author | wenzelm |
Fri, 07 Mar 1997 11:48:46 +0100 | |
changeset 2754 | 59bd96046ad6 |
parent 2689 | 6d3d893453de |
child 2813 | cc4c816dafdc |
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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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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setSWrapper compSWrapper setWrapper compWrapper |
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addSbefore addSaltern addbefore addaltern; |
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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 setSWrapper : claset * ((int -> tactic) -> (int -> tactic)) ->claset |
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val compSWrapper : claset * ((int -> tactic) -> (int -> tactic)) ->claset |
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val setWrapper : claset * ((int -> tactic) -> (int -> tactic)) ->claset |
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val compWrapper : claset * ((int -> tactic) -> (int -> tactic)) ->claset |
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val addSbefore : claset * (int -> tactic) -> claset |
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val addSaltern : claset * (int -> tactic) -> claset |
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val addbefore : claset * (int -> tactic) -> claset |
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val addaltern : claset * (int -> 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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uwrapper: (int -> tactic) -> (int -> tactic), |
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swrapper: (int -> tactic) -> (int -> 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 -> (int -> tactic) -> (int -> tactic) |
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val getSWrapper : claset -> (int -> tactic) -> (int -> 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 : (int -> int -> tactic) -> 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 slow_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 Slow_tac : int -> tactic |
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val Slow_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 = zero_var_indexes (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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uwrapper : (int -> tactic) -> |
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(int -> tactic), (*for transforming step_tac*) |
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swrapper : (int -> tactic) -> |
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(int -> tactic), (*for transform. safe_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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uwrapper = I, |
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swrapper = I, |
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safe0_netpair = (Net.empty,Net.empty), |
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safep_netpair = (Net.empty,Net.empty), |
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haz_netpair = (Net.empty,Net.empty), |
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dup_netpair = (Net.empty,Net.empty)}; |
0 | 199 |
|
200 |
fun print_cs (CS{safeIs,safeEs,hazIs,hazEs,...}) = |
|
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(writeln"Introduction rules"; prths hazIs; |
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202 |
writeln"Safe introduction rules"; prths safeIs; |
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203 |
writeln"Elimination rules"; prths hazEs; |
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writeln"Safe elimination rules"; prths safeEs; |
0 | 205 |
()); |
206 |
||
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fun rep_claset (CS args) = args; |
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208 |
|
2630 | 209 |
fun getWrapper (CS{uwrapper,...}) = uwrapper; |
210 |
||
211 |
fun getSWrapper (CS{swrapper,...}) = swrapper; |
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212 |
|
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213 |
|
1800 | 214 |
(*** Adding (un)safe introduction or elimination rules. |
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215 |
|
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216 |
In case of overlap, new rules are tried BEFORE old ones!! |
1800 | 217 |
***) |
0 | 218 |
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(*For use with biresolve_tac. Combines intr rules with swap to handle negated |
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220 |
assumptions. Pairs elim rules with true. *) |
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fun joinrules (intrs,elims) = |
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(map (pair true) (elims @ swapify intrs) @ |
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map (pair false) intrs); |
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224 |
|
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225 |
(*Priority: prefer rules with fewest subgoals, |
1231 | 226 |
then rules added most recently (preferring the head of the list).*) |
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fun tag_brls k [] = [] |
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228 |
| tag_brls k (brl::brls) = |
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(1000000*subgoals_of_brl brl + k, brl) :: |
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tag_brls (k+1) brls; |
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231 |
|
1800 | 232 |
fun insert_tagged_list kbrls netpr = foldr insert_tagged_brl (kbrls, netpr); |
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233 |
|
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234 |
(*Insert into netpair that already has nI intr rules and nE elim rules. |
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235 |
Count the intr rules double (to account for swapify). Negate to give the |
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236 |
new insertions the lowest priority.*) |
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237 |
fun insert (nI,nE) = insert_tagged_list o (tag_brls (~(2*nI+nE))) o joinrules; |
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238 |
|
1800 | 239 |
fun delete_tagged_list brls netpr = foldr delete_tagged_brl (brls, netpr); |
