author  haftmann 
Fri, 22 Feb 2008 12:01:52 +0100  
changeset 26110  06eacfd8dd9f 
parent 26101  a657683e902a 
child 26942  87e4208700d1 
permissions  rwrr 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

1 
(* Title: HOL/Tools/lin_arith.ML 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

2 
ID: $Id$ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

3 
Author: Tjark Weber and Tobias Nipkow 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

4 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

5 
HOL setup for linear arithmetic (see Provers/Arith/fast_lin_arith.ML). 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

6 
*) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

7 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

8 
signature BASIC_LIN_ARITH = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

9 
sig 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

10 
type arith_tactic 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

11 
val mk_arith_tactic: string > (Proof.context > int > tactic) > arith_tactic 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

12 
val eq_arith_tactic: arith_tactic * arith_tactic > bool 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

13 
val arith_split_add: attribute 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

14 
val arith_discrete: string > Context.generic > Context.generic 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

15 
val arith_inj_const: string * typ > Context.generic > Context.generic 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

16 
val arith_tactic_add: arith_tactic > Context.generic > Context.generic 
24112  17 
val fast_arith_split_limit: int Config.T 
18 
val fast_arith_neq_limit: int Config.T 

24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

19 
val lin_arith_pre_tac: Proof.context > int > tactic 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

20 
val fast_arith_tac: Proof.context > int > tactic 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

21 
val fast_ex_arith_tac: Proof.context > bool > int > tactic 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

22 
val trace_arith: bool ref 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

23 
val lin_arith_simproc: simpset > term > thm option 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

24 
val fast_nat_arith_simproc: simproc 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

25 
val simple_arith_tac: Proof.context > int > tactic 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

26 
val arith_tac: Proof.context > int > tactic 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

27 
val silent_arith_tac: Proof.context > int > tactic 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

28 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

29 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

30 
signature LIN_ARITH = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

31 
sig 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

32 
include BASIC_LIN_ARITH 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

33 
val map_data: 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

34 
({add_mono_thms: thm list, mult_mono_thms: thm list, inj_thms: thm list, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

35 
lessD: thm list, neqE: thm list, simpset: Simplifier.simpset} > 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

36 
{add_mono_thms: thm list, mult_mono_thms: thm list, inj_thms: thm list, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

37 
lessD: thm list, neqE: thm list, simpset: Simplifier.simpset}) > 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

38 
Context.generic > Context.generic 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

39 
val setup: Context.generic > Context.generic 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

40 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

41 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

42 
structure LinArith: LIN_ARITH = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

43 
struct 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

44 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

45 
(* Parameters data for general linear arithmetic functor *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

46 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

47 
structure LA_Logic: LIN_ARITH_LOGIC = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

48 
struct 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

49 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

50 
val ccontr = ccontr; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

51 
val conjI = conjI; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

52 
val notI = notI; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

53 
val sym = sym; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

54 
val not_lessD = @{thm linorder_not_less} RS iffD1; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

55 
val not_leD = @{thm linorder_not_le} RS iffD1; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

56 
val le0 = thm "le0"; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

57 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

58 
fun mk_Eq thm = (thm RS Eq_FalseI) handle THM _ => (thm RS Eq_TrueI); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

59 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

60 
val mk_Trueprop = HOLogic.mk_Trueprop; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

61 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

62 
fun atomize thm = case Thm.prop_of thm of 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

63 
Const("Trueprop",_) $ (Const("op &",_) $ _ $ _) => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

64 
atomize(thm RS conjunct1) @ atomize(thm RS conjunct2) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

65 
 _ => [thm]; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

66 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

67 
fun neg_prop ((TP as Const("Trueprop",_)) $ (Const("Not",_) $ t)) = TP $ t 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

68 
 neg_prop ((TP as Const("Trueprop",_)) $ t) = TP $ (HOLogic.Not $t) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

69 
 neg_prop t = raise TERM ("neg_prop", [t]); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

70 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

71 
fun is_False thm = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

72 
let val _ $ t = Thm.prop_of thm 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

73 
in t = Const("False",HOLogic.boolT) end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

74 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

75 
fun is_nat(t) = fastype_of1 t = HOLogic.natT; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

76 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

77 
fun mk_nat_thm sg t = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

78 
let val ct = cterm_of sg t and cn = cterm_of sg (Var(("n",0),HOLogic.natT)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

79 
in instantiate ([],[(cn,ct)]) le0 end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

80 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

81 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

82 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

83 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

84 
(* arith context data *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

85 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

86 
datatype arith_tactic = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

87 
ArithTactic of {name: string, tactic: Proof.context > int > tactic, id: stamp}; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

88 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

89 
fun mk_arith_tactic name tactic = ArithTactic {name = name, tactic = tactic, id = stamp ()}; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

90 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

91 
fun eq_arith_tactic (ArithTactic {id = id1, ...}, ArithTactic {id = id2, ...}) = (id1 = id2); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

92 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

93 
structure ArithContextData = GenericDataFun 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

94 
( 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

95 
type T = {splits: thm list, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

96 
inj_consts: (string * typ) list, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

97 
discrete: string list, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

98 
tactics: arith_tactic list}; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

99 
val empty = {splits = [], inj_consts = [], discrete = [], tactics = []}; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

100 
val extend = I; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

101 
fun merge _ ({splits= splits1, inj_consts= inj_consts1, discrete= discrete1, tactics= tactics1}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

102 
{splits= splits2, inj_consts= inj_consts2, discrete= discrete2, tactics= tactics2}) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

103 
{splits = Library.merge Thm.eq_thm_prop (splits1, splits2), 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

104 
inj_consts = Library.merge (op =) (inj_consts1, inj_consts2), 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

105 
discrete = Library.merge (op =) (discrete1, discrete2), 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

106 
tactics = Library.merge eq_arith_tactic (tactics1, tactics2)}; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

107 
); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

108 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

109 
val get_arith_data = ArithContextData.get o Context.Proof; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

110 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

111 
val arith_split_add = Thm.declaration_attribute (fn thm => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

112 
ArithContextData.map (fn {splits, inj_consts, discrete, tactics} => 
24112  113 
{splits = update Thm.eq_thm_prop thm splits, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

114 
inj_consts = inj_consts, discrete = discrete, tactics = tactics})); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

115 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

116 
fun arith_discrete d = ArithContextData.map (fn {splits, inj_consts, discrete, tactics} => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

117 
{splits = splits, inj_consts = inj_consts, 
24112  118 
discrete = update (op =) d discrete, tactics = tactics}); 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

119 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

120 
fun arith_inj_const c = ArithContextData.map (fn {splits, inj_consts, discrete, tactics} => 
24112  121 
{splits = splits, inj_consts = update (op =) c inj_consts, 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

122 
discrete = discrete, tactics= tactics}); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

123 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

124 
fun arith_tactic_add tac = ArithContextData.map (fn {splits, inj_consts, discrete, tactics} => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

125 
{splits = splits, inj_consts = inj_consts, discrete = discrete, 
24112  126 
tactics = update eq_arith_tactic tac tactics}); 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

