author | wenzelm |
Sat, 28 Jan 2006 17:28:51 +0100 | |
changeset 18817 | ad8bc3e55aa3 |
parent 18752 | c9c6ae9e8b88 |
child 19046 | bc5c6c9b114e |
permissions | -rw-r--r-- |
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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|
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When making clauses, avoids using the rewriter -- instead uses RS recursively |
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|
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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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|
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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 : thm -> thm |
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val check_is_fol_term : term -> term |
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end |
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|
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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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|
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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 => 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 constants in "bs" present in the term?*) |
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fun has_consts bs = |
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let fun has (Const(a,_)) = a mem bs |
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| has (Const ("Hilbert_Choice.Eps",_) $ _) = false |
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(*ignore constants within @-terms*) |
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| has (f$u) = has f orelse has u |
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| has (Abs(_,_,t)) = has t |
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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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(*Generation of unique names -- maxidx cannot be relied upon to increase! |
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Cannot rely on "variant", since variables might coincide when literals |
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are joined to make a clause... |
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19 chooses "U" as the first variable name*) |
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val name_ref = ref 19; |
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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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||
128 |
fun is_taut th = |
|
129 |
let val (poslits,neglits) = signed_lits th |
|
130 |
in exists taut_poslit poslits |
|
131 |
orelse |
|
132 |
exists (fn t => mem_term (t, neglits)) (HOLogic.false_const :: poslits) |
|
133 |
end; |
|
134 |
||
135 |
||
136 |
(*** To remove trivial negated equality literals from clauses ***) |
|
137 |
||
138 |
(*They are typically functional reflexivity axioms and are the converses of |
|
139 |
injectivity equivalences*) |
|
140 |
||
141 |
val not_refl_disj_D = thm"meson_not_refl_disj_D"; |
|
142 |
||
143 |
fun refl_clause_aux 0 th = th |
|
144 |
| refl_clause_aux n th = |
|
145 |
case HOLogic.dest_Trueprop (concl_of th) of |
|
146 |
(Const ("op |", _) $ (Const ("op |", _) $ _ $ _) $ _) => |
|
147 |
refl_clause_aux n (th RS disj_assoc) (*isolate an atom as first disjunct*) |
|
148 |
| (Const ("op |", _) $ (Const("Not",_) $ (Const("op =",_) $ t $ u)) $ _) => |
|
149 |
if is_Var t orelse is_Var u then (*Var inequation: delete or ignore*) |
|
150 |
(refl_clause_aux (n-1) (th RS not_refl_disj_D) (*delete*) |
|
151 |
handle THM _ => refl_clause_aux (n-1) (th RS disj_comm)) (*ignore*) |
|
152 |
else refl_clause_aux (n-1) (th RS disj_comm) (*not between Vars: ignore*) |
|
153 |
| (Const ("op |", _) $ _ $ _) => refl_clause_aux n (th RS disj_comm) |
|
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| _ => (*not a disjunction*) th; |
18389 | 155 |
|
156 |
fun notequal_lits_count (Const ("op |", _) $ P $ Q) = |
|
157 |
notequal_lits_count P + notequal_lits_count Q |
|
158 |
| notequal_lits_count (Const("Not",_) $ (Const("op =",_) $ _ $ _)) = 1 |
|
159 |
| notequal_lits_count _ = 0; |
|
160 |
||
161 |
(*Simplify a clause by applying reflexivity to its negated equality literals*) |
|
162 |
fun refl_clause th = |
|
163 |
let val neqs = notequal_lits_count (HOLogic.dest_Trueprop (concl_of th)) |
|
164 |
in zero_var_indexes (refl_clause_aux neqs th) end; |
|
165 |
||
166 |
||
167 |
(*** The basic CNF transformation ***) |
|
168 |
||
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169 |
(*Replaces universally quantified variables by FREE variables -- because |
