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src/Sequents/prover.ML

author | haftmann |

Fri Jun 19 21:08:07 2009 +0200 (2009-06-19) | |

changeset 31726 | ffd2dc631d88 |

parent 29269 | 5c25a2012975 |

child 32091 | 30e2ffbba718 |

permissions | -rw-r--r-- |

merged

1 (* Title: Sequents/prover.ML

2 Author: Lawrence C Paulson, Cambridge University Computer Laboratory

3 Copyright 1992 University of Cambridge

5 Simple classical reasoner for the sequent calculus, based on "theorem packs".

6 *)

9 (*Higher precedence than := facilitates use of references*)

10 infix 4 add_safes add_unsafes;

12 structure Cla =

14 struct

16 datatype pack = Pack of thm list * thm list;

18 val trace = ref false;

20 (*A theorem pack has the form (safe rules, unsafe rules)

21 An unsafe rule is incomplete or introduces variables in subgoals,

22 and is tried only when the safe rules are not applicable. *)

24 fun less (rl1,rl2) = (nprems_of rl1) < (nprems_of rl2);

26 val empty_pack = Pack([],[]);

28 fun warn_duplicates [] = []

29 | warn_duplicates dups =

30 (warning (cat_lines ("Ignoring duplicate theorems:" :: map Display.string_of_thm dups));

31 dups);

33 fun (Pack(safes,unsafes)) add_safes ths =

34 let val dups = warn_duplicates (gen_inter Thm.eq_thm_prop (ths,safes))

35 val ths' = subtract Thm.eq_thm_prop dups ths

36 in

37 Pack(sort (make_ord less) (ths'@safes), unsafes)

38 end;

40 fun (Pack(safes,unsafes)) add_unsafes ths =

41 let val dups = warn_duplicates (gen_inter Thm.eq_thm_prop (ths,unsafes))

42 val ths' = subtract Thm.eq_thm_prop dups ths

43 in

44 Pack(safes, sort (make_ord less) (ths'@unsafes))

45 end;

47 fun merge_pack (Pack(safes,unsafes), Pack(safes',unsafes')) =

48 Pack(sort (make_ord less) (safes@safes'),

49 sort (make_ord less) (unsafes@unsafes'));

52 fun print_pack (Pack(safes,unsafes)) =

53 (writeln "Safe rules:"; Display.print_thms safes;

54 writeln "Unsafe rules:"; Display.print_thms unsafes);

56 (*Returns the list of all formulas in the sequent*)

57 fun forms_of_seq (Const("SeqO'",_) $ P $ u) = P :: forms_of_seq u

58 | forms_of_seq (H $ u) = forms_of_seq u

59 | forms_of_seq _ = [];

61 (*Tests whether two sequences (left or right sides) could be resolved.

62 seqp is a premise (subgoal), seqc is a conclusion of an object-rule.

63 Assumes each formula in seqc is surrounded by sequence variables

64 -- checks that each concl formula looks like some subgoal formula.

65 It SHOULD check order as well, using recursion rather than forall/exists*)

66 fun could_res (seqp,seqc) =

67 forall (fn Qc => exists (fn Qp => Term.could_unify (Qp,Qc))

68 (forms_of_seq seqp))

69 (forms_of_seq seqc);

72 (*Tests whether two sequents or pairs of sequents could be resolved*)

73 fun could_resolve_seq (prem,conc) =

74 case (prem,conc) of

75 (_ $ Abs(_,_,leftp) $ Abs(_,_,rightp),

76 _ $ Abs(_,_,leftc) $ Abs(_,_,rightc)) =>

77 could_res (leftp,leftc) andalso could_res (rightp,rightc)

78 | (_ $ Abs(_,_,leftp) $ rightp,

79 _ $ Abs(_,_,leftc) $ rightc) =>

80 could_res (leftp,leftc) andalso Term.could_unify (rightp,rightc)

81 | _ => false;

84 (*Like filt_resolve_tac, using could_resolve_seq

85 Much faster than resolve_tac when there are many rules.

86 Resolve subgoal i using the rules, unless more than maxr are compatible. *)

87 fun filseq_resolve_tac rules maxr = SUBGOAL(fn (prem,i) =>

88 let val rls = filter_thms could_resolve_seq (maxr+1, prem, rules)

89 in if length rls > maxr then no_tac

90 else (*((rtac derelict 1 THEN rtac impl 1

91 THEN (rtac identity 2 ORELSE rtac ll_mp 2)

92 THEN rtac context1 1)

93 ORELSE *) resolve_tac rls i

94 end);

97 (*Predicate: does the rule have n premises? *)

98 fun has_prems n rule = (nprems_of rule = n);

100 (*Continuation-style tactical for resolution.

101 The list of rules is partitioned into 0, 1, 2 premises.

102 The resulting tactic, gtac, tries to resolve with rules.

103 If successful, it recursively applies nextac to the new subgoals only.

104 Else fails. (Treatment of goals due to Ph. de Groote)

105 Bind (RESOLVE_THEN rules) to a variable: it preprocesses the rules. *)

107 (*Takes rule lists separated in to 0, 1, 2, >2 premises.

108 The abstraction over state prevents needless divergence in recursion.

109 The 9999 should be a parameter, to delay treatment of flexible goals. *)

111 fun RESOLVE_THEN rules =

112 let val [rls0,rls1,rls2] = partition_list has_prems 0 2 rules;

113 fun tac nextac i state = state |>

114 (filseq_resolve_tac rls0 9999 i

115 ORELSE

116 (DETERM(filseq_resolve_tac rls1 9999 i) THEN TRY(nextac i))

117 ORELSE

118 (DETERM(filseq_resolve_tac rls2 9999 i) THEN TRY(nextac(i+1))

119 THEN TRY(nextac i)))

120 in tac end;

124 (*repeated resolution applied to the designated goal*)

125 fun reresolve_tac rules =

126 let val restac = RESOLVE_THEN rules; (*preprocessing done now*)

127 fun gtac i = restac gtac i

128 in gtac end;

130 (*tries the safe rules repeatedly before the unsafe rules. *)

131 fun repeat_goal_tac (Pack(safes,unsafes)) =

132 let val restac = RESOLVE_THEN safes

133 and lastrestac = RESOLVE_THEN unsafes;

134 fun gtac i = restac gtac i

135 ORELSE (if !trace then

136 (print_tac "" THEN lastrestac gtac i)

137 else lastrestac gtac i)

138 in gtac end;

141 (*Tries safe rules only*)

142 fun safe_tac (Pack(safes,unsafes)) = reresolve_tac safes;

144 val safe_goal_tac = safe_tac; (*backwards compatibility*)

146 (*Tries a safe rule or else a unsafe rule. Single-step for tracing. *)

147 fun step_tac (pack as Pack(safes,unsafes)) =

148 safe_tac pack ORELSE'

149 filseq_resolve_tac unsafes 9999;

152 (* Tactic for reducing a goal, using Predicate Calculus rules.

153 A decision procedure for Propositional Calculus, it is incomplete

154 for Predicate-Calculus because of allL_thin and exR_thin.

155 Fails if it can do nothing. *)

156 fun pc_tac pack = SELECT_GOAL (DEPTH_SOLVE (repeat_goal_tac pack 1));

159 (*The following two tactics are analogous to those provided by

160 Provers/classical. In fact, pc_tac is usually FASTER than fast_tac!*)

161 fun fast_tac pack =

162 SELECT_GOAL (DEPTH_SOLVE (step_tac pack 1));

164 fun best_tac pack =

165 SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm)

166 (step_tac pack 1));

168 end;

171 open Cla;