merged
authorhaftmann
Mon, 22 Feb 2010 09:24:20 +0100
changeset 35296 975b34b6cf5b
parent 35275 3745987488b2 (diff)
parent 35295 397295fa8387 (current diff)
child 35297 601ba79217e9
merged
src/HOL/List.thy
--- a/NEWS	Sat Feb 20 21:13:29 2010 +0100
+++ b/NEWS	Mon Feb 22 09:24:20 2010 +0100
@@ -4,6 +4,41 @@
 New in this Isabelle version
 ----------------------------
 
+*** General ***
+
+* Authentic syntax for *all* term constants: provides simple and
+robust correspondence between formal entities and concrete syntax.
+Substantial INCOMPATIBILITY concerning low-level syntax translations
+(translation rules and translation functions in ML).  Some hints on
+upgrading:
+
+  - Many existing uses of 'syntax' and 'translations' can be replaced
+    by more modern 'notation' and 'abbreviation', which are
+    independent of this issue.
+
+  - 'translations' require markup within the AST; the term syntax
+    provides the following special forms:
+
+      CONST c   -- produces syntax version of constant c from context
+      XCONST c  -- literally c, checked as constant from context
+      c         -- literally c, if declared by 'syntax'
+
+    Plain identifiers are treated as AST variables -- occasionally the
+    system indicates accidental variables via the error "rhs contains
+    extra variables".
+
+  - 'parse_translation' etc. in ML may use the following
+    antiquotations:
+
+      @{const_syntax c}   -- ML version of "CONST c" above
+      @{syntax_const c}   -- literally c (checked wrt. 'syntax' declarations)
+
+Note that old non-authentic syntax was based on unqualified base
+names, so all of the above would coincide.  Recall that 'print_syntax'
+and ML_command "set Syntax.trace_ast" help to diagnose syntax
+problems.
+
+
 *** Pure ***
 
 * Code generator: details of internal data cache have no impact on
@@ -17,6 +52,12 @@
 
 *** HOL ***
 
+* Multisets: changed orderings:
+  * pointwise ordering is instance of class order with standard syntax <= and <;
+  * multiset ordering has syntax <=# and <#; partial order properties are provided
+      by means of interpretation with prefix multiset_order.
+INCOMPATIBILITY.
+
 * New set of rules "ac_simps" provides combined assoc / commute rewrites
 for all interpretations of the appropriate generic locales.
 
@@ -28,7 +69,7 @@
 * Some generic constants have been put to appropriate theories:
 
     less_eq, less: Orderings
-    abs, sgn: Groups
+    zero, one, plus, minus, uminus, times, abs, sgn: Groups
     inverse, divide: Rings
 
 INCOMPATIBILITY.
@@ -88,8 +129,7 @@
 INCOMPATIBILITY.
 
 * New theory Algebras contains generic algebraic structures and
-generic algebraic operations.  INCOMPATIBILTY: constants zero, one,
-plus, minus, uminus and times have been moved from HOL.thy to Algebras.thy.
+generic algebraic operations.
 
 * HOLogic.strip_psplit: types are returned in syntactic order, similar
 to other strip and tuple operations.  INCOMPATIBILITY.
@@ -98,10 +138,11 @@
 replaced by new-style primrec, especially in theory List.  The corresponding
 constants now have authentic syntax.  INCOMPATIBILITY.
 
-* Reorganized theory Multiset: less duplication, less historical
-organization of sections, conversion from associations lists to
-multisets, rudimentary code generation.  Use insert_DiffM2 [symmetric]
-instead of elem_imp_eq_diff_union, if needed.  INCOMPATIBILITY.
+* Reorganized theory Multiset: swapped notation of pointwise and multiset
+order;  less duplication, less historical organization of sections,
+conversion from associations lists to multisets, rudimentary code generation.
+Use insert_DiffM2 [symmetric] instead of elem_imp_eq_diff_union, if needed.
+INCOMPATIBILITY.
 
 * Reorganized theory Sum_Type; Inl and Inr now have authentic syntax.
 INCOMPATIBILITY.
--- a/src/Cube/Cube.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Cube/Cube.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -18,43 +18,43 @@
   context' typing'
 
 consts
-  Abs           :: "[term, term => term] => term"
-  Prod          :: "[term, term => term] => term"
-  Trueprop      :: "[context, typing] => prop"
-  MT_context    :: "context"
-  Context       :: "[typing, context] => context"
-  star          :: "term"                               ("*")
-  box           :: "term"                               ("[]")
-  app           :: "[term, term] => term"               (infixl "^" 20)
-  Has_type      :: "[term, term] => typing"
+  Abs :: "[term, term => term] => term"
+  Prod :: "[term, term => term] => term"
+  Trueprop :: "[context, typing] => prop"
+  MT_context :: "context"
+  Context :: "[typing, context] => context"
+  star :: "term"    ("*")
+  box :: "term"    ("[]")
+  app :: "[term, term] => term"    (infixl "^" 20)
+  Has_type :: "[term, term] => typing"
 
 syntax
-  Trueprop      :: "[context', typing'] => prop"        ("(_/ |- _)")
-  Trueprop1     :: "typing' => prop"                    ("(_)")
-  ""            :: "id => context'"                     ("_")
-  ""            :: "var => context'"                    ("_")
-  MT_context    :: "context'"                           ("")
-  Context       :: "[typing', context'] => context'"    ("_ _")
-  Has_type      :: "[term, term] => typing'"            ("(_:/ _)" [0, 0] 5)
-  Lam           :: "[idt, term, term] => term"          ("(3Lam _:_./ _)" [0, 0, 0] 10)
-  Pi            :: "[idt, term, term] => term"          ("(3Pi _:_./ _)" [0, 0] 10)
-  arrow         :: "[term, term] => term"               (infixr "->" 10)
+  "\<^const>Cube.Trueprop" :: "[context', typing'] => prop"    ("(_/ |- _)")
+  "_Trueprop1" :: "typing' => prop"    ("(_)")
+  "" :: "id => context'"    ("_")
+  "" :: "var => context'"    ("_")
+  "\<^const>Cube.MT_context" :: "context'"    ("")
+  "\<^const>Cube.Context" :: "[typing', context'] => context'"    ("_ _")
+  "\<^const>Cube.Has_type" :: "[term, term] => typing'"    ("(_:/ _)" [0, 0] 5)
+  "_Lam" :: "[idt, term, term] => term"    ("(3Lam _:_./ _)" [0, 0, 0] 10)
+  "_Pi" :: "[idt, term, term] => term"    ("(3Pi _:_./ _)" [0, 0] 10)
+  "_arrow" :: "[term, term] => term"    (infixr "->" 10)
 
 translations
   ("prop") "x:X" == ("prop") "|- x:X"
-  "Lam x:A. B"   == "CONST Abs(A, %x. B)"
-  "Pi x:A. B"    => "CONST Prod(A, %x. B)"
-  "A -> B"       => "CONST Prod(A, %_. B)"
+  "Lam x:A. B" == "CONST Abs(A, %x. B)"
+  "Pi x:A. B" => "CONST Prod(A, %x. B)"
+  "A -> B" => "CONST Prod(A, %_. B)"
 
 syntax (xsymbols)
-  Trueprop      :: "[context', typing'] => prop"        ("(_/ \<turnstile> _)")
-  box           :: "term"                               ("\<box>")
-  Lam           :: "[idt, term, term] => term"          ("(3\<Lambda> _:_./ _)" [0, 0, 0] 10)
-  Pi            :: "[idt, term, term] => term"          ("(3\<Pi> _:_./ _)" [0, 0] 10)
-  arrow         :: "[term, term] => term"               (infixr "\<rightarrow>" 10)
+  "\<^const>Cube.Trueprop" :: "[context', typing'] => prop"    ("(_/ \<turnstile> _)")
+  "\<^const>Cube.box" :: "term"    ("\<box>")
+  "_Lam" :: "[idt, term, term] => term"    ("(3\<Lambda> _:_./ _)" [0, 0, 0] 10)
+  "_Pi" :: "[idt, term, term] => term"    ("(3\<Pi> _:_./ _)" [0, 0] 10)
+  "_arrow" :: "[term, term] => term"    (infixr "\<rightarrow>" 10)
 
 print_translation {*
-  [(@{const_syntax Prod}, dependent_tr' (@{syntax_const Pi}, @{syntax_const arrow}))]
+  [(@{const_syntax Prod}, dependent_tr' (@{syntax_const "_Pi"}, @{syntax_const "_arrow"}))]
 *}
 
 axioms
--- a/src/HOL/Algebra/Divisibility.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Algebra/Divisibility.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -2250,7 +2250,7 @@
   assumes ab: "a divides b"
     and afs: "wfactors G as a" and bfs: "wfactors G bs b"
     and carr: "a \<in> carrier G"  "b \<in> carrier G"  "set as \<subseteq> carrier G"  "set bs \<subseteq> carrier G"
-  shows "fmset G as \<le># fmset G bs"
+  shows "fmset G as \<le> fmset G bs"
 using ab
 proof (elim dividesE)
   fix c
@@ -2270,7 +2270,7 @@
 qed
 
 lemma (in comm_monoid_cancel) fmsubset_divides:
-  assumes msubset: "fmset G as \<le># fmset G bs"
+  assumes msubset: "fmset G as \<le> fmset G bs"
     and afs: "wfactors G as a" and bfs: "wfactors G bs b"
     and acarr: "a \<in> carrier G" and bcarr: "b \<in> carrier G"
     and ascarr: "set as \<subseteq> carrier G" and bscarr: "set bs \<subseteq> carrier G"
@@ -2323,7 +2323,7 @@
   assumes "wfactors G as a" and "wfactors G bs b"
     and "a \<in> carrier G" and "b \<in> carrier G" 
     and "set as \<subseteq> carrier G" and "set bs \<subseteq> carrier G"
-  shows "a divides b = (fmset G as \<le># fmset G bs)"
+  shows "a divides b = (fmset G as \<le> fmset G bs)"
 using assms
 by (blast intro: divides_fmsubset fmsubset_divides)
 
@@ -2331,7 +2331,7 @@
 text {* Proper factors on multisets *}
 
 lemma (in factorial_monoid) fmset_properfactor:
-  assumes asubb: "fmset G as \<le># fmset G bs"
+  assumes asubb: "fmset G as \<le> fmset G bs"
     and anb: "fmset G as \<noteq> fmset G bs"
     and "wfactors G as a" and "wfactors G bs b"
     and "a \<in> carrier G" and "b \<in> carrier G"
@@ -2341,10 +2341,10 @@
 apply (rule fmsubset_divides[of as bs], fact+)
 proof
   assume "b divides a"
-  hence "fmset G bs \<le># fmset G as"
+  hence "fmset G bs \<le> fmset G as"
       by (rule divides_fmsubset) fact+
   with asubb
-      have "fmset G as = fmset G bs" by (simp add: mset_le_antisym)
+      have "fmset G as = fmset G bs" by (rule order_antisym)
   with anb
       show "False" ..
 qed
@@ -2354,7 +2354,7 @@
     and "wfactors G as a" and "wfactors G bs b"
     and "a \<in> carrier G" and "b \<in> carrier G"
     and "set as \<subseteq> carrier G" and "set bs \<subseteq> carrier G"
-  shows "fmset G as \<le># fmset G bs \<and> fmset G as \<noteq> fmset G bs"
+  shows "fmset G as \<le> fmset G bs \<and> fmset G as \<noteq> fmset G bs"
 using pf
 apply (elim properfactorE)
 apply rule
@@ -2738,12 +2738,12 @@
   have "c gcdof a b"
   proof (simp add: isgcd_def, safe)
     from csmset
-        have "fmset G cs \<le># fmset G as"
+        have "fmset G cs \<le> fmset G as"
         by (simp add: multiset_inter_def mset_le_def)
     thus "c divides a" by (rule fmsubset_divides) fact+
   next
     from csmset
-        have "fmset G cs \<le># fmset G bs"
+        have "fmset G cs \<le> fmset G bs"
         by (simp add: multiset_inter_def mset_le_def, force)
     thus "c divides b" by (rule fmsubset_divides) fact+
   next
@@ -2756,13 +2756,13 @@
         by auto
 
     assume "y divides a"
-    hence ya: "fmset G ys \<le># fmset G as" by (rule divides_fmsubset) fact+
+    hence ya: "fmset G ys \<le> fmset G as" by (rule divides_fmsubset) fact+
 
     assume "y divides b"
-    hence yb: "fmset G ys \<le># fmset G bs" by (rule divides_fmsubset) fact+
+    hence yb: "fmset G ys \<le> fmset G bs" by (rule divides_fmsubset) fact+
 
     from ya yb csmset
-    have "fmset G ys \<le># fmset G cs" by (simp add: mset_le_def multiset_inter_count)
+    have "fmset G ys \<le> fmset G cs" by (simp add: mset_le_def multiset_inter_count)
     thus "y divides c" by (rule fmsubset_divides) fact+
   qed
 
@@ -2837,10 +2837,10 @@
 
   have "c lcmof a b"
   proof (simp add: islcm_def, safe)
-    from csmset have "fmset G as \<le># fmset G cs" by (simp add: mset_le_def, force)
+    from csmset have "fmset G as \<le> fmset G cs" by (simp add: mset_le_def, force)
     thus "a divides c" by (rule fmsubset_divides) fact+
   next
-    from csmset have "fmset G bs \<le># fmset G cs" by (simp add: mset_le_def)
+    from csmset have "fmset G bs \<le> fmset G cs" by (simp add: mset_le_def)
     thus "b divides c" by (rule fmsubset_divides) fact+
   next
     fix y
@@ -2852,13 +2852,13 @@
         by auto
 
     assume "a divides y"
-    hence ya: "fmset G as \<le># fmset G ys" by (rule divides_fmsubset) fact+
+    hence ya: "fmset G as \<le> fmset G ys" by (rule divides_fmsubset) fact+
 
     assume "b divides y"
-    hence yb: "fmset G bs \<le># fmset G ys" by (rule divides_fmsubset) fact+
+    hence yb: "fmset G bs \<le> fmset G ys" by (rule divides_fmsubset) fact+
 
     from ya yb csmset
-    have "fmset G cs \<le># fmset G ys"
+    have "fmset G cs \<le> fmset G ys"
       apply (simp add: mset_le_def, clarify)
       apply (case_tac "count (fmset G as) a < count (fmset G bs) a")
        apply simp
--- a/src/HOL/Algebra/abstract/Ring2.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Algebra/abstract/Ring2.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -205,8 +205,8 @@
 ML {*
 fun ring_ord (Const (a, _)) =
     find_index (fn a' => a = a')
-      [@{const_name Algebras.zero}, @{const_name Algebras.plus}, @{const_name Algebras.uminus},
-        @{const_name Algebras.minus}, @{const_name Algebras.one}, @{const_name Algebras.times}]
+      [@{const_name Groups.zero}, @{const_name Groups.plus}, @{const_name Groups.uminus},
+        @{const_name Groups.minus}, @{const_name Groups.one}, @{const_name Groups.times}]
   | ring_ord _ = ~1;
 
 fun termless_ring (a, b) = (TermOrd.term_lpo ring_ord (a, b) = LESS);
--- a/src/HOL/Algebras.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Algebras.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -8,8 +8,6 @@
 imports HOL
 begin
 
-subsection {* Generic algebraic structures *}
-
 text {*
   These locales provide basic structures for interpretation into
   bigger structures;  extensions require careful thinking, otherwise
@@ -54,58 +52,4 @@
 
 end
 
-
-subsection {* Generic syntactic operations *}
-
-class zero = 
-  fixes zero :: 'a  ("0")
-
-class one =
-  fixes one  :: 'a  ("1")
-
-hide (open) const zero one
-
-syntax
-  "_index1"  :: index    ("\<^sub>1")
-translations
-  (index) "\<^sub>1" => (index) "\<^bsub>\<struct>\<^esub>"
-
-lemma Let_0 [simp]: "Let 0 f = f 0"
-  unfolding Let_def ..
-
-lemma Let_1 [simp]: "Let 1 f = f 1"
-  unfolding Let_def ..
-
-setup {*
-  Reorient_Proc.add
-    (fn Const(@{const_name Algebras.zero}, _) => true
-      | Const(@{const_name Algebras.one}, _) => true
-      | _ => false)
-*}
-
-simproc_setup reorient_zero ("0 = x") = Reorient_Proc.proc
-simproc_setup reorient_one ("1 = x") = Reorient_Proc.proc
-
-typed_print_translation {*
-let
-  fun tr' c = (c, fn show_sorts => fn T => fn ts =>
-    if (not o null) ts orelse T = dummyT
-      orelse not (! show_types) andalso can Term.dest_Type T
-    then raise Match
-    else Syntax.const Syntax.constrainC $ Syntax.const c $ Syntax.term_of_typ show_sorts T);
-in map tr' [@{const_syntax Algebras.one}, @{const_syntax Algebras.zero}] end;
-*} -- {* show types that are presumably too general *}
-
-class plus =
-  fixes plus :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"  (infixl "+" 65)
-
-class minus =
-  fixes minus :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"  (infixl "-" 65)
-
-class uminus =
-  fixes uminus :: "'a \<Rightarrow> 'a"  ("- _" [81] 80)
-
-class times =
-  fixes times :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"  (infixl "*" 70)
-
 end
\ No newline at end of file
--- a/src/HOL/Decision_Procs/Dense_Linear_Order.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Decision_Procs/Dense_Linear_Order.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -670,13 +670,13 @@
  end
 
 fun whatis x ct = case term_of ct of
-  Const(@{const_name Algebras.plus}, _)$(Const(@{const_name Algebras.times},_)$_$y)$_ =>
+  Const(@{const_name Groups.plus}, _)$(Const(@{const_name Groups.times},_)$_$y)$_ =>
      if y aconv term_of x then ("c*x+t",[(funpow 2 Thm.dest_arg1) ct, Thm.dest_arg ct])
      else ("Nox",[])
-| Const(@{const_name Algebras.plus}, _)$y$_ =>
+| Const(@{const_name Groups.plus}, _)$y$_ =>
      if y aconv term_of x then ("x+t",[Thm.dest_arg ct])
      else ("Nox",[])
-| Const(@{const_name Algebras.times}, _)$_$y =>
+| Const(@{const_name Groups.times}, _)$_$y =>
      if y aconv term_of x then ("c*x",[Thm.dest_arg1 ct])
      else ("Nox",[])
 | t => if t aconv term_of x then ("x",[]) else ("Nox",[]);
@@ -684,7 +684,7 @@
 fun xnormalize_conv ctxt [] ct = reflexive ct
 | xnormalize_conv ctxt (vs as (x::_)) ct =
    case term_of ct of
-   Const(@{const_name Orderings.less},_)$_$Const(@{const_name Algebras.zero},_) =>
+   Const(@{const_name Orderings.less},_)$_$Const(@{const_name Groups.zero},_) =>
     (case whatis x (Thm.dest_arg1 ct) of
     ("c*x+t",[c,t]) =>
        let
@@ -727,7 +727,7 @@
     | _ => reflexive ct)
 
 
-|  Const(@{const_name Orderings.less_eq},_)$_$Const(@{const_name Algebras.zero},_) =>
+|  Const(@{const_name Orderings.less_eq},_)$_$Const(@{const_name Groups.zero},_) =>
    (case whatis x (Thm.dest_arg1 ct) of
     ("c*x+t",[c,t]) =>
        let
@@ -771,7 +771,7 @@
       in rth end
     | _ => reflexive ct)
 
-|  Const("op =",_)$_$Const(@{const_name Algebras.zero},_) =>
+|  Const("op =",_)$_$Const(@{const_name Groups.zero},_) =>
    (case whatis x (Thm.dest_arg1 ct) of
     ("c*x+t",[c,t]) =>
        let
--- a/src/HOL/Decision_Procs/Parametric_Ferrante_Rackoff.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Decision_Procs/Parametric_Ferrante_Rackoff.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -2947,10 +2947,10 @@
 fun rrelT rT = [rT,rT] ---> rT;
 fun rrT rT = [rT, rT] ---> bT;
 fun divt rT = Const(@{const_name Rings.divide},rrelT rT);
-fun timest rT = Const(@{const_name Algebras.times},rrelT rT);
-fun plust rT = Const(@{const_name Algebras.plus},rrelT rT);
-fun minust rT = Const(@{const_name Algebras.minus},rrelT rT);
-fun uminust rT = Const(@{const_name Algebras.uminus}, rT --> rT);
+fun timest rT = Const(@{const_name Groups.times},rrelT rT);
+fun plust rT = Const(@{const_name Groups.plus},rrelT rT);
+fun minust rT = Const(@{const_name Groups.minus},rrelT rT);
+fun uminust rT = Const(@{const_name Groups.uminus}, rT --> rT);
 fun powt rT = Const(@{const_name "power"}, [rT,@{typ "nat"}] ---> rT);
 val brT = [bT, bT] ---> bT;
 val nott = @{term "Not"};
@@ -2961,7 +2961,7 @@
 fun llt rT = Const(@{const_name Orderings.less},rrT rT);
 fun lle rT = Const(@{const_name Orderings.less},rrT rT);
 fun eqt rT = Const("op =",rrT rT);
-fun rz rT = Const(@{const_name Algebras.zero},rT);
+fun rz rT = Const(@{const_name Groups.zero},rT);
 
 fun dest_nat t = case t of
   Const ("Suc",_)$t' => 1 + dest_nat t'
@@ -2969,10 +2969,10 @@
 
 fun num_of_term m t = 
  case t of
-   Const(@{const_name Algebras.uminus},_)$t => @{code poly.Neg} (num_of_term m t)
- | Const(@{const_name Algebras.plus},_)$a$b => @{code poly.Add} (num_of_term m a, num_of_term m b)
- | Const(@{const_name Algebras.minus},_)$a$b => @{code poly.Sub} (num_of_term m a, num_of_term m b)
- | Const(@{const_name Algebras.times},_)$a$b => @{code poly.Mul} (num_of_term m a, num_of_term m b)
+   Const(@{const_name Groups.uminus},_)$t => @{code poly.Neg} (num_of_term m t)
+ | Const(@{const_name Groups.plus},_)$a$b => @{code poly.Add} (num_of_term m a, num_of_term m b)
+ | Const(@{const_name Groups.minus},_)$a$b => @{code poly.Sub} (num_of_term m a, num_of_term m b)
+ | Const(@{const_name Groups.times},_)$a$b => @{code poly.Mul} (num_of_term m a, num_of_term m b)
  | Const(@{const_name Power.power},_)$a$n => @{code poly.Pw} (num_of_term m a, dest_nat n)
  | Const(@{const_name Rings.divide},_)$a$b => @{code poly.C} (HOLogic.dest_number a |> snd, HOLogic.dest_number b |> snd)
  | _ => (@{code poly.C} (HOLogic.dest_number t |> snd,1) 
@@ -2980,10 +2980,10 @@
 
 fun tm_of_term m m' t = 
  case t of
-   Const(@{const_name Algebras.uminus},_)$t => @{code Neg} (tm_of_term m m' t)
- | Const(@{const_name Algebras.plus},_)$a$b => @{code Add} (tm_of_term m m' a, tm_of_term m m' b)
- | Const(@{const_name Algebras.minus},_)$a$b => @{code Sub} (tm_of_term m m' a, tm_of_term m m' b)
- | Const(@{const_name Algebras.times},_)$a$b => @{code Mul} (num_of_term m' a, tm_of_term m m' b)
+   Const(@{const_name Groups.uminus},_)$t => @{code Neg} (tm_of_term m m' t)
+ | Const(@{const_name Groups.plus},_)$a$b => @{code Add} (tm_of_term m m' a, tm_of_term m m' b)
+ | Const(@{const_name Groups.minus},_)$a$b => @{code Sub} (tm_of_term m m' a, tm_of_term m m' b)
+ | Const(@{const_name Groups.times},_)$a$b => @{code Mul} (num_of_term m' a, tm_of_term m m' b)
  | _ => (@{code CP} (num_of_term m' t) 
          handle TERM _ => @{code Bound} (AList.lookup (op aconv) m t |> the)
               | Option => @{code Bound} (AList.lookup (op aconv) m t |> the));
--- a/src/HOL/Decision_Procs/commutative_ring_tac.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Decision_Procs/commutative_ring_tac.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -13,8 +13,8 @@
 struct
 