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170 |
assumptions may not contain scheme variables. Later, call "generalize". *) |
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171 |
fun freeze_spec th = |
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172 |
let val sth = th RS spec |
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173 |
val newname = (name_ref := !name_ref + 1; |
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174 |
radixstring(26, "A", !name_ref)) |
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in read_instantiate [("x", newname)] sth end; |
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176 |
|
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177 |
(*Used with METAHYPS below. There is one assumption, which gets bound to prem |
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178 |
and then normalized via function nf. The normal form is given to resolve_tac, |
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179 |
presumably to instantiate a Boolean variable.*) |
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180 |
fun resop nf [prem] = resolve_tac (nf prem) 1; |
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181 |
|
18389 | 182 |
val has_meta_conn = |
183 |
exists_Const (fn (c,_) => c mem_string ["==", "==>", "all", "prop"]); |
|
184 |
||
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185 |
(*Conjunctive normal form, adding clauses from th in front of ths (for foldr). |
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|
186 |
Strips universal quantifiers and breaks up conjunctions. |
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|
187 |
Eliminates existential quantifiers using skoths: Skolemization theorems.*) |
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|
188 |
fun cnf skoths (th,ths) = |
18389 | 189 |
let fun cnf_aux (th,ths) = |
190 |
if has_meta_conn (prop_of th) then ths (*meta-level: ignore*) |
|
191 |
else if not (has_consts ["All","Ex","op &"] (prop_of th)) |
|
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192 |
then th::ths (*no work to do, terminate*) |
16588 | 193 |
else case head_of (HOLogic.dest_Trueprop (concl_of th)) of |
194 |
Const ("op &", _) => (*conjunction*) |
|
18389 | 195 |
cnf_aux (th RS conjunct1, |
196 |
cnf_aux (th RS conjunct2, ths)) |
|
16588 | 197 |
| Const ("All", _) => (*universal quantifier*) |
18389 | 198 |
cnf_aux (freeze_spec th, ths) |
16588 | 199 |
| Const ("Ex", _) => |
200 |
(*existential quantifier: Insert Skolem functions*) |
|
18389 | 201 |
cnf_aux (tryres (th,skoths), ths) |
16588 | 202 |
| Const ("op |", _) => (*disjunction*) |
203 |
let val tac = |
|
18389 | 204 |
(METAHYPS (resop cnf_nil) 1) THEN |
16588 | 205 |
(fn st' => st' |> |
206 |
METAHYPS |
|
18389 | 207 |
(resop cnf_nil) 1) |
16588 | 208 |
in Seq.list_of (tac (th RS disj_forward)) @ ths end |
209 |
| _ => (*no work to do*) th::ths |
|
18389 | 210 |
and cnf_nil th = (cnf_aux (th,[])) |
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|
211 |
in |
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|
212 |
name_ref := 19; (*It's safe to reset this in a top-level call to cnf*) |
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|
213 |
(cnf skoths (th RS conjunct1, cnf skoths (th RS conjunct2, ths)) |
18389 | 214 |
handle THM _ => (*not a conjunction*) cnf_aux (th, ths)) |
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|
215 |
end; |
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|
216 |
|
16012 | 217 |
(*Convert all suitable free variables to schematic variables, |
218 |
but don't discharge assumptions.*) |
|
16173 | 219 |
fun generalize th = Thm.varifyT (forall_elim_vars 0 (forall_intr_frees th)); |
16012 | 220 |
|
18389 | 221 |
fun make_cnf skoths th = |
222 |
filter (not o is_taut) |
|
223 |
(map (refl_clause o generalize) (cnf skoths (th, []))); |
|
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|
224 |
|
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|
225 |
|
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|
226 |
(**** Removal of duplicate literals ****) |
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|
227 |
|
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|
228 |
(*Forward proof, passing extra assumptions as theorems to the tactic*) |
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|
229 |
fun forward_res2 nf hyps st = |
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|
230 |
case Seq.pull |
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|
231 |
(REPEAT |
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|
232 |
(METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1) |
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|
233 |
st) |
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|
