author  paulson 
Tue, 26 Sep 2006 11:09:33 +0200  
changeset 20710  384bfce59254 
parent 20624  ba081ac0ed7e 
child 20774  8f947ffb5eb8 
permissions  rwrr 
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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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(*FIXME: does this signature serve any purpose?*) 
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signature RES_AXIOMS = 
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sig 

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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 cnf_axiom : (string * thm) > thm list 

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val meta_cnf_axiom : thm > thm 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 claset_rules_of_ctxt: Proof.context > (string * thm) list 
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val simpset_rules_of_ctxt : Proof.context > (string * thm) list 
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val pairname : thm > (string * thm) 
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val skolem_thm : thm > thm list 
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val to_nnf : thm > thm 
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val cnf_rules_pairs : (string * Thm.thm) list > (Thm.thm * (string * int)) list list; 
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val meson_method_setup : theory > theory 
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val setup : theory > theory 

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val atpset_rules_of_thy : theory > (string * thm) list 
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val atpset_rules_of_ctxt : Proof.context > (string * thm) list 
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end; 
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structure ResAxioms = 
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struct 
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(*FIXME DELETE: For running the comparison between combinators and abstractions. 
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CANNOT be a ref, as the setting is used while Isabelle is built.*) 

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val abstract_lambdas = true; 

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val trace_abs = ref false; 

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(*Store definitions of abstraction functions, ensuring that identical righthand 
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sides are denoted by the same functions and thereby reducing the need for 

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extensionality in proofs. 

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FIXME! Store in theory data!!*) 

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val abstraction_cache = ref Net.empty : thm Net.net ref; 

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(**** Transformation of Elimination Rules into FirstOrder Formulas****) 
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(* a tactic used to prove an elimrule. *) 
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fun elimRule_tac th = 
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(resolve_tac [impI,notI] 1) THEN (etac th 1) THEN REPEAT(fast_tac HOL_cs 1); 
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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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(*Checks for the premise ~P when the conclusion is P.*) 
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fun is_neg (Const("Trueprop",_) $ (Const("Not",_) $ Free(p,_))) 
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(Const("Trueprop",_) $ Free(q,_)) = (p = q) 
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 is_neg _ _ = false; 
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exception ELIMR2FOL; 
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(*Handles the case where the dummy "conclusion" variable appears negated in the 
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premises, so the final consequent must be kept.*) 
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fun strip_concl' prems bvs (Const ("==>",_) $ P $ Q) = 
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strip_concl' (HOLogic.dest_Trueprop P :: prems) bvs Q 
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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 add_EX (foldr1 HOLogic.mk_conj (P'::prems)) bvs end; 
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(*Recurrsion over the minor premise of an elimination rule. Final consequent 
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is ignored, as it is the dummy "conclusion" variable.*) 
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fun strip_concl prems bvs concl (Const ("all", _) $ Abs (x,xtp,body)) = 
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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 strip_concl (HOLogic.dest_Trueprop P::prems) bvs concl Q 
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 strip_concl prems bvs concl Q = 
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if concl aconv Q then add_EX (foldr1 HOLogic.mk_conj prems) bvs 
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else raise ELIMR2FOL (*expected conclusion not found!*) 
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fun trans_elim (major,[],_) = HOLogic.Not $ major 
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 trans_elim (major,minors,concl) = 
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let val disjs = foldr1 HOLogic.mk_disj (map (strip_concl [] [] concl) minors) 
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in HOLogic.mk_imp (major, disjs) 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' = #1 (Drule.freeze_thaw elimR) 
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val (prems,concl) = (prems_of elimR', concl_of elimR') 
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val cv = case concl of (*conclusion variable*) 
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Const("Trueprop",_) $ (v as Free(_,Type("bool",[]))) => v 
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 v as Free(_, Type("prop",[])) => v 
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 _ => raise ELIMR2FOL 
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in case prems of 
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[] => raise ELIMR2FOL 
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 (Const("Trueprop",_) $ major) :: minors => 
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if member (op aconv) (term_frees major) cv then raise ELIMR2FOL 
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else (trans_elim (major, minors, concl) handle TERM _ => raise ELIMR2FOL) 
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 _ => raise ELIMR2FOL 
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end; 
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(* convert an elimrule 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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let val ctm = cterm_of (sign_of_thm th) (HOLogic.mk_Trueprop (elimR2Fol th)) 
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in Goal.prove_raw [] ctm (fn _ => elimRule_tac th) end 
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handle ELIMR2FOL => th (*not an elimination rule*) 
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 exn => (warning ("transform_elim failed: " ^ Toplevel.exn_message exn ^ 
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" for theorem " ^ string_of_thm th); th) 
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(**** Transformation of Clasets and Simpsets into FirstOrder Axioms ****) 

