author | paulson |
Thu, 15 Sep 2005 11:15:52 +0200 | |
changeset 17404 | d16c3a62c396 |
parent 17279 | 7cd0099ae9bc |
child 17412 | e26cb20ef0cc |
permissions | -rw-r--r-- |
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(* Author: Jia Meng, Cambridge University Computer Laboratory |
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ID: $Id$ |
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Copyright 2004 University of Cambridge |
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Transformation of axiom rules (elim/intro/etc) into CNF forms. |
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*) |
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signature RES_AXIOMS = |
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sig |
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exception ELIMR2FOL of string |
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val tagging_enabled : bool |
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val elimRule_tac : thm -> Tactical.tactic |
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val elimR2Fol : thm -> term |
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val transform_elim : thm -> thm |
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val clausify_axiom_pairs : (string*thm) -> (ResClause.clause*thm) list |
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val cnf_axiom : (string * thm) -> thm list |
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val meta_cnf_axiom : thm -> thm list |
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val rm_Eps : (term * term) list -> thm list -> term list |
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val claset_rules_of_thy : theory -> (string * thm) list |
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val simpset_rules_of_thy : theory -> (string * thm) list |
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val clausify_rules_pairs : (string*thm) list -> thm list -> (ResClause.clause*thm) list list * thm list |
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val clause_setup : (theory -> theory) list |
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val meson_method_setup : (theory -> theory) list |
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end; |
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structure ResAxioms : RES_AXIOMS = |
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struct |
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val tagging_enabled = false (*compile_time option*) |
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(**** Transformation of Elimination Rules into First-Order Formulas****) |
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(* a tactic used to prove an elim-rule. *) |
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fun elimRule_tac th = |
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((rtac impI 1) ORELSE (rtac notI 1)) THEN (etac th 1) THEN |
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REPEAT(fast_tac HOL_cs 1); |
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exception ELIMR2FOL of string; |
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(* functions used to construct a formula *) |
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fun make_disjs [x] = x |
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| make_disjs (x :: xs) = HOLogic.mk_disj(x, make_disjs xs) |
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fun make_conjs [x] = x |
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| make_conjs (x :: xs) = HOLogic.mk_conj(x, make_conjs xs) |
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fun add_EX tm [] = tm |
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| add_EX tm ((x,xtp)::xs) = add_EX (HOLogic.exists_const xtp $ Abs(x,xtp,tm)) xs; |
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fun is_neg (Const("Trueprop",_) $ (Const("Not",_) $ Free(p,_))) (Const("Trueprop",_) $ Free(q,_)) = (p = q) |
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| is_neg _ _ = false; |
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exception STRIP_CONCL; |
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fun strip_concl' prems bvs (Const ("==>",_) $ P $ Q) = |
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let val P' = HOLogic.dest_Trueprop P |
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val prems' = P'::prems |
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in |
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strip_concl' prems' bvs Q |
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end |
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| strip_concl' prems bvs P = |
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let val P' = HOLogic.Not $ (HOLogic.dest_Trueprop P) |
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in |
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add_EX (make_conjs (P'::prems)) bvs |
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end; |
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fun strip_concl prems bvs concl (Const ("all", _) $ Abs (x,xtp,body)) = strip_concl prems ((x,xtp)::bvs) concl body |
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| strip_concl prems bvs concl (Const ("==>",_) $ P $ Q) = |
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if (is_neg P concl) then (strip_concl' prems bvs Q) |
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else |
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(let val P' = HOLogic.dest_Trueprop P |
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val prems' = P'::prems |
