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permissions  rwrr 
0  1 
(* 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 *) 
0  23 
val hyp_subst_tacs: (int > tactic) list 
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end; 

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(*Higher precedence than := facilitates use of references*) 

1800  27 
infix 4 addSIs addSEs addSDs addIs addEs addDs delrules 
2630  28 
setSWrapper compSWrapper setWrapper compWrapper 
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addSbefore addSaltern addbefore addaltern; 

0  30 

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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 
1800  44 
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 
1814  103 
val Safe_step_tac : int > tactic 
1800  104 
val Step_tac : int > tactic 
1724  105 
val Fast_tac : int > tactic 
1800  106 
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 
1724  110 

0  111 
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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1800  119 
(*** Useful tactics for classical reasoning ***) 
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1524  121 
val imp_elim = (*cannot use bind_thm within a structure!*) 
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store_thm ("imp_elim", make_elim mp); 

0  123 

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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; 
0  130 

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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)); 

0  136 

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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 = 

54  143 
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,[])) 

0  147 
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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1800  156 
(**** Classical rule sets ****) 
0  157 

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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*) 
0  173 

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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. 
1800  184 
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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*) 
0  187 

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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 = [], 
2630  193 
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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writeln"Safe introduction rules"; prths safeIs; 
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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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fun getWrapper (CS{uwrapper,...}) = uwrapper; 
210 

211 
fun getSWrapper (CS{swrapper,...}) = swrapper; 

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1800  214 
(*** Adding (un)safe introduction or elimination rules. 
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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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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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(*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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 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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1800  232 
fun insert_tagged_list kbrls netpr = foldr insert_tagged_brl (kbrls, netpr); 
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(*Insert into netpair that already has nI intr rules and nE elim rules. 
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Count the intr rules double (to account for swapify). Negate to give the 
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new insertions the lowest priority.*) 
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fun insert (nI,nE) = insert_tagged_list o (tag_brls (~(2*nI+nE))) o joinrules; 
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1800  239 
fun delete_tagged_list brls netpr = foldr delete_tagged_brl (brls, netpr); 
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1800  241 
val delete = delete_tagged_list o joinrules; 
242 

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(*Warn if the rule is already present ELSEWHERE in the claset. The addition 
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is still allowed.*) 
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fun warn_dup th (CS{safeIs, safeEs, hazIs, hazEs, ...}) = 
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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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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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else (); 
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1800  256 
(*** Safe rules ***) 
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2630  258 
fun addSI (cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper, 
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safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, 
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th) = 
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if gen_mem eq_thm (th, safeIs) then 
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(warning ("ignoring duplicate Safe Intr\n" ^ string_of_thm th); 
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cs) 
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else 
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let val (safe0_rls, safep_rls) = (*0 subgoals vs 1 or more*) 
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partition (fn rl => nprems_of rl=0) [th] 
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val nI = length safeIs + 1 
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and nE = length safeEs 
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in warn_dup th cs; 
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CS{safeIs = th::safeIs, 
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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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safeEs = safeEs, 
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hazIs = hazIs, 
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hazEs = hazEs, 
2630  276 
uwrapper = uwrapper, 
277 
swrapper = swrapper, 

278 
haz_netpair = haz_netpair, 

279 
dup_netpair = dup_netpair} 

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end; 
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2630  282 
fun addSE (cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper, 
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safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, 
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th) = 
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if gen_mem eq_thm (th, safeEs) then 
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(warning ("ignoring duplicate Safe Elim\n" ^ string_of_thm th); 
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cs) 
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else 
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let val (safe0_rls, safep_rls) = (*0 subgoals vs 1 or more*) 
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partition (fn rl => nprems_of rl=1) [th] 
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val nI = length safeIs 
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and nE = length safeEs + 1 
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in warn_dup th cs; 
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CS{safeEs = th::safeEs, 
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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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safeIs = safeIs, 
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hazIs = hazIs, 
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hazEs = hazEs, 
2630  300 
uwrapper = uwrapper, 
301 
swrapper = swrapper, 

302 
haz_netpair = haz_netpair, 

303 
dup_netpair = dup_netpair} 

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end; 
0  305 

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fun rev_foldl f (e, l) = foldl f (e, rev l); 
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val op addSIs = rev_foldl addSI; 
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val op addSEs = rev_foldl addSE; 
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0  311 
fun cs addSDs ths = cs addSEs (map make_elim ths); 
312 

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1800  314 
(*** Hazardous (unsafe) rules ***) 
0  315 

2630  316 
fun addI (cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper, 
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safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, 
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th)= 
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if gen_mem eq_thm (th, hazIs) then 
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(warning ("ignoring duplicate unsafe Intr\n" ^ string_of_thm th); 
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cs) 
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else 
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let val nI = length hazIs + 1 
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and nE = length hazEs 
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in warn_dup th cs; 
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CS{hazIs = th::hazIs, 
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haz_netpair = insert (nI,nE) ([th], []) haz_netpair, 
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dup_netpair = insert (nI,nE) (map dup_intr [th], []) dup_netpair, 
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safeIs = safeIs, 
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safeEs = safeEs, 
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hazEs = hazEs, 
2630  332 
uwrapper = uwrapper, 
333 
swrapper = swrapper, 

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safe0_netpair = safe0_netpair, 
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safep_netpair = safep_netpair} 
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336 
end; 
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337 

2630  338 
fun addE (cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper, 
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safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, 
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th) = 
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if gen_mem eq_thm (th, hazEs) then 
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(warning ("ignoring duplicate unsafe Elim\n" ^ string_of_thm th); 
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cs) 
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else 
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let val nI = length hazIs 
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and nE = length hazEs + 1 
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in warn_dup th cs; 
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CS{hazEs = th::hazEs, 
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haz_netpair = insert (nI,nE) ([], [th]) haz_netpair, 
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dup_netpair = insert (nI,nE) ([], map dup_elim [th]) dup_netpair, 
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safeIs = safeIs, 
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safeEs = safeEs, 
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hazIs = hazIs, 
2630  354 
uwrapper = uwrapper, 
355 
swrapper = swrapper, 

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safe0_netpair = safe0_netpair, 
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safep_netpair = safep_netpair} 
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358 
end; 
0  359 

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val op addIs = rev_foldl addI; 
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val op addEs = rev_foldl addE; 
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0  363 
fun cs addDs ths = cs addEs (map make_elim ths); 
364 

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365 

1800  366 
(*** Deletion of rules 
367 
Working out what to delete, requires repeating much of the code used 

368 
to insert. 

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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 
(*Nondeterministic! 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 (m1) 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 