# HG changeset patch
# User wenzelm
# Date 1375883038 -7200
# Node ID 3695ce0f9f96001f8b7d57739885b7ac3fc23a77
# Parent  34c47bc771f28ee1d7dff4b0d01e3cd1988ba137# Parent  73e32ed924b3eeec85966e00deeb8aaad0593d92
merged

diff -r 34c47bc771f2 -r 3695ce0f9f96 CONTRIBUTORS
--- a/CONTRIBUTORS	Wed Aug 07 15:40:59 2013 +0200
+++ b/CONTRIBUTORS	Wed Aug 07 15:43:58 2013 +0200
@@ -6,6 +6,10 @@
 Contributions to this Isabelle version
 --------------------------------------
 
+* Summer 2013: Christian Sternagel, JAIST
+  Improved support for adhoc overloading of constants, including
+  documentation and examples.
+
 * May 2013: Florian Haftmann, TUM
   Ephemeral interpretation in local theories.
 
diff -r 34c47bc771f2 -r 3695ce0f9f96 NEWS
--- a/NEWS	Wed Aug 07 15:40:59 2013 +0200
+++ b/NEWS	Wed Aug 07 15:43:58 2013 +0200
@@ -106,6 +106,9 @@
 
 *** HOL ***
 
+* Improved support for adhoc overloading of constants (see also
+isar-ref manual and ~~/src/HOL/ex/Adhoc_Overloading_Examples.thy).
+
 * Attibute 'code': 'code' now declares concrete and abstract code equations uniformly.
 Use explicit 'code equation' and 'code abstract' to distinguish both when desired.
 
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Doc/IsarRef/HOL_Specific.thy
--- a/src/Doc/IsarRef/HOL_Specific.thy	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Doc/IsarRef/HOL_Specific.thy	Wed Aug 07 15:43:58 2013 +0200
@@ -1,5 +1,5 @@
 theory HOL_Specific
-imports Base Main "~~/src/HOL/Library/Old_Recdef"
+imports Base Main "~~/src/HOL/Library/Old_Recdef" "~~/src/Tools/Adhoc_Overloading"
 begin
 
 chapter {* Higher-Order Logic *}
@@ -588,7 +588,7 @@
 
   There are no fixed syntactic restrictions on the body of the
   function, but the induced functional must be provably monotonic
-  wrt.\ the underlying order.  The monotonicitity proof is performed
+  wrt.\ the underlying order.  The monotonicity proof is performed
   internally, and the definition is rejected when it fails. The proof
   can be influenced by declaring hints using the
   @{attribute (HOL) partial_function_mono} attribute.
@@ -622,7 +622,7 @@
   @{const "partial_function_definitions"} appropriately.
 
   \item @{attribute (HOL) partial_function_mono} declares rules for
-  use in the internal monononicity proofs of partial function
+  use in the internal monotonicity proofs of partial function
   definitions.
 
   \end{description}
@@ -1288,7 +1288,7 @@
   "morphisms"} specification provides alternative names. @{command
   (HOL) "quotient_type"} requires the user to prove that the relation
   is an equivalence relation (predicate @{text equivp}), unless the
-  user specifies explicitely @{text partial} in which case the
+  user specifies explicitly @{text partial} in which case the
   obligation is @{text part_equivp}.  A quotient defined with @{text
   partial} is weaker in the sense that less things can be proved
   automatically.
@@ -1318,7 +1318,7 @@
     and @{method (HOL) "descending"} continues in the same way as
     @{method (HOL) "lifting"} does. @{method (HOL) "descending"} tries
     to solve the arising regularization, injection and cleaning
-    subgoals with the analoguous method @{method (HOL)
+    subgoals with the analogous method @{method (HOL)
     "descending_setup"} which leaves the four unsolved subgoals.
 