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in |
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strip_concl prems' bvs concl Q |
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end) |
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| strip_concl prems bvs concl _ = add_EX (make_conjs prems) bvs; |
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fun trans_elim (main,others,concl) = |
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let val others' = map (strip_concl [] [] concl) others |
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val disjs = make_disjs others' |
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in |
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HOLogic.mk_imp (HOLogic.dest_Trueprop main, disjs) |
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end; |
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(* aux function of elim2Fol, take away predicate variable. *) |
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fun elimR2Fol_aux prems concl = |
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let val nprems = length prems |
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val main = hd prems |
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in |
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if (nprems = 1) then HOLogic.Not $ (HOLogic.dest_Trueprop main) |
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else trans_elim (main, tl prems, concl) |
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end; |
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(* convert an elim rule into an equivalent formula, of type term. *) |
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fun elimR2Fol elimR = |
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let val elimR' = Drule.freeze_all elimR |
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val (prems,concl) = (prems_of elimR', concl_of elimR') |
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in |
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case concl of Const("Trueprop",_) $ Free(_,Type("bool",[])) |
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=> HOLogic.mk_Trueprop (elimR2Fol_aux prems concl) |
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| Free(x,Type("prop",[])) => HOLogic.mk_Trueprop(elimR2Fol_aux prems concl) |
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| _ => raise ELIMR2FOL("Not an elimination rule!") |
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end; |
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(* check if a rule is an elim rule *) |
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fun is_elimR th = |
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case (concl_of th) of (Const ("Trueprop", _) $ Var (idx,_)) => true |
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| Var(indx,Type("prop",[])) => true |
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| _ => false; |
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(* convert an elim-rule into an equivalent theorem that does not have the |
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predicate variable. Leave other theorems unchanged.*) |
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fun transform_elim th = |
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if is_elimR th then |
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let val tm = elimR2Fol th |
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val ctm = cterm_of (sign_of_thm th) tm |
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in |
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prove_goalw_cterm [] ctm (fn prems => [elimRule_tac th]) |
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end |
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else th; |
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(**** Transformation of Clasets and Simpsets into First-Order Axioms ****) |
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(* repeated resolution *) |
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fun repeat_RS thm1 thm2 = |
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let val thm1' = thm1 RS thm2 handle THM _ => thm1 |
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in |
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if eq_thm(thm1,thm1') then thm1' else (repeat_RS thm1' thm2) |
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end; |
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(*Convert a theorem into NNF and also skolemize it. Original version, using |
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Hilbert's epsilon in the resulting clauses.*) |
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fun skolem_axiom th = |
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let val th' = (skolemize o make_nnf o ObjectLogic.atomize_thm o Drule.freeze_all) th |
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in repeat_RS th' someI_ex |
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end; |
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fun cnf_rule th = make_clauses [skolem_axiom (transform_elim th)]; |
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(*Transfer a theorem into theory Reconstruction.thy if it is not already |
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inside that theory -- because it's needed for Skolemization *) |
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(*This will refer to the final version of theory Reconstruction.*) |
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val recon_thy_ref = Theory.self_ref (the_context ()); |
