author  wenzelm 
Wed, 29 Jun 2011 17:35:46 +0200  
changeset 43594  ef1ddc59b825 
parent 42368  3b8498ac2314 
child 44121  44adaa6db327 
permissions  rwrr 
30439  1 
(* Title: HOL/Decision_Procs/cooper_tac.ML 
29788  2 
Author: Amine Chaieb, TU Muenchen 
3 
*) 

4 

31240  5 
signature COOPER_TAC = 
6 
sig 

32740  7 
val trace: bool Unsynchronized.ref 
31240  8 
val linz_tac: Proof.context > bool > int > tactic 
9 
val setup: theory > theory 

10 
end 

11 

12 
structure Cooper_Tac: COOPER_TAC = 

23274  13 
struct 
14 

32740  15 
val trace = Unsynchronized.ref false; 
23274  16 
fun trace_msg s = if !trace then tracing s else (); 
17 

18 
val cooper_ss = @{simpset}; 

19 

20 
val nT = HOLogic.natT; 

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

21 
val binarith = @{thms normalize_bin_simps}; 
23318  22 
val comp_arith = binarith @ simp_thms 
23274  23 

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

24 
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

25 
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

26 
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

27 
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

28 
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

29 
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

30 
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

31 
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

32 
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

33 
val split_div' = @{thm split_div'}; 
31790  34 
val Suc_eq_plus1 = @{thm Suc_eq_plus1}; 
27651
16a26996c30e
moved op dvd to theory Ring_and_Field; generalized a couple of lemmas
haftmann
parents:
26075
diff
changeset

35 
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

36 
val conj_le_cong = @{thm conj_le_cong}; 
30034  37 
val mod_add_left_eq = @{thm mod_add_left_eq} RS sym; 
38 
val mod_add_right_eq = @{thm mod_add_right_eq} RS sym; 

30224  39 
val 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

40 
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

41 
val int_div_add_eq = @{thm zdiv_zadd1_eq} RS sym; 
23274  42 

31240  43 
fun prepare_for_linz q fm = 
23274  44 
let 
45 
val ps = Logic.strip_params fm 

46 
val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm) 

47 
val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm) 

48 
fun mk_all ((s, T), (P,n)) = 

42083
e1209fc7ecdc
added Term.is_open and Term.is_dependent convenience, to cover common situations of loose bounds;
wenzelm
parents:
38558
diff
changeset

49 
if Term.is_dependent P then 
23274  50 
(HOLogic.all_const T $ Abs (s, T, P), n) 
51 
else (incr_boundvars ~1 P, n1) 

52 
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

53 
val rhs = hs 
23274  54 
val np = length ps 
33004
715566791eb0
always qualify NJ's old List.foldl/foldr in Isabelle/ML;
wenzelm
parents:
32960
diff
changeset

55 
val (fm',np) = List.foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n))) 
715566791eb0
always qualify NJ's old List.foldl/foldr in Isabelle/ML;
wenzelm
parents:
32960
diff
changeset

56 
(List.foldr HOLogic.mk_imp c rhs, np) ps 
23274  57 
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

58 
(OldTerm.term_frees fm' @ OldTerm.term_vars fm'); 
33004
715566791eb0
always qualify NJ's old List.foldl/foldr in Isabelle/ML;
wenzelm
parents:
32960
diff
changeset

59 
val fm2 = List.foldr mk_all2 fm' vs 
23274  60 
in (fm2, np + length vs, length rhs) end; 
61 

62 
(*Object quantifier to meta *) 

63 
fun spec_step n th = if (n=0) then th else (spec_step (n1) th) RS spec ; 

64 

65 
(* object implication to meta*) 

66 
fun mp_step n th = if (n=0) then th else (mp_step (n1) th) RS mp; 

67 

68 

42368
3b8498ac2314
proper subgoal addressing via SUBGOAL/CSUBGOAL  assuming these tactics did not handle Subscript in any special way;
wenzelm
parents:
42364
diff
changeset

69 
fun linz_tac ctxt q = Object_Logic.atomize_prems_tac THEN' SUBGOAL (fn (g, i) => 
23274  70 
let 
42361  71 
val thy = Proof_Context.theory_of ctxt 
23274  72 
(* Transform the term*) 
73 
val (t,np,nh) = prepare_for_linz q g 

74 
(* Some simpsets for dealing with mod div abs and nat*) 

