author | paulson |
Thu, 12 Apr 2007 13:58:47 +0200 | |
changeset 22646 | 197f6c4ff9a5 |
parent 22546 | c40d7ab8cbc5 |
child 22724 | 3002683a6e0f |
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 finish_cnf : thm list -> 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 -> thm list) -> (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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end |
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structure Meson = |
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struct |
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|
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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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(** First-order Resolution **) |
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fun typ_pair_of (ix, (sort,ty)) = (TVar (ix,sort), ty); |
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fun term_pair_of (ix, (ty,t)) = (Var (ix,ty), t); |
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val Envir.Envir {asol = tenv0, iTs = tyenv0, ...} = Envir.empty 0 |
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|
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(*FIXME: currently does not "rename variables apart"*) |
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fun first_order_resolve thA thB = |
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let val thy = theory_of_thm thA |
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val tmA = concl_of thA |
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fun match pat = Pattern.first_order_match thy (pat,tmA) (tyenv0,tenv0) |
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val Const("==>",_) $ tmB $ _ = prop_of thB |
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val (tyenv,tenv) = match tmB |
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val ct_pairs = map (pairself (cterm_of thy) o term_pair_of) (Vartab.dest tenv) |
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in thA RS (cterm_instantiate ct_pairs thB) end |
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handle _ => raise THM ("first_order_resolve", 0, [thA,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) = (th RS rl handle THM _ => tryall rls) |
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in tryall rls end; |
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(*Permits forward proof from rules that discharge assumptions. The supplied proof state st, |
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e.g. from conj_forward, should have the form |
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"[| P' ==> ?P; Q' ==> ?Q |] ==> ?P & ?Q" |
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and the effect should be to instantiate ?P and ?Q with normalized versions of P' and Q'.*) |
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fun forward_res nf st = |
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let fun forward_tacf [prem] = rtac (nf prem) 1 |
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| forward_tacf prems = |
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error ("Bad proof state in forward_res, please inform lcp@cl.cam.ac.uk:\n" ^ |
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string_of_thm st ^ |
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"\nPremises:\n" ^ |
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cat_lines (map string_of_thm prems)) |
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in |
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case Seq.pull (ALLGOALS (METAHYPS forward_tacf) st) |
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of SOME(th,_) => th |
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| NONE => raise THM("forward_res", 0, [st]) |
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end; |
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|
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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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|
116 |
| has (Const("op &",_) $ p $ q) = member (op =) bs "op &" orelse has p orelse has q |
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|
117 |
| has (Const("All",_) $ Abs(_,_,p)) = member (op =) bs "All" orelse has p |
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|
118 |
| has (Const("Ex",_) $ Abs(_,_,p)) = member (op =) bs "Ex" orelse has p |
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|
119 |
| has _ = false |
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|
120 |
in has end; |
17716 | 121 |
|
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|
122 |
|
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|
123 |
(**** Clause handling ****) |
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|
124 |
|
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|
125 |
fun literals (Const("Trueprop",_) $ P) = literals P |
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126 |
| literals (Const("op |",_) $ P $ Q) = literals P @ literals Q |
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|
127 |
| literals (Const("Not",_) $ P) = [(false,P)] |
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|
128 |
| literals P = [(true,P)]; |
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|
129 |
|
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|
130 |
(*number of literals in a term*) |
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|
131 |
val nliterals = length o literals; |
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|
132 |
|
18389 | 133 |
|
134 |
(*** Tautology Checking ***) |
|
135 |
||
136 |
fun signed_lits_aux (Const ("op |", _) $ P $ Q) (poslits, neglits) = |
|
137 |
signed_lits_aux Q (signed_lits_aux P (poslits, neglits)) |
|
138 |
| signed_lits_aux (Const("Not",_) $ P) (poslits, neglits) = (poslits, P::neglits) |
|
139 |
| signed_lits_aux P (poslits, neglits) = (P::poslits, neglits); |
|
140 |
||
141 |
fun signed_lits th = signed_lits_aux (HOLogic.dest_Trueprop (concl_of th)) ([],[]); |
|
142 |
||
143 |
(*Literals like X=X are tautologous*) |
|
144 |
fun taut_poslit (Const("op =",_) $ t $ u) = t aconv u |
|
145 |
| taut_poslit (Const("True",_)) = true |
|
146 |
| taut_poslit _ = false; |
|
147 |
||
148 |
fun is_taut th = |
|
149 |
let val (poslits,neglits) = signed_lits th |
|
150 |
in exists taut_poslit poslits |
|
151 |
orelse |
|
20073 | 152 |
exists (member (op aconv) neglits) (HOLogic.false_const :: poslits) |
19894 | 153 |
end |
154 |
handle TERM _ => false; (*probably dest_Trueprop on a weird theorem*) |
|
18389 | 155 |
|
156 |
||
157 |
(*** To remove trivial negated equality literals from clauses ***) |
|
158 |
||
159 |
(*They are typically functional reflexivity axioms and are the converses of |
|
160 |
injectivity equivalences*) |
|
161 |
||
162 |
val not_refl_disj_D = thm"meson_not_refl_disj_D"; |
|
163 |
