author | paulson |
Wed, 21 Aug 1996 13:22:23 +0200 | |
changeset 1933 | 8b24773de6db |
parent 1927 | 6f97cb16e453 |
child 1938 | 4e29ea45520d |
permissions | -rw-r--r-- |
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(* Title: Provers/classical |
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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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Theorem prover for classical reasoning, including predicate calculus, set |
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theory, etc. |
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Rules must be classified as intr, elim, safe, hazardous. |
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A rule is unsafe unless it can be applied blindly without harmful results. |
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For a rule to be safe, its premises and conclusion should be logically |
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equivalent. There should be no variables in the premises that are not in |
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the conclusion. |
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*) |
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infix 1 THEN_MAYBE; |
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signature CLASSICAL_DATA = |
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sig |
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val mp : thm (* [| P-->Q; P |] ==> Q *) |
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val not_elim : thm (* [| ~P; P |] ==> R *) |
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val classical : thm (* (~P ==> P) ==> P *) |
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val sizef : thm -> int (* size function for BEST_FIRST *) |
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val hyp_subst_tacs: (int -> tactic) list |
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end; |
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(*Higher precedence than := facilitates use of references*) |
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infix 4 addSIs addSEs addSDs addIs addEs addDs delrules |
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setwrapper compwrapper addbefore addafter; |
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signature CLASSICAL = |
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sig |
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type claset |
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type netpair |
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val empty_cs : claset |
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val merge_cs : claset * claset -> claset |
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val addDs : claset * thm list -> claset |
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val addEs : claset * thm list -> claset |
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val addIs : claset * thm list -> claset |
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val addSDs : claset * thm list -> claset |
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val addSEs : claset * thm list -> claset |
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val addSIs : claset * thm list -> claset |
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val delrules : claset * thm list -> claset |
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val setwrapper : claset * (tactic->tactic) -> claset |
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val compwrapper : claset * (tactic->tactic) -> claset |
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val addbefore : claset * tactic -> claset |
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val addafter : claset * tactic -> claset |
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val print_cs : claset -> unit |
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val rep_claset : |
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claset -> {safeIs: thm list, safeEs: thm list, |
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hazIs: thm list, hazEs: thm list, |
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wrapper: tactic -> tactic, |
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safe0_netpair: netpair, safep_netpair: netpair, |
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haz_netpair: netpair, dup_netpair: netpair} |
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val getwrapper : claset -> tactic -> tactic |
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val THEN_MAYBE : tactic * tactic -> tactic |
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val fast_tac : claset -> int -> tactic |
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val slow_tac : claset -> int -> tactic |
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val weight_ASTAR : int ref |
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val astar_tac : claset -> int -> tactic |
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val slow_astar_tac : claset -> int -> tactic |
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val best_tac : claset -> int -> tactic |
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val slow_best_tac : claset -> int -> tactic |
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val depth_tac : claset -> int -> int -> tactic |
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val deepen_tac : claset -> int -> int -> tactic |
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val contr_tac : int -> tactic |