127 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

128 

24112  129 
val (fast_arith_split_limit, setup1) = Attrib.config_int "fast_arith_split_limit" 9; 
130 
val (fast_arith_neq_limit, setup2) = Attrib.config_int "fast_arith_neq_limit" 9; 

24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

131 
val setup_options = setup1 #> setup2; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

132 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

133 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

134 
structure LA_Data_Ref = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

135 
struct 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

136 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

137 
val fast_arith_neq_limit = fast_arith_neq_limit; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

138 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

139 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

140 
(* Decomposition of terms *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

141 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

142 
(*internal representation of linear (in)equations*) 
24328
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

143 
type decompT = 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

144 
((term * Rat.rat) list * Rat.rat * string * (term * Rat.rat) list * Rat.rat * bool); 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

145 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

146 
fun nT (Type ("fun", [N, _])) = (N = HOLogic.natT) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

147 
 nT _ = false; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

148 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

149 
fun add_atom (t : term) (m : Rat.rat) (p : (term * Rat.rat) list, i : Rat.rat) : 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

150 
(term * Rat.rat) list * Rat.rat = 
24328
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

151 
case AList.lookup (op =) p t of 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

152 
NONE => ((t, m) :: p, i) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

153 
 SOME n => (AList.update (op =) (t, Rat.add n m) p, i); 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

154 

24328
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

155 
(* decompose nested multiplications, bracketing them to the right and combining 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

156 
all their coefficients 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

157 

24328
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

158 
inj_consts: list of constants to be ignored when encountered 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

159 
(e.g. arithmetic type conversions that preserve value) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

160 

24328
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

161 
m: multiplicity associated with the entire product 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

162 

24328
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

163 
returns either (SOME term, associated multiplicity) or (NONE, constant) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

164 
*) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

165 
fun demult (inj_consts : (string * typ) list) : term * Rat.rat > term option * Rat.rat = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

166 
let 
24328
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

167 
fun demult ((mC as Const (@{const_name HOL.times}, _)) $ s $ t, m) = 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

168 
(case s of Const (@{const_name HOL.times}, _) $ s1 $ s2 => 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

169 
(* bracketing to the right: '(s1 * s2) * t' becomes 's1 * (s2 * t)' *) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

170 
demult (mC $ s1 $ (mC $ s2 $ t), m) 
24328
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

171 
 _ => 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

172 
(* product 's * t', where either factor can be 'NONE' *) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

173 
(case demult (s, m) of 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

174 
(SOME s', m') => 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

175 
(case demult (t, m') of 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

176 
(SOME t', m'') => (SOME (mC $ s' $ t'), m'') 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

177 
 (NONE, m'') => (SOME s', m'')) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

178 
 (NONE, m') => demult (t, m'))) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

179 
 demult ((mC as Const (@{const_name HOL.divide}, _)) $ s $ t, m) = 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

180 
(* FIXME: Shouldn't we simplify nested quotients, e.g. '(s/t)/u' could 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

181 
become 's/(t*u)', and '(s*t)/u' could become 's*(t/u)' ? Note that 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

182 
if we choose to do so here, the simpset used by arith must be able to 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

183 
perform the same simplifications. *) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

184 
(* FIXME: Currently we treat the numerator as atomic unless the 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

185 
denominator can be reduced to a numeric constant. It might be better 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

186 
to demult the numerator in any case, and invent a new term of the form 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

187 
'1 / t' if the numerator can be reduced, but the denominator cannot. *) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

188 
(* FIXME: Currently we even treat the whole fraction as atomic unless the 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

189 
denominator can be reduced to a numeric constant. It might be better 
25015  190 
to use the partially reduced denominator (i.e. 's / (2*t)' could be 
24328
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

191 
demult'ed to 's / t' with multiplicity .5). This would require a 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

192 
very simple change only below, but it breaks existing proofs. *) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

193 
(* quotient 's / t', where the denominator t can be NONE *) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

194 
(* Note: will raise Rat.DIVZERO iff m' is Rat.zero *) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

195 
(case demult (t, Rat.one) of 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

196 
(SOME _, _) => (SOME (mC $ s $ t), m) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

197 
 (NONE, m') => apsnd (Rat.mult (Rat.inv m')) (demult (s, m))) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

198 
(* terms that evaluate to numeric constants *) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

199 
 demult (Const (@{const_name HOL.uminus}, _) $ t, m) = demult (t, Rat.neg m) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

200 
 demult (Const (@{const_name HOL.zero}, _), m) = (NONE, Rat.zero) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

201 
 demult (Const (@{const_name HOL.one}, _), m) = (NONE, m) 
24328
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

202 
(*Warning: in rare cases number_of encloses a nonnumeral, 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

203 
in which case dest_numeral raises TERM; hence all the handles below. 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

204 
Same for Sucterms that turn out not to be numerals  
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

205 
although the simplifier should eliminate those anyway ...*) 
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset

206 
 demult (t as Const ("Int.number_class.number_of", _) $ n, m) = 
24328
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

207 
((NONE, Rat.mult m (Rat.rat_of_int (HOLogic.dest_numeral n))) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

208 
handle TERM _ => (SOME t, m)) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

209 
 demult (t as Const (@{const_name Suc}, _) $ _, m) = 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

210 
((NONE, Rat.mult m (Rat.rat_of_int (HOLogic.dest_nat t))) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

211 
handle TERM _ => (SOME t, m)) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

212 
(* injection constants are ignored *) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

213 
 demult (t as Const f $ x, m) = 
24328
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

214 
if member (op =) inj_consts f then demult (x, m) else (SOME t, m) 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

215 
(* everything else is considered atomic *) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

216 
 demult (atom, m) = (SOME atom, m) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

217 
in demult end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

218 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

219 
fun decomp0 (inj_consts : (string * typ) list) (rel : string, lhs : term, rhs : term) : 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

220 
((term * Rat.rat) list * Rat.rat * string * (term * Rat.rat) list * Rat.rat) option = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

221 
let 
24328
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

222 
(* Turns a term 'all' and associated multiplicity 'm' into a list 'p' of 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

223 
summands and associated multiplicities, plus a constant 'i' (with implicit 
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

224 
multiplicity 1) *) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

225 
fun poly (Const (@{const_name HOL.plus}, _) $ s $ t, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

226 
m : Rat.rat, pi : (term * Rat.rat) list * Rat.rat) = poly (s, m, poly (t, m, pi)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

227 
 poly (all as Const (@{const_name HOL.minus}, T) $ s $ t, m, pi) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

228 
if nT T then add_atom all m pi else poly (s, m, poly (t, Rat.neg m, pi)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

229 
 poly (all as Const (@{const_name HOL.uminus}, T) $ t, m, pi) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

230 
if nT T then add_atom all m pi else poly (t, Rat.neg m, pi) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

231 
 poly (Const (@{const_name HOL.zero}, _), _, pi) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

232 
pi 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

233 
 poly (Const (@{const_name HOL.one}, _), m, (p, i)) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

