summary |
shortlog |
changelog |
graph |
tags |
branches |
files |
changeset |
file |
revisions |
annotate |
diff |
raw

src/Tools/IsaPlanner/isand.ML

author | wenzelm |

Tue Jun 02 09:16:19 2015 +0200 (2015-06-02) | |

changeset 60358 | aebfbcab1eb8 |

parent 59641 | a2d056424d3c |

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

clarified context;

1 (* Title: Tools/IsaPlanner/isand.ML

2 Author: Lucas Dixon, University of Edinburgh

4 Natural Deduction tools (obsolete).

6 For working with Isabelle theorems in a natural detuction style.

7 ie, not having to deal with meta level quantified varaibles,

8 instead, we work with newly introduced frees, and hide the

9 "all"'s, exporting results from theorems proved with the frees, to

10 solve the all cases of the previous goal. This allows resolution

11 to do proof search normally.

13 Note: A nice idea: allow exporting to solve any subgoal, thus

14 allowing the interleaving of proof, or provide a structure for the

15 ordering of proof, thus allowing proof attempts in parrell, but

16 recording the order to apply things in.

18 THINK: are we really ok with our varify name w.r.t the prop - do

19 we also need to avoid names in the hidden hyps? What about

20 unification contraints in flex-flex pairs - might they also have

21 extra free vars?

22 *)

24 signature ISA_ND =

25 sig

26 val variant_names: Proof.context -> term list -> string list -> string list

28 (* meta level fixed params (i.e. !! vars) *)

29 val fix_alls_term: Proof.context -> int -> term -> term * term list

31 (* assumptions/subgoals *)

32 val fixed_subgoal_thms: Proof.context -> thm -> thm list * (thm list -> thm)

33 end

35 structure IsaND : ISA_ND =

36 struct

38 (* datatype to capture an exported result, ie a fix or assume. *)

39 datatype export =

40 Export of

41 {fixes : Thm.cterm list, (* fixed vars *)

42 assumes : Thm.cterm list, (* hidden hyps/assumed prems *)

43 sgid : int,

44 gth : Thm.thm}; (* subgoal/goalthm *)

46 (* exporting function that takes a solution to the fixed/assumed goal,

47 and uses this to solve the subgoal in the main theorem *)

48 fun export_solution (Export {fixes = cfvs, assumes = hcprems, sgid = i, gth = gth}) solth =

49 let

50 val solth' = solth

51 |> Drule.implies_intr_list hcprems

52 |> Drule.forall_intr_list cfvs;

53 in Drule.compose (solth', i, gth) end;

55 fun variant_names ctxt ts xs =

56 let

57 val names =

58 Variable.names_of ctxt

59 |> (fold o fold_aterms)

60 (fn Var ((a, _), _) => Name.declare a

61 | Free (a, _) => Name.declare a

62 | _ => I) ts;

63 in fst (fold_map Name.variant xs names) end;

65 (* fix parameters of a subgoal "i", as free variables, and create an

66 exporting function that will use the result of this proved goal to

67 show the goal in the original theorem.

69 Note, an advantage of this over Isar is that it supports instantiation

70 of unkowns in the earlier theorem, ie we can do instantiation of meta

71 vars!

73 avoids constant, free and vars names.

75 loosely corresponds to:

76 Given "[| SG0; ... !! x. As ==> SGi x; ... SGm |] ==> G" : thm

77 Result:

78 ("(As ==> SGi x') ==> (As ==> SGi x')" : thm,

79 expf :

80 ("As ==> SGi x'" : thm) ->

81 ("[| SG0; ... SGi-1; SGi+1; ... SGm |] ==> G") : thm)

82 *)

83 fun fix_alls_term ctxt i t =

84 let

85 val gt = Logic.get_goal t i;

86 val body = Term.strip_all_body gt;

87 val alls = rev (Term.strip_all_vars gt);

88 val xs = variant_names ctxt [t] (map fst alls);

89 val fvs = map Free (xs ~~ map snd alls);

90 in ((subst_bounds (fvs,body)), fvs) end;

