src/Sequents/modal.ML
 author wenzelm Sun, 18 Sep 2005 15:20:08 +0200 changeset 17481 75166ebb619b parent 7096 8c9278991d9c child 24584 01e83ffa6c54 permissions -rw-r--r--
converted to Isar theory format;
```
(*  Title:      LK/modal.ML
ID:         \$Id\$
Author:     Lawrence C Paulson, Cambridge University Computer Laboratory

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;
```