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val dup_elim : thm -> thm |
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val dup_intr : thm -> thm |
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val dup_step_tac : claset -> int -> tactic |
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val eq_mp_tac : int -> tactic |
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val haz_step_tac : claset -> int -> tactic |
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val joinrules : thm list * thm list -> (bool * thm) list |
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val mp_tac : int -> tactic |
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val safe_tac : claset -> tactic |
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val safe_step_tac : claset -> int -> tactic |
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val step_tac : claset -> int -> tactic |
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val swap : thm (* ~P ==> (~Q ==> P) ==> Q *) |
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val swapify : thm list -> thm list |
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val swap_res_tac : thm list -> int -> tactic |
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val inst_step_tac : claset -> int -> tactic |
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val inst0_step_tac : claset -> int -> tactic |
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val instp_step_tac : claset -> int -> tactic |
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val claset : claset ref |
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val AddDs : thm list -> unit |
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val AddEs : thm list -> unit |
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val AddIs : thm list -> unit |
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val AddSDs : thm list -> unit |
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val AddSEs : thm list -> unit |
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val AddSIs : thm list -> unit |
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val Delrules : thm list -> unit |
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val Safe_step_tac : int -> tactic |
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val Step_tac : int -> tactic |
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val Fast_tac : int -> tactic |
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val Best_tac : int -> tactic |
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val Deepen_tac : int -> int -> tactic |
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end; |
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functor ClassicalFun(Data: CLASSICAL_DATA): CLASSICAL = |
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struct |
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local open Data in |
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(*** Useful tactics for classical reasoning ***) |
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val imp_elim = (*cannot use bind_thm within a structure!*) |
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store_thm ("imp_elim", make_elim mp); |
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(*Solve goal that assumes both P and ~P. *) |
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val contr_tac = eresolve_tac [not_elim] THEN' assume_tac; |
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(*Finds P-->Q and P in the assumptions, replaces implication by Q. |
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Could do the same thing for P<->Q and P... *) |
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fun mp_tac i = eresolve_tac [not_elim, imp_elim] i THEN assume_tac i; |
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(*Like mp_tac but instantiates no variables*) |
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fun eq_mp_tac i = ematch_tac [not_elim, imp_elim] i THEN eq_assume_tac i; |
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val swap = |
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store_thm ("swap", rule_by_tactic (etac thin_rl 1) (not_elim RS classical)); |
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(*Creates rules to eliminate ~A, from rules to introduce A*) |
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fun swapify intrs = intrs RLN (2, [swap]); |
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(*Uses introduction rules in the normal way, or on negated assumptions, |
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trying rules in order. *) |
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fun swap_res_tac rls = |
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let fun addrl (rl,brls) = (false, rl) :: (true, rl RSN (2,swap)) :: brls |
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in assume_tac ORELSE' |
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contr_tac ORELSE' |
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biresolve_tac (foldr addrl (rls,[])) |
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end; |
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(*Duplication of hazardous rules, for complete provers*) |
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fun dup_intr th = standard (th RS classical); |
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fun dup_elim th = th RSN (2, revcut_rl) |> assumption 2 |> Sequence.hd |> |
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rule_by_tactic (TRYALL (etac revcut_rl)); |
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(**** Classical rule sets ****) |