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(*If called while Reconstruction is being created, it will transfer to the |
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current version. If called afterward, it will transfer to the final version.*) |
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fun transfer_to_Reconstruction th = |
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transfer (Theory.deref recon_thy_ref) th handle THM _ => th; |
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fun is_taut th = |
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case (prop_of th) of |
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(Const ("Trueprop", _) $ Const ("True", _)) => true |
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| _ => false; |
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(* remove tautologous clauses *) |
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val rm_redundant_cls = List.filter (not o is_taut); |
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(* transform an Isabelle thm into CNF *) |
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fun cnf_axiom_aux th = |
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map zero_var_indexes |
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(rm_redundant_cls (cnf_rule (transfer_to_Reconstruction th))); |
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(**** SKOLEMIZATION BY INFERENCE (lcp) ****) |
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(*Traverse a term, accumulating Skolem function definitions.*) |
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fun declare_skofuns s t thy = |
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let fun dec_sko (Const ("Ex",_) $ (xtp as Abs(_,T,p))) (n, (thy, axs)) = |
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(*Existential: declare a Skolem function, then insert into body and continue*) |
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let val cname = s ^ "_" ^ Int.toString n |
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val args = term_frees xtp (*get the formal parameter list*) |
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val Ts = map type_of args |
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val cT = Ts ---> T |
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val c = Const (Sign.full_name (Theory.sign_of thy) cname, cT) |
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val rhs = list_abs_free (map dest_Free args, HOLogic.choice_const T $ xtp) |
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(*Forms a lambda-abstraction over the formal parameters*) |
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val def = equals cT $ c $ rhs |
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val thy' = Theory.add_consts_i [(cname, cT, NoSyn)] thy |
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(*Theory is augmented with the constant, then its def*) |
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val cdef = cname ^ "_def" |
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val thy'' = Theory.add_defs_i false [(cdef, def)] thy' |
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in dec_sko (subst_bound (list_comb(c,args), p)) |
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(n+1, (thy'', get_axiom thy'' cdef :: axs)) |
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end |
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| dec_sko (Const ("All",_) $ (xtp as Abs(a,T,p))) (n, thx) = |
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(*Universal quant: insert a free variable into body and continue*) |
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let val fname = variant (add_term_names (p,[])) a |
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in dec_sko (subst_bound (Free(fname,T), p)) (n, thx) end |
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| dec_sko (Const ("op &", _) $ p $ q) nthy = |
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dec_sko q (dec_sko p nthy) |
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| dec_sko (Const ("op |", _) $ p $ q) nthy = |
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dec_sko q (dec_sko p nthy) |
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| dec_sko (Const ("HOL.tag", _) $ p) nthy = |
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dec_sko p nthy |
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| dec_sko (Const ("Trueprop", _) $ p) nthy = |
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dec_sko p nthy |
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| dec_sko t nthx = nthx (*Do nothing otherwise*) |
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in #2 (dec_sko t (1, (thy,[]))) end; |
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(*cterms are used throughout for efficiency*) |
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val cTrueprop = Thm.cterm_of (Theory.sign_of HOL.thy) 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); |
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(*Given the definition of a Skolem function, return a theorem to replace |
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an existential formula by a use of that function.*) |
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fun skolem_of_def def = |
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let val (c,rhs) = Drule.dest_equals (cprop_of (Drule.freeze_all def)) |
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val (ch, frees) = c_variant_abs_multi (rhs, []) |
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val (chil,cabs) = Thm.dest_comb ch |