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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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(**** SKOLEMIZATION BY INFERENCE (lcp) ****) 
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(*Traverse a theorem, declaring Skolem function definitions. String s is the suggested 
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prefix for the Skolem constant. Result is a new theory*) 
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fun declare_skofuns s th thy = 
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let fun dec_sko (Const ("Ex",_) $ (xtp as Abs(_,T,p))) (thy, axs) = 
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(*Existential: declare a Skolem function, then insert into body and continue*) 
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let val cname = Name.internal (gensym ("sko_" ^ s ^ "_")) 
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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 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 lambdaabstraction over the formal parameters*) 
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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 false [(cdef, equals cT $ c $ rhs)] thy' 
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in dec_sko (subst_bound (list_comb(c,args), p)) 
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(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))) thx = 
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(*Universal quant: insert a free variable into body and continue*) 
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let val fname = Name.variant (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 (*Do nothing otherwise*) 
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in dec_sko (prop_of th) (thy,[]) end; 
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(*Traverse a theorem, accumulating Skolem function definitions.*) 
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fun assume_skofuns th = 
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let fun dec_sko (Const ("Ex",_) $ (xtp as Abs(_,T,p))) defs = 
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(*Existential: declare a Skolem function, then insert into body and continue*) 
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let val skos = map (#1 o Logic.dest_equals) defs (*existing sko fns*) 
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val args = term_frees xtp \\ skos (*the formal parameters*) 
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val Ts = map type_of args 
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val cT = Ts > T 
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val c = Free (gensym "sko_", cT) 
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val rhs = list_abs_free (map dest_Free args, 
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HOLogic.choice_const T $ xtp) 
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(*Forms a lambdaabstraction over the formal parameters*) 
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val def = equals cT $ c $ rhs 
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in dec_sko (subst_bound (list_comb(c,args), p)) 
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(def :: defs) 
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end 
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 dec_sko (Const ("All",_) $ (xtp as 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 (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; 
191 

192 

193 
(**** REPLACING ABSTRACTIONS BY FUNCTION DEFINITIONS ****) 

194 

195 
(*Returns the vars of a theorem*) 

196 
fun vars_of_thm th = 

20445  197 
map (Thm.cterm_of (theory_of_thm th) o Var) (Drule.fold_terms Term.add_vars th []); 
20419  198 

199 
(*Make a version of fun_cong with a given variable name*) 

200 
local 

201 
val fun_cong' = fun_cong RS asm_rl; (*renumber f, g to prevent clashes with (a,0)*) 

202 
val cx = hd (vars_of_thm fun_cong'); 

203 
val ty = typ_of (ctyp_of_term cx); 

20445  204 
val thy = theory_of_thm fun_cong; 
20419  205 
fun mkvar a = cterm_of thy (Var((a,0),ty)); 
206 
in 

207 
fun xfun_cong x = Thm.instantiate ([], [(cx, mkvar x)]) fun_cong' 

208 
end; 

209 

210 
(*Removes the lambdas from an equation of the form t = (%x. u)*) 

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fun strip_lambdas th = 
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case prop_of th of 
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_ $ (Const ("op =", _) $ _ $ Abs (x,_,_)) => 
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strip_lambdas (#1 (Drule.freeze_thaw (th RS xfun_cong x))) 
215 
 _ => th; 

216 

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(*Convert meta to objectequality. Fails for theorems like split_comp_eq, 
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where some types have the empty sort.*) 
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fun object_eq th = th RS def_imp_eq 
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handle THM _ => error ("Theorem contains empty sort: " ^ string_of_thm th); 
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20419  222 
(*Contract all etaredexes in the theorem, lest they give rise to needless abstractions*) 
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fun eta_conversion_rule th = 

224 
equal_elim (eta_conversion (cprop_of th)) th; 

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20445  226 
fun crhs_of th = 
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case Drule.strip_comb (cprop_of th) of 
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(f, [_, rhs]) => 
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(case term_of f of Const ("==", _) => rhs 
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 _ => raise THM ("crhs_of", 0, [th])) 
231 
 _ => raise THM ("crhs_of", 1, [th]); 

232 

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fun lhs_of th = 
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case prop_of th of (Const("==",_) $ lhs $ _) => lhs 
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 _ => raise THM ("lhs_of", 1, [th]); 
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20445  237 
fun rhs_of th = 
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case prop_of th of (Const("==",_) $ _ $ rhs) => rhs 
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 _ => raise THM ("rhs_of", 1, [th]); 
20419  240 

241 
(*Apply a function definition to an argument, betareducing the result.*) 

242 
fun beta_comb cf x = 

243 
let val th1 = combination cf (reflexive x) 

20445  244 
val th2 = beta_conversion false (crhs_of th1) 
20419  245 
in transitive th1 th2 end; 
246 

247 
(*Apply a function definition to arguments, betareducing along the way.*) 

248 
fun list_combination cf [] = cf 

249 
 list_combination cf (x::xs) = list_combination (beta_comb cf x) xs; 

250 

251 
fun list_cabs ([] , t) = t 

252 
 list_cabs (v::vars, t) = Thm.cabs v (list_cabs(vars,t)); 

253 

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fun assert_eta_free ct = 
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let val t = term_of ct 
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in if (t aconv Envir.eta_contract t) then () 
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else error ("Eta redex in term: " ^ string_of_cterm ct) 
258 
end; 

259 

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fun eq_absdef (th1, th2) = 
20445  261 
Context.joinable (theory_of_thm th1, theory_of_thm th2) andalso 
262 
rhs_of th1 aconv rhs_of th2; 