234 |
of SOME(th,_) => th |
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|
235 |
| NONE => raise THM("forward_res2", 0, [st]); |
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|
236 |
|
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|
237 |
(*Remove duplicates in P|Q by assuming ~P in Q |
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|
238 |
rls (initially []) accumulates assumptions of the form P==>False*) |
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|
239 |
fun nodups_aux rls th = nodups_aux rls (th RS disj_assoc) |
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|
240 |
handle THM _ => tryres(th,rls) |
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|
241 |
handle THM _ => tryres(forward_res2 nodups_aux rls (th RS disj_forward2), |
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|
242 |
[disj_FalseD1, disj_FalseD2, asm_rl]) |
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|
243 |
handle THM _ => th; |
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changeset
|
244 |
|
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|
245 |
(*Remove duplicate literals, if there are any*) |
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|
246 |
fun nodups th = |
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|
247 |
if null(findrep(literals(prop_of th))) then th |
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|
248 |
else nodups_aux [] th; |
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|
249 |
|
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|
250 |
|
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|
251 |
(**** Generation of contrapositives ****) |
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|
252 |
|
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|
253 |
(*Associate disjuctions to right -- make leftmost disjunct a LITERAL*) |
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|
254 |
fun assoc_right th = assoc_right (th RS disj_assoc) |
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|
255 |
handle THM _ => th; |
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changeset
|
256 |
|
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|
257 |
(*Must check for negative literal first!*) |
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|
258 |
val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule]; |
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|
259 |
|
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|
260 |
(*For ordinary resolution. *) |
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|
261 |
val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule']; |
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|
262 |
|
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|
263 |
(*Create a goal or support clause, conclusing False*) |
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|
264 |
fun make_goal th = (*Must check for negative literal first!*) |
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|
265 |
make_goal (tryres(th, clause_rules)) |
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|
266 |
handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]); |
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|
267 |
|
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|
268 |
(*Sort clauses by number of literals*) |
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|
269 |
fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2); |
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|
270 |
|
18389 | 271 |
fun sort_clauses ths = sort (make_ord fewerlits) ths; |
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|
272 |
|
15581 | 273 |
(*True if the given type contains bool anywhere*) |
274 |
fun has_bool (Type("bool",_)) = true |
|
275 |
| has_bool (Type(_, Ts)) = exists has_bool Ts |
|
276 |
| has_bool _ = false; |
|
277 |
||
15613 | 278 |
(*Is the string the name of a connective? It doesn't matter if this list is |
279 |
incomplete, since when actually called, the only connectives likely to |
|
280 |
remain are & | Not.*) |
|
281 |
fun is_conn c = c mem_string |
|
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|
282 |
["Trueprop", "HOL.tag", "op &", "op |", "op -->", "op =", "Not", |
15613 | 283 |
"All", "Ex", "Ball", "Bex"]; |
284 |
||
285 |
(*True if the term contains a function where the type of any argument contains |
|
286 |
bool.*) |
|
287 |
val has_bool_arg_const = |
|
288 |
exists_Const |
|
289 |
(fn (c,T) => not(is_conn c) andalso exists (has_bool) (binder_types T)); |
|
15908 | 290 |
|
16588 | 291 |
(*Raises an exception if any Vars in the theorem mention type bool; they |
292 |
could cause make_horn to loop! Also rejects functions whose arguments are |
|
293 |
Booleans or other functions.*) |
