# HG changeset patch
# User wenzelm
# Date 1273940958 -7200
# Node ID 524a3172db5ba89738b0c4826fb197ce925d15f4
# Parent  fdefcbcb28878a9b21a7db07a7b5c8889359f1e4# Parent  897ee863885dc88f6d6ad3133493ef4cb79d7a05
merged

diff -r fdefcbcb2887 -r 524a3172db5b src/HOL/Boogie/Tools/boogie_tactics.ML
--- a/src/HOL/Boogie/Tools/boogie_tactics.ML	Sat May 15 07:48:24 2010 -0700
+++ b/src/HOL/Boogie/Tools/boogie_tactics.ML	Sat May 15 18:29:18 2010 +0200
@@ -25,8 +25,8 @@
 val label_eqs = [assert_at_def, block_at_def]
 
 fun unfold_labels_tac ctxt =
-  let val unfold = More_Conv.rewrs_conv label_eqs
-  in CONVERSION (More_Conv.top_sweep_conv (K unfold) ctxt) end
+  let val unfold = Conv.rewrs_conv label_eqs
+  in CONVERSION (Conv.top_sweep_conv (K unfold) ctxt) end
 
 fun boogie_tac ctxt rules =
   unfold_labels_tac ctxt
diff -r fdefcbcb2887 -r 524a3172db5b src/HOL/HOL.thy
--- a/src/HOL/HOL.thy	Sat May 15 07:48:24 2010 -0700
+++ b/src/HOL/HOL.thy	Sat May 15 18:29:18 2010 +0200
@@ -29,7 +29,6 @@
   "~~/src/Tools/induct.ML"
   ("~~/src/Tools/induct_tacs.ML")
   ("Tools/recfun_codegen.ML")
-  "~~/src/Tools/more_conv.ML"
 begin
 
 setup {* Intuitionistic.method_setup @{binding iprover} *}
diff -r fdefcbcb2887 -r 524a3172db5b src/HOL/IsaMakefile
--- a/src/HOL/IsaMakefile	Sat May 15 07:48:24 2010 -0700
+++ b/src/HOL/IsaMakefile	Sat May 15 18:29:18 2010 +0200
@@ -60,7 +60,7 @@
   HOL-Proofs-Extraction \
   HOL-Proofs-Lambda \
   HOL-SET_Protocol \
-  HOL-SMT_Examples \
+  HOL-Word-SMT_Examples \
   HOL-Statespace \
   HOL-Subst \
       TLA-Buffer \
@@ -128,7 +128,6 @@
   $(SRC)/Tools/induct.ML \
   $(SRC)/Tools/induct_tacs.ML \
   $(SRC)/Tools/intuitionistic.ML \
-  $(SRC)/Tools/more_conv.ML \
   $(SRC)/Tools/nbe.ML \
   $(SRC)/Tools/project_rule.ML \
   $(SRC)/Tools/quickcheck.ML \
@@ -402,7 +401,7 @@
   Library/Efficient_Nat.thy Library/Sum_Of_Squares.thy			\
   Library/Dlist.thy Library/Sum_Of_Squares/sos_wrapper.ML		\
   Library/Sum_Of_Squares/sum_of_squares.ML Library/Fset.thy		\
-  Library/Glbs.thy Library/normarith.ML Library/Executable_Set.thy	\
+  Library/Glbs.thy Library/Executable_Set.thy	\
   Library/Infinite_Set.thy Library/FuncSet.thy				\
   Library/Permutations.thy Library/Bit.thy Library/FrechetDeriv.thy	\
   Library/Fraction_Field.thy Library/Fundamental_Theorem_Algebra.thy	\
@@ -1088,27 +1087,27 @@
 
 HOL-Multivariate_Analysis: HOL $(OUT)/HOL-Multivariate_Analysis
 
-$(OUT)/HOL-Multivariate_Analysis: $(OUT)/HOL		\
-  Multivariate_Analysis/ROOT.ML				\
-  Multivariate_Analysis/document/root.tex		\
-  Multivariate_Analysis/Brouwer_Fixpoint.thy            \
-  Multivariate_Analysis/Convex_Euclidean_Space.thy      \
-  Multivariate_Analysis/Derivative.thy			\
-  Multivariate_Analysis/Determinants.thy		\
-  Multivariate_Analysis/Euclidean_Space.thy		\
-  Multivariate_Analysis/Fashoda.thy			\
-  Multivariate_Analysis/Finite_Cartesian_Product.thy	\
-  Multivariate_Analysis/Integration.thy			\
-  Multivariate_Analysis/Integration.certs		\
-  Multivariate_Analysis/L2_Norm.thy			\
-  Multivariate_Analysis/Multivariate_Analysis.thy	\
-  Multivariate_Analysis/Operator_Norm.thy		\
-  Multivariate_Analysis/Path_Connected.thy		\
-  Multivariate_Analysis/Real_Integration.thy		\
-  Multivariate_Analysis/Topology_Euclidean_Space.thy	\
-  Multivariate_Analysis/Vec1.thy Library/Glbs.thy	\
-  Library/Inner_Product.thy Library/Numeral_Type.thy	\
-  Library/Convex.thy Library/FrechetDeriv.thy		\
+$(OUT)/HOL-Multivariate_Analysis: $(OUT)/HOL				\
+  Multivariate_Analysis/Brouwer_Fixpoint.thy				\
+  Multivariate_Analysis/Convex_Euclidean_Space.thy			\
+  Multivariate_Analysis/Derivative.thy					\
+  Multivariate_Analysis/Determinants.thy				\
+  Multivariate_Analysis/Euclidean_Space.thy				\
+  Multivariate_Analysis/Fashoda.thy					\
+  Multivariate_Analysis/Finite_Cartesian_Product.thy			\
+  Multivariate_Analysis/Integration.certs				\
+  Multivariate_Analysis/Integration.thy					\
+  Multivariate_Analysis/L2_Norm.thy					\
+  Multivariate_Analysis/Multivariate_Analysis.thy			\
+  Multivariate_Analysis/Operator_Norm.thy				\
+  Multivariate_Analysis/Path_Connected.thy				\
+  Multivariate_Analysis/ROOT.ML						\
+  Multivariate_Analysis/Real_Integration.thy				\
+  Multivariate_Analysis/Topology_Euclidean_Space.thy			\
+  Multivariate_Analysis/document/root.tex				\
+  Multivariate_Analysis/normarith.ML Multivariate_Analysis/Vec1.thy	\
+  Library/Glbs.thy Library/Inner_Product.thy Library/Numeral_Type.thy	\
+  Library/Convex.thy Library/FrechetDeriv.thy				\
   Library/Product_Vector.thy Library/Product_plus.thy
 	@cd Multivariate_Analysis; $(ISABELLE_TOOL) usedir -b -g true $(OUT)/HOL HOL-Multivariate_Analysis
 
@@ -1254,11 +1253,11 @@
 	@$(ISABELLE_TOOL) usedir $(OUT)/HOL Mirabelle
 
 
-## HOL-SMT_Examples
+## HOL-Word-SMT_Examples
 
-HOL-SMT_Examples: HOL-Word $(LOG)/HOL-SMT_Examples.gz
+HOL-Word-SMT_Examples: HOL-Word $(LOG)/HOL-Word-SMT_Examples.gz
 