263 

264 
fun lambda_free (Abs _) = false 

265 
 lambda_free (t $ u) = lambda_free t andalso lambda_free u 

266 
 lambda_free _ = true; 

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fun monomorphic t = 
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Term.fold_types (Term.fold_atyps (fn TVar _ => K false  _ => I)) t true; 
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fun dest_abs_list ct = 
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let val (cv,ct') = Thm.dest_abs NONE ct 
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val (cvs,cu) = dest_abs_list ct' 
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in (cv::cvs, cu) end 
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handle CTERM _ => ([],ct); 
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fun lambda_list [] u = u 
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 lambda_list (v::vs) u = lambda v (lambda_list vs u); 
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fun abstract_rule_list [] [] th = th 
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 abstract_rule_list (v::vs) (ct::cts) th = abstract_rule v ct (abstract_rule_list vs cts th) 
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 abstract_rule_list _ _ th = raise THM ("abstract_rule_list", 0, [th]); 
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20419  284 
(*Traverse a theorem, declaring abstraction function definitions. String s is the suggested 
285 
prefix for the constants. Resulting theory is returned in the first theorem. *) 

286 
fun declare_absfuns th = 

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let fun abstract thy ct = 
20445  288 
if lambda_free (term_of ct) then (transfer thy (reflexive ct), []) 
289 
else 

290 
case term_of ct of 

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Abs _ => 
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let val cname = Name.internal (gensym "abs_"); 
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val _ = assert_eta_free ct; 
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val (cvs,cta) = dest_abs_list ct 
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val (vs,Tvs) = ListPair.unzip (map (dest_Free o term_of) cvs) 
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val (u'_th,defs) = abstract thy cta 
20445  297 
val cu' = crhs_of u'_th 
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val abs_v_u = lambda_list (map term_of cvs) (term_of cu') 
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(*get the formal parameters: ALL variables free in the term*) 
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val args = term_frees abs_v_u 
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val rhs = list_abs_free (map dest_Free args, abs_v_u) 
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(*Forms a lambdaabstraction over the formal parameters*) 
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val v_rhs = Logic.varify rhs 
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val (ax,thy) = 
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case List.find (fn ax => v_rhs aconv rhs_of ax) 
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(Net.match_term (!abstraction_cache) v_rhs) of 
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SOME ax => (ax,thy) (*cached axiom, current theory*) 
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 NONE => 
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let val Ts = map type_of args 
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val cT = Ts > (Tvs > typ_of (ctyp_of_term cu')) 
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val thy = theory_of_thm u'_th 
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val c = Const (Sign.full_name thy cname, cT) 
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val thy = Theory.add_consts_i [(cname, cT, NoSyn)] thy 
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(*Theory is augmented with the constant, 
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then its definition*) 
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val cdef = cname ^ "_def" 
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val thy = Theory.add_defs_i false false 
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[(cdef, equals cT $ c $ rhs)] thy 
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val ax = get_axiom thy cdef 
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val _ = abstraction_cache := Net.insert_term eq_absdef (v_rhs,ax) 
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(!abstraction_cache) 
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handle Net.INSERT => 
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raise THM ("declare_absfuns: INSERT", 0, [th,u'_th,ax]) 
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in (ax,thy) end 
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val _ = assert (v_rhs aconv rhs_of ax) "declare_absfuns: rhs mismatch" 
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val def = #1 (Drule.freeze_thaw ax) 
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val def_args = list_combination def (map (cterm_of thy) args) 
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in (transitive (abstract_rule_list vs cvs u'_th) (symmetric def_args), 
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def :: defs) end 
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 (t1$t2) => 
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let val (ct1,ct2) = Thm.dest_comb ct 
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val (th1,defs1) = abstract thy ct1 
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val (th2,defs2) = abstract (theory_of_thm th1) ct2 
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in (combination th1 th2, defs1@defs2) end 
20419  335 
val _ = if !trace_abs then warning (string_of_thm th) else (); 
336 
val (eqth,defs) = abstract (theory_of_thm th) (cprop_of th) 

337 
val ths = equal_elim eqth th :: 

338 
map (forall_intr_vars o strip_lambdas o object_eq) defs 

339 
in (theory_of_thm eqth, ths) end; 

340 

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fun name_of def = SOME (#1 (dest_Free (lhs_of def))) handle _ => NONE; 
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342 

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343 
(*A name is valid provided it isn't the name of a defined abstraction.*) 
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344 
fun valid_name defs (Free(x,T)) = not (x mem_string (List.mapPartial name_of defs)) 
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345 
 valid_name defs _ = false; 
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346 

20419  347 
fun assume_absfuns th = 
20445  348 
let val thy = theory_of_thm th 
349 
val cterm = cterm_of thy 

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350 
fun abstract ct = 
20445  351 
if lambda_free (term_of ct) then (reflexive ct, []) 
352 
else 

