author | wenzelm |
Wed, 13 Jul 2005 16:07:22 +0200 | |
changeset 16801 | 4bb13fa6ae72 |
parent 16588 | 8de758143786 |
child 17404 | d16c3a62c396 |
permissions | -rw-r--r-- |
9869 | 1 |
(* Title: HOL/Tools/meson.ML |
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2 |
ID: $Id$ |
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3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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4 |
Copyright 1992 University of Cambridge |
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The MESON resolution proof procedure for HOL. |
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|
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When making clauses, avoids using the rewriter -- instead uses RS recursively |
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|
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NEED TO SORT LITERALS BY # OF VARS, USING ==>I/E. ELIMINATES NEED FOR |
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FUNCTION nodups -- if done to goal clauses too! |
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*) |
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|
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signature BASIC_MESON = |
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sig |
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val size_of_subgoals : thm -> int |
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val make_cnf : thm list -> thm -> thm list |
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val make_nnf : thm -> thm |
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val skolemize : thm -> thm |
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val make_clauses : thm list -> thm list |
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val make_horns : thm list -> thm list |
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val best_prolog_tac : (thm -> int) -> thm list -> tactic |
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val depth_prolog_tac : thm list -> tactic |
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val gocls : thm list -> thm list |
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val skolemize_prems_tac : thm list -> int -> tactic |
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val MESON : (thm list -> tactic) -> int -> tactic |
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val best_meson_tac : (thm -> int) -> int -> tactic |
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val safe_best_meson_tac : int -> tactic |
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val depth_meson_tac : int -> tactic |
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val prolog_step_tac' : thm list -> int -> tactic |
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val iter_deepen_prolog_tac : thm list -> tactic |
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val iter_deepen_meson_tac : thm list -> int -> tactic |
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val meson_tac : int -> tactic |
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val negate_head : thm -> thm |
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val select_literal : int -> thm -> thm |
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val skolemize_tac : int -> tactic |
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val make_clauses_tac : int -> tactic |
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end |
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|
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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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(*raises exception if no rules apply -- unlike RL*) |
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fun tryres (th, rl::rls) = (th RS rl handle THM _ => tryres(th,rls)) |
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| tryres (th, []) = raise THM("tryres", 0, [th]); |
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(*Permits forward proof from rules that discharge assumptions*) |
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fun forward_res nf st = |
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case Seq.pull (ALLGOALS (METAHYPS (fn [prem] => rtac (nf prem) 1)) st) |
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of SOME(th,_) => th |
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| NONE => raise THM("forward_res", 0, [st]); |
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(*Are any of the constants in "bs" present in the term?*) |
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fun has_consts bs = |
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let fun has (Const(a,_)) = a mem bs |
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| has (Const ("Hilbert_Choice.Eps",_) $ _) = false |
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(*ignore constants within @-terms*) |
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| has (f$u) = has f orelse has u |
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| has (Abs(_,_,t)) = has t |
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| has _ = false |
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in has end; |
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(* for tracing: encloses each string element in brackets. *) |