|
18194
940515d2fa26
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|
294 |
fun check_is_fol_term term = |
940515d2fa26
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|
295 |
if exists (has_bool o fastype_of) (term_vars term) orelse |
940515d2fa26
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|
296 |
not (Term.is_first_order ["all","All","Ex"] term) orelse |
940515d2fa26
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|
297 |
has_bool_arg_const term orelse |
940515d2fa26
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|
298 |
has_meta_conn term |
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|
299 |
then raise TERM("check_is_fol_term",[term]) else term; |
940515d2fa26
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|
300 |
|
18508 | 301 |
fun check_is_fol th = (check_is_fol_term (prop_of th); th); |
302 |
||
18194
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|
303 |
|
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|
304 |
(*Create a meta-level Horn clause*) |
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|
305 |
fun make_horn crules th = make_horn crules (tryres(th,crules)) |
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306 |
handle THM _ => th; |
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|
307 |
|
16563 | 308 |
(*Generate Horn clauses for all contrapositives of a clause. The input, th, |
309 |
is a HOL disjunction.*) |
|
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310 |
fun add_contras crules (th,hcs) = |
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|
311 |
let fun rots (0,th) = hcs |
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312 |
| rots (k,th) = zero_var_indexes (make_horn crules th) :: |
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|
313 |
rots(k-1, assoc_right (th RS disj_comm)) |
15862 | 314 |
in case nliterals(prop_of th) of |
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|
315 |
1 => th::hcs |
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|
316 |
| n => rots(n, assoc_right th) |
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|
317 |
end; |
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|
318 |
|
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|
319 |
(*Use "theorem naming" to label the clauses*) |
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|
320 |
fun name_thms label = |
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changeset
|
321 |
let fun name1 (th, (k,ths)) = |
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|
322 |
(k-1, Thm.name_thm (label ^ string_of_int k, th) :: ths) |
9840
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diff
changeset
|
323 |
|
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|
324 |
in fn ths => #2 (foldr name1 (length ths, []) ths) end; |
9840
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changeset
|
325 |
|
16563 | 326 |
(*Is the given disjunction an all-negative support clause?*) |
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|
327 |
fun is_negative th = forall (not o #1) (literals (prop_of th)); |
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diff
changeset
|
328 |
|
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|
329 |
val neg_clauses = List.filter is_negative; |
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diff
changeset
|
330 |
|
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parents:
diff
changeset
|
331 |
|
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|
332 |
(***** MESON PROOF PROCEDURE *****) |
9840
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meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
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changeset
|
333 |
|
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|
334 |
fun rhyps (Const("==>",_) $ (Const("Trueprop",_) $ A) $ phi, |
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|
335 |
As) = rhyps(phi, A::As) |
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changeset
|
336 |
| rhyps (_, As) = As; |
9840
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meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
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changeset
|
337 |
|
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changeset
|
338 |
(** Detecting repeated assumptions in a subgoal **) |
9840
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parents:
diff
changeset
|
339 |
|
15579
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changeset
|
340 |
(*The stringtree detects repeated assumptions.*) |
16801 | 341 |
fun ins_term (net,t) = Net.insert_term (op aconv) (t,t) net; |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
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parents:
diff
changeset