-$(LOG)/HOL-SMT_Examples.gz: $(OUT)/HOL-Word SMT_Examples/ROOT.ML	\
+$(LOG)/HOL-Word-SMT_Examples.gz: $(OUT)/HOL-Word SMT_Examples/ROOT.ML	\
   SMT_Examples/SMT_Examples.thy SMT_Examples/SMT_Examples.certs		\
   SMT_Examples/SMT_Word_Examples.thy SMT_Examples/SMT_Tests.thy		\
   SMT_Examples/SMT_Word_Examples.certs SMT_Examples/SMT_Tests.certs
@@ -1346,15 +1345,15 @@
 		$(LOG)/HOL-Probability.gz $(LOG)/HOL-Prolog.gz		\
 		$(LOG)/HOL-Proofs.gz $(LOG)/HOL-Proofs-Extraction.gz	\
 		$(LOG)/HOL-Proofs-Lambda.gz $(LOG)/HOL-SET_Protocol.gz	\
-		$(LOG)/HOL-SMT_Examples.gz $(LOG)/HOL-Statespace.gz 	\
-		$(LOG)/HOL-Subst.gz $(LOG)/HOL-UNITY.gz			\
-		$(LOG)/HOL-Unix.gz $(LOG)/HOL-Word-Examples.gz		\
-		$(LOG)/HOL-Word.gz $(LOG)/HOL-ZF.gz $(LOG)/HOL-ex.gz	\
-		$(LOG)/HOL.gz $(LOG)/HOL4.gz $(LOG)/TLA-Buffer.gz	\
-		$(LOG)/TLA-Inc.gz $(LOG)/TLA-Memory.gz $(LOG)/TLA.gz	\
-		$(OUT)/HOL $(OUT)/HOL-Algebra $(OUT)/HOL-Base		\
-		$(OUT)/HOL-Boogie $(OUT)/HOL-Main			\
-		$(OUT)/HOL-Multivariate_Analysis $(OUT)/HOL-NSA		\
-		$(OUT)/HOL-Nominal $(OUT)/HOL-Plain			\
+		$(LOG)/HOL-Word-SMT_Examples.gz				\
+		$(LOG)/HOL-Statespace.gz $(LOG)/HOL-Subst.gz		\
+		$(LOG)/HOL-UNITY.gz $(LOG)/HOL-Unix.gz			\
+		$(LOG)/HOL-Word-Examples.gz $(LOG)/HOL-Word.gz		\
+		$(LOG)/HOL-ZF.gz $(LOG)/HOL-ex.gz $(LOG)/HOL.gz		\
+		$(LOG)/HOL4.gz $(LOG)/TLA-Buffer.gz $(LOG)/TLA-Inc.gz	\
+		$(LOG)/TLA-Memory.gz $(LOG)/TLA.gz $(OUT)/HOL		\
+		$(OUT)/HOL-Algebra $(OUT)/HOL-Base $(OUT)/HOL-Boogie	\
+		$(OUT)/HOL-Main $(OUT)/HOL-Multivariate_Analysis	\
+		$(OUT)/HOL-NSA $(OUT)/HOL-Nominal $(OUT)/HOL-Plain	\
 		$(OUT)/HOL-Probability $(OUT)/HOL-Proofs		\
 		$(OUT)/HOL-Word $(OUT)/HOL4 $(OUT)/TLA
diff -r fdefcbcb2887 -r 524a3172db5b src/HOL/Library/normarith.ML
--- a/src/HOL/Library/normarith.ML	Sat May 15 07:48:24 2010 -0700
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,416 +0,0 @@
-(* Title:      Library/normarith.ML
-   Author:     Amine Chaieb, University of Cambridge
-   Description: A simple decision procedure for linear problems in euclidean space
-*)
-
-  (* Now the norm procedure for euclidean spaces *)
-
-
-signature NORM_ARITH = 
-sig
- val norm_arith : Proof.context -> conv
- val norm_arith_tac : Proof.context -> int -> tactic
-end
-
-structure NormArith : NORM_ARITH = 
-struct
-
- open Conv;
- val bool_eq = op = : bool *bool -> bool
-  fun dest_ratconst t = case term_of t of
-   Const(@{const_name divide}, _)$a$b => Rat.rat_of_quotient(HOLogic.dest_number a |> snd, HOLogic.dest_number b |> snd)
- | Const(@{const_name inverse}, _)$a => Rat.rat_of_quotient(1, HOLogic.dest_number a |> snd)
- | _ => Rat.rat_of_int (HOLogic.dest_number (term_of t) |> snd)
- fun is_ratconst t = can dest_ratconst t
- fun augment_norm b t acc = case term_of t of 
-     Const(@{const_name norm}, _) $ _ => insert (eq_pair bool_eq (op aconvc)) (b,Thm.dest_arg t) acc
-   | _ => acc
- fun find_normedterms t acc = case term_of t of
-    @{term "op + :: real => _"}$_$_ =>
-            find_normedterms (Thm.dest_arg1 t) (find_normedterms (Thm.dest_arg t) acc)
-      | @{term "op * :: real => _"}$_$n =>
-            if not (is_ratconst (Thm.dest_arg1 t)) then acc else
-            augment_norm (dest_ratconst (Thm.dest_arg1 t) >=/ Rat.zero) 
-                      (Thm.dest_arg t) acc
-      | _ => augment_norm true t acc 
-
- val cterm_lincomb_neg = FuncUtil.Ctermfunc.map Rat.neg
- fun cterm_lincomb_cmul c t = 
-    if c =/ Rat.zero then FuncUtil.Ctermfunc.empty else FuncUtil.Ctermfunc.map (fn x => x */ c) t
- fun cterm_lincomb_add l r = FuncUtil.Ctermfunc.combine (curry op +/) (fn x => x =/ Rat.zero) l r
- fun cterm_lincomb_sub l r = cterm_lincomb_add l (cterm_lincomb_neg r)
- fun cterm_lincomb_eq l r = FuncUtil.Ctermfunc.is_empty (cterm_lincomb_sub l r)
-
- val int_lincomb_neg = FuncUtil.Intfunc.map Rat.neg
- fun int_lincomb_cmul c t = 
-    if c =/ Rat.zero then FuncUtil.Intfunc.empty else FuncUtil.Intfunc.map (fn x => x */ c) t
- fun int_lincomb_add l r = FuncUtil.Intfunc.combine (curry op +/) (fn x => x =/ Rat.zero) l r
- fun int_lincomb_sub l r = int_lincomb_add l (int_lincomb_neg r)
- fun int_lincomb_eq l r = FuncUtil.Intfunc.is_empty (int_lincomb_sub l r)
-
-fun vector_lincomb t = case term_of t of 
-   Const(@{const_name plus}, _) $ _ $ _ =>
-    cterm_lincomb_add (vector_lincomb (Thm.dest_arg1 t)) (vector_lincomb (Thm.dest_arg t))
- | Const(@{const_name minus}, _) $ _ $ _ =>
-    cterm_lincomb_sub (vector_lincomb (Thm.dest_arg1 t)) (vector_lincomb (Thm.dest_arg t))
- | Const(@{const_name scaleR}, _)$_$_ =>
-    cterm_lincomb_cmul (dest_ratconst (Thm.dest_arg1 t)) (vector_lincomb (Thm.dest_arg t))
- | Const(@{const_name uminus}, _)$_ =>
-     cterm_lincomb_neg (vector_lincomb (Thm.dest_arg t))
-(* FIXME: how should we handle numerals?
- | Const(@ {const_name vec},_)$_ => 
-   let 
-     val b = ((snd o HOLogic.dest_number o term_of o Thm.dest_arg) t = 0 
-               handle TERM _=> false)
-   in if b then FuncUtil.Ctermfunc.onefunc (t,Rat.one)
-      else FuncUtil.Ctermfunc.empty
-   end
-*)
- | _ => FuncUtil.Ctermfunc.onefunc (t,Rat.one)
-
- fun vector_lincombs ts =
-  fold_rev 
-   (fn t => fn fns => case AList.lookup (op aconvc) fns t of
-     NONE => 
-       let val f = vector_lincomb t 
-       in case find_first (fn (_,f') => cterm_lincomb_eq f f') fns of
-           SOME (_,f') => (t,f') :: fns
-         | NONE => (t,f) :: fns 
-       end
-   | SOME _ => fns) ts []
-
-fun replacenegnorms cv t = case term_of t of 
-  @{term "op + :: real => _"}$_$_ => binop_conv (replacenegnorms cv) t
-| @{term "op * :: real => _"}$_$_ => 
-    if dest_ratconst (Thm.dest_arg1 t) </ Rat.zero then arg_conv cv t else reflexive t
-| _ => reflexive t
-fun flip v eq = 
-  if FuncUtil.Ctermfunc.defined eq v 
-  then FuncUtil.Ctermfunc.update (v, Rat.neg (FuncUtil.Ctermfunc.apply eq v)) eq else eq
-fun allsubsets s = case s of 
-  [] => [[]]
-|(a::t) => let val res = allsubsets t in
-               map (cons a) res @ res end
-fun evaluate env lin =
- FuncUtil.Intfunc.fold (fn (x,c) => fn s => s +/ c */ (FuncUtil.Intfunc.apply env x)) 
-   lin Rat.zero
-
-fun solve (vs,eqs) = case (vs,eqs) of
-  ([],[]) => SOME (FuncUtil.Intfunc.onefunc (0,Rat.one))
- |(_,eq::oeqs) => 
-   (case filter (member (op =) vs) (FuncUtil.Intfunc.dom eq) of (*FIXME use find_first here*)
-     [] => NONE
-    | v::_ => 
-       if FuncUtil.Intfunc.defined eq v 
-       then 
-        let 
-         val c = FuncUtil.Intfunc.apply eq v
-         val vdef = int_lincomb_cmul (Rat.neg (Rat.inv c)) eq
-         fun eliminate eqn = if not (FuncUtil.Intfunc.defined eqn v) then eqn 
-                             else int_lincomb_add (int_lincomb_cmul (FuncUtil.Intfunc.apply eqn v) vdef) eqn
-        in (case solve (remove (op =) v vs, map eliminate oeqs) of
-            NONE => NONE
-          | SOME soln => SOME (FuncUtil.Intfunc.update (v, evaluate soln (FuncUtil.Intfunc.delete_safe v vdef)) soln))
-        end
-       else NONE)
-
-fun combinations k l = if k = 0 then [[]] else
- case l of 
-  [] => []
-| h::t => map (cons h) (combinations (k - 1) t) @ combinations k t
-
-
-fun forall2 p l1 l2 = case (l1,l2) of 
-   ([],[]) => true
- | (h1::t1,h2::t2) => p h1 h2 andalso forall2 p t1 t2
- | _ => false;
-
-
-fun vertices vs eqs =
- let 
-  fun vertex cmb = case solve(vs,cmb) of
-    NONE => NONE
-   | SOME soln => SOME (map (fn v => FuncUtil.Intfunc.tryapplyd soln v Rat.zero) vs)
-  val rawvs = map_filter vertex (combinations (length vs) eqs)
-  val unset = filter (forall (fn c => c >=/ Rat.zero)) rawvs 
- in fold_rev (insert (uncurry (forall2 (curry op =/)))) unset [] 
- end 
-
-fun subsumes l m = forall2 (fn x => fn y => Rat.abs x <=/ Rat.abs y) l m 
-
-fun subsume todo dun = case todo of
- [] => dun
-|v::ovs => 
-   let val dun' = if exists (fn w => subsumes w v) dun then dun
-                  else v::(filter (fn w => not(subsumes v w)) dun) 
-   in subsume ovs dun' 
-   end;
-
-fun match_mp PQ P = P RS PQ;
-
-fun cterm_of_rat x = 
-let val (a, b) = Rat.quotient_of_rat x
-in 
- if b = 1 then Numeral.mk_cnumber @{ctyp "real"} a
-  else Thm.capply (Thm.capply @{cterm "op / :: real => _"} 
-                   (Numeral.mk_cnumber @{ctyp "real"} a))
-        (Numeral.mk_cnumber @{ctyp "real"} b)
-end;
-
-fun norm_cmul_rule c th = instantiate' [] [SOME (cterm_of_rat c)] (th RS @{thm norm_cmul_rule_thm});
-
-fun norm_add_rule th1 th2 = [th1, th2] MRS @{thm norm_add_rule_thm};
-
-  (* I think here the static context should be sufficient!! *)
-fun inequality_canon_rule ctxt = 
- let 
-  (* FIXME : Should be computed statically!! *)
-  val real_poly_conv = 
-    Semiring_Normalizer.semiring_normalize_wrapper ctxt
-     (the (Semiring_Normalizer.match ctxt @{cterm "(0::real) + 1"}))
- in fconv_rule (arg_conv ((rewr_conv @{thm ge_iff_diff_ge_0}) then_conv arg_conv (Numeral_Simprocs.field_comp_conv then_conv real_poly_conv)))
-end;
-
- fun absc cv ct = case term_of ct of 
- Abs (v,_, _) => 
-  let val (x,t) = Thm.dest_abs (SOME v) ct
-  in Thm.abstract_rule ((fst o dest_Free o term_of) x) x (cv t)
-  end
- | _ => all_conv ct;
-
-fun sub_conv cv ct = (comb_conv cv else_conv absc cv) ct;
-fun botc1 conv ct = 
-  ((sub_conv (botc1 conv)) then_conv (conv else_conv all_conv)) ct;
-
- fun rewrs_conv eqs ct = first_conv (map rewr_conv eqs) ct;
- val apply_pth1 = rewr_conv @{thm pth_1};
- val apply_pth2 = rewr_conv @{thm pth_2};
- val apply_pth3 = rewr_conv @{thm pth_3};
- val apply_pth4 = rewrs_conv @{thms pth_4};
