author | haftmann |
Fri, 20 Jul 2007 14:28:25 +0200 | |
changeset 23881 | 851c74f1bb69 |
parent 23880 | 64b9806e160b |
child 25985 | 8d69087f6a4b |
permissions | -rw-r--r-- |
23274 | 1 |
structure LinZTac = |
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struct |
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val trace = ref false; |
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fun trace_msg s = if !trace then tracing s else (); |
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val cooper_ss = @{simpset}; |
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val nT = HOLogic.natT; |
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val binarith = map thm |
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["Pls_0_eq", "Min_1_eq"]; |
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val comp_arith = binarith @ simp_thms |
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val zdvd_int = thm "zdvd_int"; |
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val zdiff_int_split = thm "zdiff_int_split"; |
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val all_nat = thm "all_nat"; |
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val ex_nat = thm "ex_nat"; |
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val number_of1 = thm "number_of1"; |
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val number_of2 = thm "number_of2"; |
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val split_zdiv = thm "split_zdiv"; |
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val split_zmod = thm "split_zmod"; |
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val mod_div_equality' = thm "mod_div_equality'"; |
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val split_div' = thm "split_div'"; |
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val Suc_plus1 = thm "Suc_plus1"; |
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val imp_le_cong = thm "imp_le_cong"; |
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val conj_le_cong = thm "conj_le_cong"; |
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23469 | 27 |
val nat_mod_add_eq = @{thm mod_add1_eq} RS sym; |
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val nat_mod_add_left_eq = @{thm mod_add_left_eq} RS sym; |
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val nat_mod_add_right_eq = @{thm mod_add_right_eq} RS sym; |
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23274 | 30 |
val int_mod_add_eq = @{thm "zmod_zadd1_eq"} RS sym; |
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val int_mod_add_left_eq = @{thm "zmod_zadd_left_eq"} RS sym; |
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val int_mod_add_right_eq = @{thm "zmod_zadd_right_eq"} RS sym; |
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val nat_div_add_eq = @{thm "div_add1_eq"} RS sym; |
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val int_div_add_eq = @{thm "zdiv_zadd1_eq"} RS sym; |
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val ZDIVISION_BY_ZERO_MOD = @{thm "DIVISION_BY_ZERO"} RS conjunct2; |
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val ZDIVISION_BY_ZERO_DIV = @{thm "DIVISION_BY_ZERO"} RS conjunct1; |
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(* |
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val fn_rews = List.concat (map thms ["allpairs.simps","iupt.simps","decr.simps", "decrnum.simps","disjuncts.simps","simpnum.simps", "simpfm.simps","numadd.simps","nummul.simps","numneg_def","numsub","simp_num_pair_def","not.simps","prep.simps","qelim.simps","minusinf.simps","plusinf.simps","rsplit0.simps","rlfm.simps","\\<Upsilon>.simps","\\<upsilon>.simps","linrqe_def", "ferrack_def", "Let_def", "numsub_def", "numneg_def","DJ_def", "imp_def", "evaldjf_def", "djf_def", "split_def", "eq_def", "disj_def", "simp_num_pair_def", "conj_def", "lt_def", "neq_def","gt_def"]); |
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*) |
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fun prepare_for_linz q fm = |
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let |
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val ps = Logic.strip_params fm |
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val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm) |
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val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm) |
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fun mk_all ((s, T), (P,n)) = |
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if 0 mem loose_bnos P then |
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(HOLogic.all_const T $ Abs (s, T, P), n) |
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else (incr_boundvars ~1 P, n-1) |
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fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t; |
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val rhs = hs |
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(* val (rhs,irhs) = List.partition (relevant (rev ps)) hs *) |
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val np = length ps |
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val (fm',np) = foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n))) |
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(foldr HOLogic.mk_imp c rhs, np) ps |
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val (vs, _) = List.partition (fn t => q orelse (type_of t) = nT) |
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(term_frees fm' @ term_vars fm'); |
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val fm2 = foldr mk_all2 fm' vs |
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in (fm2, np + length vs, length rhs) end; |
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(*Object quantifier to meta --*) |
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fun spec_step n th = if (n=0) then th else (spec_step (n-1) th) RS spec ; |
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(* object implication to meta---*) |
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fun mp_step n th = if (n=0) then th else (mp_step (n-1) th) RS mp; |
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||
23590
ad95084a5c63
renamed ObjectLogic.atomize_tac to ObjectLogic.atomize_prems_tac;
wenzelm
parents:
23469
diff
changeset
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fun linz_tac ctxt q i = ObjectLogic.atomize_prems_tac i THEN (fn st => |
23274 | 69 |
let |
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val g = List.nth (prems_of st, i - 1) |