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240 |
|
1800 | 241 |
val delete = delete_tagged_list o joinrules; |
242 |
||
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243 |
(*Warn if the rule is already present ELSEWHERE in the claset. The addition |
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244 |
is still allowed.*) |
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245 |
fun warn_dup th (CS{safeIs, safeEs, hazIs, hazEs, ...}) = |
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246 |
if gen_mem eq_thm (th, safeIs) then |
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warning ("rule already in claset as Safe Intr\n" ^ string_of_thm th) |
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else if gen_mem eq_thm (th, safeEs) then |
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warning ("rule already in claset as Safe Elim\n" ^ string_of_thm th) |
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250 |
else if gen_mem eq_thm (th, hazIs) then |
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warning ("rule already in claset as unsafe Intr\n" ^ string_of_thm th) |
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else if gen_mem eq_thm (th, hazEs) then |
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warning ("rule already in claset as unsafe Elim\n" ^ string_of_thm th) |
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254 |
else (); |
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255 |
|
1800 | 256 |
(*** Safe rules ***) |
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257 |
|
2630 | 258 |
fun addSI (cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper, |
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259 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
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260 |
th) = |
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261 |
if gen_mem eq_thm (th, safeIs) then |
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262 |
(warning ("ignoring duplicate Safe Intr\n" ^ string_of_thm th); |
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263 |
cs) |
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264 |
else |
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|
265 |
let val (safe0_rls, safep_rls) = (*0 subgoals vs 1 or more*) |
1927
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266 |
partition (fn rl => nprems_of rl=0) [th] |
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267 |
val nI = length safeIs + 1 |
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268 |
and nE = length safeEs |
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269 |
in warn_dup th cs; |
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CS{safeIs = th::safeIs, |
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271 |
safe0_netpair = insert (nI,nE) (safe0_rls, []) safe0_netpair, |
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safep_netpair = insert (nI,nE) (safep_rls, []) safep_netpair, |
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273 |
safeEs = safeEs, |
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274 |
hazIs = hazIs, |
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|
275 |
hazEs = hazEs, |
2630 | 276 |
uwrapper = uwrapper, |
277 |
swrapper = swrapper, |
|
278 |
haz_netpair = haz_netpair, |
|
279 |
dup_netpair = dup_netpair} |
|
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|
280 |
end; |
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281 |
|
2630 | 282 |
fun addSE (cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper, |
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|
283 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
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|
284 |
th) = |
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|
285 |
if gen_mem eq_thm (th, safeEs) then |
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|
286 |
(warning ("ignoring duplicate Safe Elim\n" ^ string_of_thm th); |
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|
287 |
cs) |
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|
288 |
else |
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|
289 |
let val (safe0_rls, safep_rls) = (*0 subgoals vs 1 or more*) |
1927
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|
290 |
partition (fn rl => nprems_of rl=1) [th] |
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291 |
val nI = length safeIs |
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|
292 |
and nE = length safeEs + 1 |
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|
293 |
in warn_dup th cs; |
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|
294 |
CS{safeEs = th::safeEs, |
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295 |
safe0_netpair = insert (nI,nE) ([], safe0_rls) safe0_netpair, |
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296 |
safep_netpair = insert (nI,nE) ([], safep_rls) safep_netpair, |
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|
297 |
safeIs = safeIs, |
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|
298 |
hazIs = hazIs, |
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|
299 |
hazEs = hazEs, |
2630 | 300 |
uwrapper = uwrapper, |
301 |
swrapper = swrapper, |
|
302 |
haz_netpair = haz_netpair, |
|
303 |
dup_netpair = dup_netpair} |
|
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|
304 |
end; |
0 | 305 |
|
1927
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|
306 |
fun rev_foldl f (e, l) = foldl f (e, rev l); |
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|
307 |
|
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parents:
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|
308 |
val op addSIs = rev_foldl addSI; |
6f97cb16e453
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|
309 |
val op addSEs = rev_foldl addSE; |
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|
310 |
|
0 | 311 |
fun cs addSDs ths = cs addSEs (map make_elim ths); |
312 |
||
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|
313 |
|
1800 | 314 |
(*** Hazardous (unsafe) rules ***) |
0 | 315 |
|
2630 | 316 |
fun addI (cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper, |
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|
317 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
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New classical reasoner: warns of, and ignores, redundant rules.