353 
case term_of ct of 

20419  354 
Abs (_,T,u) => 
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355 
let val _ = assert_eta_free ct; 
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356 
val (cvs,cta) = dest_abs_list ct 
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357 
val (vs,Tvs) = ListPair.unzip (map (dest_Free o term_of) cvs) 
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358 
val (u'_th,defs) = abstract cta 
20445  359 
val cu' = crhs_of u'_th 
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360 
(*Could use Thm.cabs instead of lambda to work at level of cterms*) 
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361 
val abs_v_u = lambda_list (map term_of cvs) (term_of cu') 
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362 
(*get the formal parameters: free variables not present in the defs 
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363 
(to avoid taking abstraction function names as parameters) *) 
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364 
val args = filter (valid_name defs) (term_frees abs_v_u) 
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365 
val crhs = list_cabs (map cterm args, cterm abs_v_u) 
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366 
(*Forms a lambdaabstraction over the formal parameters*) 
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367 
val rhs = term_of crhs 
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368 
val def = (*FIXME: can we also reuse the constabstractions?*) 
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369 
case List.find (fn ax => rhs aconv rhs_of ax andalso 
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370 
Context.joinable (thy, theory_of_thm ax)) 
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371 
(Net.match_term (!abstraction_cache) rhs) of 
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372 
SOME ax => ax 
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373 
 NONE => 
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374 
let val Ts = map type_of args 
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375 
val const_ty = Ts > (Tvs > typ_of (ctyp_of_term cu')) 
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376 
val c = Free (gensym "abs_", const_ty) 
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377 
val ax = assume (Thm.capply (cterm (equals const_ty $ c)) crhs) 
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378 
val _ = abstraction_cache := Net.insert_term eq_absdef (rhs,ax) 
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379 
(!abstraction_cache) 
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380 
handle Net.INSERT => 
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381 
raise THM ("assume_absfuns: INSERT", 0, [th,u'_th,ax]) 
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382 
in ax end 
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383 
val _ = assert (rhs aconv rhs_of def) "assume_absfuns: rhs mismatch" 
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384 
val def_args = list_combination def (map cterm args) 
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385 
in (transitive (abstract_rule_list vs cvs u'_th) (symmetric def_args), 
20461
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386 
def :: defs) end 
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387 
 (t1$t2) => 
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388 
let val (ct1,ct2) = Thm.dest_comb ct 
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389 
val (t1',defs1) = abstract ct1 
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390 
val (t2',defs2) = abstract ct2 
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391 
in (combination t1' t2', defs1@defs2) end 
20525
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392 
val (eqth,defs) = abstract (cprop_of th) 
20419  393 
in equal_elim eqth th :: 
394 
map (forall_intr_vars o strip_lambdas o object_eq) defs 

395 
end; 

396 

16009  397 

398 
(*cterms are used throughout for efficiency*) 

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399 
val cTrueprop = Thm.cterm_of HOL.thy HOLogic.Trueprop; 
16009  400 

401 
(*cterm version of mk_cTrueprop*) 

402 
fun c_mkTrueprop A = Thm.capply cTrueprop A; 

403 

404 
(*Given an abstraction over n variables, replace the bound variables by free 

405 
ones. Return the body, along with the list of free variables.*) 

20461
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406 
fun c_variant_abs_multi (ct0, vars) = 
16009  407 
let val (cv,ct) = Thm.dest_abs NONE ct0 
408 
in c_variant_abs_multi (ct, cv::vars) end 

409 
handle CTERM _ => (ct0, rev vars); 

410 

20461
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411 
(*Given the definition of a Skolem function, return a theorem to replace 
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412 
an existential formula by a use of that function. 
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413 
Example: "EX x. x : A & x ~: B ==> sko A B : A & sko A B ~: B" [.] *) 
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414 
fun skolem_of_def def = 
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415 
let val (c,rhs) = Drule.dest_equals (cprop_of (#1 (Drule.freeze_thaw def))) 
16009  416 
val (ch, frees) = c_variant_abs_multi (rhs, []) 
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417 
val (chilbert,cabs) = Thm.dest_comb ch 
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418 
val {sign,t, ...} = rep_cterm chilbert 
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419 
val T = case t of Const ("Hilbert_Choice.Eps", Type("fun",[_,T])) => T 
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420 
 _ => raise THM ("skolem_of_def: expected Eps", 0, [def]) 
16009  421 
val cex = Thm.cterm_of sign (HOLogic.exists_const T) 
422 
val ex_tm = c_mkTrueprop (Thm.capply cex cabs) 

423 
and conc = c_mkTrueprop (Drule.beta_conv cabs (Drule.list_comb(c,frees))); 

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424 
fun tacf [prem] = rewrite_goals_tac [def] THEN rtac (prem RS someI_ex) 1 
20461
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425 
in Goal.prove_raw [ex_tm] conc tacf 
18141
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426 
> forall_intr_list frees 
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427 
> forall_elim_vars 0 (*Introduce Vars, but don't discharge defs.*) 
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428 
> Thm.varifyT 
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429 
end; 
16009  430 

18198
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mengj
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18144
diff
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431 
(*Converts an Isabelle theorem (intro, elim or simp format) into nnf.*) 
95330fc0ea8d
 combined common CNF functions used by HOL and FOL axioms, the difference between conversion of HOL and FOL theorems only comes in when theorems are converted to ResClause.clause or ResHolClause.clause format.
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432 
(*It now works for HOL too. *) 
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433 
fun to_nnf th = 
18141
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434 
th > transfer_to_Reconstruction 
20419  435 
> transform_elim > zero_var_indexes > Drule.freeze_thaw > #1 
20710
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changeset

