--- a/src/HOL/Tools/meson.ML Fri Mar 04 23:25:06 2005 +0100
+++ b/src/HOL/Tools/meson.ML Mon Mar 07 16:55:36 2005 +0100
@@ -11,236 +11,264 @@
FUNCTION nodups -- if done to goal clauses too!
*)
-local
-
- val not_conjD = thm "meson_not_conjD";
- val not_disjD = thm "meson_not_disjD";
- val not_notD = thm "meson_not_notD";
- val not_allD = thm "meson_not_allD";
- val not_exD = thm "meson_not_exD";
- val imp_to_disjD = thm "meson_imp_to_disjD";
- val not_impD = thm "meson_not_impD";
- val iff_to_disjD = thm "meson_iff_to_disjD";
- val not_iffD = thm "meson_not_iffD";
- val conj_exD1 = thm "meson_conj_exD1";
- val conj_exD2 = thm "meson_conj_exD2";
- val disj_exD = thm "meson_disj_exD";
- val disj_exD1 = thm "meson_disj_exD1";
- val disj_exD2 = thm "meson_disj_exD2";
- val disj_assoc = thm "meson_disj_assoc";
- val disj_comm = thm "meson_disj_comm";
- val disj_FalseD1 = thm "meson_disj_FalseD1";
- val disj_FalseD2 = thm "meson_disj_FalseD2";
+signature BASIC_MESON =
+sig
+ val size_of_subgoals : thm -> int
+ val make_nnf : thm -> thm
+ val skolemize : thm -> thm
+ val make_clauses : thm list -> thm list
+ val make_horns : thm list -> thm list
+ val best_prolog_tac : (thm -> int) -> thm list -> tactic
+ val depth_prolog_tac : thm list -> tactic
+ val gocls : thm list -> thm list
+ val skolemize_prems_tac : thm list -> int -> tactic
+ val MESON : (thm list -> tactic) -> int -> tactic
+ val best_meson_tac : (thm -> int) -> int -> tactic
+ val safe_best_meson_tac : int -> tactic
+ val depth_meson_tac : int -> tactic
+ val prolog_step_tac' : thm list -> int -> tactic
+ val iter_deepen_prolog_tac : thm list -> tactic
+ val iter_deepen_meson_tac : int -> tactic
+ val meson_tac : int -> tactic
+ val negate_head : thm -> thm
+ val select_literal : int -> thm -> thm
+ val skolemize_tac : int -> tactic
+ val make_clauses_tac : int -> tactic
+ val meson_setup : (theory -> theory) list
+end
- (**** Operators for forward proof ****)
-
- (*raises exception if no rules apply -- unlike RL*)
- fun tryres (th, rl::rls) = (th RS rl handle THM _ => tryres(th,rls))
- | tryres (th, []) = raise THM("tryres", 0, [th]);
+structure Meson =
+struct
- val prop_of = #prop o rep_thm;
-
- (*Permits forward proof from rules that discharge assumptions*)
- fun forward_res nf st =
- case Seq.pull (ALLGOALS (METAHYPS (fn [prem] => rtac (nf prem) 1)) st)
- of SOME(th,_) => th
- | NONE => raise THM("forward_res", 0, [st]);
+val not_conjD = thm "meson_not_conjD";
+val not_disjD = thm "meson_not_disjD";
+val not_notD = thm "meson_not_notD";
+val not_allD = thm "meson_not_allD";
+val not_exD = thm "meson_not_exD";
+val imp_to_disjD = thm "meson_imp_to_disjD";
+val not_impD = thm "meson_not_impD";
+val iff_to_disjD = thm "meson_iff_to_disjD";
+val not_iffD = thm "meson_not_iffD";
+val conj_exD1 = thm "meson_conj_exD1";
+val conj_exD2 = thm "meson_conj_exD2";
+val disj_exD = thm "meson_disj_exD";
+val disj_exD1 = thm "meson_disj_exD1";
+val disj_exD2 = thm "meson_disj_exD2";
+val disj_assoc = thm "meson_disj_assoc";
+val disj_comm = thm "meson_disj_comm";
+val disj_FalseD1 = thm "meson_disj_FalseD1";
+val disj_FalseD2 = thm "meson_disj_FalseD2";
- (*Are any of the constants in "bs" present in the term?*)
- fun has_consts bs =
- let fun has (Const(a,_)) = a mem bs
- | has (Const ("Hilbert_Choice.Eps",_) $ _) = false
- (*ignore constants within @-terms*)
- | has (f$u) = has f orelse has u