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val concat_with_and = space_implode " & " o map (enclose "(" ")"); |
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(**** Clause handling ****) |
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fun literals (Const("Trueprop",_) $ P) = literals P |
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| literals (Const("op |",_) $ P $ Q) = literals P @ literals Q |
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| literals (Const("Not",_) $ P) = [(false,P)] |
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| literals P = [(true,P)]; |
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(*number of literals in a term*) |
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val nliterals = length o literals; |
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(*to detect, and remove, tautologous clauses*) |
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fun taut_lits [] = false |
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| taut_lits ((flg,t)::ts) = (not flg,t) mem ts orelse taut_lits ts; |
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(*Include False as a literal: an occurrence of ~False is a tautology*) |
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fun is_taut th = taut_lits ((true, HOLogic.false_const) :: |
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literals (prop_of th)); |
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(*Generation of unique names -- maxidx cannot be relied upon to increase! |
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Cannot rely on "variant", since variables might coincide when literals |
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are joined to make a clause... |
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19 chooses "U" as the first variable name*) |
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val name_ref = ref 19; |
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(*Replaces universally quantified variables by FREE variables -- because |
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assumptions may not contain scheme variables. Later, call "generalize". *) |
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118 |
fun freeze_spec th = |
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119 |
let val sth = th RS spec |
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val newname = (name_ref := !name_ref + 1; |
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radixstring(26, "A", !name_ref)) |
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in read_instantiate [("x", newname)] sth end; |
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123 |
|
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124 |
(*Used with METAHYPS below. There is one assumption, which gets bound to prem |
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125 |
and then normalized via function nf. The normal form is given to resolve_tac, |
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presumably to instantiate a Boolean variable.*) |
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fun resop nf [prem] = resolve_tac (nf prem) 1; |
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128 |
|
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129 |
(*Conjunctive normal form, adding clauses from th in front of ths (for foldr). |
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130 |
Detects tautologies early, with "seen" holding the other literals of a clause. |
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131 |
Strips universal quantifiers and breaks up conjunctions. |
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132 |
Eliminates existential quantifiers using skoths: Skolemization theorems.*) |
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fun cnf skoths (th,ths) = |
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134 |
let fun cnf_aux seen (th,ths) = |
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if taut_lits (literals(prop_of th) @ seen) |
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then ths (*tautology ignored*) |
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else if not (has_consts ["All","Ex","op &"] (prop_of th)) |
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then th::ths (*no work to do, terminate*) |
16588 | 139 |
else case head_of (HOLogic.dest_Trueprop (concl_of th)) of |
140 |
Const ("op &", _) => (*conjunction*) |
|
141 |
cnf_aux seen (th RS conjunct1, |
|
142 |
cnf_aux seen (th RS conjunct2, ths)) |
|
143 |
| Const ("All", _) => (*universal quantifier*) |
|
144 |
cnf_aux seen (freeze_spec th, ths) |
|
145 |
| Const ("Ex", _) => |
|
146 |
(*existential quantifier: Insert Skolem functions*) |
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cnf_aux seen (tryres (th,skoths), ths) |
16588 | 148 |
| Const ("op |", _) => (*disjunction*) |
149 |
let val tac = |
|
150 |
(METAHYPS (resop (cnf_nil seen)) 1) THEN |
|
151 |
(fn st' => st' |> |
|
152 |
METAHYPS |
|
153 |
(resop (cnf_nil (literals (concl_of st') @ seen))) 1) |
|
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in Seq.list_of (tac (th RS disj_forward)) @ ths end |
|
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| _ => (*no work to do*) th::ths |
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and cnf_nil seen th = (cnf_aux seen (th,[])) |
