src/HOL/Decision_Procs/ferrack_tac.ML
changeset 29823 0ab754d13ccd
parent 29788 1b80ebe713a4
child 29948 cdf12a1cb963
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Decision_Procs/ferrack_tac.ML	Fri Feb 06 15:15:32 2009 +0100
@@ -0,0 +1,113 @@
+(*  Title:      HOL/Reflection/ferrack_tac.ML
+    Author:     Amine Chaieb, TU Muenchen
+*)
+
+structure Ferrack_Tac =
+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)
+      (OldTerm.term_frees fm' @ OldTerm.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