(*  Author: Jia Meng, Cambridge University Computer Laboratory

     ID: $Id$

     Copyright 2004 University of Cambridge

 Transformation of axiom rules (elim/intro/etc) into CNF forms.

 *)

 (*unused during debugging*)

 signature RES_AXIOMS =

   sig

   val elimRule_tac : thm -> Tactical.tactic

   val elimR2Fol : thm -> term

   val transform_elim : thm -> thm

   val cnf_axiom : (string * thm) -> thm list

   val cnf_name : string -> thm list

   val meta_cnf_axiom : thm -> thm list

   val claset_rules_of_thy : theory -> (string * thm) list

   val simpset_rules_of_thy : theory -> (string * thm) list

   val claset_rules_of_ctxt: Proof.context -> (string * thm) list

   val simpset_rules_of_ctxt : Proof.context -> (string * thm) list

   val pairname : thm -> (string * thm)

   val skolem_thm : thm -> thm list

   val to_nnf : thm -> thm

   val cnf_rules_pairs : (string * Thm.thm) list -> (Thm.thm * (string * int)) list list;

   val meson_method_setup : theory -> theory

   val setup : theory -> theory

   val atpset_rules_of_thy : theory -> (string * thm) list

   val atpset_rules_of_ctxt : Proof.context -> (string * thm) list

   end;

 structure ResAxioms =

 struct

 (*For running the comparison between combinators and abstractions.

   CANNOT be a ref, as the setting is used while Isabelle is built.

   Currently FALSE, i.e. all the "abstraction" code below is unused, but so far

   it seems to be inferior to combinators...*)

 val abstract_lambdas = false;

 val trace_abs = ref false;

 (* FIXME legacy *)

 fun freeze_thm th = #1 (Drule.freeze_thaw th);

 val lhs_of = #1 o Logic.dest_equals o Thm.prop_of;

 val rhs_of = #2 o Logic.dest_equals o Thm.prop_of;

 (*Store definitions of abstraction functions, ensuring that identical right-hand

   sides are denoted by the same functions and thereby reducing the need for

   extensionality in proofs.

   FIXME!  Store in theory data!!*)

 (*Populate the abstraction cache with common combinators.*)

 fun seed th net =

   let val (_,ct) = Thm.dest_abs NONE (Drule.rhs_of th)

       val t = Logic.legacy_varify (term_of ct)

   in  Net.insert_term eq_thm (t, th) net end;

 val abstraction_cache = ref 

       (seed (thm"ATP_Linkup.I_simp") 

        (seed (thm"ATP_Linkup.B_simp") 

 	(seed (thm"ATP_Linkup.K_simp") Net.empty)));

 (**** Transformation of Elimination Rules into First-Order Formulas****)

 (* a tactic used to prove an elim-rule. *)

 fun elimRule_tac th =

     (resolve_tac [impI,notI] 1) THEN (etac th 1) THEN REPEAT(fast_tac HOL_cs 1);

 fun add_EX tm [] = tm

   | add_EX tm ((x,xtp)::xs) = add_EX (HOLogic.exists_const xtp $ Abs(x,xtp,tm)) xs;

 (*Checks for the premise ~P when the conclusion is P.*)

 fun is_neg (Const("Trueprop",_) $ (Const("Not",_) $ Free(p,_)))

            (Const("Trueprop",_) $ Free(q,_)) = (p = q)

   | is_neg _ _ = false;

 exception ELIMR2FOL;

 (*Handles the case where the dummy "conclusion" variable appears negated in the

   premises, so the final consequent must be kept.*)

 fun strip_concl' prems bvs (Const ("==>",_) $ P $ Q) =

       strip_concl' (HOLogic.dest_Trueprop P :: prems) bvs  Q

   | strip_concl' prems bvs P =

       let val P' = HOLogic.Not $ (HOLogic.dest_Trueprop P)

       in add_EX (foldr1 HOLogic.mk_conj (P'::prems)) bvs end;

 (*Recurrsion over the minor premise of an elimination rule. Final consequent

   is ignored, as it is the dummy "conclusion" variable.*)

 fun strip_concl prems bvs concl (Const ("all", _) $ Abs (x,xtp,body)) =

       strip_concl prems ((x,xtp)::bvs) concl body

   | strip_concl prems bvs concl (Const ("==>",_) $ P $ Q) =

       if (is_neg P concl) then (strip_concl' prems bvs Q)

       else strip_concl (HOLogic.dest_Trueprop P::prems) bvs  concl Q

   | strip_concl prems bvs concl Q =

       if concl aconv Q andalso not (null prems) 

       then add_EX (foldr1 HOLogic.mk_conj prems) bvs

       else raise ELIMR2FOL (*expected conclusion not found!*)

 fun trans_elim (major,[],_) = HOLogic.Not $ major

   | trans_elim (major,minors,concl) =

       let val disjs = foldr1 HOLogic.mk_disj (map (strip_concl [] [] concl) minors)

       in  HOLogic.mk_imp (major, disjs)  end;

