author  paulson 
Sun, 16 Jul 2006 14:26:22 +0200  
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parent 20119  7923aacc10c6 
child 20288  8ff4a0ea49b2 
permissions  rwrr 
9869  1 
(* Title: HOL/Tools/meson.ML 
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ID: $Id$ 
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
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Copyright 1992 University of Cambridge 
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The MESON resolution proof procedure for HOL. 
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When making clauses, avoids using the rewriter  instead uses RS recursively 
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NEED TO SORT LITERALS BY # OF VARS, USING ==>I/E. ELIMINATES NEED FOR 
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FUNCTION nodups  if done to goal clauses too! 
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*) 
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signature BASIC_MESON = 
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sig 
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val size_of_subgoals : thm > int 
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val make_cnf : thm list > thm > thm list 
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val make_nnf : thm > thm 
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val make_nnf1 : thm > thm 
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val skolemize : thm > thm 
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val make_clauses : thm list > thm list 
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val make_horns : thm list > thm list 
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val best_prolog_tac : (thm > int) > thm list > tactic 
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val depth_prolog_tac : thm list > tactic 
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val gocls : thm list > thm list 
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val skolemize_prems_tac : thm list > int > tactic 
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val MESON : (thm list > tactic) > int > tactic 
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val best_meson_tac : (thm > int) > int > tactic 
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val safe_best_meson_tac : int > tactic 
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val depth_meson_tac : int > tactic 
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val prolog_step_tac' : thm list > int > tactic 
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val iter_deepen_prolog_tac : thm list > tactic 
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val iter_deepen_meson_tac : thm list > int > tactic 
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val meson_tac : int > tactic 
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val negate_head : thm > thm 
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val select_literal : int > thm > thm 
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val skolemize_tac : int > tactic 
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val make_clauses_tac : int > tactic 
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val check_is_fol_term : term > term 
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end 
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structure Meson = 
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struct 
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val not_conjD = thm "meson_not_conjD"; 
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val not_disjD = thm "meson_not_disjD"; 
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val not_notD = thm "meson_not_notD"; 
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val not_allD = thm "meson_not_allD"; 
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val not_exD = thm "meson_not_exD"; 
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val imp_to_disjD = thm "meson_imp_to_disjD"; 
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val not_impD = thm "meson_not_impD"; 
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val iff_to_disjD = thm "meson_iff_to_disjD"; 
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val not_iffD = thm "meson_not_iffD"; 
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val conj_exD1 = thm "meson_conj_exD1"; 
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val conj_exD2 = thm "meson_conj_exD2"; 
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val disj_exD = thm "meson_disj_exD"; 
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val disj_exD1 = thm "meson_disj_exD1"; 
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val disj_exD2 = thm "meson_disj_exD2"; 
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val disj_assoc = thm "meson_disj_assoc"; 
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val disj_comm = thm "meson_disj_comm"; 
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val disj_FalseD1 = thm "meson_disj_FalseD1"; 
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val disj_FalseD2 = thm "meson_disj_FalseD2"; 
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val depth_limit = ref 2000; 
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(**** Operators for forward proof ****) 
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(*Like RS, but raises Option if there are no unifiers and allows multiple unifiers.*) 
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fun resolve1 (tha,thb) = Seq.hd (biresolution false [(false,tha)] 1 thb); 
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(*raises exception if no rules apply  unlike RL*) 
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fun tryres (th, rls) = 
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let fun tryall [] = raise THM("tryres", 0, th::rls) 
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 tryall (rl::rls) = (resolve1(th,rl) handle Option.Option => tryall rls) 
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in tryall rls end; 
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(*Permits forward proof from rules that discharge assumptions*) 
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fun forward_res nf st = 
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case Seq.pull (ALLGOALS (METAHYPS (fn [prem] => rtac (nf prem) 1)) st) 
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of SOME(th,_) => th 
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 NONE => raise THM("forward_res", 0, [st]); 
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(*Are any of the logical connectives in "bs" present in the term?*) 
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fun has_conns bs = 
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let fun has (Const(a,_)) = false 
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 has (Const("Trueprop",_) $ p) = has p 
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 has (Const("Not",_) $ p) = has p 
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 has (Const("op ",_) $ p $ q) = member (op =) bs "op " orelse has p orelse has q 
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 has (Const("op &",_) $ p $ q) = member (op =) bs "op &" orelse has p orelse has q 
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 has (Const("All",_) $ Abs(_,_,p)) = member (op =) bs "All" orelse has p 
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 has (Const("Ex",_) $ Abs(_,_,p)) = member (op =) bs "Ex" orelse has p 
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 has _ = false 
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in has end; 
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(**** Clause handling ****) 
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fun literals (Const("Trueprop",_) $ P) = literals P 
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 literals (Const("op ",_) $ P $ Q) = literals P @ literals Q 
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 literals (Const("Not",_) $ P) = [(false,P)] 
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 literals P = [(true,P)]; 
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(*number of literals in a term*) 
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val nliterals = length o literals; 
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(*** Tautology Checking ***) 