 (* Zero and One of the commutative ring *)
-fun cring_zero T = Const (@{const_name Algebras.zero}, T);
-fun cring_one T = Const (@{const_name Algebras.one}, T);
+fun cring_zero T = Const (@{const_name Groups.zero}, T);
+fun cring_one T = Const (@{const_name Groups.one}, T);
 
 (* reification functions *)
 (* add two polynom expressions *)
@@ -49,13 +49,13 @@
   | reif_pol T vs t = pol_Pc T $ t;
 
 (* reification of polynom expressions *)
-fun reif_polex T vs (Const (@{const_name Algebras.plus}, _) $ a $ b) =
+fun reif_polex T vs (Const (@{const_name Groups.plus}, _) $ a $ b) =
       polex_add T $ reif_polex T vs a $ reif_polex T vs b
-  | reif_polex T vs (Const (@{const_name Algebras.minus}, _) $ a $ b) =
+  | reif_polex T vs (Const (@{const_name Groups.minus}, _) $ a $ b) =
       polex_sub T $ reif_polex T vs a $ reif_polex T vs b
-  | reif_polex T vs (Const (@{const_name Algebras.times}, _) $ a $ b) =
+  | reif_polex T vs (Const (@{const_name Groups.times}, _) $ a $ b) =
       polex_mul T $ reif_polex T vs a $ reif_polex T vs b
-  | reif_polex T vs (Const (@{const_name Algebras.uminus}, _) $ a) =
+  | reif_polex T vs (Const (@{const_name Groups.uminus}, _) $ a) =
       polex_neg T $ reif_polex T vs a
   | reif_polex T vs (Const (@{const_name Power.power}, _) $ a $ n) =
       polex_pow T $ reif_polex T vs a $ n
--- a/src/HOL/Finite_Set.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Finite_Set.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -1055,7 +1055,7 @@
 
 subsection {* Generalized summation over a set *}
 
-interpretation comm_monoid_add: comm_monoid_mult "0::'a::comm_monoid_add" "op +"
+interpretation comm_monoid_add: comm_monoid_mult "op +" "0::'a::comm_monoid_add"
   proof qed (auto intro: add_assoc add_commute)
 
 definition setsum :: "('a => 'b) => 'a set => 'b::comm_monoid_add"
--- a/src/HOL/Groups.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Groups.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -6,9 +6,64 @@
 
 theory Groups
 imports Orderings
-uses "~~/src/Provers/Arith/abel_cancel.ML"
+uses ("~~/src/Provers/Arith/abel_cancel.ML")
 begin
 
+subsection {* Generic operations *}
+
+class zero = 
+  fixes zero :: 'a  ("0")
+
+class one =
+  fixes one  :: 'a  ("1")
+
+hide (open) const zero one
+
+syntax
+  "_index1"  :: index    ("\<^sub>1")
+translations
+  (index) "\<^sub>1" => (index) "\<^bsub>\<struct>\<^esub>"
+
+lemma Let_0 [simp]: "Let 0 f = f 0"
+  unfolding Let_def ..
+
+lemma Let_1 [simp]: "Let 1 f = f 1"
+  unfolding Let_def ..
+
+setup {*
+  Reorient_Proc.add
+    (fn Const(@{const_name Groups.zero}, _) => true
+      | Const(@{const_name Groups.one}, _) => true
+      | _ => false)
+*}
+
+simproc_setup reorient_zero ("0 = x") = Reorient_Proc.proc
+simproc_setup reorient_one ("1 = x") = Reorient_Proc.proc
+
+typed_print_translation {*
+let
+  fun tr' c = (c, fn show_sorts => fn T => fn ts =>
+    if (not o null) ts orelse T = dummyT
+      orelse not (! show_types) andalso can Term.dest_Type T
+    then raise Match
+    else Syntax.const Syntax.constrainC $ Syntax.const c $ Syntax.term_of_typ show_sorts T);
+in map tr' [@{const_syntax Groups.one}, @{const_syntax Groups.zero}] end;
+*} -- {* show types that are presumably too general *}
+
+class plus =
+  fixes plus :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"  (infixl "+" 65)
+
+class minus =
+  fixes minus :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"  (infixl "-" 65)
+
+class uminus =
+  fixes uminus :: "'a \<Rightarrow> 'a"  ("- _" [81] 80)
+
+class times =
+  fixes times :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"  (infixl "*" 70)
+
+use "~~/src/Provers/Arith/abel_cancel.ML"
+
 text {*
   The theory of partially ordered groups is taken from the books:
   \begin{itemize}
@@ -1129,8 +1184,8 @@
 (* term order for abelian groups *)
 
 fun agrp_ord (Const (a, _)) = find_index (fn a' => a = a')
-      [@{const_name Algebras.zero}, @{const_name Algebras.plus},
-        @{const_name Algebras.uminus}, @{const_name Algebras.minus}]
+      [@{const_name Groups.zero}, @{const_name Groups.plus},
+        @{const_name Groups.uminus}, @{const_name Groups.minus}]
   | agrp_ord _ = ~1;
 
 fun termless_agrp (a, b) = (TermOrd.term_lpo agrp_ord (a, b) = LESS);
@@ -1139,9 +1194,9 @@
   val ac1 = mk_meta_eq @{thm add_assoc};
   val ac2 = mk_meta_eq @{thm add_commute};
   val ac3 = mk_meta_eq @{thm add_left_commute};
-  fun solve_add_ac thy _ (_ $ (Const (@{const_name Algebras.plus},_) $ _ $ _) $ _) =
+  fun solve_add_ac thy _ (_ $ (Const (@{const_name Groups.plus},_) $ _ $ _) $ _) =
         SOME ac1
-    | solve_add_ac thy _ (_ $ x $ (Const (@{const_name Algebras.plus},_) $ y $ z)) =
+    | solve_add_ac thy _ (_ $ x $ (Const (@{const_name Groups.plus},_) $ y $ z)) =
         if termless_agrp (y, x) then SOME ac3 else NONE
     | solve_add_ac thy _ (_ $ x $ y) =
         if termless_agrp (y, x) then SOME ac2 else NONE
--- a/src/HOL/Import/Generate-HOL/GenHOL4Base.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Import/Generate-HOL/GenHOL4Base.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -182,9 +182,9 @@
   ">="         > HOL4Compat.nat_ge
   FUNPOW       > HOL4Compat.FUNPOW
   "<="         > Orderings.less_eq :: "[nat,nat]=>bool"
-  "+"          > Algebras.plus :: "[nat,nat]=>nat"
-  "*"          > Algebras.times :: "[nat,nat]=>nat"
-  "-"          > Algebras.minus :: "[nat,nat]=>nat"
+  "+"          > Groups.plus :: "[nat,nat]=>nat"
+  "*"          > Groups.times :: "[nat,nat]=>nat"
+  "-"          > Groups.minus :: "[nat,nat]=>nat"
   MIN          > Orderings.min :: "[nat,nat]=>nat"
   MAX          > Orderings.max :: "[nat,nat]=>nat"
   DIV          > Divides.div :: "[nat,nat]=>nat"
--- a/src/HOL/Import/Generate-HOL/GenHOL4Real.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Import/Generate-HOL/GenHOL4Real.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -16,12 +16,12 @@
   real > RealDef.real;
 
 const_maps
-  real_0   > Algebras.zero      :: real
-  real_1   > Algebras.one       :: real
-  real_neg > Algebras.uminus    :: "real => real"
-  inv      > Algebras.inverse   :: "real => real"
-  real_add > Algebras.plus      :: "[real,real] => real"
-  real_mul > Algebras.times     :: "[real,real] => real"
+  real_0   > Groups.zero      :: real
+  real_1   > Groups.one       :: real
+  real_neg > Groups.uminus    :: "real => real"
+  inv      > Groups.inverse   :: "real => real"
+  real_add > Groups.plus      :: "[real,real] => real"
+  real_mul > Groups.times     :: "[real,real] => real"
   real_lt  > Orderings.less      :: "[real,real] => bool";
 
 ignore_thms
@@ -51,8 +51,8 @@
   real_gt     > HOL4Compat.real_gt
   real_ge     > HOL4Compat.real_ge
   real_lte    > Orderings.less_eq :: "[real,real] => bool"
-  real_sub    > Algebras.minus :: "[real,real] => real"
-  "/"         > Algebras.divide :: "[real,real] => real"
+  real_sub    > Groups.minus :: "[real,real] => real"
+  "/"         > Rings.divide :: "[real,real] => real"
   pow         > Power.power :: "[real,nat] => real"
   abs         > Groups.abs :: "real => real"
   real_of_num > RealDef.real :: "nat => real";
--- a/src/HOL/Import/Generate-HOLLight/GenHOLLight.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Import/Generate-HOLLight/GenHOLLight.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -76,9 +76,9 @@
   SUC > Suc
   PRE > HOLLightCompat.Pred
   NUMERAL > HOL4Compat.NUMERAL
-  "+" > Algebras.plus :: "nat \<Rightarrow> nat \<Rightarrow> nat" 
-  "*" > Algebras.times :: "nat \<Rightarrow> nat \<Rightarrow> nat"
-  "-" > Algebras.minus :: "nat \<Rightarrow> nat \<Rightarrow> nat"
+  "+" > Groups.plus :: "nat \<Rightarrow> nat \<Rightarrow> nat" 
+  "*" > Groups.times :: "nat \<Rightarrow> nat \<Rightarrow> nat"
+  "-" > Groups.minus :: "nat \<Rightarrow> nat \<Rightarrow> nat"
   BIT0 > HOLLightCompat.NUMERAL_BIT0
   BIT1 > HOL4Compat.NUMERAL_BIT1
   INL > Sum_Type.Inl
--- a/src/HOL/Import/HOL/arithmetic.imp	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Import/HOL/arithmetic.imp	Mon Feb 22 09:24:20 2010 +0100
@@ -24,9 +24,9 @@
   ">=" > "HOL4Compat.nat_ge"
   ">" > "HOL4Compat.nat_gt"
   "<=" > "Orderings.less_eq" :: "nat => nat => bool"
-  "-" > "Algebras.minus_class.minus" :: "nat => nat => nat"
-  "+" > "Algebras.plus_class.plus" :: "nat => nat => nat"
-  "*" > "Algebras.times_class.times" :: "nat => nat => nat"
+  "-" > "Groups.minus" :: "nat => nat => nat"
+  "+" > "Groups.plus" :: "nat => nat => nat"
+  "*" > "Groups.times" :: "nat => nat => nat"
 
 thm_maps
   "num_case_def" > "HOL4Compat.num_case_def"
--- a/src/HOL/Import/HOL/real.imp	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Import/HOL/real.imp	Mon Feb 22 09:24:20 2010 +0100
@@ -10,7 +10,7 @@
 const_maps
   "sup" > "HOL4Real.real.sup"
   "sum" > "HOL4Real.real.sum"
-  "real_sub" > "Algebras.minus" :: "real => real => real"
+  "real_sub" > "Groups.minus" :: "real => real => real"
   "real_of_num" > "RealDef.real" :: "nat => real"
   "real_lte" > "Orderings.less_eq" :: "real => real => bool"
   "real_gt" > "HOL4Compat.real_gt"
--- a/src/HOL/Import/HOL/realax.imp	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Import/HOL/realax.imp	Mon Feb 22 09:24:20 2010 +0100
@@ -27,12 +27,12 @@
   "treal_add" > "HOL4Real.realax.treal_add"
   "treal_1" > "HOL4Real.realax.treal_1"
   "treal_0" > "HOL4Real.realax.treal_0"
-  "real_neg" > "Algebras.uminus_class.uminus" :: "real => real"
-  "real_mul" > "Algebras.times_class.times" :: "real => real => real"
+  "real_neg" > "Groups.uminus" :: "real => real"
+  "real_mul" > "Groups.times" :: "real => real => real"
   "real_lt" > "Orderings.less" :: "real => real => bool"
-  "real_add" > "Algebras.plus_class.plus" :: "real => real => real"
-  "real_1" > "Algebras.one_class.one" :: "real"
-  "real_0" > "Algebras.zero_class.zero" :: "real"
+  "real_add" > "Groups.plus" :: "real => real => real"
+  "real_1" > "Groups.one" :: "real"
+  "real_0" > "Groups.zero" :: "real"
   "inv" > "Ring.inverse" :: "real => real"
   "hreal_of_treal" > "HOL4Real.realax.hreal_of_treal"
 
--- a/src/HOL/Import/HOLLight/hollight.imp	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Import/HOLLight/hollight.imp	Mon Feb 22 09:24:20 2010 +0100
@@ -238,10 +238,10 @@
   "<=" > "HOLLight.hollight.<="
   "<" > "HOLLight.hollight.<"
   "/\\" > "op &"
-  "-" > "Algebras.minus_class.minus" :: "nat => nat => nat"
+  "-" > "Groups.minus" :: "nat => nat => nat"
   "," > "Pair"
-  "+" > "Algebras.plus_class.plus" :: "nat => nat => nat"
-  "*" > "Algebras.times_class.times" :: "nat => nat => nat"
+  "+" > "Groups.plus" :: "nat => nat => nat"
+  "*" > "Groups.times" :: "nat => nat => nat"
   "$" > "HOLLight.hollight.$"
   "!" > "All"
 
--- a/src/HOL/Import/hol4rews.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Import/hol4rews.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -613,13 +613,13 @@
     end
 
 local
-    fun handle_meta [x as Appl[Appl[Constant "_constrain", Constant "==", _],_,_]] = x
-      | handle_meta [x as Appl[Appl[Constant "_constrain", Constant "all", _],_]] = x
-      | handle_meta [x as Appl[Appl[Constant "_constrain", Constant "==>", _],_,_]] = x
+    fun handle_meta [x as Appl[Appl[Constant "_constrain", Constant @{const_syntax "=="}, _],_,_]] = x
+      | handle_meta [x as Appl[Appl[Constant "_constrain", Constant @{const_syntax all}, _],_]] = x
+      | handle_meta [x as Appl[Appl[Constant "_constrain", Constant @{const_syntax "==>"}, _],_,_]] = x
       | handle_meta [x] = Appl[Constant "Trueprop",x]
       | handle_meta _ = error "hol4rews error: Trueprop not applied to single argument"
 in
-val smarter_trueprop_parsing = [("Trueprop",handle_meta)]
+val smarter_trueprop_parsing = [(@{const_syntax Trueprop},handle_meta)]
 end
 
 local
--- a/src/HOL/IsaMakefile	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/IsaMakefile	Mon Feb 22 09:24:20 2010 +0100
@@ -455,8 +455,8 @@
 $(LOG)/HOL-Induct.gz: $(OUT)/HOL Induct/Com.thy Induct/Comb.thy		\
   Induct/Ordinals.thy Induct/PropLog.thy Induct/QuoNestedDataType.thy	\
   Induct/QuoDataType.thy Induct/ROOT.ML Induct/Sexp.thy			\
-  Induct/Sigma_Algebra.thy Induct/ABexp.thy Induct/Term.thy		\
-  Induct/Tree.thy Induct/document/root.tex
+  Induct/Sigma_Algebra.thy Induct/ABexp.thy Induct/SList.thy		\
+  Induct/Term.thy Induct/Tree.thy Induct/document/root.tex
 	@$(ISABELLE_TOOL) usedir $(OUT)/HOL Induct
 
 
--- a/src/HOL/Library/LaTeXsugar.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Library/LaTeXsugar.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -64,10 +64,10 @@
 consts DUMMY :: 'a ("\<^raw:\_>")
 
 (* THEOREMS *)
+notation (Rule output)
+  "==>"  ("\<^raw:\mbox{}\inferrule{\mbox{>_\<^raw:}}>\<^raw:{\mbox{>_\<^raw:}}>")
+
 syntax (Rule output)
-  "==>" :: "prop \<Rightarrow> prop \<Rightarrow> prop"
-  ("\<^raw:\mbox{}\inferrule{\mbox{>_\<^raw:}}>\<^raw:{\mbox{>_\<^raw:}}>")
-
   "_bigimpl" :: "asms \<Rightarrow> prop \<Rightarrow> prop"
   ("\<^raw:\mbox{}\inferrule{>_\<^raw:}>\<^raw:{\mbox{>_\<^raw:}}>")
 
@@ -76,21 +76,20 @@
 
   "_asm" :: "prop \<Rightarrow> asms" ("\<^raw:\mbox{>_\<^raw:}>")
 
-syntax (Axiom output)
-  "Trueprop" :: "bool \<Rightarrow> prop"
-  ("\<^raw:\mbox{}\inferrule{\mbox{}}{\mbox{>_\<^raw:}}>")
+notation (Axiom output)
+  "Trueprop"  ("\<^raw:\mbox{}\inferrule{\mbox{}}{\mbox{>_\<^raw:}}>")
 
+notation (IfThen output)
+  "==>"  ("\<^raw:{\normalsize{}>If\<^raw:\,}> _/ \<^raw:{\normalsize \,>then\<^raw:\,}>/ _.")
 syntax (IfThen output)
-  "==>" :: "prop \<Rightarrow> prop \<Rightarrow> prop"
-  ("\<^raw:{\normalsize{}>If\<^raw:\,}> _/ \<^raw:{\normalsize \,>then\<^raw:\,}>/ _.")
   "_bigimpl" :: "asms \<Rightarrow> prop \<Rightarrow> prop"
   ("\<^raw:{\normalsize{}>If\<^raw:\,}> _ /\<^raw:{\normalsize \,>then\<^raw:\,}>/ _.")
   "_asms" :: "prop \<Rightarrow> asms \<Rightarrow> asms" ("\<^raw:\mbox{>_\<^raw:}> /\<^raw:{\normalsize \,>and\<^raw:\,}>/ _")
   "_asm" :: "prop \<Rightarrow> asms" ("\<^raw:\mbox{>_\<^raw:}>")
 
+notation (IfThenNoBox output)
+  "==>"  ("\<^raw:{\normalsize{}>If\<^raw:\,}> _/ \<^raw:{\normalsize \,>then\<^raw:\,}>/ _.")
 syntax (IfThenNoBox output)
-  "==>" :: "prop \<Rightarrow> prop \<Rightarrow> prop"
-  ("\<^raw:{\normalsize{}>If\<^raw:\,}> _/ \<^raw:{\normalsize \,>then\<^raw:\,}>/ _.")
   "_bigimpl" :: "asms \<Rightarrow> prop \<Rightarrow> prop"
   ("\<^raw:{\normalsize{}>If\<^raw:\,}> _ /\<^raw:{\normalsize \,>then\<^raw:\,}>/ _.")
   "_asms" :: "prop \<Rightarrow> asms \<Rightarrow> asms" ("_ /\<^raw:{\normalsize \,>and\<^raw:\,}>/ _")
--- a/src/HOL/Library/Multiset.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Library/Multiset.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -176,64 +176,6 @@
   by (simp add: multiset_eq_conv_count_eq)
 
 
-subsubsection {* Intersection *}
-
-definition multiset_inter :: "'a multiset \<Rightarrow> 'a multiset \<Rightarrow> 'a multiset" (infixl "#\<inter>" 70) where
-  "multiset_inter A B = A - (A - B)"
-
-lemma multiset_inter_count:
-  "count (A #\<inter> B) x = min (count A x) (count B x)"
-  by (simp add: multiset_inter_def multiset_typedef)
-
-lemma multiset_inter_commute: "A #\<inter> B = B #\<inter> A"
-  by (rule multi_count_ext) (simp add: multiset_inter_count)
-
-lemma multiset_inter_assoc: "A #\<inter> (B #\<inter> C) = A #\<inter> B #\<inter> C"
-  by (rule multi_count_ext) (simp add: multiset_inter_count)
-
-lemma multiset_inter_left_commute: "A #\<inter> (B #\<inter> C) = B #\<inter> (A #\<inter> C)"
-  by (rule multi_count_ext) (simp add: multiset_inter_count)
-
-lemmas multiset_inter_ac =
-  multiset_inter_commute
-  multiset_inter_assoc
-  multiset_inter_left_commute
-
-lemma multiset_inter_single: "a \<noteq> b \<Longrightarrow> {#a#} #\<inter> {#b#} = {#}"
-  by (rule multi_count_ext) (auto simp add: multiset_inter_count)
-
-lemma multiset_union_diff_commute:
-  assumes "B #\<inter> C = {#}"
-  shows "A + B - C = A - C + B"
-proof (rule multi_count_ext)
-  fix x
-  from assms have "min (count B x) (count C x) = 0"
-    by (auto simp add: multiset_inter_count multiset_eq_conv_count_eq)
-  then have "count B x = 0 \<or> count C x = 0"
-    by auto
-  then show "count (A + B - C) x = count (A - C + B) x"
-    by auto
-qed
-
-
-subsubsection {* Comprehension (filter) *}
-
-lemma count_MCollect [simp]:
-  "count {# x:#M. P x #} a = (if P a then count M a else 0)"
-  by (simp add: MCollect_def in_multiset multiset_typedef)
-
-lemma MCollect_empty [simp]: "MCollect {#} P = {#}"
-  by (rule multi_count_ext) simp
-
-lemma MCollect_single [simp]:
-  "MCollect {#x#} P = (if P x then {#x#} else {#})"
-  by (rule multi_count_ext) simp
-
-lemma MCollect_union [simp]:
-  "MCollect (M + N) f = MCollect M f + MCollect N f"
-  by (rule multi_count_ext) simp
-
-
 subsubsection {* Equality of multisets *}
 
 lemma single_not_empty [simp]: "{#a#} \<noteq> {#} \<and> {#} \<noteq> {#a#}"
@@ -335,64 +277,61 @@
 
 subsubsection {* Pointwise ordering induced by count *}
 
-definition mset_le :: "'a multiset \<Rightarrow> 'a multiset \<Rightarrow> bool"  (infix "\<le>#" 50) where
-  "A \<le># B \<longleftrightarrow> (\<forall>a. count A a \<le> count B a)"
+instantiation multiset :: (type) ordered_ab_semigroup_add_imp_le
+begin
+
+definition less_eq_multiset :: "'a multiset \<Rightarrow> 'a multiset \<Rightarrow> bool" where
+  mset_le_def: "A \<le> B \<longleftrightarrow> (\<forall>a. count A a \<le> count B a)"
 
-definition mset_less :: "'a multiset \<Rightarrow> 'a multiset \<Rightarrow> bool"  (infix "<#" 50) where
-  "A <# B \<longleftrightarrow> A \<le># B \<and> A \<noteq> B"
+definition less_multiset :: "'a multiset \<Rightarrow> 'a multiset \<Rightarrow> bool" where
+  mset_less_def: "(A::'a multiset) < B \<longleftrightarrow> A \<le> B \<and> A \<noteq> B"
 
-notation mset_le  (infix "\<subseteq>#" 50)
-notation mset_less  (infix "\<subset>#" 50)
+instance proof
+qed (auto simp add: mset_le_def mset_less_def multiset_eq_conv_count_eq intro: order_trans antisym)
+
+end
 
 lemma mset_less_eqI:
-  "(\<And>x. count A x \<le> count B x) \<Longrightarrow> A \<subseteq># B"
+  "(\<And>x. count A x \<le> count B x) \<Longrightarrow> A \<le> B"
   by (simp add: mset_le_def)
 
-lemma mset_le_refl[simp]: "A \<le># A"
-unfolding mset_le_def by auto
-
-lemma mset_le_trans: "A \<le># B \<Longrightarrow> B \<le># C \<Longrightarrow> A \<le># C"
-unfolding mset_le_def by (fast intro: order_trans)
-
-lemma mset_le_antisym: "A \<le># B \<Longrightarrow> B \<le># A \<Longrightarrow> A = B"
-apply (unfold mset_le_def)
-apply (rule multiset_eq_conv_count_eq [THEN iffD2])
-apply (blast intro: order_antisym)
-done
-
-lemma mset_le_exists_conv: "(A \<le># B) = (\<exists>C. B = A + C)"
+lemma mset_le_exists_conv:
+  "(A::'a multiset) \<le> B \<longleftrightarrow> (\<exists>C. B = A + C)"
 apply (unfold mset_le_def, rule iffI, rule_tac x = "B - A" in exI)
 apply (auto intro: multiset_eq_conv_count_eq [THEN iffD2])
 done
 