- val apply_pth5 = rewr_conv @{thm pth_5};
- val apply_pth6 = rewr_conv @{thm pth_6};
- val apply_pth7 = rewrs_conv @{thms pth_7};
- val apply_pth8 = rewr_conv @{thm pth_8} then_conv arg1_conv Numeral_Simprocs.field_comp_conv then_conv (try_conv (rewr_conv (mk_meta_eq @{thm scaleR_zero_left})));
- val apply_pth9 = rewrs_conv @{thms pth_9} then_conv arg1_conv (arg1_conv Numeral_Simprocs.field_comp_conv);
- val apply_ptha = rewr_conv @{thm pth_a};
- val apply_pthb = rewrs_conv @{thms pth_b};
- val apply_pthc = rewrs_conv @{thms pth_c};
- val apply_pthd = try_conv (rewr_conv @{thm pth_d});
-
-fun headvector t = case t of 
-  Const(@{const_name plus}, _)$
-   (Const(@{const_name scaleR}, _)$l$v)$r => v
- | Const(@{const_name scaleR}, _)$l$v => v
- | _ => error "headvector: non-canonical term"
-
-fun vector_cmul_conv ct =
-   ((apply_pth5 then_conv arg1_conv Numeral_Simprocs.field_comp_conv) else_conv
-    (apply_pth6 then_conv binop_conv vector_cmul_conv)) ct
-
-fun vector_add_conv ct = apply_pth7 ct 
- handle CTERM _ => 
-  (apply_pth8 ct 
-   handle CTERM _ => 
-    (case term_of ct of 
-     Const(@{const_name plus},_)$lt$rt =>
-      let 
-       val l = headvector lt 
-       val r = headvector rt
-      in (case Term_Ord.fast_term_ord (l,r) of
-         LESS => (apply_pthb then_conv arg_conv vector_add_conv 
-                  then_conv apply_pthd) ct
-        | GREATER => (apply_pthc then_conv arg_conv vector_add_conv 
-                     then_conv apply_pthd) ct 
-        | EQUAL => (apply_pth9 then_conv 
-                ((apply_ptha then_conv vector_add_conv) else_conv 
-              arg_conv vector_add_conv then_conv apply_pthd)) ct)
-      end
-     | _ => reflexive ct))
-
-fun vector_canon_conv ct = case term_of ct of
- Const(@{const_name plus},_)$_$_ =>
-  let 
-   val ((p,l),r) = Thm.dest_comb ct |>> Thm.dest_comb
-   val lth = vector_canon_conv l 
-   val rth = vector_canon_conv r
-   val th = Drule.binop_cong_rule p lth rth 
-  in fconv_rule (arg_conv vector_add_conv) th end
-
-| Const(@{const_name scaleR}, _)$_$_ =>
-  let 
-   val (p,r) = Thm.dest_comb ct
-   val rth = Drule.arg_cong_rule p (vector_canon_conv r) 
-  in fconv_rule (arg_conv (apply_pth4 else_conv vector_cmul_conv)) rth
-  end
-
-| Const(@{const_name minus},_)$_$_ => (apply_pth2 then_conv vector_canon_conv) ct
-
-| Const(@{const_name uminus},_)$_ => (apply_pth3 then_conv vector_canon_conv) ct
-
-(* FIXME
-| Const(@{const_name vec},_)$n => 
-  let val n = Thm.dest_arg ct
-  in if is_ratconst n andalso not (dest_ratconst n =/ Rat.zero) 
-     then reflexive ct else apply_pth1 ct
-  end
-*)
-| _ => apply_pth1 ct
-
-fun norm_canon_conv ct = case term_of ct of
-  Const(@{const_name norm},_)$_ => arg_conv vector_canon_conv ct
- | _ => raise CTERM ("norm_canon_conv", [ct])
-
-fun fold_rev2 f [] [] z = z
- | fold_rev2 f (x::xs) (y::ys) z = f x y (fold_rev2 f xs ys z)
- | fold_rev2 f _ _ _ = raise UnequalLengths;
-
-fun int_flip v eq = 
-  if FuncUtil.Intfunc.defined eq v 
-  then FuncUtil.Intfunc.update (v, Rat.neg (FuncUtil.Intfunc.apply eq v)) eq else eq;
-
-local
- val pth_zero = @{thm norm_zero}
- val tv_n = (ctyp_of_term o Thm.dest_arg o Thm.dest_arg1 o Thm.dest_arg o cprop_of)
-             pth_zero
- val concl = Thm.dest_arg o cprop_of 
- fun real_vector_combo_prover ctxt translator (nubs,ges,gts) = 
-  let 
-   (* FIXME: Should be computed statically!!*)
-   val real_poly_conv = 
-      Semiring_Normalizer.semiring_normalize_wrapper ctxt
-       (the (Semiring_Normalizer.match ctxt @{cterm "(0::real) + 1"}))
-   val sources = map (Thm.dest_arg o Thm.dest_arg1 o concl) nubs
-   val rawdests = fold_rev (find_normedterms o Thm.dest_arg o concl) (ges @ gts) [] 
-   val _ = if not (forall fst rawdests) then error "real_vector_combo_prover: Sanity check" 
-           else ()
-   val dests = distinct (op aconvc) (map snd rawdests)
-   val srcfuns = map vector_lincomb sources
-   val destfuns = map vector_lincomb dests 
-   val vvs = fold_rev (union (op aconvc) o FuncUtil.Ctermfunc.dom) (srcfuns @ destfuns) []
-   val n = length srcfuns
-   val nvs = 1 upto n
-   val srccombs = srcfuns ~~ nvs
-   fun consider d =
-    let 
-     fun coefficients x =
-      let 
-       val inp = if FuncUtil.Ctermfunc.defined d x then FuncUtil.Intfunc.onefunc (0, Rat.neg(FuncUtil.Ctermfunc.apply d x))
-                      else FuncUtil.Intfunc.empty 
-      in fold_rev (fn (f,v) => fn g => if FuncUtil.Ctermfunc.defined f x then FuncUtil.Intfunc.update (v, FuncUtil.Ctermfunc.apply f x) g else g) srccombs inp 
-      end
-     val equations = map coefficients vvs
-     val inequalities = map (fn n => FuncUtil.Intfunc.onefunc (n,Rat.one)) nvs
-     fun plausiblevertices f =
-      let 
-       val flippedequations = map (fold_rev int_flip f) equations
-       val constraints = flippedequations @ inequalities
-       val rawverts = vertices nvs constraints
-       fun check_solution v =
-        let 
-          val f = fold_rev2 (curry FuncUtil.Intfunc.update) nvs v (FuncUtil.Intfunc.onefunc (0, Rat.one))
-        in forall (fn e => evaluate f e =/ Rat.zero) flippedequations
-        end
-       val goodverts = filter check_solution rawverts
-       val signfixups = map (fn n => if member (op =) f n then ~1 else 1) nvs 
-      in map (map2 (fn s => fn c => Rat.rat_of_int s */ c) signfixups) goodverts
-      end
-     val allverts = fold_rev append (map plausiblevertices (allsubsets nvs)) [] 
-    in subsume allverts []
-    end
-   fun compute_ineq v =
-    let 
-     val ths = map_filter (fn (v,t) => if v =/ Rat.zero then NONE 
-                                     else SOME(norm_cmul_rule v t))
-                            (v ~~ nubs) 
-     fun end_itlist f xs = split_last xs |> uncurry (fold_rev f)
-    in inequality_canon_rule ctxt (end_itlist norm_add_rule ths)
-    end
-   val ges' = map_filter (try compute_ineq) (fold_rev (append o consider) destfuns []) @
-                 map (inequality_canon_rule ctxt) nubs @ ges
-   val zerodests = filter
-        (fn t => null (FuncUtil.Ctermfunc.dom (vector_lincomb t))) (map snd rawdests)
-
-  in fst (RealArith.real_linear_prover translator
-        (map (fn t => instantiate ([(tv_n, ctyp_of_term t)],[]) pth_zero)
-            zerodests,
-        map (fconv_rule (try_conv (More_Conv.top_sweep_conv (K norm_canon_conv) ctxt) then_conv
-                       arg_conv (arg_conv real_poly_conv))) ges',
-        map (fconv_rule (try_conv (More_Conv.top_sweep_conv (K norm_canon_conv) ctxt) then_conv 
-                       arg_conv (arg_conv real_poly_conv))) gts))
-  end
-in val real_vector_combo_prover = real_vector_combo_prover
-end;
-
-local
- val pth = @{thm norm_imp_pos_and_ge}
- val norm_mp = match_mp pth
- val concl = Thm.dest_arg o cprop_of
- fun conjunct1 th = th RS @{thm conjunct1}
- fun conjunct2 th = th RS @{thm conjunct2}
-fun real_vector_ineq_prover ctxt translator (ges,gts) = 
- let 
-(*   val _ = error "real_vector_ineq_prover: pause" *)
-  val ntms = fold_rev find_normedterms (map (Thm.dest_arg o concl) (ges @ gts)) []
-  val lctab = vector_lincombs (map snd (filter (not o fst) ntms))
-  val (fxns, ctxt') = Variable.variant_fixes (replicate (length lctab) "x") ctxt
-  fun instantiate_cterm' ty tms = Drule.cterm_rule (Drule.instantiate' ty tms)
-  fun mk_norm t = Thm.capply (instantiate_cterm' [SOME (ctyp_of_term t)] [] @{cpat "norm :: (?'a :: real_normed_vector) => real"}) t
-  fun mk_equals l r = Thm.capply (Thm.capply (instantiate_cterm' [SOME (ctyp_of_term l)] [] @{cpat "op == :: ?'a =>_"}) l) r
-  val asl = map2 (fn (t,_) => fn n => assume (mk_equals (mk_norm t) (cterm_of (ProofContext.theory_of ctxt') (Free(n,@{typ real}))))) lctab fxns
-  val replace_conv = try_conv (rewrs_conv asl)
-  val replace_rule = fconv_rule (funpow 2 arg_conv (replacenegnorms replace_conv))
-  val ges' =
-       fold_rev (fn th => fn ths => conjunct1(norm_mp th)::ths)
-              asl (map replace_rule ges)
-  val gts' = map replace_rule gts
-  val nubs = map (conjunct2 o norm_mp) asl
-  val th1 = real_vector_combo_prover ctxt' translator (nubs,ges',gts')
-  val shs = filter (member (fn (t,th) => t aconvc cprop_of th) asl) (#hyps (crep_thm th1)) 
-  val th11 = hd (Variable.export ctxt' ctxt [fold implies_intr shs th1])
-  val cps = map (swap o Thm.dest_equals) (cprems_of th11)
-  val th12 = instantiate ([], cps) th11
-  val th13 = fold Thm.elim_implies (map (reflexive o snd) cps) th12;
- in hd (Variable.export ctxt' ctxt [th13])
- end 
-in val real_vector_ineq_prover = real_vector_ineq_prover
-end;
-
-local
- val rawrule = fconv_rule (arg_conv (rewr_conv @{thm real_eq_0_iff_le_ge_0}))
- fun conj_pair th = (th RS @{thm conjunct1}, th RS @{thm conjunct2})
- fun simple_cterm_ord t u = Term_Ord.term_ord (term_of t, term_of u) = LESS;
-  (* FIXME: Lookup in the context every time!!! Fix this !!!*)
- fun splitequation ctxt th acc =
-  let 
-   val real_poly_neg_conv = #neg
-       (Semiring_Normalizer.semiring_normalizers_ord_wrapper ctxt
-        (the (Semiring_Normalizer.match ctxt @{cterm "(0::real) + 1"})) simple_cterm_ord)
-   val (th1,th2) = conj_pair(rawrule th)
-  in th1::fconv_rule (arg_conv (arg_conv real_poly_neg_conv)) th2::acc
-  end
-in fun real_vector_prover ctxt _ translator (eqs,ges,gts) =
-     (real_vector_ineq_prover ctxt translator
-         (fold_rev (splitequation ctxt) eqs ges,gts), RealArith.Trivial)
-end;
-
-  fun init_conv ctxt = 