 (* convert an elim rule into an equivalent formula, of type term. *)

 fun elimR2Fol elimR =

   let val elimR' = freeze_thm elimR

       val (prems,concl) = (prems_of elimR', concl_of elimR')

       val cv = case concl of    (*conclusion variable*)

                   Const("Trueprop",_) $ (v as Free(_,Type("bool",[]))) => v

                 | v as Free(_, Type("prop",[])) => v

                 | _ => raise ELIMR2FOL

   in case prems of

       [] => raise ELIMR2FOL

     | (Const("Trueprop",_) $ major) :: minors =>

         if member (op aconv) (term_frees major) cv then raise ELIMR2FOL

         else (trans_elim (major, minors, concl) handle TERM _ => raise ELIMR2FOL)

     | _ => raise ELIMR2FOL

   end;

 (* convert an elim-rule into an equivalent theorem that does not have the

    predicate variable.  Leave other theorems unchanged.*)

 fun transform_elim th =

     let val t = HOLogic.mk_Trueprop (elimR2Fol th)

     in 

         if Meson.too_many_clauses t then TrueI

         else Goal.prove_raw [] (cterm_of (sign_of_thm th) t) (fn _ => elimRule_tac th) 

     end

     handle ELIMR2FOL => th (*not an elimination rule*)

          | exn => (warning ("transform_elim failed: " ^ Toplevel.exn_message exn ^

                             " for theorem " ^ Thm.name_of_thm th ^ ": " ^ string_of_thm th); th)

 (**** Transformation of Clasets and Simpsets into First-Order Axioms ****)

 (*Transfer a theorem into theory ATP_Linkup.thy if it is not already

   inside that theory -- because it's needed for Skolemization *)

 (*This will refer to the final version of theory ATP_Linkup.*)

 val recon_thy_ref = Theory.self_ref (the_context ());

 (*If called while ATP_Linkup is being created, it will transfer to the

   current version. If called afterward, it will transfer to the final version.*)

 fun transfer_to_ATP_Linkup th =

     transfer (Theory.deref recon_thy_ref) th handle THM _ => th;

 fun is_taut th =

       case (prop_of th) of

            (Const ("Trueprop", _) $ Const ("True", _)) => true

          | _ => false;

 (* remove tautologous clauses *)

 val rm_redundant_cls = List.filter (not o is_taut);

 (**** SKOLEMIZATION BY INFERENCE (lcp) ****)

 (*Traverse a theorem, declaring Skolem function definitions. String s is the suggested

   prefix for the Skolem constant. Result is a new theory*)

 fun declare_skofuns s th thy =

   let val nref = ref 0

       fun dec_sko (Const ("Ex",_) $ (xtp as Abs(_,T,p))) (thy, axs) =

             (*Existential: declare a Skolem function, then insert into body and continue*)

             let val cname = Name.internal (s ^ "_sko" ^ Int.toString (inc nref))

                 val args = term_frees xtp  (*get the formal parameter list*)

                 val Ts = map type_of args

                 val cT = Ts ---> T

                 val c = Const (Sign.full_name thy cname, cT)

                 val rhs = list_abs_free (map dest_Free args, HOLogic.choice_const T $ xtp)

                         (*Forms a lambda-abstraction over the formal parameters*)

                 val thy' = Sign.add_consts_authentic [(cname, cT, NoSyn)] thy

                            (*Theory is augmented with the constant, then its def*)

                 val cdef = cname ^ "_def"

                 val thy'' = Theory.add_defs_i false false [(cdef, equals cT $ c $ rhs)] thy'

             in dec_sko (subst_bound (list_comb(c,args), p))

                        (thy'', get_axiom thy'' cdef :: axs)

             end

         | dec_sko (Const ("All",_) $ (xtp as Abs(a,T,p))) thx =

             (*Universal quant: insert a free variable into body and continue*)

             let val fname = Name.variant (add_term_names (p,[])) a

             in dec_sko (subst_bound (Free(fname,T), p)) thx end

         | dec_sko (Const ("op &", _) $ p $ q) thx = dec_sko q (dec_sko p thx)

         | dec_sko (Const ("op |", _) $ p $ q) thx = dec_sko q (dec_sko p thx)

         | dec_sko (Const ("Trueprop", _) $ p) thx = dec_sko p thx

         | dec_sko t thx = thx (*Do nothing otherwise*)

   in  dec_sko (prop_of th) (thy,[])  end;