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157 |
in |
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name_ref := 19; (*It's safe to reset this in a top-level call to cnf*) |
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(cnf skoths (th RS conjunct1, cnf skoths (th RS conjunct2, ths)) |
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handle THM _ => (*not a conjunction*) cnf_aux [] (th, ths)) |
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161 |
end; |
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162 |
|
16012 | 163 |
(*Convert all suitable free variables to schematic variables, |
164 |
but don't discharge assumptions.*) |
|
16173 | 165 |
fun generalize th = Thm.varifyT (forall_elim_vars 0 (forall_intr_frees th)); |
16012 | 166 |
|
167 |
fun make_cnf skoths th = map generalize (cnf skoths (th, [])); |
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168 |
|
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169 |
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(**** Removal of duplicate literals ****) |
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171 |
|
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172 |
(*Forward proof, passing extra assumptions as theorems to the tactic*) |
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fun forward_res2 nf hyps st = |
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174 |
case Seq.pull |
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175 |
(REPEAT |
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(METAHYPS (fn major::minors => rtac (nf (minors@hyps) major) 1) 1) |
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177 |
st) |
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of SOME(th,_) => th |
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| NONE => raise THM("forward_res2", 0, [st]); |
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180 |
|
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181 |
(*Remove duplicates in P|Q by assuming ~P in Q |
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182 |
rls (initially []) accumulates assumptions of the form P==>False*) |
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183 |
fun nodups_aux rls th = nodups_aux rls (th RS disj_assoc) |
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184 |
handle THM _ => tryres(th,rls) |
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185 |
handle THM _ => tryres(forward_res2 nodups_aux rls (th RS disj_forward2), |
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186 |
[disj_FalseD1, disj_FalseD2, asm_rl]) |
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187 |
handle THM _ => th; |
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188 |
|
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189 |
(*Remove duplicate literals, if there are any*) |
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190 |
fun nodups th = |
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191 |
if null(findrep(literals(prop_of th))) then th |
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192 |
else nodups_aux [] th; |
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193 |
|
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194 |
|
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195 |
(**** Generation of contrapositives ****) |
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196 |
|
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197 |
(*Associate disjuctions to right -- make leftmost disjunct a LITERAL*) |
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198 |
fun assoc_right th = assoc_right (th RS disj_assoc) |
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199 |
handle THM _ => th; |
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200 |
|
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201 |
(*Must check for negative literal first!*) |
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202 |
val clause_rules = [disj_assoc, make_neg_rule, make_pos_rule]; |
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203 |
|
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|
204 |
(*For ordinary resolution. *) |
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205 |
val resolution_clause_rules = [disj_assoc, make_neg_rule', make_pos_rule']; |
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206 |
|
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|
207 |
(*Create a goal or support clause, conclusing False*) |
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208 |
fun make_goal th = (*Must check for negative literal first!*) |
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209 |
make_goal (tryres(th, clause_rules)) |
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210 |
handle THM _ => tryres(th, [make_neg_goal, make_pos_goal]); |
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|
211 |
|
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|
212 |
(*Sort clauses by number of literals*) |
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213 |
fun fewerlits(th1,th2) = nliterals(prop_of th1) < nliterals(prop_of th2); |
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|
214 |
|
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215 |
(*TAUTOLOGY CHECK SHOULD NOT BE NECESSARY!*) |
16012 | 216 |