|
342 |
|
15579
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changeset
|
343 |
(*detects repetitions in a list of terms*) |
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changeset
|
344 |
fun has_reps [] = false |
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changeset
|
345 |
| has_reps [_] = false |
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changeset
|
346 |
| has_reps [t,u] = (t aconv u) |
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changeset
|
347 |
| has_reps ts = (Library.foldl ins_term (Net.empty, ts); false) |
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changeset
|
348 |
handle INSERT => true; |
9840
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meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
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diff
changeset
|
349 |
|
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changeset
|
350 |
(*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*) |
18508 | 351 |
fun TRYING_eq_assume_tac 0 st = Seq.single st |
352 |
| TRYING_eq_assume_tac i st = |
|
353 |
TRYING_eq_assume_tac (i-1) (eq_assumption i st) |
|
354 |
handle THM _ => TRYING_eq_assume_tac (i-1) st; |
|
355 |
||
356 |
fun TRYALL_eq_assume_tac st = TRYING_eq_assume_tac (nprems_of st) st; |
|
9840
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meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
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parents:
diff
changeset
|
357 |
|
15579
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changeset
|
358 |
(*Loop checking: FAIL if trying to prove the same thing twice |
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Tools/meson.ML: signature, structure and "open" rather than "local"
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diff
changeset
|
359 |
-- if *ANY* subgoal has repeated literals*) |
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Tools/meson.ML: signature, structure and "open" rather than "local"
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diff
changeset
|
360 |
fun check_tac st = |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
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parents:
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diff
changeset
|
361 |
if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st) |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
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changeset
|
362 |
then Seq.empty else Seq.single st; |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
363 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
364 |
|
15579
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Tools/meson.ML: signature, structure and "open" rather than "local"
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parents:
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diff
changeset
|
365 |
(* net_resolve_tac actually made it slower... *) |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
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diff
changeset
|
366 |
fun prolog_step_tac horns i = |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
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diff
changeset
|
367 |
(assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN |
18508 | 368 |
TRYALL_eq_assume_tac; |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
369 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
370 |
(*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*) |
15579
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changeset
|
371 |
fun addconcl(prem,sz) = size_of_term(Logic.strip_assums_concl prem) + sz |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
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diff
changeset
|
372 |
|
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Tools/meson.ML: signature, structure and "open" rather than "local"
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diff
changeset
|
373 |
fun size_of_subgoals st = foldr addconcl 0 (prems_of st); |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
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diff
changeset
|
374 |
|
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
375 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
376 |
(*Negation Normal Form*) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
377 |
val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD, |
9869 | 378 |
not_impD, not_iffD, not_allD, not_exD, not_notD]; |
15581 | 379 |
|
380 |
fun make_nnf1 th = make_nnf1 (tryres(th, nnf_rls)) |
|
9869 | 381 |
handle THM _ => |
15581 | 382 |
forward_res make_nnf1 |
9869 | 383 |
(tryres(th, [conj_forward,disj_forward,all_forward,ex_forward])) |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