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val {sign,t, ...} = rep_cterm chil |
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val (Const ("Hilbert_Choice.Eps", Type("fun",[_,T]))) = t |
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val cex = Thm.cterm_of sign (HOLogic.exists_const T) |
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val ex_tm = c_mkTrueprop (Thm.capply cex cabs) |
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and conc = c_mkTrueprop (Drule.beta_conv cabs (Drule.list_comb(c,frees))); |
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in prove_goalw_cterm [def] (Drule.mk_implies (ex_tm, conc)) |
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(fn [prem] => [ rtac (prem RS someI_ex) 1 ]) |
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end; |
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(*Converts an Isabelle theorem (intro, elim or simp format) into nnf.*) |
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fun to_nnf thy th = |
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th |> Thm.transfer thy |
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|> transform_elim |> Drule.freeze_all |
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|> ObjectLogic.atomize_thm |> make_nnf; |
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(*The cache prevents repeated clausification of a theorem, |
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and also repeated declaration of Skolem functions*) (* FIXME better use Termtab!? *) |
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val clause_cache = ref (Symtab.empty : (thm * thm list) Symtab.table) |
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(*Declare Skolem functions for a theorem, supplied in nnf and with its name*) |
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fun skolem thy (name,th) = |
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let val cname = (case name of "" => gensym "sko" | s => Sign.base_name s) |
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val (thy',axs) = declare_skofuns cname (#prop (rep_thm th)) thy |
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in (map skolem_of_def axs, thy') end; |
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(*Populate the clause cache using the supplied theorems*) |
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fun skolemlist [] thy = thy |
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| skolemlist ((name,th)::nths) thy = |
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(case Symtab.curried_lookup (!clause_cache) name of |
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NONE => |
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let val (nnfth,ok) = (to_nnf thy th, true) |
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handle THM _ => (asm_rl, false) |
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in |
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if ok then |
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let val (skoths,thy') = skolem thy (name, nnfth) |
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val cls = Meson.make_cnf skoths nnfth |
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in change clause_cache (Symtab.curried_update (name, (th, cls))); |
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skolemlist nths thy' |
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end |
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else skolemlist nths thy |
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end |
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| SOME _ => skolemlist nths thy) (*FIXME: check for duplicate names?*) |
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(*Exported function to convert Isabelle theorems into axiom clauses*) |
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fun cnf_axiom (name,th) = |
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case name of |
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"" => cnf_axiom_aux th (*no name, so can't cache*) |
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| s => case Symtab.curried_lookup (!clause_cache) s of |
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NONE => |
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let val cls = cnf_axiom_aux th |
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in change clause_cache (Symtab.curried_update (s, (th, cls))); cls end |
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| SOME(th',cls) => |
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if eq_thm(th,th') then cls |
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else (*New theorem stored under the same name? Possible??*) |
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let val cls = cnf_axiom_aux th |
17261 | 291 |
in change clause_cache (Symtab.curried_update (s, (th, cls))); cls end; |
15347 | 292 |
|
15956 | 293 |
fun pairname th = (Thm.name_of_thm th, th); |
294 |
||
295 |
fun meta_cnf_axiom th = |
|
296 |
map Meson.make_meta_clause (cnf_axiom (pairname th)); |
|
15499 | 297 |
|
15347 | 298 |
|
299 |
(* changed: with one extra case added *) |
|
15956 | 300 |
fun univ_vars_of_aux (Const ("Hilbert_Choice.Eps",_) $ Abs(_,_,body)) vars = |
301 |
univ_vars_of_aux body vars |
|
302 |
| univ_vars_of_aux (Const ("Ex",_) $ Abs(_,_,body)) vars = |
|
303 |
univ_vars_of_aux body vars (* EX x. body *) |
|
15347 | 304 |
| univ_vars_of_aux (P $ Q) vars = |
15956 | 305 |
univ_vars_of_aux Q (univ_vars_of_aux P vars) |
15347 | 306 |
| univ_vars_of_aux (t as Var(_,_)) vars = |