234 
(p, Rat.add i m) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

235 
 poly (Const (@{const_name Suc}, _) $ t, m, (p, i)) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

236 
poly (t, m, (p, Rat.add i m)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

237 
 poly (all as Const (@{const_name HOL.times}, _) $ _ $ _, m, pi as (p, i)) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

238 
(case demult inj_consts (all, m) of 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

239 
(NONE, m') => (p, Rat.add i m') 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

240 
 (SOME u, m') => add_atom u m' pi) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

241 
 poly (all as Const (@{const_name HOL.divide}, _) $ _ $ _, m, pi as (p, i)) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

242 
(case demult inj_consts (all, m) of 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

243 
(NONE, m') => (p, Rat.add i m') 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

244 
 (SOME u, m') => add_atom u m' pi) 
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset

245 
 poly (all as Const ("Int.number_class.number_of", Type(_,[_,T])) $ t, m, pi as (p, i)) = 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

246 
(let val k = HOLogic.dest_numeral t 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

247 
val k2 = if k < 0 andalso T = HOLogic.natT then 0 else k 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

248 
in (p, Rat.add i (Rat.mult m (Rat.rat_of_int k2))) end 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

249 
handle TERM _ => add_atom all m pi) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

250 
 poly (all as Const f $ x, m, pi) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

251 
if f mem inj_consts then poly (x, m, pi) else add_atom all m pi 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

252 
 poly (all, m, pi) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

253 
add_atom all m pi 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

254 
val (p, i) = poly (lhs, Rat.one, ([], Rat.zero)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

255 
val (q, j) = poly (rhs, Rat.one, ([], Rat.zero)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

256 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

257 
case rel of 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

258 
@{const_name HOL.less} => SOME (p, i, "<", q, j) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

259 
 @{const_name HOL.less_eq} => SOME (p, i, "<=", q, j) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

260 
 "op =" => SOME (p, i, "=", q, j) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

261 
 _ => NONE 
24328
83afe527504d
fixed a bug in demult: a in (a * b) is no longer treated as atomic
webertj
parents:
24271
diff
changeset

262 
end handle Rat.DIVZERO => NONE; 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

263 

24271  264 
fun of_lin_arith_sort thy U = 
265 
Sign.of_sort thy (U, ["Ring_and_Field.ordered_idom"]); 

24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

266 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

267 
fun allows_lin_arith sg (discrete : string list) (U as Type (D, [])) : bool * bool = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

268 
if of_lin_arith_sort sg U then 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

269 
(true, D mem discrete) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

270 
else (* special cases *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

271 
if D mem discrete then (true, true) else (false, false) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

272 
 allows_lin_arith sg discrete U = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

273 
(of_lin_arith_sort sg U, false); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

274 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

275 
fun decomp_typecheck (thy, discrete, inj_consts) (T : typ, xxx) : decompT option = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

276 
case T of 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

277 
Type ("fun", [U, _]) => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

278 
(case allows_lin_arith thy discrete U of 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

279 
(true, d) => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

280 
(case decomp0 inj_consts xxx of 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

281 
NONE => NONE 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

282 
 SOME (p, i, rel, q, j) => SOME (p, i, rel, q, j, d)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

283 
 (false, _) => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

284 
NONE) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

285 
 _ => NONE; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

286 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

287 
fun negate (SOME (x, i, rel, y, j, d)) = SOME (x, i, "~" ^ rel, y, j, d) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

288 
 negate NONE = NONE; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

289 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

290 
fun decomp_negation data 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

291 
((Const ("Trueprop", _)) $ (Const (rel, T) $ lhs $ rhs)) : decompT option = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

292 
decomp_typecheck data (T, (rel, lhs, rhs)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

293 
 decomp_negation data ((Const ("Trueprop", _)) $ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

294 
(Const ("Not", _) $ (Const (rel, T) $ lhs $ rhs))) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

295 
negate (decomp_typecheck data (T, (rel, lhs, rhs))) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

296 
 decomp_negation data _ = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

297 
NONE; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

298 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

299 
fun decomp ctxt : term > decompT option = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

300 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

301 
val thy = ProofContext.theory_of ctxt 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

302 
val {discrete, inj_consts, ...} = get_arith_data ctxt 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

303 
in decomp_negation (thy, discrete, inj_consts) end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

304 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

305 
fun domain_is_nat (_ $ (Const (_, T) $ _ $ _)) = nT T 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

306 
 domain_is_nat (_ $ (Const ("Not", _) $ (Const (_, T) $ _ $ _))) = nT T 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

307 
 domain_is_nat _ = false; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

308 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

309 
fun number_of (n, T) = HOLogic.mk_number T n; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

310 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

311 
(**) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

312 
(* the following code performs splitting of certain constants (e.g. min, *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

313 
(* max) in a linear arithmetic problem; similar to what split_tac later does *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

314 
(* to the proof state *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

315 
(**) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

316 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

317 
(* checks if splitting with 'thm' is implemented *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

318 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

319 
fun is_split_thm (thm : thm) : bool = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

320 
case concl_of thm of _ $ (_ $ (_ $ lhs) $ _) => ( 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

321 
(* Trueprop $ ((op =) $ (?P $ lhs) $ rhs) *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

322 
case head_of lhs of 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

323 
Const (a, _) => member (op =) [@{const_name Orderings.max}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

324 
@{const_name Orderings.min}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

325 
@{const_name HOL.abs}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

326 
@{const_name HOL.minus}, 
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset

327 
"Int.nat", 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

328 
"Divides.div_class.mod", 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

329 
"Divides.div_class.div"] a 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

330 
 _ => (warning ("Lin. Arith.: wrong format for split rule " ^ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

331 
Display.string_of_thm thm); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

332 
false)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

333 
 _ => (warning ("Lin. Arith.: wrong format for split rule " ^ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

334 
Display.string_of_thm thm); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

335 
false); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

336 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

337 
(* substitute new for occurrences of old in a term, incrementing bound *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

338 
(* variables as needed when substituting inside an abstraction *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

339 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

340 
fun subst_term ([] : (term * term) list) (t : term) = t 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

341 
 subst_term pairs t = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

342 
(case AList.lookup (op aconv) pairs t of 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

343 
SOME new => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

344 
new 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

345 
 NONE => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

346 
(case t of Abs (a, T, body) => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

347 
let val pairs' = map (pairself (incr_boundvars 1)) pairs 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

348 
in Abs (a, T, subst_term pairs' body) end 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

349 
 t1 $ t2 => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

350 
subst_term pairs t1 $ subst_term pairs t2 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

351 
 _ => t)); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

352 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

353 
(* approximates the effect of one application of split_tac (followed by NNF *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

354 
(* normalization) on the subgoal represented by '(Ts, terms)'; returns a *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

355 
(* list of new subgoals (each again represented by a typ list for bound *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

356 
(* variables and a term list for premises), or NONE if split_tac would fail *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

357 
(* on the subgoal *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

358 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

359 
(* FIXME: currently only the effect of certain split theorems is reproduced *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

