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src/Pure/deriv.ML

author | paulson |

Mon Dec 07 18:26:25 1998 +0100 (1998-12-07) | |

changeset 6019 | 0e55c2fb2ebb |

parent 2672 | 85d7e800d754 |

child 6085 | 3d8dcb09dbfb |

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

tidying

1 (* Title: Pure/deriv.ML

2 ID: $Id$

3 Author: Lawrence C Paulson, Cambridge University Computer Laboratory

4 Copyright 1996 University of Cambridge

6 Derivations (proof objects) and functions for examining them

7 *)

9 signature DERIV =

10 sig

11 (*Object-level rules*)

12 datatype orule = Subgoal of cterm

13 | Asm of int

14 | Res of deriv

15 | Equal of deriv

16 | Thm of string

17 | Other of deriv;

19 val size : deriv -> int

20 val drop : 'a mtree * int -> 'a mtree

21 val linear : deriv -> deriv list

22 val tree : deriv -> orule mtree

23 end;

25 structure Deriv : DERIV =

26 struct

28 fun size (Join(Theorem _, _)) = 1

29 | size (Join(_, ders)) = foldl op+ (1, map size ders);

31 (*Conversion to linear format. Children of a node are the LIST of inferences

32 justifying ONE of the premises*)

33 fun rev_deriv (Join (rl, [])) = [Join(rl,[])]

34 | rev_deriv (Join (Theorem name, _)) = [Join(Theorem name, [])]

35 | rev_deriv (Join (Assumption arg, [der])) =

36 Join(Assumption arg,[]) :: rev_deriv der

37 | rev_deriv (Join (Bicompose arg, [rder, sder])) =

38 Join (Bicompose arg, linear rder) :: rev_deriv sder

39 | rev_deriv (Join (_, [der])) = rev_deriv der

40 | rev_deriv (Join (rl, der::ders)) = (*catch-all case; doubtful?*)

41 Join(rl, List.concat (map linear ders)) :: rev_deriv der

42 and linear der = rev (rev_deriv der);

45 (*** Conversion of object-level proof trees ***)

47 (*Object-level rules*)

48 datatype orule = Subgoal of cterm

49 | Asm of int

50 | Res of deriv

51 | Equal of deriv

52 | Thm of string

53 | Other of deriv;

55 (*At position i, splice in value x, removing ngoal elements*)

56 fun splice (i,x,ngoal,prfs) =

57 let val prfs0 = take(i-1,prfs)

58 and prfs1 = drop(i-1,prfs)

59 val prfs2 = Join (x, take(ngoal, prfs1)) :: drop(ngoal, prfs1)

60 in prfs0 @ prfs2 end;

62 (*Deletes trivial uses of Equal_elim; hides derivations of Theorems*)

63 fun simp_deriv (Join (Equal_elim, [Join (Rewrite_cterm _, []), der])) =

64 simp_deriv der

65 | simp_deriv (Join (Equal_elim, [Join (Reflexive _, []), der])) =

66 simp_deriv der

67 | simp_deriv (Join (rule as Theorem name, [_])) = Join (rule, [])

68 | simp_deriv (Join (rule, ders)) = Join (rule, map simp_deriv ders);

70 (*Proof term is an equality: first premise of equal_elim.

71 Attempt to decode proof terms made by Drule.goals_conv.

72 Subgoal numbers are returned; they are wrong if original subgoal

73 had flexflex pairs!