-   Simplifier.rewrite (Simplifier.context ctxt 
-     (HOL_basic_ss addsimps ([(*@{thm vec_0}, @{thm vec_1},*) @{thm dist_norm}, @{thm diff_0_right}, @{thm right_minus}, @{thm diff_self}, @{thm norm_zero}] @ @{thms arithmetic_simps} @ @{thms norm_pths})))
-   then_conv Numeral_Simprocs.field_comp_conv 
-   then_conv nnf_conv
-
- fun pure ctxt = fst o RealArith.gen_prover_real_arith ctxt (real_vector_prover ctxt);
- fun norm_arith ctxt ct = 
-  let 
-   val ctxt' = Variable.declare_term (term_of ct) ctxt
-   val th = init_conv ctxt' ct
-  in equal_elim (Drule.arg_cong_rule @{cterm Trueprop} (symmetric th)) 
-                (pure ctxt' (Thm.rhs_of th))
- end
-
- fun norm_arith_tac ctxt = 
-   clarify_tac HOL_cs THEN'
-   Object_Logic.full_atomize_tac THEN'
-   CSUBGOAL ( fn (p,i) => rtac (norm_arith ctxt (Thm.dest_arg p )) i);
-
-end;
diff -r fdefcbcb2887 -r 524a3172db5b src/HOL/Multivariate_Analysis/normarith.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Multivariate_Analysis/normarith.ML	Sat May 15 18:29:18 2010 +0200
@@ -0,0 +1,402 @@
+(*  Title:      Library/normarith.ML
+    Author:     Amine Chaieb, University of Cambridge
+
+Simple decision procedure for linear problems in Euclidean space.
+*)
+
+signature NORM_ARITH =
+sig
+ val norm_arith : Proof.context -> conv
+ val norm_arith_tac : Proof.context -> int -> tactic
+end
+
+structure NormArith : NORM_ARITH =
+struct
+
+ open Conv;
+ val bool_eq = op = : bool *bool -> bool
+  fun dest_ratconst t = case term_of t of
+   Const(@{const_name divide}, _)$a$b => Rat.rat_of_quotient(HOLogic.dest_number a |> snd, HOLogic.dest_number b |> snd)
+ | Const(@{const_name inverse}, _)$a => Rat.rat_of_quotient(1, HOLogic.dest_number a |> snd)
+ | _ => Rat.rat_of_int (HOLogic.dest_number (term_of t) |> snd)
+ fun is_ratconst t = can dest_ratconst t
+ fun augment_norm b t acc = case term_of t of
+     Const(@{const_name norm}, _) $ _ => insert (eq_pair bool_eq (op aconvc)) (b,Thm.dest_arg t) acc
+   | _ => acc
+ fun find_normedterms t acc = case term_of t of
+    @{term "op + :: real => _"}$_$_ =>
+            find_normedterms (Thm.dest_arg1 t) (find_normedterms (Thm.dest_arg t) acc)
+      | @{term "op * :: real => _"}$_$n =>
+            if not (is_ratconst (Thm.dest_arg1 t)) then acc else
+            augment_norm (dest_ratconst (Thm.dest_arg1 t) >=/ Rat.zero)
+                      (Thm.dest_arg t) acc
+      | _ => augment_norm true t acc
+
+ val cterm_lincomb_neg = FuncUtil.Ctermfunc.map Rat.neg
+ fun cterm_lincomb_cmul c t =
+    if c =/ Rat.zero then FuncUtil.Ctermfunc.empty else FuncUtil.Ctermfunc.map (fn x => x */ c) t
+ fun cterm_lincomb_add l r = FuncUtil.Ctermfunc.combine (curry op +/) (fn x => x =/ Rat.zero) l r
+ fun cterm_lincomb_sub l r = cterm_lincomb_add l (cterm_lincomb_neg r)
+ fun cterm_lincomb_eq l r = FuncUtil.Ctermfunc.is_empty (cterm_lincomb_sub l r)
+
+ val int_lincomb_neg = FuncUtil.Intfunc.map Rat.neg
+ fun int_lincomb_cmul c t =
+    if c =/ Rat.zero then FuncUtil.Intfunc.empty else FuncUtil.Intfunc.map (fn x => x */ c) t
+ fun int_lincomb_add l r = FuncUtil.Intfunc.combine (curry op +/) (fn x => x =/ Rat.zero) l r
+ fun int_lincomb_sub l r = int_lincomb_add l (int_lincomb_neg r)
+ fun int_lincomb_eq l r = FuncUtil.Intfunc.is_empty (int_lincomb_sub l r)
+
+fun vector_lincomb t = case term_of t of
+   Const(@{const_name plus}, _) $ _ $ _ =>
+    cterm_lincomb_add (vector_lincomb (Thm.dest_arg1 t)) (vector_lincomb (Thm.dest_arg t))
+ | Const(@{const_name minus}, _) $ _ $ _ =>
+    cterm_lincomb_sub (vector_lincomb (Thm.dest_arg1 t)) (vector_lincomb (Thm.dest_arg t))
+ | Const(@{const_name scaleR}, _)$_$_ =>
+    cterm_lincomb_cmul (dest_ratconst (Thm.dest_arg1 t)) (vector_lincomb (Thm.dest_arg t))
+ | Const(@{const_name uminus}, _)$_ =>
+     cterm_lincomb_neg (vector_lincomb (Thm.dest_arg t))
+(* FIXME: how should we handle numerals?
+ | Const(@ {const_name vec},_)$_ =>
+   let
+     val b = ((snd o HOLogic.dest_number o term_of o Thm.dest_arg) t = 0
+               handle TERM _=> false)
+   in if b then FuncUtil.Ctermfunc.onefunc (t,Rat.one)
+      else FuncUtil.Ctermfunc.empty
+   end
+*)
+ | _ => FuncUtil.Ctermfunc.onefunc (t,Rat.one)
+
+ fun vector_lincombs ts =
+  fold_rev
+   (fn t => fn fns => case AList.lookup (op aconvc) fns t of
+     NONE =>
+       let val f = vector_lincomb t
+       in case find_first (fn (_,f') => cterm_lincomb_eq f f') fns of
+           SOME (_,f') => (t,f') :: fns
+         | NONE => (t,f) :: fns
+       end
+   | SOME _ => fns) ts []
+
+fun replacenegnorms cv t = case term_of t of
+  @{term "op + :: real => _"}$_$_ => binop_conv (replacenegnorms cv) t
+| @{term "op * :: real => _"}$_$_ =>
+    if dest_ratconst (Thm.dest_arg1 t) </ Rat.zero then arg_conv cv t else reflexive t
+| _ => reflexive t
+fun flip v eq =
+  if FuncUtil.Ctermfunc.defined eq v
+  then FuncUtil.Ctermfunc.update (v, Rat.neg (FuncUtil.Ctermfunc.apply eq v)) eq else eq
+fun allsubsets s = case s of
+  [] => [[]]
+|(a::t) => let val res = allsubsets t in
+               map (cons a) res @ res end
+fun evaluate env lin =
+ FuncUtil.Intfunc.fold (fn (x,c) => fn s => s +/ c */ (FuncUtil.Intfunc.apply env x))
+   lin Rat.zero
+
+fun solve (vs,eqs) = case (vs,eqs) of
+  ([],[]) => SOME (FuncUtil.Intfunc.onefunc (0,Rat.one))
+ |(_,eq::oeqs) =>
+   (case filter (member (op =) vs) (FuncUtil.Intfunc.dom eq) of (*FIXME use find_first here*)
+     [] => NONE
+    | v::_ =>
+       if FuncUtil.Intfunc.defined eq v
+       then
+        let
+         val c = FuncUtil.Intfunc.apply eq v
+         val vdef = int_lincomb_cmul (Rat.neg (Rat.inv c)) eq
+         fun eliminate eqn = if not (FuncUtil.Intfunc.defined eqn v) then eqn
+                             else int_lincomb_add (int_lincomb_cmul (FuncUtil.Intfunc.apply eqn v) vdef) eqn
+        in (case solve (remove (op =) v vs, map eliminate oeqs) of
+            NONE => NONE
+          | SOME soln => SOME (FuncUtil.Intfunc.update (v, evaluate soln (FuncUtil.Intfunc.delete_safe v vdef)) soln))
+        end
+       else NONE)
+
+fun combinations k l = if k = 0 then [[]] else
+ case l of
+  [] => []
+| h::t => map (cons h) (combinations (k - 1) t) @ combinations k t
+
+
+fun forall2 p l1 l2 = case (l1,l2) of
+   ([],[]) => true
+ | (h1::t1,h2::t2) => p h1 h2 andalso forall2 p t1 t2
+ | _ => false;
+
+
+fun vertices vs eqs =
+ let
+  fun vertex cmb = case solve(vs,cmb) of
+    NONE => NONE
+   | SOME soln => SOME (map (fn v => FuncUtil.Intfunc.tryapplyd soln v Rat.zero) vs)
+  val rawvs = map_filter vertex (combinations (length vs) eqs)
+  val unset = filter (forall (fn c => c >=/ Rat.zero)) rawvs
+ in fold_rev (insert (uncurry (forall2 (curry op =/)))) unset []
+ end
+
+fun subsumes l m = forall2 (fn x => fn y => Rat.abs x <=/ Rat.abs y) l m
+
+fun subsume todo dun = case todo of
+ [] => dun
+|v::ovs =>
+   let val dun' = if exists (fn w => subsumes w v) dun then dun
+                  else v::(filter (fn w => not(subsumes v w)) dun)
+   in subsume ovs dun'
+   end;
+
+fun match_mp PQ P = P RS PQ;
+
+fun cterm_of_rat x =
+let val (a, b) = Rat.quotient_of_rat x
+in
+ if b = 1 then Numeral.mk_cnumber @{ctyp "real"} a
+  else Thm.capply (Thm.capply @{cterm "op / :: real => _"}
+                   (Numeral.mk_cnumber @{ctyp "real"} a))
+        (Numeral.mk_cnumber @{ctyp "real"} b)
+end;
+
+fun norm_cmul_rule c th = instantiate' [] [SOME (cterm_of_rat c)] (th RS @{thm norm_cmul_rule_thm});
+
+fun norm_add_rule th1 th2 = [th1, th2] MRS @{thm norm_add_rule_thm};
+
+  (* I think here the static context should be sufficient!! *)
+fun inequality_canon_rule ctxt =
+ let
+  (* FIXME : Should be computed statically!! *)
+  val real_poly_conv =
+    Semiring_Normalizer.semiring_normalize_wrapper ctxt
+     (the (Semiring_Normalizer.match ctxt @{cterm "(0::real) + 1"}))
+ in fconv_rule (arg_conv ((rewr_conv @{thm ge_iff_diff_ge_0}) then_conv arg_conv (Numeral_Simprocs.field_comp_conv then_conv real_poly_conv)))
+end;
+
+ val apply_pth1 = rewr_conv @{thm pth_1};
+ val apply_pth2 = rewr_conv @{thm pth_2};
+ val apply_pth3 = rewr_conv @{thm pth_3};
+ val apply_pth4 = rewrs_conv @{thms pth_4};
+ val apply_pth5 = rewr_conv @{thm pth_5};
+ val apply_pth6 = rewr_conv @{thm pth_6};
+ val apply_pth7 = rewrs_conv @{thms pth_7};
+ val apply_pth8 = rewr_conv @{thm pth_8} then_conv arg1_conv Numeral_Simprocs.field_comp_conv then_conv (try_conv (rewr_conv (mk_meta_eq @{thm scaleR_zero_left})));
+ val apply_pth9 = rewrs_conv @{thms pth_9} then_conv arg1_conv (arg1_conv Numeral_Simprocs.field_comp_conv);
+ val apply_ptha = rewr_conv @{thm pth_a};
+ val apply_pthb = rewrs_conv @{thms pth_b};
+ val apply_pthc = rewrs_conv @{thms pth_c};
+ val apply_pthd = try_conv (rewr_conv @{thm pth_d});
+
+fun headvector t = case t of
+  Const(@{const_name plus}, _)$
+   (Const(@{const_name scaleR}, _)$l$v)$r => v
+ | Const(@{const_name scaleR}, _)$l$v => v
+ | _ => error "headvector: non-canonical term"
+
+fun vector_cmul_conv ct =
+   ((apply_pth5 then_conv arg1_conv Numeral_Simprocs.field_comp_conv) else_conv
+    (apply_pth6 then_conv binop_conv vector_cmul_conv)) ct
+
+fun vector_add_conv ct = apply_pth7 ct
+ handle CTERM _ =>
+  (apply_pth8 ct
+   handle CTERM _ =>
+    (case term_of ct of
+     Const(@{const_name plus},_)$lt$rt =>
+      let
+       val l = headvector lt
+       val r = headvector rt
+      in (case Term_Ord.fast_term_ord (l,r) of
+         LESS => (apply_pthb then_conv arg_conv vector_add_conv
