author  paulson 
Tue, 20 Aug 1996 12:39:30 +0200  
changeset 1927  6f97cb16e453 
parent 1814  89f8d4a88cca 
child 1938  4e29ea45520d 
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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infix 1 THEN_MAYBE; 
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0  19 
signature CLASSICAL_DATA = 
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sig 

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val mp : thm (* [ P>Q; P ] ==> Q *) 
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val not_elim : thm (* [ ~P; P ] ==> R *) 
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val classical : thm (* (~P ==> P) ==> P *) 
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val sizef : thm > int (* size function for BEST_FIRST *) 
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val hyp_subst_tacs: (int > tactic) list 
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end; 

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

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infix 4 addSIs addSEs addSDs addIs addEs addDs delrules 
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setwrapper compwrapper addbefore addafter; 
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signature CLASSICAL = 

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sig 

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type claset 

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type netpair 
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val empty_cs : claset 
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val merge_cs : claset * claset > claset 
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val addDs : claset * thm list > claset 
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val addEs : claset * thm list > claset 
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val addIs : claset * thm list > claset 
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val addSDs : claset * thm list > claset 
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val addSEs : claset * thm list > claset 
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val addSIs : claset * thm list > claset 
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val delrules : claset * thm list > claset 
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val setwrapper : claset * (tactic>tactic) > claset 
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val compwrapper : claset * (tactic>tactic) > claset 
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val addbefore : claset * tactic > claset 
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val addafter : claset * tactic > claset 
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val print_cs : claset > unit 
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val rep_claset : 
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claset > {safeIs: thm list, safeEs: thm list, 
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hazIs: thm list, hazEs: thm list, 
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wrapper: tactic > tactic, 
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safe0_netpair: netpair, safep_netpair: netpair, 
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haz_netpair: netpair, dup_netpair: netpair} 
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val getwrapper : claset > tactic > tactic 
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val THEN_MAYBE : tactic * tactic > tactic 
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val fast_tac : claset > int > tactic 
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val slow_tac : claset > int > tactic 
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val weight_ASTAR : int ref 
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val astar_tac : claset > int > tactic 
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val slow_astar_tac : claset > int > tactic 
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val best_tac : claset > int > tactic 
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val slow_best_tac : claset > int > tactic 
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val depth_tac : claset > int > int > tactic 
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val deepen_tac : claset > int > int > tactic 
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val contr_tac : int > tactic 
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val dup_elim : thm > thm 
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val dup_intr : thm > thm 
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val dup_step_tac : claset > int > tactic 
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val eq_mp_tac : int > tactic 
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val haz_step_tac : claset > int > tactic 
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val joinrules : thm list * thm list > (bool * thm) list 
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val mp_tac : int > tactic 
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val safe_tac : claset > tactic 
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val safe_step_tac : claset > int > tactic 
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val step_tac : claset > int > tactic 
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val swap : thm (* ~P ==> (~Q ==> P) ==> Q *) 
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val swapify : thm list > thm list 
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val swap_res_tac : thm list > int > tactic 
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val inst_step_tac : claset > int > tactic 
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val inst0_step_tac : claset > int > tactic 
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val instp_step_tac : claset > int > tactic 
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val claset : claset ref 

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val AddDs : thm list > unit 

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val AddEs : thm list > unit 

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val AddIs : thm list > unit 

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val AddSDs : thm list > unit 

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val AddSEs : thm list > unit 

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val AddSIs : thm list > unit 

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val Delrules : thm list > unit 
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val Safe_step_tac : int > tactic 
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val Step_tac : int > tactic 
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val Fast_tac : int > tactic 
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val Best_tac : int > tactic 
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val Deepen_tac : int > int > tactic 

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end; 
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functor ClassicalFun(Data: CLASSICAL_DATA): CLASSICAL = 

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struct 

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local open Data in 

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

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(*Solve goal that assumes both P and ~P. *) 

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val contr_tac = eresolve_tac [not_elim] THEN' assume_tac; 

