author  nipkow 
Fri, 20 Feb 2009 23:46:03 +0100  
changeset 30031  bd786c37af84 
parent 29948  cdf12a1cb963 
child 30034  60f64f112174 
permissions  rwrr 
29788  1 
(* Title: HOL/Reflection/cooper_tac.ML 
2 
Author: Amine Chaieb, TU Muenchen 

3 
*) 

4 

5 
structure Cooper_Tac = 

23274  6 
struct 
7 

8 
val trace = ref false; 

9 
fun trace_msg s = if !trace then tracing s else (); 

10 

11 
val cooper_ss = @{simpset}; 

12 

13 
val nT = HOLogic.natT; 

26075
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
25985
diff
changeset

14 
val binarith = @{thms normalize_bin_simps}; 
23318  15 
val comp_arith = binarith @ simp_thms 
23274  16 

27651
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

17 
val zdvd_int = @{thm zdvd_int}; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

18 
val zdiff_int_split = @{thm zdiff_int_split}; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

19 
val all_nat = @{thm all_nat}; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

20 
val ex_nat = @{thm ex_nat}; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

21 
val number_of1 = @{thm number_of1}; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

22 
val number_of2 = @{thm number_of2}; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

23 
val split_zdiv = @{thm split_zdiv}; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

24 
val split_zmod = @{thm split_zmod}; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

25 
val mod_div_equality' = @{thm mod_div_equality'}; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

26 
val split_div' = @{thm split_div'}; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

27 
val Suc_plus1 = @{thm Suc_plus1}; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

28 
val imp_le_cong = @{thm imp_le_cong}; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

29 
val conj_le_cong = @{thm conj_le_cong}; 
23469  30 
val nat_mod_add_eq = @{thm mod_add1_eq} RS sym; 
31 
val nat_mod_add_left_eq = @{thm mod_add_left_eq} RS sym; 

32 
val nat_mod_add_right_eq = @{thm mod_add_right_eq} RS sym; 

29948  33 
val int_mod_add_eq = @{thm mod_add_eq} RS sym; 
27651
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

34 
val int_mod_add_left_eq = @{thm zmod_zadd_left_eq} RS sym; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

35 
val int_mod_add_right_eq = @{thm zmod_zadd_right_eq} RS sym; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

36 
val nat_div_add_eq = @{thm div_add1_eq} RS sym; 
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

37 
val int_div_add_eq = @{thm zdiv_zadd1_eq} RS sym; 
23274  38 

39 
fun prepare_for_linz q fm = 

40 
let 

41 
val ps = Logic.strip_params fm 

42 
val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm) 

43 
val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm) 

44 
fun mk_all ((s, T), (P,n)) = 

45 
if 0 mem loose_bnos P then 

46 
(HOLogic.all_const T $ Abs (s, T, P), n) 

47 
else (incr_boundvars ~1 P, n1) 

48 
fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t; 

27651
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

49 
val rhs = hs 
23274  50 
val np = length ps 
51 
val (fm',np) = foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n))) 

52 
(foldr HOLogic.mk_imp c rhs, np) ps 

53 
val (vs, _) = List.partition (fn t => q orelse (type_of t) = nT) 

29265
5b4247055bd7
moved old add_term_vars, add_term_frees etc. to structure OldTerm;
wenzelm
parents:
28290
diff
changeset

54 
(OldTerm.term_frees fm' @ OldTerm.term_vars fm'); 
23274  55 
val fm2 = foldr mk_all2 fm' vs 
56 
in (fm2, np + length vs, length rhs) end; 

57 

58 
(*Object quantifier to meta *) 

59 
fun spec_step n th = if (n=0) then th else (spec_step (n1) th) RS spec ; 

60 

61 
(* object implication to meta*) 

62 
fun mp_step n th = if (n=0) then th else (mp_step (n1) th) RS mp; 

63 

64 

23590
ad95084a5c63
renamed ObjectLogic.atomize_tac to ObjectLogic.atomize_prems_tac;
wenzelm
parents:
23469
diff
changeset

65 
fun linz_tac ctxt q i = ObjectLogic.atomize_prems_tac i THEN (fn st => 
23274  66 
let 
67 
val g = List.nth (prems_of st, i  1) 

68 
val thy = ProofContext.theory_of ctxt 

69 
(* Transform the term*) 

70 
val (t,np,nh) = prepare_for_linz q g 

71 
(* Some simpsets for dealing with mod div abs and nat*) 