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fun signed_lits_aux (Const ("op ", _) $ P $ Q) (poslits, neglits) = 

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signed_lits_aux Q (signed_lits_aux P (poslits, neglits)) 

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 signed_lits_aux (Const("Not",_) $ P) (poslits, neglits) = (poslits, P::neglits) 

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 signed_lits_aux P (poslits, neglits) = (P::poslits, neglits); 

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fun signed_lits th = signed_lits_aux (HOLogic.dest_Trueprop (concl_of th)) ([],[]); 

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(*Literals like X=X are tautologous*) 

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fun taut_poslit (Const("op =",_) $ t $ u) = t aconv u 

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 taut_poslit (Const("True",_)) = true 

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 taut_poslit _ = false; 

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fun is_taut th = 

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let val (poslits,neglits) = signed_lits th 

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in exists taut_poslit poslits 

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orelse 

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exists (member (op aconv) neglits) (HOLogic.false_const :: poslits) 
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end 
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handle TERM _ => false; (*probably dest_Trueprop on a weird theorem*) 

18389  130 

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(*** To remove trivial negated equality literals from clauses ***) 

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(*They are typically functional reflexivity axioms and are the converses of 

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injectivity equivalences*) 

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val not_refl_disj_D = thm"meson_not_refl_disj_D"; 

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(*Is either term a Var that does not properly occur in the other term?*) 
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fun eliminable (t as Var _, u) = t aconv u orelse not (Logic.occs(t,u)) 

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 eliminable (u, t as Var _) = t aconv u orelse not (Logic.occs(t,u)) 

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 eliminable _ = false; 

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fun refl_clause_aux 0 th = th 
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 refl_clause_aux n th = 

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case HOLogic.dest_Trueprop (concl_of th) of 

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

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refl_clause_aux n (th RS disj_assoc) (*isolate an atom as first disjunct*) 

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 (Const ("op ", _) $ (Const("Not",_) $ (Const("op =",_) $ t $ u)) $ _) => 

20119  150 
if eliminable(t,u) 
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then refl_clause_aux (n1) (th RS not_refl_disj_D) (*Var inequation: delete*) 

18389  152 
else refl_clause_aux (n1) (th RS disj_comm) (*not between Vars: ignore*) 
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 (Const ("op ", _) $ _ $ _) => refl_clause_aux n (th RS disj_comm) 

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 _ => (*not a disjunction*) th; 
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fun notequal_lits_count (Const ("op ", _) $ P $ Q) = 

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notequal_lits_count P + notequal_lits_count Q 

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 notequal_lits_count (Const("Not",_) $ (Const("op =",_) $ _ $ _)) = 1 

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 notequal_lits_count _ = 0; 

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(*Simplify a clause by applying reflexivity to its negated equality literals*) 

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fun refl_clause th = 

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let val neqs = notequal_lits_count (HOLogic.dest_Trueprop (concl_of th)) 

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in zero_var_indexes (refl_clause_aux neqs th) end 
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handle TERM _ => th; (*probably dest_Trueprop on a weird theorem*) 

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(*** The basic CNF transformation ***) 

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19894  170 
(*Estimate the number of clauses in order to detect infeasible theorems*) 
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fun nclauses (Const("Trueprop",_) $ t) = nclauses t 