fun sort_clauses ths = |
217 |
sort (make_ord fewerlits) (List.filter (not o is_taut) ths); |
|
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218 |
|
15581 | 219 |
(*True if the given type contains bool anywhere*) |
220 |
fun has_bool (Type("bool",_)) = true |
|
221 |
| has_bool (Type(_, Ts)) = exists has_bool Ts |
|
222 |
| has_bool _ = false; |
|
223 |
||
15613 | 224 |
(*Is the string the name of a connective? It doesn't matter if this list is |
225 |
incomplete, since when actually called, the only connectives likely to |
|
226 |
remain are & | Not.*) |
|
227 |
fun is_conn c = c mem_string |
|
228 |
["Trueprop", "op &", "op |", "op -->", "op =", "Not", |
|
229 |
"All", "Ex", "Ball", "Bex"]; |
|
230 |
||
231 |
(*True if the term contains a function where the type of any argument contains |
|
232 |
bool.*) |
|
233 |
val has_bool_arg_const = |
|
234 |
exists_Const |
|
235 |
(fn (c,T) => not(is_conn c) andalso exists (has_bool) (binder_types T)); |
|
15908 | 236 |
|
237 |
val has_meta_conn = |
|
238 |
exists_Const (fn (c,_) => c mem_string ["==", "==>", "all", "Goal"]); |
|
15613 | 239 |
|
16588 | 240 |
(*Raises an exception if any Vars in the theorem mention type bool; they |
241 |
could cause make_horn to loop! Also rejects functions whose arguments are |
|
242 |
Booleans or other functions.*) |
|
243 |
fun check_is_fol th = |
|
15613 | 244 |
let val {prop,...} = rep_thm th |
15908 | 245 |
in if exists (has_bool o fastype_of) (term_vars prop) orelse |
16588 | 246 |
not (Term.is_first_order ["all","All","Ex"] prop) orelse |
15908 | 247 |
has_bool_arg_const prop orelse |
248 |
has_meta_conn prop |
|
16588 | 249 |
then raise THM ("check_is_fol", 0, [th]) else th |
15613 | 250 |
end; |
15581 | 251 |
|
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252 |
(*Create a meta-level Horn clause*) |
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253 |
fun make_horn crules th = make_horn crules (tryres(th,crules)) |
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254 |
handle THM _ => th; |
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|
255 |
|
16563 | 256 |
(*Generate Horn clauses for all contrapositives of a clause. The input, th, |
257 |
is a HOL disjunction.*) |
|
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258 |
fun add_contras crules (th,hcs) = |
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259 |
let fun rots (0,th) = hcs |
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260 |
| rots (k,th) = zero_var_indexes (make_horn crules th) :: |
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|
261 |
rots(k-1, assoc_right (th RS disj_comm)) |
15862 | 262 |
in case nliterals(prop_of th) of |
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|
263 |
1 => th::hcs |
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|
264 |
| n => rots(n, assoc_right th) |
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|
265 |
end; |
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|
266 |
|
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|
267 |
(*Use "theorem naming" to label the clauses*) |
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268 |
fun name_thms label = |
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269 |
let fun name1 (th, (k,ths)) = |
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|
270 |
(k-1, Thm.name_thm (label ^ string_of_int k, th) :: ths) |
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|
271 |
|
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272 |
in fn ths => #2 (foldr name1 (length ths, []) ths) end; |
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273 |
|
16563 | 274 |
(*Is the given disjunction an all-negative support clause?*) |
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275 |
fun is_negative th = forall (not o #1) (literals (prop_of th)); |
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|
276 |
|
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|
277 |
val neg_clauses = List.filter is_negative; |
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|
278 |
|
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changeset
|
279 |
|
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|
280 |
(***** MESON PROOF PROCEDURE *****) |
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|
281 |
|
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|
282 |
fun rhyps (Const("==>",_) $ (Const("Trueprop",_) $ A) $ phi, |
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|
283 |
As) = rhyps(phi, A::As) |
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|
284 |
| rhyps (_, As) = As; |
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changeset
|
285 |
|
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|
286 |
(** Detecting repeated assumptions in a subgoal **) |
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changeset
|
287 |
|
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|
288 |
(*The stringtree detects repeated assumptions.*) |
16801 | 289 |
fun ins_term (net,t) = Net.insert_term (op aconv) (t,t) net; |
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|
290 |
|
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|
291 |
(*detects repetitions in a list of terms*) |
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|
292 |
fun has_reps [] = false |
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|
293 |