92 fun fix_alls_cterm ctxt i th =

93 let

94 val (fixedbody, fvs) = fix_alls_term ctxt i (Thm.prop_of th);

95 val cfvs = rev (map (Thm.cterm_of ctxt) fvs);

96 val ct_body = Thm.cterm_of ctxt fixedbody;

97 in (ct_body, cfvs) end;

99 fun fix_alls' ctxt i = apfst Thm.trivial o fix_alls_cterm ctxt i;

102 (* hide other goals *)

103 (* note the export goal is rotated by (i - 1) and will have to be

104 unrotated to get backto the originial position(s) *)

105 fun hide_other_goals th =

106 let

107 (* tl beacuse fst sg is the goal we are interested in *)

108 val cprems = tl (Drule.cprems_of th);

109 val aprems = map Thm.assume cprems;

110 in (Drule.implies_elim_list (Drule.rotate_prems 1 th) aprems, cprems) end;

112 (* a nicer version of the above that leaves only a single subgoal (the

113 other subgoals are hidden hyps, that the exporter suffles about)

114 namely the subgoal that we were trying to solve. *)

115 (* loosely corresponds to:

116 Given "[| SG0; ... !! x. As ==> SGi x; ... SGm |] ==> G" : thm

117 Result:

118 ("(As ==> SGi x') ==> SGi x'" : thm,

119 expf :

120 ("SGi x'" : thm) ->

121 ("[| SG0; ... SGi-1; SGi+1; ... SGm |] ==> G") : thm)

122 *)

123 fun fix_alls ctxt i th =

124 let

125 val (fixed_gth, fixedvars) = fix_alls' ctxt i th

126 val (sml_gth, othergoals) = hide_other_goals fixed_gth

127 in (sml_gth, Export {fixes = fixedvars, assumes = othergoals, sgid = i, gth = th}) end;

130 (* Fixme: allow different order of subgoals given to expf *)

131 (* make each subgoal into a separate thm that needs to be proved *)

132 (* loosely corresponds to:

133 Given

134 "[| SG0; ... SGm |] ==> G" : thm

135 Result:

136 (["SG0 ==> SG0", ... ,"SGm ==> SGm"] : thm list, -- goals

137 ["SG0", ..., "SGm"] : thm list -> -- export function

138 "G" : thm)

139 *)

140 fun subgoal_thms ctxt th =

141 let

142 val t = Thm.prop_of th;

144 val prems = Logic.strip_imp_prems t;

145 val aprems = map (Thm.trivial o Thm.cterm_of ctxt) prems;

147 fun explortf premths = Drule.implies_elim_list th premths;

148 in (aprems, explortf) end;

151 (* Fixme: allow different order of subgoals in exportf *)

152 (* as above, but also fix all parameters in all subgoals, and uses

153 fix_alls, not fix_alls', ie doesn't leave extra asumptions as apparent

154 subgoals. *)

155 (* loosely corresponds to:

156 Given

157 "[| !! x0s. A0s x0s ==> SG0 x0s;

158 ...; !! xms. Ams xms ==> SGm xms|] ==> G" : thm

159 Result:

160 (["(A0s x0s' ==> SG0 x0s') ==> SG0 x0s'",

161 ... ,"(Ams xms' ==> SGm xms') ==> SGm xms'"] : thm list, -- goals

162 ["SG0 x0s'", ..., "SGm xms'"] : thm list -> -- export function

163 "G" : thm)

164 *)

165 (* requires being given solutions! *)

166 fun fixed_subgoal_thms ctxt th =

167 let

168 val (subgoals, expf) = subgoal_thms ctxt th;

169 (* fun export_sg (th, exp) = exp th; *)

170 fun export_sgs expfs solthms =

171 expf (map2 (curry (op |>)) solthms expfs);

172 (* expf (map export_sg (ths ~~ expfs)); *)

173 in

174 apsnd export_sgs

175 (Library.split_list (map (apsnd export_solution o fix_alls ctxt 1) subgoals))

176 end;

178 end;