172 
 nclauses (Const("op &",_) $ t $ u) = nclauses t + nclauses u 

173 
 nclauses (Const("Ex", _) $ Abs (_,_,t)) = nclauses t 

174 
 nclauses (Const("All",_) $ Abs (_,_,t)) = nclauses t 

175 
 nclauses (Const("op ",_) $ t $ u) = nclauses t * nclauses u 

176 
 nclauses _ = 1; (* literal *) 

177 

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(*Replaces universally quantified variables by FREE variables  because 
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assumptions may not contain scheme variables. Later, call "generalize". *) 
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fun freeze_spec th = 
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let val newname = gensym "A_" 
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val spec' = read_instantiate [("x", newname)] spec 
183 
in th RS spec' end; 

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(*Used with METAHYPS below. There is one assumption, which gets bound to prem 
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and then normalized via function nf. The normal form is given to resolve_tac, 
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presumably to instantiate a Boolean variable.*) 
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fun resop nf [prem] = resolve_tac (nf prem) 1; 
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18389  190 
val has_meta_conn = 
191 
exists_Const (fn (c,_) => c mem_string ["==", "==>", "all", "prop"]); 

192 

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(*Conjunctive normal form, adding clauses from th in front of ths (for foldr). 
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Strips universal quantifiers and breaks up conjunctions. 
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Eliminates existential quantifiers using skoths: Skolemization theorems.*) 
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fun cnf skoths (th,ths) = 
18389  197 
let fun cnf_aux (th,ths) = 
19894  198 
if has_meta_conn (prop_of th) then ths (*metalevel: ignore*) 
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else if not (has_conns ["All","Ex","op &"] (prop_of th)) 
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then th::ths (*no work to do, terminate*) 
16588  201 
else case head_of (HOLogic.dest_Trueprop (concl_of th)) of 
202 
Const ("op &", _) => (*conjunction*) 

18389  203 
cnf_aux (th RS conjunct1, 
204 
cnf_aux (th RS conjunct2, ths)) 

16588  205 
 Const ("All", _) => (*universal quantifier*) 
18389  206 
cnf_aux (freeze_spec th, ths) 
16588  207 
 Const ("Ex", _) => 
208 
(*existential quantifier: Insert Skolem functions*) 

18389  209 
cnf_aux (tryres (th,skoths), ths) 
16588  210 
 Const ("op ", _) => (*disjunction*) 
211 
let val tac = 

18389  212 
(METAHYPS (resop cnf_nil) 1) THEN 
19154  213 
(fn st' => st' > METAHYPS (resop cnf_nil) 1) 
16588  214 
in Seq.list_of (tac (th RS disj_forward)) @ ths end 
215 
 _ => (*no work to do*) th::ths 

19154  216 
and cnf_nil th = cnf_aux (th,[]) 
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in 
19894  218 
if nclauses (concl_of th) > 20 
219 
then (Output.debug ("cnf is ignoring: " ^ string_of_thm th); ths) 

220 
else cnf_aux (th,ths) 

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end; 
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16012  223 
(*Convert all suitable free variables to schematic variables, 
224 
but don't discharge assumptions.*) 

16173  225 
fun generalize th = Thm.varifyT (forall_elim_vars 0 (forall_intr_frees th)); 
16012  226 

18389  227 
fun make_cnf skoths th = 
228 
filter (not o is_taut) 

229 
(map (refl_clause o generalize) (cnf skoths (th, []))); 

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230 

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231 

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(**** Removal of duplicate literals ****) 
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233 

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(*Forward proof, passing extra assumptions as theorems to the tactic*) 
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fun forward_res2 nf hyps st = 
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case Seq.pull 
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(REPEAT 
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(METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1) 
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st) 
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of SOME(th,_) => th 
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 NONE => raise THM("forward_res2", 0, [st]); 
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242 