||
20119 | 164 |
(*Is either term a Var that does not properly occur in the other term?*) |
165 |
fun eliminable (t as Var _, u) = t aconv u orelse not (Logic.occs(t,u)) |
|
166 |
| eliminable (u, t as Var _) = t aconv u orelse not (Logic.occs(t,u)) |
|
167 |
| eliminable _ = false; |
|
168 |
||
18389 | 169 |
fun refl_clause_aux 0 th = th |
170 |
| refl_clause_aux n th = |
|
171 |
case HOLogic.dest_Trueprop (concl_of th) of |
|
172 |
(Const ("op |", _) $ (Const ("op |", _) $ _ $ _) $ _) => |
|
173 |
refl_clause_aux n (th RS disj_assoc) (*isolate an atom as first disjunct*) |
|
174 |
| (Const ("op |", _) $ (Const("Not",_) $ (Const("op =",_) $ t $ u)) $ _) => |
|
20119 | 175 |
if eliminable(t,u) |
176 |
then refl_clause_aux (n-1) (th RS not_refl_disj_D) (*Var inequation: delete*) |
|
18389 | 177 |
else refl_clause_aux (n-1) (th RS disj_comm) (*not between Vars: ignore*) |
178 |
| (Const ("op |", _) $ _ $ _) => refl_clause_aux n (th RS disj_comm) |
|
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|
179 |
| _ => (*not a disjunction*) th; |
18389 | 180 |
|
181 |
fun notequal_lits_count (Const ("op |", _) $ P $ Q) = |
|
182 |
notequal_lits_count P + notequal_lits_count Q |
|
183 |
| notequal_lits_count (Const("Not",_) $ (Const("op =",_) $ _ $ _)) = 1 |
|
184 |
| notequal_lits_count _ = 0; |
|
185 |
||
186 |
(*Simplify a clause by applying reflexivity to its negated equality literals*) |
|
187 |
fun refl_clause th = |
|
188 |
let val neqs = notequal_lits_count (HOLogic.dest_Trueprop (concl_of th)) |
|
19894 | 189 |
in zero_var_indexes (refl_clause_aux neqs th) end |
190 |
handle TERM _ => th; (*probably dest_Trueprop on a weird theorem*) |
|
18389 | 191 |
|
192 |
||
193 |
(*** The basic CNF transformation ***) |
|
194 |
||
21900 | 195 |
val max_clauses = ref 40; |
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|
196 |
|
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|
197 |
fun sum x y = if x < !max_clauses andalso y < !max_clauses then x+y else !max_clauses; |
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|
198 |
fun prod x y = if x < !max_clauses andalso y < !max_clauses then x*y else !max_clauses; |
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changeset
|
199 |
|
19894 | 200 |
(*Estimate the number of clauses in order to detect infeasible theorems*) |
21069
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changeset
|
201 |
fun signed_nclauses b (Const("Trueprop",_) $ t) = signed_nclauses b t |
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changeset
|
202 |
| signed_nclauses b (Const("Not",_) $ t) = signed_nclauses (not b) t |
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changeset
|
203 |
| signed_nclauses b (Const("op &",_) $ t $ u) = |
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changeset
|
204 |
if b then sum (signed_nclauses b t) (signed_nclauses b u) |
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parents:
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diff
changeset
|
205 |
else prod (signed_nclauses b t) (signed_nclauses b u) |
e55b507d0c61
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paulson
parents:
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diff
changeset
|
206 |
| signed_nclauses b (Const("op |",_) $ t $ u) = |
e55b507d0c61
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parents:
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diff
changeset
|
207 |
if b then prod (signed_nclauses b t) (signed_nclauses b u) |
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parents:
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diff
changeset
|
208 |
else sum (signed_nclauses b t) (signed_nclauses b u) |
e55b507d0c61
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paulson
parents:
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diff
changeset
|
209 |
| signed_nclauses b (Const("op -->",_) $ t $ u) = |
e55b507d0c61
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paulson
parents:
21050
diff
changeset
|
210 |
if b then prod (signed_nclauses (not b) t) (signed_nclauses b u) |
e55b507d0c61
nclauses no longer requires its input to be in NNF
paulson
parents:
21050
diff
changeset
|
211 |
else sum (signed_nclauses (not b) t) (signed_nclauses b u) |
21616
296e0c318c3e
Fixed a MAJOR BUG in clause-counting: only Boolean equalities now count as iffs
paulson
parents:
21588
diff
changeset
|
212 |
| signed_nclauses b (Const("op =", Type ("fun", [T, _])) $ t $ u) = |
296e0c318c3e
Fixed a MAJOR BUG in clause-counting: only Boolean equalities now count as iffs
paulson
parents:
21588
diff
changeset
|
213 |
if T = HOLogic.boolT then (*Boolean equality is if-and-only-if*) |
296e0c318c3e
Fixed a MAJOR BUG in clause-counting: only Boolean equalities now count as iffs
paulson
parents:
21588
diff
changeset
|
214 |
if b then sum (prod (signed_nclauses (not b) t) (signed_nclauses b u)) |
296e0c318c3e
Fixed a MAJOR BUG in clause-counting: only Boolean equalities now count as iffs
paulson
parents:
21588
diff
changeset
|
215 |
(prod (signed_nclauses (not b) u) (signed_nclauses b t)) |
296e0c318c3e
Fixed a MAJOR BUG in clause-counting: only Boolean equalities now count as iffs
paulson
parents:
21588
diff
changeset
|
216 |
else sum (prod (signed_nclauses b t) (signed_nclauses b u)) |
296e0c318c3e
Fixed a MAJOR BUG in clause-counting: only Boolean equalities now count as iffs
paulson
parents:
21588
diff
changeset
|
217 |
(prod (signed_nclauses (not b) t) (signed_nclauses (not b) u)) |
296e0c318c3e
Fixed a MAJOR BUG in clause-counting: only Boolean equalities now count as iffs
paulson
parents:
21588
diff
changeset
|
218 |
else 1 |
21069
e55b507d0c61
nclauses no longer requires its input to be in NNF
paulson
parents:
21050
diff
changeset
|
219 |
| signed_nclauses b (Const("Ex", _) $ Abs (_,_,t)) = signed_nclauses b t |
e55b507d0c61
nclauses no longer requires its input to be in NNF
paulson
parents:
21050
diff
changeset
|
220 |
| signed_nclauses b (Const("All",_) $ Abs (_,_,t)) = signed_nclauses b t |
e55b507d0c61
nclauses no longer requires its input to be in NNF
paulson
parents:
21050
diff
changeset
|
221 |
| signed_nclauses _ _ = 1; (* literal *) |
e55b507d0c61
nclauses no longer requires its input to be in NNF
paulson
parents:
21050
diff
changeset
|
222 |
|
e55b507d0c61
nclauses no longer requires its input to be in NNF
paulson
parents:
21050
diff
changeset
|
223 |
val nclauses = signed_nclauses true; |
e55b507d0c61
nclauses no longer requires its input to be in NNF
paulson
parents:
21050
diff
changeset
|
224 |
|
e55b507d0c61
nclauses no longer requires its input to be in NNF
paulson
parents:
21050
diff
changeset
|
225 |
fun too_many_clauses t = nclauses t >= !max_clauses; |
19894 | 226 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
227 |
(*Replaces universally quantified variables by FREE variables -- because |
22515
f4061faa5fda
"generalize" now replaces ugly mes_XXX generated symbols by 1-letter identifiers.
