author  nipkow 
Fri, 23 Aug 2002 07:41:05 +0200  
changeset 13517  42efec18f5b2 
parent 13499  f95f5818f24f 
child 13877  a6b825ee48d9 
permissions  rwrr 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

1 
(* Title: HOL/arith_data.ML 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

2 
ID: $Id$ 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

3 
Author: Markus Wenzel, Stefan Berghofer and Tobias Nipkow 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

4 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

5 
Various arithmetic proof procedures. 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

6 
*) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

7 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

8 
(**) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

9 
(* 1. Cancellation of common terms *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

10 
(**) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

11 

13517  12 
structure NatArithUtils = 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

13 
struct 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

14 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

15 
(** abstract syntax of structure nat: 0, Suc, + **) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

16 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

17 
(* mk_sum, mk_norm_sum *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

18 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

19 
val one = HOLogic.mk_nat 1; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

20 
val mk_plus = HOLogic.mk_binop "op +"; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

21 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

22 
fun mk_sum [] = HOLogic.zero 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

23 
 mk_sum [t] = t 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

24 
 mk_sum (t :: ts) = mk_plus (t, mk_sum ts); 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

25 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

26 
(*normal form of sums: Suc (... (Suc (a + (b + ...))))*) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

27 
fun mk_norm_sum ts = 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

28 
let val (ones, sums) = partition (equal one) ts in 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

29 
funpow (length ones) HOLogic.mk_Suc (mk_sum sums) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

30 
end; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

31 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

32 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

33 
(* dest_sum *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

34 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

35 
val dest_plus = HOLogic.dest_bin "op +" HOLogic.natT; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

36 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

37 
fun dest_sum tm = 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

38 
if HOLogic.is_zero tm then [] 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

39 
else 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

40 
(case try HOLogic.dest_Suc tm of 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

41 
Some t => one :: dest_sum t 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

42 
 None => 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

43 
(case try dest_plus tm of 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

44 
Some (t, u) => dest_sum t @ dest_sum u 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

45 
 None => [tm])); 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

46 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

47 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

48 
(** generic proof tools **) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

49 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

50 
(* prove conversions *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

51 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

52 
val mk_eqv = HOLogic.mk_Trueprop o HOLogic.mk_eq; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

53 

13517  54 
fun prove_conv expand_tac norm_tac sg tu = 
55 
mk_meta_eq (prove_goalw_cterm_nocheck [] (cterm_of sg (mk_eqv tu)) 

9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

56 
(K [expand_tac, norm_tac])) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

57 
handle ERROR => error ("The error(s) above occurred while trying to prove " ^ 
13517  58 
(string_of_cterm (cterm_of sg (mk_eqv tu)))); 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

59 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

60 
val subst_equals = prove_goal HOL.thy "[ t = s; u = t ] ==> u = s" 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

61 
(fn prems => [cut_facts_tac prems 1, SIMPSET' asm_simp_tac 1]); 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

62 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

63 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

64 
(* rewriting *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

65 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

66 
fun simp_all rules = ALLGOALS (simp_tac (HOL_ss addsimps rules)); 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

67 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

68 
val add_rules = [add_Suc, add_Suc_right, add_0, add_0_right]; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

69 
val mult_rules = [mult_Suc, mult_Suc_right, mult_0, mult_0_right]; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

70 

13517  71 
fun prep_simproc (name, pats, proc) = 
72 
Simplifier.simproc (Theory.sign_of (the_context ())) name pats proc; 

73 

74 
end; 

75 

76 
signature ARITH_DATA = 

77 
sig 

78 
val nat_cancel_sums_add: simproc list 

79 
val nat_cancel_sums: simproc list 

80 
end; 

81 

82 
structure ArithData: ARITH_DATA = 

83 
struct 

84 

85 
open NatArithUtils; 

9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

86 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

87 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

88 
(** cancel common summands **) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

89 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

90 
structure Sum = 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

91 
struct 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

92 
val mk_sum = mk_norm_sum; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

93 
val dest_sum = dest_sum; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

94 
val prove_conv = prove_conv; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

95 
val norm_tac = simp_all add_rules THEN simp_all add_ac; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

96 
end; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

97 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

98 
fun gen_uncancel_tac rule ct = 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

99 
rtac (instantiate' [] [None, Some ct] (rule RS subst_equals)) 1; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