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(*Remove duplicates in PQ by assuming ~P in Q 
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rls (initially []) accumulates assumptions of the form P==>False*) 
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fun nodups_aux rls th = nodups_aux rls (th RS disj_assoc) 
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handle THM _ => tryres(th,rls) 
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handle THM _ => tryres(forward_res2 nodups_aux rls (th RS disj_forward2), 
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[disj_FalseD1, disj_FalseD2, asm_rl]) 
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handle THM _ => th; 
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250 

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(*Remove duplicate literals, if there are any*) 
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fun nodups th = 
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if null(findrep(literals(prop_of th))) then th 
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else nodups_aux [] th; 
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255 

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256 

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(**** Generation of contrapositives ****) 
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258 

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(*Associate disjuctions to right  make leftmost disjunct a LITERAL*) 
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fun assoc_right th = assoc_right (th RS disj_assoc) 
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handle THM _ => th; 
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262 

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(*Must check for negative literal first!*) 
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val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule]; 
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265 

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(*For ordinary resolution. *) 
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val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule']; 
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268 

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(*Create a goal or support clause, conclusing False*) 
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fun make_goal th = (*Must check for negative literal first!*) 
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make_goal (tryres(th, clause_rules)) 
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handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]); 
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273 

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(*Sort clauses by number of literals*) 
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fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2); 
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276 

18389  277 
fun sort_clauses ths = sort (make_ord fewerlits) ths; 
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278 

15581  279 
(*True if the given type contains bool anywhere*) 
280 
fun has_bool (Type("bool",_)) = true 

281 
 has_bool (Type(_, Ts)) = exists has_bool Ts 

282 
 has_bool _ = false; 

283 

15613  284 
(*Is the string the name of a connective? It doesn't matter if this list is 
285 
incomplete, since when actually called, the only connectives likely to 

286 
remain are &  Not.*) 

19875  287 
val is_conn = member (op =) 
20018  288 
["Trueprop", "op &", "op ", "op >", "op =", "Not", 
15613  289 
"All", "Ex", "Ball", "Bex"]; 
290 

291 
(*True if the term contains a function where the type of any argument contains 

292 
bool.*) 

293 
val has_bool_arg_const = 

294 
exists_Const 

295 
(fn (c,T) => not(is_conn c) andalso exists (has_bool) (binder_types T)); 

15908  296 

16588  297 
(*Raises an exception if any Vars in the theorem mention type bool; they 
298 
could cause make_horn to loop! Also rejects functions whose arguments are 

299 
Booleans or other functions.*) 

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fun is_fol_term t = 
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not (exists (has_bool o fastype_of) (term_vars t) orelse 
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not (Term.is_first_order ["all","All","Ex"] t) orelse 
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has_bool_arg_const t orelse 
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has_meta_conn t); 
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305 

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(*FIXME: replace this by the booleanvalued version above!*) 
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fun check_is_fol_term t = 
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308 
if is_fol_term t then t else raise TERM("check_is_fol_term",[t]); 
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309 

18508  310 
fun check_is_fol th = (check_is_fol_term (prop_of th); th); 
311 

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312 

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(*Create a metalevel Horn clause*) 
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fun make_horn crules th = make_horn crules (tryres(th,crules)) 
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handle THM _ => th; 
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16563  317 
(*Generate Horn clauses for all contrapositives of a clause. The input, th, 
318 
is a HOL disjunction.*) 

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fun add_contras crules (th,hcs) = 
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let fun rots (0,th) = hcs 
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 rots (k,th) = zero_var_indexes (make_horn crules th) :: 
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rots(k1, assoc_right (th RS disj_comm)) 
15862  323 
in case nliterals(prop_of th) of 
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1 => th::hcs 
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 n => rots(n, assoc_right th) 
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326 
end; 
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327 

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(*Use "theorem naming" to label the clauses*) 
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fun name_thms label = 
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let fun name1 (th, (k,ths)) = 
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(k1, Thm.name_thm (label ^ string_of_int k, th) :: ths) 
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332 

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in fn ths => #2 (foldr name1 (length ths, []) ths) end; 
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334 

16563  335 
(*Is the given disjunction an allnegative support clause?*) 
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fun is_negative th = forall (not o #1) (literals (prop_of th)); 
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337 

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val neg_clauses = List.filter is_negative; 
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339 