- | has (Abs(_,_,t)) = has t
- | has _ = false
- in has end;
+(**** Operators for forward proof ****)
+
+(*raises exception if no rules apply -- unlike RL*)
+fun tryres (th, rl::rls) = (th RS rl handle THM _ => tryres(th,rls))
+ | tryres (th, []) = raise THM("tryres", 0, [th]);
+
+val prop_of = #prop o rep_thm;
+
+(*Permits forward proof from rules that discharge assumptions*)
+fun forward_res nf st =
+ case Seq.pull (ALLGOALS (METAHYPS (fn [prem] => rtac (nf prem) 1)) st)
+ of SOME(th,_) => th
+ | NONE => raise THM("forward_res", 0, [st]);
+
+
+(*Are any of the constants in "bs" present in the term?*)
+fun has_consts bs =
+ let fun has (Const(a,_)) = a mem bs
+ | has (Const ("Hilbert_Choice.Eps",_) $ _) = false
+ (*ignore constants within @-terms*)
+ | has (f$u) = has f orelse has u
+ | has (Abs(_,_,t)) = has t
+ | has _ = false
+ in has end;
- (**** Clause handling ****)
+(**** Clause handling ****)
- fun literals (Const("Trueprop",_) $ P) = literals P
- | literals (Const("op |",_) $ P $ Q) = literals P @ literals Q
- | literals (Const("Not",_) $ P) = [(false,P)]
- | literals P = [(true,P)];
+fun literals (Const("Trueprop",_) $ P) = literals P
+ | literals (Const("op |",_) $ P $ Q) = literals P @ literals Q
+ | literals (Const("Not",_) $ P) = [(false,P)]
+ | literals P = [(true,P)];
- (*number of literals in a term*)
- val nliterals = length o literals;
+(*number of literals in a term*)
+val nliterals = length o literals;
- (*to detect, and remove, tautologous clauses*)
- fun taut_lits [] = false
- | taut_lits ((flg,t)::ts) = (not flg,t) mem ts orelse taut_lits ts;
+(*to detect, and remove, tautologous clauses*)
+fun taut_lits [] = false
+ | taut_lits ((flg,t)::ts) = (not flg,t) mem ts orelse taut_lits ts;
- (*Include False as a literal: an occurrence of ~False is a tautology*)
- fun is_taut th = taut_lits ((true, HOLogic.false_const) ::
- literals (prop_of th));
+(*Include False as a literal: an occurrence of ~False is a tautology*)
+fun is_taut th = taut_lits ((true, HOLogic.false_const) ::
+ literals (prop_of th));
- (*Generation of unique names -- maxidx cannot be relied upon to increase!
- Cannot rely on "variant", since variables might coincide when literals
- are joined to make a clause...
- 19 chooses "U" as the first variable name*)
- val name_ref = ref 19;
+(*Generation of unique names -- maxidx cannot be relied upon to increase!
+ Cannot rely on "variant", since variables might coincide when literals
+ are joined to make a clause...
+ 19 chooses "U" as the first variable name*)
+val name_ref = ref 19;
- (*Replaces universally quantified variables by FREE variables -- because
- assumptions may not contain scheme variables. Later, call "generalize". *)
- fun freeze_spec th =
- let val sth = th RS spec
- val newname = (name_ref := !name_ref + 1;
- radixstring(26, "A", !name_ref))
- in read_instantiate [("x", newname)] sth end;
+(*Replaces universally quantified variables by FREE variables -- because
+ assumptions may not contain scheme variables. Later, call "generalize". *)
+fun freeze_spec th =
+ let val sth = th RS spec
+ val newname = (name_ref := !name_ref + 1;
+ radixstring(26, "A", !name_ref))
+ in read_instantiate [("x", newname)] sth end;
- fun resop nf [prem] = resolve_tac (nf prem) 1;
+fun resop nf [prem] = resolve_tac (nf prem) 1;
- (*Conjunctive normal form, detecting tautologies early.