436 
> ObjectLogic.atomize_thm > make_nnf > strip_lambdas; 
16009  437 

20461
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438 
(*The cache prevents repeated clausification of a theorem, 
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changeset

439 
and also repeated declaration of Skolem functions*) 
18510
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440 
(* FIXME better use Termtab!? No, we MUST use theory data!!*) 
15955
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memoization of ResAxioms.cnf_axiom rather than of Reconstruction.clausify_rule
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diff
changeset

441 
val clause_cache = ref (Symtab.empty : (thm * thm list) Symtab.table) 
87cf2ce8ede8
memoization of ResAxioms.cnf_axiom rather than of Reconstruction.clausify_rule
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442 

18141
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443 

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444 
(*Generate Skolem functions for a theorem supplied in nnf*) 
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445 
fun skolem_of_nnf th = 
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446 
map (skolem_of_def o assume o (cterm_of (theory_of_thm th))) (assume_skofuns th); 
89e2e8bed08f
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paulson
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changeset

447 

20457
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448 
fun assert_lambda_free ths = assert (forall (lambda_free o prop_of) ths); 
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refinements to conversion into clause form, esp for the HO case
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449 

20445  450 
fun assume_abstract th = 
20457
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refinements to conversion into clause form, esp for the HO case
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changeset

451 
if lambda_free (prop_of th) then [th] 
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changeset

452 
else th > eta_conversion_rule > assume_absfuns 
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diff
changeset

453 
> tap (fn ths => assert_lambda_free ths "assume_abstract: lambdas") 
20445  454 

20419  455 
(*Replace lambdas by assumed function definitions in the theorems*) 
20445  456 
fun assume_abstract_list ths = 
457 
if abstract_lambdas then List.concat (map assume_abstract ths) 

20419  458 
else map eta_conversion_rule ths; 
459 

460 
(*Replace lambdas by declared function definitions in the theorems*) 

461 
fun declare_abstract' (thy, []) = (thy, []) 

462 
 declare_abstract' (thy, th::ths) = 

20461
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changeset

463 
let val (thy', th_defs) = 
20457
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464 
if lambda_free (prop_of th) then (thy, [th]) 
20445  465 
else 
20461
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changeset

466 
th > zero_var_indexes > Drule.freeze_thaw > #1 
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changeset

467 
> eta_conversion_rule > transfer thy > declare_absfuns 
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changeset

468 
val _ = assert_lambda_free th_defs "declare_abstract: lambdas" 
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changeset

469 
val (thy'', ths') = declare_abstract' (thy', ths) 
20419  470 
in (thy'', th_defs @ ths') end; 
471 

20421  472 
(*FIXME DELETE if we decide to switch to abstractions*) 
20419  473 
fun declare_abstract (thy, ths) = 
474 
if abstract_lambdas then declare_abstract' (thy, ths) 

475 
else (thy, map eta_conversion_rule ths); 

476 

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changeset

477 
(*Skolemize a named theorem, with Skolem functions as additional premises.*) 
20461
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changeset

478 
(*also works for HOL*) 
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changeset

479 
fun skolem_thm th = 
18510
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changeset

480 
let val nnfth = to_nnf th 
20419  481 
in Meson.make_cnf (skolem_of_nnf nnfth) nnfth 
20445  482 
> assume_abstract_list > Meson.finish_cnf > rm_redundant_cls 
18510
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changeset

483 
end 
0a6c24f549c3
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paulson
parents:
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diff
changeset

484 
handle THM _ => []; 
18141
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Skolemization by inference, but not quite finished
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parents:
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diff
changeset

485 

18510
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diff
changeset

486 
(*Declare Skolem functions for a theorem, supplied in nnf and with its name. 
0a6c24f549c3
the "skolem" attribute and better initialization of the clause database
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diff
changeset

487 
It returns a modified theory, unless skolemization fails.*) 
16009  488 
fun skolem thy (name,th) = 
20419  489 
let val cname = (case name of "" => gensym ""  s => Sign.base_name s) 
490 
val _ = Output.debug ("skolemizing " ^ name ^ ": ") 

20461
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parents:
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diff
changeset

491 
in Option.map 
d689ad772b2c
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changeset

492 
(fn nnfth => 
18141
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diff
changeset

493 
let val (thy',defs) = declare_skofuns cname nnfth thy 
20419  494 
val cnfs = Meson.make_cnf (map skolem_of_def defs) nnfth 
495 
val (thy'',cnfs') = declare_abstract (thy',cnfs) 

496 
in (thy'', rm_redundant_cls (Meson.finish_cnf cnfs')) 

497 
end) 

20461
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diff
changeset

498 
(SOME (to_nnf th) handle THM _ => NONE) 
18141
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Skolemization by inference, but not quite finished
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parents:
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diff
changeset

499 
end; 
16009  500 

18510
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diff
changeset

501 
(*Populate the clause cache using the supplied theorem. Return the clausal form 
0a6c24f549c3
the "skolem" attribute and better initialization of the clause database
paulson
parents:
18404
diff
changeset