+                  then_conv apply_pthd) ct
+        | GREATER => (apply_pthc then_conv arg_conv vector_add_conv
+                     then_conv apply_pthd) ct
+        | EQUAL => (apply_pth9 then_conv
+                ((apply_ptha then_conv vector_add_conv) else_conv
+              arg_conv vector_add_conv then_conv apply_pthd)) ct)
+      end
+     | _ => reflexive ct))
+
+fun vector_canon_conv ct = case term_of ct of
+ Const(@{const_name plus},_)$_$_ =>
+  let
+   val ((p,l),r) = Thm.dest_comb ct |>> Thm.dest_comb
+   val lth = vector_canon_conv l
+   val rth = vector_canon_conv r
+   val th = Drule.binop_cong_rule p lth rth
+  in fconv_rule (arg_conv vector_add_conv) th end
+
+| Const(@{const_name scaleR}, _)$_$_ =>
+  let
+   val (p,r) = Thm.dest_comb ct
+   val rth = Drule.arg_cong_rule p (vector_canon_conv r)
+  in fconv_rule (arg_conv (apply_pth4 else_conv vector_cmul_conv)) rth
+  end
+
+| Const(@{const_name minus},_)$_$_ => (apply_pth2 then_conv vector_canon_conv) ct
+
+| Const(@{const_name uminus},_)$_ => (apply_pth3 then_conv vector_canon_conv) ct
+
+(* FIXME
+| Const(@{const_name vec},_)$n =>
+  let val n = Thm.dest_arg ct
+  in if is_ratconst n andalso not (dest_ratconst n =/ Rat.zero)
+     then reflexive ct else apply_pth1 ct
+  end
+*)
+| _ => apply_pth1 ct
+
+fun norm_canon_conv ct = case term_of ct of
+  Const(@{const_name norm},_)$_ => arg_conv vector_canon_conv ct
+ | _ => raise CTERM ("norm_canon_conv", [ct])
+
+fun fold_rev2 f [] [] z = z
+ | fold_rev2 f (x::xs) (y::ys) z = f x y (fold_rev2 f xs ys z)
+ | fold_rev2 f _ _ _ = raise UnequalLengths;
+
+fun int_flip v eq =
+  if FuncUtil.Intfunc.defined eq v
+  then FuncUtil.Intfunc.update (v, Rat.neg (FuncUtil.Intfunc.apply eq v)) eq else eq;
+
+local
+ val pth_zero = @{thm norm_zero}
+ val tv_n = (ctyp_of_term o Thm.dest_arg o Thm.dest_arg1 o Thm.dest_arg o cprop_of)
+             pth_zero
+ val concl = Thm.dest_arg o cprop_of
+ fun real_vector_combo_prover ctxt translator (nubs,ges,gts) =
+  let
+   (* FIXME: Should be computed statically!!*)
+   val real_poly_conv =
+      Semiring_Normalizer.semiring_normalize_wrapper ctxt
+       (the (Semiring_Normalizer.match ctxt @{cterm "(0::real) + 1"}))
+   val sources = map (Thm.dest_arg o Thm.dest_arg1 o concl) nubs
+   val rawdests = fold_rev (find_normedterms o Thm.dest_arg o concl) (ges @ gts) []
+   val _ = if not (forall fst rawdests) then error "real_vector_combo_prover: Sanity check"
+           else ()
+   val dests = distinct (op aconvc) (map snd rawdests)
+   val srcfuns = map vector_lincomb sources
+   val destfuns = map vector_lincomb dests
+   val vvs = fold_rev (union (op aconvc) o FuncUtil.Ctermfunc.dom) (srcfuns @ destfuns) []
+   val n = length srcfuns
+   val nvs = 1 upto n
+   val srccombs = srcfuns ~~ nvs
+   fun consider d =
+    let
+     fun coefficients x =
+      let
+       val inp = if FuncUtil.Ctermfunc.defined d x then FuncUtil.Intfunc.onefunc (0, Rat.neg(FuncUtil.Ctermfunc.apply d x))
+                      else FuncUtil.Intfunc.empty
+      in fold_rev (fn (f,v) => fn g => if FuncUtil.Ctermfunc.defined f x then FuncUtil.Intfunc.update (v, FuncUtil.Ctermfunc.apply f x) g else g) srccombs inp
+      end
+     val equations = map coefficients vvs
+     val inequalities = map (fn n => FuncUtil.Intfunc.onefunc (n,Rat.one)) nvs
+     fun plausiblevertices f =
+      let
+       val flippedequations = map (fold_rev int_flip f) equations
+       val constraints = flippedequations @ inequalities
+       val rawverts = vertices nvs constraints
+       fun check_solution v =
+        let
+          val f = fold_rev2 (curry FuncUtil.Intfunc.update) nvs v (FuncUtil.Intfunc.onefunc (0, Rat.one))
+        in forall (fn e => evaluate f e =/ Rat.zero) flippedequations
+        end
+       val goodverts = filter check_solution rawverts
+       val signfixups = map (fn n => if member (op =) f n then ~1 else 1) nvs
+      in map (map2 (fn s => fn c => Rat.rat_of_int s */ c) signfixups) goodverts
+      end
+     val allverts = fold_rev append (map plausiblevertices (allsubsets nvs)) []
+    in subsume allverts []
+    end
+   fun compute_ineq v =
+    let
+     val ths = map_filter (fn (v,t) => if v =/ Rat.zero then NONE
+                                     else SOME(norm_cmul_rule v t))
+                            (v ~~ nubs)
+     fun end_itlist f xs = split_last xs |> uncurry (fold_rev f)
+    in inequality_canon_rule ctxt (end_itlist norm_add_rule ths)
+    end
+   val ges' = map_filter (try compute_ineq) (fold_rev (append o consider) destfuns []) @
+                 map (inequality_canon_rule ctxt) nubs @ ges
+   val zerodests = filter
+        (fn t => null (FuncUtil.Ctermfunc.dom (vector_lincomb t))) (map snd rawdests)
+
+  in fst (RealArith.real_linear_prover translator
+        (map (fn t => instantiate ([(tv_n, ctyp_of_term t)],[]) pth_zero)
+            zerodests,
+        map (fconv_rule (try_conv (Conv.top_sweep_conv (K norm_canon_conv) ctxt) then_conv
+                       arg_conv (arg_conv real_poly_conv))) ges',
+        map (fconv_rule (try_conv (Conv.top_sweep_conv (K norm_canon_conv) ctxt) then_conv
+                       arg_conv (arg_conv real_poly_conv))) gts))
+  end
+in val real_vector_combo_prover = real_vector_combo_prover
+end;
+
+local
+ val pth = @{thm norm_imp_pos_and_ge}
+ val norm_mp = match_mp pth
+ val concl = Thm.dest_arg o cprop_of
+ fun conjunct1 th = th RS @{thm conjunct1}
+ fun conjunct2 th = th RS @{thm conjunct2}
+fun real_vector_ineq_prover ctxt translator (ges,gts) =
+ let
+(*   val _ = error "real_vector_ineq_prover: pause" *)
+  val ntms = fold_rev find_normedterms (map (Thm.dest_arg o concl) (ges @ gts)) []
+  val lctab = vector_lincombs (map snd (filter (not o fst) ntms))
+  val (fxns, ctxt') = Variable.variant_fixes (replicate (length lctab) "x") ctxt
+  fun instantiate_cterm' ty tms = Drule.cterm_rule (Drule.instantiate' ty tms)
+  fun mk_norm t = Thm.capply (instantiate_cterm' [SOME (ctyp_of_term t)] [] @{cpat "norm :: (?'a :: real_normed_vector) => real"}) t
+  fun mk_equals l r = Thm.capply (Thm.capply (instantiate_cterm' [SOME (ctyp_of_term l)] [] @{cpat "op == :: ?'a =>_"}) l) r
+  val asl = map2 (fn (t,_) => fn n => assume (mk_equals (mk_norm t) (cterm_of (ProofContext.theory_of ctxt') (Free(n,@{typ real}))))) lctab fxns
+  val replace_conv = try_conv (rewrs_conv asl)
+  val replace_rule = fconv_rule (funpow 2 arg_conv (replacenegnorms replace_conv))
+  val ges' =
+       fold_rev (fn th => fn ths => conjunct1(norm_mp th)::ths)
+              asl (map replace_rule ges)
+  val gts' = map replace_rule gts
+  val nubs = map (conjunct2 o norm_mp) asl
+  val th1 = real_vector_combo_prover ctxt' translator (nubs,ges',gts')
+  val shs = filter (member (fn (t,th) => t aconvc cprop_of th) asl) (#hyps (crep_thm th1))
+  val th11 = hd (Variable.export ctxt' ctxt [fold implies_intr shs th1])
+  val cps = map (swap o Thm.dest_equals) (cprems_of th11)
+  val th12 = instantiate ([], cps) th11
+  val th13 = fold Thm.elim_implies (map (reflexive o snd) cps) th12;
+ in hd (Variable.export ctxt' ctxt [th13])
+ end
+in val real_vector_ineq_prover = real_vector_ineq_prover
+end;
+
+local
+ val rawrule = fconv_rule (arg_conv (rewr_conv @{thm real_eq_0_iff_le_ge_0}))
+ fun conj_pair th = (th RS @{thm conjunct1}, th RS @{thm conjunct2})
+ fun simple_cterm_ord t u = Term_Ord.term_ord (term_of t, term_of u) = LESS;
+  (* FIXME: Lookup in the context every time!!! Fix this !!!*)
+ fun splitequation ctxt th acc =
+  let
+   val real_poly_neg_conv = #neg
+       (Semiring_Normalizer.semiring_normalizers_ord_wrapper ctxt
+        (the (Semiring_Normalizer.match ctxt @{cterm "(0::real) + 1"})) simple_cterm_ord)
+   val (th1,th2) = conj_pair(rawrule th)
+  in th1::fconv_rule (arg_conv (arg_conv real_poly_neg_conv)) th2::acc
+  end
+in fun real_vector_prover ctxt _ translator (eqs,ges,gts) =
+     (real_vector_ineq_prover ctxt translator
+         (fold_rev (splitequation ctxt) eqs ges,gts), RealArith.Trivial)
+end;
+
+  fun init_conv ctxt =
+   Simplifier.rewrite (Simplifier.context ctxt
+     (HOL_basic_ss addsimps ([(*@{thm vec_0}, @{thm vec_1},*) @{thm dist_norm}, @{thm diff_0_right}, @{thm right_minus}, @{thm diff_self}, @{thm norm_zero}] @ @{thms arithmetic_simps} @ @{thms norm_pths})))
+   then_conv Numeral_Simprocs.field_comp_conv
+   then_conv nnf_conv
+
+ fun pure ctxt = fst o RealArith.gen_prover_real_arith ctxt (real_vector_prover ctxt);
+ fun norm_arith ctxt ct =
+  let
+   val ctxt' = Variable.declare_term (term_of ct) ctxt
+   val th = init_conv ctxt' ct
+  in equal_elim (Drule.arg_cong_rule @{cterm Trueprop} (symmetric th))
+                (pure ctxt' (Thm.rhs_of th))
+ end
+
+ fun norm_arith_tac ctxt =
+   clarify_tac HOL_cs THEN'
+   Object_Logic.full_atomize_tac THEN'
+   CSUBGOAL ( fn (p,i) => rtac (norm_arith ctxt (Thm.dest_arg p )) i);
+
+end;
diff -r fdefcbcb2887 -r 524a3172db5b src/HOL/Tools/Function/function_core.ML
--- a/src/HOL/Tools/Function/function_core.ML	Sat May 15 07:48:24 2010 -0700
+++ b/src/HOL/Tools/Function/function_core.ML	Sat May 15 18:29:18 2010 +0200
@@ -617,7 +617,7 @@
         local open Conv in
           val lhs_D = fconv_rule (arg_conv (arg_conv (case_hyp_conv))) x_D
           val sih =
-            fconv_rule (More_Conv.binder_conv
+            fconv_rule (Conv.binder_conv
               (K (arg1_conv (arg_conv (arg_conv case_hyp_conv)))) ctxt) aihyp
         end
 