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type netpair = (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net; |
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datatype claset = |
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CS of {safeIs : thm list, (*safe introduction rules*) |
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safeEs : thm list, (*safe elimination rules*) |
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hazIs : thm list, (*unsafe introduction rules*) |
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hazEs : thm list, (*unsafe elimination rules*) |
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wrapper : tactic->tactic, (*for transforming step_tac*) |
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safe0_netpair : netpair, (*nets for trivial cases*) |
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safep_netpair : netpair, (*nets for >0 subgoals*) |
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haz_netpair : netpair, (*nets for unsafe rules*) |
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dup_netpair : netpair}; (*nets for duplication*) |
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(*Desired invariants are |
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safe0_netpair = build safe0_brls, |
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safep_netpair = build safep_brls, |
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haz_netpair = build (joinrules(hazIs, hazEs)), |
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dup_netpair = build (joinrules(map dup_intr hazIs, |
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map dup_elim hazEs))} |
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where build = build_netpair(Net.empty,Net.empty), |
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safe0_brls contains all brules that solve the subgoal, and |
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safep_brls contains all brules that generate 1 or more new subgoals. |
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The theorem lists are largely comments, though they are used in merge_cs. |
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Nets must be built incrementally, to save space and time. |
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*) |
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val empty_cs = |
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CS{safeIs = [], |
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safeEs = [], |
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hazIs = [], |
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hazEs = [], |
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wrapper = I, |
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safe0_netpair = (Net.empty,Net.empty), |
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184 |
safep_netpair = (Net.empty,Net.empty), |
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185 |
haz_netpair = (Net.empty,Net.empty), |
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dup_netpair = (Net.empty,Net.empty)}; |
0 | 187 |
|
188 |
fun print_cs (CS{safeIs,safeEs,hazIs,hazEs,...}) = |
|
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189 |
(writeln"Introduction rules"; prths hazIs; |
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190 |
writeln"Safe introduction rules"; prths safeIs; |
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191 |
writeln"Elimination rules"; prths hazEs; |
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192 |
writeln"Safe elimination rules"; prths safeEs; |
0 | 193 |
()); |
194 |
||
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195 |
fun rep_claset (CS args) = args; |
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196 |
|
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197 |
fun getwrapper (CS{wrapper,...}) = wrapper; |
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198 |
|
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199 |
|
1800 | 200 |
(*** Adding (un)safe introduction or elimination rules. |
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201 |
|
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202 |
In case of overlap, new rules are tried BEFORE old ones!! |
1800 | 203 |
***) |
0 | 204 |
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205 |
(*For use with biresolve_tac. Combines intr rules with swap to handle negated |
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206 |
assumptions. Pairs elim rules with true. *) |
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207 |
fun joinrules (intrs,elims) = |
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208 |
(map (pair true) (elims @ swapify intrs) @ |
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209 |
map (pair false) intrs); |
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210 |
|
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211 |
(*Priority: prefer rules with fewest subgoals, |
1231 | 212 |
then rules added most recently (preferring the head of the list).*) |
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213 |
fun tag_brls k [] = [] |
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214 |
| tag_brls k (brl::brls) = |
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215 |
(1000000*subgoals_of_brl brl + k, brl) :: |
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216 |
tag_brls (k+1) brls; |
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217 |
|
1800 | 218 |
fun insert_tagged_list kbrls netpr = foldr insert_tagged_brl (kbrls, netpr); |