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(*Finds P>Q and P in the assumptions, replaces implication by Q. 
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Could do the same thing for P<>Q and P... *) 
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fun mp_tac i = eresolve_tac [not_elim, imp_elim] i THEN assume_tac i; 
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(*Like mp_tac but instantiates no variables*) 

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fun eq_mp_tac i = ematch_tac [not_elim, imp_elim] i THEN eq_assume_tac i; 
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val swap = 
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store_thm ("swap", rule_by_tactic (etac thin_rl 1) (not_elim RS classical)); 

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(*Creates rules to eliminate ~A, from rules to introduce A*) 

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fun swapify intrs = intrs RLN (2, [swap]); 

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(*Uses introduction rules in the normal way, or on negated assumptions, 

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trying rules in order. *) 

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fun swap_res_tac rls = 

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let fun addrl (rl,brls) = (false, rl) :: (true, rl RSN (2,swap)) :: brls 
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in assume_tac ORELSE' 

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contr_tac ORELSE' 

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biresolve_tac (foldr addrl (rls,[])) 

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end; 
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(*Duplication of hazardous rules, for complete provers*) 
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fun dup_intr th = standard (th RS classical); 
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fun dup_elim th = th RSN (2, revcut_rl) > assumption 2 > Sequence.hd > 
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rule_by_tactic (TRYALL (etac revcut_rl)); 
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(**** Classical rule sets ****) 
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type netpair = (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net; 

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datatype claset = 

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CS of {safeIs : thm list, (*safe introduction rules*) 
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safeEs : thm list, (*safe elimination rules*) 
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hazIs : thm list, (*unsafe introduction rules*) 
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hazEs : thm list, (*unsafe elimination rules*) 
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wrapper : tactic>tactic, (*for transforming step_tac*) 
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safe0_netpair : netpair, (*nets for trivial cases*) 
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safep_netpair : netpair, (*nets for >0 subgoals*) 
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haz_netpair : netpair, (*nets for unsafe rules*) 
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dup_netpair : netpair}; (*nets for duplication*) 
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(*Desired invariants are 
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safe0_netpair = build safe0_brls, 
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safep_netpair = build safep_brls, 
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haz_netpair = build (joinrules(hazIs, hazEs)), 
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dup_netpair = build (joinrules(map dup_intr hazIs, 
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map dup_elim hazEs))} 
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where build = build_netpair(Net.empty,Net.empty), 
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safe0_brls contains all brules that solve the subgoal, and 
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safep_brls contains all brules that generate 1 or more new subgoals. 
1800  173 
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  176 

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val empty_cs = 
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CS{safeIs = [], 
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safeEs = [], 
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hazIs = [], 
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hazEs = [], 
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wrapper = I, 
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safe0_netpair = (Net.empty,Net.empty), 
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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  187 

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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  193 
()); 
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fun rep_claset (CS args) = args; 
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fun getwrapper (CS{wrapper,...}) = wrapper; 
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1800  200 
(*** Adding (un)safe introduction or elimination rules. 
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In case of overlap, new rules are tried BEFORE old ones!! 
1800  203 
***) 
0  204 

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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  212 
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  218 
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  225 
fun delete_tagged_list brls netpr = foldr delete_tagged_brl (brls, netpr); 
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1800  227 
val delete = delete_tagged_list o joinrules; 
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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  242 
(*** Safe rules ***) 
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fun addSI (cs as CS{safeIs, safeEs, hazIs, hazEs, wrapper, 
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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, 
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wrapper = wrapper, 
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haz_netpair = haz_netpair, 
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dup_netpair = dup_netpair} 
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end; 
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fun addSE (cs as CS{safeIs, safeEs, hazIs, hazEs, wrapper, 
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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, 
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wrapper = wrapper, 
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haz_netpair = haz_netpair, 
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dup_netpair = dup_netpair} 
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end; 
0  289 

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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  295 
fun cs addSDs ths = cs addSEs (map make_elim ths); 
296 