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340 

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(***** MESON PROOF PROCEDURE *****) 
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342 

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343 
fun rhyps (Const("==>",_) $ (Const("Trueprop",_) $ A) $ phi, 
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344 
As) = rhyps(phi, A::As) 
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345 
 rhyps (_, As) = As; 
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346 

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347 
(** Detecting repeated assumptions in a subgoal **) 
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348 

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349 
(*The stringtree detects repeated assumptions.*) 
16801  350 
fun ins_term (net,t) = Net.insert_term (op aconv) (t,t) net; 
9840
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351 

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352 
(*detects repetitions in a list of terms*) 
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353 
fun has_reps [] = false 
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354 
 has_reps [_] = false 
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355 
 has_reps [t,u] = (t aconv u) 
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356 
 has_reps ts = (Library.foldl ins_term (Net.empty, ts); false) 
19875  357 
handle Net.INSERT => true; 
9840
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358 

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359 
(*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*) 
18508  360 
fun TRYING_eq_assume_tac 0 st = Seq.single st 
361 
 TRYING_eq_assume_tac i st = 

362 
TRYING_eq_assume_tac (i1) (eq_assumption i st) 

363 
handle THM _ => TRYING_eq_assume_tac (i1) st; 

364 

365 
fun TRYALL_eq_assume_tac st = TRYING_eq_assume_tac (nprems_of st) st; 

9840
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366 

15579
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367 
(*Loop checking: FAIL if trying to prove the same thing twice 
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368 
 if *ANY* subgoal has repeated literals*) 
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369 
fun check_tac st = 
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370 
if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st) 
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371 
then Seq.empty else Seq.single st; 
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372 

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373 

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374 
(* net_resolve_tac actually made it slower... *) 
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375 
fun prolog_step_tac horns i = 
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376 
(assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN 
18508  377 
TRYALL_eq_assume_tac; 
9840
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378 

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379 
(*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*) 
15579
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380 
fun addconcl(prem,sz) = size_of_term(Logic.strip_assums_concl prem) + sz 
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381 

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382 
fun size_of_subgoals st = foldr addconcl 0 (prems_of st); 
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383 

9840
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384 

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changeset

385 
(*Negation Normal Form*) 
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changeset

386 
val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD, 
9869  387 
not_impD, not_iffD, not_allD, not_exD, not_notD]; 
15581  388 

389 
fun make_nnf1 th = make_nnf1 (tryres(th, nnf_rls)) 

9869  390 
handle THM _ => 
15581  391 
forward_res make_nnf1 
9869  392 
(tryres(th, [conj_forward,disj_forward,all_forward,ex_forward])) 
9840
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changeset

393 
handle THM _ => th; 
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394 

20018  395 
(*The simplification removes defined quantifiers and occurrences of True and False. 
396 
nnf_ss also includes the onepoint simprocs, 

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397 
which are needed to avoid the various onepoint theorems from generating junk clauses.*) 
19894  398 
val nnf_simps = 
20018  399 
[simp_implies_def, Ex1_def, Ball_def, Bex_def, if_True, 
19894  400 
if_False, if_cancel, if_eq_cancel, cases_simp]; 
401 
val nnf_extra_simps = 

402 
thms"split_ifs" @ ex_simps @ all_simps @ simp_thms; 

18405
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403 

afb1a52a7011
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changeset

404 
val nnf_ss = 
19894  405 
HOL_basic_ss addsimps nnf_extra_simps 
406 
addsimprocs [defALL_regroup,defEX_regroup,neq_simproc,let_simproc]; 

15872  407 

19894  408 
fun make_nnf th = th > rewrite_rule (map safe_mk_meta_eq nnf_simps) 
409 
> simplify nnf_ss (*But this doesn't simplify premises...*) 

18194
940515d2fa26
 removed "check_is_fol" from "make_nnf" so that the NNF procedure doesn't check whether a thm is FOL.
mengj
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diff
changeset

410 
> make_nnf1 
15581  411 

15965
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412 
(*Pull existential quantifiers to front. This accomplishes Skolemization for 
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
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changeset

