr, Object_Logic.atomize_prems_tac, Meson.skolemize_tac ctxt]
blanchet@36398
   535
blanchet@35869
   536
val neg_clausify =
blanchet@37349
   537
  single
blanchet@37349
   538
  #> Meson.make_clauses_unsorted
blanchet@37349
   539
  #> map introduce_combinators
blanchet@37349
   540
  #> Meson.finish_cnf
paulson@21999
   541
wenzelm@32257
   542
fun neg_conjecture_clauses ctxt st0 n =
wenzelm@32257
   543
  let
blanchet@37332
   544
    (* "Option" is thrown if the assumptions contain schematic variables. *)
blanchet@37332
   545
    val st = Seq.hd (neg_skolemize_tac ctxt n st0) handle Option.Option => st0
blanchet@37332
   546
    val ({params, prems, ...}, _) =
blanchet@37332
   547
      Subgoal.focus (Variable.set_body false ctxt) n st
blanchet@37332
   548
  in (map neg_clausify prems, map (dest_Free o term_of o #2) params) end
paulson@21999
   549
wenzelm@24669
   550
(*Conversion of a subgoal to conjecture clauses. Each clause has
paulson@21999
   551
  leading !!-bound universal variables, to express generality. *)
wenzelm@32257
   552
fun neg_clausify_tac ctxt =
wenzelm@32262
   553
  neg_skolemize_tac ctxt THEN'
wenzelm@32257
   554
  SUBGOAL (fn (prop, i) =>
wenzelm@32257
   555
    let val ts = Logic.strip_assums_hyp prop in
wenzelm@32257
   556
      EVERY'
wenzelm@32283
   557
       [Subgoal.FOCUS
wenzelm@32257
   558
         (fn {prems, ...} =>
wenzelm@32257
   559
           (Method.insert_tac
blanchet@36398
   560
             (map forall_intr_vars (maps neg_clausify prems)) i)) ctxt,
wenzelm@32257
   561
        REPEAT_DETERM_N (length ts) o etac thin_rl] i
paulson@21999
   562
     end);
paulson@21999
   563
wenzelm@27184
   564
wenzelm@27184
   565
(** setup **)
wenzelm@27184
   566
wenzelm@27184
   567
val setup =
blanchet@37348
   568
  perhaps saturate_skolem_cache
blanchet@37348
   569
  #> Theory.at_end clause_cache_endtheory
paulson@18510
   570
wenzelm@20461
   571
end;