diff -r 6ac12b9478d5 -r fb0655539d05 src/Sequents/prover.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/Sequents/prover.ML Wed Oct 09 13:32:33 1996 +0200 @@ -0,0 +1,223 @@ +(* Title: LK/LK.ML + ID: $Id$ + Author: Lawrence C Paulson, Cambridge University Computer Laboratory + Copyright 1992 University of Cambridge +*) + + +(**** Theorem Packs ****) + +(* based largely on LK *) + +datatype pack = Pack of thm list * thm list; + +(*A theorem pack has the form (safe rules, unsafe rules) + An unsafe rule is incomplete or introduces variables in subgoals, + and is tried only when the safe rules are not applicable. *) + +fun less (rl1,rl2) = (nprems_of rl1) < (nprems_of rl2); + +val empty_pack = Pack([],[]); + +infix 4 add_safes add_unsafes; + +fun (Pack(safes,unsafes)) add_safes ths = + Pack(sort less (ths@safes), unsafes); + +fun (Pack(safes,unsafes)) add_unsafes ths = + Pack(safes, sort less (ths@unsafes)); + + +(*Returns the list of all formulas in the sequent*) +fun forms_of_seq (Const("SeqO'",_) $ P $ u) = P :: forms_of_seq u + | forms_of_seq (H $ u) = forms_of_seq u + | forms_of_seq _ = []; + +(*Tests whether two sequences (left or right sides) could be resolved. + seqp is a premise (subgoal), seqc is a conclusion of an object-rule. + Assumes each formula in seqc is surrounded by sequence variables + -- checks that each concl formula looks like some subgoal formula. + It SHOULD check order as well, using recursion rather than forall/exists*) +fun could_res (seqp,seqc) = + forall (fn Qc => exists (fn Qp => could_unify (Qp,Qc)) + (forms_of_seq seqp)) + (forms_of_seq seqc); + + +(*Tests whether two sequents or pairs of sequents could be resolved*) +fun could_resolve_seq (prem,conc) = + case (prem,conc) of + (_ $ Abs(_,_,leftp) $ Abs(_,_,rightp), + _ $ Abs(_,_,leftc) $ Abs(_,_,rightc)) => + could_res (leftp,leftc) andalso could_res (rightp,rightc) + | (_ $ Abs(_,_,leftp) $ rightp, + _ $ Abs(_,_,leftc) $ rightc) => + could_res (leftp,leftc) andalso could_unify (rightp,rightc) + | _ => false; + + +(*Like filt_resolve_tac, using could_resolve_seq + Much faster than resolve_tac when there are many rules. + Resolve subgoal i using the rules, unless more than maxr are compatible. *) +fun filseq_resolve_tac rules maxr = SUBGOAL(fn (prem,i) => + let val rls = filter_thms could_resolve_seq (maxr+1, prem, rules) + in if length rls > maxr then no_tac + else (*((rtac derelict 1 THEN rtac impl 1 + THEN (rtac identity 2 ORELSE rtac ll_mp 2) + THEN rtac context1 1) + ORELSE *) resolve_tac rls i + end); + + +(*Predicate: does the rule have n premises? *) +fun has_prems n rule = (nprems_of rule = n); + +(*Continuation-style tactical for resolution. + The list of rules is partitioned into 0, 1, 2 premises. + The resulting tactic, gtac, tries to resolve with rules. + If successful, it recursively applies nextac to the new subgoals only. + Else fails. (Treatment of goals due to Ph. de Groote) + Bind (RESOLVE_THEN rules) to a variable: it preprocesses the rules. *) + +(*Takes rule lists separated in to 0, 1, 2, >2 premises. + The abstraction over state prevents needless divergence in recursion. + The 9999 should be a parameter, to delay treatment of flexible goals. *) + +fun RESOLVE_THEN rules = + let val [rls0,rls1,rls2] = partition_list has_prems 0 2 rules; + fun tac nextac i = STATE (fn state => + filseq_resolve_tac rls0 9999 i + ORELSE + (DETERM(filseq_resolve_tac rls1 9999 i) THEN TRY(nextac i)) + ORELSE + (DETERM(filseq_resolve_tac rls2 9999 i) THEN TRY(nextac(i+1)) + THEN TRY(nextac i)) ) + in tac end; + + + +(*repeated resolution applied to the designated goal*) +fun reresolve_tac rules = + let val restac = RESOLVE_THEN rules; (*preprocessing done now*) + fun gtac i = restac gtac i + in gtac end; + +(*tries the safe rules repeatedly before the unsafe rules. *) +fun repeat_goal_tac (Pack(safes,unsafes)) = + let val restac = RESOLVE_THEN