-lemma mset_le_mono_add_right_cancel[simp]: "(A + C \<le># B + C) = (A \<le># B)"
-unfolding mset_le_def by auto
+lemma mset_le_mono_add_right_cancel [simp]:
+  "(A::'a multiset) + C \<le> B + C \<longleftrightarrow> A \<le> B"
+  by (fact add_le_cancel_right)
 
-lemma mset_le_mono_add_left_cancel[simp]: "(C + A \<le># C + B) = (A \<le># B)"
-unfolding mset_le_def by auto
+lemma mset_le_mono_add_left_cancel [simp]:
+  "C + (A::'a multiset) \<le> C + B \<longleftrightarrow> A \<le> B"
+  by (fact add_le_cancel_left)
+
+lemma mset_le_mono_add:
+  "(A::'a multiset) \<le> B \<Longrightarrow> C \<le> D \<Longrightarrow> A + C \<le> B + D"
+  by (fact add_mono)
 
-lemma mset_le_mono_add: "\<lbrakk> A \<le># B; C \<le># D \<rbrakk> \<Longrightarrow> A + C \<le># B + D"
-apply (unfold mset_le_def)
-apply auto
-apply (erule_tac x = a in allE)+
-apply auto
-done
+lemma mset_le_add_left [simp]:
+  "(A::'a multiset) \<le> A + B"
+  unfolding mset_le_def by auto
+
+lemma mset_le_add_right [simp]:
+  "B \<le> (A::'a multiset) + B"
+  unfolding mset_le_def by auto
 
-lemma mset_le_add_left[simp]: "A \<le># A + B"
-unfolding mset_le_def by auto
-
-lemma mset_le_add_right[simp]: "B \<le># A + B"
-unfolding mset_le_def by auto
+lemma mset_le_single:
+  "a :# B \<Longrightarrow> {#a#} \<le> B"
+  by (simp add: mset_le_def)
 
-lemma mset_le_single: "a :# B \<Longrightarrow> {#a#} \<le># B"
-by (simp add: mset_le_def)
-
-lemma multiset_diff_union_assoc: "C \<le># B \<Longrightarrow> A + B - C = A + (B - C)"
-by (simp add: multiset_eq_conv_count_eq mset_le_def)
+lemma multiset_diff_union_assoc:
+  "C \<le> B \<Longrightarrow> (A::'a multiset) + B - C = A + (B - C)"
+  by (simp add: multiset_eq_conv_count_eq mset_le_def)
 
 lemma mset_le_multiset_union_diff_commute:
-assumes "B \<le># A"
-shows "A - B + C = A + C - B"
+  assumes "B \<le> A"
+  shows "(A::'a multiset) - B + C = A + C - B"
 proof -
   from mset_le_exists_conv [of "B" "A"] assms have "\<exists>D. A = B + D" ..
   from this obtain D where "A = B + D" ..
@@ -410,31 +349,19 @@
     done
 qed
 
-interpretation mset_order: order "op \<le>#" "op <#"
-proof qed (auto intro: order.intro mset_le_refl mset_le_antisym
-  mset_le_trans simp: mset_less_def)
-
-interpretation mset_order_cancel_semigroup:
-  ordered_cancel_ab_semigroup_add "op +" "op \<le>#" "op <#"
-proof qed (erule mset_le_mono_add [OF mset_le_refl])
-
-interpretation mset_order_semigroup_cancel:
-  ordered_ab_semigroup_add_imp_le "op +" "op \<le>#" "op <#"
-proof qed simp
-
-lemma mset_lessD: "A \<subset># B \<Longrightarrow> x \<in># A \<Longrightarrow> x \<in># B"
+lemma mset_lessD: "A < B \<Longrightarrow> x \<in># A \<Longrightarrow> x \<in># B"
 apply (clarsimp simp: mset_le_def mset_less_def)
 apply (erule_tac x=x in allE)
 apply auto
 done
 
-lemma mset_leD: "A \<subseteq># B \<Longrightarrow> x \<in># A \<Longrightarrow> x \<in># B"
+lemma mset_leD: "A \<le> B \<Longrightarrow> x \<in># A \<Longrightarrow> x \<in># B"
 apply (clarsimp simp: mset_le_def mset_less_def)
 apply (erule_tac x = x in allE)
 apply auto
 done
   
-lemma mset_less_insertD: "(A + {#x#} \<subset># B) \<Longrightarrow> (x \<in># B \<and> A \<subset># B)"
+lemma mset_less_insertD: "(A + {#x#} < B) \<Longrightarrow> (x \<in># B \<and> A < B)"
 apply (rule conjI)
  apply (simp add: mset_lessD)
 apply (clarsimp simp: mset_le_def mset_less_def)
@@ -443,30 +370,90 @@
  apply (auto split: split_if_asm)
 done
 
-lemma mset_le_insertD: "(A + {#x#} \<subseteq># B) \<Longrightarrow> (x \<in># B \<and> A \<subseteq># B)"
+lemma mset_le_insertD: "(A + {#x#} \<le> B) \<Longrightarrow> (x \<in># B \<and> A \<le> B)"
 apply (rule conjI)
  apply (simp add: mset_leD)
 apply (force simp: mset_le_def mset_less_def split: split_if_asm)
 done
 
-lemma mset_less_of_empty[simp]: "A \<subset># {#} \<longleftrightarrow> False"
+lemma mset_less_of_empty[simp]: "A < {#} \<longleftrightarrow> False"
   by (auto simp add: mset_less_def mset_le_def multiset_eq_conv_count_eq)
 
-lemma multi_psub_of_add_self[simp]: "A \<subset># A + {#x#}"
-by (auto simp: mset_le_def mset_less_def)
+lemma multi_psub_of_add_self[simp]: "A < A + {#x#}"
+  by (auto simp: mset_le_def mset_less_def)
 
-lemma multi_psub_self[simp]: "A \<subset># A = False"
-by (auto simp: mset_le_def mset_less_def)
+lemma multi_psub_self[simp]: "(A::'a multiset) < A = False"
+  by simp
 
 lemma mset_less_add_bothsides:
-  "T + {#x#} \<subset># S + {#x#} \<Longrightarrow> T \<subset># S"
-by (auto simp: mset_le_def mset_less_def)
+  "T + {#x#} < S + {#x#} \<Longrightarrow> T < S"
+  by (fact add_less_imp_less_right)
+
+lemma mset_less_empty_nonempty:
+  "{#} < S \<longleftrightarrow> S \<noteq> {#}"
+  by (auto simp: mset_le_def mset_less_def)
+
+lemma mset_less_diff_self:
+  "c \<in># B \<Longrightarrow> B - {#c#} < B"
+  by (auto simp: mset_le_def mset_less_def multiset_eq_conv_count_eq)
+
+
+subsubsection {* Intersection *}
+
+instantiation multiset :: (type) semilattice_inf
+begin
+
+definition inf_multiset :: "'a multiset \<Rightarrow> 'a multiset \<Rightarrow> 'a multiset" where
+  multiset_inter_def: "inf_multiset A B = A - (A - B)"
+
+instance proof -
+  have aux: "\<And>m n q :: nat. m \<le> n \<Longrightarrow> m \<le> q \<Longrightarrow> m \<le> n - (n - q)" by arith
+  show "OFCLASS('a multiset, semilattice_inf_class)" proof
+  qed (auto simp add: multiset_inter_def mset_le_def aux)
+qed
+
+end
+
+abbreviation multiset_inter :: "'a multiset \<Rightarrow> 'a multiset \<Rightarrow> 'a multiset" (infixl "#\<inter>" 70) where
+  "multiset_inter \<equiv> inf"
 
-lemma mset_less_empty_nonempty: "({#} \<subset># S) = (S \<noteq> {#})"
-by (auto simp: mset_le_def mset_less_def)
+lemma multiset_inter_count:
+  "count (A #\<inter> B) x = min (count A x) (count B x)"
+  by (simp add: multiset_inter_def multiset_typedef)
+
+lemma multiset_inter_single: "a \<noteq> b \<Longrightarrow> {#a#} #\<inter> {#b#} = {#}"
+  by (rule multi_count_ext) (auto simp add: multiset_inter_count)
 
-lemma mset_less_diff_self: "c \<in># B \<Longrightarrow> B - {#c#} \<subset># B"
-  by (auto simp: mset_le_def mset_less_def multiset_eq_conv_count_eq)
+lemma multiset_union_diff_commute:
+  assumes "B #\<inter> C = {#}"
+  shows "A + B - C = A - C + B"
+proof (rule multi_count_ext)
+  fix x
+  from assms have "min (count B x) (count C x) = 0"
+    by (auto simp add: multiset_inter_count multiset_eq_conv_count_eq)
+  then have "count B x = 0 \<or> count C x = 0"
+    by auto
+  then show "count (A + B - C) x = count (A - C + B) x"
+    by auto
+qed
+
+
+subsubsection {* Comprehension (filter) *}
+
+lemma count_MCollect [simp]:
+  "count {# x:#M. P x #} a = (if P a then count M a else 0)"
+  by (simp add: MCollect_def in_multiset multiset_typedef)
+
+lemma MCollect_empty [simp]: "MCollect {#} P = {#}"
+  by (rule multi_count_ext) simp
+
+lemma MCollect_single [simp]:
+  "MCollect {#x#} P = (if P x then {#x#} else {#})"
+  by (rule multi_count_ext) simp
+
+lemma MCollect_union [simp]:
+  "MCollect (M + N) f = MCollect M f + MCollect N f"
+  by (rule multi_count_ext) simp
 
 
 subsubsection {* Set of elements *}
@@ -657,7 +644,7 @@
 apply auto
 done
 
-lemma mset_less_size: "A \<subset># B \<Longrightarrow> size A < size B"
+lemma mset_less_size: "(A::'a multiset) < B \<Longrightarrow> size A < size B"
 proof (induct A arbitrary: B)
   case (empty M)
   then have "M \<noteq> {#}" by (simp add: mset_less_empty_nonempty)
@@ -666,12 +653,12 @@
   then show ?case by simp
 next
   case (add S x T)
-  have IH: "\<And>B. S \<subset># B \<Longrightarrow> size S < size B" by fact
-  have SxsubT: "S + {#x#} \<subset># T" by fact
-  then have "x \<in># T" and "S \<subset># T" by (auto dest: mset_less_insertD)
+  have IH: "\<And>B. S < B \<Longrightarrow> size S < size B" by fact
+  have SxsubT: "S + {#x#} < T" by fact
+  then have "x \<in># T" and "S < T" by (auto dest: mset_less_insertD)
   then obtain T' where T: "T = T' + {#x#}" 
     by (blast dest: multi_member_split)
-  then have "S \<subset># T'" using SxsubT 
+  then have "S < T'" using SxsubT 
     by (blast intro: mset_less_add_bothsides)
   then have "size S < size T'" using IH by simp
   then show ?case using T by simp
@@ -686,7 +673,7 @@
 
 definition
   mset_less_rel :: "('a multiset * 'a multiset) set" where
-  "mset_less_rel = {(A,B). A \<subset># B}"
+  "mset_less_rel = {(A,B). A < B}"
 
 lemma multiset_add_sub_el_shuffle: 
   assumes "c \<in># B" and "b \<noteq> c" 
@@ -709,29 +696,29 @@
 text {* The induction rules: *}
 
 lemma full_multiset_induct [case_names less]:
-assumes ih: "\<And>B. \<forall>A. A \<subset># B \<longrightarrow> P A \<Longrightarrow> P B"
+assumes ih: "\<And>B. \<forall>(A::'a multiset). A < B \<longrightarrow> P A \<Longrightarrow> P B"
 shows "P B"
 apply (rule wf_mset_less_rel [THEN wf_induct])
 apply (rule ih, auto simp: mset_less_rel_def)
 done
 
 lemma multi_subset_induct [consumes 2, case_names empty add]:
-assumes "F \<subseteq># A"
+assumes "F \<le> A"
   and empty: "P {#}"
   and insert: "\<And>a F. a \<in># A \<Longrightarrow> P F \<Longrightarrow> P (F + {#a#})"
 shows "P F"
 proof -
-  from `F \<subseteq># A`
+  from `F \<le> A`
   show ?thesis
   proof (induct F)
     show "P {#}" by fact
   next
     fix x F
-    assume P: "F \<subseteq># A \<Longrightarrow> P F" and i: "F + {#x#} \<subseteq># A"
+    assume P: "F \<le> A \<Longrightarrow> P F" and i: "F + {#x#} \<le> A"
     show "P (F + {#x#})"
     proof (rule insert)
       from i show "x \<in># A" by (auto dest: mset_le_insertD)
-      from i have "F \<subseteq># A" by (auto dest: mset_le_insertD)
+      from i have "F \<le> A" by (auto dest: mset_le_insertD)
       with P show "P F" .
     qed
   qed
@@ -875,12 +862,8 @@
     by (simp add: sorted_remove1 multiset_of_remove1 insort_remove1)
 qed
 
-lemma multiset_of_remdups_le: "multiset_of (remdups xs) \<le># multiset_of xs"
-apply (induct xs)
- apply auto
-apply (rule mset_le_trans)
- apply auto
-done
+lemma multiset_of_remdups_le: "multiset_of (remdups xs) \<le> multiset_of xs"
+  by (induct xs) (auto intro: order_trans)
 
 lemma multiset_of_update:
   "i < length ls \<Longrightarrow> multiset_of (ls[i := v]) = multiset_of ls - {#ls ! i#} + {#v#}"
@@ -969,7 +952,7 @@
   by (simp add: multiset_eq_conv_count_eq count_of_filter)
 
 lemma mset_less_eq_Bag [code]:
-  "Bag xs \<subseteq># A \<longleftrightarrow> (\<forall>(x, n) \<in> set xs. count_of xs x \<le> count A x)"
+  "Bag xs \<le> A \<longleftrightarrow> (\<forall>(x, n) \<in> set xs. count_of xs x \<le> count A x)"
     (is "?lhs \<longleftrightarrow> ?rhs")
 proof
   assume ?lhs then show ?rhs
@@ -990,10 +973,10 @@
 begin
 
 definition
-  "HOL.eq A B \<longleftrightarrow> A \<subseteq># B \<and> B \<subseteq># A"
+  "HOL.eq A B \<longleftrightarrow> (A::'a multiset) \<le> B \<and> B \<le> A"
 
 instance proof
-qed (simp add: eq_multiset_def mset_order.eq_iff)
+qed (simp add: eq_multiset_def eq_iff)
 
 end
 
@@ -1223,76 +1206,46 @@
 
 subsubsection {* Partial-order properties *}
 
-instantiation multiset :: (order) order
-begin
-
-definition less_multiset_def:
-  "M' < M \<longleftrightarrow> (M', M) \<in> mult {(x', x). x' < x}"
-
-definition le_multiset_def:
-  "M' <= M \<longleftrightarrow> M' = M \<or> M' < (M::'a multiset)"
-
-lemma trans_base_order: "trans {(x', x). x' < (x::'a::order)}"
-unfolding trans_def by (blast intro: order_less_trans)
-
-text {*
- \medskip Irreflexivity.
-*}
+definition less_multiset :: "'a\<Colon>order multiset \<Rightarrow> 'a multiset \<Rightarrow> bool" (infix "<#" 50) where
+  "M' <# M \<longleftrightarrow> (M', M) \<in> mult {(x', x). x' < x}"
 
-lemma mult_irrefl_aux:
-  "finite A ==> (\<forall>x \<in> A. \<exists>y \<in> A. x < (y::'a::order)) \<Longrightarrow> A = {}"
-by (induct rule: finite_induct) (auto intro: order_less_trans)
+definition le_multiset :: "'a\<Colon>order multiset \<Rightarrow> 'a multiset \<Rightarrow> bool" (infix "<=#" 50) where
+  "M' <=# M \<longleftrightarrow> M' <# M \<or> M' = M"
 
-lemma mult_less_not_refl: "\<not> M < (M::'a::order multiset)"
-apply (unfold less_multiset_def, auto)
-apply (drule trans_base_order [THEN mult_implies_one_step], auto)
-apply (drule finite_set_of [THEN mult_irrefl_aux [rule_format (no_asm)]])
-apply (simp add: set_of_eq_empty_iff)
-done
-
-lemma mult_less_irrefl [elim!]: "M < (M::'a::order multiset) ==> R"
-using insert mult_less_not_refl by fast
-
-
-text {* Transitivity. *}
+notation (xsymbol) less_multiset (infix "\<subset>#" 50)
+notation (xsymbol) le_multiset (infix "\<subseteq>#" 50)
 
-theorem mult_less_trans: "K < M ==> M < N ==> K < (N::'a::order multiset)"
-unfolding less_multiset_def mult_def by (blast intro: trancl_trans)
-
-text {* Asymmetry. *}
-
-theorem mult_less_not_sym: "M < N ==> \<not> N < (M::'a::order multiset)"
-apply auto
-apply (rule mult_less_not_refl [THEN notE])
-apply (erule mult_less_trans, assumption)
-done
-
-theorem mult_less_asym:
-  "M < N ==> (\<not> P ==> N < (M::'a::order multiset)) ==> P"
-using mult_less_not_sym by blast
-
-theorem mult_le_refl [iff]: "M <= (M::'a::order multiset)"
-unfolding le_multiset_def by auto
+interpretation multiset_order: order le_multiset less_multiset
+proof -
+  have irrefl: "\<And>M :: 'a multiset. \<not> M \<subset># M"
+  proof
+    fix M :: "'a multiset"
+    assume "M \<subset># M"
+    then have MM: "(M, M) \<in> mult {(x, y). x < y}" by (simp add: less_multiset_def)
+    have "trans {(x'::'a, x). x' < x}"
+      by (rule transI) simp
+    moreover note MM
+    ultimately have "\<exists>I J K. M = I + J \<and> M = I + K
+      \<and> J \<noteq> {#} \<and> (\<forall>k\<in>set_of K. \<exists>j\<in>set_of J. (k, j) \<in> {(x, y). x < y})"
+      by (rule mult_implies_one_step)
+    then obtain I J K where "M = I + J" and "M = I + K"
+      and "J \<noteq> {#}" and "(\<forall>k\<in>set_of K. \<exists>j\<in>set_of J. (k, j) \<in> {(x, y). x < y})" by blast
+    then have aux1: "K \<noteq> {#}" and aux2: "\<forall>k\<in>set_of K. \<exists>j\<in>set_of K. k < j" by auto
+    have "finite (set_of K)" by simp
+    moreover note aux2
+    ultimately have "set_of K = {}"
+      by (induct rule: finite_induct) (auto intro: order_less_trans)
+    with aux1 show False by simp
+  qed
+  have trans: "\<And>K M N :: 'a multiset. K \<subset># M \<Longrightarrow> M \<subset># N \<Longrightarrow> K \<subset># N"
+    unfolding less_multiset_def mult_def by (blast intro: trancl_trans)
+  show "order (le_multiset :: 'a multiset \<Rightarrow> _) less_multiset" proof
+  qed (auto simp add: le_multiset_def irrefl dest: trans)
+qed
 
-text {* Anti-symmetry. *}
-
-theorem mult_le_antisym:
-  "M <= N ==> N <= M ==> M = (N::'a::order multiset)"
-unfolding le_multiset_def by (blast dest: mult_less_not_sym)
-
-text {* Transitivity. *}
-
-theorem mult_le_trans:
-  "K <= M ==> M <= N ==> K <= (N::'a::order multiset)"
-unfolding le_multiset_def by (blast intro: mult_less_trans)
-
-theorem mult_less_le: "(M < N) = (M <= N \<and> M \<noteq> (N::'a::order multiset))"
-unfolding le_multiset_def by auto
-
-instance proof
-qed (auto simp add: mult_less_le dest: mult_le_antisym elim: mult_le_trans)
-
-end
+lemma mult_less_irrefl [elim!]:
+  "M \<subset># (M::'a::order multiset) ==> R"
+  by (simp add: multiset_order.less_irrefl)
 
 
 subsubsection {* Monotonicity of multiset union *}
@@ -1306,52 +1259,26 @@
 apply (simp add: add_assoc)
 done
 
-lemma union_less_mono2: "B < D ==> C + B < C + (D::'a::order multiset)"
+lemma union_less_mono2: "B \<subset># D ==> C + B \<subset># C + (D::'a::order multiset)"
 apply (unfold less_multiset_def mult_def)
 apply (erule trancl_induct)
  apply (blast intro: mult1_union transI order_less_trans r_into_trancl)
 apply (blast intro: mult1_union transI order_less_trans r_into_trancl trancl_trans)
 done
 
-lemma union_less_mono1: "B < D ==> B + C < D + (C::'a::order multiset)"
+lemma union_less_mono1: "B \<subset># D ==> B + C \<subset># D + (C::'a::order multiset)"
 apply (subst add_commute [of B C])
 apply (subst add_commute [of D C])
 apply (erule union_less_mono2)
 done
 
 lemma union_less_mono:
-  "A < C ==> B < D ==> A + B < C + (D::'a::order multiset)"
-by (blast intro!: union_less_mono1 union_less_mono2 mult_less_trans)
-
-lemma union_le_mono:
-  "A <= C ==> B <= D ==> A + B <= C + (D::'a::order multiset)"
-unfolding le_multiset_def
-by (blast intro: union_less_mono union_less_mono1 union_less_mono2)
+  "A \<subset># C ==> B \<subset># D ==> A + B \<subset># C + (D::'a::order multiset)"
+  by (blast intro!: union_less_mono1 union_less_mono2 multiset_order.less_trans)
 
-lemma empty_leI [iff]: "{#} <= (M::'a::order multiset)"
-apply (unfold le_multiset_def less_multiset_def)
-apply (case_tac "M = {#}")
- prefer 2
- apply (subgoal_tac "({#} + {#}, {#} + M) \<in> mult (Collect (split op <))")
-  prefer 2
-  apply (rule one_step_implies_mult)
-    apply (simp only: trans_def)
-    apply auto
-done
-
-lemma union_upper1: "A <= A + (B::'a::order multiset)"
-proof -
-  have "A + {#} <= A + B" by (blast intro: union_le_mono)
-  then show ?thesis by simp
-qed
-
-lemma union_upper2: "B <= A + (B::'a::order multiset)"
-by (subst add_commute) (rule union_upper1)
-
-instance multiset :: (order) ordered_ab_semigroup_add
-apply intro_classes
-apply (erule union_le_mono[OF mult_le_refl])
-done
+interpretation multiset_order: ordered_ab_semigroup_add plus le_multiset less_multiset
+proof
+qed (auto simp add: le_multiset_def intro: union_less_mono2)
 
 
 subsection {* The fold combinator *}
@@ -1406,7 +1333,7 @@
   "fold_msetG f z A x \<Longrightarrow> fold_msetG f z A y \<Longrightarrow> y = x"
 proof (induct arbitrary: x y z rule: full_multiset_induct)
   case (less M x\<^isub>1 x\<^isub>2 Z)
-  have IH: "\<forall>A. A \<subset># M \<longrightarrow> 
+  have IH: "\<forall>A. A < M \<longrightarrow> 
     (\<forall>x x' x''. fold_msetG f x'' A x \<longrightarrow> fold_msetG f x'' A x'
                \<longrightarrow> x' = x)" by fact
   have Mfoldx\<^isub>1: "fold_msetG f Z M x\<^isub>1" and Mfoldx\<^isub>2: "fold_msetG f Z M x\<^isub>2" by fact+
@@ -1426,8 +1353,8 @@
       fix C c v
       assume "M = C + {#c#}" and "x\<^isub>2 = f c v" and Cv: "fold_msetG f Z C v"
       then have MCc: "M = C + {#c#}" and x\<^isub>2: "x\<^isub>2 = f c v" by auto
-      then have CsubM: "C \<subset># M" by simp
-      from MBb have BsubM: "B \<subset># M" by simp
+      then have CsubM: "C < M" by simp
+      from MBb have BsubM: "B < M" by simp
       show ?case
       proof cases
         assume "b=c"
@@ -1438,8 +1365,8 @@
         let ?D = "B - {#c#}"
         have cinB: "c \<in># B" and binC: "b \<in># C" using MBb MCc diff
           by (auto intro: insert_noteq_member dest: sym)
-        have "B - {#c#} \<subset># B" using cinB by (rule mset_less_diff_self)
-        then have DsubM: "?D \<subset># M" using BsubM by (blast intro: mset_order.less_trans)
+        have "B - {#c#} < B" using cinB by (rule mset_less_diff_self)
+        then have DsubM: "?D < M" using BsubM by (blast intro: order_less_trans)
         from MBb MCc have "B + {#b#} = C + {#c#}" by blast
         then have [simp]: "B + {#b#} - {#c#} = C"
           using MBb MCc binC cinB by auto
@@ -1769,6 +1696,37 @@
 lemma multi_union_self_other_eq: "(A::'a multiset) + X = A + Y \<Longrightarrow> X = Y"
   by (fact add_imp_eq)
 