502 
and modified theory.*) 
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

503 
fun skolem_cache_thm (name,th) thy = 
18144
4edcb5fdc3b0
duplicate axioms in ATP linkup, and general fixes
paulson
parents:
18141
diff
changeset

504 
case Symtab.lookup (!clause_cache) name of 
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

505 
NONE => 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

506 
(case skolem thy (name, Thm.transfer thy th) of 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

507 
NONE => ([th],thy) 
20473
7ef72f030679
Using Drule.local_standard to reduce the space usage
paulson
parents:
20461
diff
changeset

508 
 SOME (thy',cls) => 
7ef72f030679
Using Drule.local_standard to reduce the space usage
paulson
parents:
20461
diff
changeset

509 
let val cls = map Drule.local_standard cls 
7ef72f030679
Using Drule.local_standard to reduce the space usage
paulson
parents:
20461
diff
changeset

510 
in 
7ef72f030679
Using Drule.local_standard to reduce the space usage
paulson
parents:
20461
diff
changeset

511 
if null cls then warning ("skolem_cache: empty clause set for " ^ name) 
7ef72f030679
Using Drule.local_standard to reduce the space usage
paulson
parents:
20461
diff
changeset

512 
else (); 
7ef72f030679
Using Drule.local_standard to reduce the space usage
paulson
parents:
20461
diff
changeset

513 
change clause_cache (Symtab.update (name, (th, cls))); 
7ef72f030679
Using Drule.local_standard to reduce the space usage
paulson
parents:
20461
diff
changeset

514 
(cls,thy') 
7ef72f030679
Using Drule.local_standard to reduce the space usage
paulson
parents:
20461
diff
changeset

515 
end) 
18144
4edcb5fdc3b0
duplicate axioms in ATP linkup, and general fixes
paulson
parents:
18141
diff
changeset

516 
 SOME (th',cls) => 
18510
0a6c24f549c3
the "skolem" attribute and better initialization of the clause database
paulson
parents:
18404
diff
changeset

517 
if eq_thm(th,th') then (cls,thy) 
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

518 
else (Output.debug ("skolem_cache: Ignoring variant of theorem " ^ name); 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

519 
Output.debug (string_of_thm th); 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

520 
Output.debug (string_of_thm th'); 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

521 
([th],thy)); 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

522 

d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
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diff
changeset

523 
(*Exported function to convert Isabelle theorems into axiom clauses*) 
19894  524 
fun cnf_axiom (name,th) = 
18144
4edcb5fdc3b0
duplicate axioms in ATP linkup, and general fixes
paulson
parents:
18141
diff
changeset

525 
case name of 
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

526 
"" => skolem_thm th (*no name, so can't cache*) 
18144
4edcb5fdc3b0
duplicate axioms in ATP linkup, and general fixes
paulson
parents:
18141
diff
changeset

527 
 s => case Symtab.lookup (!clause_cache) s of 
20473
7ef72f030679
Using Drule.local_standard to reduce the space usage
paulson
parents:
20461
diff
changeset

528 
NONE => 
7ef72f030679
Using Drule.local_standard to reduce the space usage
paulson
parents:
20461
diff
changeset

529 
let val cls = map Drule.local_standard (skolem_thm th) 
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

530 
in change clause_cache (Symtab.update (s, (th, cls))); cls end 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

531 
 SOME(th',cls) => 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

532 
if eq_thm(th,th') then cls 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

533 
else (Output.debug ("cnf_axiom: duplicate or variant of theorem " ^ name); 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

534 
Output.debug (string_of_thm th); 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

535 
Output.debug (string_of_thm th'); 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

536 
cls); 
15347  537 

18141
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18009
diff
changeset

538 
fun pairname th = (Thm.name_of_thm th, th); 
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18009
diff
changeset

539 

20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

540 
fun meta_cnf_axiom th = 
15956  541 
map Meson.make_meta_clause (cnf_axiom (pairname th)); 
15499  542 

15347  543 

15872  544 
(**** Extract and Clausify theorems from a theory's claset and simpset ****) 
15347  545 

17404
d16c3a62c396
the experimental tagging system, and the usual tidying
paulson
parents:
17279
diff
changeset

546 
(*Preserve the name of "th" after the transformation "f"*) 
d16c3a62c396
the experimental tagging system, and the usual tidying
paulson
parents:
17279
diff
changeset

547 
fun preserve_name f th = Thm.name_thm (Thm.name_of_thm th, f th); 
d16c3a62c396
the experimental tagging system, and the usual tidying
paulson
parents:
17279
diff
changeset

548 

17484
f6a225f97f0a
simplification of the IsabelleATP code; hooks for batch generation of problems
paulson
parents:
17412
diff
changeset

549 
fun rules_of_claset cs = 
f6a225f97f0a
simplification of the IsabelleATP code; hooks for batch generation of problems
paulson
parents:
17412
diff
changeset

550 
let val {safeIs,safeEs,hazIs,hazEs,...} = rep_cs cs 
19175  551 
val intros = safeIs @ hazIs 
18532  552 
val elims = map Classical.classical_rule (safeEs @ hazEs) 
17404
d16c3a62c396
the experimental tagging system, and the usual tidying
paulson
parents:
17279
diff
changeset