 (*Traverse a theorem, accumulating Skolem function definitions.*)

 fun assume_skofuns th =

   let fun dec_sko (Const ("Ex",_) $ (xtp as Abs(_,T,p))) defs =

             (*Existential: declare a Skolem function, then insert into body and continue*)

             let val skos = map (#1 o Logic.dest_equals) defs  (*existing sko fns*)

                 val args = term_frees xtp \\ skos  (*the formal parameters*)

                 val Ts = map type_of args

                 val cT = Ts ---> T

                 val c = Free (gensym "sko_", cT)

                 val rhs = list_abs_free (map dest_Free args,

                                          HOLogic.choice_const T $ xtp)

                       (*Forms a lambda-abstraction over the formal parameters*)

                 val def = equals cT $ c $ rhs

             in dec_sko (subst_bound (list_comb(c,args), p))

                        (def :: defs)

             end

         | dec_sko (Const ("All",_) $ (xtp as Abs(a,T,p))) defs =

             (*Universal quant: insert a free variable into body and continue*)

             let val fname = Name.variant (add_term_names (p,[])) a

             in dec_sko (subst_bound (Free(fname,T), p)) defs end

         | dec_sko (Const ("op &", _) $ p $ q) defs = dec_sko q (dec_sko p defs)

         | dec_sko (Const ("op |", _) $ p $ q) defs = dec_sko q (dec_sko p defs)

         | dec_sko (Const ("Trueprop", _) $ p) defs = dec_sko p defs

         | dec_sko t defs = defs (*Do nothing otherwise*)

   in  dec_sko (prop_of th) []  end;

 (**** REPLACING ABSTRACTIONS BY FUNCTION DEFINITIONS ****)

 (*Returns the vars of a theorem*)

 fun vars_of_thm th =

   map (Thm.cterm_of (theory_of_thm th) o Var) (Drule.fold_terms Term.add_vars th []);

 (*Make a version of fun_cong with a given variable name*)

 local

     val fun_cong' = fun_cong RS asm_rl; (*renumber f, g to prevent clashes with (a,0)*)

     val cx = hd (vars_of_thm fun_cong');

     val ty = typ_of (ctyp_of_term cx);

     val thy = theory_of_thm fun_cong;

     fun mkvar a = cterm_of thy (Var((a,0),ty));

 in

 fun xfun_cong x = Thm.instantiate ([], [(cx, mkvar x)]) fun_cong'

 end;

 (*Removes the lambdas from an equation of the form t = (%x. u).  A non-negative n,

   serves as an upper bound on how many to remove.*)

 fun strip_lambdas 0 th = th

   | strip_lambdas n th = 

       case prop_of th of

 	  _ $ (Const ("op =", _) $ _ $ Abs (x,_,_)) =>

 	      strip_lambdas (n-1) (freeze_thm (th RS xfun_cong x))

 	| _ => th;

 (*Convert meta- to object-equality. Fails for theorems like split_comp_eq,

   where some types have the empty sort.*)

 fun mk_object_eq th = th RS def_imp_eq

     handle THM _ => error ("Theorem contains empty sort: " ^ string_of_thm th);

 (*Apply a function definition to an argument, beta-reducing the result.*)

 fun beta_comb cf x =

   let val th1 = combination cf (reflexive x)

       val th2 = beta_conversion false (Drule.rhs_of th1)

   in  transitive th1 th2  end;

 (*Apply a function definition to arguments, beta-reducing along the way.*)

 fun list_combination cf [] = cf

   | list_combination cf (x::xs) = list_combination (beta_comb cf x) xs;

 fun list_cabs ([] ,     t) = t

   | list_cabs (v::vars, t) = Thm.cabs v (list_cabs(vars,t));

 fun assert_eta_free ct =

   let val t = term_of ct

   in if (t aconv Envir.eta_contract t) then ()

      else error ("Eta redex in term: " ^ string_of_cterm ct)

   end;

 fun eq_absdef (th1, th2) =

     Context.joinable (theory_of_thm th1, theory_of_thm th2)  andalso

     rhs_of th1 aconv rhs_of th2;

 fun lambda_free (Abs _) = false

   | lambda_free (t $ u) = lambda_free t andalso lambda_free u

   | lambda_free _ = true;