- Strips universal quantifiers and breaks up conjunctions. *)
- fun cnf_aux seen (th,ths) =
- if taut_lits (literals(prop_of th) @ seen)
- then ths (*tautology ignored*)
- else if not (has_consts ["All","op &"] (prop_of th))
- then th::ths (*no work to do, terminate*)
- else (*conjunction?*)
- cnf_aux seen (th RS conjunct1,
- cnf_aux seen (th RS conjunct2, ths))
- handle THM _ => (*universal quant?*)
- cnf_aux seen (freeze_spec th, ths)
- handle THM _ => (*disjunction?*)
- let val tac =
- (METAHYPS (resop (cnf_nil seen)) 1) THEN
- (fn st' => st' |>
- METAHYPS (resop (cnf_nil (literals (concl_of st') @ seen))) 1)
- in Seq.list_of (tac (th RS disj_forward)) @ ths end
- and cnf_nil seen th = cnf_aux seen (th,[]);
+(*Conjunctive normal form, detecting tautologies early.
+ Strips universal quantifiers and breaks up conjunctions. *)
+fun cnf_aux seen (th,ths) =
+ if taut_lits (literals(prop_of th) @ seen)
+ then ths (*tautology ignored*)
+ else if not (has_consts ["All","op &"] (prop_of th))
+ then th::ths (*no work to do, terminate*)
+ else (*conjunction?*)
+ cnf_aux seen (th RS conjunct1,
+ cnf_aux seen (th RS conjunct2, ths))
+ handle THM _ => (*universal quant?*)
+ cnf_aux seen (freeze_spec th, ths)
+ handle THM _ => (*disjunction?*)
+ let val tac =
+ (METAHYPS (resop (cnf_nil seen)) 1) THEN
+ (fn st' => st' |>
+ METAHYPS (resop (cnf_nil (literals (concl_of st') @ seen))) 1)
+ in Seq.list_of (tac (th RS disj_forward)) @ ths end
+and cnf_nil seen th = cnf_aux seen (th,[]);
- (*Top-level call to cnf -- it's safe to reset name_ref*)
- fun cnf (th,ths) =
- (name_ref := 19; cnf (th RS conjunct1, cnf (th RS conjunct2, ths))
- handle THM _ => (*not a conjunction*) cnf_aux [] (th, ths));
+(*Top-level call to cnf -- it's safe to reset name_ref*)
+fun cnf (th,ths) =
+ (name_ref := 19; cnf (th RS conjunct1, cnf (th RS conjunct2, ths))
+ handle THM _ => (*not a conjunction*) cnf_aux [] (th, ths));
- (**** Removal of duplicate literals ****)
+(**** Removal of duplicate literals ****)
- (*Forward proof, passing extra assumptions as theorems to the tactic*)
- fun forward_res2 nf hyps st =
- case Seq.pull
- (REPEAT
- (METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1)
- st)
- of SOME(th,_) => th
- | NONE => raise THM("forward_res2", 0, [st]);
+(*Forward proof, passing extra assumptions as theorems to the tactic*)
+fun forward_res2 nf hyps st =
+ case Seq.pull
+ (REPEAT
+ (METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1)
+ st)
+ of SOME(th,_) => th
+ | NONE => raise THM("forward_res2", 0, [st]);
- (*Remove duplicates in P|Q by assuming ~P in Q
- rls (initially []) accumulates assumptions of the form P==>False*)
- fun nodups_aux rls th = nodups_aux rls (th RS disj_assoc)
- handle THM _ => tryres(th,rls)
- handle THM _ => tryres(forward_res2 nodups_aux rls (th RS disj_forward2),
- [disj_FalseD1, disj_FalseD2, asm_rl])
- handle THM _ => th;
+(*Remove duplicates in P|Q by assuming ~P in Q
+ rls (initially []) accumulates assumptions of the form P==>False*)
+fun nodups_aux rls th = nodups_aux rls (th RS disj_assoc)
+ handle THM _ => tryres(th,rls)
+ handle THM _ => tryres(forward_res2 nodups_aux rls (th RS disj_forward2),
+ [disj_FalseD1, disj_FalseD2, asm_rl])
+ handle THM _ => th;
- (*Remove duplicate literals, if there are any*)
- fun nodups th =
- if null(findrep(literals(prop_of th))) then th
- else nodups_aux [] th;