-lemmas mset_less_trans = mset_order.less_trans
+lemma mset_less_trans: "(M::'a multiset) < K \<Longrightarrow> K < N \<Longrightarrow> M < N"
+  by (fact order_less_trans)
+
+lemma multiset_inter_commute: "A #\<inter> B = B #\<inter> A"
+  by (fact inf.commute)
+
+lemma multiset_inter_assoc: "A #\<inter> (B #\<inter> C) = A #\<inter> B #\<inter> C"
+  by (fact inf.assoc [symmetric])
+
+lemma multiset_inter_left_commute: "A #\<inter> (B #\<inter> C) = B #\<inter> (A #\<inter> C)"
+  by (fact inf.left_commute)
+
+lemmas multiset_inter_ac =
+  multiset_inter_commute
+  multiset_inter_assoc
+  multiset_inter_left_commute
+
+lemma mult_less_not_refl:
+  "\<not> M \<subset># (M::'a::order multiset)"
+  by (fact multiset_order.less_irrefl)
+
+lemma mult_less_trans:
+  "K \<subset># M ==> M \<subset># N ==> K \<subset># (N::'a::order multiset)"
+  by (fact multiset_order.less_trans)
+    
+lemma mult_less_not_sym:
+  "M \<subset># N ==> \<not> N \<subset># (M::'a::order multiset)"
+  by (fact multiset_order.less_not_sym)
+
+lemma mult_less_asym:
+  "M \<subset># N ==> (\<not> P ==> N \<subset># (M::'a::order multiset)) ==> P"
+  by (fact multiset_order.less_asym)
 
 end
\ No newline at end of file
--- a/src/HOL/Library/OptionalSugar.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Library/OptionalSugar.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -37,15 +37,15 @@
 
 (* Let *)
 translations 
-  "_bind (p,DUMMY) e" <= "_bind p (CONST fst e)"
-  "_bind (DUMMY,p) e" <= "_bind p (CONST snd e)"
+  "_bind (p, CONST DUMMY) e" <= "_bind p (CONST fst e)"
+  "_bind (CONST DUMMY, p) e" <= "_bind p (CONST snd e)"
 
   "_tuple_args x (_tuple_args y z)" ==
     "_tuple_args x (_tuple_arg (_tuple y z))"
 
-  "_bind (Some p) e" <= "_bind p (CONST the e)"
-  "_bind (p#DUMMY) e" <= "_bind p (CONST hd e)"
-  "_bind (DUMMY#p) e" <= "_bind p (CONST tl e)"
+  "_bind (CONST Some p) e" <= "_bind p (CONST the e)"
+  "_bind (p # CONST DUMMY) e" <= "_bind p (CONST hd e)"
+  "_bind (CONST DUMMY # p) e" <= "_bind p (CONST tl e)"
 
 (* type constraints with spacing *)
 setup {*
--- a/src/HOL/Library/Permutation.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Library/Permutation.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -154,7 +154,7 @@
   done
 
 lemma multiset_of_le_perm_append:
-    "(multiset_of xs \<le># multiset_of ys) = (\<exists>zs. xs @ zs <~~> ys)"
+    "multiset_of xs \<le> multiset_of ys \<longleftrightarrow> (\<exists>zs. xs @ zs <~~> ys)"
   apply (auto simp: multiset_of_eq_perm[THEN sym] mset_le_exists_conv)
   apply (insert surj_multiset_of, drule surjD)
   apply (blast intro: sym)+
--- a/src/HOL/Library/SetsAndFunctions.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Library/SetsAndFunctions.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -119,14 +119,14 @@
   apply (force simp add: mult_assoc)
   done
 
-interpretation set_comm_monoid_add: comm_monoid_add "{0}" "op \<oplus> :: ('a::comm_monoid_add) set => 'a set => 'a set"
+interpretation set_comm_monoid_add: comm_monoid_add "op \<oplus> :: ('a::comm_monoid_add) set => 'a set => 'a set" "{0}"
   apply default
    apply (unfold set_plus_def)
    apply (force simp add: add_ac)
   apply force
   done
 
-interpretation set_comm_monoid_mult: comm_monoid_mult "{1}" "op \<otimes> :: ('a::comm_monoid_mult) set => 'a set => 'a set"
+interpretation set_comm_monoid_mult: comm_monoid_mult "op \<otimes> :: ('a::comm_monoid_mult) set => 'a set => 'a set" "{1}"
   apply default
    apply (unfold set_times_def)
    apply (force simp add: mult_ac)
--- a/src/HOL/List.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/List.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -358,11 +358,11 @@
 
 parse_translation (advanced) {*
 let
-  val NilC = Syntax.const @{const_name Nil};
-  val ConsC = Syntax.const @{const_name Cons};
-  val mapC = Syntax.const @{const_name map};
-  val concatC = Syntax.const @{const_name concat};
-  val IfC = Syntax.const @{const_name If};
+  val NilC = Syntax.const @{const_syntax Nil};
+  val ConsC = Syntax.const @{const_syntax Cons};
+  val mapC = Syntax.const @{const_syntax map};
+  val concatC = Syntax.const @{const_syntax concat};
+  val IfC = Syntax.const @{const_syntax If};
 
   fun singl x = ConsC $ x $ NilC;
 
@@ -371,12 +371,14 @@
       val x = Free (Name.variant (fold Term.add_free_names [p, e] []) "x", dummyT);
       val e = if opti then singl e else e;
       val case1 = Syntax.const @{syntax_const "_case1"} $ p $ e;
-      val case2 = Syntax.const @{syntax_const "_case1"} $ Syntax.const Term.dummy_patternN $ NilC;
+      val case2 =
+        Syntax.const @{syntax_const "_case1"} $
+          Syntax.const @{const_syntax dummy_pattern} $ NilC;
       val cs = Syntax.const @{syntax_const "_case2"} $ case1 $ case2;
       val ft = Datatype_Case.case_tr false Datatype.info_of_constr ctxt [x, cs];
     in lambda x ft end;
 
-  fun abs_tr ctxt (p as Free(s,T)) e opti =
+  fun abs_tr ctxt (p as Free (s, T)) e opti =
         let
           val thy = ProofContext.theory_of ctxt;
           val s' = Sign.intern_const thy s;
@@ -2363,7 +2365,7 @@
 proof (induct xss arbitrary: xs)
   case Nil show ?case by simp
 next
-  interpret monoid_add "[]" "op @" proof qed simp_all
+  interpret monoid_add "op @" "[]" proof qed simp_all
   case Cons then show ?case by (simp add: foldl_absorb0)
 qed
 
--- a/src/HOL/MicroJava/DFA/Semilat.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/MicroJava/DFA/Semilat.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -22,16 +22,17 @@
   "lesssub" :: "'a \<Rightarrow> 'a ord \<Rightarrow> 'a \<Rightarrow> bool"
   "plussub" :: "'a \<Rightarrow> ('a \<Rightarrow> 'b \<Rightarrow> 'c) \<Rightarrow> 'b \<Rightarrow> 'c" 
 (*<*)
-syntax 
-  "lesub"   :: "'a \<Rightarrow> 'a ord \<Rightarrow> 'a \<Rightarrow> bool" ("(_ /<='__ _)" [50, 1000, 51] 50)
-  "lesssub" :: "'a \<Rightarrow> 'a ord \<Rightarrow> 'a \<Rightarrow> bool" ("(_ /<'__ _)" [50, 1000, 51] 50)
-  "plussub" :: "'a \<Rightarrow> ('a \<Rightarrow> 'b \<Rightarrow> 'c) \<Rightarrow> 'b \<Rightarrow> 'c" ("(_ /+'__ _)" [65, 1000, 66] 65)
+notation
+  "lesub"  ("(_ /<='__ _)" [50, 1000, 51] 50) and
+  "lesssub"  ("(_ /<'__ _)" [50, 1000, 51] 50) and
+  "plussub"  ("(_ /+'__ _)" [65, 1000, 66] 65)
 (*>*)
-syntax (xsymbols)
-  "lesub" :: "'a \<Rightarrow> 'a ord \<Rightarrow> 'a \<Rightarrow> bool" ("(_ /\<sqsubseteq>\<^bsub>_\<^esub> _)" [50, 0, 51] 50)
-  "lesssub" :: "'a \<Rightarrow> 'a ord \<Rightarrow> 'a \<Rightarrow> bool" ("(_ /\<sqsubset>\<^bsub>_\<^esub> _)" [50, 0, 51] 50)
-  "plussub" :: "'a \<Rightarrow> ('a \<Rightarrow> 'b \<Rightarrow> 'c) \<Rightarrow> 'b \<Rightarrow> 'c" ("(_ /\<squnion>\<^bsub>_\<^esub> _)" [65, 0, 66] 65)
+notation (xsymbols)
+  "lesub"  ("(_ /\<sqsubseteq>\<^bsub>_\<^esub> _)" [50, 0, 51] 50) and
+  "lesssub"  ("(_ /\<sqsubset>\<^bsub>_\<^esub> _)" [50, 0, 51] 50) and
+  "plussub"  ("(_ /\<squnion>\<^bsub>_\<^esub> _)" [65, 0, 66] 65)
 (*<*)
+syntax
  (* allow \<sub> instead of \<bsub>..\<esub> *)  
   "_lesub" :: "'a \<Rightarrow> 'a ord \<Rightarrow> 'a \<Rightarrow> bool" ("(_ /\<sqsubseteq>\<^sub>_ _)" [50, 1000, 51] 50)
   "_lesssub" :: "'a \<Rightarrow> 'a ord \<Rightarrow> 'a \<Rightarrow> bool" ("(_ /\<sqsubset>\<^sub>_ _)" [50, 1000, 51] 50)
--- a/src/HOL/Multivariate_Analysis/Euclidean_Space.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Multivariate_Analysis/Euclidean_Space.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -1,4 +1,4 @@
-(*  Title:      Library/Euclidean_Space
+(*  Title:      Library/Multivariate_Analysis/Euclidean_Space.thy
     Author:     Amine Chaieb, University of Cambridge
 *)
 
@@ -66,8 +66,8 @@
 
 instantiation cart :: (plus,finite) plus
 begin
-definition  vector_add_def : "op + \<equiv> (\<lambda> x y.  (\<chi> i. (x$i) + (y$i)))"
-instance ..
+  definition  vector_add_def : "op + \<equiv> (\<lambda> x y.  (\<chi> i. (x$i) + (y$i)))"
+  instance ..
 end
 
 instantiation cart :: (times,finite) times
@@ -76,39 +76,42 @@
   instance ..
 end
 
-instantiation cart :: (minus,finite) minus begin
+instantiation cart :: (minus,finite) minus
+begin
   definition vector_minus_def : "op - \<equiv> (\<lambda> x y.  (\<chi> i. (x$i) - (y$i)))"
-instance ..
+  instance ..
 end
 
-instantiation cart :: (uminus,finite) uminus begin
+instantiation cart :: (uminus,finite) uminus
+begin
   definition vector_uminus_def : "uminus \<equiv> (\<lambda> x.  (\<chi> i. - (x$i)))"
-instance ..
+  instance ..
 end
 
-instantiation cart :: (zero,finite) zero begin
+instantiation cart :: (zero,finite) zero
+begin
   definition vector_zero_def : "0 \<equiv> (\<chi> i. 0)"
-instance ..
+  instance ..
 end
 
-instantiation cart :: (one,finite) one begin
+instantiation cart :: (one,finite) one
+begin
   definition vector_one_def : "1 \<equiv> (\<chi> i. 1)"
-instance ..
+  instance ..
 end
 
 instantiation cart :: (ord,finite) ord
- begin
-definition vector_le_def:
-  "less_eq (x :: 'a ^'b) y = (ALL i. x$i <= y$i)"
-definition vector_less_def: "less (x :: 'a ^'b) y = (ALL i. x$i < y$i)"
-
-instance by (intro_classes)
+begin
+  definition vector_le_def:
+    "less_eq (x :: 'a ^'b) y = (ALL i. x$i <= y$i)"
+  definition vector_less_def: "less (x :: 'a ^'b) y = (ALL i. x$i < y$i)"
+  instance by (intro_classes)
 end
 
 instantiation cart :: (scaleR, finite) scaleR
 begin
-definition vector_scaleR_def: "scaleR = (\<lambda> r x.  (\<chi> i. scaleR r (x$i)))"
-instance ..
+  definition vector_scaleR_def: "scaleR = (\<lambda> r x.  (\<chi> i. scaleR r (x$i)))"
+  instance ..
 end
 
 text{* Also the scalar-vector multiplication. *}
--- a/src/HOL/Multivariate_Analysis/Finite_Cartesian_Product.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Multivariate_Analysis/Finite_Cartesian_Product.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -1,11 +1,11 @@
-(* Title:      HOL/Library/Finite_Cartesian_Product
-   Author:     Amine Chaieb, University of Cambridge
+(*  Title:      HOL/Multivariate_Analysis/Finite_Cartesian_Product.thy
+    Author:     Amine Chaieb, University of Cambridge
 *)
 
 header {* Definition of finite Cartesian product types. *}
 
 theory Finite_Cartesian_Product
-imports Main (*FIXME: ATP_Linkup is only needed for metis at a few places. We could dispense of that by changing the proofs.*)
+imports Main
 begin
 
 subsection {* Finite Cartesian products, with indexing and lambdas. *}
@@ -14,9 +14,9 @@
   ('a, 'b) cart = "UNIV :: (('b::finite) \<Rightarrow> 'a) set"
   morphisms Cart_nth Cart_lambda ..
 
-notation Cart_nth (infixl "$" 90)
-
-notation (xsymbols) Cart_lambda (binder "\<chi>" 10)
+notation
+  Cart_nth (infixl "$" 90) and
+  Cart_lambda (binder "\<chi>" 10)
 
 (*
   Translate "'b ^ 'n" into "'b ^ ('n :: finite)". When 'n has already more than
@@ -39,10 +39,7 @@
 *}
 
 lemma stupid_ext: "(\<forall>x. f x = g x) \<longleftrightarrow> (f = g)"
-  apply auto
-  apply (rule ext)
-  apply auto
-  done
+  by (auto intro: ext)
 
 lemma Cart_eq: "(x = y) \<longleftrightarrow> (\<forall>i. x$i = y$i)"
   by (simp add: Cart_nth_inject [symmetric] expand_fun_eq)
@@ -75,7 +72,10 @@
   unfolding sndcart_def by simp
 
 lemma finite_sum_image: "(UNIV::('a + 'b) set) = range Inl \<union> range Inr"
-by (auto, case_tac x, auto)
+  apply auto
+  apply (case_tac x)
+   apply auto
+  done
 
 lemma fstcart_pastecart[simp]: "fstcart (pastecart x y) = x"
   by (simp add: Cart_eq)
@@ -90,9 +90,9 @@
   using pastecart_fst_snd[of x] pastecart_fst_snd[of y] by metis
 
 lemma forall_pastecart: "(\<forall>p. P p) \<longleftrightarrow> (\<forall>x y. P (pastecart x y))"
-  by (metis pastecart_fst_snd fstcart_pastecart sndcart_pastecart)
+  by (metis pastecart_fst_snd)
 
-lemma exists_pastecart: "(\<exists>p. P p)  \<longleftrightarrow> (\<exists>x y. P (pastecart x y))"
-  by (metis pastecart_fst_snd fstcart_pastecart sndcart_pastecart)
+lemma exists_pastecart: "(\<exists>p. P p) \<longleftrightarrow> (\<exists>x y. P (pastecart x y))"
+  by (metis pastecart_fst_snd)
 
 end
--- a/src/HOL/Mutabelle/Mutabelle.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Mutabelle/Mutabelle.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -14,7 +14,7 @@
   (@{const_name HOL.undefined}, "'a"),
   (@{const_name HOL.default}, "'a"),
   (@{const_name dummy_pattern}, "'a::{}"),
-  (@{const_name Algebras.uminus}, "'a"),
+  (@{const_name Groups.uminus}, "'a"),
   (@{const_name Nat.size}, "'a"),
   (@{const_name Groups.abs}, "'a")];
 
--- a/src/HOL/NSA/NSA.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/NSA/NSA.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -671,12 +671,12 @@
   0 = x, 1 = x, nnn = x provided x isn't 0, 1 or a numeral.*)
 fun reorient_proc sg _ (_ $ t $ u) =
   case u of
-      Const(@{const_name Algebras.zero}, _) => NONE
-    | Const(@{const_name Algebras.one}, _) => NONE
+      Const(@{const_name Groups.zero}, _) => NONE
+    | Const(@{const_name Groups.one}, _) => NONE
     | Const(@{const_name Int.number_of}, _) $ _ => NONE
     | _ => SOME (case t of
-                Const(@{const_name Algebras.zero}, _) => meta_zero_approx_reorient
-              | Const(@{const_name Algebras.one}, _) => meta_one_approx_reorient
+                Const(@{const_name Groups.zero}, _) => meta_zero_approx_reorient
+              | Const(@{const_name Groups.one}, _) => meta_one_approx_reorient
               | Const(@{const_name Int.number_of}, _) $ _ =>
                                  meta_number_of_approx_reorient);
 
--- a/src/HOL/Prolog/Func.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Prolog/Func.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -10,31 +10,28 @@
 
 typedecl tm
 
-consts
-  abs     :: "(tm => tm) => tm"
-  app     :: "tm => tm => tm"
+axiomatization
+  abs     :: "(tm \<Rightarrow> tm) \<Rightarrow> tm" and
+  app     :: "tm \<Rightarrow> tm \<Rightarrow> tm" and
 
-  cond    :: "tm => tm => tm => tm"
-  "fix"   :: "(tm => tm) => tm"
-
-  true    :: tm
-  false   :: tm
-  "and"   :: "tm => tm => tm"       (infixr "and" 999)
-  eq      :: "tm => tm => tm"       (infixr "eq" 999)
+  cond    :: "tm \<Rightarrow> tm \<Rightarrow> tm \<Rightarrow> tm" and
+  "fix"   :: "(tm \<Rightarrow> tm) \<Rightarrow> tm" and
 
-  Z       :: tm                     ("Z")
-  S       :: "tm => tm"
-(*
-        "++", "--",
-        "**"    :: tm => tm => tm       (infixr 999)
-*)
-        eval    :: "[tm, tm] => bool"
+  true    :: tm and
+  false   :: tm and
+  "and"   :: "tm \<Rightarrow> tm \<Rightarrow> tm"       (infixr "and" 999) and
+  eq      :: "tm \<Rightarrow> tm \<Rightarrow> tm"       (infixr "eq" 999) and
+
+  Z       :: tm                     ("Z") and
+  S       :: "tm \<Rightarrow> tm" and
 
-instance tm :: plus ..
-instance tm :: minus ..
-instance tm :: times ..
+  plus    :: "tm \<Rightarrow> tm \<Rightarrow> tm"       (infixl "+" 65) and
+  minus   :: "tm \<Rightarrow> tm \<Rightarrow> tm"       (infixl "-" 65) and
+  times   :: "tm \<Rightarrow> tm \<Rightarrow> tm"       (infixl "*" 70) and
 
-axioms   eval: "
+  eval    :: "tm \<Rightarrow> tm \<Rightarrow> bool" where
+
+eval: "
 
 eval (abs RR) (abs RR)..
 eval (app F X) V :- eval F (abs R) & eval X U & eval (R U) V..
@@ -59,7 +56,6 @@
 eval ( Z    * M) Z..
 eval ((S N) * M) K :- eval (N * M) L & eval (L + M) K"
 
-
 lemmas prog_Func = eval
 
 lemma "eval ((S (S Z)) + (S Z)) ?X"
--- a/src/HOL/Random.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Random.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -168,6 +168,7 @@
 hide (open) type seed
 hide (open) const inc_shift minus_shift log "next" split_seed
   iterate range select pick select_weight
+hide (open) fact range_def
 
 no_notation fcomp (infixl "o>" 60)
 no_notation scomp (infixl "o\<rightarrow>" 60)
--- a/src/HOL/Tools/Datatype/datatype_case.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/Datatype/datatype_case.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -310,6 +310,8 @@
 fun case_tr err tab_of ctxt [t, u] =
     let
       val thy = ProofContext.theory_of ctxt;
+      val intern_const_syntax = Consts.intern_syntax (Sign.consts_of thy);
+
       (* replace occurrences of dummy_pattern by distinct variables *)
       (* internalize constant names                                 *)
       fun prep_pat ((c as Const (@{syntax_const "_constrain"}, _)) $ t $ tT) used =
@@ -319,9 +321,7 @@
             let val x = Name.variant used "x"
             in (Free (x, T), x :: used) end
         | prep_pat (Const (s, T)) used =
-            (case try (unprefix Syntax.constN) s of
-               SOME c => (Const (c, T), used)
-             | NONE => (Const (Sign.intern_const thy s, T), used))
+            (Const (intern_const_syntax s, T), used)
         | prep_pat (v as Free (s, T)) used =
             let val s' = Sign.intern_const thy s
             in
@@ -422,8 +422,7 @@
   | _ => NONE;
 
 val dest_case = gen_dest_case (try (dest_Const #> fst)) fastype_of;
-val dest_case' = gen_dest_case
-  (try (dest_Const #> fst #> unprefix Syntax.constN)) (K dummyT);
+val dest_case' = gen_dest_case (try (dest_Const #> fst #> Syntax.unmark_const)) (K dummyT);
 
 
 (* destruct nested patterns *)
@@ -455,14 +454,13 @@
 fun case_tr' tab_of cname ctxt ts =
   let
     val thy = ProofContext.theory_of ctxt;
-    val consts = ProofContext.consts_of ctxt;
     fun mk_clause (pat, rhs) =
       let val xs = Term.add_frees pat []
       in
         Syntax.const @{syntax_const "_case1"} $
           map_aterms
             (fn Free p => Syntax.mark_boundT p
-              | Const (s, _) => Const (Consts.extern_early consts s, dummyT)
+              | Const (s, _) => Syntax.const (Syntax.mark_const s)
               | t => t) pat $
           map_aterms
             (fn x as Free (s, T) =>
--- a/src/HOL/Tools/Datatype/datatype_data.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/Datatype/datatype_data.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -223,7 +223,7 @@
 fun add_case_tr' case_names thy =
   Sign.add_advanced_trfuns ([], [],
     map (fn case_name =>
-      let val case_name' = Sign.const_syntax_name thy case_name
+      let val case_name' = Syntax.mark_const case_name
       in (case_name', Datatype_Case.case_tr' info_of_case case_name')
       end) case_names, []) thy;
 
--- a/src/HOL/Tools/Function/size.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/Function/size.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -25,7 +25,7 @@
 
 val lookup_size = SizeData.get #> Symtab.lookup;
 