384 |
handle THM _ => th; |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
385 |
|
18405
afb1a52a7011
removal of some redundancies (e.g. one-point-rules) in clause production
paulson
parents:
18389
diff
changeset
|
386 |
(*The simplification removes defined quantifiers and occurrences of True and False, |
afb1a52a7011
removal of some redundancies (e.g. one-point-rules) in clause production
paulson
parents:
18389
diff
changeset
|
387 |
as well as tags applied to True and False. nnf_ss also includes the one-point simprocs, |
afb1a52a7011
removal of some redundancies (e.g. one-point-rules) in clause production
paulson
parents:
18389
diff
changeset
|
388 |
which are needed to avoid the various one-point theorems from generating junk clauses.*) |
17404
d16c3a62c396
the experimental tagging system, and the usual tidying
paulson
parents:
16801
diff
changeset
|
389 |
val tag_True = thm "tag_True"; |
d16c3a62c396
the experimental tagging system, and the usual tidying
paulson
parents:
16801
diff
changeset
|
390 |
val tag_False = thm "tag_False"; |
d16c3a62c396
the experimental tagging system, and the usual tidying
paulson
parents:
16801
diff
changeset
|
391 |
val nnf_simps = [Ex1_def,Ball_def,Bex_def,tag_True,tag_False] |
18405
afb1a52a7011
removal of some redundancies (e.g. one-point-rules) in clause production
paulson
parents:
18389
diff
changeset
|
392 |
|
afb1a52a7011
removal of some redundancies (e.g. one-point-rules) in clause production
paulson
parents:
18389
diff
changeset
|
393 |
val nnf_ss = |
afb1a52a7011
removal of some redundancies (e.g. one-point-rules) in clause production
paulson
parents:
18389
diff
changeset
|
394 |
HOL_basic_ss addsimps |
18752
c9c6ae9e8b88
Clausification now handles some IFs in rewrite rules (if-split did not work)
paulson
parents:
18708
diff
changeset
|
395 |
(nnf_simps @ [if_True, if_False, if_cancel, if_eq_cancel, cases_simp] @ |
c9c6ae9e8b88
Clausification now handles some IFs in rewrite rules (if-split did not work)
paulson
parents:
18708
diff
changeset
|
396 |
thms"split_ifs" @ ex_simps @ all_simps @ simp_thms) |
c9c6ae9e8b88
Clausification now handles some IFs in rewrite rules (if-split did not work)
paulson
parents:
18708
diff
changeset
|
397 |
addsimprocs [defALL_regroup,defEX_regroup,neq_simproc,let_simproc]; |
15872 | 398 |
|
399 |
fun make_nnf th = th |> simplify nnf_ss |
|
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
|
400 |
|> make_nnf1 |
15581 | 401 |
|
15965
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15946
diff
changeset
|
402 |
(*Pull existential quantifiers to front. This accomplishes Skolemization for |
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15946
diff
changeset
|
403 |
clauses that arise from a subgoal.*) |
9869 | 404 |
fun skolemize th = |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
405 |
if not (has_consts ["Ex"] (prop_of th)) then th |
15773
f14ae2432710
Completed integration of reconstruction code. Now finds and displays proofs when used with modified version
quigley
parents:
15736
diff
changeset
|
406 |
else (skolemize (tryres(th, [choice, conj_exD1, conj_exD2, |
15679
28eb0fe50533
Integrating the reconstruction files into the building of HOL
quigley
parents:
15653
diff
changeset
|
407 |
disj_exD, disj_exD1, disj_exD2]))) |
9869 | 408 |
handle THM _ => |
409 |
skolemize (forward_res skolemize |
|
410 |
(tryres (th, [conj_forward, disj_forward, all_forward]))) |
|
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
411 |
handle THM _ => forward_res skolemize (th RS ex_forward); |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
412 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
413 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
414 |
(*Make clauses from a list of theorems, previously Skolemized and put into nnf. |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
415 |
The resulting clauses are HOL disjunctions.*) |
9869 | 416 |
fun make_clauses ths = |
15998
bc916036cf84
new cnf function taking Skolemization theorems as an extra argument
paulson
parents:
15965
diff
changeset
|
417 |
(sort_clauses (map (generalize o nodups) (foldr (cnf[]) [] ths))); |
15773
f14ae2432710
Completed integration of reconstruction code. Now finds and displays proofs when used with modified version
quigley
parents:
15736
diff
changeset
|
418 |
|
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
419 |
|
16563 | 420 |
(*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*) |
9869 | 421 |
fun make_horns ths = |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
422 |
name_thms "Horn#" |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
423 |
(gen_distinct Drule.eq_thm_prop (foldr (add_contras clause_rules) [] ths)); |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