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|
318 |
th)= |
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|
319 |
if gen_mem eq_thm (th, hazIs) then |
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|
320 |
(warning ("ignoring duplicate unsafe Intr\n" ^ string_of_thm th); |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
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parents:
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changeset
|
321 |
cs) |
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New classical reasoner: warns of, and ignores, redundant rules.
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parents:
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|
322 |
else |
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New classical reasoner: warns of, and ignores, redundant rules.
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|
323 |
let val nI = length hazIs + 1 |
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|
324 |
and nE = length hazEs |
1927
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paulson
parents:
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|
325 |
in warn_dup th cs; |
6f97cb16e453
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parents:
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|
326 |
CS{hazIs = th::hazIs, |
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parents:
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|
327 |
haz_netpair = insert (nI,nE) ([th], []) haz_netpair, |
6f97cb16e453
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parents:
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|
328 |
dup_netpair = insert (nI,nE) (map dup_intr [th], []) dup_netpair, |
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|
329 |
safeIs = safeIs, |
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parents:
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|
330 |
safeEs = safeEs, |
b3f190995bc9
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|
331 |
hazEs = hazEs, |
2630 | 332 |
uwrapper = uwrapper, |
333 |
swrapper = swrapper, |
|
1073
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|
334 |
safe0_netpair = safe0_netpair, |
b3f190995bc9
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|
335 |
safep_netpair = safep_netpair} |
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Recoded addSIs, etc., so that nets are built incrementally
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parents:
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changeset
|
336 |
end; |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
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parents:
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diff
changeset
|
337 |
|
2630 | 338 |
fun addE (cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper, |
1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
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diff
changeset
|
339 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
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changeset
|
340 |
th) = |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
341 |
if gen_mem eq_thm (th, hazEs) then |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
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changeset
|
342 |
(warning ("ignoring duplicate unsafe Elim\n" ^ string_of_thm th); |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
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changeset
|
343 |
cs) |
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New classical reasoner: warns of, and ignores, redundant rules.
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changeset
|
344 |
else |
1073
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
345 |
let val nI = length hazIs |
1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
346 |
and nE = length hazEs + 1 |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
347 |
in warn_dup th cs; |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
348 |
CS{hazEs = th::hazEs, |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
349 |
