(* Title: Sequents/modal.ML ID: $Id: modal.ML,v 1.2 2007/09/15 17:27:38 haftmann Exp $ Author: Lawrence C Paulson, Cambridge University Computer Laboratory Copyright 1992 University of Cambridge Simple modal reasoner *) 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<n then all_tac else tf(i) THEN tac(i-1) in fn st => tac (nprems_of st) st end; (* Depth first search bounded by d *) fun solven_tac d n state = 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 = COND (has_fewer_prems 1) all_tac (DETERM(fres_safe_tac n) ORELSE (fres_unsafe_tac n APPEND fres_bound_tac n)); end; end;