| has_reps [_] = false |
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|
294 |
| has_reps [t,u] = (t aconv u) |
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295 |
| has_reps ts = (Library.foldl ins_term (Net.empty, ts); false) |
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|
296 |
handle INSERT => true; |
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changeset
|
297 |
|
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|
298 |
(*Like TRYALL eq_assume_tac, but avoids expensive THEN calls*) |
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|
299 |
fun TRYALL_eq_assume_tac 0 st = Seq.single st |
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|
300 |
| TRYALL_eq_assume_tac i st = |
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|
301 |
TRYALL_eq_assume_tac (i-1) (eq_assumption i st) |
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|
302 |
handle THM _ => TRYALL_eq_assume_tac (i-1) st; |
9840
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changeset
|
303 |
|
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|
304 |
(*Loop checking: FAIL if trying to prove the same thing twice |
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|
305 |
-- if *ANY* subgoal has repeated literals*) |
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|
306 |
fun check_tac st = |
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|
307 |
if exists (fn prem => has_reps (rhyps(prem,[]))) (prems_of st) |
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|
308 |
then Seq.empty else Seq.single st; |
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changeset
|
309 |
|
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changeset
|
310 |
|
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|
311 |
(* net_resolve_tac actually made it slower... *) |
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|
312 |
fun prolog_step_tac horns i = |
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changeset
|
313 |
(assume_tac i APPEND resolve_tac horns i) THEN check_tac THEN |
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changeset
|
314 |
TRYALL eq_assume_tac; |
9840
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changeset
|
315 |
|
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|
316 |
(*Sums the sizes of the subgoals, ignoring hypotheses (ancestors)*) |
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|
317 |
fun addconcl(prem,sz) = size_of_term(Logic.strip_assums_concl prem) + sz |
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|
318 |
|
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|
319 |
fun size_of_subgoals st = foldr addconcl 0 (prems_of st); |
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changeset
|
320 |
|
9840
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diff
changeset
|
321 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
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changeset
|
322 |
(*Negation Normal Form*) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
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changeset
|
323 |
val nnf_rls = [imp_to_disjD, iff_to_disjD, not_conjD, not_disjD, |
9869 | 324 |
not_impD, not_iffD, not_allD, not_exD, not_notD]; |
15581 | 325 |
|
326 |
fun make_nnf1 th = make_nnf1 (tryres(th, nnf_rls)) |
|
9869 | 327 |
handle THM _ => |
15581 | 328 |
forward_res make_nnf1 |
9869 | 329 |
(tryres(th, [conj_forward,disj_forward,all_forward,ex_forward])) |
9840
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meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
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diff
changeset
|
330 |
handle THM _ => th; |
9dfcb0224f8c
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parents:
diff
changeset
|
331 |
|
15946 | 332 |
(*The simplification removes defined quantifiers and occurrences of True and False.*) |
333 |
val nnf_ss = HOL_basic_ss addsimps Ex1_def::Ball_def::Bex_def::simp_thms; |
|
15872 | 334 |
|
335 |
fun make_nnf th = th |> simplify nnf_ss |
|
16588 | 336 |
|> check_is_fol |> make_nnf1 |
15581 | 337 |
|
15965
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
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changeset
|
338 |
(*Pull existential quantifiers to front. This accomplishes Skolemization for |
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
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changeset
|
339 |
clauses that arise from a subgoal.*) |
9869 | 340 |
fun skolemize th = |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
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diff
changeset
|
341 |
if not (has_consts ["Ex"] (prop_of th)) then th |
15773
f14ae2432710
Completed integration of reconstruction code. Now finds and displays proofs when used with modified version
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diff
changeset
|
342 |
else (skolemize (tryres(th, [choice, conj_exD1, conj_exD2, |
15679
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Integrating the reconstruction files into the building of HOL
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changeset
|
343 |
disj_exD, disj_exD1, disj_exD2]))) |
9869 | 344 |
handle THM _ => |
345 |
skolemize (forward_res skolemize |
|
346 |
(tryres (th, [conj_forward, disj_forward, all_forward]))) |
|
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
