1(* Title: Sequents/modal.ML 2 Author: Lawrence C Paulson, Cambridge University Computer Laboratory 3 Copyright 1992 University of Cambridge 4 5Simple modal reasoner. 6*) 7 8signature MODAL_PROVER_RULE = 9sig 10 val rewrite_rls : thm list 11 val safe_rls : thm list 12 val unsafe_rls : thm list 13 val bound_rls : thm list 14 val aside_rls : thm list 15end; 16 17signature MODAL_PROVER = 18sig 19 val rule_tac : Proof.context -> thm list -> int ->tactic 20 val step_tac : Proof.context -> int -> tactic 21 val solven_tac : Proof.context -> int -> int -> tactic 22 val solve_tac : Proof.context -> int -> tactic 23end; 24 25functor Modal_ProverFun (Modal_Rule: MODAL_PROVER_RULE) : MODAL_PROVER = 26struct 27 28(*Returns the list of all formulas in the sequent*) 29fun forms_of_seq (Const(\<^const_name>\<open>SeqO'\<close>,_) $ P $ u) = P :: forms_of_seq u 30 | forms_of_seq (H $ u) = forms_of_seq u 31 | forms_of_seq _ = []; 32 33(*Tests whether two sequences (left or right sides) could be resolved. 34 seqp is a premise (subgoal), seqc is a conclusion of an object-rule. 35 Assumes each formula in seqc is surrounded by sequence variables 36 -- checks that each concl formula looks like some subgoal formula.*) 37fun could_res (seqp,seqc) = 38 forall (fn Qc => exists (fn Qp => Term.could_unify (Qp,Qc)) 39 (forms_of_seq seqp)) 40 (forms_of_seq seqc); 41 42(*Tests whether two sequents G|-H could be resolved, comparing each side.*) 43fun could_resolve_seq (prem,conc) = 44 case (prem,conc) of 45 (_ $ Abs(_,_,leftp) $ Abs(_,_,rightp), 46 _ $ Abs(_,_,leftc) $ Abs(_,_,rightc)) => 47 could_res (leftp,leftc) andalso could_res (rightp,rightc) 48 | _ => false; 49 50(*Like filt_resolve_tac, using could_resolve_seq 51 Much faster than resolve_tac when there are many rules. 52 Resolve subgoal i using the rules, unless more than maxr are compatible. *) 53fun filseq_resolve_tac ctxt rules maxr = SUBGOAL(fn (prem,i) => 54 let val rls = filter_thms could_resolve_seq (maxr+1, prem, rules) 55 in if length rls > maxr then no_tac else resolve_tac ctxt rls i 56 end); 57 58fun fresolve_tac ctxt rls n = filseq_resolve_tac ctxt rls 999 n; 59 60(* NB No back tracking possible with aside rules *) 61 62val aside_net = Tactic.build_net Modal_Rule.aside_rls; 63fun aside_tac ctxt n = DETERM (REPEAT (filt_resolve_from_net_tac ctxt 999 aside_net n)); 64fun rule_tac ctxt rls n = fresolve_tac ctxt rls n THEN aside_tac ctxt n; 65 66fun fres_safe_tac ctxt = fresolve_tac ctxt Modal_Rule.safe_rls; 67fun fres_unsafe_tac ctxt = fresolve_tac ctxt Modal_Rule.unsafe_rls THEN' aside_tac ctxt; 68fun fres_bound_tac ctxt = fresolve_tac ctxt Modal_Rule.bound_rls; 69 70fun UPTOGOAL n tf = let fun tac i = if i<n then all_tac 71 else tf(i) THEN tac(i-1) 72 in fn st => tac (Thm.nprems_of st) st end; 73 74(* Depth first search bounded by d *) 75fun solven_tac ctxt d n st = st |> 76 (if d < 0 then no_tac 77 else if Thm.nprems_of st = 0 then all_tac 78 else (DETERM(fres_safe_tac ctxt n) THEN UPTOGOAL n (solven_tac ctxt d)) ORELSE 79 ((fres_unsafe_tac ctxt n THEN UPTOGOAL n (solven_tac ctxt d)) APPEND 80 (fres_bound_tac ctxt n THEN UPTOGOAL n (solven_tac ctxt (d - 1))))); 81 82fun solve_tac ctxt d = 83 rewrite_goals_tac ctxt Modal_Rule.rewrite_rls THEN solven_tac ctxt d 1; 84 85fun step_tac ctxt n = 86 COND (has_fewer_prems 1) all_tac 87 (DETERM(fres_safe_tac ctxt n) ORELSE 88 (fres_unsafe_tac ctxt n APPEND fres_bound_tac ctxt n)); 89 90end; 91