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1800  298 
(*** Hazardous (unsafe) rules ***) 
0  299 

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fun addI (cs as CS{safeIs, safeEs, hazIs, hazEs, wrapper, 
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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, 
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wrapper = wrapper, 
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safe0_netpair = safe0_netpair, 
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safep_netpair = safep_netpair} 
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319 
end; 
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fun addE (cs as CS{safeIs, safeEs, hazIs, hazEs, wrapper, 
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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, 
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wrapper = wrapper, 
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safe0_netpair = safe0_netpair, 
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safep_netpair = safep_netpair} 
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end; 
0  341 

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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  345 
fun cs addDs ths = cs addEs (map make_elim ths); 
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lcp
parents:
1010
diff
changeset

347 

1800  348 
(*** Deletion of rules 
349 
Working out what to delete, requires repeating much of the code used 

350 
to insert. 

1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset

351 
Separate functions delSI, etc., are not exported; instead delrules 
1800  352 
searches in all the lists and chooses the relevant delXX function. 
353 
***) 

354 

1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset

355 
fun delSI (CS{safeIs, safeEs, hazIs, hazEs, wrapper, 
1800  356 
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, 
357 
th) = 

358 
let val (safe0_rls, safep_rls) = partition (fn rl => nprems_of rl=0) [th] 

359 
in CS{safeIs = gen_rem eq_thm (safeIs,th), 

360 
safe0_netpair = delete (safe0_rls, []) safe0_netpair, 

361 
safep_netpair = delete (safep_rls, []) safep_netpair, 

362 
safeEs = safeEs, 

363 
hazIs = hazIs, 

364 
hazEs = hazEs, 

365 
wrapper = wrapper, 

366 
haz_netpair = haz_netpair, 

367 
dup_netpair = dup_netpair} 

368 
end; 

369 

1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset

370 
fun delSE (CS{safeIs, safeEs, hazIs, hazEs, wrapper, 
1800  371 
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, 
372 
th) = 

373 
let val (safe0_rls, safep_rls) = partition (fn rl => nprems_of rl=1) [th] 

374 
in CS{safeEs = gen_rem eq_thm (safeEs,th), 

375 
safe0_netpair = delete ([], safe0_rls) safe0_netpair, 

376 
safep_netpair = delete ([], safep_rls) safep_netpair, 

377 
safeIs = safeIs, 

378 
hazIs = hazIs, 

379 
hazEs = hazEs, 

380 
wrapper = wrapper, 

381 
haz_netpair = haz_netpair, 

382 
dup_netpair = dup_netpair} 

383 
end; 

384 

385 

1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset

386 
fun delI (CS{safeIs, safeEs, hazIs, hazEs, wrapper, 
1800  387 
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, 
388 
th) = 

389 
CS{hazIs = gen_rem eq_thm (hazIs,th), 

390 
haz_netpair = delete ([th], []) haz_netpair, 

391 
dup_netpair = delete ([dup_intr th], []) dup_netpair, 

392 
safeIs = safeIs, 

393 
safeEs = safeEs, 

394 
hazEs = hazEs, 

395 
wrapper = wrapper, 

396 
safe0_netpair = safe0_netpair, 

397 
safep_netpair = safep_netpair}; 

398 

1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset

399 
fun delE (CS{safeIs, safeEs, hazIs, hazEs, wrapper, 
1800  400 
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}, 
401 
th) = 

402 
CS{hazEs = gen_rem eq_thm (hazEs,th), 

403 
haz_netpair = delete ([], [th]) haz_netpair, 

404 
dup_netpair = delete ([], [dup_elim th]) dup_netpair, 

405 
safeIs = safeIs, 

406 
safeEs = safeEs, 

407 
hazIs = hazIs, 

408 
wrapper = wrapper, 

409 
safe0_netpair = safe0_netpair, 

410 
safep_netpair = safep_netpair}; 

411 

412 
fun delrule (cs as CS{safeIs, safeEs, hazIs, hazEs, ...}, th) = 

1927
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset

413 
if gen_mem eq_thm (th, safeIs) then delSI(cs,th) 
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset

414 
else if gen_mem eq_thm (th, safeEs) then delSE(cs,th) 
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset

415 
else if gen_mem eq_thm (th, hazIs) then delI(cs,th) 
6f97cb16e453
New classical reasoner: warns of, and ignores, redundant rules.
paulson
parents:
1814
diff
changeset

416 
else if gen_mem eq_thm (th, hazEs) then delE(cs,th) 
1800  417 
else (warning ("rule not in claset\n" ^ (string_of_thm th)); 
418 
cs); 

419 

420 
val op delrules = foldl delrule; 

421 

422 

423 
(*** Setting or modifying the wrapper tactical ***) 

982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

424 

4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

425 
(*Set a new wrapper*) 
1073
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset

426 
fun (CS{safeIs, safeEs, hazIs, hazEs, 
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset

427 
safe0_netpair, safep_netpair, haz_netpair, dup_netpair, ...}) 
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset

428 
setwrapper new_wrapper = 
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset

429 
CS{wrapper = new_wrapper, 
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset

430 
safeIs = safeIs, 
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset

431 
safeEs = safeEs, 
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset

432 
hazIs = hazIs, 
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset

433 
hazEs = hazEs, 
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset

434 
safe0_netpair = safe0_netpair, 
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset

435 
safep_netpair = safep_netpair, 
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset

436 
haz_netpair = haz_netpair, 
b3f190995bc9
Recoded addSIs, etc., so that nets are built incrementally
lcp
parents:
1010
diff
changeset

437 
dup_netpair = dup_netpair}; 
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

438 

4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

439 
(*Compose a tactical with the existing wrapper*) 
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

440 
fun cs compwrapper wrapper' = cs setwrapper (wrapper' o getwrapper cs); 
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

441 

4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

442 
(*Execute tac1, but only execute tac2 if there are at least as many subgoals 
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

443 
as before. This ensures that tac2 is only applied to an outcome of tac1.*) 
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

444 
fun tac1 THEN_MAYBE tac2 = 
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

445 
STATE (fn state => 
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

446 
tac1 THEN 
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

447 
COND (has_fewer_prems (nprems_of state)) all_tac tac2); 
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

448 

4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

449 
(*Cause a tactic to be executed before/after the step tactic*) 
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

450 
fun cs addbefore tac2 = cs compwrapper (fn tac1 => tac2 THEN_MAYBE tac1); 
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

451 
fun cs addafter tac2 = cs compwrapper (fn tac1 => tac1 THEN_MAYBE tac2); 
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

452 

4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

453 

1711  454 
(*Merge works by adding all new rules of the 2nd claset into the 1st claset. 
455 
Merging the term nets may look more efficient, but the rather delicate 

456 
treatment of priority might get muddled up.*) 

457 
fun merge_cs 

458 
(cs as CS{safeIs, safeEs, hazIs, hazEs, wrapper, ...}, 

459 
CS{safeIs=safeIs2, safeEs=safeEs2, hazIs=hazIs2, hazEs=hazEs2,...}) = 

460 
let val safeIs' = gen_rems eq_thm (safeIs2,safeIs) 

461 
val safeEs' = gen_rems eq_thm (safeEs2,safeEs) 

462 
val hazIs' = gen_rems eq_thm (hazIs2,hazIs) 

463 
val hazEs' = gen_rems eq_thm (hazEs2,hazEs) 

464 
in cs addSIs safeIs' 

465 
addSEs safeEs' 

466 
addIs hazIs' 

467 
addEs hazEs' 

468 
end; 

469 

982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

470 

1800  471 
(**** Simple tactics for theorem proving ****) 
0  472 

473 
(*Attack subgoals using safe inferences  matching, not resolution*) 

474 
fun safe_step_tac (CS{safe0_netpair,safep_netpair,...}) = 

475 
FIRST' [eq_assume_tac, 

476 
eq_mp_tac, 

477 
bimatch_from_nets_tac safe0_netpair, 

478 
FIRST' hyp_subst_tacs, 

479 
bimatch_from_nets_tac safep_netpair] ; 