-fun plus (t1, t2) = Const (@{const_name Algebras.plus},
+fun plus (t1, t2) = Const (@{const_name Groups.plus},
   HOLogic.natT --> HOLogic.natT --> HOLogic.natT) $ t1 $ t2;
 
 fun size_of_type f g h (T as Type (s, Ts)) =
--- a/src/HOL/Tools/Predicate_Compile/predicate_compile_core.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_core.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -2436,8 +2436,8 @@
       val [polarity, depth] = additional_arguments
       val polarity' = (case prem of Prem _ => I | Negprem _ => HOLogic.mk_not | _ => I) polarity
       val depth' =
-        Const ("Algebras.minus", @{typ "code_numeral => code_numeral => code_numeral"})
-          $ depth $ Const ("Algebras.one", @{typ "Code_Numeral.code_numeral"})
+        Const (@{const_name Groups.minus}, @{typ "code_numeral => code_numeral => code_numeral"})
+          $ depth $ Const (@{const_name Groups.one}, @{typ "Code_Numeral.code_numeral"})
     in [polarity', depth'] end
   }
 
--- a/src/HOL/Tools/Predicate_Compile/predicate_compile_data.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_data.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -224,8 +224,8 @@
   @{const_name Suc}, @{const_name Nat.zero_nat_inst.zero_nat},
   @{const_name Nat.one_nat_inst.one_nat},
   @{const_name Orderings.less}, @{const_name Orderings.less_eq},
-  @{const_name Algebras.zero},
-  @{const_name Algebras.one},  @{const_name Algebras.plus},
+  @{const_name Groups.zero},
+  @{const_name Groups.one},  @{const_name Groups.plus},
   @{const_name Nat.ord_nat_inst.less_eq_nat},
   @{const_name Nat.ord_nat_inst.less_nat},
   @{const_name number_nat_inst.number_of_nat},
--- a/src/HOL/Tools/Qelim/cooper.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/Qelim/cooper.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -79,9 +79,9 @@
 | Const (@{const_name Orderings.less_eq}, _) $ y $ z =>
    if term_of x aconv y then Le (Thm.dest_arg ct)
    else if term_of x aconv z then Ge (Thm.dest_arg1 ct) else Nox
-| Const (@{const_name Rings.dvd},_)$_$(Const(@{const_name Algebras.plus},_)$y$_) =>
+| Const (@{const_name Rings.dvd},_)$_$(Const(@{const_name Groups.plus},_)$y$_) =>
    if term_of x aconv y then Dvd (Thm.dest_binop ct ||> Thm.dest_arg) else Nox
-| Const (@{const_name Not},_) $ (Const (@{const_name Rings.dvd},_)$_$(Const(@{const_name Algebras.plus},_)$y$_)) =>
+| Const (@{const_name Not},_) $ (Const (@{const_name Rings.dvd},_)$_$(Const(@{const_name Groups.plus},_)$y$_)) =>
    if term_of x aconv y then
    NDvd (Thm.dest_binop (Thm.dest_arg ct) ||> Thm.dest_arg) else Nox
 | _ => Nox)
@@ -175,18 +175,18 @@
   (fn _ => EVERY [simp_tac lin_ss 1, TRY (Lin_Arith.tac ctxt 1)]);
 fun linear_cmul 0 tm = zero
   | linear_cmul n tm = case tm of
-      Const (@{const_name Algebras.plus}, _) $ a $ b => addC $ linear_cmul n a $ linear_cmul n b
-    | Const (@{const_name Algebras.times}, _) $ c $ x => mulC $ numeral1 (fn m => n * m) c $ x
-    | Const (@{const_name Algebras.minus}, _) $ a $ b => subC $ linear_cmul n a $ linear_cmul n b
-    | (m as Const (@{const_name Algebras.uminus}, _)) $ a => m $ linear_cmul n a
+      Const (@{const_name Groups.plus}, _) $ a $ b => addC $ linear_cmul n a $ linear_cmul n b
+    | Const (@{const_name Groups.times}, _) $ c $ x => mulC $ numeral1 (fn m => n * m) c $ x
+    | Const (@{const_name Groups.minus}, _) $ a $ b => subC $ linear_cmul n a $ linear_cmul n b
+    | (m as Const (@{const_name Groups.uminus}, _)) $ a => m $ linear_cmul n a
     | _ => numeral1 (fn m => n * m) tm;
 fun earlier [] x y = false
   | earlier (h::t) x y =
     if h aconv y then false else if h aconv x then true else earlier t x y;
 
 fun linear_add vars tm1 tm2 = case (tm1, tm2) of
-    (Const (@{const_name Algebras.plus}, _) $ (Const (@{const_name Algebras.times}, _) $ c1 $ x1) $ r1,
-    Const (@{const_name Algebras.plus}, _) $ (Const (@{const_name Algebras.times}, _) $ c2 $ x2) $ r2) =>
+    (Const (@{const_name Groups.plus}, _) $ (Const (@{const_name Groups.times}, _) $ c1 $ x1) $ r1,
+    Const (@{const_name Groups.plus}, _) $ (Const (@{const_name Groups.times}, _) $ c2 $ x2) $ r2) =>
    if x1 = x2 then
      let val c = numeral2 Integer.add c1 c2
       in if c = zero then linear_add vars r1 r2
@@ -194,9 +194,9 @@
      end
      else if earlier vars x1 x2 then addC $ (mulC $ c1 $ x1) $ linear_add vars r1 tm2
    else addC $ (mulC $ c2 $ x2) $ linear_add vars tm1 r2
- | (Const (@{const_name Algebras.plus}, _) $ (Const (@{const_name Algebras.times}, _) $ c1 $ x1) $ r1, _) =>
+ | (Const (@{const_name Groups.plus}, _) $ (Const (@{const_name Groups.times}, _) $ c1 $ x1) $ r1, _) =>
       addC $ (mulC $ c1 $ x1) $ linear_add vars r1 tm2
- | (_, Const (@{const_name Algebras.plus}, _) $ (Const (@{const_name Algebras.times}, _) $ c2 $ x2) $ r2) =>
+ | (_, Const (@{const_name Groups.plus}, _) $ (Const (@{const_name Groups.times}, _) $ c2 $ x2) $ r2) =>
       addC $ (mulC $ c2 $ x2) $ linear_add vars tm1 r2
  | (_, _) => numeral2 Integer.add tm1 tm2;
 
@@ -205,10 +205,10 @@
 
 
 fun lint vars tm =  if is_numeral tm then tm  else case tm of
-  Const (@{const_name Algebras.uminus}, _) $ t => linear_neg (lint vars t)
-| Const (@{const_name Algebras.plus}, _) $ s $ t => linear_add vars (lint vars s) (lint vars t)
-| Const (@{const_name Algebras.minus}, _) $ s $ t => linear_sub vars (lint vars s) (lint vars t)
-| Const (@{const_name Algebras.times}, _) $ s $ t =>
+  Const (@{const_name Groups.uminus}, _) $ t => linear_neg (lint vars t)
+| Const (@{const_name Groups.plus}, _) $ s $ t => linear_add vars (lint vars s) (lint vars t)
+| Const (@{const_name Groups.minus}, _) $ s $ t => linear_sub vars (lint vars s) (lint vars t)
+| Const (@{const_name Groups.times}, _) $ s $ t =>
   let val s' = lint vars s
       val t' = lint vars t
   in if is_numeral s' then (linear_cmul (dest_numeral s') t')
@@ -270,7 +270,7 @@
       val d'' = Thm.rhs_of dth |> Thm.dest_arg1
      in
       case tt' of
-        Const(@{const_name Algebras.plus},_)$(Const(@{const_name Algebras.times},_)$c$_)$_ =>
+        Const(@{const_name Groups.plus},_)$(Const(@{const_name Groups.times},_)$c$_)$_ =>
         let val x = dest_numeral c
         in if x < 0 then Conv.fconv_rule (arg_conv (arg_conv (lint_conv ctxt vs)))
                                        (Thm.transitive dth (inst' [d'',t'] dvd_uminus'))
@@ -293,15 +293,15 @@
   val ins = insert (op = : int * int -> bool)
   fun h (acc,dacc) t =
    case (term_of t) of
-    Const(s,_)$(Const(@{const_name Algebras.times},_)$c$y)$ _ =>
+    Const(s,_)$(Const(@{const_name Groups.times},_)$c$y)$ _ =>
     if x aconv y andalso member (op =)
       ["op =", @{const_name Orderings.less}, @{const_name Orderings.less_eq}] s
     then (ins (dest_numeral c) acc,dacc) else (acc,dacc)
-  | Const(s,_)$_$(Const(@{const_name Algebras.times},_)$c$y) =>
+  | Const(s,_)$_$(Const(@{const_name Groups.times},_)$c$y) =>
     if x aconv y andalso member (op =)
        [@{const_name Orderings.less}, @{const_name Orderings.less_eq}] s
     then (ins (dest_numeral c) acc, dacc) else (acc,dacc)
-  | Const(@{const_name Rings.dvd},_)$_$(Const(@{const_name Algebras.plus},_)$(Const(@{const_name Algebras.times},_)$c$y)$_) =>
+  | Const(@{const_name Rings.dvd},_)$_$(Const(@{const_name Groups.plus},_)$(Const(@{const_name Groups.times},_)$c$y)$_) =>
     if x aconv y then (acc,ins (dest_numeral c) dacc) else (acc,dacc)
   | Const("op &",_)$_$_ => h (h (acc,dacc) (Thm.dest_arg1 t)) (Thm.dest_arg t)
   | Const("op |",_)$_$_ => h (h (acc,dacc) (Thm.dest_arg1 t)) (Thm.dest_arg t)
@@ -335,15 +335,15 @@
    Const("op &",_)$_$_ => binop_conv unit_conv t
   | Const("op |",_)$_$_ => binop_conv unit_conv t
   | Const (@{const_name Not},_)$_ => arg_conv unit_conv t
-  | Const(s,_)$(Const(@{const_name Algebras.times},_)$c$y)$ _ =>
+  | Const(s,_)$(Const(@{const_name Groups.times},_)$c$y)$ _ =>
     if x=y andalso member (op =)
       ["op =", @{const_name Orderings.less}, @{const_name Orderings.less_eq}] s
     then cv (l div dest_numeral c) t else Thm.reflexive t
-  | Const(s,_)$_$(Const(@{const_name Algebras.times},_)$c$y) =>
+  | Const(s,_)$_$(Const(@{const_name Groups.times},_)$c$y) =>
     if x=y andalso member (op =)
       [@{const_name Orderings.less}, @{const_name Orderings.less_eq}] s
     then cv (l div dest_numeral c) t else Thm.reflexive t
-  | Const(@{const_name Rings.dvd},_)$d$(r as (Const(@{const_name Algebras.plus},_)$(Const(@{const_name Algebras.times},_)$c$y)$_)) =>
+  | Const(@{const_name Rings.dvd},_)$d$(r as (Const(@{const_name Groups.plus},_)$(Const(@{const_name Groups.times},_)$c$y)$_)) =>
     if x=y then
       let
        val k = l div dest_numeral c
@@ -546,10 +546,10 @@
   | @{term "0::int"} => C 0
   | @{term "1::int"} => C 1
   | Term.Bound i => Bound i
-  | Const(@{const_name Algebras.uminus},_)$t' => Neg (i_of_term vs t')
-  | Const(@{const_name Algebras.plus},_)$t1$t2 => Add (i_of_term vs t1,i_of_term vs t2)
-  | Const(@{const_name Algebras.minus},_)$t1$t2 => Sub (i_of_term vs t1,i_of_term vs t2)
-  | Const(@{const_name Algebras.times},_)$t1$t2 =>
+  | Const(@{const_name Groups.uminus},_)$t' => Neg (i_of_term vs t')
+  | Const(@{const_name Groups.plus},_)$t1$t2 => Add (i_of_term vs t1,i_of_term vs t2)
+  | Const(@{const_name Groups.minus},_)$t1$t2 => Sub (i_of_term vs t1,i_of_term vs t2)
+  | Const(@{const_name Groups.times},_)$t1$t2 =>
      (Mul (HOLogic.dest_number t1 |> snd, i_of_term vs t2)
     handle TERM _ =>
        (Mul (HOLogic.dest_number t2 |> snd, i_of_term vs t1)
--- a/src/HOL/Tools/Qelim/presburger.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/Qelim/presburger.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -52,15 +52,15 @@
 
 local
  fun isnum t = case t of 
-   Const(@{const_name Algebras.zero},_) => true
- | Const(@{const_name Algebras.one},_) => true
+   Const(@{const_name Groups.zero},_) => true
+ | Const(@{const_name Groups.one},_) => true
  | @{term "Suc"}$s => isnum s
  | @{term "nat"}$s => isnum s
  | @{term "int"}$s => isnum s
- | Const(@{const_name Algebras.uminus},_)$s => isnum s
- | Const(@{const_name Algebras.plus},_)$l$r => isnum l andalso isnum r
- | Const(@{const_name Algebras.times},_)$l$r => isnum l andalso isnum r
- | Const(@{const_name Algebras.minus},_)$l$r => isnum l andalso isnum r
+ | Const(@{const_name Groups.uminus},_)$s => isnum s
+ | Const(@{const_name Groups.plus},_)$l$r => isnum l andalso isnum r
+ | Const(@{const_name Groups.times},_)$l$r => isnum l andalso isnum r
+ | Const(@{const_name Groups.minus},_)$l$r => isnum l andalso isnum r
  | Const(@{const_name Power.power},_)$l$r => isnum l andalso isnum r
  | Const(@{const_name Divides.mod},_)$l$r => isnum l andalso isnum r
  | Const(@{const_name Divides.div},_)$l$r => isnum l andalso isnum r
--- a/src/HOL/Tools/arith_data.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/arith_data.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -75,11 +75,11 @@
 
 fun mk_number T n = HOLogic.number_of_const T $ HOLogic.mk_numeral n;
 
-val mk_plus = HOLogic.mk_binop @{const_name Algebras.plus};
+val mk_plus = HOLogic.mk_binop @{const_name Groups.plus};
 
 fun mk_minus t = 
   let val T = Term.fastype_of t
-  in Const (@{const_name Algebras.uminus}, T --> T) $ t end;
+  in Const (@{const_name Groups.uminus}, T --> T) $ t end;
 
 (*Thus mk_sum[t] yields t+0; longer sums don't have a trailing zero*)
 fun mk_sum T []        = mk_number T 0
@@ -91,9 +91,9 @@
   | long_mk_sum T (t :: ts) = mk_plus (t, mk_sum T ts);
 
 (*decompose additions AND subtractions as a sum*)
-fun dest_summing (pos, Const (@{const_name Algebras.plus}, _) $ t $ u, ts) =
+fun dest_summing (pos, Const (@{const_name Groups.plus}, _) $ t $ u, ts) =
         dest_summing (pos, t, dest_summing (pos, u, ts))
-  | dest_summing (pos, Const (@{const_name Algebras.minus}, _) $ t $ u, ts) =
+  | dest_summing (pos, Const (@{const_name Groups.minus}, _) $ t $ u, ts) =
         dest_summing (pos, t, dest_summing (not pos, u, ts))
   | dest_summing (pos, t, ts) =
         if pos then t::ts else mk_minus t :: ts;
--- a/src/HOL/Tools/hologic.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/hologic.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -440,9 +440,9 @@
 
 val natT = Type ("nat", []);
 
-val zero = Const ("Algebras.zero_class.zero", natT);
+val zero = Const ("Groups.zero_class.zero", natT);
 
-fun is_zero (Const ("Algebras.zero_class.zero", _)) = true
+fun is_zero (Const ("Groups.zero_class.zero", _)) = true
   | is_zero _ = false;
 
 fun mk_Suc t = Const ("Suc", natT --> natT) $ t;
@@ -458,7 +458,7 @@
       | mk n = mk_Suc (mk (n - 1));
   in if n < 0 then raise TERM ("mk_nat: negative number", []) else mk n end;
 
-fun dest_nat (Const ("Algebras.zero_class.zero", _)) = 0
+fun dest_nat (Const ("Groups.zero_class.zero", _)) = 0
   | dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1
   | dest_nat t = raise TERM ("dest_nat", [t]);
 
@@ -508,12 +508,12 @@
   | add_numerals (Abs (_, _, t)) = add_numerals t
   | add_numerals _ = I;
 
-fun mk_number T 0 = Const ("Algebras.zero_class.zero", T)
-  | mk_number T 1 = Const ("Algebras.one_class.one", T)
+fun mk_number T 0 = Const ("Groups.zero_class.zero", T)
+  | mk_number T 1 = Const ("Groups.one_class.one", T)
   | mk_number T i = number_of_const T $ mk_numeral i;
 
-fun dest_number (Const ("Algebras.zero_class.zero", T)) = (T, 0)
-  | dest_number (Const ("Algebras.one_class.one", T)) = (T, 1)
+fun dest_number (Const ("Groups.zero_class.zero", T)) = (T, 0)
+  | dest_number (Const ("Groups.one_class.one", T)) = (T, 1)
   | dest_number (Const ("Int.number_class.number_of", Type ("fun", [_, T])) $ t) =
       (T, dest_numeral t)
   | dest_number t = raise TERM ("dest_number", [t]);
--- a/src/HOL/Tools/int_arith.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/int_arith.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -49,12 +49,12 @@
   make_simproc {lhss = lhss1, name = "one_to_of_int_one_simproc",
   proc = proc1, identifier = []};
 
-fun check (Const (@{const_name Algebras.one}, @{typ int})) = false
-  | check (Const (@{const_name Algebras.one}, _)) = true
+fun check (Const (@{const_name Groups.one}, @{typ int})) = false
+  | check (Const (@{const_name Groups.one}, _)) = true
   | check (Const (s, _)) = member (op =) [@{const_name "op ="},
-      @{const_name Algebras.times}, @{const_name Algebras.uminus},
-      @{const_name Algebras.minus}, @{const_name Algebras.plus},
-      @{const_name Algebras.zero},
+      @{const_name Groups.times}, @{const_name Groups.uminus},
+      @{const_name Groups.minus}, @{const_name Groups.plus},
+      @{const_name Groups.zero},
       @{const_name Orderings.less}, @{const_name Orderings.less_eq}] s
   | check (a $ b) = check a andalso check b
   | check _ = false;
--- a/src/HOL/Tools/lin_arith.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/lin_arith.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -138,8 +138,8 @@
 *)
 fun demult (inj_consts : (string * typ) list) : term * Rat.rat -> term option * Rat.rat =
 let
-  fun demult ((mC as Const (@{const_name Algebras.times}, _)) $ s $ t, m) =
-      (case s of Const (@{const_name Algebras.times}, _) $ s1 $ s2 =>
+  fun demult ((mC as Const (@{const_name Groups.times}, _)) $ s $ t, m) =
+      (case s of Const (@{const_name Groups.times}, _) $ s1 $ s2 =>
         (* bracketing to the right: '(s1 * s2) * t' becomes 's1 * (s2 * t)' *)
         demult (mC $ s1 $ (mC $ s2 $ t), m)
       | _ =>
@@ -170,9 +170,9 @@
         (SOME _, _) => (SOME (mC $ s $ t), m)
       | (NONE,  m') => apsnd (Rat.mult (Rat.inv m')) (demult (s, m)))
     (* terms that evaluate to numeric constants *)
-    | demult (Const (@{const_name Algebras.uminus}, _) $ t, m) = demult (t, Rat.neg m)
-    | demult (Const (@{const_name Algebras.zero}, _), m) = (NONE, Rat.zero)
-    | demult (Const (@{const_name Algebras.one}, _), m) = (NONE, m)
+    | demult (Const (@{const_name Groups.uminus}, _) $ t, m) = demult (t, Rat.neg m)
+    | demult (Const (@{const_name Groups.zero}, _), m) = (NONE, Rat.zero)
+    | demult (Const (@{const_name Groups.one}, _), m) = (NONE, m)
     (*Warning: in rare cases number_of encloses a non-numeral,
       in which case dest_numeral raises TERM; hence all the handles below.
       Same for Suc-terms that turn out not to be numerals -
@@ -196,19 +196,19 @@
   (* Turns a term 'all' and associated multiplicity 'm' into a list 'p' of
      summands and associated multiplicities, plus a constant 'i' (with implicit
      multiplicity 1) *)
-  fun poly (Const (@{const_name Algebras.plus}, _) $ s $ t,
+  fun poly (Const (@{const_name Groups.plus}, _) $ s $ t,
         m : Rat.rat, pi : (term * Rat.rat) list * Rat.rat) = poly (s, m, poly (t, m, pi))
-    | poly (all as Const (@{const_name Algebras.minus}, T) $ s $ t, m, pi) =
+    | poly (all as Const (@{const_name Groups.minus}, T) $ s $ t, m, pi) =
         if nT T then add_atom all m pi else poly (s, m, poly (t, Rat.neg m, pi))
-    | poly (all as Const (@{const_name Algebras.uminus}, T) $ t, m, pi) =
+    | poly (all as Const (@{const_name Groups.uminus}, T) $ t, m, pi) =
         if nT T then add_atom all m pi else poly (t, Rat.neg m, pi)
-    | poly (Const (@{const_name Algebras.zero}, _), _, pi) =
+    | poly (Const (@{const_name Groups.zero}, _), _, pi) =
         pi
-    | poly (Const (@{const_name Algebras.one}, _), m, (p, i)) =
+    | poly (Const (@{const_name Groups.one}, _), m, (p, i)) =
         (p, Rat.add i m)
     | poly (Const (@{const_name Suc}, _) $ t, m, (p, i)) =
         poly (t, m, (p, Rat.add i m))
-    | poly (all as Const (@{const_name Algebras.times}, _) $ _ $ _, m, pi as (p, i)) =
+    | poly (all as Const (@{const_name Groups.times}, _) $ _ $ _, m, pi as (p, i)) =
         (case demult inj_consts (all, m) of
            (NONE,   m') => (p, Rat.add i m')
          | (SOME u, m') => add_atom u m' pi)
@@ -293,7 +293,7 @@
       Const (a, _) => member (op =) [@{const_name Orderings.max},
                                     @{const_name Orderings.min},
                                     @{const_name Groups.abs},
-                                    @{const_name Algebras.minus},
+                                    @{const_name Groups.minus},
                                     "Int.nat" (*DYNAMIC BINDING!*),
                                     "Divides.div_class.mod" (*DYNAMIC BINDING!*),
                                     "Divides.div_class.div" (*DYNAMIC BINDING!*)] a
@@ -401,9 +401,9 @@
       let
         val rev_terms   = rev terms
         val terms1      = map (subst_term [(split_term, t1)]) rev_terms
-        val terms2      = map (subst_term [(split_term, Const (@{const_name Algebras.uminus},
+        val terms2      = map (subst_term [(split_term, Const (@{const_name Groups.uminus},
                             split_type --> split_type) $ t1)]) rev_terms
-        val zero        = Const (@{const_name Algebras.zero}, split_type)
+        val zero        = Const (@{const_name Groups.zero}, split_type)
         val zero_leq_t1 = Const (@{const_name Orderings.less_eq},
                             split_type --> split_type --> HOLogic.boolT) $ zero $ t1
         val t1_lt_zero  = Const (@{const_name Orderings.less},
@@ -415,12 +415,12 @@
         SOME [(Ts, subgoal1), (Ts, subgoal2)]
       end
     (* ?P (?a - ?b) = ((?a < ?b --> ?P 0) & (ALL d. ?a = ?b + d --> ?P d)) *)
-    | (Const (@{const_name Algebras.minus}, _), [t1, t2]) =>
+    | (Const (@{const_name Groups.minus}, _), [t1, t2]) =>
       let
         (* "d" in the above theorem becomes a new bound variable after NNF   *)
         (* transformation, therefore some adjustment of indices is necessary *)
         val rev_terms       = rev terms
-        val zero            = Const (@{const_name Algebras.zero}, split_type)
+        val zero            = Const (@{const_name Groups.zero}, split_type)
         val d               = Bound 0
         val terms1          = map (subst_term [(split_term, zero)]) rev_terms
         val terms2          = map (subst_term [(incr_boundvars 1 split_term, d)])
@@ -430,7 +430,7 @@
         val t1_lt_t2        = Const (@{const_name Orderings.less},
                                 split_type --> split_type --> HOLogic.boolT) $ t1 $ t2
         val t1_eq_t2_plus_d = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $
-                                (Const (@{const_name Algebras.plus},
+                                (Const (@{const_name Groups.plus},
                                   split_type --> split_type --> split_type) $ t2' $ d)
         val not_false       = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
         val subgoal1        = (HOLogic.mk_Trueprop t1_lt_t2) :: terms1 @ [not_false]
@@ -442,8 +442,8 @@
     | (Const ("Int.nat", _), [t1]) =>
       let
         val rev_terms   = rev terms
-        val zero_int    = Const (@{const_name Algebras.zero}, HOLogic.intT)
-        val zero_nat    = Const (@{const_name Algebras.zero}, HOLogic.natT)
+        val zero_int    = Const (@{const_name Groups.zero}, HOLogic.intT)
+        val zero_nat    = Const (@{const_name Groups.zero}, HOLogic.natT)
         val n           = Bound 0
         val terms1      = map (subst_term [(incr_boundvars 1 split_term, n)])
                             (map (incr_boundvars 1) rev_terms)
@@ -465,7 +465,7 @@
     | (Const ("Divides.div_class.mod", Type ("fun", [Type ("nat", []), _])), [t1, t2]) =>
       let
         val rev_terms               = rev terms
-        val zero                    = Const (@{const_name Algebras.zero}, split_type)
+        val zero                    = Const (@{const_name Groups.zero}, split_type)
         val i                       = Bound 1
         val j                       = Bound 0
         val terms1                  = map (subst_term [(split_term, t1)]) rev_terms
@@ -480,8 +480,8 @@
         val j_lt_t2                 = Const (@{const_name Orderings.less},
                                         split_type --> split_type--> HOLogic.boolT) $ j $ t2'
         val t1_eq_t2_times_i_plus_j = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $
-                                       (Const (@{const_name Algebras.plus}, split_type --> split_type --> split_type) $
-                                         (Const (@{const_name Algebras.times},
+                                       (Const (@{const_name Groups.plus}, split_type --> split_type --> split_type) $
+                                         (Const (@{const_name Groups.times},
                                            split_type --> split_type --> split_type) $ t2' $ i) $ j)
         val not_false               = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
         val subgoal1                = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false]
@@ -497,7 +497,7 @@
     | (Const ("Divides.div_class.div", Type ("fun", [Type ("nat", []), _])), [t1, t2]) =>
       let
         val rev_terms               = rev terms
-        val zero                    = Const (@{const_name Algebras.zero}, split_type)
+        val zero                    = Const (@{const_name Groups.zero}, split_type)
         val i                       = Bound 1
         val j                       = Bound 0
         val terms1                  = map (subst_term [(split_term, zero)]) rev_terms
@@ -512,8 +512,8 @@
         val j_lt_t2                 = Const (@{const_name Orderings.less},
                                         split_type --> split_type--> HOLogic.boolT) $ j $ t2'
         val t1_eq_t2_times_i_plus_j = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $
-                                       (Const (@{const_name Algebras.plus}, split_type --> split_type --> split_type) $
-                                         (Const (@{const_name Algebras.times},
+                                       (Const (@{const_name Groups.plus}, split_type --> split_type --> split_type) $
+                                         (Const (@{const_name Groups.times},
                                            split_type --> split_type --> split_type) $ t2' $ i) $ j)
         val not_false               = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
         val subgoal1                = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false]
@@ -535,7 +535,7 @@
         Type ("fun", [Type ("Int.int", []), _])), [t1, t2]) =>
       let
         val rev_terms               = rev terms
-        val zero                    = Const (@{const_name Algebras.zero}, split_type)
+        val zero                    = Const (@{const_name Groups.zero}, split_type)
         val i                       = Bound 1
         val j                       = Bound 0
         val terms1                  = map (subst_term [(split_term, t1)]) rev_terms
@@ -558,8 +558,8 @@
         val t2_lt_j                 = Const (@{const_name Orderings.less},
                                         split_type --> split_type--> HOLogic.boolT) $ t2' $ j
         val t1_eq_t2_times_i_plus_j = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $
-                                       (Const (@{const_name Algebras.plus}, split_type --> split_type --> split_type) $
-                                         (Const (@{const_name Algebras.times},
+                                       (Const (@{const_name Groups.plus}, split_type --> split_type --> split_type) $
+                                         (Const (@{const_name Groups.times},
                                            split_type --> split_type --> split_type) $ t2' $ i) $ j)
         val not_false               = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
         val subgoal1                = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false]
@@ -589,7 +589,7 @@
         Type ("fun", [Type ("Int.int", []), _])), [t1, t2]) =>
       let
         val rev_terms               = rev terms
-        val zero                    = Const (@{const_name Algebras.zero}, split_type)
+        val zero                    = Const (@{const_name Groups.zero}, split_type)
         val i                       = Bound 1
         val j                       = Bound 0
         val terms1                  = map (subst_term [(split_term, zero)]) rev_terms
@@ -612,8 +612,8 @@
         val t2_lt_j                 = Const (@{const_name Orderings.less},
                                         split_type --> split_type--> HOLogic.boolT) $ t2' $ j
         val t1_eq_t2_times_i_plus_j = Const ("op =", split_type --> split_type --> HOLogic.boolT) $ t1' $
-                                       (Const (@{const_name Algebras.plus}, split_type --> split_type --> split_type) $
-                                         (Const (@{const_name Algebras.times},
+                                       (Const (@{const_name Groups.plus}, split_type --> split_type --> split_type) $
+                                         (Const (@{const_name Groups.times},
                                            split_type --> split_type --> split_type) $ t2' $ i) $ j)
         val not_false               = HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.false_const)
         val subgoal1                = (HOLogic.mk_Trueprop t2_eq_zero) :: terms1 @ [not_false]
--- a/src/HOL/Tools/nat_arith.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/nat_arith.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -19,8 +19,8 @@
 