 fun monomorphic t =

   Term.fold_types (Term.fold_atyps (fn TVar _ => K false | _ => I)) t true;

 fun dest_abs_list ct =

   let val (cv,ct') = Thm.dest_abs NONE ct

       val (cvs,cu) = dest_abs_list ct'

   in (cv::cvs, cu) end

   handle CTERM _ => ([],ct);

 fun lambda_list [] u = u

   | lambda_list (v::vs) u = lambda v (lambda_list vs u);

 fun abstract_rule_list [] [] th = th

   | abstract_rule_list (v::vs) (ct::cts) th = abstract_rule v ct (abstract_rule_list vs cts th)

   | abstract_rule_list _ _ th = raise THM ("abstract_rule_list", 0, [th]);

 val Envir.Envir {asol = tenv0, iTs = tyenv0, ...} = Envir.empty 0

 (*Does an existing abstraction definition have an RHS that matches the one we need now?

   thy is the current theory, which must extend that of theorem th.*)

 fun match_rhs thy t th =

   let val _ = if !trace_abs then warning ("match_rhs: " ^ string_of_cterm (cterm_of thy t) ^ 

                                           " against\n" ^ string_of_thm th) else ();

       val (tyenv,tenv) = Pattern.first_order_match thy (rhs_of th, t) (tyenv0,tenv0)

       val term_insts = map Meson.term_pair_of (Vartab.dest tenv)

       val ct_pairs = if subthy (theory_of_thm th, thy) andalso 

                         forall lambda_free (map #2 term_insts) 

                      then map (pairself (cterm_of thy)) term_insts

                      else raise Pattern.MATCH (*Cannot allow lambdas in the instantiation*)

       fun ctyp2 (ixn, (S, T)) = (ctyp_of thy (TVar (ixn, S)), ctyp_of thy T)

       val th' = cterm_instantiate ct_pairs th

   in  SOME (th, instantiate (map ctyp2 (Vartab.dest tyenv), []) th')  end

   handle _ => NONE;

 (*Traverse a theorem, declaring abstraction function definitions. String s is the suggested

   prefix for the constants. Resulting theory is returned in the first theorem. *)

 fun declare_absfuns th =

   let fun abstract thy ct =

         if lambda_free (term_of ct) then (transfer thy (reflexive ct), [])

         else

         case term_of ct of

           Abs _ =>

             let val cname = Name.internal (gensym "abs_");

                 val _ = assert_eta_free ct;

                 val (cvs,cta) = dest_abs_list ct

                 val (vs,Tvs) = ListPair.unzip (map (dest_Free o term_of) cvs)

                 val _ = if !trace_abs then warning ("Nested lambda: " ^ string_of_cterm cta) else ();

                 val (u'_th,defs) = abstract thy cta

                 val _ = if !trace_abs then warning ("Returned " ^ string_of_thm u'_th) else ();

                 val cu' = Drule.rhs_of u'_th

                 val u' = term_of cu'

                 val abs_v_u = lambda_list (map term_of cvs) u'

                 (*get the formal parameters: ALL variables free in the term*)

                 val args = term_frees abs_v_u

                 val _ = if !trace_abs then warning (Int.toString (length args) ^ " arguments") else ();

                 val rhs = list_abs_free (map dest_Free args, abs_v_u)

                       (*Forms a lambda-abstraction over the formal parameters*)

                 val _ = if !trace_abs then warning ("Looking up " ^ string_of_cterm cu') else ();

                 val thy = theory_of_thm u'_th

                 val (ax,ax',thy) =

                  case List.mapPartial (match_rhs thy abs_v_u) 

                          (Net.match_term (!abstraction_cache) u') of

                      (ax,ax')::_ => 

                        (if !trace_abs then warning ("Re-using axiom " ^ string_of_thm ax) else ();

                         (ax,ax',thy))

                    | [] =>

                       let val _ = if !trace_abs then warning "Lookup was empty" else ();

                           val Ts = map type_of args

                           val cT = Ts ---> (Tvs ---> typ_of (ctyp_of_term cu'))

                           val c = Const (Sign.full_name thy cname, cT)

                           val thy = Sign.add_consts_authentic [(cname, cT, NoSyn)] thy

                                      (*Theory is augmented with the constant,

                                        then its definition*)

                           val cdef = cname ^ "_def"

                           val thy = Theory.add_defs_i false false

                                        [(cdef, equals cT $ c $ rhs)] thy

                           val _ = if !trace_abs then (warning ("Definition is " ^ 

                                                       string_of_thm (get_axiom thy cdef))) 