15956 | 307 |
if (t mem vars) then vars else (t::vars) |
15347 | 308 |
| univ_vars_of_aux _ vars = vars; |
309 |
||
310 |
fun univ_vars_of t = univ_vars_of_aux t []; |
|
311 |
||
312 |
||
313 |
fun get_new_skolem epss (t as (Const ("Hilbert_Choice.Eps",_) $ Abs(_,tp,_))) = |
|
314 |
let val all_vars = univ_vars_of t |
|
315 |
val sk_term = ResSkolemFunction.gen_skolem all_vars tp |
|
316 |
in |
|
317 |
(sk_term,(t,sk_term)::epss) |
|
318 |
end; |
|
319 |
||
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320 |
(*FIXME: use a-list lookup!!*) |
15531 | 321 |
fun sk_lookup [] t = NONE |
322 |
| sk_lookup ((tm,sk_tm)::tms) t = if (t = tm) then SOME (sk_tm) else (sk_lookup tms t); |
|
15347 | 323 |
|
15390 | 324 |
(* get the proper skolem term to replace epsilon term *) |
15347 | 325 |
fun get_skolem epss t = |
15956 | 326 |
case (sk_lookup epss t) of NONE => get_new_skolem epss t |
327 |
| SOME sk => (sk,epss); |
|
15347 | 328 |
|
16009 | 329 |
fun rm_Eps_cls_aux epss (t as (Const ("Hilbert_Choice.Eps",_) $ Abs(_,_,_))) = |
330 |
get_skolem epss t |
|
15347 | 331 |
| rm_Eps_cls_aux epss (P $ Q) = |
16009 | 332 |
let val (P',epss') = rm_Eps_cls_aux epss P |
333 |
val (Q',epss'') = rm_Eps_cls_aux epss' Q |
|
334 |
in (P' $ Q',epss'') end |
|
15347 | 335 |
| rm_Eps_cls_aux epss t = (t,epss); |
336 |
||
16009 | 337 |
fun rm_Eps_cls epss th = rm_Eps_cls_aux epss (prop_of th); |
15347 | 338 |
|
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339 |
(* replace the epsilon terms in a formula by skolem terms. *) |
15347 | 340 |
fun rm_Eps _ [] = [] |
16009 | 341 |
| rm_Eps epss (th::thms) = |
342 |
let val (th',epss') = rm_Eps_cls epss th |
|
343 |
in th' :: (rm_Eps epss' thms) end; |
|
15347 | 344 |
|
345 |
||
346 |
||
15872 | 347 |
(**** Extract and Clausify theorems from a theory's claset and simpset ****) |
15347 | 348 |
|
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349 |
(*Preserve the name of "th" after the transformation "f"*) |
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350 |
fun preserve_name f th = Thm.name_thm (Thm.name_of_thm th, f th); |
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351 |
|
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352 |
(*Tags identify the major premise or conclusion, as hints to resolution provers. |
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353 |
However, they don't appear to help in recent tests, and they complicate the code.*) |
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|
354 |
val tagI = thm "tagI"; |
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355 |
val tagD = thm "tagD"; |
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356 |
|
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357 |
val tag_intro = preserve_name (fn th => th RS tagI); |
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358 |
val tag_elim = preserve_name (fn th => tagD RS th); |
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359 |
|
15347 | 360 |
fun claset_rules_of_thy thy = |
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361 |
let val cs = rep_cs (claset_of thy) |
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362 |
val intros = (#safeIs cs) @ (#hazIs cs) |
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|
363 |
val elims = (#safeEs cs) @ (#hazEs cs) |
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|
364 |
in |
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365 |
if tagging_enabled |
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366 |
then map pairname (map tag_intro intros @ map tag_elim elims) |
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367 |
else map pairname (intros @ elims) |
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368 |
end; |
15347 | 369 |
|
370 |
fun simpset_rules_of_thy thy = |
|
16800 | 371 |
let val rules = #rules (fst (rep_ss (simpset_of thy))) |
372 |
in map (fn r => (#name r, #thm r)) (Net.entries rules) end; |
|
15347 | 373 |
|
374 |
||
15872 | 375 |
(**** Translate a set of classical/simplifier rules into CNF (still as type "thm") ****) |
15347 | 376 |
|
377 |
(* classical rules *) |
|
15872 | 378 |
fun cnf_rules [] err_list = ([],err_list) |
16009 | 379 |
| cnf_rules ((name,th) :: thms) err_list = |
15872 | 380 |
let val (ts,es) = cnf_rules thms err_list |
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381 |
in (cnf_axiom (name,th) :: ts,es) handle _ => (ts, (th::es)) end; |
15347 | 382 |
|
383 |
||
15872 | 384 |
(**** Convert all theorems of a claset/simpset into clauses (ResClause.clause) ****) |
15347 | 385 |
|
17404
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386 |
fun addclause (c,th) l = |
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387 |
if ResClause.isTaut c then l else (c,th) :: l; |
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|
388 |
|
16156
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Fixed array containing clasimpset rules. Added flags to turn on and off reconstruction and full spass
quigley
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|
389 |
(* outputs a list of (clause,thm) pairs *) |
16039
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Moved some of the clausify functions from ATP/res_clasimpset.ML to res_axioms.ML.
quigley
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|
390 |
fun clausify_axiom_pairs (thm_name,thm) = |
17404
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|
391 |
let val isa_clauses = cnf_axiom (thm_name,thm) |
16039
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Moved some of the clausify functions from ATP/res_clasimpset.ML to res_axioms.ML.