 (** abstract syntax of structure nat: 0, Suc, + **)
 
-val mk_plus = HOLogic.mk_binop @{const_name Algebras.plus};
-val dest_plus = HOLogic.dest_bin @{const_name Algebras.plus} HOLogic.natT;
+val mk_plus = HOLogic.mk_binop @{const_name Groups.plus};
+val dest_plus = HOLogic.dest_bin @{const_name Groups.plus} HOLogic.natT;
 
 fun mk_sum [] = HOLogic.zero
   | mk_sum [t] = t
@@ -85,8 +85,8 @@
 structure DiffCancelSums = CancelSumsFun
 (struct
   open CommonCancelSums;
-  val mk_bal = HOLogic.mk_binop @{const_name Algebras.minus};
-  val dest_bal = HOLogic.dest_bin @{const_name Algebras.minus} HOLogic.natT;
+  val mk_bal = HOLogic.mk_binop @{const_name Groups.minus};
+  val dest_bal = HOLogic.dest_bin @{const_name Groups.minus} HOLogic.natT;
   val uncancel_tac = gen_uncancel_tac @{thm "diff_cancel"};
 end);
 
--- a/src/HOL/Tools/nat_numeral_simprocs.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/nat_numeral_simprocs.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -32,7 +32,7 @@
   | find_first_numeral past [] = raise TERM("find_first_numeral", []);
 
 val zero = mk_number 0;
-val mk_plus = HOLogic.mk_binop @{const_name Algebras.plus};
+val mk_plus = HOLogic.mk_binop @{const_name Groups.plus};
 
 (*Thus mk_sum[t] yields t+0; longer sums don't have a trailing zero*)
 fun mk_sum []        = zero
@@ -43,7 +43,7 @@
 fun long_mk_sum []        = HOLogic.zero
   | long_mk_sum (t :: ts) = mk_plus (t, mk_sum ts);
 
-val dest_plus = HOLogic.dest_bin @{const_name Algebras.plus} HOLogic.natT;
+val dest_plus = HOLogic.dest_bin @{const_name Groups.plus} HOLogic.natT;
 
 
 (** Other simproc items **)
@@ -61,14 +61,14 @@
 (*** CancelNumerals simprocs ***)
 
 val one = mk_number 1;
-val mk_times = HOLogic.mk_binop @{const_name Algebras.times};
+val mk_times = HOLogic.mk_binop @{const_name Groups.times};
 
 fun mk_prod [] = one
   | mk_prod [t] = t
   | mk_prod (t :: ts) = if t = one then mk_prod ts
                         else mk_times (t, mk_prod ts);
 
-val dest_times = HOLogic.dest_bin @{const_name Algebras.times} HOLogic.natT;
+val dest_times = HOLogic.dest_bin @{const_name Groups.times} HOLogic.natT;
 
 fun dest_prod t =
       let val (t,u) = dest_times t
@@ -194,8 +194,8 @@
 structure DiffCancelNumerals = CancelNumeralsFun
  (open CancelNumeralsCommon
   val prove_conv = Arith_Data.prove_conv
-  val mk_bal   = HOLogic.mk_binop @{const_name Algebras.minus}
-  val dest_bal = HOLogic.dest_bin @{const_name Algebras.minus} HOLogic.natT
+  val mk_bal   = HOLogic.mk_binop @{const_name Groups.minus}
+  val dest_bal = HOLogic.dest_bin @{const_name Groups.minus} HOLogic.natT
   val bal_add1 = @{thm nat_diff_add_eq1} RS trans
   val bal_add2 = @{thm nat_diff_add_eq2} RS trans
 );
--- a/src/HOL/Tools/numeral_simprocs.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/numeral_simprocs.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -34,12 +34,12 @@
 val long_mk_sum = Arith_Data.long_mk_sum;
 val dest_sum = Arith_Data.dest_sum;
 
-val mk_diff = HOLogic.mk_binop @{const_name Algebras.minus};
-val dest_diff = HOLogic.dest_bin @{const_name Algebras.minus} Term.dummyT;
+val mk_diff = HOLogic.mk_binop @{const_name Groups.minus};
+val dest_diff = HOLogic.dest_bin @{const_name Groups.minus} Term.dummyT;
 
-val mk_times = HOLogic.mk_binop @{const_name Algebras.times};
+val mk_times = HOLogic.mk_binop @{const_name Groups.times};
 
-fun one_of T = Const(@{const_name Algebras.one}, T);
+fun one_of T = Const(@{const_name Groups.one}, T);
 
 (* build product with trailing 1 rather than Numeral 1 in order to avoid the
    unnecessary restriction to type class number_ring
@@ -56,7 +56,7 @@
 fun long_mk_prod T []        = one_of T
   | long_mk_prod T (t :: ts) = mk_times (t, mk_prod T ts);
 
-val dest_times = HOLogic.dest_bin @{const_name Algebras.times} Term.dummyT;
+val dest_times = HOLogic.dest_bin @{const_name Groups.times} Term.dummyT;
 
 fun dest_prod t =
       let val (t,u) = dest_times t
@@ -72,7 +72,7 @@
 fun mk_coeff (k, t) = mk_times (mk_number (Term.fastype_of t) k, t);
 
 (*Express t as a product of (possibly) a numeral with other sorted terms*)
-fun dest_coeff sign (Const (@{const_name Algebras.uminus}, _) $ t) = dest_coeff (~sign) t
+fun dest_coeff sign (Const (@{const_name Groups.uminus}, _) $ t) = dest_coeff (~sign) t
   | dest_coeff sign t =
     let val ts = sort TermOrd.term_ord (dest_prod t)
         val (n, ts') = find_first_numeral [] ts
@@ -104,7 +104,7 @@
   in mk_times (mk_divide (mk_number T p, mk_number T q), t) end;
 
 (*Express t as a product of a fraction with other sorted terms*)
-fun dest_fcoeff sign (Const (@{const_name Algebras.uminus}, _) $ t) = dest_fcoeff (~sign) t
+fun dest_fcoeff sign (Const (@{const_name Groups.uminus}, _) $ t) = dest_fcoeff (~sign) t
   | dest_fcoeff sign (Const (@{const_name Rings.divide}, _) $ t $ u) =
     let val (p, t') = dest_coeff sign t
         val (q, u') = dest_coeff 1 u
@@ -484,7 +484,7 @@
 in
 fun sign_conv pos_th neg_th ss t =
   let val T = fastype_of t;
-      val zero = Const(@{const_name Algebras.zero}, T);
+      val zero = Const(@{const_name Groups.zero}, T);
       val less = Const(@{const_name Orderings.less}, [T,T] ---> HOLogic.boolT);
       val pos = less $ zero $ t and neg = less $ t $ zero
       fun prove p =
--- a/src/HOL/Tools/record.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/record.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -799,7 +799,7 @@
                   let
                     val (args, rest) = split_args (map fst (but_last fields)) fargs;
                     val more' = mk_ext rest;
-                  in list_comb (Syntax.const (Syntax.constN ^ ext ^ extN), args @ [more']) end
+                  in list_comb (Syntax.const (Syntax.mark_const (ext ^ extN)), args @ [more']) end
               | NONE => err ("no fields defined for " ^ ext))
           | NONE => err (name ^ " is no proper field"))
       | mk_ext [] = more;
@@ -977,7 +977,7 @@
     fun strip_fields t =
       (case strip_comb t of
         (Const (ext, _), args as (_ :: _)) =>
-          (case try (unprefix Syntax.constN o unsuffix extN) ext of
+          (case try (Syntax.unmark_const o unsuffix extN) ext of
             SOME ext' =>
               (case get_extfields thy ext' of
                 SOME fields =>
@@ -1004,7 +1004,7 @@
 
 fun record_ext_tr' name =
   let
-    val ext_name = Syntax.constN ^ name ^ extN;
+    val ext_name = Syntax.mark_const (name ^ extN);
     fun tr' ctxt ts = record_tr' ctxt (list_comb (Syntax.const ext_name, ts));
   in (ext_name, tr') end;
 
@@ -1024,7 +1024,7 @@
               if null (loose_bnos t) then t else raise Match
           | _ => raise Match);
       in
-        (case try (unprefix Syntax.constN) c |> Option.map extern of
+        (case Option.map extern (try Syntax.unmark_const c) of
           SOME update_name =>
             (case try (unsuffix updateN) update_name of
               SOME name =>
@@ -1046,7 +1046,7 @@
 
 fun field_update_tr' name =
   let
-    val update_name = Syntax.constN ^ name ^ updateN;
+    val update_name = Syntax.mark_const (name ^ updateN);
     fun tr' ctxt [t, u] = record_update_tr' ctxt (Syntax.const update_name $ t $ u)
       | tr' _ _ = raise Match;
   in (update_name, tr') end;
--- a/src/HOL/Tools/refute.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/refute.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -710,11 +710,11 @@
       | Const (@{const_name Finite_Set.finite}, _) => t
       | Const (@{const_name Orderings.less}, Type ("fun", [Type ("nat", []),
         Type ("fun", [Type ("nat", []), Type ("bool", [])])])) => t
-      | Const (@{const_name Algebras.plus}, Type ("fun", [Type ("nat", []),
+      | Const (@{const_name Groups.plus}, Type ("fun", [Type ("nat", []),
         Type ("fun", [Type ("nat", []), Type ("nat", [])])])) => t
-      | Const (@{const_name Algebras.minus}, Type ("fun", [Type ("nat", []),
+      | Const (@{const_name Groups.minus}, Type ("fun", [Type ("nat", []),
         Type ("fun", [Type ("nat", []), Type ("nat", [])])])) => t
-      | Const (@{const_name Algebras.times}, Type ("fun", [Type ("nat", []),
+      | Const (@{const_name Groups.times}, Type ("fun", [Type ("nat", []),
         Type ("fun", [Type ("nat", []), Type ("nat", [])])])) => t
       | Const (@{const_name List.append}, _) => t
       | Const (@{const_name lfp}, _) => t
@@ -886,13 +886,13 @@
       | Const (@{const_name Orderings.less}, T as Type ("fun", [Type ("nat", []),
         Type ("fun", [Type ("nat", []), Type ("bool", [])])])) =>
           collect_type_axioms T axs
-      | Const (@{const_name Algebras.plus}, T as Type ("fun", [Type ("nat", []),
+      | Const (@{const_name Groups.plus}, T as Type ("fun", [Type ("nat", []),
         Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
           collect_type_axioms T axs
-      | Const (@{const_name Algebras.minus}, T as Type ("fun", [Type ("nat", []),
+      | Const (@{const_name Groups.minus}, T as Type ("fun", [Type ("nat", []),
         Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
           collect_type_axioms T axs
-      | Const (@{const_name Algebras.times}, T as Type ("fun", [Type ("nat", []),
+      | Const (@{const_name Groups.times}, T as Type ("fun", [Type ("nat", []),
         Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
           collect_type_axioms T axs
       | Const (@{const_name List.append}, T) => collect_type_axioms T axs
@@ -2794,7 +2794,7 @@
 
   fun Nat_plus_interpreter thy model args t =
     case t of
-      Const (@{const_name Algebras.plus}, Type ("fun", [Type ("nat", []),
+      Const (@{const_name Groups.plus}, Type ("fun", [Type ("nat", []),
         Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
       let
         val size_of_nat = size_of_type thy model (Type ("nat", []))
@@ -2825,7 +2825,7 @@
 
   fun Nat_minus_interpreter thy model args t =
     case t of
-      Const (@{const_name Algebras.minus}, Type ("fun", [Type ("nat", []),
+      Const (@{const_name Groups.minus}, Type ("fun", [Type ("nat", []),
         Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
       let
         val size_of_nat = size_of_type thy model (Type ("nat", []))
@@ -2853,7 +2853,7 @@
 
   fun Nat_times_interpreter thy model args t =
     case t of
-      Const (@{const_name Algebras.times}, Type ("fun", [Type ("nat", []),
+      Const (@{const_name Groups.times}, Type ("fun", [Type ("nat", []),
         Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
       let
         val size_of_nat = size_of_type thy model (Type ("nat", []))
--- a/src/HOL/Tools/string_syntax.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/Tools/string_syntax.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -15,15 +15,14 @@
 
 (* nibble *)
 
-val nib_prefix = "String.nibble.";
-
 val mk_nib =
-  Syntax.Constant o unprefix nib_prefix o
+  Syntax.Constant o Syntax.mark_const o
     fst o Term.dest_Const o HOLogic.mk_nibble;
 
-fun dest_nib (Syntax.Constant c) =
-  HOLogic.dest_nibble (Const (nib_prefix ^ c, dummyT))
-    handle TERM _ => raise Match;
+fun dest_nib (Syntax.Constant s) =
+  (case try Syntax.unmark_const s of
+    NONE => raise Match
+  | SOME c => (HOLogic.dest_nibble (Const (c, HOLogic.nibbleT)) handle TERM _ => raise Match));
 
 
 (* char *)
--- a/src/HOL/UNITY/Comp/AllocBase.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/UNITY/Comp/AllocBase.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -58,9 +58,8 @@
 apply (rule monoI)
 apply (unfold prefix_def)
 apply (erule genPrefix.induct, auto)
-apply (simp add: union_le_mono)
 apply (erule order_trans)
-apply (rule union_upper1)
+apply simp
 done
 
 (** setsum **)
--- a/src/HOL/UNITY/Follows.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/UNITY/Follows.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -176,7 +176,7 @@
 apply (drule_tac x = "f xa" in spec)
 apply (drule_tac x = "g xa" in spec)
 apply (drule bspec, assumption) 
-apply (blast intro: union_le_mono order_trans)
+apply (blast intro: add_mono order_trans)
 done
 
 lemma Increasing_union: 
@@ -187,14 +187,14 @@
 apply (drule_tac x = "f xa" in spec)
 apply (drule_tac x = "g xa" in spec)
 apply (drule bspec, assumption) 
-apply (blast intro: union_le_mono order_trans)
+apply (blast intro: add_mono order_trans)
 done
 
 lemma Always_union:
      "[| F \<in> Always {s. f' s \<le> f s}; F \<in> Always {s. g' s \<le> g s} |]  
       ==> F \<in> Always {s. f' s + g' s \<le> f s + (g s :: ('a::order) multiset)}"
 apply (simp add: Always_eq_includes_reachable)
-apply (blast intro: union_le_mono)
+apply (blast intro: add_mono)
 done
 
 (*Except the last line, IDENTICAL to the proof script for Follows_Un_lemma*)
@@ -211,7 +211,7 @@
 apply (rule PSP_Stable)
 apply (erule_tac x = "f s" in spec)
 apply (erule Stable_Int, assumption, blast)
-apply (blast intro: union_le_mono order_trans)
+apply (blast intro: add_mono order_trans)
 done
 
 (*The !! is there to influence to effect of permutative rewriting at the end*)
--- a/src/HOL/ex/Arith_Examples.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/ex/Arith_Examples.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -33,7 +33,7 @@
 *)
 
 subsection {* Splitting of Operators: @{term max}, @{term min}, @{term abs},
-           @{term Algebras.minus}, @{term nat}, @{term Divides.mod},
+           @{term minus}, @{term nat}, @{term Divides.mod},
            @{term Divides.div} *}
 
 lemma "(i::nat) <= max i j"
--- a/src/HOL/ex/Binary.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/ex/Binary.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -24,8 +24,8 @@
     | dest_bit (Const (@{const_name True}, _)) = 1
     | dest_bit t = raise TERM ("dest_bit", [t]);
 
-  fun dest_binary (Const (@{const_name Algebras.zero}, Type (@{type_name nat}, _))) = 0
-    | dest_binary (Const (@{const_name Algebras.one}, Type (@{type_name nat}, _))) = 1
+  fun dest_binary (Const (@{const_name Groups.zero}, Type (@{type_name nat}, _))) = 0
+    | dest_binary (Const (@{const_name Groups.one}, Type (@{type_name nat}, _))) = 1
     | dest_binary (Const (@{const_name bit}, _) $ bs $ b) = 2 * dest_binary bs + dest_bit b
     | dest_binary t = raise TERM ("dest_binary", [t]);
 
@@ -191,7 +191,7 @@
 parse_translation {*
 let
   val syntax_consts =
-    map_aterms (fn Const (c, T) => Const (Syntax.constN ^ c, T) | a => a);
+    map_aterms (fn Const (c, T) => Const (Syntax.mark_const c, T) | a => a);
 
   fun binary_tr [Const (num, _)] =
         let
--- a/src/HOL/ex/SVC_Oracle.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/ex/SVC_Oracle.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -63,21 +63,21 @@
     (*abstraction of a numeric literal*)
     fun lit t = if can HOLogic.dest_number t then t else replace t;
     (*abstraction of a real/rational expression*)
-    fun rat ((c as Const(@{const_name Algebras.plus}, _)) $ x $ y) = c $ (rat x) $ (rat y)
-      | rat ((c as Const(@{const_name Algebras.minus}, _)) $ x $ y) = c $ (rat x) $ (rat y)
+    fun rat ((c as Const(@{const_name Groups.plus}, _)) $ x $ y) = c $ (rat x) $ (rat y)
+      | rat ((c as Const(@{const_name Groups.minus}, _)) $ x $ y) = c $ (rat x) $ (rat y)
       | rat ((c as Const(@{const_name Rings.divide}, _)) $ x $ y) = c $ (rat x) $ (rat y)
-      | rat ((c as Const(@{const_name Algebras.times}, _)) $ x $ y) = c $ (rat x) $ (rat y)
-      | rat ((c as Const(@{const_name Algebras.uminus}, _)) $ x) = c $ (rat x)
+      | rat ((c as Const(@{const_name Groups.times}, _)) $ x $ y) = c $ (rat x) $ (rat y)
+      | rat ((c as Const(@{const_name Groups.uminus}, _)) $ x) = c $ (rat x)
       | rat t = lit t
     (*abstraction of an integer expression: no div, mod*)
-    fun int ((c as Const(@{const_name Algebras.plus}, _)) $ x $ y) = c $ (int x) $ (int y)
-      | int ((c as Const(@{const_name Algebras.minus}, _)) $ x $ y) = c $ (int x) $ (int y)
-      | int ((c as Const(@{const_name Algebras.times}, _)) $ x $ y) = c $ (int x) $ (int y)
-      | int ((c as Const(@{const_name Algebras.uminus}, _)) $ x) = c $ (int x)
+    fun int ((c as Const(@{const_name Groups.plus}, _)) $ x $ y) = c $ (int x) $ (int y)
+      | int ((c as Const(@{const_name Groups.minus}, _)) $ x $ y) = c $ (int x) $ (int y)
+      | int ((c as Const(@{const_name Groups.times}, _)) $ x $ y) = c $ (int x) $ (int y)
+      | int ((c as Const(@{const_name Groups.uminus}, _)) $ x) = c $ (int x)
       | int t = lit t
     (*abstraction of a natural number expression: no minus*)
-    fun nat ((c as Const(@{const_name Algebras.plus}, _)) $ x $ y) = c $ (nat x) $ (nat y)
-      | nat ((c as Const(@{const_name Algebras.times}, _)) $ x $ y) = c $ (nat x) $ (nat y)
+    fun nat ((c as Const(@{const_name Groups.plus}, _)) $ x $ y) = c $ (nat x) $ (nat y)
+      | nat ((c as Const(@{const_name Groups.times}, _)) $ x $ y) = c $ (nat x) $ (nat y)
       | nat ((c as Const(@{const_name Suc}, _)) $ x) = c $ (nat x)
       | nat t = lit t
     (*abstraction of a relation: =, <, <=*)
--- a/src/HOL/ex/Summation.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/ex/Summation.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -28,7 +28,7 @@
 
 lemma \<Delta>_same_shift:
   assumes "\<Delta> f = \<Delta> g"
-  shows "\<exists>l. (op +) l \<circ> f = g"
+  shows "\<exists>l. plus l \<circ> f = g"
 proof -
   fix k
   from assms have "\<And>k. \<Delta> f k = \<Delta> g k" by simp
@@ -44,9 +44,9 @@
     show "f k - g k = f 0 - g 0"
       by (induct k rule: int_induct) (simp_all add: k_incr k_decr)
   qed
-  then have "\<And>k. ((op +) (g 0 - f 0) \<circ> f) k = g k"
+  then have "\<And>k. (plus (g 0 - f 0) \<circ> f) k = g k"
     by (simp add: algebra_simps)
-  then have "(op +) (g 0 - f 0) \<circ> f = g" ..
+  then have "plus (g 0 - f 0) \<circ> f = g" ..
   then show ?thesis ..
 qed
 