   \item @{method (HOL) "partiality_descending"} finds the regularized
@@ -1416,6 +1416,46 @@
   problem, one should use @{command (HOL) "ax_specification"}.
 *}
 
+section {* Adhoc overloading of constants *}
+
+text {*
+  \begin{tabular}{rcll}
+  @{command_def "adhoc_overloading"} & : & @{text "local_theory \<rightarrow> local_theory"} \\
+  @{command_def "no_adhoc_overloading"} & : & @{text "local_theory \<rightarrow> local_theory"} \\
+  @{attribute_def "show_variants"} & : & @{text "attribute"} & default @{text false} \\
+  \end{tabular}
+
+  \medskip
+
+  Adhoc overloading allows to overload a constant depending on
+  its type. Typically this involves the introduction of an
+  uninterpreted constant (used for input and output) and the addition
+  of some variants (used internally). For examples see
+  @{file "~~/src/HOL/ex/Adhoc_Overloading_Examples.thy"} and
+  @{file "~~/src/HOL/Library/Monad_Syntax.thy"}.
+
+  @{rail "
+    (@@{command adhoc_overloading} | @@{command no_adhoc_overloading})
+    (@{syntax nameref} (@{syntax term} + ) + @'and')
+  "}
+
+  \begin{description}
+
+  \item @{command "adhoc_overloading"}~@{text "c v\<^isub>1 ... v\<^isub>n"}
+  associates variants with an existing constant.
+
+  \item @{command "no_adhoc_overloading"} is similar to
+  @{command "adhoc_overloading"}, but removes the specified variants
+  from the present context.
+  
+  \item @{attribute "show_variants"} controls printing of variants
+  of overloaded constants. If enabled, the internally used variants
+  are printed instead of their respective overloaded constants. This
+  is occasionally useful to check whether the system agrees with a
+  user's expectations about derived variants.
+
+  \end{description}
+*}
 
 chapter {* Proof tools *}
 
@@ -1553,7 +1593,7 @@
     equations in the code generator.  The option @{text "no_code"}
     of the command @{command (HOL) "setup_lifting"} can turn off that
     behavior and causes that code certificate theorems generated by
-    @{command (HOL) "lift_definition"} are not registred as abstract
+    @{command (HOL) "lift_definition"} are not registered as abstract
     code equations.
 
   \item @{command (HOL) "lift_definition"} @{text "f :: \<tau> is t"}
@@ -1607,7 +1647,7 @@
     files.
 
   \item @{attribute (HOL) reflexivity_rule} registers a theorem that shows
-    that a relator respects reflexivity and left-totality. For exampless 
+    that a relator respects reflexivity and left-totality. For examples 
     see @{file "~~/src/HOL/Library/Quotient_List.thy"} or other Quotient_*.thy
     The property is used in generation of abstraction function equations.
 
@@ -2009,7 +2049,7 @@
   counterexamples using a series of assignments for its free
   variables; by default the first subgoal is tested, an other can be
   selected explicitly using an optional goal index.  Assignments can
-  be chosen exhausting the search space upto a given size, or using a
+  be chosen exhausting the search space up to a given size, or using a
   fixed number of random assignments in the search space, or exploring
   the search space symbolically using narrowing.  By default,
   quickcheck uses exhaustive testing.  A number of configuration
@@ -2373,12 +2413,12 @@
   internally.
 
   Constants may be specified by giving them literally, referring to
-  all executable contants within a certain theory by giving @{text
+  all executable constants within a certain theory by giving @{text
   "name.*"}, or referring to \emph{all} executable constants currently
   available by giving @{text "*"}.
 
   By default, for each involved theory one corresponding name space
-  module is generated.  Alternativly, a module name may be specified
+  module is generated.  Alternatively, a module name may be specified
   after the @{keyword "module_name"} keyword; then \emph{all} code is
   placed in this module.
 
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Doc/IsarRef/document/root.tex
--- a/src/Doc/IsarRef/document/root.tex	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Doc/IsarRef/document/root.tex	Wed Aug 07 15:43:58 2013 +0200
@@ -40,7 +40,8 @@
   Lars Noschinski, \\
   David von Oheimb,
   Larry Paulson,
-  Sebastian Skalberg
+  Sebastian Skalberg, \\
+  Christian Sternagel
 }
 
 \makeindex
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/HOL/Library/Formal_Power_Series.thy
--- a/src/HOL/Library/Formal_Power_Series.thy	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/HOL/Library/Formal_Power_Series.thy	Wed Aug 07 15:43:58 2013 +0200
@@ -101,9 +101,9 @@
 lemma fps_mult_nth: "(f * g) $ n = (\<Sum>i=0..n. f$i * g$(n - i))"
   unfolding fps_times_def by simp
 