31240  75 
val mod_div_simpset = HOL_basic_ss 
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
32740
diff
changeset

76 
addsimps [refl,mod_add_eq, mod_add_left_eq, 
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
32740
diff
changeset

77 
mod_add_right_eq, 
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
32740
diff
changeset

78 
nat_div_add_eq, int_div_add_eq, 
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
32740
diff
changeset

79 
@{thm mod_self}, @{thm "zmod_self"}, 
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
32740
diff
changeset

80 
@{thm mod_by_0}, @{thm div_by_0}, 
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
32740
diff
changeset

81 
@{thm "zdiv_zero"}, @{thm "zmod_zero"}, @{thm "div_0"}, @{thm "mod_0"}, 
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
32740
diff
changeset

82 
@{thm "div_by_1"}, @{thm "mod_by_1"}, @{thm "div_1"}, @{thm "mod_1"}, 
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
32740
diff
changeset

83 
Suc_eq_plus1] 
69916a850301
eliminated hard tabulators, guessing at each author's individual tabwidth;
wenzelm
parents:
32740
diff
changeset

84 
addsimps @{thms add_ac} 
43594  85 
addsimprocs [@{simproc cancel_div_mod_nat}, @{simproc cancel_div_mod_int}] 
23274  86 
val simpset0 = HOL_basic_ss 
31790  87 
addsimps [mod_div_equality', Suc_eq_plus1] 
23274  88 
addsimps comp_arith 
89 
addsplits [split_zdiv, split_zmod, split_div', @{thm "split_min"}, @{thm "split_max"}] 

90 
(* Simp rules for changing (n::int) to int n *) 

91 
val simpset1 = HOL_basic_ss 

31070  92 
addsimps [@{thm nat_number_of_def}, zdvd_int] @ map (fn r => r RS sym) 
23364  93 
[@{thm int_int_eq}, @{thm zle_int}, @{thm zless_int}, @{thm zadd_int}, @{thm zmult_int}] 
23274  94 
addsplits [zdiff_int_split] 
95 
(*simp rules for elimination of int n*) 

96 

97 
val simpset2 = HOL_basic_ss 

23364  98 
addsimps [@{thm nat_0_le}, @{thm all_nat}, @{thm ex_nat}, @{thm number_of1}, @{thm number_of2}, @{thm int_0}, @{thm int_1}] 
99 
addcongs [@{thm conj_le_cong}, @{thm imp_le_cong}] 

23274  100 
(* simp rules for elimination of abs *) 
23364  101 
val simpset3 = HOL_basic_ss addsplits [@{thm abs_split}] 
23274  102 
val ct = cterm_of thy (HOLogic.mk_Trueprop t) 
103 
(* Theorem for the nat > int transformation *) 

104 
val pre_thm = Seq.hd (EVERY 

105 
[simp_tac mod_div_simpset 1, simp_tac simpset0 1, 

106 
TRY (simp_tac simpset1 1), TRY (simp_tac simpset2 1), 

107 
TRY (simp_tac simpset3 1), TRY (simp_tac cooper_ss 1)] 

36945  108 
(Thm.trivial ct)) 
23274  109 
fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i) 
110 
(* The result of the quantifier elimination *) 

111 
val (th, tac) = case (prop_of pre_thm) of 

38558  112 
Const ("==>", _) $ (Const (@{const_name Trueprop}, _) $ t1) $ _ => 
28290  113 
let val pth = linzqe_oracle (cterm_of thy (Pattern.eta_long [] t1)) 
31240  114 
in 
23274  115 
((pth RS iffD2) RS pre_thm, 
116 
assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i)) 

117 
end 

118 
 _ => (pre_thm, assm_tac i) 

42368
3b8498ac2314
proper subgoal addressing via SUBGOAL/CSUBGOAL  assuming these tactics did not handle Subscript in any special way;
wenzelm
parents:
42364
diff
changeset

119 
in rtac (((mp_step nh) o (spec_step np)) th) i THEN tac end); 
23274  120 

121 
val setup = 

31240  122 
Method.setup @{binding cooper} 
123 
let 

124 
val parse_flag = Args.$$$ "no_quantify" >> K (K false) 

125 
in 

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

127 
curry (Library.foldl op >) true) >> 

128 
(fn q => fn ctxt => SIMPLE_METHOD' (linz_tac ctxt q)) 

129 
end 

130 
"decision procedure for linear integer arithmetic"; 

23274  131 

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

132 
end 