--- a/src/HOL/HOL_lemmas.ML Tue Sep 05 18:59:22 2000 +0200
+++ b/src/HOL/HOL_lemmas.ML Tue Sep 05 21:06:01 2000 +0200
@@ -144,7 +144,7 @@
by (REPEAT (resolve_tac (prems @ [major RS spec]) 1)) ;
qed "allE";
-val prems = goal (the_context ())
+val prems = goal (the_context ())
"[| ALL x. P(x); [| P(x); ALL x. P(x) |] ==> R |] ==> R";
by (REPEAT (resolve_tac (prems @ (prems RL [spec])) 1)) ;
qed "all_dupE";
@@ -224,7 +224,7 @@
by (etac selectI 1) ;
qed "exI";
-val [major,minor] =
+val [major,minor] =
Goalw [Ex_def] "[| EX x::'a. P(x); !!x. P(x) ==> Q |] ==> Q";
by (rtac (major RS minor) 1);
qed "exE";
@@ -451,8 +451,8 @@
val major::prems = Goal
"[| P=Q; [| P; Q |] ==> R; [| ~P; ~Q |] ==> R |] ==> R";
by (rtac (major RS iffE) 1);
-by (REPEAT (DEPTH_SOLVE_1
- (eresolve_tac ([asm_rl,impCE,notE]@prems) 1)));
+by (REPEAT (DEPTH_SOLVE_1
+ (eresolve_tac ([asm_rl,impCE,notE]@prems) 1)));
qed "iffCE";
val prems = Goal "(ALL x. ~P(x) ==> P(a)) ==> EX x. P(x)";
@@ -471,9 +471,9 @@
by (rtac (thm"plus_ac0.zero") 1);
qed "plus_ac0_zero_right";
-bind_thms ("plus_ac0", [thm"plus_ac0.assoc", thm"plus_ac0.commute",
- plus_ac0_left_commute,
- thm"plus_ac0.zero", plus_ac0_zero_right]);
+bind_thms ("plus_ac0", [thm"plus_ac0.assoc", thm"plus_ac0.commute",
+ plus_ac0_left_commute,
+ thm"plus_ac0.zero", plus_ac0_zero_right]);
(* case distinction *)
@@ -488,7 +488,7 @@
(** Standard abbreviations **)
-(* combination of (spec RS spec RS ...(j times) ... spec RS mp *)
+(* combination of (spec RS spec RS ...(j times) ... spec RS mp *)
local
fun wrong_prem (Const ("All", _) $ (Abs (_, _, t))) = wrong_prem t
| wrong_prem (Bound _) = true
@@ -500,4 +500,4 @@
end;
-fun strip_tac i = REPEAT(resolve_tac [impI,allI] i);
+fun strip_tac i = REPEAT(resolve_tac [impI,allI] i);
--- a/src/HOL/Tools/meson.ML Tue Sep 05 18:59:22 2000 +0200
+++ b/src/HOL/Tools/meson.ML Tue Sep 05 21:06:01 2000 +0200
@@ -1,9 +1,9 @@
-(* Title: HOL/ex/meson
+(* Title: HOL/Tools/meson.ML
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1992 University of Cambridge
-The MESON resolution proof procedure for HOL
+The MESON resolution proof procedure for HOL.
When making clauses, avoids using the rewriter -- instead uses RS recursively
@@ -11,100 +11,12 @@
FUNCTION nodups -- if done to goal clauses too!