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219 |
|
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220 |
(*Insert into netpair that already has nI intr rules and nE elim rules. |
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221 |
Count the intr rules double (to account for swapify). Negate to give the |
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222 |
new insertions the lowest priority.*) |
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223 |
fun insert (nI,nE) = insert_tagged_list o (tag_brls (~(2*nI+nE))) o joinrules; |
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224 |
|
1800 | 225 |
fun delete_tagged_list brls netpr = foldr delete_tagged_brl (brls, netpr); |
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226 |
|
1800 | 227 |
val delete = delete_tagged_list o joinrules; |
228 |
||
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229 |
(*Warn if the rule is already present ELSEWHERE in the claset. The addition |
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230 |
is still allowed.*) |
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231 |
fun warn_dup th (CS{safeIs, safeEs, hazIs, hazEs, ...}) = |
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232 |
if gen_mem eq_thm (th, safeIs) then |
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233 |
warning ("rule already in claset as Safe Intr\n" ^ string_of_thm th) |
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234 |
else if gen_mem eq_thm (th, safeEs) then |
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235 |
warning ("rule already in claset as Safe Elim\n" ^ string_of_thm th) |
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236 |
else if gen_mem eq_thm (th, hazIs) then |
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237 |
warning ("rule already in claset as unsafe Intr\n" ^ string_of_thm th) |
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238 |
else if gen_mem eq_thm (th, hazEs) then |
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239 |
warning ("rule already in claset as unsafe Elim\n" ^ string_of_thm th) |
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240 |
else (); |
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241 |
|
1800 | 242 |
(*** Safe rules ***) |
982
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243 |
|
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244 |
fun addSI (cs as CS{safeIs, safeEs, hazIs, hazEs, wrapper, |
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245 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
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246 |
th) = |
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247 |
if gen_mem eq_thm (th, safeIs) then |
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248 |
(warning ("ignoring duplicate Safe Intr\n" ^ string_of_thm th); |
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249 |
cs) |
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250 |
else |
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251 |
let val (safe0_rls, safep_rls) = (*0 subgoals vs 1 or more*) |
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252 |
partition (fn rl => nprems_of rl=0) [th] |
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253 |
val nI = length safeIs + 1 |
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254 |
and nE = length safeEs |
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255 |
in warn_dup th cs; |
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256 |
CS{safeIs = th::safeIs, |
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257 |
safe0_netpair = insert (nI,nE) (safe0_rls, []) safe0_netpair, |
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258 |
safep_netpair = insert (nI,nE) (safep_rls, []) safep_netpair, |
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259 |
safeEs = safeEs, |
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260 |
hazIs = hazIs, |
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261 |
hazEs = hazEs, |
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262 |
wrapper = wrapper, |
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263 |
haz_netpair = haz_netpair, |
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|
264 |
dup_netpair = dup_netpair} |
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|
265 |
end; |
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266 |
|
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267 |
fun addSE (cs as CS{safeIs, safeEs, hazIs, hazEs, wrapper, |
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268 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
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|
269 |
th) = |
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|
270 |
if gen_mem eq_thm (th, safeEs) then |
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|
271 |
(warning ("ignoring duplicate Safe Elim\n" ^ string_of_thm th); |
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|
272 |
cs) |
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273 |
else |
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274 |
let val (safe0_rls, safep_rls) = (*0 subgoals vs 1 or more*) |
1927
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275 |
partition (fn rl => nprems_of rl=1) [th] |
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276 |
val nI = length safeIs |
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|
277 |
and nE = length safeEs + 1 |
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|
278 |
in warn_dup th cs; |
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|