                                   else ();

                           val ax = get_axiom thy cdef |> freeze_thm

                                      |> mk_object_eq |> strip_lambdas (length args)

                                      |> mk_meta_eq |> Meson.generalize

                           val (_,ax') = Option.valOf (match_rhs thy abs_v_u ax)

                           val _ = if !trace_abs then 

                                     (warning ("Declaring: " ^ string_of_thm ax);

                                      warning ("Instance: " ^ string_of_thm ax')) 

                                   else ();

                           val _ = abstraction_cache := Net.insert_term eq_absdef 

                                             ((Logic.varify u'), ax) (!abstraction_cache)

                             handle Net.INSERT =>

                               raise THM ("declare_absfuns: INSERT", 0, [th,u'_th,ax])

                        in  (ax,ax',thy)  end

             in if !trace_abs then warning ("Lookup result: " ^ string_of_thm ax') else ();

                (transitive (abstract_rule_list vs cvs u'_th) (symmetric ax'), ax::defs) end

         | (t1$t2) =>

             let val (ct1,ct2) = Thm.dest_comb ct

                 val (th1,defs1) = abstract thy ct1

                 val (th2,defs2) = abstract (theory_of_thm th1) ct2

             in  (combination th1 th2, defs1@defs2)  end

       val _ = if !trace_abs then warning ("declare_absfuns, Abstracting: " ^ string_of_thm th) else ();

       val (eqth,defs) = abstract (theory_of_thm th) (cprop_of th)

       val ths = equal_elim eqth th :: map (strip_lambdas ~1 o mk_object_eq o freeze_thm) defs

       val _ = if !trace_abs then warning ("declare_absfuns, Result: " ^ string_of_thm (hd ths)) else ();

   in  (theory_of_thm eqth, map Drule.eta_contraction_rule ths)  end;

 fun name_of def = try (#1 o dest_Free o lhs_of) def;

 (*A name is valid provided it isn't the name of a defined abstraction.*)

 fun valid_name defs (Free(x,T)) = not (x mem_string (List.mapPartial name_of defs))

   | valid_name defs _ = false;

 fun assume_absfuns th =

   let val thy = theory_of_thm th

       val cterm = cterm_of thy

       fun abstract ct =

         if lambda_free (term_of ct) then (reflexive ct, [])

         else

         case term_of ct of

           Abs (_,T,u) =>

             let val _ = assert_eta_free ct;

                 val (cvs,cta) = dest_abs_list ct

                 val (vs,Tvs) = ListPair.unzip (map (dest_Free o term_of) cvs)

                 val (u'_th,defs) = abstract cta

                 val cu' = Drule.rhs_of u'_th

                 val u' = term_of cu'

                 (*Could use Thm.cabs instead of lambda to work at level of cterms*)

                 val abs_v_u = lambda_list (map term_of cvs) (term_of cu')

                 (*get the formal parameters: free variables not present in the defs

                   (to avoid taking abstraction function names as parameters) *)

                 val args = filter (valid_name defs) (term_frees abs_v_u)

                 val crhs = list_cabs (map cterm args, cterm abs_v_u)

                       (*Forms a lambda-abstraction over the formal parameters*)

                 val rhs = term_of crhs

                 val (ax,ax') =

                  case List.mapPartial (match_rhs thy abs_v_u) 

                         (Net.match_term (!abstraction_cache) u') of

                      (ax,ax')::_ => 

                        (if !trace_abs then warning ("Re-using axiom " ^ string_of_thm ax) else ();

                         (ax,ax'))

                    | [] =>

                       let val Ts = map type_of args

                           val const_ty = Ts ---> (Tvs ---> typ_of (ctyp_of_term cu'))

                           val c = Free (gensym "abs_", const_ty)

                           val ax = assume (Thm.capply (cterm (equals const_ty $ c)) crhs)

                                      |> mk_object_eq |> strip_lambdas (length args)

                                      |> mk_meta_eq |> Meson.generalize

                           val (_,ax') = Option.valOf (match_rhs thy abs_v_u ax)

                           val _ = abstraction_cache := Net.insert_term eq_absdef (rhs,ax)

                                     (!abstraction_cache)

                             handle Net.INSERT =>

                               raise THM ("assume_absfuns: INSERT", 0, [th,u'_th,ax])

                       in (ax,ax') end

             in if !trace_abs then warning ("Lookup result: " ^ string_of_thm ax') else ();