*)
-
-(**** LEMMAS : outside the "local" block ****)
-
-(** "Axiom" of Choice, proved using the description operator **)
-
-Goal "ALL x. EX y. Q x y ==> EX f. ALL x. Q x (f x)";
-by (fast_tac (claset() addEs [selectI]) 1);
-qed "choice";
-
-(*** Generation of contrapositives ***)
-
-(*Inserts negated disjunct after removing the negation; P is a literal*)
-val [major,minor] = Goal "~P|Q ==> ((~P==>P) ==> Q)";
-by (rtac (major RS disjE) 1);
-by (rtac notE 1);
-by (etac minor 2);
-by (ALLGOALS assume_tac);
-qed "make_neg_rule";
-
-(*For Plaisted's "Postive refinement" of the MESON procedure*)
-Goal "~P|Q ==> (P ==> Q)";
-by (Blast_tac 1);
-qed "make_refined_neg_rule";
-
-(*P should be a literal*)
-val [major,minor] = Goal "P|Q ==> ((P==>~P) ==> Q)";
-by (rtac (major RS disjE) 1);
-by (rtac notE 1);
-by (etac minor 1);
-by (ALLGOALS assume_tac);
-qed "make_pos_rule";
-
-(*** Generation of a goal clause -- put away the final literal ***)
-
-val [major,minor] = Goal "~P ==> ((~P==>P) ==> False)";
-by (rtac notE 1);
-by (rtac minor 2);
-by (ALLGOALS (rtac major));
-qed "make_neg_goal";
-
-val [major,minor] = Goal "P ==> ((P==>~P) ==> False)";
-by (rtac notE 1);
-by (rtac minor 1);
-by (ALLGOALS (rtac major));
-qed "make_pos_goal";
-
-
-(**** Lemmas for forward proof (like congruence rules) ****)
-
-(*NOTE: could handle conjunctions (faster?) by
- nf(th RS conjunct2) RS (nf(th RS conjunct1) RS conjI) *)
-val major::prems = Goal
- "[| P'&Q'; P' ==> P; Q' ==> Q |] ==> P&Q";
-by (rtac (major RS conjE) 1);
-by (rtac conjI 1);
-by (ALLGOALS (eresolve_tac prems));
-qed "conj_forward";
-
-val major::prems = Goal
- "[| P'|Q'; P' ==> P; Q' ==> Q |] ==> P|Q";
-by (rtac (major RS disjE) 1);
-by (ALLGOALS (dresolve_tac prems));
-by (ALLGOALS (eresolve_tac [disjI1,disjI2]));
-qed "disj_forward";
-
-(*Version for removal of duplicate literals*)
-val major::prems = Goal
- "[| P'|Q'; P' ==> P; [| Q'; P==>False |] ==> Q |] ==> P|Q";
-by (cut_facts_tac [major] 1);
-by (blast_tac (claset() addIs prems) 1);
-qed "disj_forward2";
-
-val major::prems = Goal
- "[| ALL x. P'(x); !!x. P'(x) ==> P(x) |] ==> ALL x. P(x)";
-by (rtac allI 1);
-by (resolve_tac prems 1);
-by (rtac (major RS spec) 1);
-qed "all_forward";
-
-val major::prems = Goal
- "[| EX x. P'(x); !!x. P'(x) ==> P(x) |] ==> EX x. P(x)";
-by (rtac (major RS exE) 1);
-by (rtac exI 1);
-by (eresolve_tac prems 1);
-qed "ex_forward";
-
-(**** END OF LEMMAS ****)
-
local
(*Prove theorems using fast_tac*)
- fun prove_fun s =
+ fun prove_fun s =
prove_goal (the_context ()) s
- (fn prems => [ cut_facts_tac prems 1, Fast_tac 1 ]);
+ (fn prems => [ cut_facts_tac prems 1, Fast_tac 1 ]);
(**** Negation Normal Form ****)
@@ -174,11 +86,11 @@
(*Are any of the constants in "bs" present in the term?*)
- fun has_consts bs =
+ fun has_consts bs =
let fun has (Const(a,_)) = a mem bs
- | has (f$u) = has f orelse has u
- | has (Abs(_,_,t)) = has t
- | has _ = false
+ | has (f$u) = has f orelse has u
+ | has (Abs(_,_,t)) = has t
+ | has _ = false
in has end;
@@ -197,12 +109,12 @@
| 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));
+ 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...
+ are joined to make a clause...