@@ -99,7 +99,7 @@
   "\<Sigma> (\<Delta> f) j l = f l - f j"
 proof -
   from \<Delta>_\<Sigma> have "\<Delta> (\<Sigma> (\<Delta> f) j) = \<Delta> f" .
-  then obtain k where "(op +) k \<circ> \<Sigma> (\<Delta> f) j = f" by (blast dest: \<Delta>_same_shift)
+  then obtain k where "plus k \<circ> \<Sigma> (\<Delta> f) j = f" by (blast dest: \<Delta>_same_shift)
   then have "\<And>q. f q = k + \<Sigma> (\<Delta> f) j q" by (simp add: expand_fun_eq)
   then show ?thesis by simp
 qed
--- a/src/HOL/ex/svc_funcs.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOL/ex/svc_funcs.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -146,16 +146,16 @@
     (*translation of a literal*)
     val lit = snd o HOLogic.dest_number;
     (*translation of a literal expression [no variables]*)
-    fun litExp (Const(@{const_name Algebras.plus}, T) $ x $ y) =
+    fun litExp (Const(@{const_name Groups.plus}, T) $ x $ y) =
           if is_numeric_op T then (litExp x) + (litExp y)
           else fail t
-      | litExp (Const(@{const_name Algebras.minus}, T) $ x $ y) =
+      | litExp (Const(@{const_name Groups.minus}, T) $ x $ y) =
           if is_numeric_op T then (litExp x) - (litExp y)
           else fail t
-      | litExp (Const(@{const_name Algebras.times}, T) $ x $ y) =
+      | litExp (Const(@{const_name Groups.times}, T) $ x $ y) =
           if is_numeric_op T then (litExp x) * (litExp y)
           else fail t
-      | litExp (Const(@{const_name Algebras.uminus}, T) $ x)   =
+      | litExp (Const(@{const_name Groups.uminus}, T) $ x)   =
           if is_numeric_op T then ~(litExp x)
           else fail t
       | litExp t = lit t
@@ -163,21 +163,21 @@
     (*translation of a real/rational expression*)
     fun suc t = Interp("+", [Int 1, t])
     fun tm (Const(@{const_name Suc}, T) $ x) = suc (tm x)
-      | tm (Const(@{const_name Algebras.plus}, T) $ x $ y) =
+      | tm (Const(@{const_name Groups.plus}, T) $ x $ y) =
           if is_numeric_op T then Interp("+", [tm x, tm y])
           else fail t
-      | tm (Const(@{const_name Algebras.minus}, T) $ x $ y) =
+      | tm (Const(@{const_name Groups.minus}, T) $ x $ y) =
           if is_numeric_op T then
               Interp("+", [tm x, Interp("*", [Int ~1, tm y])])
           else fail t
-      | tm (Const(@{const_name Algebras.times}, T) $ x $ y) =
+      | tm (Const(@{const_name Groups.times}, T) $ x $ y) =
           if is_numeric_op T then Interp("*", [tm x, tm y])
           else fail t
       | tm (Const(@{const_name Rings.inverse}, T) $ x) =
           if domain_type T = HOLogic.realT then
               Rat(1, litExp x)
           else fail t
-      | tm (Const(@{const_name Algebras.uminus}, T) $ x) =
+      | tm (Const(@{const_name Groups.uminus}, T) $ x) =
           if is_numeric_op T then Interp("*", [Int ~1, tm x])
           else fail t
       | tm t = Int (lit t)
--- a/src/HOLCF/IOA/meta_theory/Seq.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOLCF/IOA/meta_theory/Seq.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -8,7 +8,7 @@
 imports HOLCF
 begin
 
-domain 'a seq = nil | cons (HD :: 'a) (lazy TL :: "'a seq")  (infixr "##" 65)
+domain 'a seq = nil  ("nil") | cons (HD :: 'a) (lazy TL :: "'a seq")  (infixr "##" 65)
 
 consts
    sfilter       :: "('a -> tr) -> 'a seq -> 'a seq"
--- a/src/HOLCF/IOA/meta_theory/Sequence.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOLCF/IOA/meta_theory/Sequence.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -40,7 +40,7 @@
   "_partlist"     :: "args => 'a Seq"              ("[(_)?]")
 translations
   "[x, xs!]"     == "x>>[xs!]"
-  "[x!]"         == "x>>CONST nil"
+  "[x!]"         == "x>>nil"
   "[x, xs?]"     == "x>>[xs?]"
   "[x?]"         == "x>>CONST UU"
 
--- a/src/HOLCF/Tools/Domain/domain_syntax.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOLCF/Tools/Domain/domain_syntax.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -7,6 +7,7 @@
 signature DOMAIN_SYNTAX =
 sig
   val calc_syntax:
+      theory ->
       bool ->
       typ ->
       (string * typ list) *
@@ -28,7 +29,7 @@
 open Domain_Library;
 infixr 5 -->; infixr 6 ->>;
 
-fun calc_syntax  (* FIXME authentic syntax *)
+fun calc_syntax thy
     (definitional : bool)
     (dtypeprod : typ)
     ((dname : string, typevars : typ list), 
@@ -60,7 +61,7 @@
       val escape = let
         fun esc (c::cs) = if c mem ["'","_","(",")","/"] then "'"::c::esc cs
                           else      c::esc cs
-          |   esc []      = []
+          | esc []      = []
       in implode o esc o Symbol.explode end;
 
       fun dis_name_ con =
@@ -113,41 +114,45 @@
 
 (* ----- case translation --------------------------------------------------- *)
 
+    fun syntax b = Syntax.mark_const (Sign.full_bname thy b);
+
     local open Syntax in
     local
-      fun c_ast con mx = Constant (Binding.name_of con);   (* FIXME proper const syntax *)
-      fun expvar n     = Variable ("e"^(string_of_int n));
-      fun argvar n m _ = Variable ("a"^(string_of_int n)^"_"^
-                                   (string_of_int m));
+      fun c_ast authentic con = Constant ((authentic ? syntax) (Binding.name_of con));
+      fun expvar n = Variable ("e" ^ string_of_int n);
+      fun argvar n m _ = Variable ("a" ^ string_of_int n ^ "_" ^ string_of_int m);
       fun argvars n args = mapn (argvar n) 1 args;
-      fun app s (l,r)  = mk_appl (Constant s) [l,r];
+      fun app s (l, r) = mk_appl (Constant s) [l, r];
       val cabs = app "_cabs";
-      val capp = app "Rep_CFun";
-      fun con1 n (con,args,mx) = Library.foldl capp (c_ast con mx, argvars n args);
-      fun case1 n (con,args,mx) = app "_case1" (con1 n (con,args,mx), expvar n);
+      val capp = app @{const_syntax Rep_CFun};
+      fun con1 authentic n (con,args,mx) =
+        Library.foldl capp (c_ast authentic con, argvars n args);
+      fun case1 authentic n (con,args,mx) =
+        app "_case1" (con1 authentic n (con,args,mx), expvar n);
       fun arg1 n (con,args,_) = List.foldr cabs (expvar n) (argvars n args);
-      fun when1 n m = if n = m then arg1 n else K (Constant "UU");
+      fun when1 n m = if n = m then arg1 n else K (Constant @{const_syntax UU});
           
       fun app_var x = mk_appl (Constant "_variable") [x, Variable "rhs"];
       fun app_pat x = mk_appl (Constant "_pat") [x];
       fun args_list [] = Constant "_noargs"
-        |   args_list xs = foldr1 (app "_args") xs;
+        | args_list xs = foldr1 (app "_args") xs;
     in
-    val case_trans =
-        ParsePrintRule
-          (app "_case_syntax" (Variable "x", foldr1 (app "_case2") (mapn case1 1 cons')),
-           capp (Library.foldl capp (Constant (dnam^"_when"), mapn arg1 1 cons'), Variable "x"));
-        
-    fun one_abscon_trans n (con,mx,args) =
+    fun case_trans authentic =
         ParsePrintRule
-          (cabs (con1 n (con,mx,args), expvar n),
-           Library.foldl capp (Constant (dnam^"_when"), mapn (when1 n) 1 cons'));
-    val abscon_trans = mapn one_abscon_trans 1 cons';
+          (app "_case_syntax" (Variable "x", foldr1 (app "_case2") (mapn (case1 authentic) 1 cons')),
+           capp (Library.foldl capp
+            (Constant (syntax (dnam ^ "_when")), mapn arg1 1 cons'), Variable "x"));
         
-    fun one_case_trans (con,args,mx) =
+    fun one_abscon_trans authentic n (con,mx,args) =
+        ParsePrintRule
+          (cabs (con1 authentic n (con,mx,args), expvar n),
+           Library.foldl capp (Constant (syntax (dnam ^ "_when")), mapn (when1 n) 1 cons'));
+    fun abscon_trans authentic = mapn (one_abscon_trans authentic) 1 cons';
+        
+    fun one_case_trans authentic (con,args,mx) =
       let
-        val cname = c_ast con mx;
-        val pname = Constant (strip_esc (Binding.name_of con) ^ "_pat");
+        val cname = c_ast authentic con;
+        val pname = Constant (syntax (strip_esc (Binding.name_of con) ^ "_pat"));
         val ns = 1 upto length args;
         val xs = map (fn n => Variable ("x"^(string_of_int n))) ns;
         val ps = map (fn n => Variable ("p"^(string_of_int n))) ns;
@@ -160,7 +165,7 @@
          PrintRule (Library.foldl capp (cname, ListPair.map (app "_match") (ps,vs)),
                     app "_match" (mk_appl pname ps, args_list vs))]
         end;
-    val Case_trans = maps one_case_trans cons';
+    val Case_trans = maps (one_case_trans false) cons' @ maps (one_case_trans true) cons';
     end;
     end;
     val optional_consts =
@@ -169,7 +174,7 @@
   in (optional_consts @ [const_when] @ 
       consts_con @ consts_dis @ consts_mat @ consts_pat @ consts_sel @
       [const_take, const_finite],
-      (case_trans::(abscon_trans @ Case_trans)))
+      (case_trans false :: case_trans true :: (abscon_trans false @ abscon_trans true @ Case_trans)))
   end; (* let *)
 
 (* ----- putting all the syntax stuff together ------------------------------ *)
@@ -192,9 +197,9 @@
     val const_bisim =
         (Binding.name (comp_dnam^"_bisim"), relprod --> boolT, NoSyn);
     val ctt : ((binding * typ * mixfix) list * ast Syntax.trrule list) list =
-        map (calc_syntax definitional funprod) eqs';
+        map (calc_syntax thy'' definitional funprod) eqs';
   in thy''
-       |> ContConsts.add_consts_i
+       |> Cont_Consts.add_consts
            (maps fst ctt @ 
             (if length eqs'>1 andalso not definitional
              then [const_copy] else []) @
--- a/src/HOLCF/Tools/cont_consts.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/HOLCF/Tools/cont_consts.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -7,37 +7,28 @@
 
 signature CONT_CONSTS =
 sig
-  val add_consts: (binding * string * mixfix) list -> theory -> theory
-  val add_consts_i: (binding * typ * mixfix) list -> theory -> theory
+  val add_consts: (binding * typ * mixfix) list -> theory -> theory
+  val add_consts_cmd: (binding * string * mixfix) list -> theory -> theory
 end;
 
-structure ContConsts: CONT_CONSTS =
+structure Cont_Consts: CONT_CONSTS =
 struct
 
 
 (* misc utils *)
 
-fun first  (x,_,_) = x;
-fun second (_,x,_) = x;
-fun third  (_,_,x) = x;
-fun upd_first  f (x,y,z) = (f x,   y,   z);
-fun upd_second f (x,y,z) = (  x, f y,   z);
-fun upd_third  f (x,y,z) = (  x,   y, f z);
-
-fun change_arrow 0 T               = T
-|   change_arrow n (Type(_,[S,T])) = Type ("fun",[S,change_arrow (n-1) T])
-|   change_arrow _ _               = sys_error "cont_consts: change_arrow";
+fun change_arrow 0 T = T
+  | change_arrow n (Type (_, [S, T])) = Type ("fun", [S, change_arrow (n - 1) T])
+  | change_arrow _ T = raise TYPE ("cont_consts: change_arrow", [T], []);
 
 fun trans_rules name2 name1 n mx =
   let
-    fun argnames _ 0 = []
-    |   argnames c n = chr c::argnames (c+1) (n-1);
-    val vnames = argnames (ord "A") n;
+    val vnames = Name.invents Name.context "a" n;
     val extra_parse_rule = Syntax.ParseRule (Constant name2, Constant name1);
   in
     [Syntax.ParsePrintRule
       (Syntax.mk_appl (Constant name2) (map Variable vnames),
-        fold (fn arg => fn t => Syntax.mk_appl (Constant "Rep_CFun") [t, Variable arg])
+        fold (fn a => fn t => Syntax.mk_appl (Constant @{const_syntax Rep_CFun}) [t, Variable a])
           vnames (Constant name1))] @
     (case mx of
       Infix _ => [extra_parse_rule]
@@ -53,42 +44,51 @@
    declaration with the original name, type ...=>..., and the original mixfix
    is generated and connected to the other declaration via some translation.
 *)
-fun transform (c, T, mx) =
-    let
-        val c1 = Binding.name_of c;
-        val c2 = "_cont_" ^ c1;
-        val n  = Syntax.mixfix_args mx
-    in     ((c, T, NoSyn),
-            (Binding.name c2, change_arrow n T, mx),
-            trans_rules c2 c1 n mx) end;
+fun transform thy (c, T, mx) =
+  let
+    fun syntax b = Syntax.mark_const (Sign.full_bname thy b);
+    val c1 = Binding.name_of c;
+    val c2 = c1 ^ "_cont_syntax";
+    val n = Syntax.mixfix_args mx;
+  in
+    ((c, T, NoSyn),
+      (Binding.name c2, change_arrow n T, mx),
+      trans_rules (syntax c2) (syntax c1) n mx)
+  end;
 
-fun cfun_arity (Type(n,[_,T])) = if n = @{type_name "->"} then 1+cfun_arity T else 0
-|   cfun_arity _               = 0;
+fun cfun_arity (Type (n, [_, T])) = if n = @{type_name "->"} then 1 + cfun_arity T else 0
+  | cfun_arity _ = 0;
 
-fun is_contconst (_,_,NoSyn   ) = false
-|   is_contconst (_,_,Binder _) = false
-|   is_contconst (c,T,mx      ) =
-      cfun_arity T >= Syntax.mixfix_args mx
-        handle ERROR msg => cat_error msg ("in mixfix annotation for " ^ quote (Binding.str_of c));
+fun is_contconst (_, _, NoSyn) = false
+  | is_contconst (_, _, Binder _) = false    (* FIXME ? *)
+  | is_contconst (c, T, mx) =
+      let
+        val n = Syntax.mixfix_args mx handle ERROR msg =>
+          cat_error msg ("in mixfix annotation for " ^ quote (Binding.str_of c));
+      in cfun_arity T >= n end;
 
 
-(* add_consts(_i) *)
+(* add_consts *)
+
+local
 
 fun gen_add_consts prep_typ raw_decls thy =
   let
-    val decls = map (upd_second (prep_typ thy)) raw_decls;
+    val decls = map (fn (c, T, mx) => (c, prep_typ thy T, mx)) raw_decls;
     val (contconst_decls, normal_decls) = List.partition is_contconst decls;
-    val transformed_decls = map transform contconst_decls;
+    val transformed_decls = map (transform thy) contconst_decls;
   in
     thy
-    |> Sign.add_consts_i
-      (normal_decls @ map first transformed_decls @ map second transformed_decls)
-    (* FIXME authentic syntax *)
-    |> Sign.add_trrules_i (maps third transformed_decls)
+    |> Sign.add_consts_i (normal_decls @ map #1 transformed_decls @ map #2 transformed_decls)
+    |> Sign.add_trrules_i (maps #3 transformed_decls)
   end;
 
-val add_consts = gen_add_consts Syntax.read_typ_global;
-val add_consts_i = gen_add_consts Sign.certify_typ;
+in
+
+val add_consts = gen_add_consts Sign.certify_typ;
+val add_consts_cmd = gen_add_consts Syntax.read_typ_global;
+
+end;
 
 
 (* outer syntax *)
@@ -97,7 +97,7 @@
 
 val _ =
   OuterSyntax.command "consts" "declare constants (HOLCF)" K.thy_decl
-    (Scan.repeat1 P.const_binding >> (Toplevel.theory o add_consts));
+    (Scan.repeat1 P.const_binding >> (Toplevel.theory o add_consts_cmd));
 
 end;
 
--- a/src/Provers/Arith/abel_cancel.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Provers/Arith/abel_cancel.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -28,29 +28,29 @@
 
 (* FIXME dependent on abstract syntax *)
 
-fun zero t = Const (@{const_name Algebras.zero}, t);
-fun minus t = Const (@{const_name Algebras.uminus}, t --> t);
+fun zero t = Const (@{const_name Groups.zero}, t);
+fun minus t = Const (@{const_name Groups.uminus}, t --> t);
 
-fun add_terms pos (Const (@{const_name Algebras.plus}, _) $ x $ y, ts) =
+fun add_terms pos (Const (@{const_name Groups.plus}, _) $ x $ y, ts) =
       add_terms pos (x, add_terms pos (y, ts))
-  | add_terms pos (Const (@{const_name Algebras.minus}, _) $ x $ y, ts) =
+  | add_terms pos (Const (@{const_name Groups.minus}, _) $ x $ y, ts) =
       add_terms pos (x, add_terms (not pos) (y, ts))
-  | add_terms pos (Const (@{const_name Algebras.uminus}, _) $ x, ts) =
+  | add_terms pos (Const (@{const_name Groups.uminus}, _) $ x, ts) =
       add_terms (not pos) (x, ts)
   | add_terms pos (x, ts) = (pos,x) :: ts;
 
 fun terms fml = add_terms true (fml, []);
 
-fun zero1 pt (u as (c as Const(@{const_name Algebras.plus},_)) $ x $ y) =
+fun zero1 pt (u as (c as Const(@{const_name Groups.plus},_)) $ x $ y) =
       (case zero1 pt x of NONE => (case zero1 pt y of NONE => NONE
                                    | SOME z => SOME(c $ x $ z))
        | SOME z => SOME(c $ z $ y))
-  | zero1 (pos,t) (u as (c as Const(@{const_name Algebras.minus},_)) $ x $ y) =
+  | zero1 (pos,t) (u as (c as Const(@{const_name Groups.minus},_)) $ x $ y) =
       (case zero1 (pos,t) x of
          NONE => (case zero1 (not pos,t) y of NONE => NONE
                   | SOME z => SOME(c $ x $ z))
        | SOME z => SOME(c $ z $ y))
-  | zero1 (pos,t) (u as (c as Const(@{const_name Algebras.uminus},_)) $ x) =
+  | zero1 (pos,t) (u as (c as Const(@{const_name Groups.uminus},_)) $ x) =
       (case zero1 (not pos,t) x of NONE => NONE
        | SOME z => SOME(c $ z))
   | zero1 (pos,t) u =
@@ -71,7 +71,7 @@
 fun cancel t =
   let
     val c $ lhs $ rhs = t
-    val opp = case c of Const(@{const_name Algebras.plus},_) => true | _ => false;
+    val opp = case c of Const(@{const_name Groups.plus},_) => true | _ => false;
     val (pos,l) = find_common opp (terms lhs) (terms rhs)
     val posr = if opp then not pos else pos
     val t' = c $ (the(zero1 (pos,l) lhs)) $ (the(zero1 (posr,l) rhs))
--- a/src/Provers/Arith/cancel_div_mod.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Provers/Arith/cancel_div_mod.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -34,12 +34,12 @@
 functor CancelDivModFun(Data: CANCEL_DIV_MOD_DATA): CANCEL_DIV_MOD =
 struct
 
-fun coll_div_mod (Const(@{const_name Algebras.plus},_) $ s $ t) dms =
+fun coll_div_mod (Const(@{const_name Groups.plus},_) $ s $ t) dms =
       coll_div_mod t (coll_div_mod s dms)
-  | coll_div_mod (Const(@{const_name Algebras.times},_) $ m $ (Const(d,_) $ s $ n))
+  | coll_div_mod (Const(@{const_name Groups.times},_) $ m $ (Const(d,_) $ s $ n))
                  (dms as (divs,mods)) =
       if d = Data.div_name andalso m=n then ((s,n)::divs,mods) else dms
-  | coll_div_mod (Const(@{const_name Algebras.times},_) $ (Const(d,_) $ s $ n) $ m)
+  | coll_div_mod (Const(@{const_name Groups.times},_) $ (Const(d,_) $ s $ n) $ m)
                  (dms as (divs,mods)) =
       if d = Data.div_name andalso m=n then ((s,n)::divs,mods) else dms
   | coll_div_mod (Const(m,_) $ s $ n) (dms as (divs,mods)) =
@@ -55,8 +55,8 @@
    ==> thesis by transitivity
 *)
 
-val mk_plus = Data.mk_binop @{const_name Algebras.plus};
-val mk_times = Data.mk_binop @{const_name Algebras.times};
+val mk_plus = Data.mk_binop @{const_name Groups.plus};
+val mk_times = Data.mk_binop @{const_name Groups.times};
 
 fun rearrange t pq =
   let val ts = Data.dest_sum t;
--- a/src/Pure/Isar/expression.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Pure/Isar/expression.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -604,7 +604,7 @@
 
 (* achieve plain syntax for locale predicates (without "PROP") *)
 