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diff
changeset
|
347 |
handle THM _ => forward_res skolemize (th RS ex_forward); |
9dfcb0224f8c
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changeset
|
348 |
|
9dfcb0224f8c
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changeset
|
349 |
|
9dfcb0224f8c
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paulson
parents:
diff
changeset
|
350 |
(*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
|
351 |
The resulting clauses are HOL disjunctions.*) |
9869 | 352 |
fun make_clauses ths = |
15998
bc916036cf84
new cnf function taking Skolemization theorems as an extra argument
paulson
parents:
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diff
changeset
|
353 |
(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
|
354 |
|
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
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diff
changeset
|
355 |
|
16563 | 356 |
(*Convert a list of clauses (disjunctions) to Horn clauses (contrapositives)*) |
9869 | 357 |
fun make_horns ths = |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
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changeset
|
358 |
name_thms "Horn#" |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
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parents:
15570
diff
changeset
|
359 |
(gen_distinct Drule.eq_thm_prop (foldr (add_contras clause_rules) [] ths)); |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
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diff
changeset
|
360 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
361 |
(*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
|
362 |
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
|
363 |
|
9869 | 364 |
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
|
365 |
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
|
366 |
|
9869 | 367 |
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
|
368 |
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
|
369 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
370 |
(*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
|
371 |
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
|
372 |
|
15008 | 373 |
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
|
374 |
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
|
375 |
REPEAT o (etac exE); |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
376 |
|
16588 | 377 |
(*Basis of all meson-tactics. Supplies cltac with clauses: HOL disjunctions*) |
378 |
fun MESON cltac i st = |
|
379 |
SELECT_GOAL |
|
380 |
(EVERY1 [rtac ccontr, |
|
381 |
METAHYPS (fn negs => |
|
382 |
EVERY1 [skolemize_prems_tac negs, |
|
383 |
METAHYPS (cltac o make_clauses)])]) i st |
|
384 |
handle THM _ => no_tac st; (*probably from check_is_fol*) |
|
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
385 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
386 |
(** Best-first search versions **) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
387 |
|
16563 | 388 |
(*ths is a list of additional clauses (HOL disjunctions) to use.*) |
9869 | 389 |
fun best_meson_tac sizef = |
390 |
MESON (fn cls => |
|
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
391 |
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
|
392 |
(has_fewer_prems 1, sizef) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
393 |
(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
|
394 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
395 |
(*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
|
396 |
val safe_best_meson_tac = |
9869 | 397 |
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
|
398 |
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
|
399 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
400 |
(** Depth-first search version **) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
401 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
402 |
val depth_meson_tac = |
9869 | 403 |
MESON (fn cls => EVERY [resolve_tac (gocls cls) 1, |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
404 |
depth_prolog_tac (make_horns cls)]); |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
405 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
406 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
407 |
(** Iterative deepening version **) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
408 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
409 |
(*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
|
410 |
having only one eq_assume_tac speeds it up!*) |
9869 | 411 |
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
|
412 |
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
|
413 |
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
|
414 |
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
|
415 |
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
|
416 |
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
|
417 |
((assume_tac i APPEND nrtac i) THEN check_tac) |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
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parents:
diff
changeset
|
418 |
end; |
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
419 |
|
9869 | 420 |
fun iter_deepen_prolog_tac horns = |
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9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