diff -r fdefcbcb2887 -r 524a3172db5b src/HOL/Tools/Quotient/quotient_tacs.ML
--- a/src/HOL/Tools/Quotient/quotient_tacs.ML	Sat May 15 07:48:24 2010 -0700
+++ b/src/HOL/Tools/Quotient/quotient_tacs.ML	Sat May 15 18:29:18 2010 +0200
@@ -490,7 +490,7 @@
       end
   | _ => Conv.all_conv ctrm
 
-fun lambda_prs_conv ctxt = More_Conv.top_conv lambda_prs_simple_conv ctxt
+fun lambda_prs_conv ctxt = Conv.top_conv lambda_prs_simple_conv ctxt
 fun lambda_prs_tac ctxt = CONVERSION (lambda_prs_conv ctxt)
 
 
diff -r fdefcbcb2887 -r 524a3172db5b src/HOL/Tools/SMT/smt_normalize.ML
--- a/src/HOL/Tools/SMT/smt_normalize.ML	Sat May 15 07:48:24 2010 -0700
+++ b/src/HOL/Tools/SMT/smt_normalize.ML	Sat May 15 18:29:18 2010 +0200
@@ -47,11 +47,11 @@
     "distinct [x, y] == (x ~= y)"
     by simp_all}
   fun distinct_conv _ =
-    if_true_conv is_trivial_distinct (More_Conv.rewrs_conv thms)
+    if_true_conv is_trivial_distinct (Conv.rewrs_conv thms)
 in
 fun trivial_distinct ctxt =
   map ((Term.exists_subterm is_trivial_distinct o Thm.prop_of) ??
-    Conv.fconv_rule (More_Conv.top_conv distinct_conv ctxt))
+    Conv.fconv_rule (Conv.top_conv distinct_conv ctxt))
 end
 
