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