haz_netpair = insert (nI,nE) ([], [th]) haz_netpair, |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
350 |
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
|
351 |
safeIs = safeIs, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
352 |
safeEs = safeEs, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
353 |
hazIs = hazIs, |
2630 | 354 |
uwrapper = uwrapper, |
355 |
swrapper = swrapper, |
|
1073
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
356 |
safe0_netpair = safe0_netpair, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
357 |
safep_netpair = safep_netpair} |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
358 |
end; |
0 | 359 |
|
1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
360 |
val op addIs = rev_foldl addI; |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
361 |
val op addEs = rev_foldl addE; |
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
362 |
|
0 | 363 |
fun cs addDs ths = cs addEs (map make_elim ths); |
364 |
||
1073
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
365 |
|
1800 | 366 |
(*** Deletion of rules |
367 |
Working out what to delete, requires repeating much of the code used |
|
368 |
to insert. |
|
1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset
|
369 |
Separate functions delSI, etc., are not exported; instead delrules |
1800 | 370 |
searches in all the lists and chooses the relevant delXX function. |
371 |
***) |
|
372 |
||
2630 | 373 |
fun delSI (CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper, |
1800 | 374 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
375 |
th) = |
|
376 |
let val (safe0_rls, safep_rls) = partition (fn rl => nprems_of rl=0) [th] |
|
377 |
in CS{safeIs = gen_rem eq_thm (safeIs,th), |
|
378 |
safe0_netpair = delete (safe0_rls, []) safe0_netpair, |
|
379 |
safep_netpair = delete (safep_rls, []) safep_netpair, |
|
380 |
safeEs = safeEs, |
|
381 |
hazIs = hazIs, |
|
382 |
hazEs = hazEs, |
|
2630 | 383 |
uwrapper = uwrapper, |
384 |
swrapper = swrapper, |
|
385 |
haz_netpair = haz_netpair, |
|
386 |
dup_netpair = dup_netpair} |
|
1800 | 387 |
end; |
388 |
||
2630 | 389 |
fun delSE (CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper, |
1800 | 390 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
391 |
th) = |
|
392 |
let val (safe0_rls, safep_rls) = partition (fn rl => nprems_of rl=1) [th] |
|
393 |
in CS{safeEs = gen_rem eq_thm (safeEs,th), |
|
394 |
safe0_netpair = delete ([], safe0_rls) safe0_netpair, |
|
395 |
safep_netpair = delete ([], safep_rls) safep_netpair, |
|
396 |
safeIs = safeIs, |
|
397 |
hazIs = hazIs, |
|
398 |
hazEs = hazEs, |
|
2630 | 399 |
uwrapper = uwrapper, |
400 |
swrapper = swrapper, |
|
401 |
haz_netpair = haz_netpair, |
|
402 |
dup_netpair = dup_netpair} |
|
1800 | 403 |
end; |
404 |
||
405 |
||
2630 | 406 |
fun delI (CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper, |
1800 | 407 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
408 |
th) = |
|
409 |
CS{hazIs = gen_rem eq_thm (hazIs,th), |
|
410 |
haz_netpair = delete ([th], []) haz_netpair, |
|
411 |
dup_netpair = delete ([dup_intr th], []) dup_netpair, |
|
412 |
safeIs = safeIs, |
|
413 |
safeEs = safeEs, |
|
414 |
hazEs = hazEs, |
|
2630 | 415 |
uwrapper = uwrapper, |
416 |
swrapper = swrapper, |
|
1800 | 417 |
safe0_netpair = safe0_netpair, |
418 |
safep_netpair = safep_netpair}; |
|
419 |
||
2630 | 420 |
fun delE (CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper, |
1800 | 421 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, |
422 |
th) = |
|
423 |
CS{hazEs = gen_rem eq_thm (hazEs,th), |
|
424 |
haz_netpair = delete ([], [th]) haz_netpair, |
|
425 |
dup_netpair = delete ([], [dup_elim th]) dup_netpair, |
|
426 |
safeIs = safeIs, |
|
427 |
safeEs = safeEs, |
|
428 |
hazIs = hazIs, |
|
2630 | 429 |
uwrapper = uwrapper, |
430 |
swrapper = swrapper, |
|
1800 | 431 |
safe0_netpair = safe0_netpair, |
432 |
safep_netpair = safep_netpair}; |
|
433 |
||
434 |
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
|
435 |
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
|
436 |
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
|
437 |
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