553 
in 
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

554 
Output.debug ("rules_of_claset intros: " ^ Int.toString(length intros) ^ 
17484
f6a225f97f0a
simplification of the IsabelleATP code; hooks for batch generation of problems
paulson
parents:
17412
diff
changeset

555 
" elims: " ^ Int.toString(length elims)); 
20017
a2070352371c
made the conversion of elimination rules more robust
paulson
parents:
19894
diff
changeset

556 
map pairname (intros @ elims) 
17404
d16c3a62c396
the experimental tagging system, and the usual tidying
paulson
parents:
17279
diff
changeset

557 
end; 
15347  558 

17484
f6a225f97f0a
simplification of the IsabelleATP code; hooks for batch generation of problems
paulson
parents:
17412
diff
changeset

559 
fun rules_of_simpset ss = 
f6a225f97f0a
simplification of the IsabelleATP code; hooks for batch generation of problems
paulson
parents:
17412
diff
changeset

560 
let val ({rules,...}, _) = rep_ss ss 
f6a225f97f0a
simplification of the IsabelleATP code; hooks for batch generation of problems
paulson
parents:
17412
diff
changeset

561 
val simps = Net.entries rules 
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

562 
in 
18680  563 
Output.debug ("rules_of_simpset: " ^ Int.toString(length simps)); 
17484
f6a225f97f0a
simplification of the IsabelleATP code; hooks for batch generation of problems
paulson
parents:
17412
diff
changeset

564 
map (fn r => (#name r, #thm r)) simps 
f6a225f97f0a
simplification of the IsabelleATP code; hooks for batch generation of problems
paulson
parents:
17412
diff
changeset

565 
end; 
f6a225f97f0a
simplification of the IsabelleATP code; hooks for batch generation of problems
paulson
parents:
17412
diff
changeset

566 

f6a225f97f0a
simplification of the IsabelleATP code; hooks for batch generation of problems
paulson
parents:
17412
diff
changeset

567 
fun claset_rules_of_thy thy = rules_of_claset (claset_of thy); 
f6a225f97f0a
simplification of the IsabelleATP code; hooks for batch generation of problems
paulson
parents:
17412
diff
changeset

568 
fun simpset_rules_of_thy thy = rules_of_simpset (simpset_of thy); 
f6a225f97f0a
simplification of the IsabelleATP code; hooks for batch generation of problems
paulson
parents:
17412
diff
changeset

569 

19196
62ee8c10d796
Added functions to retrieve local and global atpset rules.
mengj
parents:
19175
diff
changeset

570 
fun atpset_rules_of_thy thy = map pairname (ResAtpSet.atp_rules_of_thy thy); 
62ee8c10d796
Added functions to retrieve local and global atpset rules.
mengj
parents:
19175
diff
changeset

571 

62ee8c10d796
Added functions to retrieve local and global atpset rules.
mengj
parents:
19175
diff
changeset

572 

17484
f6a225f97f0a
simplification of the IsabelleATP code; hooks for batch generation of problems
paulson
parents:
17412
diff
changeset

573 
fun claset_rules_of_ctxt ctxt = rules_of_claset (local_claset_of ctxt); 
f6a225f97f0a
simplification of the IsabelleATP code; hooks for batch generation of problems
paulson
parents:
17412
diff
changeset

574 
fun simpset_rules_of_ctxt ctxt = rules_of_simpset (local_simpset_of ctxt); 
15347  575 

19196
62ee8c10d796
Added functions to retrieve local and global atpset rules.
mengj
parents:
19175
diff
changeset

576 
fun atpset_rules_of_ctxt ctxt = map pairname (ResAtpSet.atp_rules_of_ctxt ctxt); 
15347  577 

15872  578 
(**** Translate a set of classical/simplifier rules into CNF (still as type "thm") ****) 
15347  579 

19894  580 
(* classical rules: works for both FOL and HOL *) 
581 
fun cnf_rules [] err_list = ([],err_list) 

20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

582 
 cnf_rules ((name,th) :: ths) err_list = 
19894  583 
let val (ts,es) = cnf_rules ths err_list 
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

584 
in (cnf_axiom (name,th) :: ts,es) handle _ => (ts, (th::es)) end; 
15347  585 

19894  586 
fun pair_name_cls k (n, []) = [] 
587 
 pair_name_cls k (n, cls::clss) = (cls, (n,k)) :: pair_name_cls (k+1) (n, clss) 

20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

588 

19894  589 
fun cnf_rules_pairs_aux pairs [] = pairs 
590 
 cnf_rules_pairs_aux pairs ((name,th)::ths) = 

20457
85414caac94a
refinements to conversion into clause form, esp for the HO case
paulson
parents:
20445
diff
changeset

591 
let val pairs' = (pair_name_cls 0 (name, cnf_axiom(name,th))) @ pairs 
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

592 
handle THM _ => pairs  ResClause.CLAUSE _ => pairs 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

593 
 ResHolClause.LAM2COMB _ => pairs 
19894  594 
in cnf_rules_pairs_aux pairs' ths end; 
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

