author | huffman |
Sun, 25 Mar 2012 20:15:39 +0200 | |
changeset 47108 | 2a1953f0d20d |
parent 45654 | cf10bde35973 |
child 47142 | d64fa2ca54b8 |
permissions | -rw-r--r-- |
30439 | 1 |
(* Title: HOL/Decision_Procs/ferrack_tac.ML |
29788 | 2 |
Author: Amine Chaieb, TU Muenchen |
3 |
*) |
|
4 |
||
31302 | 5 |
signature FERRACK_TAC = |
6 |
sig |
|
32740 | 7 |
val trace: bool Unsynchronized.ref |
31302 | 8 |
val linr_tac: Proof.context -> bool -> int -> tactic |
9 |
val setup: theory -> theory |
|
10 |
end |
|
11 |
||
29788 | 12 |
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
|
13 |
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
|
14 |
|
32740 | 15 |
val trace = Unsynchronized.ref false; |
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
|
16 |
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
|
17 |
|
26075
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset
|
18 |
val ferrack_ss = let val ths = [@{thm real_of_int_inject}, @{thm real_of_int_less_iff}, |
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents:
32740
diff
changeset
|
19 |
@{thm real_of_int_le_iff}] |
69916a850301
eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents:
32740
diff
changeset
|
20 |
in @{simpset} delsimps ths addsimps (map (fn th => th RS sym) ths) |
69916a850301
eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents:
32740
diff
changeset
|
21 |
end; |
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
|
22 |
|
47108
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
45654
diff
changeset
|
23 |
val binarith = @{thms arith_simps} |
2a1953f0d20d
merged fork with new numeral representation (see NEWS)
huffman
parents:
45654
diff
changeset
|
24 |
val comp_arith = binarith @ @{thms 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
|
25 |
|
26075
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset
|
26 |
val zdvd_int = @{thm zdvd_int}; |
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset
|
27 |
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
|
28 |
val all_nat = @{thm all_nat}; |
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset
|
29 |
val ex_nat = @{thm ex_nat}; |
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset
|
30 |
val split_zdiv = @{thm split_zdiv}; |
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset
|
31 |
val split_zmod = @{thm split_zmod}; |
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset
|
32 |
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
|
33 |
val split_div' = @{thm split_div'}; |
31790 | 34 |
val Suc_eq_plus1 = @{thm Suc_eq_plus1}; |
26075
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset
|
35 |
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
|
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; |
|
26075
815f3ccc0b45
added lemma lists {normalize,succ,pred,minus,add,mult}_bin_simps
huffman
parents:
23590
diff
changeset
|
39 |
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
|
40 |
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
|
41 |
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
|
42 |
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
|
43 |
|
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 |
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
|
45 |
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
|
46 |
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
|
47 |
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
|
48 |
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
|
49 |
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
|
50 |
if Term.is_dependent P then |
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
|
51 |
(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
|
52 |
else (incr_boundvars ~1 P, n-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
|
53 |
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
|
54 |
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
|
55 |
(* 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
|
56 |
val np = length ps |
33004
715566791eb0
always qualify NJ's old List.foldl/foldr in Isabelle/ML;
wenzelm
parents:
32960
diff
changeset
|
57 |
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
|
58 |
(List.foldr HOLogic.mk_imp c rhs, np) ps |
27436 | 59 |
val (vs, _) = List.partition (fn t => q orelse (type_of t) = HOLogic.natT) |
44121 | 60 |
(Misc_Legacy.term_frees fm' @ Misc_Legacy.term_vars fm'); |
33004
715566791eb0
always qualify NJ's old List.foldl/foldr in Isabelle/ML;
wenzelm
parents:
32960
diff
changeset
|
61 |
val fm2 = List.foldr mk_all2 fm' vs |
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
|
62 |
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
|
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 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
|
65 |
fun spec_step n th = if (n=0) then th else (spec_step (n-1) 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
|
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 |
(* 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
|
68 |
fun mp_step n th = if (n=0) then th else (mp_step (n-1) 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
|
69 |
|
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
|
70 |
|
35233 | 71 |
fun linr_tac ctxt q = |
35625 | 72 |
Object_Logic.atomize_prems_tac |
35233 | 73 |
THEN' (REPEAT_DETERM o split_tac [@{thm split_min}, @{thm split_max}, @{thm abs_split}]) |
74 |
THEN' SUBGOAL (fn (g, 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
|
75 |
let |
42361 | 76 |
val thy = Proof_Context.theory_of ctxt |
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
|
77 |
(* 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
|
78 |
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
|
79 |
(* Some simpsets for dealing with mod div abs and nat*) |
35233 | 80 |
val simpset0 = Simplifier.context ctxt HOL_basic_ss addsimps comp_arith |
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
|
81 |
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
|
82 |
(* 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
|
83 |
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
|
84 |
[simp_tac simpset0 1, |
35233 | 85 |
TRY (simp_tac (Simplifier.context ctxt ferrack_ss) 1)] |
36945 | 86 |
(Thm.trivial ct)) |
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
|
87 |
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
|
88 |
(* The result of the quantifier elimination *) |
35233 | 89 |
val (th, tac) = case prop_of pre_thm of |
38558 | 90 |
Const ("==>", _) $ (Const (@{const_name Trueprop}, _) $ t1) $ _ => |
36853 | 91 |
let val pth = linr_oracle (ctxt, 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
|
92 |
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
|
93 |
(trace_msg ("calling procedure with term:\n" ^ |
26939
1035c89b4c02
moved global pretty/string_of functions from Sign to Syntax;
wenzelm
parents:
26075
diff
changeset
|
94 |
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
|
95 |
((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
|
96 |
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
|
97 |
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
|
98 |
| _ => (pre_thm, assm_tac i) |
35233 | 99 |
in rtac ((mp_step nh o spec_step np) th) i THEN tac end); |
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 |
val setup = |
31302 | 102 |
Method.setup @{binding rferrack} |
103 |
(Args.mode "no_quantify" >> (fn q => fn ctxt => |
|
104 |
SIMPLE_METHOD' (linr_tac ctxt (not q)))) |
|
105 |
"decision procedure for linear real arithmetic"; |
|
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
|
106 |
|
23469 | 107 |
end |