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|
392 |
val isa_clauses' = rm_Eps [] isa_clauses |
dfe264950511
Moved some of the clausify functions from ATP/res_clasimpset.ML to res_axioms.ML.
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|
393 |
val clauses_n = length isa_clauses |
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|
394 |
fun make_axiom_clauses _ [] []= [] |
16897 | 395 |
| make_axiom_clauses i (cls::clss) (cls'::clss') = |
17404
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|
396 |
addclause (ResClause.make_axiom_clause cls (thm_name,i), cls') |
d16c3a62c396
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|
397 |
(make_axiom_clauses (i+1) clss clss') |
15347 | 398 |
in |
16039
dfe264950511
Moved some of the clausify functions from ATP/res_clasimpset.ML to res_axioms.ML.
quigley
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changeset
|
399 |
make_axiom_clauses 0 isa_clauses' isa_clauses |
17404
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|
400 |
end |
15347 | 401 |
|
16039
dfe264950511
Moved some of the clausify functions from ATP/res_clasimpset.ML to res_axioms.ML.
quigley
parents:
16012
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changeset
|
402 |
fun clausify_rules_pairs [] err_list = ([],err_list) |
dfe264950511
Moved some of the clausify functions from ATP/res_clasimpset.ML to res_axioms.ML.
quigley
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|
403 |
| clausify_rules_pairs ((name,thm)::thms) err_list = |
16897 | 404 |
let val (ts,es) = clausify_rules_pairs thms err_list |
405 |
in |
|
406 |
((clausify_axiom_pairs (name,thm))::ts, es) |
|
17404
d16c3a62c396
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|
407 |
handle THM (msg,_,_) => |
d16c3a62c396
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|
408 |
(debug ("Cannot clausify " ^ name ^ ": " ^ msg); |
d16c3a62c396
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|
409 |
(ts, (thm::es))) |
d16c3a62c396
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|
410 |
| ResClause.CLAUSE (msg,t) => |
d16c3a62c396
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|
411 |
(debug ("Cannot clausify " ^ name ^ ": " ^ msg ^ |
d16c3a62c396
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|
412 |
": " ^ TermLib.string_of_term t); |
d16c3a62c396
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|
413 |
(ts, (thm::es))) |
d16c3a62c396
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|
414 |
|
16897 | 415 |
end; |
16039
dfe264950511
Moved some of the clausify functions from ATP/res_clasimpset.ML to res_axioms.ML.
quigley
parents:
16012
diff
changeset
|
416 |
|
15347 | 417 |
|
16009 | 418 |
(*Setup function: takes a theory and installs ALL simprules and claset rules |
419 |
into the clause cache*) |
|
420 |
fun clause_cache_setup thy = |
|
421 |
let val simps = simpset_rules_of_thy thy |
|
422 |
and clas = claset_rules_of_thy thy |
|
423 |
in skolemlist clas (skolemlist simps thy) end; |
|
424 |
||
16563 | 425 |
val clause_setup = [clause_cache_setup]; |
426 |
||
427 |
||
428 |
(*** meson proof methods ***) |
|
429 |
||
430 |
fun cnf_rules_of_ths ths = List.concat (#1 (cnf_rules (map pairname ths) [])); |
|
431 |
||
432 |
fun meson_meth ths ctxt = |
|
433 |
Method.SIMPLE_METHOD' HEADGOAL |
|
434 |
(CHANGED_PROP o Meson.meson_claset_tac (cnf_rules_of_ths ths) (local_claset_of ctxt)); |
|
435 |
||
436 |
val meson_method_setup = |
|
437 |
[Method.add_methods |
|
438 |
[("meson", Method.thms_ctxt_args meson_meth, |
|
439 |
"The MESON resolution proof procedure")]]; |
|
15347 | 440 |
|
441 |
end; |