100 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

101 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

102 
(* nat eq *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

103 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

104 
structure EqCancelSums = CancelSumsFun 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

105 
(struct 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

106 
open Sum; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

107 
val mk_bal = HOLogic.mk_eq; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

108 
val dest_bal = HOLogic.dest_bin "op =" HOLogic.natT; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

109 
val uncancel_tac = gen_uncancel_tac add_left_cancel; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

110 
end); 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

111 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

112 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

113 
(* nat less *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

114 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

115 
structure LessCancelSums = CancelSumsFun 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

116 
(struct 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

117 
open Sum; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

118 
val mk_bal = HOLogic.mk_binrel "op <"; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

119 
val dest_bal = HOLogic.dest_bin "op <" HOLogic.natT; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

120 
val uncancel_tac = gen_uncancel_tac add_left_cancel_less; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

121 
end); 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

122 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

123 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

124 
(* nat le *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

125 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

126 
structure LeCancelSums = CancelSumsFun 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

127 
(struct 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

128 
open Sum; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

129 
val mk_bal = HOLogic.mk_binrel "op <="; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

130 
val dest_bal = HOLogic.dest_bin "op <=" HOLogic.natT; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

131 
val uncancel_tac = gen_uncancel_tac add_left_cancel_le; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

132 
end); 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

133 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

134 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

135 
(* nat diff *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

136 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

137 
structure DiffCancelSums = CancelSumsFun 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

138 
(struct 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

139 
open Sum; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

140 
val mk_bal = HOLogic.mk_binop "op "; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

141 
val dest_bal = HOLogic.dest_bin "op " HOLogic.natT; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

142 
val uncancel_tac = gen_uncancel_tac diff_cancel; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

143 
end); 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

144 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

145 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

146 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

147 
(** prepare nat_cancel simprocs **) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

148 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

149 
val nat_cancel_sums_add = map prep_simproc 
13462  150 
[("nateq_cancel_sums", 
151 
["(l::nat) + m = n", "(l::nat) = m + n", "Suc m = n", "m = Suc n"], EqCancelSums.proc), 

152 
("natless_cancel_sums", 

153 
["(l::nat) + m < n", "(l::nat) < m + n", "Suc m < n", "m < Suc n"], LessCancelSums.proc), 

154 
("natle_cancel_sums", 

155 
["(l::nat) + m <= n", "(l::nat) <= m + n", "Suc m <= n", "m <= Suc n"], LeCancelSums.proc)]; 

9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

156 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

157 
val nat_cancel_sums = nat_cancel_sums_add @ 
13462  158 
[prep_simproc ("natdiff_cancel_sums", 
159 
["((l::nat) + m)  n", "(l::nat)  (m + n)", "Suc m  n", "m  Suc n"], DiffCancelSums.proc)]; 

9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

160 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

161 
end; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

162 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

163 
open ArithData; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

164 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

165 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

166 
(**) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

167 
(* 2. Linear arithmetic *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

168 
(**) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

169 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

170 
(* Parameters data for general linear arithmetic functor *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

171 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

172 
structure LA_Logic: LIN_ARITH_LOGIC = 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

173 
struct 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

174 
val ccontr = ccontr; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

175 
val conjI = conjI; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

176 
val neqE = linorder_neqE; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

177 
val notI = notI; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

178 
val sym = sym; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

179 
val not_lessD = linorder_not_less RS iffD1; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

180 
val not_leD = linorder_not_le RS iffD1; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

181 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

182 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

183 
fun mk_Eq thm = (thm RS Eq_FalseI) handle THM _ => (thm RS Eq_TrueI); 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

184 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

185 
val mk_Trueprop = HOLogic.mk_Trueprop; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

186 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

187 
fun neg_prop(TP$(Const("Not",_)$t)) = TP$t 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

188 
 neg_prop(TP$t) = TP $ (Const("Not",HOLogic.boolT>HOLogic.boolT)$t); 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

189 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

190 
fun is_False thm = 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

191 
let val _ $ t = #prop(rep_thm thm) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

192 
in t = Const("False",HOLogic.boolT) end; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

193 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

194 
fun is_nat(t) = fastype_of1 t = HOLogic.natT; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