                (transitive (abstract_rule_list vs cvs u'_th) (symmetric ax'), ax::defs) end

         | (t1$t2) =>

             let val (ct1,ct2) = Thm.dest_comb ct

                 val (t1',defs1) = abstract ct1

                 val (t2',defs2) = abstract ct2

             in  (combination t1' t2', defs1@defs2)  end

       val _ = if !trace_abs then warning ("assume_absfuns, Abstracting: " ^ string_of_thm th) else ();

       val (eqth,defs) = abstract (cprop_of th)

       val ths = equal_elim eqth th :: map (strip_lambdas ~1 o mk_object_eq o freeze_thm) defs

       val _ = if !trace_abs then warning ("assume_absfuns, Result: " ^ string_of_thm (hd ths)) else ();

   in  map Drule.eta_contraction_rule ths  end;

 (*cterms are used throughout for efficiency*)

 val cTrueprop = Thm.cterm_of HOL.thy HOLogic.Trueprop;

 (*cterm version of mk_cTrueprop*)

 fun c_mkTrueprop A = Thm.capply cTrueprop A;

 (*Given an abstraction over n variables, replace the bound variables by free

   ones. Return the body, along with the list of free variables.*)

 fun c_variant_abs_multi (ct0, vars) =

       let val (cv,ct) = Thm.dest_abs NONE ct0

       in  c_variant_abs_multi (ct, cv::vars)  end

       handle CTERM _ => (ct0, rev vars);

 (*Given the definition of a Skolem function, return a theorem to replace

   an existential formula by a use of that function.

    Example: "EX x. x : A & x ~: B ==> sko A B : A & sko A B ~: B"  [.] *)

 fun skolem_of_def def =

   let val (c,rhs) = Drule.dest_equals (cprop_of (freeze_thm def))

       val (ch, frees) = c_variant_abs_multi (rhs, [])

       val (chilbert,cabs) = Thm.dest_comb ch

       val {sign,t, ...} = rep_cterm chilbert

       val T = case t of Const ("Hilbert_Choice.Eps", Type("fun",[_,T])) => T

                       | _ => raise THM ("skolem_of_def: expected Eps", 0, [def])

       val cex = Thm.cterm_of sign (HOLogic.exists_const T)

       val ex_tm = c_mkTrueprop (Thm.capply cex cabs)

       and conc =  c_mkTrueprop (Drule.beta_conv cabs (Drule.list_comb(c,frees)));

       fun tacf [prem] = rewrite_goals_tac [def] THEN rtac (prem RS someI_ex) 1

   in  Goal.prove_raw [ex_tm] conc tacf

        |> forall_intr_list frees

        |> forall_elim_vars 0  (*Introduce Vars, but don't discharge defs.*)

        |> Thm.varifyT

   end;

 (*Converts an Isabelle theorem (intro, elim or simp format, even higher-order) into NNF.*)

 fun to_nnf th =

     th |> transfer_to_ATP_Linkup

        |> transform_elim |> zero_var_indexes |> freeze_thm

        |> ObjectLogic.atomize_thm |> make_nnf |> strip_lambdas ~1;

 (*The cache prevents repeated clausification of a theorem,

   and also repeated declaration of Skolem functions*)

   (* FIXME better use Termtab!? No, we MUST use theory data!!*)

 val clause_cache = ref (Symtab.empty : (thm * thm list) Symtab.table)

 (*Generate Skolem functions for a theorem supplied in nnf*)

 fun skolem_of_nnf th =

   map (skolem_of_def o assume o (cterm_of (theory_of_thm th))) (assume_skofuns th);

 fun assert_lambda_free ths msg = 

   case filter (not o lambda_free o prop_of) ths of

       [] => ()

      | ths' => error (msg ^ "\n" ^ space_implode "\n" (map string_of_thm ths'));

 fun assume_abstract th =

   if lambda_free (prop_of th) then [th]

   else th |> Drule.eta_contraction_rule |> assume_absfuns

           |> tap (fn ths => assert_lambda_free ths "assume_abstract: lambdas")

 (*Replace lambdas by assumed function definitions in the theorems*)

 fun assume_abstract_list ths =

   if abstract_lambdas then List.concat (map assume_abstract ths)

   else map Drule.eta_contraction_rule ths;

 (*Replace lambdas by declared function definitions in the theorems*)

 fun declare_abstract' (thy, []) = (thy, [])

   | declare_abstract' (thy, th::ths) =

       let val (thy', th_defs) =

             if lambda_free (prop_of th) then (thy, [th])

             else

                 th |> zero_var_indexes |> freeze_thm

                    |> Drule.eta_contraction_rule |> transfer thy |> declare_absfuns

           val _ = assert_lambda_free th_defs "declare_abstract: lambdas"

           val (thy'', ths') = declare_abstract' (thy', ths)

       in  (thy'', th_defs @ ths')  end;

 fun declare_abstract (thy, ths) =

   if abstract_lambdas then declare_abstract' (thy, ths)

   else (thy, map Drule.eta_contraction_rule ths);

