--- a/src/HOL/Complex/ex/linrtac.ML Wed Dec 03 09:53:58 2008 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,109 +0,0 @@
-structure LinrTac =
-struct
-
-val trace = ref false;
-fun trace_msg s = if !trace then tracing s else ();
-
-val ferrack_ss = let val ths = [@{thm real_of_int_inject}, @{thm real_of_int_less_iff},
- @{thm real_of_int_le_iff}]
- in @{simpset} delsimps ths addsimps (map (fn th => th RS sym) ths)
- end;
-
-val binarith =
- @{thms normalize_bin_simps} @ @{thms pred_bin_simps} @ @{thms succ_bin_simps} @
- @{thms add_bin_simps} @ @{thms minus_bin_simps} @ @{thms mult_bin_simps};
-val comp_arith = binarith @ simp_thms
-
-val zdvd_int = @{thm zdvd_int};
-val zdiff_int_split = @{thm zdiff_int_split};
-val all_nat = @{thm all_nat};
-val ex_nat = @{thm ex_nat};
-val number_of1 = @{thm number_of1};
-val number_of2 = @{thm number_of2};
-val split_zdiv = @{thm split_zdiv};
-val split_zmod = @{thm split_zmod};
-val mod_div_equality' = @{thm mod_div_equality'};
-val split_div' = @{thm split_div'};
-val Suc_plus1 = @{thm Suc_plus1};
-val imp_le_cong = @{thm imp_le_cong};
-val conj_le_cong = @{thm conj_le_cong};
-val nat_mod_add_eq = @{thm mod_add1_eq} RS sym;
-val nat_mod_add_left_eq = @{thm mod_add_left_eq} RS sym;
-val nat_mod_add_right_eq = @{thm mod_add_right_eq} RS sym;
-val int_mod_add_eq = @{thm zmod_zadd1_eq} RS sym;
-val int_mod_add_left_eq = @{thm zmod_zadd_left_eq} RS sym;
-val int_mod_add_right_eq = @{thm zmod_zadd_right_eq} RS sym;
-val nat_div_add_eq = @{thm div_add1_eq} RS sym;
-val int_div_add_eq = @{thm zdiv_zadd1_eq} RS sym;
-val ZDIVISION_BY_ZERO_MOD = @{thm DIVISION_BY_ZERO} RS conjunct2;
-val ZDIVISION_BY_ZERO_DIV = @{thm DIVISION_BY_ZERO} RS conjunct1;
-
-fun prepare_for_linr sg q fm =
- let
- val ps = Logic.strip_params fm
- val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm)
- val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm)
- fun mk_all ((s, T), (P,n)) =
- if 0 mem loose_bnos P then
- (HOLogic.all_const T $ Abs (s, T, P), n)
- else (incr_boundvars ~1 P, n-1)
- fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t;
- val rhs = hs
-(* val (rhs,irhs) = List.partition (relevant (rev ps)) hs *)
- val np = length ps
- val (fm',np) = foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n)))
- (foldr HOLogic.mk_imp c rhs, np) ps
- val (vs, _) = List.partition (fn t => q orelse (type_of t) = HOLogic.natT)
- (term_frees fm' @ term_vars fm');
- val fm2 = foldr mk_all2 fm' vs
- in (fm2, np + length vs, length rhs) end;
-
-(*Object quantifier to meta --*)
-fun spec_step n th = if (n=0) then th else (spec_step (n-1) th) RS spec ;
-
-(* object implication to meta---*)
-fun mp_step n th = if (n=0) then th else (mp_step (n-1) th) RS mp;
-
-
-fun linr_tac ctxt q i =
- (ObjectLogic.atomize_prems_tac i)
- THEN (REPEAT_DETERM (split_tac [@{thm split_min}, @{thm split_max}, @{thm abs_split}] i))
- THEN (fn st =>
- let
- val g = List.nth (prems_of st, i - 1)
- val thy = ProofContext.theory_of ctxt
- (* Transform the term*)
- val (t,np,nh) = prepare_for_linr thy q g
- (* Some simpsets for dealing with mod div abs and nat*)
- val simpset0 = Simplifier.theory_context thy HOL_basic_ss addsimps comp_arith
- val ct = cterm_of thy (HOLogic.mk_Trueprop t)
- (* Theorem for the nat --> int transformation *)
- val pre_thm = Seq.hd (EVERY
- [simp_tac simpset0 1,
- TRY (simp_tac (Simplifier.theory_context thy ferrack_ss) 1)]
- (trivial ct))
- fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i)
- (* The result of the quantifier elimination *)
- val (th, tac) = case (prop_of pre_thm) of
- Const ("==>", _) $ (Const ("Trueprop", _) $ t1) $ _ =>
- let val pth = linr_oracle (cterm_of thy (Pattern.eta_long [] t1))
- in
- (trace_msg ("calling procedure with term:\n" ^
- Syntax.string_of_term ctxt t1);
- ((pth RS iffD2) RS pre_thm,
- assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i)))
- end
- | _ => (pre_thm, assm_tac i)
- in (rtac (((mp_step nh) o (spec_step np)) th) i
- THEN tac) st
- end handle Subscript => no_tac st);
-
-fun linr_meth src =
- Method.syntax (Args.mode "no_quantify") src
- #> (fn (q, ctxt) => Method.SIMPLE_METHOD' (linr_tac ctxt (not q)));
-
-val setup =
- Method.add_method ("rferrack", linr_meth,
- "decision procedure for linear real arithmetic");
-
-end