195 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

196 
fun mk_nat_thm sg t = 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

197 
let val ct = cterm_of sg t and cn = cterm_of sg (Var(("n",0),HOLogic.natT)) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

198 
in instantiate ([],[(cn,ct)]) le0 end; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

199 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

200 
end; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

201 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

202 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

203 
(* arith theory data *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

204 

9593  205 
structure ArithTheoryDataArgs = 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

206 
struct 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

207 
val name = "HOL/arith"; 
10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

208 
type T = {splits: thm list, inj_consts: (string * typ)list, discrete: (string * bool) list}; 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

209 

10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

210 
val empty = {splits = [], inj_consts = [], discrete = []}; 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

211 
val copy = I; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

212 
val prep_ext = I; 
10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

213 
fun merge ({splits= splits1, inj_consts= inj_consts1, discrete= discrete1}, 
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

214 
{splits= splits2, inj_consts= inj_consts2, discrete= discrete2}) = 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

215 
{splits = Drule.merge_rules (splits1, splits2), 
10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

216 
inj_consts = merge_lists inj_consts1 inj_consts2, 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

217 
discrete = merge_alists discrete1 discrete2}; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

218 
fun print _ _ = (); 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

219 
end; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

220 

9593  221 
structure ArithTheoryData = TheoryDataFun(ArithTheoryDataArgs); 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

222 

10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

223 
fun arith_split_add (thy, thm) = (ArithTheoryData.map (fn {splits,inj_consts,discrete} => 
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

224 
{splits= thm::splits, inj_consts= inj_consts, discrete= discrete}) thy, thm); 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

225 

10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

226 
fun arith_discrete d = ArithTheoryData.map (fn {splits,inj_consts,discrete} => 
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

227 
{splits = splits, inj_consts = inj_consts, discrete = d :: discrete}); 
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

228 

8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

229 
fun arith_inj_const c = ArithTheoryData.map (fn {splits,inj_consts,discrete} => 
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

230 
{splits = splits, inj_consts = c :: inj_consts, discrete = discrete}); 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

231 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

232 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

233 
structure LA_Data_Ref: LIN_ARITH_DATA = 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

234 
struct 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

235 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

236 
(* Decomposition of terms *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

237 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

238 
fun nT (Type("fun",[N,_])) = N = HOLogic.natT 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

239 
 nT _ = false; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

240 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

241 
fun add_atom(t,m,(p,i)) = (case assoc(p,t) of None => ((t,m)::p,i) 
10693  242 
 Some n => (overwrite(p,(t,ratadd(n,m))), i)); 
243 

244 
exception Zero; 

9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

245 

10693  246 
fun rat_of_term(numt,dent) = 
247 
let val num = HOLogic.dest_binum numt and den = HOLogic.dest_binum dent 

248 
in if den = 0 then raise Zero else int_ratdiv(num,den) end; 

10718  249 

250 
(* Warning: in rare cases number_of encloses a nonnumeral, 

251 
in which case dest_binum raises TERM; hence all the handles below. 

11334
a16eaf2a1edd
Allow Sucnumerals as coefficients in linarith formulae
nipkow
parents:
10906
diff
changeset

252 
Same for Sucterms that turn out not to be numerals  
a16eaf2a1edd
Allow Sucnumerals as coefficients in linarith formulae
nipkow
parents:
10906
diff
changeset

253 
although the simplifier should eliminate those anyway... 
10718  254 
*) 
255 

11334
a16eaf2a1edd
Allow Sucnumerals as coefficients in linarith formulae
nipkow
parents:
10906
diff
changeset

256 
fun number_of_Sucs (Const("Suc",_) $ n) = number_of_Sucs n + 1 
a16eaf2a1edd
Allow Sucnumerals as coefficients in linarith formulae
nipkow
parents:
10906
diff
changeset

257 
 number_of_Sucs t = if HOLogic.is_zero t then 0 
a16eaf2a1edd
Allow Sucnumerals as coefficients in linarith formulae
nipkow
parents:
10906
diff
changeset

258 
else raise TERM("number_of_Sucs",[]) 
a16eaf2a1edd
Allow Sucnumerals as coefficients in linarith formulae
nipkow
parents:
10906
diff
changeset

259 

10718  260 
(* decompose nested multiplications, bracketing them to the right and combining all 
261 
their coefficients 

262 
*) 