424 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
425 |
(*Could simply use nprems_of, which would count remaining subgoals -- no |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
426 |
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
|
427 |
|
9869 | 428 |
fun best_prolog_tac sizef horns = |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
429 |
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
parents:
diff
changeset
|
430 |
|
9869 | 431 |
fun depth_prolog_tac horns = |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
432 |
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
|
433 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
434 |
(*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
|
435 |
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
|
436 |
|
15008 | 437 |
fun skolemize_prems_tac prems = |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
438 |
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
|
439 |
REPEAT o (etac exE); |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
440 |
|
18141
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset
|
441 |
(*Expand all definitions (presumably of Skolem functions) in a proof state.*) |
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset
|
442 |
fun expand_defs_tac st = |
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset
|
443 |
let val defs = filter (can dest_equals) (#hyps (crep_thm st)) |
18817 | 444 |
in LocalDefs.def_export false defs st end; |
18141
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset
|
445 |
|
16588 | 446 |
(*Basis of all meson-tactics. Supplies cltac with clauses: HOL disjunctions*) |
447 |
fun MESON cltac i st = |
|
448 |
SELECT_GOAL |
|
18141
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset
|
449 |
(EVERY [rtac ccontr 1, |
16588 | 450 |
METAHYPS (fn negs => |
451 |
EVERY1 [skolemize_prems_tac negs, |
|
18141
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset
|
452 |
METAHYPS (cltac o make_clauses)]) 1, |
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset
|
453 |
expand_defs_tac]) i st |
18508 | 454 |
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
|
455 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
456 |
(** Best-first search versions **) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
457 |
|
16563 | 458 |
(*ths is a list of additional clauses (HOL disjunctions) to use.*) |
9869 | 459 |
fun best_meson_tac sizef = |
460 |
MESON (fn cls => |
|
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
461 |
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
|
462 |
(has_fewer_prems 1, sizef) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
463 |
(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
|
464 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
465 |
(*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
|
466 |
val safe_best_meson_tac = |
9869 | 467 |
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
|
468 |
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
|
469 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
470 |
(** Depth-first search version **) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
471 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
472 |
val depth_meson_tac = |
9869 | 473 |
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
|
474 |
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
|
475 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
476 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
477 |
(** Iterative deepening version **) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
478 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
479 |
(*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
|
480 |
having only one eq_assume_tac speeds it up!*) |
9869 | 481 |
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
|
482 |
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
|
483 |
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
|
484 |
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
|
485 |
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
|
486 |
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
|
487 |
((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
|
488 |
end; |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
489 |
|
9869 | 490 |
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
|
491 |
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
|
492 |
|
16563 | 493 |
fun iter_deepen_meson_tac ths = |
9869 | 494 |
MESON (fn cls => |
16563 | 495 |
case (gocls (cls@ths)) of |
496 |
[] => no_tac (*no goal clauses*) |
|
497 |
| goes => |
|
498 |
(THEN_ITER_DEEPEN (resolve_tac goes 1) |
|
499 |
(has_fewer_prems 1) |
|
500 |
(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