paulson
parents:
22381
diff
changeset
|
228 |
assumptions may not contain scheme variables. Later, we call "generalize". *) |
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
229 |
fun freeze_spec th = |
20361 | 230 |
let val newname = gensym "mes_" |
19154 | 231 |
val spec' = read_instantiate [("x", newname)] spec |
232 |
in th RS spec' end; |
|
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
233 |
|
15998
bc916036cf84
new cnf function taking Skolemization theorems as an extra argument
paulson
parents:
15965
diff
changeset
|
234 |
(*Used with METAHYPS below. There is one assumption, which gets bound to prem |
bc916036cf84
new cnf function taking Skolemization theorems as an extra argument
paulson
parents:
15965
diff
changeset
|
235 |
and then normalized via function nf. The normal form is given to resolve_tac, |
22515
f4061faa5fda
"generalize" now replaces ugly mes_XXX generated symbols by 1-letter identifiers.
paulson
parents:
22381
diff
changeset
|
236 |
instantiate a Boolean variable created by resolution with disj_forward. Since |
f4061faa5fda
"generalize" now replaces ugly mes_XXX generated symbols by 1-letter identifiers.
paulson
parents:
22381
diff
changeset
|
237 |
(nf prem) returns a LIST of theorems, we can backtrack to get all combinations.*) |
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
238 |
fun resop nf [prem] = resolve_tac (nf prem) 1; |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
239 |
|
20822
634070b40731
Now checks explicitly for Trueprop, thereby ignoring junk theorems involving OF_CLASS, etc.
paulson
parents:
20524
diff
changeset
|
240 |
(*Any need to extend this list with |
21046
fe1db2f991a7
moved HOL code generator setup to Code_Generator
haftmann
parents:
20972
diff
changeset
|
241 |
"HOL.type_class","Code_Generator.eq_class","ProtoPure.term"?*) |
18389 | 242 |
val has_meta_conn = |
243 |
exists_Const (fn (c,_) => c mem_string ["==", "==>", "all", "prop"]); |
|
20417
c611b1412056
better skolemization, using first-order resolution rather than hoping for the right result
paulson
parents:
20361
diff
changeset
|
244 |
|
c611b1412056
better skolemization, using first-order resolution rather than hoping for the right result
paulson
parents:
20361
diff
changeset
|
245 |
fun apply_skolem_ths (th, rls) = |
c611b1412056
better skolemization, using first-order resolution rather than hoping for the right result
paulson
parents:
20361
diff
changeset
|
246 |
let fun tryall [] = raise THM("apply_skolem_ths", 0, th::rls) |
c611b1412056
better skolemization, using first-order resolution rather than hoping for the right result
paulson
parents:
20361
diff
changeset
|
247 |
| tryall (rl::rls) = (first_order_resolve th rl handle THM _ => tryall rls) |
c611b1412056
better skolemization, using first-order resolution rather than hoping for the right result
paulson
parents:
20361
diff
changeset
|
248 |
in tryall rls end; |
22515
f4061faa5fda
"generalize" now replaces ugly mes_XXX generated symbols by 1-letter identifiers.
paulson
parents:
22381
diff
changeset
|
249 |
|
15998
bc916036cf84
new cnf function taking Skolemization theorems as an extra argument
paulson
parents:
15965
diff
changeset
|
250 |
(*Conjunctive normal form, adding clauses from th in front of ths (for foldr). |
bc916036cf84
new cnf function taking Skolemization theorems as an extra argument
paulson
parents:
15965
diff
changeset
|
251 |
Strips universal quantifiers and breaks up conjunctions. |
bc916036cf84
new cnf function taking Skolemization theorems as an extra argument
paulson
parents:
15965
diff
changeset
|
252 |
Eliminates existential quantifiers using skoths: Skolemization theorems.*) |
bc916036cf84
new cnf function taking Skolemization theorems as an extra argument
paulson
parents:
15965
diff
changeset
|
253 |
fun cnf skoths (th,ths) = |
18389 | 254 |
let fun cnf_aux (th,ths) = |
21174
4d733b76b5fa
removed is_Trueprop (use can dest_Trueprop'' instead);
wenzelm
parents:
21102
diff
changeset
|
255 |
if not (can HOLogic.dest_Trueprop (prop_of th)) then ths (*meta-level: ignore*) |
20134
73cb53843190
has_consts renamed to has_conn, now actually parses the first-order formula
paulson
parents:
20119
diff
changeset
|
256 |
else if not (has_conns ["All","Ex","op &"] (prop_of th)) |
15998
bc916036cf84
new cnf function taking Skolemization theorems as an extra argument
paulson
parents:
15965
diff
changeset
|
257 |
then th::ths (*no work to do, terminate*) |
16588 | 258 |
else case head_of (HOLogic.dest_Trueprop (concl_of th)) of |
259 |
Const ("op &", _) => (*conjunction*) |
|
20417
c611b1412056
better skolemization, using first-order resolution rather than hoping for the right result
paulson
parents:
20361
diff
changeset
|
260 |
cnf_aux (th RS conjunct1, cnf_aux (th RS conjunct2, ths)) |
16588 | 261 |
| Const ("All", _) => (*universal quantifier*) |
22515
f4061faa5fda
"generalize" now replaces ugly mes_XXX generated symbols by 1-letter identifiers.