72 
val mod_div_simpset = HOL_basic_ss 

73 
addsimps [refl,nat_mod_add_eq, nat_mod_add_left_eq, 

74 
nat_mod_add_right_eq, int_mod_add_eq, 

75 
int_mod_add_right_eq, int_mod_add_left_eq, 

76 
nat_div_add_eq, int_div_add_eq, 

23469  77 
@{thm mod_self}, @{thm "zmod_self"}, 
27651
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

78 
@{thm mod_by_0}, @{thm div_by_0}, 
23274  79 
@{thm "zdiv_zero"}, @{thm "zmod_zero"}, @{thm "div_0"}, @{thm "mod_0"}, 
30031  80 
@{thm "div_by_1"}, @{thm "mod_by_1"}, @{thm "div_1"}, @{thm "mod_1"}, 
23274  81 
Suc_plus1] 
23880  82 
addsimps @{thms add_ac} 
23274  83 
addsimprocs [cancel_div_mod_proc] 
84 
val simpset0 = HOL_basic_ss 

85 
addsimps [mod_div_equality', Suc_plus1] 

86 
addsimps comp_arith 

87 
addsplits [split_zdiv, split_zmod, split_div', @{thm "split_min"}, @{thm "split_max"}] 

88 
(* Simp rules for changing (n::int) to int n *) 

89 
val simpset1 = HOL_basic_ss 

90 
addsimps [nat_number_of_def, zdvd_int] @ map (fn r => r RS sym) 

23364  91 
[@{thm int_int_eq}, @{thm zle_int}, @{thm zless_int}, @{thm zadd_int}, @{thm zmult_int}] 
23274  92 
addsplits [zdiff_int_split] 
93 
(*simp rules for elimination of int n*) 

94 

95 
val simpset2 = HOL_basic_ss 

23364  96 
addsimps [@{thm nat_0_le}, @{thm all_nat}, @{thm ex_nat}, @{thm number_of1}, @{thm number_of2}, @{thm int_0}, @{thm int_1}] 
97 
addcongs [@{thm conj_le_cong}, @{thm imp_le_cong}] 

23274  98 
(* simp rules for elimination of abs *) 
23364  99 
val simpset3 = HOL_basic_ss addsplits [@{thm abs_split}] 
23274  100 
val ct = cterm_of thy (HOLogic.mk_Trueprop t) 
101 
(* Theorem for the nat > int transformation *) 

102 
val pre_thm = Seq.hd (EVERY 

103 
[simp_tac mod_div_simpset 1, simp_tac simpset0 1, 

104 
TRY (simp_tac simpset1 1), TRY (simp_tac simpset2 1), 

105 
TRY (simp_tac simpset3 1), TRY (simp_tac cooper_ss 1)] 

106 
(trivial ct)) 

107 
fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i) 

108 
(* The result of the quantifier elimination *) 

109 
val (th, tac) = case (prop_of pre_thm) of 

110 
Const ("==>", _) $ (Const ("Trueprop", _) $ t1) $ _ => 

28290  111 
let val pth = linzqe_oracle (cterm_of thy (Pattern.eta_long [] t1)) 
23274  112 
in 
113 
((pth RS iffD2) RS pre_thm, 

114 
assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i)) 

115 
end 

116 
 _ => (pre_thm, assm_tac i) 

117 
in (rtac (((mp_step nh) o (spec_step np)) th) i 

118 
THEN tac) st 

119 
end handle Subscript => no_tac st); 

120 

121 
fun linz_args meth = 

122 
let val parse_flag = 

123 
Args.$$$ "no_quantify" >> (K (K false)); 

124 
in 

125 
Method.simple_args 

126 
(Scan.optional (Args.$$$ "("  Scan.repeat1 parse_flag  Args.$$$ ")") [] >> 

127 
curry (Library.foldl op >) true) 

128 
(fn q => fn ctxt => meth ctxt q 1) 

129 
end; 

130 

131 
fun linz_method ctxt q i = Method.METHOD (fn facts => 

132 
Method.insert_tac facts 1 THEN linz_tac ctxt q i); 

133 

134 
val setup = 

135 
Method.add_method ("cooper", 

136 
linz_args linz_method, 

137 
"decision procedure for linear integer arithmetic"); 

138 

23590
ad95084a5c63
renamed ObjectLogic.atomize_tac to ObjectLogic.atomize_prems_tac;
wenzelm
parents:
23469
diff
changeset

139 
end 