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val thy = ProofContext.theory_of ctxt |
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(* Transform the term*) |
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val (t,np,nh) = prepare_for_linz q g |
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(* Some simpsets for dealing with mod div abs and nat*) |
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val mod_div_simpset = HOL_basic_ss |
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addsimps [refl,nat_mod_add_eq, nat_mod_add_left_eq, |
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nat_mod_add_right_eq, int_mod_add_eq, |
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int_mod_add_right_eq, int_mod_add_left_eq, |
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nat_div_add_eq, int_div_add_eq, |
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@{thm mod_self}, @{thm "zmod_self"}, |
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@{thm DIVISION_BY_ZERO_MOD}, @{thm DIVISION_BY_ZERO_DIV}, |
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ZDIVISION_BY_ZERO_MOD,ZDIVISION_BY_ZERO_DIV, |
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@{thm "zdiv_zero"}, @{thm "zmod_zero"}, @{thm "div_0"}, @{thm "mod_0"}, |
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@{thm "zdiv_1"}, @{thm "zmod_1"}, @{thm "div_1"}, @{thm "mod_1"}, |
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Suc_plus1] |
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addsimps @{thms add_ac} |
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addsimprocs [cancel_div_mod_proc] |
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val simpset0 = HOL_basic_ss |
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addsimps [mod_div_equality', Suc_plus1] |
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addsimps comp_arith |
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addsplits [split_zdiv, split_zmod, split_div', @{thm "split_min"}, @{thm "split_max"}] |
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(* Simp rules for changing (n::int) to int n *) |
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val simpset1 = HOL_basic_ss |
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addsimps [nat_number_of_def, zdvd_int] @ map (fn r => r RS sym) |
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[@{thm int_int_eq}, @{thm zle_int}, @{thm zless_int}, @{thm zadd_int}, @{thm zmult_int}] |
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addsplits [zdiff_int_split] |
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(*simp rules for elimination of int n*) |
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val simpset2 = HOL_basic_ss |
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addsimps [@{thm nat_0_le}, @{thm all_nat}, @{thm ex_nat}, @{thm number_of1}, @{thm number_of2}, @{thm int_0}, @{thm int_1}] |
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addcongs [@{thm conj_le_cong}, @{thm imp_le_cong}] |
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(* simp rules for elimination of abs *) |
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val simpset3 = HOL_basic_ss addsplits [@{thm abs_split}] |
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val ct = cterm_of thy (HOLogic.mk_Trueprop t) |
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(* Theorem for the nat --> int transformation *) |
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val pre_thm = Seq.hd (EVERY |
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[simp_tac mod_div_simpset 1, simp_tac simpset0 1, |
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TRY (simp_tac simpset1 1), TRY (simp_tac simpset2 1), |
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TRY (simp_tac simpset3 1), TRY (simp_tac cooper_ss 1)] |
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(trivial ct)) |
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fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i) |
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(* The result of the quantifier elimination *) |
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val (th, tac) = case (prop_of pre_thm) of |
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Const ("==>", _) $ (Const ("Trueprop", _) $ t1) $ _ => |
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let val pth = linzqe_oracle thy (Pattern.eta_long [] t1) |
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in |
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((pth RS iffD2) RS pre_thm, |
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assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i)) |
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end |
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| _ => (pre_thm, assm_tac i) |
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in (rtac (((mp_step nh) o (spec_step np)) th) i |
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THEN tac) st |
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end handle Subscript => no_tac st); |
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fun linz_args meth = |
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let val parse_flag = |
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Args.$$$ "no_quantify" >> (K (K false)); |
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in |
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Method.simple_args |
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(Scan.optional (Args.$$$ "(" |-- Scan.repeat1 parse_flag --| Args.$$$ ")") [] >> |
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curry (Library.foldl op |>) true) |
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(fn q => fn ctxt => meth ctxt q 1) |
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end; |
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fun linz_method ctxt q i = Method.METHOD (fn facts => |
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Method.insert_tac facts 1 THEN linz_tac ctxt q i); |
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val setup = |
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Method.add_method ("cooper", |
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linz_args linz_method, |
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"decision procedure for linear integer arithmetic"); |
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||
23590
ad95084a5c63
renamed ObjectLogic.atomize_tac to ObjectLogic.atomize_prems_tac;
wenzelm
parents:
23469
diff
changeset
|
143 |
end |