279 |
CS{safeEs = th::safeEs, |
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280 |
safe0_netpair = insert (nI,nE) ([], safe0_rls) safe0_netpair, |
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281 |
safep_netpair = insert (nI,nE) ([], safep_rls) safep_netpair, |
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282 |
safeIs = safeIs, |
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|
283 |
hazIs = hazIs, |
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|
284 |
hazEs = hazEs, |
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|
285 |
wrapper = wrapper, |
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|
286 |
haz_netpair = haz_netpair, |
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|
287 |
dup_netpair = dup_netpair} |
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|
288 |
end; |
0 | 289 |
|
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290 |
fun rev_foldl f (e, l) = foldl f (e, rev l); |
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291 |
|
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292 |
val op addSIs = rev_foldl addSI; |
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293 |
val op addSEs = rev_foldl addSE; |
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294 |
|
0 | 295 |
fun cs addSDs ths = cs addSEs (map make_elim ths); |
296 |
||
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297 |
|
1800 | 298 |
(*** Hazardous (unsafe) rules ***) |
0 | 299 |
|
1927
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|
300 |
fun addI (cs as CS{safeIs, safeEs, hazIs, hazEs, wrapper, |
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|
301 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
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|
302 |
th)= |
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|
303 |
if gen_mem eq_thm (th, hazIs) then |
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|
304 |
(warning ("ignoring duplicate unsafe Intr\n" ^ string_of_thm th); |
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New classical reasoner: warns of, and ignores, redundant rules.
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|
305 |
cs) |
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|
306 |
else |
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New classical reasoner: warns of, and ignores, redundant rules.
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|
307 |
let val nI = length hazIs + 1 |
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|
308 |
and nE = length hazEs |
1927
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|
309 |
in warn_dup th cs; |
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|
310 |
CS{hazIs = th::hazIs, |
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|
311 |
haz_netpair = insert (nI,nE) ([th], []) haz_netpair, |
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|
312 |
dup_netpair = insert (nI,nE) (map dup_intr [th], []) dup_netpair, |
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|
313 |
safeIs = safeIs, |
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|
314 |
safeEs = safeEs, |
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|
315 |
hazEs = hazEs, |
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|
316 |
wrapper = wrapper, |
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|
317 |
safe0_netpair = safe0_netpair, |
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|
318 |
safep_netpair = safep_netpair} |
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diff
changeset
|
319 |
end; |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
320 |
|
1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
321 |
fun addE (cs as CS{safeIs, safeEs, hazIs, hazEs, wrapper, |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
322 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
323 |
th) = |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
324 |
if gen_mem eq_thm (th, hazEs) then |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
325 |
(warning ("ignoring duplicate unsafe Elim\n" ^ string_of_thm th); |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
326 |
cs) |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
327 |
else |
1073
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
328 |
let val nI = length hazIs |
1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
329 |
and nE = length hazEs + 1 |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
330 |
in warn_dup th cs; |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
331 |
CS{hazEs = th::hazEs, |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
332 |
haz_netpair = insert (nI,nE) ([], [th]) haz_netpair, |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
333 |
dup_netpair = insert (nI,nE) ([], map dup_elim [th]) dup_netpair, |
1073
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
334 |
safeIs = safeIs, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
335 |
safeEs = safeEs, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
336 |
hazIs = hazIs, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
337 |
wrapper = wrapper, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
338 |
safe0_netpair = safe0_netpair, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
339 |
safep_netpair = safep_netpair} |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
340 |
end; |
0 | 341 |
|
1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
342 |
val op addIs = rev_foldl addI; |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
343 |
val op addEs = rev_foldl addE; |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