|
438 |
else if gen_mem eq_thm (th, hazEs) then delE(cs,th) |
1800 | 439 |
else (warning ("rule not in claset\n" ^ (string_of_thm th)); |
440 |
cs); |
|
441 |
||
442 |
val op delrules = foldl delrule; |
|
443 |
||
444 |
||
2630 | 445 |
(*** Setting or modifying the wrapper tacticals ***) |
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
446 |
|
2630 | 447 |
(*Set a new uwrapper*) |
448 |
fun (CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper, |
|
1073
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
449 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair, ...}) |
2630 | 450 |
setWrapper new_uwrapper = |
451 |
CS{safeIs = safeIs, |
|
1073
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
452 |
safeEs = safeEs, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
453 |
hazIs = hazIs, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
454 |
hazEs = hazEs, |
2630 | 455 |
uwrapper = new_uwrapper, |
456 |
swrapper = swrapper, |
|
1073
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
457 |
safe0_netpair = safe0_netpair, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
458 |
safep_netpair = safep_netpair, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
459 |
haz_netpair = haz_netpair, |
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset
|
460 |
dup_netpair = dup_netpair}; |
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
461 |
|
2630 | 462 |
(*Set a new swrapper*) |
463 |
fun (CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper, |
|
464 |
safe0_netpair, safep_netpair, haz_netpair, dup_netpair, ...}) |
|
465 |
setSWrapper new_swrapper = |
|
466 |
CS{safeIs = safeIs, |
|
467 |
safeEs = safeEs, |
|
468 |
hazIs = hazIs, |
|
469 |
hazEs = hazEs, |
|
470 |
uwrapper = uwrapper, |
|
471 |
swrapper = new_swrapper, |
|
472 |
safe0_netpair = safe0_netpair, |
|
473 |
safep_netpair = safep_netpair, |
|
474 |
haz_netpair = haz_netpair, |
|
475 |
dup_netpair = dup_netpair}; |
|
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
476 |
|
2630 | 477 |
(*Compose a tactical with the existing uwrapper*) |
478 |
fun cs compWrapper uwrapper' = cs setWrapper (uwrapper' o getWrapper cs); |
|
479 |
||
480 |
(*Compose a tactical with the existing swrapper*) |
|
481 |
fun cs compSWrapper swrapper' = cs setSWrapper (swrapper' o getSWrapper cs); |
|
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
482 |
|
2630 | 483 |
(*compose a safe tactic sequentially before/alternatively after safe_step_tac*) |
484 |
fun cs addSbefore tac1 = cs compSWrapper (fn tac2 => tac1 THEN_MAYBE' tac2); |
|
485 |
fun cs addSaltern tac2 = cs compSWrapper (fn tac1 => tac1 ORELSE' tac2); |
|
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
486 |
|
2630 | 487 |
(*compose a tactic sequentially before/alternatively after the step tactic*) |
488 |
fun cs addbefore tac1 = cs compWrapper (fn tac2 => tac1 THEN_MAYBE' tac2); |
|
489 |
fun cs addaltern tac2 = cs compWrapper (fn tac1 => tac1 APPEND' tac2); |
|
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
490 |
|
1711 | 491 |
(*Merge works by adding all new rules of the 2nd claset into the 1st claset. |
492 |
Merging the term nets may look more efficient, but the rather delicate |
|
493 |
treatment of priority might get muddled up.*) |
|
494 |
fun merge_cs |
|
2630 | 495 |
(cs as CS{safeIs, safeEs, hazIs, hazEs, ...}, |
1711 | 496 |
CS{safeIs=safeIs2, safeEs=safeEs2, hazIs=hazIs2, hazEs=hazEs2,...}) = |
497 |
let val safeIs' = gen_rems eq_thm (safeIs2,safeIs) |
|
498 |
val safeEs' = gen_rems eq_thm (safeEs2,safeEs) |
|
2630 | 499 |
val hazIs' = gen_rems eq_thm ( hazIs2, hazIs) |
500 |
val hazEs' = gen_rems eq_thm ( hazEs2, hazEs) |
|
1711 | 501 |
in cs addSIs safeIs' |
502 |
addSEs safeEs' |
|
503 |
addIs hazIs' |
|
504 |
addEs hazEs' |
|
505 |
end; |
|
506 |
||
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
507 |
|
1800 | 508 |
(**** Simple tactics for theorem proving ****) |
0 | 509 |
|
510 |
(*Attack subgoals using safe inferences -- matching, not resolution*) |
|
2630 | 511 |
fun safe_step_tac (cs as CS{safe0_netpair,safep_netpair,...}) = |
512 |
getSWrapper cs (FIRST' [ |
|
513 |
eq_assume_tac, |
|
514 |
eq_mp_tac, |