paulson
parents:
22381
diff
changeset
|
262 |
cnf_aux (freeze_spec th, ths) |
16588 | 263 |
| Const ("Ex", _) => |
264 |
(*existential quantifier: Insert Skolem functions*) |
|
20417
c611b1412056
better skolemization, using first-order resolution rather than hoping for the right result
paulson
parents:
20361
diff
changeset
|
265 |
cnf_aux (apply_skolem_ths (th,skoths), ths) |
22515
f4061faa5fda
"generalize" now replaces ugly mes_XXX generated symbols by 1-letter identifiers.
paulson
parents:
22381
diff
changeset
|
266 |
| Const ("op |", _) => |
f4061faa5fda
"generalize" now replaces ugly mes_XXX generated symbols by 1-letter identifiers.
paulson
parents:
22381
diff
changeset
|
267 |
(*Disjunction of P, Q: Create new goal of proving ?P | ?Q and solve it using |
f4061faa5fda
"generalize" now replaces ugly mes_XXX generated symbols by 1-letter identifiers.
paulson
parents:
22381
diff
changeset
|
268 |
all combinations of converting P, Q to CNF.*) |
16588 | 269 |
let val tac = |
18389 | 270 |
(METAHYPS (resop cnf_nil) 1) THEN |
19154 | 271 |
(fn st' => st' |> METAHYPS (resop cnf_nil) 1) |
16588 | 272 |
in Seq.list_of (tac (th RS disj_forward)) @ ths end |
273 |
| _ => (*no work to do*) th::ths |
|
19154 | 274 |
and cnf_nil th = cnf_aux (th,[]) |
15998
bc916036cf84
new cnf function taking Skolemization theorems as an extra argument
paulson
parents:
15965
diff
changeset
|
275 |
in |
21069
e55b507d0c61
nclauses no longer requires its input to be in NNF
paulson
parents:
21050
diff
changeset
|
276 |
if too_many_clauses (concl_of th) |
22130 | 277 |
then (Output.debug (fn () => ("cnf is ignoring: " ^ string_of_thm th)); ths) |
19894 | 278 |
else cnf_aux (th,ths) |
15998
bc916036cf84
new cnf function taking Skolemization theorems as an extra argument
paulson
parents:
15965
diff
changeset
|
279 |
end; |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
280 |
|
22515
f4061faa5fda
"generalize" now replaces ugly mes_XXX generated symbols by 1-letter identifiers.
paulson
parents:
22381
diff
changeset
|
281 |
fun all_names (Const ("all", _) $ Abs(x,_,P)) = x :: all_names P |
f4061faa5fda
"generalize" now replaces ugly mes_XXX generated symbols by 1-letter identifiers.
paulson
parents:
22381
diff
changeset
|
282 |
| all_names _ = []; |
f4061faa5fda
"generalize" now replaces ugly mes_XXX generated symbols by 1-letter identifiers.
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283 |
|
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|
284 |
fun new_names n [] = [] |
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|
285 |
| new_names n (x::xs) = |
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|
286 |
if String.isPrefix "mes_" x then (x, radixstring(26,"A",n)) :: new_names (n+1) xs |
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|
287 |
else new_names n xs; |
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|
288 |
|
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|
289 |
(*The gensym names are ugly, so don't let the user see them. When forall_elim_vars |
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|
290 |
is called, it will ensure that no name clauses ensue.*) |
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|
291 |
fun nice_names th = |
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292 |
let val old_names = all_names (prop_of th) |
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|
293 |
in Drule.rename_bvars (new_names 0 old_names) th end; |
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294 |
|
16012 | 295 |
(*Convert all suitable free variables to schematic variables, |
296 |
but don't discharge assumptions.*) |
|
22515
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297 |
fun generalize th = Thm.varifyT (forall_elim_vars 0 (nice_names (forall_intr_frees th))); |
16012 | 298 |
|
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299 |
fun make_cnf skoths th = cnf skoths (th, []); |
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300 |
|
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301 |
(*Generalization, removal of redundant equalities, removal of tautologies.*) |
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302 |
fun finish_cnf ths = filter (not o is_taut) (map (refl_clause o generalize) ths); |
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303 |
|
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|
304 |
|
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|
305 |
(**** Removal of duplicate literals ****) |
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|
306 |
|
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|
307 |
(*Forward proof, passing extra assumptions as theorems to the tactic*) |
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|
308 |
fun forward_res2 nf hyps st = |
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309 |
case Seq.pull |
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310 |
(REPEAT |
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311 |
(METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1) |
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312 |
st) |
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313 |
of SOME(th,_) => th |
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314 |
| NONE => raise THM("forward_res2", 0, [st]); |
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|
315 |
|
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|
316 |
(*Remove duplicates in P|Q by assuming ~P in Q |
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317 |
rls (initially []) accumulates assumptions of the form P==>False*) |
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318 |
fun nodups_aux rls th = nodups_aux rls (th RS disj_assoc) |
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319 |
handle THM _ => tryres(th,rls) |
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320 |
handle THM _ => tryres(forward_res2 nodups_aux rls (th RS disj_forward2), |
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|
321 |
[disj_FalseD1, disj_FalseD2, asm_rl]) |
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322 |
handle THM _ => th; |
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|
323 |
|
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324 |
(*Remove duplicate literals, if there are any*) |
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325 |
fun nodups th = |
20972 | 326 |
if has_duplicates (op =) (literals (prop_of th)) |
327 |
then nodups_aux [] th |
|
328 |
else th; |
|
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|
329 |
|
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|
330 |
|
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|
331 |
(**** Generation of contrapositives ****) |
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|
332 |
|
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333 |
fun is_left (Const ("Trueprop", _) $ |
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|
334 |
(Const ("op |", _) $ (Const ("op |", _) $ _ $ _) $ _)) = true |
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335 |
| is_left _ = false; |
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336 |
|
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|
337 |
(*Associate disjuctions to right -- make leftmost disjunct a LITERAL*) |
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|
338 |
fun assoc_right th = |
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|
339 |
if is_left (prop_of th) then assoc_right (th RS disj_assoc) |
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|
340 |
else th; |
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|
341 |
|
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|
342 |
(*Must check for negative literal first!*) |
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|
343 |
val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule]; |
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|
344 |
|
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|