360 
(* (which is why we need 'is_split_thm'). A more canonical *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

361 
(* implementation should analyze the righthand side of the split *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

362 
(* theorem that can be applied, and modify the subgoal accordingly. *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

363 
(* Or even better, the splitter should be extended to provide *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

364 
(* splitting on terms as well as splitting on theorems (where the *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

365 
(* former can have a faster implementation as it does not need to be *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

366 
(* proofproducing). *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

367 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

368 
fun split_once_items ctxt (Ts : typ list, terms : term list) : 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

369 
(typ list * term list) list option = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

370 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

371 
val thy = ProofContext.theory_of ctxt 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

372 
(* takes a list [t1, ..., tn] to the term *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

373 
(* tn' > ... > t1' > False , *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

374 
(* where ti' = HOLogic.dest_Trueprop ti *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

375 
fun REPEAT_DETERM_etac_rev_mp terms' = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

376 
fold (curry HOLogic.mk_imp) (map HOLogic.dest_Trueprop terms') HOLogic.false_const 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

377 
val split_thms = filter is_split_thm (#splits (get_arith_data ctxt)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

378 
val cmap = Splitter.cmap_of_split_thms split_thms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

379 
val splits = Splitter.split_posns cmap thy Ts (REPEAT_DETERM_etac_rev_mp terms) 
24112  380 
val split_limit = Config.get ctxt fast_arith_split_limit 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

381 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

382 
if length splits > split_limit then 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

383 
(tracing ("fast_arith_split_limit exceeded (current value is " ^ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

384 
string_of_int split_limit ^ ")"); NONE) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

385 
else ( 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

386 
case splits of [] => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

387 
(* split_tac would fail: no possible split *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

388 
NONE 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

389 
 ((_, _, _, split_type, split_term) :: _) => ( 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

390 
(* ignore all but the first possible split *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

391 
case strip_comb split_term of 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

392 
(* ?P (max ?i ?j) = ((?i <= ?j > ?P ?j) & (~ ?i <= ?j > ?P ?i)) *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

393 
(Const (@{const_name Orderings.max}, _), [t1, t2]) => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

394 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

395 
val rev_terms = rev terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

396 
val terms1 = map (subst_term [(split_term, t1)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

397 
val terms2 = map (subst_term [(split_term, t2)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

398 
val t1_leq_t2 = Const (@{const_name HOL.less_eq}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

399 
split_type > split_type > HOLogic.boolT) $ t1 $ t2 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

400 
val not_t1_leq_t2 = HOLogic.Not $ t1_leq_t2 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

401 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

402 
val subgoal1 = (HOLogic.mk_Trueprop t1_leq_t2) :: terms2 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

403 
val subgoal2 = (HOLogic.mk_Trueprop not_t1_leq_t2) :: terms1 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

404 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

405 
SOME [(Ts, subgoal1), (Ts, subgoal2)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

406 
end 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

407 
(* ?P (min ?i ?j) = ((?i <= ?j > ?P ?i) & (~ ?i <= ?j > ?P ?j)) *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

408 
 (Const (@{const_name Orderings.min}, _), [t1, t2]) => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

409 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

410 
val rev_terms = rev terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

411 
val terms1 = map (subst_term [(split_term, t1)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

412 
val terms2 = map (subst_term [(split_term, t2)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

413 
val t1_leq_t2 = Const (@{const_name HOL.less_eq}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

414 
split_type > split_type > HOLogic.boolT) $ t1 $ t2 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

415 
val not_t1_leq_t2 = HOLogic.Not $ t1_leq_t2 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

416 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

417 
val subgoal1 = (HOLogic.mk_Trueprop t1_leq_t2) :: terms1 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

418 
val subgoal2 = (HOLogic.mk_Trueprop not_t1_leq_t2) :: terms2 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

419 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

420 
SOME [(Ts, subgoal1), (Ts, subgoal2)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

421 
end 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

422 
(* ?P (abs ?a) = ((0 <= ?a > ?P ?a) & (?a < 0 > ?P ( ?a))) *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

423 
 (Const (@{const_name HOL.abs}, _), [t1]) => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

424 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

425 
val rev_terms = rev terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

426 
val terms1 = map (subst_term [(split_term, t1)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

427 
val terms2 = map (subst_term [(split_term, Const (@{const_name HOL.uminus}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

428 
split_type > split_type) $ t1)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

429 
val zero = Const (@{const_name HOL.zero}, split_type) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

430 
val zero_leq_t1 = Const (@{const_name HOL.less_eq}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

431 
split_type > split_type > HOLogic.boolT) $ zero $ t1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

432 
val t1_lt_zero = Const (@{const_name HOL.less}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

433 
split_type > split_type > HOLogic.boolT) $ t1 $ zero 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

434 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

435 
val subgoal1 = (HOLogic.mk_Trueprop zero_leq_t1) :: terms1 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

436 
val subgoal2 = (HOLogic.mk_Trueprop t1_lt_zero) :: terms2 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

437 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

438 
SOME [(Ts, subgoal1), (Ts, subgoal2)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

439 
end 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

440 
(* ?P (?a  ?b) = ((?a < ?b > ?P 0) & (ALL d. ?a = ?b + d > ?P d)) *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

441 
 (Const (@{const_name HOL.minus}, _), [t1, t2]) => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

442 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

443 
(* "d" in the above theorem becomes a new bound variable after NNF *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

444 
(* transformation, therefore some adjustment of indices is necessary *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

445 
val rev_terms = rev terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

446 
val zero = Const (@{const_name HOL.zero}, split_type) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

447 
val d = Bound 0 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

448 
val terms1 = map (subst_term [(split_term, zero)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

449 
val terms2 = map (subst_term [(incr_boundvars 1 split_term, d)]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

450 
(map (incr_boundvars 1) rev_terms) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

451 
val t1' = incr_boundvars 1 t1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

452 
val t2' = incr_boundvars 1 t2 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

453 
val t1_lt_t2 = Const (@{const_name HOL.less}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

454 
split_type > split_type > HOLogic.boolT) $ t1 $ t2 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

455 
val t1_eq_t2_plus_d = Const ("op =", split_type > split_type > HOLogic.boolT) $ t1' $ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

456 
(Const (@{const_name HOL.plus}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

457 
split_type > split_type > split_type) $ t2' $ d) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

458 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

459 
val subgoal1 = (HOLogic.mk_Trueprop t1_lt_t2) :: terms1 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

460 
val subgoal2 = (HOLogic.mk_Trueprop t1_eq_t2_plus_d) :: terms2 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

461 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

462 
SOME [(Ts, subgoal1), (split_type :: Ts, subgoal2)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

463 
end 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

464 
(* ?P (nat ?i) = ((ALL n. ?i = int n > ?P n) & (?i < 0 > ?P 0)) *) 
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset

465 
 (Const ("Int.nat", _), [t1]) => 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

466 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

467 
val rev_terms = rev terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