 
@@ -67,11 +67,11 @@
     "(case P of True => x | False => y) == (if P then x else y)"
     "(case P of False => y | True => x) == (if P then x else y)"
     by (rule eq_reflection, simp)+}
-  val unfold_conv = if_true_conv is_bool_case (More_Conv.rewrs_conv thms)
+  val unfold_conv = if_true_conv is_bool_case (Conv.rewrs_conv thms)
 in
 fun rewrite_bool_cases ctxt =
   map ((Term.exists_subterm is_bool_case o Thm.prop_of) ??
-    Conv.fconv_rule (More_Conv.top_conv (K unfold_conv) ctxt))
+    Conv.fconv_rule (Conv.top_conv (K unfold_conv) ctxt))
 end
 
 
@@ -107,7 +107,7 @@
 in
 fun normalize_numerals ctxt =
   map ((Term.exists_subterm (is_strange_number ctxt) o Thm.prop_of) ??
-    Conv.fconv_rule (More_Conv.top_sweep_conv pos_conv ctxt))
+    Conv.fconv_rule (Conv.top_sweep_conv pos_conv ctxt))
 end
 
 
@@ -193,7 +193,7 @@
 local
   val eta_conv = eta_expand_conv
 
-  fun keep_conv ctxt = More_Conv.binder_conv norm_conv ctxt
+  fun keep_conv ctxt = Conv.binder_conv (norm_conv o snd) ctxt
   and eta_binder_conv ctxt = Conv.arg_conv (eta_conv norm_conv ctxt)
   and keep_let_conv ctxt = Conv.combination_conv
     (Conv.arg_conv (norm_conv ctxt)) (Conv.abs_conv (norm_conv o snd) ctxt)
@@ -267,7 +267,7 @@
       Conv.binop_conv (atomize_conv ctxt) then_conv
       Conv.rewr_conv @{thm atomize_eq}
   | Const (@{const_name all}, _) $ Abs _ =>
-      More_Conv.binder_conv atomize_conv ctxt then_conv
+      Conv.binder_conv (atomize_conv o snd) ctxt then_conv
       Conv.rewr_conv @{thm atomize_all}
   | _ => Conv.all_conv) ct
 
diff -r fdefcbcb2887 -r 524a3172db5b src/HOL/Tools/SMT/smtlib_interface.ML
--- a/src/HOL/Tools/SMT/smtlib_interface.ML	Sat May 15 07:48:24 2010 -0700
+++ b/src/HOL/Tools/SMT/smtlib_interface.ML	Sat May 15 18:29:18 2010 +0200
@@ -81,7 +81,7 @@
 
 fun unfold_abs_min_max_defs ctxt thm =
   if exists_abs_min_max (Thm.prop_of thm)
-  then Conv.fconv_rule (More_Conv.top_conv unfold_def_conv ctxt) thm
+  then Conv.fconv_rule (Conv.top_conv unfold_def_conv ctxt) thm
   else thm
 
 
diff -r fdefcbcb2887 -r 524a3172db5b src/HOL/Tools/SMT/z3_proof_reconstruction.ML
--- a/src/HOL/Tools/SMT/z3_proof_reconstruction.ML	Sat May 15 07:48:24 2010 -0700
+++ b/src/HOL/Tools/SMT/z3_proof_reconstruction.ML	Sat May 15 18:29:18 2010 +0200
@@ -540,7 +540,7 @@
 