74 NEGATIVE i means "could affect all subgoals starting from i"*)

75 fun scan_equals (i, Join (Combination,

76 [Join (Combination, [_, der1]), der2])) =

77 (case der1 of (*ignore trivial cases*)

78 Join (Reflexive _, _) => scan_equals (i+1, der2)

79 | Join (Rewrite_cterm _, []) => scan_equals (i+1, der2)

80 | Join (Rewrite_cterm _, _) => (i,der1) :: scan_equals (i+1, der2)

81 | _ (*impossible in gconv*) => [])

82 | scan_equals (i, Join (Reflexive _, [])) = []

83 | scan_equals (i, Join (Rewrite_cterm _, [])) = []

84 (*Anything else could affect ALL following goals*)

85 | scan_equals (i, der) = [(~i,der)];

87 (*Record uses of equality reasoning on 1 or more subgoals*)

88 fun update_equals ((i,der), prfs) =

89 if i>0 then splice (i, Equal (simp_deriv der), 1, prfs)

90 else take (~i-1, prfs) @

91 map (fn prf => Join (Equal (simp_deriv der), [prf]))

92 (drop (~i-1, prfs));

94 fun delift (Join (Lift_rule _, [der])) = der

95 | delift der = der;

97 (*Conversion to an object-level proof tree.

98 Uses embedded Lift_rules to "annotate" the proof tree with subgoals;

99 -- assumes that Lift_rule never occurs except with resolution

100 -- may contain Vars that, in fact, are instantiated in that step*)

101 fun tree_aux (Join (Trivial ct, []), prfs) = Join(Subgoal ct, prfs)

102 | tree_aux (Join (Assumption(i,_), [der]), prfs) =

103 tree_aux (der, splice (i, Asm i, 0, prfs))

104 | tree_aux (Join (Equal_elim, [der1,der2]), prfs) =

105 tree_aux (der2, foldr update_equals (scan_equals (1, der1), prfs))

106 | tree_aux (Join (Bicompose (match,true,i,ngoal,env), ders), prfs) =

107 (*change eresolve_tac to proof by assumption*)

108 tree_aux (Join (Assumption(i, Some env),

109 [Join (Bicompose (match,false,i,ngoal,env), ders)]),

110 prfs)

111 | tree_aux (Join (Lift_rule (ct,i), [der]), prfs) =

112 tree_aux (der, splice (i, Subgoal ct, 1, prfs))

113 | tree_aux (Join (Bicompose arg,

114 [Join (Instantiate _, [rder]), sder]), prfs) =

115 (*Ignore Instantiate*)

116 tree_aux (Join (Bicompose arg, [rder, sder]), prfs)

117 | tree_aux (Join (Bicompose arg,

118 [Join (Lift_rule larg, [rder]), sder]), prfs) =

119 (*Move Lift_rule: to make a Subgoal on the result*)

120 tree_aux (Join (Bicompose arg, [rder,

121 Join(Lift_rule larg, [sder])]), prfs)

122 | tree_aux (Join (Bicompose (match,ef,i,ngoal,env),

123 [Join (Bicompose (match',ef',i',ngoal',env'),

124 [der1,der2]),

125 der3]), prfs) =

126 (*associate resolutions to the right*)

127 tree_aux (Join (Bicompose (match', ef', i'+i-1, ngoal', env'),

128 [delift der1, (*This Lift_rule would be wrong!*)

129 Join (Bicompose (match, ef, i, ngoal-ngoal'+1, env),

130 [der2, der3])]), prfs)

131 | tree_aux (Join (Bicompose (arg as (_,_,i,ngoal,_)),

132 [rder, sder]), prfs) =

133 (*resolution with basic rule/assumption -- we hope!*)

134 tree_aux (sder, splice (i, Res (simp_deriv rder), ngoal, prfs))

135 | tree_aux (Join (Theorem name, _), prfs) = Join(Thm name, prfs)

136 | tree_aux (Join (_, [der]), prfs) = tree_aux (der,prfs)

137 | tree_aux (der, prfs) = Join(Other (simp_deriv der), prfs);

140 fun tree der = tree_aux (der,[]);

142 (*Currently declared at end, to avoid conflicting with library's drop

143 Can put it after "size" once we switch to List.drop*)

144 fun drop (der,0) = der

145 | drop (Join (_, der::_), n) = drop (der, n-1)

146 | drop (der,_) = der;

148 end;

151 (*We do NOT open this structure*)