+(*Remove duplicate literals, if there are any*)
+fun nodups th =
+ if null(findrep(literals(prop_of th))) then th
+ else nodups_aux [] th;
- (**** Generation of contrapositives ****)
+(**** Generation of contrapositives ****)
- (*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
- fun assoc_right th = assoc_right (th RS disj_assoc)
- handle THM _ => th;
+(*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
+fun assoc_right th = assoc_right (th RS disj_assoc)
+ handle THM _ => th;
- (*Must check for negative literal first!*)
- val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
+(*Must check for negative literal first!*)
+val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
- (*For ordinary resolution. *)
- val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule'];
+(*For ordinary resolution. *)
+val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule'];
- (*Create a goal or support clause, conclusing False*)
- fun make_goal th = (*Must check for negative literal first!*)
- make_goal (tryres(th, clause_rules))
- handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
+(*Create a goal or support clause, conclusing False*)
+fun make_goal th = (*Must check for negative literal first!*)
+ make_goal (tryres(th, clause_rules))
+ handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
- (*Sort clauses by number of literals*)
- fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2);
+(*Sort clauses by number of literals*)
+fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2);
- (*TAUTOLOGY CHECK SHOULD NOT BE NECESSARY!*)
- fun sort_clauses ths = sort (make_ord fewerlits) (List.filter (not o is_taut) ths);
+(*TAUTOLOGY CHECK SHOULD NOT BE NECESSARY!*)
+fun sort_clauses ths = sort (make_ord fewerlits) (List.filter (not o is_taut) ths);
- (*Convert all suitable free variables to schematic variables*)
- fun generalize th = forall_elim_vars 0 (forall_intr_frees th);
+(*Convert all suitable free variables to schematic variables*)
+fun generalize th = forall_elim_vars 0 (forall_intr_frees th);
- (*Create a meta-level Horn clause*)
- fun make_horn crules th = make_horn crules (tryres(th,crules))
- handle THM _ => th;
+(*Create a meta-level Horn clause*)
+fun make_horn crules th = make_horn crules (tryres(th,crules))
+ handle THM _ => th;
- (*Generate Horn clauses for all contrapositives of a clause*)
- fun add_contras crules (th,hcs) =
- let fun rots (0,th) = hcs
- | rots (k,th) = zero_var_indexes (make_horn crules th) ::
- rots(k-1, assoc_right (th RS disj_comm))
- in case nliterals(prop_of th) of
- 1 => th::hcs
- | n => rots(n, assoc_right th)
- end;
+(*Generate Horn clauses for all contrapositives of a clause*)
+fun add_contras crules (th,hcs) =
+ let fun rots (0,th) = hcs
+ | rots (k,th) = zero_var_indexes (make_horn crules th) ::
+ rots(k-1, assoc_right (th RS disj_comm))
+ in case nliterals(prop_of th) of
+ 1 => th::hcs
+ | n => rots(n, assoc_right th)
+ end;
- (*Use "theorem naming" to label the clauses*)
- fun name_thms label =
- let fun name1 (th, (k,ths)) =
- (k-1, Thm.name_thm (label ^ string_of_int k, th) :: ths)
+(*Use "theorem naming" to label the clauses*)
+fun name_thms label =
+ let fun name1 (th, (k,ths)) =
+ (k-1, Thm.name_thm (label ^ string_of_int k, th) :: ths)
- in fn ths => #2 (foldr name1 (length ths, []) ths) end;
+ in fn ths => #2 (foldr name1 (length ths, []) ths) end;
- (*Find an all-negative support clause*)