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parents:
diff
changeset
|
421 |
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
|
422 |
|
16563 | 423 |
fun iter_deepen_meson_tac ths = |
9869 | 424 |
MESON (fn cls => |
16563 | 425 |
case (gocls (cls@ths)) of |
426 |
[] => no_tac (*no goal clauses*) |
|
427 |
| goes => |
|
428 |
(THEN_ITER_DEEPEN (resolve_tac goes 1) |
|
429 |
(has_fewer_prems 1) |
|
430 |
(prolog_step_tac' (make_horns (cls@ths))))); |
|
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
431 |
|
16563 | 432 |
fun meson_claset_tac ths cs = |
433 |
SELECT_GOAL (TRY (safe_tac cs) THEN TRYALL (iter_deepen_meson_tac ths)); |
|
9869 | 434 |
|
16563 | 435 |
val meson_tac = CLASET' (meson_claset_tac []); |
9869 | 436 |
|
437 |
||
14813 | 438 |
(**** Code to support ordinary resolution, rather than Model Elimination ****) |
14744 | 439 |
|
15008 | 440 |
(*Convert a list of clauses (disjunctions) to meta-level clauses (==>), |
441 |
with no contrapositives, for ordinary resolution.*) |
|
14744 | 442 |
|
443 |
(*Rules to convert the head literal into a negated assumption. If the head |
|
444 |
literal is already negated, then using notEfalse instead of notEfalse' |
|
445 |
prevents a double negation.*) |
|
446 |
val notEfalse = read_instantiate [("R","False")] notE; |
|
447 |
val notEfalse' = rotate_prems 1 notEfalse; |
|
448 |
||
15448 | 449 |
fun negated_asm_of_head th = |
14744 | 450 |
th RS notEfalse handle THM _ => th RS notEfalse'; |
451 |
||
452 |
(*Converting one clause*) |
|
15581 | 453 |
fun make_meta_clause th = |
16588 | 454 |
negated_asm_of_head (make_horn resolution_clause_rules (check_is_fol th)); |
14744 | 455 |
|
456 |
fun make_meta_clauses ths = |
|
457 |
name_thms "MClause#" |
|
458 |
(gen_distinct Drule.eq_thm_prop (map make_meta_clause ths)); |
|
459 |
||
460 |
(*Permute a rule's premises to move the i-th premise to the last position.*) |
|
461 |
fun make_last i th = |
|
462 |
let val n = nprems_of th |
|
463 |
in if 1 <= i andalso i <= n |
|
464 |
then Thm.permute_prems (i-1) 1 th |
|
15118 | 465 |
else raise THM("select_literal", i, [th]) |
14744 | 466 |
end; |
467 |
||
468 |
(*Maps a rule that ends "... ==> P ==> False" to "... ==> ~P" while suppressing |
|
469 |
double-negations.*) |
|
470 |
val negate_head = rewrite_rule [atomize_not, not_not RS eq_reflection]; |
|
471 |
||
472 |
(*Maps the clause [P1,...Pn]==>False to [P1,...,P(i-1),P(i+1),...Pn] ==> ~P*) |
|
473 |
fun select_literal i cl = negate_head (make_last i cl); |
|
474 |
||
14813 | 475 |
(*Top-level Skolemization. Allows part of the conversion to clauses to be |
476 |
expressed as a tactic (or Isar method). Each assumption of the selected |
|
477 |
goal is converted to NNF and then its existential quantifiers are pulled |
|
478 |
to the front. Finally, all existential quantifiers are eliminated, |
|
479 |
leaving !!-quantified variables. Perhaps Safe_tac should follow, but it |
|
480 |
might generate many subgoals.*) |
|
481 |
val skolemize_tac = |
|
482 |
SUBGOAL |
|
483 |
(fn (prop,_) => |
|
484 |
let val ts = Logic.strip_assums_hyp prop |
|
485 |
in EVERY1 |
|
486 |
[METAHYPS |
|
15773
f14ae2432710
Completed integration of reconstruction code. Now finds and displays proofs when used with modified version
quigley
parents:
15736
diff
changeset
|
487 |
(fn hyps => (cut_facts_tac (map (skolemize o make_nnf) hyps) 1 |
14813 | 488 |
THEN REPEAT (etac exE 1))), |
489 |
REPEAT_DETERM_N (length ts) o (etac thin_rl)] |
|
490 |
end); |
|
491 |
||
15118 | 492 |
(*Top-level conversion to meta-level clauses. Each clause has |
493 |
leading !!-bound universal variables, to express generality. To get |
|
494 |
disjunctions instead of meta-clauses, remove "make_meta_clauses" below.*) |
|
15008 | 495 |
val make_clauses_tac = |
496 |
SUBGOAL |
|
497 |
(fn (prop,_) => |
|
498 |
let val ts = Logic.strip_assums_hyp prop |
|
499 |
in EVERY1 |
|
500 |
[METAHYPS |
|
501 |
(fn hyps => |
|
15151 | 502 |
(Method.insert_tac |
15118 | 503 |
(map forall_intr_vars |
504 |
(make_meta_clauses (make_clauses hyps))) 1)), |
|
15008 | 505 |
REPEAT_DETERM_N (length ts) o (etac thin_rl)] |
506 |
end); |
|
16563 | 507 |
|
508 |
||
509 |
(*** setup the special skoklemization methods ***) |
|
9869 | 510 |
|
16563 | 511 |
(*No CHANGED_PROP here, since these always appear in the preamble*) |
9869 | 512 |
|
16563 | 513 |
val skolemize_meth = Method.SIMPLE_METHOD' HEADGOAL skolemize_tac; |
514 |
||
515 |
val make_clauses_meth = Method.SIMPLE_METHOD' HEADGOAL make_clauses_tac; |
|
14890 | 516 |
|
16563 | 517 |
val skolemize_setup = |
9869 | 518 |
[Method.add_methods |
16563 | 519 |
[("skolemize", Method.no_args skolemize_meth, |
15008 | 520 |
"Skolemization into existential quantifiers"), |
521 |
("make_clauses", Method.no_args make_clauses_meth, |
|
15118 | 522 |
"Conversion to !!-quantified meta-level clauses")]]; |
9840
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
523 |
|
9dfcb0224f8c
meson.ML moved from HOL/ex to HOL/Tools: meson_tac installed by default
paulson
parents:
diff
changeset
|
524 |
end; |
9869 | 525 |
|
15579
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
526 |
structure BasicMeson: BASIC_MESON = Meson; |
32bee18c675f
Tools/meson.ML: signature, structure and "open" rather than "local"
paulson
parents:
15574
diff
changeset
|
527 |
open BasicMeson; |