468 
val zero_int = Const (@{const_name HOL.zero}, HOLogic.intT) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

469 
val zero_nat = Const (@{const_name HOL.zero}, HOLogic.natT) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

470 
val n = Bound 0 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

471 
val terms1 = map (subst_term [(incr_boundvars 1 split_term, n)]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

472 
(map (incr_boundvars 1) rev_terms) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

473 
val terms2 = map (subst_term [(split_term, zero_nat)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

474 
val t1' = incr_boundvars 1 t1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

475 
val t1_eq_int_n = Const ("op =", HOLogic.intT > HOLogic.intT > HOLogic.boolT) $ t1' $ 
24196  476 
(Const (@{const_name of_nat}, HOLogic.natT > HOLogic.intT) $ n) 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

477 
val t1_lt_zero = Const (@{const_name HOL.less}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

478 
HOLogic.intT > HOLogic.intT > HOLogic.boolT) $ t1 $ zero_int 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

479 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

480 
val subgoal1 = (HOLogic.mk_Trueprop t1_eq_int_n) :: terms1 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

481 
val subgoal2 = (HOLogic.mk_Trueprop t1_lt_zero) :: terms2 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

482 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

483 
SOME [(HOLogic.natT :: Ts, subgoal1), (Ts, subgoal2)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

484 
end 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

485 
(* "?P ((?n::nat) mod (number_of ?k)) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

486 
((number_of ?k = 0 > ?P ?n) & (~ (number_of ?k = 0) > 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

487 
(ALL i j. j < number_of ?k > ?n = number_of ?k * i + j > ?P j))) *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

488 
 (Const ("Divides.div_class.mod", Type ("fun", [Type ("nat", []), _])), [t1, t2]) => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

489 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

490 
val rev_terms = rev terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

491 
val zero = Const (@{const_name HOL.zero}, split_type) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

492 
val i = Bound 1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

493 
val j = Bound 0 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

494 
val terms1 = map (subst_term [(split_term, t1)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

495 
val terms2 = map (subst_term [(incr_boundvars 2 split_term, j)]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

496 
(map (incr_boundvars 2) rev_terms) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

497 
val t1' = incr_boundvars 2 t1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

498 
val t2' = incr_boundvars 2 t2 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

499 
val t2_eq_zero = Const ("op =", 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

500 
split_type > split_type > HOLogic.boolT) $ t2 $ zero 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

501 
val t2_neq_zero = HOLogic.mk_not (Const ("op =", 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

502 
split_type > split_type > HOLogic.boolT) $ t2' $ zero) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

503 
val j_lt_t2 = Const (@{const_name HOL.less}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

504 
split_type > split_type> HOLogic.boolT) $ j $ t2' 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

505 
val t1_eq_t2_times_i_plus_j = Const ("op =", split_type > split_type > HOLogic.boolT) $ t1' $ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

506 
(Const (@{const_name HOL.plus}, split_type > split_type > split_type) $ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

507 
(Const (@{const_name HOL.times}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

508 
split_type > split_type > split_type) $ t2' $ i) $ j) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

509 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

510 
val subgoal1 = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

511 
val subgoal2 = (map HOLogic.mk_Trueprop 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

512 
[t2_neq_zero, j_lt_t2, t1_eq_t2_times_i_plus_j]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

513 
@ terms2 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

514 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

515 
SOME [(Ts, subgoal1), (split_type :: split_type :: Ts, subgoal2)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

516 
end 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

517 
(* "?P ((?n::nat) div (number_of ?k)) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

518 
((number_of ?k = 0 > ?P 0) & (~ (number_of ?k = 0) > 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

519 
(ALL i j. j < number_of ?k > ?n = number_of ?k * i + j > ?P i))) *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

520 
 (Const ("Divides.div_class.div", Type ("fun", [Type ("nat", []), _])), [t1, t2]) => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

521 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

522 
val rev_terms = rev terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

523 
val zero = Const (@{const_name HOL.zero}, split_type) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

524 
val i = Bound 1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

525 
val j = Bound 0 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

526 
val terms1 = map (subst_term [(split_term, zero)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

527 
val terms2 = map (subst_term [(incr_boundvars 2 split_term, i)]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

528 
(map (incr_boundvars 2) rev_terms) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

529 
val t1' = incr_boundvars 2 t1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

530 
val t2' = incr_boundvars 2 t2 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

531 
val t2_eq_zero = Const ("op =", 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

532 
split_type > split_type > HOLogic.boolT) $ t2 $ zero 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

533 
val t2_neq_zero = HOLogic.mk_not (Const ("op =", 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

534 
split_type > split_type > HOLogic.boolT) $ t2' $ zero) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

535 
val j_lt_t2 = Const (@{const_name HOL.less}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

536 
split_type > split_type> HOLogic.boolT) $ j $ t2' 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

537 
val t1_eq_t2_times_i_plus_j = Const ("op =", split_type > split_type > HOLogic.boolT) $ t1' $ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

538 
(Const (@{const_name HOL.plus}, split_type > split_type > split_type) $ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

539 
(Const (@{const_name HOL.times}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

540 
split_type > split_type > split_type) $ t2' $ i) $ j) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

541 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

542 
val subgoal1 = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

543 
val subgoal2 = (map HOLogic.mk_Trueprop 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

544 
[t2_neq_zero, j_lt_t2, t1_eq_t2_times_i_plus_j]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

545 
@ terms2 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

546 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

547 
SOME [(Ts, subgoal1), (split_type :: split_type :: Ts, subgoal2)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

548 
end 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

549 
(* "?P ((?n::int) mod (number_of ?k)) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

550 
((iszero (number_of ?k) > ?P ?n) & 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

551 
(neg (number_of (uminus ?k)) > 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

552 
(ALL i j. 0 <= j & j < number_of ?k & ?n = number_of ?k * i + j > ?P j)) & 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

553 
(neg (number_of ?k) > 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

554 
(ALL i j. number_of ?k < j & j <= 0 & ?n = number_of ?k * i + j > ?P j))) *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

555 
 (Const ("Divides.div_class.mod", 
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset

556 
Type ("fun", [Type ("Int.int", []), _])), [t1, t2 as (number_of $ k)]) => 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

557 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

558 
val rev_terms = rev terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

559 
val zero = Const (@{const_name HOL.zero}, split_type) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

560 
val i = Bound 1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

561 
val j = Bound 0 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

562 
val terms1 = map (subst_term [(split_term, t1)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

563 
val terms2_3 = map (subst_term [(incr_boundvars 2 split_term, j)]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

564 
(map (incr_boundvars 2) rev_terms) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

565 
val t1' = incr_boundvars 2 t1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

566 
val (t2' as (_ $ k')) = incr_boundvars 2 t2 
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset

567 
val iszero_t2 = Const ("Int.iszero", split_type > HOLogic.boolT) $ t2 
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset

568 
val neg_minus_k = Const ("Int.neg", split_type > HOLogic.boolT) $ 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

569 
(number_of $ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

570 
(Const (@{const_name HOL.uminus}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

