src/Sequents/modal.ML
author wenzelm
Mon Mar 19 21:10:33 2012 +0100 (2012-03-19)
changeset 47022 8eac39af4ec0
parent 41449 7339f0e7c513
child 54742 7a86358a3c0b
permissions -rw-r--r--
moved some legacy stuff;
     1 (*  Title:      Sequents/modal.ML
     2     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     3     Copyright   1992  University of Cambridge
     4 
     5 Simple modal reasoner.
     6 *)
     7 
     8 signature MODAL_PROVER_RULE =
     9 sig
    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
    15 end;
    16 
    17 signature MODAL_PROVER = 
    18 sig
    19     val rule_tac   : thm list -> int ->tactic
    20     val step_tac   : int -> tactic
    21     val solven_tac : int -> int -> tactic
    22     val solve_tac  : int -> tactic
    23 end;
    24 
    25 functor Modal_ProverFun (Modal_Rule: MODAL_PROVER_RULE) : MODAL_PROVER = 
    26 struct
    27 
    28 (*Returns the list of all formulas in the sequent*)
    29 fun forms_of_seq (Const(@{const_name SeqO'},_) $ 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.*)
    37 fun 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.*)
    43 fun 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. *)
    53 fun filseq_resolve_tac 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 rls i
    56   end);
    57 
    58 fun fresolve_tac rls n = filseq_resolve_tac rls 999 n;
    59 
    60 (* NB No back tracking possible with aside rules *)
    61 
    62 fun aside_tac n = DETERM(REPEAT (filt_resolve_tac Modal_Rule.aside_rls 999 n));
    63 fun rule_tac rls n = fresolve_tac rls n THEN aside_tac n;
    64 
    65 val fres_safe_tac = fresolve_tac Modal_Rule.safe_rls;
    66 val fres_unsafe_tac = fresolve_tac Modal_Rule.unsafe_rls THEN' aside_tac;
    67 val fres_bound_tac = fresolve_tac Modal_Rule.bound_rls;
    68 
    69 fun UPTOGOAL n tf = let fun tac i = if i<n then all_tac
    70                                     else tf(i) THEN tac(i-1)
    71                     in fn st => tac (nprems_of st) st end;
    72 
    73 (* Depth first search bounded by d *)
    74 fun solven_tac d n state = state |>
    75        (if d<0 then no_tac
    76         else if (nprems_of state = 0) then all_tac 
    77         else (DETERM(fres_safe_tac n) THEN UPTOGOAL n (solven_tac d)) ORELSE
    78                  ((fres_unsafe_tac n  THEN UPTOGOAL n (solven_tac d)) APPEND
    79                    (fres_bound_tac n  THEN UPTOGOAL n (solven_tac (d-1)))));
    80 
    81 fun solve_tac d = rewrite_goals_tac Modal_Rule.rewrite_rls THEN solven_tac d 1;
    82 
    83 fun step_tac n = 
    84     COND (has_fewer_prems 1) all_tac 
    85          (DETERM(fres_safe_tac n) ORELSE 
    86           (fres_unsafe_tac n APPEND fres_bound_tac n));
    87 
    88 end;