author  hoelzl 
Wed, 11 Mar 2009 10:58:18 +0100  
changeset 30439  57c68b3af2ea 
parent 30242  aea5d7fa7ef5 
child 30510  4120fc59dd85 
permissions  rwrr 
30439  1 
(* Title: HOL/Decision_Procs/ferrack_tac.ML 
29788  2 
Author: Amine Chaieb, TU Muenchen 
3 
*) 

4 

5 
structure Ferrack_Tac = 

23264
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

6 
struct 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

7 

324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

8 
val trace = ref false; 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

9 
fun trace_msg s = if !trace then tracing s else (); 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

10 

26075
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

11 
val ferrack_ss = let val ths = [@{thm real_of_int_inject}, @{thm real_of_int_less_iff}, 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

12 
@{thm real_of_int_le_iff}] 
23264
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

13 
in @{simpset} delsimps ths addsimps (map (fn th => th RS sym) ths) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

14 
end; 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

15 

26075
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

16 
val binarith = 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

17 
@{thms normalize_bin_simps} @ @{thms pred_bin_simps} @ @{thms succ_bin_simps} @ 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

18 
@{thms add_bin_simps} @ @{thms minus_bin_simps} @ @{thms mult_bin_simps}; 
23318  19 
val comp_arith = binarith @ simp_thms 
23264
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

20 

26075
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

21 
val zdvd_int = @{thm zdvd_int}; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

22 
val zdiff_int_split = @{thm zdiff_int_split}; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

23 
val all_nat = @{thm all_nat}; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

24 
val ex_nat = @{thm ex_nat}; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

25 
val number_of1 = @{thm number_of1}; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

26 
val number_of2 = @{thm number_of2}; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

27 
val split_zdiv = @{thm split_zdiv}; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

28 
val split_zmod = @{thm split_zmod}; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

29 
val mod_div_equality' = @{thm mod_div_equality'}; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

30 
val split_div' = @{thm split_div'}; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

31 
val Suc_plus1 = @{thm Suc_plus1}; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

32 
val imp_le_cong = @{thm imp_le_cong}; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

33 
val conj_le_cong = @{thm conj_le_cong}; 
30034  34 
val mod_add_left_eq = @{thm mod_add_left_eq} RS sym; 
35 
val mod_add_right_eq = @{thm mod_add_right_eq} RS sym; 

26075
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

36 
val nat_div_add_eq = @{thm div_add1_eq} RS sym; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

37 
val int_div_add_eq = @{thm zdiv_zadd1_eq} RS sym; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

38 
val ZDIVISION_BY_ZERO_MOD = @{thm DIVISION_BY_ZERO} RS conjunct2; 
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

39 
val ZDIVISION_BY_ZERO_DIV = @{thm DIVISION_BY_ZERO} RS conjunct1; 
23264
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

40 

324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

41 
fun prepare_for_linr sg q fm = 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

42 
let 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

43 
val ps = Logic.strip_params fm 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

44 
val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

45 
val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

46 
fun mk_all ((s, T), (P,n)) = 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

47 
if 0 mem loose_bnos P then 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

48 
(HOLogic.all_const T $ Abs (s, T, P), n) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

49 
else (incr_boundvars ~1 P, n1) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

50 
fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t; 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

51 
val rhs = hs 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

52 
(* val (rhs,irhs) = List.partition (relevant (rev ps)) hs *) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

53 
val np = length ps 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

54 
val (fm',np) = foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n))) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

55 
(foldr HOLogic.mk_imp c rhs, np) ps 
27436  56 
val (vs, _) = List.partition (fn t => q orelse (type_of t) = HOLogic.natT) 
29265
5b4247055bd7
moved old add_term_vars, add_term_frees etc. to structure OldTerm;
wenzelm
parents:
28952
diff
changeset

57 
(OldTerm.term_frees fm' @ OldTerm.term_vars fm'); 
23264
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

58 
val fm2 = foldr mk_all2 fm' vs 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

59 
in (fm2, np + length vs, length rhs) end; 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

60 

324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

61 
(*Object quantifier to meta *) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

62 
fun spec_step n th = if (n=0) then th else (spec_step (n1) th) RS spec ; 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

63 

324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

64 
(* object implication to meta*) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

65 
fun mp_step n th = if (n=0) then th else (mp_step (n1) th) RS mp; 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

66 

324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

67 

324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

68 
fun linr_tac ctxt q i = 
23590
ad95084a5c63
renamed ObjectLogic.atomize_tac to ObjectLogic.atomize_prems_tac;
wenzelm
parents:
23469
diff
changeset

69 
(ObjectLogic.atomize_prems_tac i) 
26075
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset

70 
THEN (REPEAT_DETERM (split_tac [@{thm split_min}, @{thm split_max}, @{thm abs_split}] i)) 
23264
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

71 
THEN (fn st => 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

72 
let 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

73 
val g = List.nth (prems_of st, i  1) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

74 
val thy = ProofContext.theory_of ctxt 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

75 
(* Transform the term*) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

76 
val (t,np,nh) = prepare_for_linr thy q g 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

77 
(* Some simpsets for dealing with mod div abs and nat*) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

78 
val simpset0 = Simplifier.theory_context thy HOL_basic_ss addsimps comp_arith 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

79 
val ct = cterm_of thy (HOLogic.mk_Trueprop t) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

80 
(* Theorem for the nat > int transformation *) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

81 
val pre_thm = Seq.hd (EVERY 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

82 
[simp_tac simpset0 1, 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

83 
TRY (simp_tac (Simplifier.theory_context thy ferrack_ss) 1)] 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

84 
(trivial ct)) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

85 
fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

86 
(* The result of the quantifier elimination *) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

87 
val (th, tac) = case (prop_of pre_thm) of 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

88 
Const ("==>", _) $ (Const ("Trueprop", _) $ t1) $ _ => 
28290  89 
let val pth = linr_oracle (cterm_of thy (Pattern.eta_long [] t1)) 
23264
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

90 
in 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

91 
(trace_msg ("calling procedure with term:\n" ^ 
26939
1035c89b4c02
moved global pretty/string_of functions from Sign to Syntax;
wenzelm
parents:
26075
diff
changeset

92 
Syntax.string_of_term ctxt t1); 
23264
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

93 
((pth RS iffD2) RS pre_thm, 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

94 
assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i))) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

95 
end 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

96 
 _ => (pre_thm, assm_tac i) 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

97 
in (rtac (((mp_step nh) o (spec_step np)) th) i 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

98 
THEN tac) st 
27436  99 
end handle Subscript => no_tac st); 
23264
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

100 

324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

101 
fun linr_meth src = 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

102 
Method.syntax (Args.mode "no_quantify") src 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

103 
#> (fn (q, ctxt) => Method.SIMPLE_METHOD' (linr_tac ctxt (not q))); 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

104 

324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

105 
val setup = 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

106 
Method.add_method ("rferrack", linr_meth, 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

107 
"decision procedure for linear real arithmetic"); 
324622260d29
Added twe Examples for Quantifier elimination ofer linear real arithmetic and over the mixed theory of linear real artihmetic with integers
chaieb
parents:
diff
changeset

108 

23469  109 
end 