263 

13499  264 
fun demult inj_consts = 
265 
let 

10718  266 
fun demult((mC as Const("op *",_)) $ s $ t,m) = ((case s of 
267 
Const("Numeral.number_of",_)$n 

268 
=> demult(t,ratmul(m,rat_of_int(HOLogic.dest_binum n))) 

12480
32e67277a4b9
tuned conversion from terms to "polynomials" for arith_tac: takes care
nipkow
parents:
12338
diff
changeset

269 
 Const("uminus",_)$(Const("Numeral.number_of",_)$n) 
32e67277a4b9
tuned conversion from terms to "polynomials" for arith_tac: takes care
nipkow
parents:
12338
diff
changeset

270 
=> demult(t,ratmul(m,rat_of_int(~(HOLogic.dest_binum n)))) 
11334
a16eaf2a1edd
Allow Sucnumerals as coefficients in linarith formulae
nipkow
parents:
10906
diff
changeset

271 
 Const("Suc",_) $ _ 
a16eaf2a1edd
Allow Sucnumerals as coefficients in linarith formulae
nipkow
parents:
10906
diff
changeset

272 
=> demult(t,ratmul(m,rat_of_int(number_of_Sucs s))) 
10718  273 
 Const("op *",_) $ s1 $ s2 => demult(mC $ s1 $ (mC $ s2 $ t),m) 
274 
 Const("HOL.divide",_) $ numt $ (Const("Numeral.number_of",_)$dent) => 

275 
let val den = HOLogic.dest_binum dent 

276 
in if den = 0 then raise Zero 

277 
else demult(mC $ numt $ t,ratmul(m, ratinv(rat_of_int den))) 

278 
end 

279 
 _ => atomult(mC,s,t,m) 

280 
) handle TERM _ => atomult(mC,s,t,m)) 

281 
 demult(atom as Const("HOL.divide",_) $ t $ (Const("Numeral.number_of",_)$dent), m) = 

282 
(let val den = HOLogic.dest_binum dent 

283 
in if den = 0 then raise Zero else demult(t,ratmul(m, ratinv(rat_of_int den))) end 

284 
handle TERM _ => (Some atom,m)) 

285 
 demult(t as Const("Numeral.number_of",_)$n,m) = 

286 
((None,ratmul(m,rat_of_int(HOLogic.dest_binum n))) 

287 
handle TERM _ => (Some t,m)) 

12480
32e67277a4b9
tuned conversion from terms to "polynomials" for arith_tac: takes care
nipkow
parents:
12338
diff
changeset

288 
 demult(Const("uminus",_)$t, m) = demult(t,ratmul(m,rat_of_int(~1))) 
13499  289 
 demult(t as Const f $ x, m) = 
290 
(if f mem inj_consts then Some x else Some t,m) 

10718  291 
 demult(atom,m) = (Some atom,m) 
292 

293 
and atomult(mC,atom,t,m) = (case demult(t,m) of (None,m') => (Some atom,m') 

294 
 (Some t',m') => (Some(mC $ atom $ t'),m')) 

13499  295 
in demult end; 
10718  296 

10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

297 
fun decomp2 inj_consts (rel,lhs,rhs) = 
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

298 
let 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

299 
(* Turn term into list of summand * multiplicity plus a constant *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

300 
fun poly(Const("op +",_) $ s $ t, m, pi) = poly(s,m,poly(t,m,pi)) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

301 
 poly(all as Const("op ",T) $ s $ t, m, pi) = 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

302 
if nT T then add_atom(all,m,pi) 
10693  303 
else poly(s,m,poly(t,ratneg m,pi)) 
304 
 poly(Const("uminus",_) $ t, m, pi) = poly(t,ratneg m,pi) 

9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

305 
 poly(Const("0",_), _, pi) = pi 
11464  306 
 poly(Const("1",_), m, (p,i)) = (p,ratadd(i,m)) 
10693  307 
 poly(Const("Suc",_)$t, m, (p,i)) = poly(t, m, (p,ratadd(i,m))) 
10718  308 
 poly(t as Const("op *",_) $ _ $ _, m, pi as (p,i)) = 
13499  309 
(case demult inj_consts (t,m) of 
10718  310 
(None,m') => (p,ratadd(i,m)) 
311 
 (Some u,m') => add_atom(u,m',pi)) 