344 |
|
0 | 345 |
fun cs addDs ths = cs addEs (map make_elim ths); |
346 |
||
1073
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
347 |
|
1800 | 348 |
(*** Deletion of rules |
349 |
Working out what to delete, requires repeating much of the code used |
|
350 |
to insert. |
|
1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
351 |
Separate functions delSI, etc., are not exported; instead delrules |
1800 | 352 |
searches in all the lists and chooses the relevant delXX function. |
353 |
***) |
|
354 |
||
1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
355 |
fun delSI (CS{safeIs, safeEs, hazIs, hazEs, wrapper, |
1800 | 356 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
357 |
th) = |
|
358 |
let val (safe0_rls, safep_rls) = partition (fn rl => nprems_of rl=0) [th] |
|
359 |
in CS{safeIs = gen_rem eq_thm (safeIs,th), |
|
360 |
safe0_netpair = delete (safe0_rls, []) safe0_netpair, |
|
361 |
safep_netpair = delete (safep_rls, []) safep_netpair, |
|
362 |
safeEs = safeEs, |
|
363 |
hazIs = hazIs, |
|
364 |
hazEs = hazEs, |
|
365 |
wrapper = wrapper, |
|
366 |
haz_netpair = haz_netpair, |
|
367 |
dup_netpair = dup_netpair} |
|
368 |
end; |
|
369 |
||
1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
370 |
fun delSE (CS{safeIs, safeEs, hazIs, hazEs, wrapper, |
1800 | 371 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
372 |
th) = |
|
373 |
let val (safe0_rls, safep_rls) = partition (fn rl => nprems_of rl=1) [th] |
|
374 |
in CS{safeEs = gen_rem eq_thm (safeEs,th), |
|
375 |
safe0_netpair = delete ([], safe0_rls) safe0_netpair, |
|
376 |
safep_netpair = delete ([], safep_rls) safep_netpair, |
|
377 |
safeIs = safeIs, |
|
378 |
hazIs = hazIs, |
|
379 |
hazEs = hazEs, |
|
380 |
wrapper = wrapper, |
|
381 |
haz_netpair = haz_netpair, |
|
382 |
dup_netpair = dup_netpair} |
|
383 |
end; |
|
384 |
||
385 |
||
1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
386 |
fun delI (CS{safeIs, safeEs, hazIs, hazEs, wrapper, |
1800 | 387 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
388 |
th) = |
|
389 |
CS{hazIs = gen_rem eq_thm (hazIs,th), |
|
390 |
haz_netpair = delete ([th], []) haz_netpair, |
|
391 |
dup_netpair = delete ([dup_intr th], []) dup_netpair, |
|
392 |
safeIs = safeIs, |
|
393 |
safeEs = safeEs, |
|
394 |
hazEs = hazEs, |
|
395 |
wrapper = wrapper, |
|
396 |
safe0_netpair = safe0_netpair, |
|
397 |
safep_netpair = safep_netpair}; |
|
398 |
||
1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
399 |
fun delE (CS{safeIs, safeEs, hazIs, hazEs, wrapper, |
1800 | 400 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
401 |
th) = |
|
402 |
CS{hazEs = gen_rem eq_thm (hazEs,th), |
|
403 |
haz_netpair = delete ([], [th]) haz_netpair, |
|
404 |
dup_netpair = delete ([], [dup_elim th]) dup_netpair, |
|
405 |
safeIs = safeIs, |
|
406 |
safeEs = safeEs, |
|
407 |
hazIs = hazIs, |
|
408 |
wrapper = wrapper, |
|
409 |
safe0_netpair = safe0_netpair, |
|
410 |
safep_netpair = safep_netpair}; |
|
411 |
||
412 |
fun delrule (cs as CS{safeIs, safeEs, hazIs, hazEs, ...}, th) = |
|
1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
413 |
if gen_mem eq_thm (th, safeIs) then delSI(cs,th) |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
414 |
else if gen_mem eq_thm (th, safeEs) then delSE(cs,th) |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
415 |
else if gen_mem eq_thm (th, hazIs) then delI(cs,th) |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
416 |
else if gen_mem eq_thm (th, hazEs) then delE(cs,th) |
1800 | 417 |
else (warning ("rule not in claset\n" ^ (string_of_thm th)); |
418 |
cs); |
|
419 |
||
420 |
val op delrules = foldl delrule; |
|
421 |
||
422 |
||
423 |
(*** Setting or modifying the wrapper tactical ***) |
|
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
424 |
|
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
425 |
(*Set a new wrapper*) |
1073
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
426 |
fun (CS{safeIs, safeEs, hazIs, hazEs, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
427 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair, ...}) |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
428 |
setwrapper new_wrapper = |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
429 |
CS{wrapper = new_wrapper, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
430 |
safeIs = safeIs, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
431 |
safeEs = safeEs, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
432 |
hazIs = hazIs, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
433 |
hazEs = hazEs, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
434 |
safe0_netpair = safe0_netpair, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
435 |
safep_netpair = safep_netpair, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
436 |
haz_netpair = haz_netpair, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
437 |
dup_netpair = dup_netpair}; |
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
438 |
|
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
439 |
(*Compose a tactical with the existing wrapper*) |
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
440 |
fun cs compwrapper wrapper' = cs setwrapper (wrapper' o getwrapper cs); |
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
441 |
|
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
442 |
(*Execute tac1, but only execute tac2 if there are at least as many subgoals |
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
443 |
as before. This ensures that tac2 is only applied to an outcome of tac1.*) |
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