 (*Skolemize a named theorem, with Skolem functions as additional premises.*)

 fun skolem_thm th =

   let val nnfth = to_nnf th

   in  Meson.make_cnf (skolem_of_nnf nnfth) nnfth

       |> assume_abstract_list |> Meson.finish_cnf |> rm_redundant_cls

   end

   handle THM _ => [];

 (*Keep the full complexity of the original name*)

 fun flatten_name s = space_implode "_X" (NameSpace.unpack s);

 (*Declare Skolem functions for a theorem, supplied in nnf and with its name.

   It returns a modified theory, unless skolemization fails.*)

 fun skolem thy (name,th) =

   let val cname = (case name of "" => gensym "" | s => flatten_name s)

       val _ = Output.debug ("skolemizing " ^ name ^ ": ")

   in Option.map

         (fn nnfth =>

           let val (thy',defs) = declare_skofuns cname nnfth thy

               val cnfs = Meson.make_cnf (map skolem_of_def defs) nnfth

               val (thy'',cnfs') = declare_abstract (thy',cnfs)

           in (thy'', rm_redundant_cls (Meson.finish_cnf cnfs'))

           end)

       (SOME (to_nnf th)  handle THM _ => NONE)

   end;

 (*Populate the clause cache using the supplied theorem. Return the clausal form

   and modified theory.*)

 fun skolem_cache_thm (name,th) thy =

   case Symtab.lookup (!clause_cache) name of

       NONE =>

         (case skolem thy (name, Thm.transfer thy th) of

              NONE => ([th],thy)

            | SOME (thy',cls) => 

                let val cls = map Drule.local_standard cls

                in

                   if null cls then warning ("skolem_cache: empty clause set for " ^ name)

                   else ();

                   change clause_cache (Symtab.update (name, (th, cls))); 

                   (cls,thy')

                end)

     | SOME (th',cls) =>

         if eq_thm(th,th') then (cls,thy)

         else (Output.debug ("skolem_cache: Ignoring variant of theorem " ^ name);

               Output.debug (string_of_thm th);

               Output.debug (string_of_thm th');

               ([th],thy));

 (*Exported function to convert Isabelle theorems into axiom clauses*)

 fun cnf_axiom (name,th) =

  (Output.debug ("cnf_axiom called, theorem name = " ^ name);

   case name of

         "" => skolem_thm th (*no name, so can't cache*)

       | s  => case Symtab.lookup (!clause_cache) s of

                 NONE => 

                   let val cls = map Drule.local_standard (skolem_thm th)

                   in Output.debug "inserted into cache";

                      change clause_cache (Symtab.update (s, (th, cls))); cls 

                   end

               | SOME(th',cls) =>

                   if eq_thm(th,th') then cls

                   else (Output.debug ("cnf_axiom: duplicate or variant of theorem " ^ name);

                         Output.debug (string_of_thm th);

                         Output.debug (string_of_thm th');

                         cls)

  );

 fun pairname th = (Thm.name_of_thm th, th);

 (*Principally for debugging*)

 fun cnf_name s = 

   let val th = thm s

   in cnf_axiom (Thm.name_of_thm th, th) end;

 (**** Extract and Clausify theorems from a theory's claset and simpset ****)

 (*Preserve the name of "th" after the transformation "f"*)

 fun preserve_name f th = Thm.name_thm (Thm.name_of_thm th, f th);

 fun rules_of_claset cs =

   let val {safeIs,safeEs,hazIs,hazEs,...} = rep_cs cs

       val intros = safeIs @ hazIs

       val elims  = map Classical.classical_rule (safeEs @ hazEs)

   in

      Output.debug ("rules_of_claset intros: " ^ Int.toString(length intros) ^

             " elims: " ^ Int.toString(length elims));

      map pairname (intros @ elims)

   end;

 fun rules_of_simpset ss =

   let val ({rules,...}, _) = rep_ss ss

       val simps = Net.entries rules

   in

       Output.debug ("rules_of_simpset: " ^ Int.toString(length simps));

       map (fn r => (#name r, #thm r)) simps

   end;

 fun claset_rules_of_thy thy = rules_of_claset (claset_of thy);

 fun simpset_rules_of_thy thy = rules_of_simpset (simpset_of thy);

 fun atpset_rules_of_thy thy = map pairname (ResAtpset.get_atpset (Context.Theory thy));

 fun claset_rules_of_ctxt ctxt = rules_of_claset (local_claset_of ctxt);

 fun simpset_rules_of_ctxt ctxt = rules_of_simpset (local_simpset_of ctxt);

 fun atpset_rules_of_ctxt ctxt = map pairname (ResAtpset.get_atpset (Context.Proof ctxt));