   fun elim_unused_conv ctxt =
     Conv.params_conv ~1 (K (Conv.arg_conv (Conv.arg1_conv
-      (More_Conv.rewrs_conv [elim_all, elim_ex])))) ctxt
+      (Conv.rewrs_conv [elim_all, elim_ex])))) ctxt
 
   fun elim_unused_tac ctxt =
     REPEAT_ALL_NEW (
diff -r fdefcbcb2887 -r 524a3172db5b src/HOL/Tools/SMT/z3_proof_tools.ML
--- a/src/HOL/Tools/SMT/z3_proof_tools.ML	Sat May 15 07:48:24 2010 -0700
+++ b/src/HOL/Tools/SMT/z3_proof_tools.ML	Sat May 15 18:29:18 2010 +0200
@@ -96,7 +96,7 @@
 
 fun unfold_eqs _ [] = Conv.all_conv
   | unfold_eqs ctxt eqs =
-      More_Conv.top_sweep_conv (K (More_Conv.rewrs_conv eqs)) ctxt
+      Conv.top_sweep_conv (K (Conv.rewrs_conv eqs)) ctxt
 
 fun match_instantiate f ct thm =
   Thm.instantiate (Thm.match (f (Thm.cprop_of thm), ct)) thm
@@ -256,7 +256,7 @@
   val set5 = @{lemma "x ~: set (y # ys) == x ~= y & x ~: set ys" by simp}
 
   fun set_conv ct =
-    (More_Conv.rewrs_conv [set1, set2, set3, set4] else_conv
+    (Conv.rewrs_conv [set1, set2, set3, set4] else_conv
     (Conv.rewr_conv set5 then_conv Conv.arg_conv set_conv)) ct
 
   val dist1 = @{lemma "distinct [] == ~False" by simp}
@@ -267,7 +267,7 @@
   fun binop_conv cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
 in
 fun unfold_distinct_conv ct =
-  (More_Conv.rewrs_conv [dist1, dist2] else_conv
+  (Conv.rewrs_conv [dist1, dist2] else_conv
   (Conv.rewr_conv dist3 then_conv binop_conv set_conv unfold_distinct_conv)) ct
 end
 
diff -r fdefcbcb2887 -r 524a3172db5b src/Pure/axclass.ML
--- a/src/Pure/axclass.ML	Sat May 15 07:48:24 2010 -0700
+++ b/src/Pure/axclass.ML	Sat May 15 18:29:18 2010 +0200
@@ -412,8 +412,6 @@
 
 (* primitive rules *)
 
-val shyps_topped = forall null o #shyps o Thm.rep_thm;
-
 fun add_classrel raw_th thy =
   let
     val th = Thm.strip_shyps (Thm.transfer thy raw_th);
@@ -422,9 +420,8 @@
     val rel = Logic.dest_classrel prop handle TERM _ => err ();
     val (c1, c2) = cert_classrel thy rel handle TYPE _ => err ();
     val th' = th
-      |> Drule.instantiate' [SOME (ctyp_of thy (TVar ((Name.aT, 0), [c1])))] []
-      |> Thm.unconstrainT;
-    val _ = shyps_topped th' orelse raise Fail "add_classrel: nontop shyps after unconstrain";
+      |> Thm.unconstrainT
+      |> Drule.instantiate' [SOME (ctyp_of thy (TVar ((Name.aT, 0), [])))] [];
   in
     thy
     |> Sign.primitive_classrel (c1, c2)
@@ -441,16 +438,15 @@
 
     val args = Name.names Name.context Name.aT Ss;
     val T = Type (t, map TFree args);
-    val std_vars = map (fn (a, S) => SOME (ctyp_of thy (TVar ((a, 0), S)))) args;
+    val std_vars = map (fn (a, S) => SOME (ctyp_of thy (TVar ((a, 0), [])))) args;
 
     val missing_params = Sign.complete_sort thy [c]
       |> maps (these o Option.map #params o try (get_info thy))
       |> filter_out (fn (const, _) => can (get_inst_param thy) (const, t))
       |> (map o apsnd o map_atyps) (K T);
     val th' = th
-      |> Drule.instantiate' std_vars []
-      |> Thm.unconstrainT;
-    val _ = shyps_topped th' orelse raise Fail "add_arity: nontop shyps after unconstrain";
+      |> Thm.unconstrainT
+      |> Drule.instantiate' std_vars [];
   in
     thy
     |> fold (#2 oo declare_overloaded) missing_params
diff -r fdefcbcb2887 -r 524a3172db5b src/Pure/conv.ML
--- a/src/Pure/conv.ML	Sat May 15 07:48:24 2010 -0700
+++ b/src/Pure/conv.ML	Sat May 15 18:29:18 2010 +0200
@@ -1,5 +1,6 @@
 (*  Title:      Pure/conv.ML
     Author:     Amine Chaieb, TU Muenchen
+    Author:     Sascha Boehme, TU Muenchen
     Author:     Makarius
 
 Conversions: primitive equality reasoning.
@@ -32,10 +33,16 @@
   val arg1_conv: conv -> conv
   val fun2_conv: conv -> conv
   val binop_conv: conv -> conv
+  val binder_conv: (cterm * Proof.context -> conv) -> Proof.context -> conv
   val forall_conv: (cterm * Proof.context -> conv) -> Proof.context -> conv
   val implies_conv: conv -> conv -> conv
   val implies_concl_conv: conv -> conv
   val rewr_conv: thm -> conv
+  val rewrs_conv: thm list -> conv
+  val sub_conv: (Proof.context -> conv) -> Proof.context -> conv
+  val bottom_conv: (Proof.context -> conv) -> Proof.context -> conv
+  val top_conv: (Proof.context -> conv) -> Proof.context -> conv
+  val top_sweep_conv: (Proof.context -> conv) -> Proof.context -> conv
   val params_conv: int -> (Proof.context -> conv) -> Proof.context -> conv
   val prems_conv: int -> conv -> conv
   val concl_conv: int -> conv -> conv
@@ -105,6 +112,29 @@
 
 fun binop_conv cv = combination_conv (arg_conv cv) cv;
 
+fun binder_conv cv ctxt = arg_conv (abs_conv cv ctxt);
+
+
+(* subterm structure *)
+
+(*cf. SUB_CONV in HOL*)
+fun sub_conv conv ctxt =
+  comb_conv (conv ctxt) else_conv
+  abs_conv (conv o snd) ctxt else_conv
+  all_conv;
+
+(*cf. BOTTOM_CONV in HOL*)
+fun bottom_conv conv ctxt ct =
+  (sub_conv (bottom_conv conv) ctxt then_conv conv ctxt) ct;
+
+(*cf. TOP_CONV in HOL*)
+fun top_conv conv ctxt ct =
+  (conv ctxt then_conv sub_conv (top_conv conv) ctxt) ct;
+
+(*cf. TOP_SWEEP_CONV in HOL*)
+fun top_sweep_conv conv ctxt ct =
+  (conv ctxt else_conv sub_conv (top_sweep_conv conv) ctxt) ct;
+
 
 (* primitive logic *)
 
@@ -136,6 +166,8 @@
       handle Pattern.MATCH => raise CTERM ("rewr_conv", [lhs, ct])
   end;
 
+fun rewrs_conv rules = first_conv (map rewr_conv rules);
+
 
 (* conversions on HHF rules *)
 
diff -r fdefcbcb2887 -r 524a3172db5b src/Tools/more_conv.ML
--- a/src/Tools/more_conv.ML	Sat May 15 07:48:24 2010 -0700
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,43 +0,0 @@
-(*  Title:       Tools/more_conv.ML
-    Author:      Sascha Boehme, TU Muenchen
-
-Further conversions and conversionals.
-*)
-
-signature MORE_CONV =
-sig
-  val rewrs_conv: thm list -> conv
-
-  val sub_conv: (Proof.context -> conv) -> Proof.context -> conv
-  val bottom_conv: (Proof.context -> conv) -> Proof.context -> conv
-  val top_conv: (Proof.context -> conv) -> Proof.context -> conv
-  val top_sweep_conv: (Proof.context -> conv) -> Proof.context -> conv
-
-  val binder_conv: (Proof.context -> conv) -> Proof.context -> conv
-end
-
-structure More_Conv : MORE_CONV =
-struct
-
-fun rewrs_conv eqs = Conv.first_conv (map Conv.rewr_conv eqs)
-
-
-fun sub_conv conv ctxt =
-  Conv.comb_conv (conv ctxt) else_conv
-  Conv.abs_conv (fn (_, cx) => conv cx) ctxt else_conv
-  Conv.all_conv
-
-fun bottom_conv conv ctxt ct =
-  (sub_conv (bottom_conv conv) ctxt then_conv conv ctxt) ct
-
-fun top_conv conv ctxt ct =
-  (conv ctxt then_conv sub_conv (top_conv conv) ctxt) ct
-
-fun top_sweep_conv conv ctxt ct =
-  (conv ctxt else_conv sub_conv (top_sweep_conv conv) ctxt) ct
-
-
-fun binder_conv cv ctxt =
-  Conv.arg_conv (Conv.abs_conv (fn (_, cx) => cv cx) ctxt)
-
-end