571 
HOLogic.intT > HOLogic.intT) $ k')) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

572 
val zero_leq_j = Const (@{const_name HOL.less_eq}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

573 
split_type > split_type > HOLogic.boolT) $ zero $ j 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

574 
val j_lt_t2 = Const (@{const_name HOL.less}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

575 
split_type > split_type> HOLogic.boolT) $ j $ t2' 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

576 
val t1_eq_t2_times_i_plus_j = Const ("op =", split_type > split_type > HOLogic.boolT) $ t1' $ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

577 
(Const (@{const_name HOL.plus}, split_type > split_type > split_type) $ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

578 
(Const (@{const_name HOL.times}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

579 
split_type > split_type > split_type) $ t2' $ i) $ j) 
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset

580 
val neg_t2 = Const ("Int.neg", split_type > HOLogic.boolT) $ t2' 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

581 
val t2_lt_j = Const (@{const_name HOL.less}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

582 
split_type > split_type> HOLogic.boolT) $ t2' $ j 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

583 
val j_leq_zero = Const (@{const_name HOL.less_eq}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

584 
split_type > split_type > HOLogic.boolT) $ j $ zero 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

585 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

586 
val subgoal1 = (HOLogic.mk_Trueprop iszero_t2) :: terms1 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

587 
val subgoal2 = (map HOLogic.mk_Trueprop [neg_minus_k, zero_leq_j]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

588 
@ hd terms2_3 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

589 
:: (if tl terms2_3 = [] then [not_false] else []) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

590 
@ (map HOLogic.mk_Trueprop [j_lt_t2, t1_eq_t2_times_i_plus_j]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

591 
@ (if tl terms2_3 = [] then [] else tl terms2_3 @ [not_false]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

592 
val subgoal3 = (map HOLogic.mk_Trueprop [neg_t2, t2_lt_j]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

593 
@ hd terms2_3 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

594 
:: (if tl terms2_3 = [] then [not_false] else []) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

595 
@ (map HOLogic.mk_Trueprop [j_leq_zero, t1_eq_t2_times_i_plus_j]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

596 
@ (if tl terms2_3 = [] then [] else tl terms2_3 @ [not_false]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

597 
val Ts' = split_type :: split_type :: Ts 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

598 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

599 
SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

600 
end 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

601 
(* "?P ((?n::int) div (number_of ?k)) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

602 
((iszero (number_of ?k) > ?P 0) & 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

603 
(neg (number_of (uminus ?k)) > 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

604 
(ALL i. (EX j. 0 <= j & j < number_of ?k & ?n = number_of ?k * i + j) > ?P i)) & 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

605 
(neg (number_of ?k) > 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

606 
(ALL i. (EX j. number_of ?k < j & j <= 0 & ?n = number_of ?k * i + j) > ?P i))) *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

607 
 (Const ("Divides.div_class.div", 
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset

608 
Type ("fun", [Type ("Int.int", []), _])), [t1, t2 as (number_of $ k)]) => 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

609 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

610 
val rev_terms = rev terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

611 
val zero = Const (@{const_name HOL.zero}, split_type) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

612 
val i = Bound 1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

613 
val j = Bound 0 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

614 
val terms1 = map (subst_term [(split_term, zero)]) rev_terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

615 
val terms2_3 = map (subst_term [(incr_boundvars 2 split_term, i)]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

616 
(map (incr_boundvars 2) rev_terms) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

617 
val t1' = incr_boundvars 2 t1 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

618 
val (t2' as (_ $ k')) = incr_boundvars 2 t2 
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset

619 
val iszero_t2 = Const ("Int.iszero", split_type > HOLogic.boolT) $ t2 
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset

620 
val neg_minus_k = Const ("Int.neg", split_type > HOLogic.boolT) $ 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

621 
(number_of $ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

622 
(Const (@{const_name HOL.uminus}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

623 
HOLogic.intT > HOLogic.intT) $ k')) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

624 
val zero_leq_j = Const (@{const_name HOL.less_eq}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

625 
split_type > split_type > HOLogic.boolT) $ zero $ j 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

626 
val j_lt_t2 = Const (@{const_name HOL.less}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

627 
split_type > split_type> HOLogic.boolT) $ j $ t2' 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

628 
val t1_eq_t2_times_i_plus_j = Const ("op =", 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

629 
split_type > split_type > HOLogic.boolT) $ t1' $ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

630 
(Const (@{const_name HOL.plus}, split_type > split_type > split_type) $ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

631 
(Const (@{const_name HOL.times}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

632 
split_type > split_type > split_type) $ t2' $ i) $ j) 
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25015
diff
changeset

633 
val neg_t2 = Const ("Int.neg", split_type > HOLogic.boolT) $ t2' 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

634 
val t2_lt_j = Const (@{const_name HOL.less}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

635 
split_type > split_type> HOLogic.boolT) $ t2' $ j 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

636 
val j_leq_zero = Const (@{const_name HOL.less_eq}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

637 
split_type > split_type > HOLogic.boolT) $ j $ zero 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

638 
val not_false = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

639 
val subgoal1 = (HOLogic.mk_Trueprop iszero_t2) :: terms1 @ [not_false] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

640 
val subgoal2 = (HOLogic.mk_Trueprop neg_minus_k) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

641 
:: terms2_3 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

642 
@ not_false 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

643 
:: (map HOLogic.mk_Trueprop 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

644 
[zero_leq_j, j_lt_t2, t1_eq_t2_times_i_plus_j]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

645 
val subgoal3 = (HOLogic.mk_Trueprop neg_t2) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

646 
:: terms2_3 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

647 
@ not_false 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

648 
:: (map HOLogic.mk_Trueprop 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

649 
[t2_lt_j, j_leq_zero, t1_eq_t2_times_i_plus_j]) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

650 
val Ts' = split_type :: split_type :: Ts 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

651 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

652 
SOME [(Ts, subgoal1), (Ts', subgoal2), (Ts', subgoal3)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

653 
end 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

654 
(* this will only happen if a split theorem can be applied for which no *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

655 
(* code exists above  in which case either the split theorem should be *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

656 
(* implemented above, or 'is_split_thm' should be modified to filter it *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

657 
(* out *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

658 
 (t, ts) => ( 
24920  659 
warning ("Lin. Arith.: split rule for " ^ Syntax.string_of_term ctxt t ^ 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

660 
" (with " ^ string_of_int (length ts) ^ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

661 
" argument(s)) not implemented; proof reconstruction is likely to fail"); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

662 
NONE 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

663 
)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

664 
) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

665 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

666 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

667 
(* remove terms that do not satisfy 'p'; change the order of the remaining *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

668 
(* terms in the same way as filter_prems_tac does *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

669 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

670 
fun filter_prems_tac_items (p : term > bool) (terms : term list) : term list = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

671 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

672 
fun filter_prems (t, (left, right)) = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

673 
if p t then (left, right @ [t]) else (left @ right, []) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

674 
val (left, right) = foldl filter_prems ([], []) terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