safes + and lastrestac = RESOLVE_THEN unsafes; + fun gtac i = restac gtac i ORELSE (print_tac THEN lastrestac gtac i) + in gtac end; + + +(*Tries safe rules only*) +fun safe_goal_tac (Pack(safes,unsafes)) = reresolve_tac safes; + +(*Tries a safe rule or else a unsafe rule. Single-step for tracing. *) +fun step_tac (thm_pack as Pack(safes,unsafes)) = + safe_goal_tac thm_pack ORELSE' + filseq_resolve_tac unsafes 9999; + + +(* Tactic for reducing a goal, using Predicate Calculus rules. + A decision procedure for Propositional Calculus, it is incomplete + for Predicate-Calculus because of allL_thin and exR_thin. + Fails if it can do nothing. *) +fun pc_tac thm_pack = SELECT_GOAL (DEPTH_SOLVE (repeat_goal_tac thm_pack 1)); + + +(*The following two tactics are analogous to those provided by + Provers/classical. In fact, pc_tac is usually FASTER than fast_tac!*) +fun fast_tac thm_pack = + SELECT_GOAL (DEPTH_SOLVE (step_tac thm_pack 1)); + +fun best_tac thm_pack = + SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm) + (step_tac thm_pack 1)); + + + +signature MODAL_PROVER_RULE = +sig + val rewrite_rls : thm list + val safe_rls : thm list + val unsafe_rls : thm list + val bound_rls : thm list + val aside_rls : thm list +end; + +signature MODAL_PROVER = +sig + val rule_tac : thm list -> int ->tactic + val step_tac : int -> tactic + val solven_tac : int -> int -> tactic + val solve_tac : int -> tactic +end; + +functor Modal_ProverFun (Modal_Rule: MODAL_PROVER_RULE) : MODAL_PROVER = +struct +local open Modal_Rule +in + +(*Returns the list of all formulas in the sequent*) +fun forms_of_seq (Const("SeqO",_) $ P $ u) = P :: forms_of_seq u + | forms_of_seq (H $ u) = forms_of_seq u + | forms_of_seq _ = []; + +(*Tests whether two sequences (left or right sides) could be resolved. + seqp is a premise (subgoal), seqc is a conclusion of an object-rule. + Assumes each formula in seqc is surrounded by sequence variables + -- checks that each concl formula looks like some subgoal formula.*) +fun could_res (seqp,seqc) = + forall (fn Qc => exists (fn Qp => could_unify (Qp,Qc)) + (forms_of_seq seqp)) + (forms_of_seq seqc); + +(*Tests whether two sequents G|-H could be resolved, comparing each side.*) +fun could_resolve_seq (prem,conc) = + case (prem,conc) of + (_ $ Abs(_,_,leftp) $ Abs(_,_,rightp), + _ $ Abs(_,_,leftc) $ Abs(_,_,rightc)) => + could_res (leftp,leftc) andalso could_res (rightp,rightc) + | _ => false; + +(*Like filt_resolve_tac, using could_resolve_seq + Much faster than resolve_tac when there are many rules. + Resolve subgoal i using the rules, unless more than maxr are compatible. *) +fun filseq_resolve_tac rules maxr = SUBGOAL(fn (prem,i) => + let val rls = filter_thms could_resolve_seq (maxr+1, prem, rules) + in if length rls > maxr then no_tac else resolve_tac rls i + end); + +fun fresolve_tac rls n = filseq_resolve_tac rls 999 n; + +(* NB No back tracking possible with aside rules *) + +fun aside_tac n = DETERM(REPEAT (filt_resolve_tac aside_rls 999 n)); +fun rule_tac rls n = fresolve_tac rls n THEN aside_tac n; + +val fres_safe_tac = fresolve_tac safe_rls; +val fres_unsafe_tac = fresolve_tac unsafe_rls THEN' aside_tac; +val fres_bound_tac = fresolve_tac bound_rls; + +fun UPTOGOAL n tf = let fun tac i = if i tac(nprems_of state)) end; + +(* Depth first search bounded by d *) +fun solven_tac d n = STATE (fn state => + if d<0 then no_tac + else if (nprems_of state = 0) then all_tac + else (DETERM(fres_safe_tac n) THEN UPTOGOAL n (solven_tac d)) ORELSE + ((fres_unsafe_tac n THEN UPTOGOAL n (solven_tac d)) APPEND + (fres_bound_tac n THEN UPTOGOAL n (solven_tac (d-1))))); + +fun solve_tac d = rewrite_goals_tac rewrite_rls THEN solven_tac d 1; + +fun step_tac n = STATE (fn state => + if (nprems_of state = 0) then all_tac + else (DETERM(fres_safe_tac n)) ORELSE + (fres_unsafe_tac n APPEND fres_bound_tac n)); + +end; +end;