 (**** Translate a set of classical/simplifier rules into CNF (still as type "thm")  ****)

 (* classical rules: works for both FOL and HOL *)

 fun cnf_rules [] err_list = ([],err_list)

   | cnf_rules ((name,th) :: ths) err_list =

       let val (ts,es) = cnf_rules ths err_list

       in  (cnf_axiom (name,th) :: ts,es) handle  _ => (ts, (th::es))  end;

 fun pair_name_cls k (n, []) = []

   | pair_name_cls k (n, cls::clss) = (cls, (n,k)) :: pair_name_cls (k+1) (n, clss)

 fun cnf_rules_pairs_aux pairs [] = pairs

   | cnf_rules_pairs_aux pairs ((name,th)::ths) =

       let val pairs' = (pair_name_cls 0 (name, cnf_axiom(name,th))) @ pairs

                        handle THM _ => pairs | ResClause.CLAUSE _ => pairs

       in  cnf_rules_pairs_aux pairs' ths  end;

 (*The combination of rev and tail recursion preserves the original order*)

 fun cnf_rules_pairs l = cnf_rules_pairs_aux [] (rev l);

 (**** Convert all theorems of a claset/simpset into clauses (ResClause.clause, or ResHolClause.clause) ****)

 (*Setup function: takes a theory and installs ALL known theorems into the clause cache*)

 fun skolem_cache (name,th) thy =

   let val prop = Thm.prop_of th

   in

       if lambda_free prop 

          (*Monomorphic theorems can be Skolemized on demand,

            but there are problems with re-use of abstraction functions if we don't

            do them now, even for monomorphic theorems.*)

       then thy  

       else #2 (skolem_cache_thm (name,th) thy)

   end;

 (*The cache can be kept smaller by augmenting the condition above with 

     orelse (not abstract_lambdas andalso monomorphic prop).

   However, while this step does not reduce the time needed to build HOL, 

   it doubles the time taken by the first call to the ATP link-up.*)

 fun clause_cache_setup thy = fold skolem_cache (PureThy.all_thms_of thy) thy;

 (*** meson proof methods ***)

 fun skolem_use_cache_thm th =

   case Symtab.lookup (!clause_cache) (Thm.name_of_thm th) of

       NONE => skolem_thm th

     | SOME (th',cls) =>

         if eq_thm(th,th') then cls else skolem_thm th;

 fun cnf_rules_of_ths ths = List.concat (map skolem_use_cache_thm ths);

 fun meson_meth ths ctxt =

   Method.SIMPLE_METHOD' HEADGOAL

     (CHANGED_PROP o Meson.meson_claset_tac (cnf_rules_of_ths ths) HOL_cs);

 val meson_method_setup =

   Method.add_methods

     [("meson", Method.thms_ctxt_args meson_meth,

       "MESON resolution proof procedure")];

 (** Attribute for converting a theorem into clauses **)

 fun meta_cnf_axiom th = map Meson.make_meta_clause (cnf_axiom (pairname th));

 fun clausify_rule (th,i) = List.nth (meta_cnf_axiom th, i)

 val clausify = Attrib.syntax (Scan.lift Args.nat

   >> (fn i => Thm.rule_attribute (fn _ => fn th => clausify_rule (th, i))));

 (** The Skolemization attribute **)

 fun conj2_rule (th1,th2) = conjI OF [th1,th2];

 (*Conjoin a list of theorems to form a single theorem*)

 fun conj_rule []  = TrueI

   | conj_rule ths = foldr1 conj2_rule ths;

 fun skolem_attr (Context.Theory thy, th) =

       let val name = Thm.name_of_thm th

           val (cls, thy') = skolem_cache_thm (name, th) thy

       in (Context.Theory thy', conj_rule cls) end

   | skolem_attr (context, th) = (context, conj_rule (skolem_use_cache_thm th));

 val setup_attrs = Attrib.add_attributes

   [("skolem", Attrib.no_args skolem_attr, "skolemization of a theorem"),

    ("clausify", clausify, "conversion to clauses")];

 val setup = clause_cache_setup #> setup_attrs;

 end;