413 
clauses that arise from a subgoal.*) 
9869  414 
fun skolemize th = 
20134
73cb53843190
has_consts renamed to has_conn, now actually parses the firstorder formula
paulson
parents:
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diff
changeset

415 
if not (has_conns ["Ex"] (prop_of th)) then th 
15773
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Completed integration of reconstruction code. Now finds and displays proofs when used with modified version
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416 
else (skolemize (tryres(th, [choice, conj_exD1, conj_exD2, 
15679
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Integrating the reconstruction files into the building of HOL
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changeset

417 
disj_exD, disj_exD1, disj_exD2]))) 
9869  418 
handle THM _ => 
419 
skolemize (forward_res skolemize 

420 
(tryres (th, [conj_forward, disj_forward, all_forward]))) 

9840
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421 
handle THM _ => forward_res skolemize (th RS ex_forward); 
9dfcb0224f8c
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paulson
parents:
diff
changeset

422 

9dfcb0224f8c
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paulson
parents:
diff
changeset

423 

9dfcb0224f8c
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424 
(*Make clauses from a list of theorems, previously Skolemized and put into nnf. 
9dfcb0224f8c
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425 
The resulting clauses are HOL disjunctions.*) 
9869  426 
fun make_clauses ths = 
15998
bc916036cf84
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paulson
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changeset

427 
(sort_clauses (map (generalize o nodups) (foldr (cnf[]) [] ths))); 
15773
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quigley
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changeset

428 

9840
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429 

16563  430 
(*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*) 
9869  431 
fun make_horns ths = 
9840
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changeset

432 
name_thms "Horn#" 
19046
bc5c6c9b114e
removed distinct, renamed gen_distinct to distinct;
wenzelm
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18817
diff
changeset

433 
(distinct Drule.eq_thm_prop (foldr (add_contras clause_rules) [] ths)); 
9840
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paulson
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changeset

434 

9dfcb0224f8c
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paulson
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diff
changeset

435 
(*Could simply use nprems_of, which would count remaining subgoals  no 
9dfcb0224f8c
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paulson
parents:
diff
changeset

436 
discrimination as to their size! With BEST_FIRST, fails for problem 41.*) 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

437 

9869  438 
fun best_prolog_tac sizef horns = 
9840
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paulson
parents:
diff
changeset

439 
BEST_FIRST (has_fewer_prems 1, sizef) (prolog_step_tac horns 1); 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
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diff
changeset

440 

9869  441 
fun depth_prolog_tac horns = 
9840
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paulson
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changeset

442 
DEPTH_FIRST (has_fewer_prems 1) (prolog_step_tac horns 1); 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

443 

9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

444 
(*Return all negative clauses, as possible goal clauses*) 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

445 
fun gocls cls = name_thms "Goal#" (map make_goal (neg_clauses cls)); 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

446 

15008  447 
fun skolemize_prems_tac prems = 
9840
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meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

448 
cut_facts_tac (map (skolemize o make_nnf) prems) THEN' 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

449 
REPEAT o (etac exE); 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

450 

18141
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Skolemization by inference, but not quite finished
paulson
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18024
diff
changeset

451 
(*Expand all definitions (presumably of Skolem functions) in a proof state.*) 
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
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18024
diff
changeset

452 
fun expand_defs_tac st = 
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
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diff
changeset

453 
let val defs = filter (can dest_equals) (#hyps (crep_thm st)) 
18817  454 
in LocalDefs.def_export false defs st end; 
18141
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset

455 

16588  456 
(*Basis of all mesontactics. Supplies cltac with clauses: HOL disjunctions*) 
457 
fun MESON cltac i st = 

458 
SELECT_GOAL 

18141
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Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset

459 
(EVERY [rtac ccontr 1, 
16588  460 
METAHYPS (fn negs => 
461 
EVERY1 [skolemize_prems_tac negs, 

18141
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset

462 
METAHYPS (cltac o make_clauses)]) 1, 
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset

463 
expand_defs_tac]) i st 
18508  464 
handle TERM _ => no_tac st; (*probably from check_is_fol*) 
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

465 

9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

466 
(** Bestfirst search versions **) 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