|
515 |
bimatch_from_nets_tac safe0_netpair, |
|
516 |
FIRST' hyp_subst_tacs, |
|
517 |
bimatch_from_nets_tac safep_netpair]); |
|
0 | 518 |
|
519 |
(*Repeatedly attack subgoals using safe inferences -- it's deterministic!*) |
|
2630 | 520 |
fun safe_tac cs = REPEAT_DETERM_FIRST |
521 |
(fn i => COND (has_fewer_prems i) no_tac (safe_step_tac cs i)); |
|
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
522 |
|
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
523 |
(*But these unsafe steps at least solve a subgoal!*) |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
524 |
fun inst0_step_tac (CS{safe0_netpair,safep_netpair,...}) = |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
525 |
assume_tac APPEND' |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
526 |
contr_tac APPEND' |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
527 |
biresolve_from_nets_tac safe0_netpair; |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
528 |
|
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
529 |
(*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
|
530 |
fun instp_step_tac (CS{safep_netpair,...}) = |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
531 |
biresolve_from_nets_tac safep_netpair; |
0 | 532 |
|
533 |
(*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
|
534 |
fun inst_step_tac cs = inst0_step_tac cs APPEND' instp_step_tac cs; |
0 | 535 |
|
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset
|
536 |
fun haz_step_tac (CS{haz_netpair,...}) = |
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
537 |
biresolve_from_nets_tac haz_netpair; |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
538 |
|
0 | 539 |
(*Single step for the prover. FAILS unless it makes progress. *) |
2630 | 540 |
fun step_tac cs i = getWrapper cs |
541 |
(K (safe_tac cs) ORELSE' (inst_step_tac cs ORELSE' haz_step_tac cs)) i; |
|
0 | 542 |
|
543 |
(*Using a "safe" rule to instantiate variables is unsafe. This tactic |
|
544 |
allows backtracking from "safe" rules to "unsafe" rules here.*) |
|
2630 | 545 |
fun slow_step_tac cs i = getWrapper cs |
546 |
(K (safe_tac cs) ORELSE' (inst_step_tac cs APPEND' haz_step_tac cs)) i; |
|
0 | 547 |
|
1800 | 548 |
(**** The following tactics all fail unless they solve one goal ****) |
0 | 549 |
|
550 |
(*Dumb but fast*) |
|
551 |
fun fast_tac cs = SELECT_GOAL (DEPTH_SOLVE (step_tac cs 1)); |
|
552 |
||
553 |
(*Slower but smarter than fast_tac*) |
|
554 |
fun best_tac cs = |
|
555 |
SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, sizef) (step_tac cs 1)); |
|
556 |
||
557 |
fun slow_tac cs = SELECT_GOAL (DEPTH_SOLVE (slow_step_tac cs 1)); |
|
558 |
||
559 |
fun slow_best_tac cs = |
|
560 |
SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, sizef) (slow_step_tac cs 1)); |
|
561 |
||
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
562 |
|
1800 | 563 |
(***ASTAR with weight weight_ASTAR, by Norbert Voelker*) |
1587
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
564 |
val weight_ASTAR = ref 5; |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
565 |
|
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
566 |
fun astar_tac cs = |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
567 |
SELECT_GOAL ( ASTAR (has_fewer_prems 1 |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
568 |
, 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
|
569 |
(step_tac cs 1)); |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
570 |
|
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
571 |
fun slow_astar_tac cs = |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
572 |
SELECT_GOAL ( ASTAR (has_fewer_prems 1 |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
573 |
, 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
|
574 |
(slow_step_tac cs 1)); |
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset
|
575 |
|
1800 | 576 |
(**** 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
|
577 |
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
|
578 |
easy theorems faster, but loses completeness -- and many of the harder |
1800 | 579 |
theorems such as 43. ****) |
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