-fun aprop_tr' n c = (Syntax.constN ^ c, fn ctxt => fn args =>
+fun aprop_tr' n c = (Syntax.mark_const c, fn ctxt => fn args =>
   if length args = n then
     Syntax.const "_aprop" $   (* FIXME avoid old-style early externing (!??) *)
       Term.list_comb (Syntax.free (Consts.extern (ProofContext.consts_of ctxt) c), args)
--- a/src/Pure/Isar/proof_context.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Pure/Isar/proof_context.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -28,7 +28,6 @@
   val full_name: Proof.context -> binding -> string
   val syn_of: Proof.context -> Syntax.syntax
   val consts_of: Proof.context -> Consts.T
-  val const_syntax_name: Proof.context -> string -> string
   val the_const_constraint: Proof.context -> string -> typ
   val set_syntax_mode: Syntax.mode -> Proof.context -> Proof.context
   val restore_syntax_mode: Proof.context -> Proof.context -> Proof.context
@@ -235,7 +234,6 @@
 val restore_syntax_mode = map_syntax o Local_Syntax.restore_mode o syntax_of;
 
 val consts_of = #1 o #consts o rep_context;
-val const_syntax_name = Consts.syntax_name o consts_of;
 val the_const_constraint = Consts.the_constraint o consts_of;
 
 val facts_of = #facts o rep_context;
@@ -707,10 +705,10 @@
     val consts = consts_of ctxt;
   in
     t
-    |> Sign.extern_term (Consts.extern_early consts) thy
+    |> Sign.extern_term thy
     |> Local_Syntax.extern_term syntax
-    |> Syntax.standard_unparse_term (Consts.extern consts) ctxt (Local_Syntax.syn_of syntax)
-        (not (PureThy.old_appl_syntax thy))
+    |> Syntax.standard_unparse_term (Consts.extern consts) ctxt
+        (Local_Syntax.syn_of syntax) (not (PureThy.old_appl_syntax thy))
   end;
 
 in
@@ -990,7 +988,7 @@
 fun const_ast_tr intern ctxt [Syntax.Variable c] =
       let
         val Const (c', _) = read_const_proper ctxt c;
-        val d = if intern then const_syntax_name ctxt c' else c;
+        val d = if intern then Syntax.mark_const c' else c;
       in Syntax.Constant d end
   | const_ast_tr _ _ asts = raise Syntax.AST ("const_ast_tr", asts);
 
@@ -1018,7 +1016,9 @@
 
 fun const_syntax _ (Free (x, T), mx) = SOME (true, (x, T, mx))
   | const_syntax ctxt (Const (c, _), mx) =
-      Option.map (pair false) (try (Consts.syntax (consts_of ctxt)) (c, mx))
+      (case try (Consts.type_scheme (consts_of ctxt)) c of
+        SOME T => SOME (false, (Syntax.mark_const c, T, mx))
+      | NONE => NONE)
   | const_syntax _ _ = NONE;
 
 in
--- a/src/Pure/ML/ml_antiquote.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Pure/ML/ml_antiquote.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -114,7 +114,7 @@
 
 fun const syn = Args.context -- Scan.lift Args.name_source >> (fn (ctxt, c) =>
   #1 (Term.dest_Const (ProofContext.read_const_proper ctxt c))
-  |> syn ? ProofContext.const_syntax_name ctxt
+  |> syn ? Syntax.mark_const
   |> ML_Syntax.print_string);
 
 val _ = inline "const_name" (const false);
--- a/src/Pure/Proof/proof_syntax.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Pure/Proof/proof_syntax.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -67,8 +67,8 @@
        ("", paramT --> paramsT, Delimfix "_")]
   |> Sign.add_modesyntax_i (Symbol.xsymbolsN, true)
       [("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(1\\<Lambda>_./ _)", [0, 3], 3)),
-       (Syntax.constN ^ "Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ \\<cdot>/ _)", [4, 5], 4)),
-       (Syntax.constN ^ "AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ \\<bullet>/ _)", [4, 5], 4))]
+       (Syntax.mark_const "Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ \\<cdot>/ _)", [4, 5], 4)),
+       (Syntax.mark_const "AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ \\<bullet>/ _)", [4, 5], 4))]
   |> Sign.add_modesyntax_i ("latex", false)
       [("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(1\\<^bold>\\<lambda>_./ _)", [0, 3], 3))]
   |> Sign.add_trrules_i (map Syntax.ParsePrintRule
@@ -78,10 +78,10 @@
           [Variable "l", Syntax.mk_appl (Constant "_Lam") [Variable "m", Variable "A"]]),
        (Syntax.mk_appl (Constant "_Lam")
           [Syntax.mk_appl (Constant "_Lam1") [Variable "x", Variable "A"], Variable "B"],
-        Syntax.mk_appl (Constant (Syntax.constN ^ "AbsP")) [Variable "A",
+        Syntax.mk_appl (Constant (Syntax.mark_const "AbsP")) [Variable "A",
           (Syntax.mk_appl (Constant "_abs") [Variable "x", Variable "B"])]),
        (Syntax.mk_appl (Constant "_Lam") [Variable "x", Variable "A"],
-        Syntax.mk_appl (Constant (Syntax.constN ^ "Abst"))
+        Syntax.mk_appl (Constant (Syntax.mark_const "Abst"))
           [(Syntax.mk_appl (Constant "_abs") [Variable "x", Variable "A"])])]);
 
 
--- a/src/Pure/Syntax/lexicon.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Pure/Syntax/lexicon.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -31,7 +31,11 @@
   val read_xnum: string -> {radix: int, leading_zeros: int, value: int}
   val read_float: string -> {mant: int, exp: int}
   val fixedN: string
+  val mark_fixed: string -> string
+  val unmark_fixed: string -> string
   val constN: string
+  val mark_const: string -> string
+  val unmark_const: string -> string
 end;
 
 signature LEXICON =
@@ -331,8 +335,13 @@
 
 (* specific identifiers *)
 
+val fixedN = "\\<^fixed>";
+val mark_fixed = prefix fixedN;
+val unmark_fixed = unprefix fixedN;
+
 val constN = "\\<^const>";
-val fixedN = "\\<^fixed>";
+val mark_const = prefix constN;
+val unmark_const = unprefix constN;
 
 
 (* read numbers *)
--- a/src/Pure/Syntax/printer.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Pure/Syntax/printer.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -321,10 +321,10 @@
             else pr, args))
 
     and atomT a =
-      (case try (unprefix Lexicon.constN) a of
+      (case try Lexicon.unmark_const a of
         SOME c => Pretty.mark (Markup.const c) (Pretty.str (extern_const c))
       | NONE =>
-          (case try (unprefix Lexicon.fixedN) a of
+          (case try Lexicon.unmark_fixed a of
             SOME x => the (token_trans "_free" x)
           | NONE => Pretty.str a))
 
@@ -340,8 +340,8 @@
       let
         val nargs = length args;
         val markup = Pretty.mark
-          (Markup.const (unprefix Lexicon.constN a) handle Fail _ =>
-            (Markup.fixed (unprefix Lexicon.fixedN a)))
+          (Markup.const (Lexicon.unmark_const a) handle Fail _ =>
+            (Markup.fixed (Lexicon.unmark_fixed a)))
           handle Fail _ => I;
 
         (*find matching table entry, or print as prefix / postfix*)
--- a/src/Pure/Syntax/syn_trans.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Pure/Syntax/syn_trans.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -129,13 +129,15 @@
 
 (* type propositions *)
 
-fun mk_type ty = Lexicon.const "_constrain" $ Lexicon.const "TYPE" $ (Lexicon.const "itself" $ ty);
+fun mk_type ty =
+  Lexicon.const "_constrain" $
+    Lexicon.const "\\<^const>TYPE" $ (Lexicon.const "itself" $ ty);
 
 fun ofclass_tr (*"_ofclass"*) [ty, cls] = cls $ mk_type ty
   | ofclass_tr (*"_ofclass"*) ts = raise TERM ("ofclass_tr", ts);
 
 fun sort_constraint_tr (*"_sort_constraint"*) [ty] =
-      Lexicon.const "Pure.sort_constraint" $ mk_type ty
+      Lexicon.const "\\<^const>Pure.sort_constraint" $ mk_type ty
   | sort_constraint_tr (*"_sort_constraint"*) ts = raise TERM ("sort_constraint_tr", ts);
 
 
@@ -152,7 +154,7 @@
         (case Ast.unfold_ast_p "_asms" asms of
           (asms', Ast.Appl [Ast.Constant "_asm", asm']) => asms' @ [asm']
         | _ => raise Ast.AST ("bigimpl_ast_tr", asts))
-      in Ast.fold_ast_p "==>" (prems, concl) end
+      in Ast.fold_ast_p "\\<^const>==>" (prems, concl) end
   | bigimpl_ast_tr (*"_bigimpl"*) asts = raise Ast.AST ("bigimpl_ast_tr", asts);
 
 
@@ -350,7 +352,7 @@
 
 (* type propositions *)
 
-fun type_prop_tr' _ (*"_type_prop"*) T [Const ("Pure.sort_constraint", _)] =
+fun type_prop_tr' _ (*"_type_prop"*) T [Const ("\\<^const>Pure.sort_constraint", _)] =
       Lexicon.const "_sort_constraint" $ TypeExt.term_of_typ true T
   | type_prop_tr' show_sorts (*"_type_prop"*) T [t] =
       Lexicon.const "_ofclass" $ TypeExt.term_of_typ show_sorts T $ t
@@ -366,7 +368,7 @@
     fun is_prop Ts t =
       fastype_of1 (Ts, t) = propT handle TERM _ => false;
 
-    fun is_term (Const ("Pure.term", _) $ _) = true
+    fun is_term (Const ("\\<^const>Pure.term", _) $ _) = true
       | is_term _ = false;
 
     fun tr' _ (t as Const _) = t
@@ -379,7 +381,7 @@
       | tr' Ts (t as Bound _) =
           if is_prop Ts t then aprop t else t
       | tr' Ts (Abs (x, T, t)) = Abs (x, T, tr' (T :: Ts) t)
-      | tr' Ts (t as t1 $ (t2 as Const ("TYPE", Type ("itself", [T])))) =
+      | tr' Ts (t as t1 $ (t2 as Const ("\\<^const>TYPE", Type ("itself", [T])))) =
           if is_prop Ts t andalso not (is_term t) then Const ("_type_prop", T) $ tr' Ts t1
           else tr' Ts t1 $ tr' Ts t2
       | tr' Ts (t as t1 $ t2) =
@@ -393,7 +395,7 @@
 fun impl_ast_tr' (*"==>"*) asts =
   if TypeExt.no_brackets () then raise Match
   else
-    (case Ast.unfold_ast_p "==>" (Ast.Appl (Ast.Constant "==>" :: asts)) of
+    (case Ast.unfold_ast_p "\\<^const>==>" (Ast.Appl (Ast.Constant "\\<^const>==>" :: asts)) of
       (prems as _ :: _ :: _, concl) =>
         let
           val (asms, asm) = split_last prems;
@@ -514,11 +516,13 @@
    [("_abs", abs_ast_tr'),
     ("_idts", idtyp_ast_tr' "_idts"),
     ("_pttrns", idtyp_ast_tr' "_pttrns"),
-    ("==>", impl_ast_tr'),
+    ("\\<^const>==>", impl_ast_tr'),
     ("_index", index_ast_tr')]);
 
 val pure_trfunsT =
-  [("_type_prop", type_prop_tr'), ("TYPE", type_tr'), ("_type_constraint_", type_constraint_tr')];
+ [("_type_prop", type_prop_tr'),
+  ("\\<^const>TYPE", type_tr'),
+  ("_type_constraint_", type_constraint_tr')];
 
 fun struct_trfuns structs =
   ([], [("_struct", struct_tr structs)], [], [("_struct", struct_ast_tr' structs)]);
--- a/src/Pure/Syntax/syntax.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Pure/Syntax/syntax.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -302,7 +302,7 @@
       lexicon =
         if changed then fold Scan.extend_lexicon (SynExt.delims_of xprods) lexicon else lexicon,
       gram = if changed then Parser.extend_gram gram xprods else gram,
-      consts = Library.merge (op =) (consts1, filter_out Long_Name.is_qualified consts2),
+      consts = Library.merge (op =) (consts1, filter_out (can Lexicon.unmark_const) consts2),
       prmodes = insert (op =) mode (Library.merge (op =) (prmodes1, prmodes2)),
       parse_ast_trtab =
         update_trtab "parse ast translation" (if_inout parse_ast_translation) parse_ast_trtab,
--- a/src/Pure/Syntax/type_ext.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Pure/Syntax/type_ext.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -123,7 +123,9 @@
       | decode (t $ u) = decode t $ decode u
       | decode (Const (a, T)) =
           let val c =
-            (case try (unprefix Lexicon.constN) a of SOME c => c | NONE => snd (map_const a))
+            (case try Lexicon.unmark_const a of
+              SOME c => c
+            | NONE => snd (map_const a))
           in Const (c, map_type T) end
       | decode (Free (a, T)) =
           (case (map_free a, map_const a) of
--- a/src/Pure/consts.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Pure/consts.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -21,15 +21,13 @@
   val space_of: T -> Name_Space.T
   val is_concealed: T -> string -> bool
   val intern: T -> xstring -> string
+  val intern_syntax: T -> xstring -> string
   val extern: T -> string -> xstring
-  val extern_early: T -> string -> xstring
-  val syntax: T -> string * mixfix -> string * typ * mixfix
-  val syntax_name: T -> string -> string
   val read_const: T -> string -> term
   val certify: Pretty.pp -> Type.tsig -> bool -> T -> term -> term  (*exception TYPE*)
   val typargs: T -> string * typ -> typ list
   val instance: T -> string * typ list -> typ
-  val declare: bool -> Name_Space.naming -> binding * typ -> T -> T
+  val declare: Name_Space.naming -> binding * typ -> T -> T
   val constrain: string * typ option -> T -> T
   val abbreviate: Pretty.pp -> Type.tsig -> Name_Space.naming -> string ->
     binding * term -> T -> (term * term) * T
@@ -46,7 +44,7 @@
 
 (* datatype T *)
 
-type decl = {T: typ, typargs: int list list, authentic: bool};
+type decl = {T: typ, typargs: int list list};
 type abbrev = {rhs: term, normal_rhs: term, force_expand: bool};
 
 datatype T = Consts of
@@ -128,18 +126,10 @@
 val intern = Name_Space.intern o space_of;
 val extern = Name_Space.extern o space_of;
 
-fun extern_early consts c =
-  (case try (the_const consts) c of
-    SOME ({authentic = true, ...}, _) => Syntax.constN ^ c
-  | _ => extern consts c);
-
-fun syntax consts (c, mx) =
-  let
-    val ({T, authentic, ...}, _) = the_const consts c handle TYPE (msg, _, _) => error msg;
-    val c' = if authentic then Syntax.constN ^ c else Long_Name.base_name c;
-  in (c', T, mx) end;
-
-fun syntax_name consts c = #1 (syntax consts (c, NoSyn));
+fun intern_syntax consts name =
+  (case try Syntax.unmark_const name of
+    SOME c => c
+  | NONE => intern consts name);
 
 
 (* read_const *)
@@ -231,10 +221,10 @@
 
 (* declarations *)
 
-fun declare authentic naming (b, declT) =
+fun declare naming (b, declT) =
   map_consts (fn (decls, constraints, rev_abbrevs) =>
     let
-      val decl = {T = declT, typargs = typargs_of declT, authentic = authentic};
+      val decl = {T = declT, typargs = typargs_of declT};
       val (_, decls') = decls |> Name_Space.define true naming (b, (decl, NONE));
     in (decls', constraints, rev_abbrevs) end);
 
@@ -285,7 +275,7 @@
   in
     consts |> map_consts (fn (decls, constraints, rev_abbrevs) =>
       let
-        val decl = {T = T, typargs = typargs_of T, authentic = true};
+        val decl = {T = T, typargs = typargs_of T};
         val abbr = {rhs = rhs, normal_rhs = normal_rhs, force_expand = force_expand};
         val (_, decls') = decls
           |> Name_Space.define true naming (b, (decl, SOME abbr));
--- a/src/Pure/pure_thy.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Pure/pure_thy.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -225,6 +225,7 @@
 
 val typ = Simple_Syntax.read_typ;
 val prop = Simple_Syntax.read_prop;
+val const = Syntax.mark_const;
 
 val typeT = Syntax.typeT;
 val spropT = Syntax.spropT;
@@ -310,11 +311,11 @@
     ("_indexvar",   typ "index",                       Delimfix "'\\<index>"),
     ("_struct",     typ "index => logic",              Mixfix ("\\<struct>_", [1000], 1000)),
     ("_update_name", typ "idt",                        NoSyn),
-    ("==>",         typ "prop => prop => prop",        Delimfix "op ==>"),
-    (Term.dummy_patternN, typ "aprop",                 Delimfix "'_"),
+    (const "==>",   typ "prop => prop => prop",        Delimfix "op ==>"),
+    (const Term.dummy_patternN, typ "aprop",           Delimfix "'_"),
     ("_sort_constraint", typ "type => prop",           Delimfix "(1SORT'_CONSTRAINT/(1'(_')))"),
-    ("Pure.term",   typ "logic => prop",               Delimfix "TERM _"),
-    ("Pure.conjunction", typ "prop => prop => prop",   Infixr ("&&&", 2))]
+    (const "Pure.term", typ "logic => prop",           Delimfix "TERM _"),
+    (const "Pure.conjunction", typ "prop => prop => prop", Infixr ("&&&", 2))]
   #> Sign.add_syntax_i applC_syntax
   #> Sign.add_modesyntax_i (Symbol.xsymbolsN, true)
    [("fun",      typ "type => type => type",   Mixfix ("(_/ \\<Rightarrow> _)", [1, 0], 0)),
@@ -326,14 +327,14 @@
     ("_idtypdummy", typ "type => idt",         Mixfix ("'_()\\<Colon>_", [], 0)),
     ("_type_constraint_", typ "'a",            NoSyn),
     ("_lambda",  typ "pttrns => 'a => logic",  Mixfix ("(3\\<lambda>_./ _)", [0, 3], 3)),
-    ("==",       typ "'a => 'a => prop",       Infixr ("\\<equiv>", 2)),
-    ("all_binder", typ "idts => prop => prop", Mixfix ("(3\\<And>_./ _)", [0, 0], 0)),
-    ("==>",      typ "prop => prop => prop",   Infixr ("\\<Longrightarrow>", 1)),
+    (const "==", typ "'a => 'a => prop",       Infixr ("\\<equiv>", 2)),
+    (const "all_binder", typ "idts => prop => prop", Mixfix ("(3\\<And>_./ _)", [0, 0], 0)),
+    (const "==>", typ "prop => prop => prop",  Infixr ("\\<Longrightarrow>", 1)),
     ("_DDDOT",   typ "aprop",                  Delimfix "\\<dots>"),
     ("_bigimpl", typ "asms => prop => prop",   Mixfix ("((1\\<lbrakk>_\\<rbrakk>)/ \\<Longrightarrow> _)", [0, 1], 1)),
     ("_DDDOT",   typ "logic",                  Delimfix "\\<dots>")]
   #> Sign.add_modesyntax_i ("", false)
-   [("prop", typ "prop => prop", Mixfix ("_", [0], 0))]
+   [(const "prop", typ "prop => prop", Mixfix ("_", [0], 0))]
   #> Sign.add_modesyntax_i ("HTML", false)
    [("_lambda", typ "pttrns => 'a => logic", Mixfix ("(3\\<lambda>_./ _)", [0, 3], 3))]
   #> Sign.add_consts_i
--- a/src/Pure/sign.ML	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Pure/sign.ML	Mon Feb 22 09:24:20 2010 +0100
@@ -41,7 +41,6 @@
   val declared_tyname: theory -> string -> bool
   val declared_const: theory -> string -> bool
   val const_monomorphic: theory -> string -> bool
-  val const_syntax_name: theory -> string -> string
   val const_typargs: theory -> string * typ -> typ list
   val const_instance: theory -> string * typ list -> typ
   val mk_const: theory -> string * typ list -> term
@@ -59,7 +58,7 @@
   val intern_typ: theory -> typ -> typ
   val extern_typ: theory -> typ -> typ
   val intern_term: theory -> term -> term
-  val extern_term: (string -> xstring) -> theory -> term -> term
+  val extern_term: theory -> term -> term
   val intern_tycons: theory -> typ -> typ
   val arity_number: theory -> string -> int
   val arity_sorts: theory -> string -> sort -> sort list
@@ -226,7 +225,6 @@
 val the_const_type = Consts.the_type o consts_of;
 val const_type = try o the_const_type;
 val const_monomorphic = Consts.is_monomorphic o consts_of;
-val const_syntax_name = Consts.syntax_name o consts_of;
 val const_typargs = Consts.typargs o consts_of;
 val const_instance = Consts.instance o consts_of;
 
@@ -299,7 +297,7 @@
 val intern_typ = typ_mapping intern_class intern_type;
 val extern_typ = typ_mapping extern_class extern_type;
 val intern_term = term_mapping intern_class intern_type intern_const;
-fun extern_term h = term_mapping extern_class extern_type (K h);
+val extern_term = term_mapping extern_class extern_type (K Syntax.mark_const);
 val intern_tycons = typ_mapping (K I) intern_type;
 
 end;
@@ -486,7 +484,10 @@
 fun notation add mode args thy =
   let
     val change_gram = if add then Syntax.update_const_gram else Syntax.remove_const_gram;
-    fun const_syntax (Const (c, _), mx) = try (Consts.syntax (consts_of thy)) (c, mx)
+    fun const_syntax (Const (c, _), mx) =
+          (case try (Consts.type_scheme (consts_of thy)) c of
+            SOME T => SOME (Syntax.mark_const c, T, mx)
+          | NONE => NONE)
       | const_syntax _ = NONE;
   in gen_syntax change_gram (K I) mode (map_filter const_syntax args) thy end;
 
@@ -495,35 +496,34 @@
 
 local
 
-fun gen_add_consts parse_typ authentic raw_args thy =
+fun gen_add_consts parse_typ raw_args thy =
   let
     val ctxt = ProofContext.init thy;
     val prepT = Type.no_tvars o Term.no_dummyT o certify_typ thy o parse_typ ctxt;
     fun prep (b, raw_T, mx) =
       let
         val c = full_name thy b;
-        val c_syn = if authentic then Syntax.constN ^ c else Name.of_binding b;
         val T = (prepT raw_T handle TYPE (msg, _, _) => error msg) handle ERROR msg =>
           cat_error msg ("in declaration of constant " ^ quote (Binding.str_of b));
         val T' = Logic.varifyT T;
-      in ((b, T'), (c_syn, T', mx), Const (c, T)) end;
+      in ((b, T'), (Syntax.mark_const c, T', mx), Const (c, T)) end;
     val args = map prep raw_args;
   in
     thy
-    |> map_consts (fold (Consts.declare authentic (naming_of thy) o #1) args)
+    |> map_consts (fold (Consts.declare (naming_of thy) o #1) args)
     |> add_syntax_i (map #2 args)
     |> pair (map #3 args)
   end;
 
 in
 
-fun add_consts args = snd o gen_add_consts Syntax.parse_typ false args;
-fun add_consts_i args = snd o gen_add_consts (K I) false args;
+fun add_consts args = snd o gen_add_consts Syntax.parse_typ args;
+fun add_consts_i args = snd o gen_add_consts (K I) args;
 
 fun declare_const ((b, T), mx) thy =
   let
     val pos = Binding.pos_of b;
-    val ([const as Const (c, _)], thy') = gen_add_consts (K I) true [(b, T, mx)] thy;
+    val ([const as Const (c, _)], thy') = gen_add_consts (K I) [(b, T, mx)] thy;
     val _ = Position.report (Markup.const_decl c) pos;
   in (const, thy') end;
 
--- a/src/Sequents/ILL_predlog.thy	Sat Feb 20 21:13:29 2010 +0100
+++ b/src/Sequents/ILL_predlog.thy	Mon Feb 22 09:24:20 2010 +0100
@@ -11,7 +11,7 @@
   disj :: "[plf,plf] => plf"   (infixr "|" 35)
   impl :: "[plf,plf] => plf"   (infixr ">" 35)
   eq :: "[plf,plf] => plf"   (infixr "=" 35)
-  ff    :: "plf"
+  ff :: "plf"    ("ff")
 
   PL    :: "plf => o"      ("[* / _ / *]" [] 100)
 
@@ -22,8 +22,8 @@
 
   "[* A & B *]" == "[*A*] && [*B*]"
   "[* A | B *]" == "![*A*] ++ ![*B*]"
-  "[* - A *]"   == "[*A > CONST ff*]"
-  "[* XCONST ff *]" == "0"
+  "[* - A *]" == "[*A > ff*]"
+  "[* ff *]" == "0"
   "[* A = B *]" => "[* (A > B) & (B > A) *]"
 
   "[* A > B *]" == "![*A*] -o [*B*]"