480 

481 
(*Repeatedly attack subgoals using safe inferences  it's deterministic!*) 

747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

482 
fun safe_tac cs = REPEAT_DETERM_FIRST (safe_step_tac cs); 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

483 

bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

484 
(*But these unsafe steps at least solve a subgoal!*) 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

485 
fun inst0_step_tac (CS{safe0_netpair,safep_netpair,...}) = 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

486 
assume_tac APPEND' 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

487 
contr_tac APPEND' 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

488 
biresolve_from_nets_tac safe0_netpair; 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

489 

bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

490 
(*These are much worse since they could generate more and more subgoals*) 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

491 
fun instp_step_tac (CS{safep_netpair,...}) = 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

492 
biresolve_from_nets_tac safep_netpair; 
0  493 

494 
(*These steps could instantiate variables and are therefore unsafe.*) 

747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

495 
fun inst_step_tac cs = inst0_step_tac cs APPEND' instp_step_tac cs; 
0  496 

982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

497 
fun haz_step_tac (CS{haz_netpair,...}) = 
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

498 
biresolve_from_nets_tac haz_netpair; 
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

499 

0  500 
(*Single step for the prover. FAILS unless it makes progress. *) 
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

501 
fun step_tac cs i = 
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

502 
getwrapper cs 
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

503 
(FIRST [safe_tac cs, inst_step_tac cs i, haz_step_tac cs i]); 
0  504 

505 
(*Using a "safe" rule to instantiate variables is unsafe. This tactic 

506 
allows backtracking from "safe" rules to "unsafe" rules here.*) 

681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

507 
fun slow_step_tac cs i = 
982
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

508 
getwrapper cs 
4fe0b642b7d5
Addition of wrappers for integration with the simplifier.
lcp
parents:
747
diff
changeset

509 
(safe_tac cs ORELSE (inst_step_tac cs i APPEND haz_step_tac cs i)); 
0  510 

1800  511 
(**** The following tactics all fail unless they solve one goal ****) 
0  512 

513 
(*Dumb but fast*) 

514 
fun fast_tac cs = SELECT_GOAL (DEPTH_SOLVE (step_tac cs 1)); 

515 

516 
(*Slower but smarter than fast_tac*) 

517 
fun best_tac cs = 

518 
SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, sizef) (step_tac cs 1)); 

519 

520 
fun slow_tac cs = SELECT_GOAL (DEPTH_SOLVE (slow_step_tac cs 1)); 

521 

522 
fun slow_best_tac cs = 

523 
SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, sizef) (slow_step_tac cs 1)); 

524 

681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

525 

1800  526 
(***ASTAR with weight weight_ASTAR, by Norbert Voelker*) 
1587
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset

527 
val weight_ASTAR = ref 5; 
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset

528 

e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset

529 
fun astar_tac cs = 
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset

530 
SELECT_GOAL ( ASTAR (has_fewer_prems 1 
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset

531 
, fn level =>(fn thm =>size_of_thm thm + !weight_ASTAR *level)) 
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset

532 
(step_tac cs 1)); 
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset

533 

e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset

534 
fun slow_astar_tac cs = 
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset

535 
SELECT_GOAL ( ASTAR (has_fewer_prems 1 
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset

536 
, fn level =>(fn thm =>size_of_thm thm + !weight_ASTAR *level)) 
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset

537 
(slow_step_tac cs 1)); 
e7d8a4957bac
Now provides astar versions (thanks to Norbert Voelker)
paulson
parents:
1524
diff
changeset

538 

1800  539 
(**** Complete tactic, loosely based upon LeanTaP. This tactic is the outcome 
747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

540 
of much experimentation! Changing APPEND to ORELSE below would prove 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

541 
easy theorems faster, but loses completeness  and many of the harder 
1800  542 
theorems such as 43. ****) 
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