595 

19894  596 
val cnf_rules_pairs = cnf_rules_pairs_aux []; 
19353  597 

19196
62ee8c10d796
Added functions to retrieve local and global atpset rules.
mengj
parents:
19175
diff
changeset

598 

18198
95330fc0ea8d
 combined common CNF functions used by HOL and FOL axioms, the difference between conversion of HOL and FOL theorems only comes in when theorems are converted to ResClause.clause or ResHolClause.clause format.
mengj
parents:
18144
diff
changeset

599 
(**** Convert all theorems of a claset/simpset into clauses (ResClause.clause, or ResHolClause.clause) ****) 
15347  600 

20419  601 
(*Setup function: takes a theory and installs ALL known theorems into the clause cache*) 
20457
85414caac94a
refinements to conversion into clause form, esp for the HO case
paulson
parents:
20445
diff
changeset

602 

20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

603 
fun skolem_cache (name,th) thy = 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

604 
let val prop = Thm.prop_of th 
20457
85414caac94a
refinements to conversion into clause form, esp for the HO case
paulson
parents:
20445
diff
changeset

605 
in 
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

606 
if lambda_free prop orelse monomorphic prop 
20457
85414caac94a
refinements to conversion into clause form, esp for the HO case
paulson
parents:
20445
diff
changeset

607 
then thy (*monomorphic theorems can be Skolemized on demand*) 
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

608 
else #2 (skolem_cache_thm (name,th) thy) 
20457
85414caac94a
refinements to conversion into clause form, esp for the HO case
paulson
parents:
20445
diff
changeset

609 
end; 
85414caac94a
refinements to conversion into clause form, esp for the HO case
paulson
parents:
20445
diff
changeset

610 

20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

611 
fun clause_cache_setup thy = fold skolem_cache (PureThy.all_thms_of thy) thy; 
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

612 

16563  613 

614 
(*** meson proof methods ***) 

615 

616 
fun cnf_rules_of_ths ths = List.concat (#1 (cnf_rules (map pairname ths) [])); 

617 

618 
fun meson_meth ths ctxt = 

619 
Method.SIMPLE_METHOD' HEADGOAL 

620 
(CHANGED_PROP o Meson.meson_claset_tac (cnf_rules_of_ths ths) (local_claset_of ctxt)); 

621 

622 
val meson_method_setup = 

18708  623 
Method.add_methods 
20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

624 
[("meson", Method.thms_ctxt_args meson_meth, 
18833  625 
"MESON resolution proof procedure")]; 
15347  626 

18510
0a6c24f549c3
the "skolem" attribute and better initialization of the clause database
paulson
parents:
18404
diff
changeset

627 

0a6c24f549c3
the "skolem" attribute and better initialization of the clause database
paulson
parents:
18404
diff
changeset

628 

0a6c24f549c3
the "skolem" attribute and better initialization of the clause database
paulson
parents:
18404
diff
changeset

629 
(*** The Skolemization attribute ***) 
0a6c24f549c3
the "skolem" attribute and better initialization of the clause database
paulson
parents:
18404
diff
changeset

630 

0a6c24f549c3
the "skolem" attribute and better initialization of the clause database
paulson
parents:
18404
diff
changeset

631 
fun conj2_rule (th1,th2) = conjI OF [th1,th2]; 
0a6c24f549c3
the "skolem" attribute and better initialization of the clause database
paulson
parents:
18404
diff
changeset

632 

20457
85414caac94a
refinements to conversion into clause form, esp for the HO case
paulson
parents:
20445
diff
changeset

633 
(*Conjoin a list of theorems to form a single theorem*) 
85414caac94a
refinements to conversion into clause form, esp for the HO case
paulson
parents:
20445
diff
changeset

634 
fun conj_rule [] = TrueI 
20445  635 
 conj_rule ths = foldr1 conj2_rule ths; 
18510
0a6c24f549c3
the "skolem" attribute and better initialization of the clause database
paulson
parents:
18404
diff
changeset

636 

20419  637 
fun skolem_attr (Context.Theory thy, th) = 
638 
let val name = Thm.name_of_thm th 

20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

639 
val (cls, thy') = skolem_cache_thm (name, th) thy 
18728  640 
in (Context.Theory thy', conj_rule cls) end 
20419  641 
 skolem_attr (context, th) = (context, conj_rule (skolem_thm th)); 
18510
0a6c24f549c3
the "skolem" attribute and better initialization of the clause database
paulson
parents:
18404
diff
changeset

642 

0a6c24f549c3
the "skolem" attribute and better initialization of the clause database
paulson
parents:
18404
diff
changeset

643 
val setup_attrs = Attrib.add_attributes 
20419  644 
[("skolem", Attrib.no_args skolem_attr, "skolemization of a theorem")]; 
18510
0a6c24f549c3
the "skolem" attribute and better initialization of the clause database
paulson
parents:
18404
diff
changeset

645 

18708  646 
val setup = clause_cache_setup #> setup_attrs; 
18510
0a6c24f549c3
the "skolem" attribute and better initialization of the clause database
paulson
parents:
18404
diff
changeset

647 

20461
d689ad772b2c
skolem_cache_thm: Drule.close_derivation on clauses preserves some space;
wenzelm
parents:
20457
diff
changeset

648 
end; 