345 |
(*For ordinary resolution. *) |
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|
346 |
val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule']; |
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|
347 |
|
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348 |
(*Create a goal or support clause, conclusing False*) |
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|
349 |
fun make_goal th = (*Must check for negative literal first!*) |
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|
350 |
make_goal (tryres(th, clause_rules)) |
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|
351 |
handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]); |
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|
352 |
|
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|
353 |
(*Sort clauses by number of literals*) |
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|
354 |
fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2); |
9840
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|
355 |
|
18389 | 356 |
fun sort_clauses ths = sort (make_ord fewerlits) ths; |
9840
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|
357 |
|
15581 | 358 |
(*True if the given type contains bool anywhere*) |
359 |
fun has_bool (Type("bool",_)) = true |
|
360 |
| has_bool (Type(_, Ts)) = exists has_bool Ts |
|
361 |
| has_bool _ = false; |
|
362 |
||
20524
1493053fc111
Tweaks to is_fol_term, the first-order test. We don't count "=" as a connective
paulson
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|
363 |
(*Is the string the name of a connective? Really only | and Not can remain, |
1493053fc111
Tweaks to is_fol_term, the first-order test. We don't count "=" as a connective
paulson
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changeset
|
364 |
since this code expects to be called on a clause form.*) |
19875 | 365 |
val is_conn = member (op =) |
20524
1493053fc111
Tweaks to is_fol_term, the first-order test. We don't count "=" as a connective
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|
366 |
["Trueprop", "op &", "op |", "op -->", "Not", |
15613 | 367 |
"All", "Ex", "Ball", "Bex"]; |
368 |
||
20524
1493053fc111
Tweaks to is_fol_term, the first-order test. We don't count "=" as a connective
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|
369 |
(*True if the term contains a function--not a logical connective--where the type |
1493053fc111
Tweaks to is_fol_term, the first-order test. We don't count "=" as a connective
paulson
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diff
changeset
|
370 |
of any argument contains bool.*) |
15613 | 371 |
val has_bool_arg_const = |
372 |
exists_Const |
|
373 |
(fn (c,T) => not(is_conn c) andalso exists (has_bool) (binder_types T)); |
|
22381
cb145d434284
The first-order test now tests for the obscure case of a polymorphic constant like 1 being
paulson
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|
374 |
|
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The first-order test now tests for the obscure case of a polymorphic constant like 1 being
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changeset
|
375 |
(*A higher-order instance of a first-order constant? Example is the definition of |
cb145d434284
The first-order test now tests for the obscure case of a polymorphic constant like 1 being
paulson
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|
376 |
HOL.one, 1, at a function type in theory SetsAndFunctions.*) |
cb145d434284
The first-order test now tests for the obscure case of a polymorphic constant like 1 being
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|
377 |
fun higher_inst_const thy (c,T) = |
cb145d434284
The first-order test now tests for the obscure case of a polymorphic constant like 1 being
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|
378 |
case binder_types T of |
cb145d434284
The first-order test now tests for the obscure case of a polymorphic constant like 1 being
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|
379 |
[] => false (*not a function type, OK*) |
cb145d434284
The first-order test now tests for the obscure case of a polymorphic constant like 1 being
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changeset
|
380 |
| Ts => length (binder_types (Sign.the_const_type thy c)) <> length Ts; |
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The first-order test now tests for the obscure case of a polymorphic constant like 1 being
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|
381 |
|
21102
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
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diff
changeset
|
382 |
(*Raises an exception if any Vars in the theorem mention type bool. |
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
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21095
diff
changeset
|
383 |
Also rejects functions whose arguments are Booleans or other functions.*) |
22381
cb145d434284
The first-order test now tests for the obscure case of a polymorphic constant like 1 being
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diff
changeset
|
384 |
fun is_fol_term thy t = |
cb145d434284
The first-order test now tests for the obscure case of a polymorphic constant like 1 being
paulson
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22360
diff
changeset
|
385 |
Term.is_first_order ["all","All","Ex"] t andalso |
19204
b8f7de7ef629
Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
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19154
diff
changeset
|
386 |
not (exists (has_bool o fastype_of) (term_vars t) orelse |
b8f7de7ef629
Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents:
19154
diff
changeset
|
387 |
has_bool_arg_const t orelse |
22381
cb145d434284
The first-order test now tests for the obscure case of a polymorphic constant like 1 being
paulson
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changeset
|
388 |
exists_Const (higher_inst_const thy) t orelse |
19204
b8f7de7ef629
Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
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changeset
|
389 |
has_meta_conn t); |
b8f7de7ef629
Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents:
19154
diff
changeset
|
390 |
|
21102
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
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parents:
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diff
changeset
|
391 |
fun rigid t = not (is_Var (head_of t)); |
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
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diff
changeset
|
392 |
|
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
393 |
fun ok4horn (Const ("Trueprop",_) $ (Const ("op |", _) $ t $ _)) = rigid t |
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
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diff
changeset
|
394 |
| ok4horn (Const ("Trueprop",_) $ t) = rigid t |
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
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diff
changeset
|
395 |
| ok4horn _ = false; |
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
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diff
changeset
|
396 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
397 |
(*Create a meta-level Horn clause*) |
21102
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
398 |
fun make_horn crules th = |
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
399 |
if ok4horn (concl_of th) |
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
400 |
then make_horn crules (tryres(th,crules)) handle THM _ => th |
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
401 |
else th; |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
402 |
|
16563 | 403 |
(*Generate Horn clauses for all contrapositives of a clause. The input, th, |
404 |
is a HOL disjunction.*) |
|
15579
32bee18c675f
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parents:
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diff
changeset
|
405 |
fun add_contras crules (th,hcs) = |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
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changeset
|
406 |
let fun rots (0,th) = hcs |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
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diff
changeset
|
407 |
| rots (k,th) = zero_var_indexes (make_horn crules th) :: |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
408 |
rots(k-1, assoc_right (th RS disj_comm)) |
15862 | 409 |
in case nliterals(prop_of th) of |
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
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diff
changeset
|
410 |
1 => th::hcs |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
411 |
| n => rots(n, assoc_right th) |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
412 |
end; |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
413 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
414 |
(*Use "theorem naming" to label the clauses*) |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
415 |
fun name_thms label = |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
416 |
let fun name1 (th, (k,ths)) = |
21646
c07b5b0e8492
thm/prf: separate official name vs. additional tags;
wenzelm
parents:
21616
diff
changeset
|
417 |
(k-1, PureThy.put_name_hint (label ^ string_of_int k) th :: ths) |
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
418 |
in fn ths => #2 (foldr name1 (length ths, []) ths) end; |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
419 |
|
16563 | 420 |
(*Is the given disjunction an all-negative support clause?*) |
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
421 |
fun is_negative th = forall (not o #1) (literals (prop_of th)); |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
422 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
423 |
val neg_clauses = List.filter is_negative; |
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 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
426 |
(***** MESON PROOF PROCEDURE *****) |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
427 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
428 |
fun rhyps (Const("==>",_) $ (Const("Trueprop",_) $ A) $ phi, |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
429 |
As) = rhyps(phi, A::As) |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
430 |
| rhyps (_, As) = As; |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
431 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
432 |
(** Detecting repeated assumptions in a subgoal **) |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
433 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
434 |
(*The stringtree detects repeated assumptions.*) |
16801 | 435 |
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
paulson
parents:
diff
changeset
|
436 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
437 |
(*detects repetitions in a list of terms*) |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
438 |
fun has_reps [] = false |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
439 |
| has_reps [_] = false |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
440 |
| has_reps [t,u] = (t aconv u) |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
441 |
| has_reps ts = (Library.foldl ins_term (Net.empty, ts); false) |
19875 | 442 |
handle Net.INSERT => true; |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
443 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
444 |
(*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*) |
18508 | 445 |
fun TRYING_eq_assume_tac 0 st = Seq.single st |
446 |
| TRYING_eq_assume_tac i st = |
|
447 |
TRYING_eq_assume_tac (i-1) (eq_assumption i st) |
|
448 |
handle THM _ => TRYING_eq_assume_tac (i-1) st; |
|
449 |
||
450 |
fun TRYALL_eq_assume_tac st = TRYING_eq_assume_tac (nprems_of st) st; |
|
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
451 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
452 |
(*Loop checking: FAIL if trying to prove the same thing twice |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
453 |
-- if *ANY* subgoal has repeated literals*) |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
454 |
fun check_tac st = |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
455 |
if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st) |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
456 |
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
|
457 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
458 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
459 |
(* net_resolve_tac actually made it slower... *) |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
460 |
fun prolog_step_tac horns i = |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
461 |
(assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN |
18508 | 462 |
TRYALL_eq_assume_tac; |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
463 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
464 |
(*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*) |
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
465 |
fun addconcl(prem,sz) = size_of_term(Logic.strip_assums_concl prem) + sz |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
466 |
|
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
467 |
fun size_of_subgoals st = foldr addconcl 0 (prems_of st); |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
468 |
|
9840
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 |
(*Negation Normal Form*) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
471 |
val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD, |
9869 | 472 |
not_impD, not_iffD, not_allD, not_exD, not_notD]; |
15581 | 473 |
|
21102
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
474 |
fun ok4nnf (Const ("Trueprop",_) $ (Const ("Not", _) $ t)) = rigid t |
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
475 |
| ok4nnf (Const ("Trueprop",_) $ t) = rigid t |
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
476 |
| ok4nnf _ = false; |
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
477 |
|
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
478 |
fun make_nnf1 th = |
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
479 |
if ok4nnf (concl_of th) |
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
480 |
then make_nnf1 (tryres(th, nnf_rls)) |
9869 | 481 |
handle THM _ => |
15581 | 482 |
forward_res make_nnf1 |
9869 | 483 |
(tryres(th, [conj_forward,disj_forward,all_forward,ex_forward])) |
21102
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
484 |
handle THM _ => th |
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
485 |
else th; |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
486 |
|
20018 | 487 |
(*The simplification removes defined quantifiers and occurrences of True and False. |
488 |
nnf_ss also includes the one-point simprocs, |
|
18405
afb1a52a7011
removal of some redundancies (e.g. one-point-rules) in clause production
paulson
parents:
18389
diff
changeset
|
489 |
which are needed to avoid the various one-point theorems from generating junk clauses.*) |
19894 | 490 |
val nnf_simps = |
20018 | 491 |
[simp_implies_def, Ex1_def, Ball_def, Bex_def, if_True, |
19894 | 492 |
if_False, if_cancel, if_eq_cancel, cases_simp]; |
493 |
val nnf_extra_simps = |
|
494 |
thms"split_ifs" @ ex_simps @ all_simps @ simp_thms; |
|
18405
afb1a52a7011
removal of some redundancies (e.g. one-point-rules) in clause production
paulson
parents:
18389
diff
changeset
|
495 |
|
afb1a52a7011
removal of some redundancies (e.g. one-point-rules) in clause production
paulson
parents:
18389
diff
changeset
|
496 |
val nnf_ss = |
19894 | 497 |
HOL_basic_ss addsimps nnf_extra_simps |
498 |
addsimprocs [defALL_regroup,defEX_regroup,neq_simproc,let_simproc]; |
|
15872 | 499 |
|
21050
d0447a511edb
More robust error handling in make_nnf and forward_res
