author | kuncar |
Tue, 03 Apr 2012 16:26:48 +0200 | |
changeset 47308 | 9caab698dbe4 |
parent 47142 | d64fa2ca54b8 |
child 47432 | e1576d13e933 |
permissions | -rw-r--r-- |
30439 | 1 |
(* Title: HOL/Decision_Procs/cooper_tac.ML |
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Author: Amine Chaieb, TU Muenchen |
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*) |
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signature COOPER_TAC = |
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sig |
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val trace: bool Unsynchronized.ref |
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val linz_tac: Proof.context -> bool -> int -> tactic |
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val setup: theory -> theory |
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end |
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structure Cooper_Tac: COOPER_TAC = |
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struct |
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val trace = Unsynchronized.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 comp_arith = @{thms 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 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_eq_plus1 = @{thm Suc_eq_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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val mod_add_left_eq = @{thm mod_add_left_eq} RS sym; |
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val mod_add_right_eq = @{thm mod_add_right_eq} RS sym; |
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val mod_add_eq = @{thm mod_add_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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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 Term.is_dependent 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 np = length ps |
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val (fm',np) = List.foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n))) |
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(List.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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(Misc_Legacy.term_frees fm' @ Misc_Legacy.term_vars fm'); |
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val fm2 = List.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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fun linz_tac ctxt q = Object_Logic.atomize_prems_tac THEN' SUBGOAL (fn (g, i) => |
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let |
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val thy = Proof_Context.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,mod_add_eq, mod_add_left_eq, |
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mod_add_right_eq, |
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nat_div_add_eq, int_div_add_eq, |
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@{thm mod_self}, |
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@{thm div_by_0}, @{thm mod_by_0}, @{thm div_0}, @{thm mod_0}, |
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@{thm div_by_1}, @{thm mod_by_1}, @{thm div_1}, @{thm mod_1}, |
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Suc_eq_plus1] |
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addsimps @{thms add_ac} |
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addsimprocs [@{simproc cancel_div_mod_nat}, @{simproc cancel_div_mod_int}] |
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val simpset0 = HOL_basic_ss |
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addsimps [mod_div_equality', Suc_eq_plus1] |
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addsimps comp_arith |
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|> fold Splitter.add_split |
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[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 [zdvd_int] @ map (fn r => r RS sym) |
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[@{thm int_numeral}, @{thm int_int_eq}, @{thm zle_int}, @{thm zless_int}, @{thm zadd_int}, @{thm zmult_int}] |
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|> Splitter.add_split 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 zero_le_numeral}, @{thm order_refl}(* FIXME: necessary? *), @{thm int_0}, @{thm int_1}] |
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|> fold Simplifier.add_cong [@{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 |> Splitter.add_split @{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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(Thm.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 (@{const_name Trueprop}, _) $ t1) $ _ => |
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let val pth = linzqe_oracle (cterm_of 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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wenzelm
parents:
42364
diff
changeset
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in rtac (((mp_step nh) o (spec_step np)) th) i THEN tac end); |
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val setup = |
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Method.setup @{binding cooper} |
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let |
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val parse_flag = Args.$$$ "no_quantify" >> K (K false) |
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in |
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Scan.lift (Scan.optional (Args.$$$ "(" |-- Scan.repeat1 parse_flag --| Args.$$$ ")") [] >> |
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curry (Library.foldl op |>) true) >> |
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(fn q => fn ctxt => SIMPLE_METHOD' (linz_tac ctxt q)) |
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end |
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"decision procedure for linear integer arithmetic"; |
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end |