444 |
fun tac1 THEN_MAYBE tac2 = |
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
445 |
STATE (fn state => |
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
446 |
tac1 THEN |
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
447 |
COND (has_fewer_prems (nprems_of state)) all_tac tac2); |
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
448 |
|
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
449 |
(*Cause a tactic to be executed before/after the step tactic*) |
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
450 |
fun cs addbefore tac2 = cs compwrapper (fn tac1 => tac2 THEN_MAYBE tac1); |
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
451 |
fun cs addafter tac2 = cs compwrapper (fn tac1 => tac1 THEN_MAYBE tac2); |
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
452 |
|
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
453 |
|
1711 | 454 |
(*Merge works by adding all new rules of the 2nd claset into the 1st claset. |
455 |
Merging the term nets may look more efficient, but the rather delicate |
|
456 |
treatment of priority might get muddled up.*) |
|
457 |
fun merge_cs |
|
458 |
(cs as CS{safeIs, safeEs, hazIs, hazEs, wrapper, ...}, |
|
459 |
CS{safeIs=safeIs2, safeEs=safeEs2, hazIs=hazIs2, hazEs=hazEs2,...}) = |
|
460 |
let val safeIs' = gen_rems eq_thm (safeIs2,safeIs) |
|
461 |
val safeEs' = gen_rems eq_thm (safeEs2,safeEs) |
|
462 |
val hazIs' = gen_rems eq_thm (hazIs2,hazIs) |
|
463 |
val hazEs' = gen_rems eq_thm (hazEs2,hazEs) |
|
464 |
in cs addSIs safeIs' |
|
465 |
addSEs safeEs' |
|
466 |
addIs hazIs' |
|
467 |
addEs hazEs' |
|
468 |
end; |
|
469 |
||
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
470 |
|
1800 | 471 |
(**** Simple tactics for theorem proving ****) |
0 | 472 |
|
473 |
(*Attack subgoals using safe inferences -- matching, not resolution*) |
|
474 |
fun safe_step_tac (CS{safe0_netpair,safep_netpair,...}) = |
|
475 |
FIRST' [eq_assume_tac, |
|
476 |
eq_mp_tac, |
|
477 |
bimatch_from_nets_tac safe0_netpair, |
|
478 |
FIRST' hyp_subst_tacs, |
|
479 |
bimatch_from_nets_tac safep_netpair] ; |
|
480 |
||
481 |
(*Repeatedly attack subgoals using safe inferences -- it's deterministic!*) |
|
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
482 |
fun safe_tac cs = REPEAT_DETERM_FIRST (safe_step_tac cs); |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
483 |
|
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
484 |
(*But these unsafe steps at least solve a subgoal!*) |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
485 |
fun inst0_step_tac (CS{safe0_netpair,safep_netpair,...}) = |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
486 |
assume_tac APPEND' |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
487 |
contr_tac APPEND' |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
488 |
biresolve_from_nets_tac safe0_netpair; |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
489 |
|
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
490 |
(*These are much worse since they could generate more and more subgoals*) |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
491 |
fun instp_step_tac (CS{safep_netpair,...}) = |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
492 |
biresolve_from_nets_tac safep_netpair; |
0 | 493 |
|
494 |
(*These steps could instantiate variables and are therefore unsafe.*) |
|
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
495 |
fun inst_step_tac cs = inst0_step_tac cs APPEND' instp_step_tac cs; |
0 | 496 |
|
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
497 |
fun haz_step_tac (CS{haz_netpair,...}) = |
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
498 |
biresolve_from_nets_tac haz_netpair; |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
499 |
|
0 | 500 |
(*Single step for the prover. FAILS unless it makes progress. *) |
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
501 |
fun step_tac cs i = |
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
502 |
getwrapper cs |
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
503 |
(FIRST [safe_tac cs, inst_step_tac cs i, haz_step_tac cs i]); |
0 | 504 |
|
505 |
(*Using a "safe" rule to instantiate variables is unsafe. This tactic |
|
506 |
allows backtracking from "safe" rules to "unsafe" rules here.*) |
|
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
507 |
fun slow_step_tac cs i = |
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
508 |
getwrapper cs |
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
509 |
(safe_tac cs ORELSE (inst_step_tac cs i APPEND haz_step_tac cs i)); |
0 | 510 |
|
1800 | 511 |
(**** The following tactics all fail unless they solve one goal ****) |
0 | 512 |
|
513 |
(*Dumb but fast*) |
|
514 |
fun fast_tac cs = SELECT_GOAL (DEPTH_SOLVE (step_tac cs 1)); |
|
515 |
||
516 |
(*Slower but smarter than fast_tac*) |
|
517 |
fun best_tac cs = |
|
518 |
SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, sizef) (step_tac cs 1)); |
|
519 |
||
520 |
fun slow_tac cs = SELECT_GOAL (DEPTH_SOLVE (slow_step_tac cs 1)); |
|
521 |
||
522 |
fun slow_best_tac cs = |
|
523 |
SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, sizef) (slow_step_tac cs 1)); |
|
524 |
||
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
525 |
|
1800 | 526 |
(***ASTAR with weight weight_ASTAR, by Norbert Voelker*) |
1587
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
527 |
val weight_ASTAR = ref 5; |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
528 |
|
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
529 |