paulson
parents:
21046
diff
changeset
|
500 |
fun make_nnf th = case prems_of th of |
d0447a511edb
More robust error handling in make_nnf and forward_res
paulson
parents:
21046
diff
changeset
|
501 |
[] => th |> rewrite_rule (map safe_mk_meta_eq nnf_simps) |
21102
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
502 |
|> simplify nnf_ss |
21050
d0447a511edb
More robust error handling in make_nnf and forward_res
paulson
parents:
21046
diff
changeset
|
503 |
|> make_nnf1 |
d0447a511edb
More robust error handling in make_nnf and forward_res
paulson
parents:
21046
diff
changeset
|
504 |
| _ => raise THM ("make_nnf: premises in argument", 0, [th]); |
15581 | 505 |
|
15965
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15946
diff
changeset
|
506 |
(*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
|
507 |
clauses that arise from a subgoal.*) |
9869 | 508 |
fun skolemize th = |
20134
73cb53843190
has_consts renamed to has_conn, now actually parses the first-order formula
paulson
parents:
20119
diff
changeset
|
509 |
if not (has_conns ["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
|
510 |
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
|
511 |
disj_exD, disj_exD1, disj_exD2]))) |
9869 | 512 |
handle THM _ => |
513 |
skolemize (forward_res skolemize |
|
514 |
(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
|
515 |
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
|
516 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
517 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
518 |
(*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
|
519 |
The resulting clauses are HOL disjunctions.*) |
9869 | 520 |
fun make_clauses ths = |
15998
bc916036cf84
new cnf function taking Skolemization theorems as an extra argument
paulson
parents:
15965
diff
changeset
|
521 |
(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
|
522 |
|
16563 | 523 |
(*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*) |
9869 | 524 |
fun make_horns ths = |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
525 |
name_thms "Horn#" |
22360
26ead7ed4f4b
moved eq_thm etc. to structure Thm in Pure/more_thm.ML;
wenzelm
parents:
22130
diff
changeset
|
526 |
(distinct Thm.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
|
527 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
528 |
(*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
|
529 |
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
|
530 |
|
9869 | 531 |
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
|
532 |
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
|
533 |
|
9869 | 534 |
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
|
535 |
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
|
536 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
537 |
(*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
|
538 |
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
|
539 |
|
15008 | 540 |
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
|
541 |
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
|
542 |
REPEAT o (etac exE); |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
543 |
|
18141
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset
|
544 |
(*Expand all definitions (presumably of Skolem functions) in a proof state.*) |
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset
|
545 |
fun expand_defs_tac st = |
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset
|
546 |
let val defs = filter (can dest_equals) (#hyps (crep_thm st)) |
21678 | 547 |
in PRIMITIVE (LocalDefs.expand defs) st end; |
18141
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset
|
548 |
|
22546
c40d7ab8cbc5
MESON tactical takes an additional argument: the clausification function.
paulson
parents:
22515
diff
changeset
|
549 |
(*Basis of all meson-tactics. Supplies cltac with clauses: HOL disjunctions. |
c40d7ab8cbc5
MESON tactical takes an additional argument: the clausification function.
paulson
parents:
22515
diff
changeset
|
550 |
Function mkcl converts theorems to clauses.*) |
c40d7ab8cbc5
MESON tactical takes an additional argument: the clausification function.
paulson
parents:
22515
diff
changeset
|
551 |
fun MESON mkcl cltac i st = |
16588 | 552 |
SELECT_GOAL |
18141
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset
|
553 |
(EVERY [rtac ccontr 1, |
16588 | 554 |
METAHYPS (fn negs => |
555 |
EVERY1 [skolemize_prems_tac negs, |
|
22546
c40d7ab8cbc5
MESON tactical takes an additional argument: the clausification function.
paulson
parents:
22515
diff
changeset
|
556 |
METAHYPS (cltac o mkcl)]) 1, |
18141
89e2e8bed08f
Skolemization by inference, but not quite finished
paulson
parents:
18024
diff
changeset
|
557 |
expand_defs_tac]) i st |
20417
c611b1412056
better skolemization, using first-order resolution rather than hoping for the right result
paulson
parents:
20361
diff
changeset
|
558 |
handle THM _ => no_tac st; (*probably from make_meta_clause, not first-order*) |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
559 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
560 |
(** Best-first search versions **) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
561 |
|
16563 | 562 |
(*ths is a list of additional clauses (HOL disjunctions) to use.*) |
9869 | 563 |
fun best_meson_tac sizef = |
22546
c40d7ab8cbc5
MESON tactical takes an additional argument: the clausification function.
paulson
parents:
22515
diff
changeset
|
564 |
MESON make_clauses |
c40d7ab8cbc5
MESON tactical takes an additional argument: the clausification function.
paulson
parents:
22515
diff
changeset
|
565 |
(fn cls => |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
566 |
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
|
567 |
(has_fewer_prems 1, sizef) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
568 |
(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
|
569 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
570 |
(*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
|
571 |
val safe_best_meson_tac = |
9869 | 572 |
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
|
573 |
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
|
574 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
575 |
(** Depth-first search version **) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
576 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
577 |
val depth_meson_tac = |
22546
c40d7ab8cbc5
MESON tactical takes an additional argument: the clausification function.
paulson
parents:
22515
diff
changeset
|
578 |
MESON make_clauses |
c40d7ab8cbc5
MESON tactical takes an additional argument: the clausification function.
paulson
parents:
22515
diff
changeset
|
579 |
(fn cls => EVERY [resolve_tac (gocls cls) 1, depth_prolog_tac (make_horns cls)]); |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
580 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
581 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
582 |
(** Iterative deepening version **) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
583 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
584 |
(*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
|
585 |
having only one eq_assume_tac speeds it up!*) |
9869 | 586 |
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
|
587 |
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
|
588 |
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
|
589 |
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
|
590 |
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
|
591 |
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
|
592 |
((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
|
593 |
end; |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
594 |
|
9869 | 595 |
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
|
596 |
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
|
597 |
|
22546
c40d7ab8cbc5
MESON tactical takes an additional argument: the clausification function.