467 

16563  468 
(*ths is a list of additional clauses (HOL disjunctions) to use.*) 
9869  469 
fun best_meson_tac sizef = 
470 
MESON (fn cls => 

9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

471 
THEN_BEST_FIRST (resolve_tac (gocls cls) 1) 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

472 
(has_fewer_prems 1, sizef) 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

473 
(prolog_step_tac (make_horns cls) 1)); 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

474 

9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

475 
(*First, breaks the goal into independent units*) 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

476 
val safe_best_meson_tac = 
9869  477 
SELECT_GOAL (TRY Safe_tac THEN 
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

478 
TRYALL (best_meson_tac size_of_subgoals)); 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

479 

9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

480 
(** Depthfirst search version **) 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

481 

9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

482 
val depth_meson_tac = 
9869  483 
MESON (fn cls => EVERY [resolve_tac (gocls cls) 1, 
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

484 
depth_prolog_tac (make_horns cls)]); 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

485 

9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

486 

9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

487 
(** Iterative deepening version **) 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

488 

9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

489 
(*This version does only one inference per call; 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

490 
having only one eq_assume_tac speeds it up!*) 
9869  491 
fun prolog_step_tac' horns = 
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

492 
let val (horn0s, hornps) = (*0 subgoals vs 1 or more*) 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

493 
take_prefix Thm.no_prems horns 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

494 
val nrtac = net_resolve_tac horns 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

495 
in fn i => eq_assume_tac i ORELSE 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

496 
match_tac horn0s i ORELSE (*no backtracking if unit MATCHES*) 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

497 
((assume_tac i APPEND nrtac i) THEN check_tac) 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

498 
end; 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

499 

9869  500 
fun iter_deepen_prolog_tac horns = 
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

501 
ITER_DEEPEN (has_fewer_prems 1) (prolog_step_tac' horns); 
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

502 

16563  503 
fun iter_deepen_meson_tac ths = 
9869  504 
MESON (fn cls => 
16563  505 
case (gocls (cls@ths)) of 
506 
[] => no_tac (*no goal clauses*) 

507 
 goes => 

508 
(THEN_ITER_DEEPEN (resolve_tac goes 1) 

509 
(has_fewer_prems 1) 

510 
(prolog_step_tac' (make_horns (cls@ths))))); 

9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

511 

16563  512 
fun meson_claset_tac ths cs = 
513 
SELECT_GOAL (TRY (safe_tac cs) THEN TRYALL (iter_deepen_meson_tac ths)); 

9869  514 

16563  515 
val meson_tac = CLASET' (meson_claset_tac []); 
9869  516 

517 

14813  518 
(**** Code to support ordinary resolution, rather than Model Elimination ****) 
14744  519 

15008  520 
(*Convert a list of clauses (disjunctions) to metalevel clauses (==>), 
521 
with no contrapositives, for ordinary resolution.*) 

14744  522 

523 
(*Rules to convert the head literal into a negated assumption. If the head 

524 
literal is already negated, then using notEfalse instead of notEfalse' 

525 
prevents a double negation.*) 

526 
val notEfalse = read_instantiate [("R","False")] notE; 

527 
val notEfalse' = rotate_prems 1 notEfalse; 

528 

15448  529 
fun negated_asm_of_head th = 
14744  530 
th RS notEfalse handle THM _ => th RS notEfalse'; 
531 

532 
(*Converting one clause*) 

15581  533 
fun make_meta_clause th = 
16588  534 
negated_asm_of_head (make_horn resolution_clause_rules (check_is_fol th)); 
14744  535 

536 
fun make_meta_clauses ths = 

537 
name_thms "MClause#" 

19046
bc5c6c9b114e
removed distinct, renamed gen_distinct to distinct;
wenzelm
parents:
18817
diff
changeset

538 
(distinct Drule.eq_thm_prop (map make_meta_clause ths)); 
14744  539 

540 
(*Permute a rule's premises to move the ith premise to the last position.*) 

541 
fun make_last i th = 

542 
let val n = nprems_of th 

543 
in if 1 <= i andalso i <= n 

544 
then Thm.permute_prems (i1) 1 th 

15118  545 
else raise THM("select_literal", i, [th]) 
14744  546 
end; 
547 

548 
(*Maps a rule that ends "... ==> P ==> False" to "... ==> ~P" while suppressing 