19 chooses "U" as the first variable name*)
val name_ref = ref 19;
@@ -211,31 +123,31 @@
fun freeze_spec th =
let val sth = th RS spec
val newname = (name_ref := !name_ref + 1;
- radixstring(26, "A", !name_ref))
+ radixstring(26, "A", !name_ref))
in read_instantiate [("x", newname)] sth end;
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) =
+ fun cnf_aux seen (th,ths) =
if taut_lits (literals(prop_of th) @ seen) then ths
else if not (has_consts ["All","op &"] (prop_of th)) then th::ths
else (*conjunction?*)
- cnf_aux seen (th RS conjunct1,
- cnf_aux seen (th RS conjunct2, ths))
+ cnf_aux seen (th RS conjunct1,
+ cnf_aux seen (th RS conjunct2, ths))
handle THM _ => (*universal quant?*)
- cnf_aux seen (freeze_spec th, ths)
+ 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)
+ 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) =
+ 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));
@@ -244,9 +156,9 @@
(*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)
+ (REPEAT
+ (METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1)
+ st)
of Some(th,_) => th
| None => raise THM("forward_res2", 0, [st]);
@@ -255,7 +167,7 @@
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])
+ [disj_FalseD1, disj_FalseD2, asm_rl])
handle THM _ => th;
(*Remove duplicate literals, if there are any*)
@@ -268,7 +180,7 @@
(*Associate disjuctions to right -- make leftmost disjunct a LITERAL*)
fun assoc_right th = assoc_right (th RS disj_assoc)
- handle THM _ => th;
+ handle THM _ => th;
(*Must check for negative literal first!*)
val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule];
@@ -278,7 +190,7 @@
(*Create a goal or support clause, conclusing False*)
fun make_goal th = (*Must check for negative literal first!*)
- make_goal (tryres(th, clause_rules))
+ make_goal (tryres(th, clause_rules))
handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]);
(*Sort clauses by number of literals*)
@@ -291,23 +203,23 @@
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;
+ 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) =
+ 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))
+ | 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
+ 1 => th::hcs
| n => rots(n, assoc_right th)
end;
(*Use "theorem naming" to label the clauses*)
- fun name_thms label =
+ fun name_thms label =
let fun name1 (th, (k,ths)) =
- (k-1, Thm.name_thm (label ^ string_of_int k, th) :: ths)
+ (k-1, Thm.name_thm (label ^ string_of_int k, th) :: ths)
in fn ths => #2 (foldr name1 (ths, (length ths, []))) end;
@@ -320,7 +232,7 @@
(***** MESON PROOF PROCEDURE *****)
fun rhyps (Const("==>",_) $ (Const("Trueprop",_) $ A) $ phi,
- As) = rhyps(phi, A::As)
+ As) = rhyps(phi, A::As)
| rhyps (_, As) = As;
(** Detecting repeated assumptions in a subgoal **)
@@ -333,23 +245,23 @@
| has_reps [_] = false
| has_reps [t,u] = (t aconv u)
| has_reps ts = (foldl ins_term (Net.empty, ts); false)
- handle INSERT => true;
+ 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;
+ | 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 =
+ 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 =
+ fun prolog_step_tac horns i =
(assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN
TRYALL eq_assume_tac;
@@ -365,48 +277,48 @@
(*Negation Normal Form*)
val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD,
- not_impD, not_iffD, not_allD, not_exD, not_notD];
+ not_impD, not_iffD, not_allD, not_exD, not_notD];
fun make_nnf th = make_nnf (tryres(th, nnf_rls))
- handle THM _ =>
- forward_res make_nnf
- (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
+ handle THM _ =>
+ forward_res make_nnf
+ (tryres(th, [conj_forward,disj_forward,all_forward,ex_forward]))
handle THM _ => th;
(*Pull existential quantifiers (Skolemization)*)
-fun skolemize th =
+fun skolemize th =
if not (has_consts ["Ex"] (prop_of th)) then th
else skolemize (tryres(th, [choice, conj_exD1, conj_exD2,
- disj_exD, disj_exD1, disj_exD2]))
- handle THM _ =>
- skolemize (forward_res skolemize
- (tryres (th, [conj_forward, disj_forward, all_forward])))
+ disj_exD, disj_exD1, disj_exD2]))
+ handle THM _ =>
+ skolemize (forward_res skolemize
+ (tryres (th, [conj_forward, disj_forward, all_forward])))
handle THM _ => forward_res skolemize (th RS ex_forward);
(*Make clauses from a list of theorems, previously Skolemized and put into nnf.