543 

747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

544 
(*Nondeterministic! Could always expand the first unsafe connective. 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

545 
That's hard to implement and did not perform better in experiments, due to 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

546 
greater search depth required.*) 
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

547 
fun dup_step_tac (cs as (CS{dup_netpair,...})) = 
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

548 
biresolve_from_nets_tac dup_netpair; 
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

549 

747
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

550 
(*Searching to depth m.*) 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

551 
fun depth_tac cs m i = STATE(fn state => 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

552 
SELECT_GOAL 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

553 
(REPEAT_DETERM1 (safe_step_tac cs 1) THEN_ELSE 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

554 
(DEPTH_SOLVE (depth_tac cs m 1), 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

555 
inst0_step_tac cs 1 APPEND 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

556 
COND (K(m=0)) no_tac 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

557 
((instp_step_tac cs 1 APPEND dup_step_tac cs 1) 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

558 
THEN DEPTH_SOLVE (depth_tac cs (m1) 1)))) 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

559 
i); 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

560 

bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

561 
(*Iterative deepening tactical. Allows us to "deepen" any search tactic*) 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

562 
fun DEEPEN tacf m i = STATE(fn state => 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

563 
if has_fewer_prems i state then no_tac 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

564 
else (writeln ("Depth = " ^ string_of_int m); 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

565 
tacf m i ORELSE DEEPEN tacf (m+2) i)); 
bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

566 

bdc066781063
deepen_tac: modified due to outcome of experiments. Its
lcp
parents:
681
diff
changeset

567 
fun safe_depth_tac cs m = 
681
9b02474744ca
Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

568 
SUBGOAL 
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Provers/classical: now takes theorem "classical" as argument, proves "swap"
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469
diff
changeset

569 
(fn (prem,i) => 
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Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

570 
let val deti = 
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Provers/classical: now takes theorem "classical" as argument, proves "swap"
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parents:
469
diff
changeset

571 
(*No Vars in the goal? No need to backtrack between goals.*) 
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Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

572 
case term_vars prem of 
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Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
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diff
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573 
[] => DETERM 
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Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

574 
 _::_ => I 
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Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

575 
in SELECT_GOAL (TRY (safe_tac cs) THEN 
747
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deepen_tac: modified due to outcome of experiments. Its
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diff
changeset

576 
DEPTH_SOLVE (deti (depth_tac cs m 1))) i 
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deepen_tac: modified due to outcome of experiments. Its
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diff
changeset

577 
end); 
681
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Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
469
diff
changeset

578 

747
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deepen_tac: modified due to outcome of experiments. Its
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parents:
681
diff
changeset

579 
fun deepen_tac cs = DEEPEN (safe_depth_tac cs); 
681
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Provers/classical: now takes theorem "classical" as argument, proves "swap"
lcp
parents:
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diff
changeset

580 

1724  581 
val claset = ref empty_cs; 
582 

583 
fun AddDs ts = (claset := !claset addDs ts); 

584 

585 
fun AddEs ts = (claset := !claset addEs ts); 

586 

587 
fun AddIs ts = (claset := !claset addIs ts); 

588 

589 
fun AddSDs ts = (claset := !claset addSDs ts); 

590 

591 
fun AddSEs ts = (claset := !claset addSEs ts); 

592 

593 
fun AddSIs ts = (claset := !claset addSIs ts); 

594 

1807  595 
fun Delrules ts = (claset := !claset delrules ts); 
596 

1800  597 
(*Cannot have Safe_tac, as it takes no arguments; must delay dereferencing!*) 
598 

1814  599 
fun Safe_step_tac i = safe_step_tac (!claset) i; 
600 

1800  601 
fun Step_tac i = step_tac (!claset) i; 
602 

1724  603 
fun Fast_tac i = fast_tac (!claset) i; 
604 

1800  605 
fun Best_tac i = best_tac (!claset) i; 
606 

607 
fun Deepen_tac m = deepen_tac (!claset) m; 

608 

0  609 
end; 
610 
end; 