312 
 poly(t as Const("HOL.divide",_) $ _ $ _, m, pi as (p,i)) = 

13499  313 
(case demult inj_consts (t,m) of 
10718  314 
(None,m') => (p,ratadd(i,m)) 
315 
 (Some u,m') => add_atom(u,m',pi)) 

316 
 poly(all as (Const("Numeral.number_of",_)$t,m,(p,i))) = 

317 
((p,ratadd(i,ratmul(m,rat_of_int(HOLogic.dest_binum t)))) 

318 
handle TERM _ => add_atom all) 

10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

319 
 poly(all as Const f $ x, m, pi) = 
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

320 
if f mem inj_consts then poly(x,m,pi) else add_atom(all,m,pi) 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

321 
 poly x = add_atom x; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

322 

10718  323 
val (p,i) = poly(lhs,rat_of_int 1,([],rat_of_int 0)) 
324 
and (q,j) = poly(rhs,rat_of_int 1,([],rat_of_int 0)) 

10693  325 

9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

326 
in case rel of 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

327 
"op <" => Some(p,i,"<",q,j) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

328 
 "op <=" => Some(p,i,"<=",q,j) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

329 
 "op =" => Some(p,i,"=",q,j) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

330 
 _ => None 
10693  331 
end handle Zero => None; 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

332 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

333 
fun negate(Some(x,i,rel,y,j,d)) = Some(x,i,"~"^rel,y,j,d) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

334 
 negate None = None; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

335 

10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

336 
fun decomp1 (discrete,inj_consts) (T,xxx) = 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

337 
(case T of 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

338 
Type("fun",[Type(D,[]),_]) => 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

339 
(case assoc(discrete,D) of 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

340 
None => None 
10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

341 
 Some d => (case decomp2 inj_consts xxx of 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

342 
None => None 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

343 
 Some(p,i,rel,q,j) => Some(p,i,rel,q,j,d))) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

344 
 _ => None); 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

345 

10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

346 
fun decomp2 data (_$(Const(rel,T)$lhs$rhs)) = decomp1 data (T,(rel,lhs,rhs)) 
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

347 
 decomp2 data (_$(Const("Not",_)$(Const(rel,T)$lhs$rhs))) = 
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

348 
negate(decomp1 data (T,(rel,lhs,rhs))) 
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

349 
 decomp2 data _ = None 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

350 

10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

351 
fun decomp sg = 
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

352 
let val {discrete, inj_consts, ...} = ArithTheoryData.get_sg sg 
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

353 
in decomp2 (discrete,inj_consts) end 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

354 

10693  355 
fun number_of(n,T) = HOLogic.number_of_const T $ (HOLogic.mk_bin n) 
356 

9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

357 
end; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

358 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

359 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

360 
structure Fast_Arith = 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

361 
Fast_Lin_Arith(structure LA_Logic=LA_Logic and LA_Data=LA_Data_Ref); 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

362 

13499  363 
val fast_arith_tac = Fast_Arith.lin_arith_tac false 
364 
and fast_ex_arith_tac = Fast_Arith.lin_arith_tac 

9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

365 
and trace_arith = Fast_Arith.trace; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

366 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

367 
local 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

368 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

369 
(* reduce contradictory <= to False. 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

370 
Most of the work is done by the cancel tactics. 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

371 
*) 
12931
2c0251fada94
solved the problem that Larry's simproce cancle_numerals(?) returns
nipkow
parents:
12480
diff
changeset

372 
val add_rules = 
2c0251fada94
solved the problem that Larry's simproce cancle_numerals(?) returns
nipkow
parents:
12480
diff
changeset

373 
[add_0,add_0_right,Zero_not_Suc,Suc_not_Zero,le_0_eq, 
2c0251fada94
solved the problem that Larry's simproce cancle_numerals(?) returns
nipkow
parents:
12480
diff
changeset

374 
One_nat_def]; 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

375 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

376 
val add_mono_thms_nat = map (fn s => prove_goal (the_context ()) s 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

377 
(fn prems => [cut_facts_tac prems 1, 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

378 
blast_tac (claset() addIs [add_le_mono]) 1])) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

379 
["(i <= j) & (k <= l) ==> i + k <= j + (l::nat)", 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

380 
"(i = j) & (k <= l) ==> i + k <= j + (l::nat)", 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