The resulting clauses are HOL disjunctions.*)
-fun make_clauses ths =
+fun make_clauses ths =
sort_clauses (map (generalize o nodups) (foldr cnf (ths,[])));
(*Convert a list of clauses to (contrapositive) Horn clauses*)
-fun make_horns ths =
+fun make_horns ths =
name_thms "Horn#"
(gen_distinct eq_thm (foldr (add_contras clause_rules) (ths,[])));
(*Could simply use nprems_of, which would count remaining subgoals -- no
discrimination as to their size! With BEST_FIRST, fails for problem 41.*)
-fun best_prolog_tac sizef horns =
+fun best_prolog_tac sizef horns =
BEST_FIRST (has_fewer_prems 1, sizef) (prolog_step_tac horns 1);
-fun depth_prolog_tac horns =
+fun depth_prolog_tac horns =
DEPTH_FIRST (has_fewer_prems 1) (prolog_step_tac horns 1);
(*Return all negative clauses, as possible goal clauses*)
fun gocls cls = name_thms "Goal#" (map make_goal (neg_clauses cls));
-fun skolemize_tac prems =
+fun skolemize_tac prems =
cut_facts_tac (map (skolemize o make_nnf) prems) THEN'
REPEAT o (etac exE);
@@ -419,21 +331,21 @@
(** Best-first search versions **)
-fun best_meson_tac sizef =
- MESON (fn cls =>
+fun best_meson_tac sizef =
+ MESON (fn cls =>
THEN_BEST_FIRST (resolve_tac (gocls cls) 1)
(has_fewer_prems 1, sizef)
(prolog_step_tac (make_horns cls) 1));
(*First, breaks the goal into independent units*)
val safe_best_meson_tac =
- SELECT_GOAL (TRY Safe_tac THEN
+ SELECT_GOAL (TRY Safe_tac THEN
TRYALL (best_meson_tac size_of_subgoals));
(** Depth-first search version **)
val depth_meson_tac =
- MESON (fn cls => EVERY [resolve_tac (gocls cls) 1,
+ MESON (fn cls => EVERY [resolve_tac (gocls cls) 1,
depth_prolog_tac (make_horns cls)]);
@@ -442,7 +354,7 @@
(*This version does only one inference per call;
having only one eq_assume_tac speeds it up!*)
-fun prolog_step_tac' horns =
+fun prolog_step_tac' horns =
let val (horn0s, hornps) = (*0 subgoals vs 1 or more*)
take_prefix Thm.no_prems horns
val nrtac = net_resolve_tac horns
@@ -451,17 +363,34 @@
((assume_tac i APPEND nrtac i) THEN check_tac)
end;
-fun iter_deepen_prolog_tac horns =
+fun iter_deepen_prolog_tac horns =
ITER_DEEPEN (has_fewer_prems 1) (prolog_step_tac' horns);
-val iter_deepen_meson_tac =
- MESON (fn cls =>
+val iter_deepen_meson_tac =
+ MESON (fn cls =>
(THEN_ITER_DEEPEN (resolve_tac (gocls cls) 1)
(has_fewer_prems 1)
(prolog_step_tac' (make_horns cls))));
-val meson_tac =
- SELECT_GOAL (TRY Safe_tac THEN
- TRYALL (iter_deepen_meson_tac));
+fun meson_claset_tac cs =
+ SELECT_GOAL (TRY (safe_tac cs) THEN TRYALL iter_deepen_meson_tac);
+
+val meson_tac = CLASET' meson_claset_tac;
+
+
+(* proof method setup *)
+
+local
+
+fun meson_meth ctxt =
+ Method.SIMPLE_METHOD' HEADGOAL (CHANGED o meson_claset_tac (Classical.get_local_claset ctxt));
+
+in
+
+val meson_setup =
+ [Method.add_methods
+ [("meson", Method.ctxt_args meson_meth, "The MESON resolution proof procedure")]];
end;
+
+end;