549 
doublenegations.*) 

550 
val negate_head = rewrite_rule [atomize_not, not_not RS eq_reflection]; 

551 

552 
(*Maps the clause [P1,...Pn]==>False to [P1,...,P(i1),P(i+1),...Pn] ==> ~P*) 

553 
fun select_literal i cl = negate_head (make_last i cl); 

554 

18508  555 

14813  556 
(*Toplevel Skolemization. Allows part of the conversion to clauses to be 
557 
expressed as a tactic (or Isar method). Each assumption of the selected 

558 
goal is converted to NNF and then its existential quantifiers are pulled 

559 
to the front. Finally, all existential quantifiers are eliminated, 

560 
leaving !!quantified variables. Perhaps Safe_tac should follow, but it 

561 
might generate many subgoals.*) 

18194
940515d2fa26
 removed "check_is_fol" from "make_nnf" so that the NNF procedure doesn't check whether a thm is FOL.
mengj
parents:
18175
diff
changeset

562 

19204
b8f7de7ef629
Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents:
19154
diff
changeset

563 
fun skolemize_tac i st = 
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Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents:
19154
diff
changeset

564 
let val ts = Logic.strip_assums_hyp (List.nth (prems_of st, i1)) 
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Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents:
19154
diff
changeset

565 
in 
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Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents:
19154
diff
changeset

566 
EVERY' [METAHYPS 
15773
f14ae2432710
Completed integration of reconstruction code. Now finds and displays proofs when used with modified version
quigley
parents:
15736
diff
changeset

567 
(fn hyps => (cut_facts_tac (map (skolemize o make_nnf) hyps) 1 
14813  568 
THEN REPEAT (etac exE 1))), 
19204
b8f7de7ef629
Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents:
19154
diff
changeset

569 
REPEAT_DETERM_N (length ts) o (etac thin_rl)] i st 
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Tidying, and getting rid of SELECT_GOAL (as it does something different now)
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diff
changeset

570 
end 
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Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents:
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diff
changeset

571 
handle Subscript => Seq.empty; 
18194
940515d2fa26
 removed "check_is_fol" from "make_nnf" so that the NNF procedure doesn't check whether a thm is FOL.
mengj
parents:
18175
diff
changeset

572 

15118  573 
(*Toplevel conversion to metalevel clauses. Each clause has 
574 
leading !!bound universal variables, to express generality. To get 

575 
disjunctions instead of metaclauses, remove "make_meta_clauses" below.*) 

15008  576 
val make_clauses_tac = 
577 
SUBGOAL 

578 
(fn (prop,_) => 

579 
let val ts = Logic.strip_assums_hyp prop 

580 
in EVERY1 

581 
[METAHYPS 

582 
(fn hyps => 

15151  583 
(Method.insert_tac 
15118  584 
(map forall_intr_vars 
585 
(make_meta_clauses (make_clauses hyps))) 1)), 

15008  586 
REPEAT_DETERM_N (length ts) o (etac thin_rl)] 
587 
end); 

16563  588 

589 

590 
(*** setup the special skoklemization methods ***) 

9869  591 

16563  592 
(*No CHANGED_PROP here, since these always appear in the preamble*) 
9869  593 

16563  594 
val skolemize_meth = Method.SIMPLE_METHOD' HEADGOAL skolemize_tac; 
595 

596 
val make_clauses_meth = Method.SIMPLE_METHOD' HEADGOAL make_clauses_tac; 

14890  597 

16563  598 
val skolemize_setup = 
18708  599 
Method.add_methods 
600 
[("skolemize", Method.no_args skolemize_meth, 

601 
"Skolemization into existential quantifiers"), 

602 
("make_clauses", Method.no_args make_clauses_meth, 

603 
"Conversion to !!quantified metalevel clauses")]; 

9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

604 

9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset

605 
end; 
9869  606 

15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset

607 
structure BasicMeson: BASIC_MESON = Meson; 
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset

608 
open BasicMeson; 