# File modal.ML

    (*  Title:      LK/modal.ML
        ID:         $Id: modal.ML,v 1.1 1999/07/27 17:00:55 paulson 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;