|
501 |
|
16563 | 502 |
fun meson_claset_tac ths cs = |
503 |
SELECT_GOAL (TRY (safe_tac cs) THEN TRYALL (iter_deepen_meson_tac ths)); |
|
9869 | 504 |
|
16563 | 505 |
val meson_tac = CLASET' (meson_claset_tac []); |
9869 | 506 |
|
507 |
||
14813 | 508 |
(**** Code to support ordinary resolution, rather than Model Elimination ****) |
14744 | 509 |
|
15008 | 510 |
(*Convert a list of clauses (disjunctions) to meta-level clauses (==>), |
511 |
with no contrapositives, for ordinary resolution.*) |
|
14744 | 512 |
|
513 |
(*Rules to convert the head literal into a negated assumption. If the head |
|
514 |
literal is already negated, then using notEfalse instead of notEfalse' |
|
515 |
prevents a double negation.*) |
|
516 |
val notEfalse = read_instantiate [("R","False")] notE; |
|
517 |
val notEfalse' = rotate_prems 1 notEfalse; |
|
518 |
||
15448 | 519 |
fun negated_asm_of_head th = |
14744 | 520 |
th RS notEfalse handle THM _ => th RS notEfalse'; |
521 |
||
522 |
(*Converting one clause*) |
|
15581 | 523 |
fun make_meta_clause th = |
16588 | 524 |
negated_asm_of_head (make_horn resolution_clause_rules (check_is_fol th)); |
14744 | 525 |
|
526 |
fun make_meta_clauses ths = |
|
527 |
name_thms "MClause#" |
|
528 |
(gen_distinct Drule.eq_thm_prop (map make_meta_clause ths)); |
|
529 |
||
530 |
(*Permute a rule's premises to move the i-th premise to the last position.*) |
|
531 |
fun make_last i th = |
|
532 |
let val n = nprems_of th |
|
533 |
in if 1 <= i andalso i <= n |
|
534 |
then Thm.permute_prems (i-1) 1 th |
|
15118 | 535 |
else raise THM("select_literal", i, [th]) |
14744 | 536 |
end; |
537 |
||
538 |
(*Maps a rule that ends "... ==> P ==> False" to "... ==> ~P" while suppressing |
|
539 |
double-negations.*) |
|
540 |
val negate_head = rewrite_rule [atomize_not, not_not RS eq_reflection]; |
|
541 |
||
542 |
(*Maps the clause [P1,...Pn]==>False to [P1,...,P(i-1),P(i+1),...Pn] ==> ~P*) |
|
543 |
fun select_literal i cl = negate_head (make_last i cl); |
|
544 |
||
18508 | 545 |
|
14813 | 546 |
(*Top-level Skolemization. Allows part of the conversion to clauses to be |
547 |
expressed as a tactic (or Isar method). Each assumption of the selected |
|
548 |
goal is converted to NNF and then its existential quantifiers are pulled |
|
549 |
to the front. Finally, all existential quantifiers are eliminated, |
|
550 |
leaving !!-quantified variables. Perhaps Safe_tac should follow, but it |
|
551 |
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
|
552 |
|
14813 | 553 |
val skolemize_tac = |
554 |
SUBGOAL |
|
555 |
(fn (prop,_) => |
|
556 |
let val ts = Logic.strip_assums_hyp prop |
|
557 |
in EVERY1 |
|
558 |
[METAHYPS |
|
15773
f14ae2432710
Completed integration of reconstruction code. Now finds and displays proofs when used with modified version
quigley
parents:
15736
diff
changeset
|
559 |
(fn hyps => (cut_facts_tac (map (skolemize o make_nnf) hyps) 1 |
14813 | 560 |
THEN REPEAT (etac exE 1))), |
561 |
REPEAT_DETERM_N (length ts) o (etac thin_rl)] |
|
562 |
end); |
|
563 |
||
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
|
564 |
|
15118 | 565 |
(*Top-level conversion to meta-level clauses. Each clause has |
566 |
leading !!-bound universal variables, to express generality. To get |
|
567 |
disjunctions instead of meta-clauses, remove "make_meta_clauses" below.*) |
|
15008 | 568 |
val make_clauses_tac = |
569 |
SUBGOAL |
|
570 |
(fn (prop,_) => |
|
571 |
let val ts = Logic.strip_assums_hyp prop |
|
572 |
in EVERY1 |
|
573 |
[METAHYPS |
|
574 |
(fn hyps => |
|
15151 | 575 |
(Method.insert_tac |
15118 | 576 |
(map forall_intr_vars |
577 |
(make_meta_clauses (make_clauses hyps))) 1)), |
|
15008 | 578 |
REPEAT_DETERM_N (length ts) o (etac thin_rl)] |
579 |
end); |
|
16563 | 580 |
|
581 |
||
582 |
(*** setup the special skoklemization methods ***) |
|
9869 | 583 |
|
16563 | 584 |
(*No CHANGED_PROP here, since these always appear in the preamble*) |
9869 | 585 |
|
16563 | 586 |
val skolemize_meth = Method.SIMPLE_METHOD' HEADGOAL skolemize_tac; |
587 |
||
588 |
val make_clauses_meth = Method.SIMPLE_METHOD' HEADGOAL make_clauses_tac; |
|
14890 | 589 |
|
16563 | 590 |
val skolemize_setup = |
18708 | 591 |
Method.add_methods |
592 |
[("skolemize", Method.no_args skolemize_meth, |
|
593 |
"Skolemization into existential quantifiers"), |
|
594 |
("make_clauses", Method.no_args make_clauses_meth, |
|
595 |
"Conversion to !!-quantified meta-level clauses")]; |
|
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
596 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
597 |
end; |
9869 | 598 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
599 |
structure BasicMeson: BASIC_MESON = Meson; |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
600 |
open BasicMeson; |