fun astar_tac cs = |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
530 |
SELECT_GOAL ( ASTAR (has_fewer_prems 1 |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
531 |
, fn level =>(fn thm =>size_of_thm thm + !weight_ASTAR *level)) |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
532 |
(step_tac cs 1)); |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
533 |
|
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
534 |
fun slow_astar_tac cs = |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
535 |
SELECT_GOAL ( ASTAR (has_fewer_prems 1 |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
536 |
, fn level =>(fn thm =>size_of_thm thm + !weight_ASTAR *level)) |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
537 |
(slow_step_tac cs 1)); |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
538 |
|
1800 | 539 |
(**** Complete tactic, loosely based upon LeanTaP. This tactic is the outcome |
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
540 |
of much experimentation! Changing APPEND to ORELSE below would prove |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
541 |
easy theorems faster, but loses completeness -- and many of the harder |
1800 | 542 |
theorems such as 43. ****) |
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
543 |
|
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
544 |
(*Non-deterministic! Could always expand the first unsafe connective. |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
545 |
That's hard to implement and did not perform better in experiments, due to |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
546 |
greater search depth required.*) |
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
547 |
fun dup_step_tac (cs as (CS{dup_netpair,...})) = |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
548 |
biresolve_from_nets_tac dup_netpair; |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
549 |
|
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
550 |
(*Searching to depth m.*) |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
551 |
fun depth_tac cs m i = STATE(fn state => |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
552 |
SELECT_GOAL |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
553 |
(REPEAT_DETERM1 (safe_step_tac cs 1) THEN_ELSE |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
554 |
(DEPTH_SOLVE (depth_tac cs m 1), |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
555 |
inst0_step_tac cs 1 APPEND |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
556 |
COND (K(m=0)) no_tac |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
557 |
((instp_step_tac cs 1 APPEND dup_step_tac cs 1) |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
558 |
THEN DEPTH_SOLVE (depth_tac cs (m-1) 1)))) |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
559 |
i); |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
560 |
|
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
561 |
(*Iterative deepening tactical. Allows us to "deepen" any search tactic*) |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
562 |
fun DEEPEN tacf m i = STATE(fn state => |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
563 |
if has_fewer_prems i state then no_tac |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
564 |
else (writeln ("Depth = " ^ string_of_int m); |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
565 |
tacf m i ORELSE DEEPEN tacf (m+2) i)); |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
566 |
|
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
567 |
fun safe_depth_tac cs m = |
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
568 |
SUBGOAL |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
569 |
(fn (prem,i) => |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
570 |
let val deti = |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
571 |
(*No Vars in the goal? No need to backtrack between goals.*) |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
572 |
case term_vars prem of |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
573 |
[] => DETERM |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
574 |
| _::_ => I |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
575 |
in SELECT_GOAL (TRY (safe_tac cs) THEN |
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
576 |
DEPTH_SOLVE (deti (depth_tac cs m 1))) i |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
577 |
end); |
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
578 |
|
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
579 |
fun deepen_tac cs = DEEPEN (safe_depth_tac cs); |
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
580 |
|
1724 | 581 |
val claset = ref empty_cs; |
582 |
||
583 |
fun AddDs ts = (claset := !claset addDs ts); |
|
584 |
||
585 |
fun AddEs ts = (claset := !claset addEs ts); |
|
586 |
||
587 |
fun AddIs ts = (claset := !claset addIs ts); |
|
588 |
||
589 |
fun AddSDs ts = (claset := !claset addSDs ts); |
|
590 |
||
591 |
fun AddSEs ts = (claset := !claset addSEs ts); |
|
592 |
||
593 |
fun AddSIs ts = (claset := !claset addSIs ts); |
|
594 |
||
1807 | 595 |
fun Delrules ts = (claset := !claset delrules ts); |
596 |
||
1800 | 597 |
(*Cannot have Safe_tac, as it takes no arguments; must delay dereferencing!*) |
598 |
||
1814 | 599 |
fun Safe_step_tac i = safe_step_tac (!claset) i; |
600 |
||
1800 | 601 |
fun Step_tac i = step_tac (!claset) i; |
602 |
||
1724 | 603 |
fun Fast_tac i = fast_tac (!claset) i; |
604 |
||
1800 | 605 |
fun Best_tac i = best_tac (!claset) i; |
606 |
||
607 |
fun Deepen_tac m = deepen_tac (!claset) m; |
|
608 |
||
0 | 609 |
end; |
610 |
end; |