- fun is_negative th = forall (not o #1) (literals (prop_of th));
+(*Find an all-negative support clause*)
+fun is_negative th = forall (not o #1) (literals (prop_of th));
- val neg_clauses = List.filter is_negative;
+val neg_clauses = List.filter is_negative;
- (***** MESON PROOF PROCEDURE *****)
+(***** MESON PROOF PROCEDURE *****)
- fun rhyps (Const("==>",_) $ (Const("Trueprop",_) $ A) $ phi,
- As) = rhyps(phi, A::As)
- | rhyps (_, As) = As;
+fun rhyps (Const("==>",_) $ (Const("Trueprop",_) $ A) $ phi,
+ As) = rhyps(phi, A::As)
+ | rhyps (_, As) = As;
- (** Detecting repeated assumptions in a subgoal **)
+(** Detecting repeated assumptions in a subgoal **)
- (*The stringtree detects repeated assumptions.*)
- fun ins_term (net,t) = Net.insert_term((t,t), net, op aconv);
+(*The stringtree detects repeated assumptions.*)
+fun ins_term (net,t) = Net.insert_term((t,t), net, op aconv);
- (*detects repetitions in a list of terms*)
- fun has_reps [] = false
- | has_reps [_] = false
- | has_reps [t,u] = (t aconv u)
- | has_reps ts = (Library.foldl ins_term (Net.empty, ts); false)
- handle INSERT => true;
+(*detects repetitions in a list of terms*)
+fun has_reps [] = false
+ | has_reps [_] = false
+ | has_reps [t,u] = (t aconv u)
+ | has_reps ts = (Library.foldl ins_term (Net.empty, ts); false)
+ handle INSERT => true;
- (*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*)
- fun TRYALL_eq_assume_tac 0 st = Seq.single st
- | TRYALL_eq_assume_tac i st =
- TRYALL_eq_assume_tac (i-1) (eq_assumption i st)
- handle THM _ => TRYALL_eq_assume_tac (i-1) st;
+(*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*)
+fun TRYALL_eq_assume_tac 0 st = Seq.single st
+ | TRYALL_eq_assume_tac i st =
+ TRYALL_eq_assume_tac (i-1) (eq_assumption i st)
+ handle THM _ => TRYALL_eq_assume_tac (i-1) st;
- (*Loop checking: FAIL if trying to prove the same thing twice
- -- if *ANY* subgoal has repeated literals*)
- fun check_tac st =
- if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st)
- then Seq.empty else Seq.single st;
+(*Loop checking: FAIL if trying to prove the same thing twice
+ -- if *ANY* subgoal has repeated literals*)
+fun check_tac st =
+ if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st)
+ then Seq.empty else Seq.single st;
- (* net_resolve_tac actually made it slower... *)
- fun prolog_step_tac horns i =
- (assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
- TRYALL eq_assume_tac;
+(* net_resolve_tac actually made it slower... *)
+fun prolog_step_tac horns i =
+ (assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
+ TRYALL eq_assume_tac;
-in
+
(*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*)
-local fun addconcl(prem,sz) = size_of_term(Logic.strip_assums_concl prem) + sz
-in
-fun size_of_subgoals st = foldr addconcl 0 (prems_of st)
-end;
+fun addconcl(prem,sz) = size_of_term(Logic.strip_assums_concl prem) + sz
+
+fun size_of_subgoals st = foldr addconcl 0 (prems_of st);
+
(*Negation Normal Form*)
val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD,
@@ -415,9 +443,7 @@
end);
-(** proof method setup **)
-
-local
+(*** proof method setup ***)
fun meson_meth ctxt =
Method.SIMPLE_METHOD' HEADGOAL
@@ -431,7 +457,6 @@
Method.SIMPLE_METHOD' HEADGOAL
(CHANGED_PROP o make_clauses_tac);
-in
val meson_setup =
[Method.add_methods
@@ -444,4 +469,5 @@
end;
-end;
+structure BasicMeson: BASIC_MESON = Meson;
+open BasicMeson;