381 
"(i <= j) & (k = l) ==> i + k <= j + (l::nat)", 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

382 
"(i = j) & (k = l) ==> i + k = j + (l::nat)" 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

383 
]; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

384 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

385 
in 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

386 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

387 
val init_lin_arith_data = 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

388 
Fast_Arith.setup @ 
10693  389 
[Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, simpset = _} => 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

390 
{add_mono_thms = add_mono_thms @ add_mono_thms_nat, 
10693  391 
mult_mono_thms = mult_mono_thms, 
10574
8f98f0301d67
Linear arithmetic now copes with mixed nat/int formulae.
nipkow
parents:
10516
diff
changeset

392 
inj_thms = inj_thms, 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

393 
lessD = lessD @ [Suc_leI], 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

394 
simpset = HOL_basic_ss addsimps add_rules addsimprocs nat_cancel_sums_add}), 
9593  395 
ArithTheoryData.init, arith_discrete ("nat", true)]; 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

396 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

397 
end; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

398 

13462  399 
val fast_nat_arith_simproc = 
400 
Simplifier.simproc (Theory.sign_of (the_context ())) "fast_nat_arith" 

401 
["(m::nat) < n","(m::nat) <= n", "(m::nat) = n"] Fast_Arith.lin_arith_prover; 

9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

402 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

403 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

404 
(* Because of fast_nat_arith_simproc, the arithmetic solver is really only 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

405 
useful to detect inconsistencies among the premises for subgoals which are 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

406 
*not* themselves (in)equalities, because the latter activate 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

407 
fast_nat_arith_simproc anyway. However, it seems cheaper to activate the 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

408 
solver all the time rather than add the additional check. *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

409 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

410 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

411 
(* arith proof method *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

412 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

413 
(* FIXME: K true should be replaced by a sensible test to speed things up 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

414 
in case there are lots of irrelevant terms involved; 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

415 
elimination of min/max can be optimized: 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

416 
(max m n + k <= r) = (m+k <= r & n+k <= r) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

417 
(l <= min m n + k) = (l <= m+k & l <= n+k) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

418 
*) 
10516  419 
local 
420 

13499  421 
fun raw_arith_tac ex i st = 
422 
refute_tac (K true) 

423 
(REPEAT o split_tac (#splits (ArithTheoryData.get_sg (Thm.sign_of_thm st)))) 

424 
((REPEAT_DETERM o etac linorder_neqE) THEN' fast_ex_arith_tac ex) 

425 
i st; 

9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

426 

10516  427 
in 
428 

13499  429 
val arith_tac = fast_arith_tac ORELSE' 
430 
(ObjectLogic.atomize_tac THEN' raw_arith_tac true); 

431 
val silent_arith_tac = fast_arith_tac ORELSE' 

432 
(ObjectLogic.atomize_tac THEN' raw_arith_tac false); 

10516  433 

9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

434 
fun arith_method prems = 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

435 
Method.METHOD (fn facts => HEADGOAL (Method.insert_tac (prems @ facts) THEN' arith_tac)); 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

436 

10516  437 
end; 
438 

9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

439 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

440 
(* theory setup *) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

441 

62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

442 
val arith_setup = 
10766  443 
[Simplifier.change_simpset_of (op addsimprocs) nat_cancel_sums] @ 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

444 
init_lin_arith_data @ 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

445 
[Simplifier.change_simpset_of (op addSolver) 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

446 
(mk_solver "lin. arith." Fast_Arith.cut_lin_arith_tac), 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

447 
Simplifier.change_simpset_of (op addsimprocs) [fast_nat_arith_simproc], 
11704
3c50a2cd6f00
* sane numerals (stage 2): plain "num" syntax (removed "#");
wenzelm
parents:
11701
diff
changeset

448 
Method.add_methods [("arith", (arith_method o #2) oo Method.syntax Args.bang_facts, 
9436
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

449 
"decide linear arithmethic")], 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

450 
Attrib.add_attributes [("arith_split", 
62bb04ab4b01
rearranged setup of arithmetic procedures, avoiding global reference values;
wenzelm
parents:
diff
changeset

451 
(Attrib.no_args arith_split_add, Attrib.no_args Attrib.undef_local_attribute), 
9893  452 
"declaration of split rules for arithmetic procedure")]]; 