580 |
|
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
581 |
(*Non-deterministic! Could always expand the first unsafe connective. |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
582 |
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
|
583 |
greater search depth required.*) |
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
584 |
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
|
585 |
biresolve_from_nets_tac dup_netpair; |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
586 |
|
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
587 |
(*Searching to depth m.*) |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
588 |
fun depth_tac cs m i = STATE(fn state => |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
589 |
SELECT_GOAL |
2630 | 590 |
(getWrapper cs |
591 |
(fn i => REPEAT_DETERM1 (safe_step_tac cs i) THEN_ELSE |
|
592 |
(DEPTH_SOLVE (depth_tac cs m i), |
|
593 |
inst0_step_tac cs i APPEND |
|
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
594 |
COND (K(m=0)) no_tac |
2630 | 595 |
((instp_step_tac cs i APPEND dup_step_tac cs i) |
596 |
THEN DEPTH_SOLVE (depth_tac cs (m-1) i)))) 1) |
|
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
597 |
i); |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
598 |
|
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
599 |
(*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
|
600 |
fun DEEPEN tacf m i = STATE(fn state => |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
601 |
if has_fewer_prems i state then no_tac |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
602 |
else (writeln ("Depth = " ^ string_of_int m); |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
603 |
tacf m i ORELSE DEEPEN tacf (m+2) i)); |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
604 |
|
2173 | 605 |
(*Search, with depth bound m. |
606 |
This is the "entry point", which does safe inferences first.*) |
|
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
607 |
fun safe_depth_tac cs m = |
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
608 |
SUBGOAL |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
609 |
(fn (prem,i) => |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
610 |
let val deti = |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
611 |
(*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
|
612 |
case term_vars prem of |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
613 |
[] => DETERM |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
614 |
| _::_ => I |
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
615 |
in SELECT_GOAL (TRY (safe_tac cs) THEN |
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
616 |
DEPTH_SOLVE (deti (depth_tac cs m 1))) i |
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
617 |
end); |
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset
|
618 |
|
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset
|
619 |
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
|
620 |
|
1724 | 621 |
val claset = ref empty_cs; |
622 |
||
623 |
fun AddDs ts = (claset := !claset addDs ts); |
|
624 |
||
625 |
fun AddEs ts = (claset := !claset addEs ts); |
|
626 |
||
627 |
fun AddIs ts = (claset := !claset addIs ts); |
|
628 |
||
629 |
fun AddSDs ts = (claset := !claset addSDs ts); |
|
630 |
||
631 |
fun AddSEs ts = (claset := !claset addSEs ts); |
|
632 |
||
633 |
fun AddSIs ts = (claset := !claset addSIs ts); |
|
634 |
||
1807 | 635 |
fun Delrules ts = (claset := !claset delrules ts); |
636 |
||
1800 | 637 |
(*Cannot have Safe_tac, as it takes no arguments; must delay dereferencing!*) |
638 |
||
1814 | 639 |
fun Safe_step_tac i = safe_step_tac (!claset) i; |
640 |
||
1800 | 641 |
fun Step_tac i = step_tac (!claset) i; |
642 |
||
1724 | 643 |
fun Fast_tac i = fast_tac (!claset) i; |
644 |
||
1800 | 645 |
fun Best_tac i = best_tac (!claset) i; |
646 |
||
2066 | 647 |
fun Slow_tac i = slow_tac (!claset) i; |
648 |
||
649 |
fun Slow_best_tac i = slow_best_tac (!claset) i; |
|
650 |
||
1800 | 651 |
fun Deepen_tac m = deepen_tac (!claset) m; |
652 |
||
0 | 653 |
end; |
654 |
end; |
|
2630 | 655 |
|
656 |