675 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

676 
right @ left 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

677 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

678 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

679 
(* return true iff TRY (etac notE) THEN eq_assume_tac would succeed on a *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

680 
(* subgoal that has 'terms' as premises *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

681 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

682 
fun negated_term_occurs_positively (terms : term list) : bool = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

683 
List.exists 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

684 
(fn (Trueprop $ (Const ("Not", _) $ t)) => member (op aconv) terms (Trueprop $ t) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

685 
 _ => false) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

686 
terms; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

687 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

688 
fun pre_decomp ctxt (Ts : typ list, terms : term list) : (typ list * term list) list = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

689 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

690 
(* repeatedly split (including newly emerging subgoals) until no further *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

691 
(* splitting is possible *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

692 
fun split_loop ([] : (typ list * term list) list) = ([] : (typ list * term list) list) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

693 
 split_loop (subgoal::subgoals) = ( 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

694 
case split_once_items ctxt subgoal of 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

695 
SOME new_subgoals => split_loop (new_subgoals @ subgoals) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

696 
 NONE => subgoal :: split_loop subgoals 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

697 
) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

698 
fun is_relevant t = isSome (decomp ctxt t) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

699 
(* filter_prems_tac is_relevant: *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

700 
val relevant_terms = filter_prems_tac_items is_relevant terms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

701 
(* split_tac, NNF normalization: *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

702 
val split_goals = split_loop [(Ts, relevant_terms)] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

703 
(* necessary because split_once_tac may normalize terms: *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

704 
val beta_eta_norm = map (apsnd (map (Envir.eta_contract o Envir.beta_norm))) split_goals 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

705 
(* TRY (etac notE) THEN eq_assume_tac: *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

706 
val result = List.filter (not o negated_term_occurs_positively o snd) beta_eta_norm 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

707 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

708 
result 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

709 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

710 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

711 
(* takes the ith subgoal [ A1; ...; An ] ==> B to *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

712 
(* An > ... > A1 > B, performs splitting with the given 'split_thms' *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

713 
(* (resulting in a different subgoal P), takes P to ~P ==> False, *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

714 
(* performs NNFnormalization of ~P, and eliminates conjunctions, *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

715 
(* disjunctions and existential quantifiers from the premises, possibly (in *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

716 
(* the case of disjunctions) resulting in several new subgoals, each of the *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

717 
(* general form [ Q1; ...; Qm ] ==> False. Fails if more than *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

718 
(* !fast_arith_split_limit splits are possible. *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

719 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

720 
local 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

721 
val nnf_simpset = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

722 
empty_ss setmkeqTrue mk_eq_True 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

723 
setmksimps (mksimps mksimps_pairs) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

724 
addsimps [imp_conv_disj, iff_conv_conj_imp, de_Morgan_disj, de_Morgan_conj, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

725 
not_all, not_ex, not_not] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

726 
fun prem_nnf_tac i st = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

727 
full_simp_tac (Simplifier.theory_context (Thm.theory_of_thm st) nnf_simpset) i st 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

728 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

729 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

730 
fun split_once_tac ctxt split_thms = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

731 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

732 
val thy = ProofContext.theory_of ctxt 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

733 
val cond_split_tac = SUBGOAL (fn (subgoal, i) => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

734 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

735 
val Ts = rev (map snd (Logic.strip_params subgoal)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

736 
val concl = HOLogic.dest_Trueprop (Logic.strip_assums_concl subgoal) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

737 
val cmap = Splitter.cmap_of_split_thms split_thms 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

738 
val splits = Splitter.split_posns cmap thy Ts concl 
24112  739 
val split_limit = Config.get ctxt fast_arith_split_limit 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

740 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

741 
if length splits > split_limit then no_tac 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

742 
else split_tac split_thms i 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

743 
end) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

744 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

745 
EVERY' [ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

746 
REPEAT_DETERM o etac rev_mp, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

747 
cond_split_tac, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

748 
rtac ccontr, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

749 
prem_nnf_tac, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

750 
TRY o REPEAT_ALL_NEW (DETERM o (eresolve_tac [conjE, exE] ORELSE' etac disjE)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

751 
] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

752 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

753 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

754 
end; (* local *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

755 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

756 
(* remove irrelevant premises, then split the ith subgoal (and all new *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

757 
(* subgoals) by using 'split_once_tac' repeatedly. Betaetanormalize new *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

758 
(* subgoals and finally attempt to solve them by finding an immediate *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

759 
(* contradiction (i.e. a term and its negation) in their premises. *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

760 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

761 
fun pre_tac ctxt i = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

762 
let 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

763 
val split_thms = filter is_split_thm (#splits (get_arith_data ctxt)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

764 
fun is_relevant t = isSome (decomp ctxt t) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

765 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

766 
DETERM ( 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

767 
TRY (filter_prems_tac is_relevant i) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

768 
THEN ( 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

769 
(TRY o REPEAT_ALL_NEW (split_once_tac ctxt split_thms)) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

770 
THEN_ALL_NEW 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

771 
(CONVERSION Drule.beta_eta_conversion 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

772 
THEN' 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

773 
(TRY o (etac notE THEN' eq_assume_tac))) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

774 
) i 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

775 
) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

776 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

777 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

778 
end; (* LA_Data_Ref *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

779 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

780 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

781 
val lin_arith_pre_tac = LA_Data_Ref.pre_tac; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

782 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

783 
structure Fast_Arith = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

784 
Fast_Lin_Arith(structure LA_Logic=LA_Logic and LA_Data=LA_Data_Ref); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

785 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

786 
val map_data = Fast_Arith.map_data; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

787 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

788 
fun fast_arith_tac ctxt = Fast_Arith.lin_arith_tac ctxt false; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

789 
val fast_ex_arith_tac = Fast_Arith.lin_arith_tac; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

790 
val trace_arith = Fast_Arith.trace; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

791 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

792 
(* reduce contradictory <= to False. 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

793 
Most of the work is done by the cancel tactics. *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

794 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

795 
val init_arith_data = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

796 
Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, ...} => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

797 
{add_mono_thms = add_mono_thms @ 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

798 
@{thms add_mono_thms_ordered_semiring} @ @{thms add_mono_thms_ordered_field}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

799 
mult_mono_thms = mult_mono_thms, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

800 
inj_thms = inj_thms, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

801 
lessD = lessD @ [thm "Suc_leI"], 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

802 
neqE = [@{thm linorder_neqE_nat}, @{thm linorder_neqE_ordered_idom}], 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

803 
simpset = HOL_basic_ss 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

804 
addsimps 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

805 
[@{thm "monoid_add_class.zero_plus.add_0_left"}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

806 
@{thm "monoid_add_class.zero_plus.add_0_right"}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

807 
@{thm "Zero_not_Suc"}, @{thm "Suc_not_Zero"}, @{thm "le_0_eq"}, @{thm "One_nat_def"}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

808 
@{thm "order_less_irrefl"}, @{thm "zero_neq_one"}, @{thm "zero_less_one"}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