paulson
parents:
22515
diff
changeset
|
598 |
fun iter_deepen_meson_tac ths = MESON make_clauses |
21095 | 599 |
(fn cls => |
600 |
case (gocls (cls@ths)) of |
|
601 |
[] => no_tac (*no goal clauses*) |
|
602 |
| goes => |
|
603 |
let val horns = make_horns (cls@ths) |
|
22130 | 604 |
val _ = |
605 |
Output.debug (fn () => ("meson method called:\n" ^ |
|
21095 | 606 |
space_implode "\n" (map string_of_thm (cls@ths)) ^ |
607 |
"\nclauses:\n" ^ |
|
22130 | 608 |
space_implode "\n" (map string_of_thm horns))) |
21095 | 609 |
in THEN_ITER_DEEPEN (resolve_tac goes 1) (has_fewer_prems 1) (prolog_step_tac' horns) |
610 |
end |
|
611 |
); |
|
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
612 |
|
16563 | 613 |
fun meson_claset_tac ths cs = |
614 |
SELECT_GOAL (TRY (safe_tac cs) THEN TRYALL (iter_deepen_meson_tac ths)); |
|
9869 | 615 |
|
16563 | 616 |
val meson_tac = CLASET' (meson_claset_tac []); |
9869 | 617 |
|
618 |
||
14813 | 619 |
(**** Code to support ordinary resolution, rather than Model Elimination ****) |
14744 | 620 |
|
15008 | 621 |
(*Convert a list of clauses (disjunctions) to meta-level clauses (==>), |
622 |
with no contrapositives, for ordinary resolution.*) |
|
14744 | 623 |
|
624 |
(*Rules to convert the head literal into a negated assumption. If the head |
|
625 |
literal is already negated, then using notEfalse instead of notEfalse' |
|
626 |
prevents a double negation.*) |
|
627 |
val notEfalse = read_instantiate [("R","False")] notE; |
|
628 |
val notEfalse' = rotate_prems 1 notEfalse; |
|
629 |
||
15448 | 630 |
fun negated_asm_of_head th = |
14744 | 631 |
th RS notEfalse handle THM _ => th RS notEfalse'; |
632 |
||
633 |
(*Converting one clause*) |
|
22646 | 634 |
val make_meta_clause = |
635 |
zero_var_indexes o negated_asm_of_head o make_horn resolution_clause_rules; |
|
21102
7f2ebe5c5b72
Conversion to clause form now tolerates Boolean variables without looping.
paulson
parents:
21095
diff
changeset
|
636 |
|
14744 | 637 |
fun make_meta_clauses ths = |
638 |
name_thms "MClause#" |
|
22360
26ead7ed4f4b
moved eq_thm etc. to structure Thm in Pure/more_thm.ML;
wenzelm
parents:
22130
diff
changeset
|
639 |
(distinct Thm.eq_thm_prop (map make_meta_clause ths)); |
14744 | 640 |
|
641 |
(*Permute a rule's premises to move the i-th premise to the last position.*) |
|
642 |
fun make_last i th = |
|
643 |
let val n = nprems_of th |
|
644 |
in if 1 <= i andalso i <= n |
|
645 |
then Thm.permute_prems (i-1) 1 th |
|
15118 | 646 |
else raise THM("select_literal", i, [th]) |
14744 | 647 |
end; |
648 |
||
649 |
(*Maps a rule that ends "... ==> P ==> False" to "... ==> ~P" while suppressing |
|
650 |
double-negations.*) |
|
651 |
val negate_head = rewrite_rule [atomize_not, not_not RS eq_reflection]; |
|
652 |
||
653 |
(*Maps the clause [P1,...Pn]==>False to [P1,...,P(i-1),P(i+1),...Pn] ==> ~P*) |
|
654 |
fun select_literal i cl = negate_head (make_last i cl); |
|
655 |
||
18508 | 656 |
|
14813 | 657 |
(*Top-level Skolemization. Allows part of the conversion to clauses to be |
658 |
expressed as a tactic (or Isar method). Each assumption of the selected |
|
659 |
goal is converted to NNF and then its existential quantifiers are pulled |
|
660 |
to the front. Finally, all existential quantifiers are eliminated, |
|
661 |
leaving !!-quantified variables. Perhaps Safe_tac should follow, but it |
|
662 |
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
|
663 |
|
19204
b8f7de7ef629
Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents:
19154
diff
changeset
|
664 |
fun skolemize_tac i st = |
b8f7de7ef629
Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents:
19154
diff
changeset
|
665 |
let val ts = Logic.strip_assums_hyp (List.nth (prems_of st, i-1)) |
b8f7de7ef629
Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents:
19154
diff
changeset
|
666 |
in |
b8f7de7ef629
Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents:
19154
diff
changeset
|
667 |
EVERY' [METAHYPS |
15773
f14ae2432710
Completed integration of reconstruction code. Now finds and displays proofs when used with modified version
quigley
parents:
15736
diff
changeset
|
668 |
(fn hyps => (cut_facts_tac (map (skolemize o make_nnf) hyps) 1 |
14813 | 669 |
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
|
670 |
REPEAT_DETERM_N (length ts) o (etac thin_rl)] i st |
b8f7de7ef629
Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents:
19154
diff
changeset
|
671 |
end |
b8f7de7ef629
Tidying, and getting rid of SELECT_GOAL (as it does something different now)
paulson
parents:
19154
diff
changeset
|
672 |
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
|
673 |
|
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
674 |
end; |
9869 | 675 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
676 |
structure BasicMeson: BASIC_MESON = Meson; |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
677 |
open BasicMeson; |