809 
@{thm "zero_le_one"}, @{thm "zero_neq_one"} RS not_sym, @{thm "not_one_le_zero"}, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

810 
@{thm "not_one_less_zero"}] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

811 
addsimprocs [ab_group_add_cancel.sum_conv, ab_group_add_cancel.rel_conv] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

812 
(*abel_cancel helps it work in abstract algebraic domains*) 
26101  813 
addsimprocs ArithData.nat_cancel_sums_add}) #> 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

814 
arith_discrete "nat"; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

815 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

816 
val lin_arith_simproc = Fast_Arith.lin_arith_simproc; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

817 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

818 
val fast_nat_arith_simproc = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

819 
Simplifier.simproc (the_context ()) "fast_nat_arith" 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

820 
["(m::nat) < n","(m::nat) <= n", "(m::nat) = n"] (K Fast_Arith.lin_arith_simproc); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

821 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

822 
(* Because of fast_nat_arith_simproc, the arithmetic solver is really only 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

823 
useful to detect inconsistencies among the premises for subgoals which are 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

824 
*not* themselves (in)equalities, because the latter activate 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

825 
fast_nat_arith_simproc anyway. However, it seems cheaper to activate the 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

826 
solver all the time rather than add the additional check. *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

827 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

828 

26110  829 
(* generic refutation procedure *) 
830 

831 
(* parameters: 

832 

833 
test: term > bool 

834 
tests if a term is at all relevant to the refutation proof; 

835 
if not, then it can be discarded. Can improve performance, 

836 
esp. if disjunctions can be discarded (no case distinction needed!). 

837 

838 
prep_tac: int > tactic 

839 
A preparation tactic to be applied to the goal once all relevant premises 

840 
have been moved to the conclusion. 

841 

842 
ref_tac: int > tactic 

843 
the actual refutation tactic. Should be able to deal with goals 

844 
[ A1; ...; An ] ==> False 

845 
where the Ai are atomic, i.e. no toplevel &,  or EX 

846 
*) 

847 

848 
local 

849 
val nnf_simpset = 

850 
empty_ss setmkeqTrue mk_eq_True 

851 
setmksimps (mksimps mksimps_pairs) 

852 
addsimps [@{thm imp_conv_disj}, @{thm iff_conv_conj_imp}, @{thm de_Morgan_disj}, 

853 
@{thm de_Morgan_conj}, @{thm not_all}, @{thm not_ex}, @{thm not_not}]; 

854 
fun prem_nnf_tac i st = 

855 
full_simp_tac (Simplifier.theory_context (Thm.theory_of_thm st) nnf_simpset) i st; 

856 
in 

857 
fun refute_tac test prep_tac ref_tac = 

858 
let val refute_prems_tac = 

859 
REPEAT_DETERM 

860 
(eresolve_tac [@{thm conjE}, @{thm exE}] 1 ORELSE 

861 
filter_prems_tac test 1 ORELSE 

862 
etac @{thm disjE} 1) THEN 

863 
(DETERM (etac @{thm notE} 1 THEN eq_assume_tac 1) ORELSE 

864 
ref_tac 1); 

865 
in EVERY'[TRY o filter_prems_tac test, 

866 
REPEAT_DETERM o etac @{thm rev_mp}, prep_tac, rtac @{thm ccontr}, prem_nnf_tac, 

867 
SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)] 

868 
end; 

869 
end; 

870 

871 

24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

872 
(* arith proof method *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

873 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

874 
local 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

875 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

876 
fun raw_arith_tac ctxt ex = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

877 
(* FIXME: K true should be replaced by a sensible test (perhaps "isSome o 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

878 
decomp sg"?  but note that the test is applied to terms already before 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

879 
they are split/normalized) to speed things up in case there are lots of 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

880 
irrelevant terms involved; elimination of min/max can be optimized: 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

881 
(max m n + k <= r) = (m+k <= r & n+k <= r) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

882 
(l <= min m n + k) = (l <= m+k & l <= n+k) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

883 
*) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

884 
refute_tac (K true) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

885 
(* Splitting is also done inside fast_arith_tac, but not completely  *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

886 
(* split_tac may use split theorems that have not been implemented in *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

887 
(* fast_arith_tac (cf. pre_decomp and split_once_items above), and *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

888 
(* fast_arith_split_limit may trigger. *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

889 
(* Therefore splitting outside of fast_arith_tac may allow us to prove *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

890 
(* some goals that fast_arith_tac alone would fail on. *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

891 
(REPEAT_DETERM o split_tac (#splits (get_arith_data ctxt))) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

892 
(fast_ex_arith_tac ctxt ex); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

893 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

894 
fun more_arith_tacs ctxt = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

895 
let val tactics = #tactics (get_arith_data ctxt) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

896 
in FIRST' (map (fn ArithTactic {tactic, ...} => tactic ctxt) tactics) end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

897 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

898 
in 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

899 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

900 
fun simple_arith_tac ctxt = FIRST' [fast_arith_tac ctxt, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

901 
ObjectLogic.full_atomize_tac THEN' (REPEAT_DETERM o rtac impI) THEN' raw_arith_tac ctxt true]; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

902 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

903 
fun arith_tac ctxt = FIRST' [fast_arith_tac ctxt, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

904 
ObjectLogic.full_atomize_tac THEN' (REPEAT_DETERM o rtac impI) THEN' raw_arith_tac ctxt true, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

905 
more_arith_tacs ctxt]; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

906 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

907 
fun silent_arith_tac ctxt = FIRST' [fast_arith_tac ctxt, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

908 
ObjectLogic.full_atomize_tac THEN' (REPEAT_DETERM o rtac impI) THEN' raw_arith_tac ctxt false, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

909 
more_arith_tacs ctxt]; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

910 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

911 
fun arith_method src = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

912 
Method.syntax Args.bang_facts src 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

913 
#> (fn (prems, ctxt) => Method.METHOD (fn facts => 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

914 
HEADGOAL (Method.insert_tac (prems @ facts) THEN' arith_tac ctxt))); 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

915 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

916 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

917 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

918 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

919 
(* context setup *) 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

920 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

921 
val setup = 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

922 
init_arith_data #> 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

923 
Simplifier.map_ss (fn ss => ss addsimprocs [fast_nat_arith_simproc] 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

924 
addSolver (mk_solver' "lin_arith" Fast_Arith.cut_lin_arith_tac)) #> 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

925 
Context.mapping 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

926 
(setup_options #> 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

927 
Method.add_methods 
26061  928 
[("arith", arith_method, "decide linear arithmetic")] #> 
24092
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

929 
Attrib.add_attributes [("arith_split", Attrib.no_args arith_split_add, 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

930 
"declaration of split rules for arithmetic procedure")]) I; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

931 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

932 
end; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

933 

71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

934 
structure BasicLinArith: BASIC_LIN_ARITH = LinArith; 
71c27b320610
HOL setup for linear arithmetic  moved here from arith_data.ML;
wenzelm
parents:
diff
changeset

935 
open BasicLinArith; 