-declare atLeastAtMost_iff[presburger]
-declare Bex_def[presburger]
-declare Ball_def[presburger]
+declare atLeastAtMost_iff [presburger]
+declare Bex_def [presburger]
+declare Ball_def [presburger]
 
 lemma mult_delta_left:
   fixes x y :: "'a::mult_zero"
@@ -117,6 +117,7 @@
 
 lemma cond_value_iff: "f (if b then x else y) = (if b then f x else f y)"
   by auto
+
 lemma cond_application_beta: "(if b then f else g) x = (if b then f x else g x)"
   by auto
 
@@ -125,13 +126,15 @@
 
 instance fps :: (semigroup_add) semigroup_add
 proof
-  fix a b c :: "'a fps" show "a + b + c = a + (b + c)"
+  fix a b c :: "'a fps"
+  show "a + b + c = a + (b + c)"
     by (simp add: fps_ext add_assoc)
 qed
 
 instance fps :: (ab_semigroup_add) ab_semigroup_add
 proof
-  fix a b :: "'a fps" show "a + b = b + a"
+  fix a b :: "'a fps"
+  show "a + b = b + a"
     by (simp add: fps_ext add_commute)
 qed
 
@@ -140,11 +143,12 @@
   shows "(\<Sum>j=0..k. \<Sum>i=0..j. f i (j - i) (n - j)) =
          (\<Sum>j=0..k. \<Sum>i=0..k - j. f j i (n - j - i))"
 proof (induct k)
-  case 0 show ?case by simp
+  case 0
+  show ?case by simp
 next
-  case (Suc k) thus ?case
-    by (simp add: Suc_diff_le setsum_addf add_assoc
-             cong: strong_setsum_cong)
+  case (Suc k)
+  then show ?case
+    by (simp add: Suc_diff_le setsum_addf add_assoc cong: strong_setsum_cong)
 qed
 
 instance fps :: (semiring_0) semigroup_mult
@@ -156,9 +160,8 @@
     have "(\<Sum>j=0..n. \<Sum>i=0..j. a$i * b$(j - i) * c$(n - j)) =
           (\<Sum>j=0..n. \<Sum>i=0..n - j. a$j * b$i * c$(n - j - i))"
       by (rule fps_mult_assoc_lemma)
-    thus "((a * b) * c) $ n = (a * (b * c)) $ n"
-      by (simp add: fps_mult_nth setsum_right_distrib
-                    setsum_left_distrib mult_assoc)
+    then show "((a * b) * c) $ n = (a * (b * c)) $ n"
+      by (simp add: fps_mult_nth setsum_right_distrib setsum_left_distrib mult_assoc)
   qed
 qed
 
@@ -171,9 +174,10 @@
   show "{0..n} = (\<lambda>i. n - i) ` {0..n}"
     by (auto, rule_tac x="n - x" in image_eqI, simp_all)
 next
-  fix i assume "i \<in> {0..n}"
-  hence "n - (n - i) = i" by simp
-  thus "f (n - i) i = f (n - i) (n - (n - i))" by simp
+  fix i
+  assume "i \<in> {0..n}"
+  then have "n - (n - i) = i" by simp
+  then show "f (n - i) i = f (n - i) (n - (n - i))" by simp
 qed
 
 instance fps :: (comm_semiring_0) ab_semigroup_mult
@@ -184,73 +188,61 @@
     fix n :: nat
     have "(\<Sum>i=0..n. a$i * b$(n - i)) = (\<Sum>i=0..n. a$(n - i) * b$i)"
       by (rule fps_mult_commute_lemma)
-    thus "(a * b) $ n = (b * a) $ n"
+    then show "(a * b) $ n = (b * a) $ n"
       by (simp add: fps_mult_nth mult_commute)
   qed
 qed
 
 instance fps :: (monoid_add) monoid_add
 proof
-  fix a :: "'a fps" show "0 + a = a "
-    by (simp add: fps_ext)
-next
-  fix a :: "'a fps" show "a + 0 = a "
-    by (simp add: fps_ext)
+  fix a :: "'a fps"
+  show "0 + a = a" by (simp add: fps_ext)
+  show "a + 0 = a" by (simp add: fps_ext)
 qed
 
 instance fps :: (comm_monoid_add) comm_monoid_add
 proof
-  fix a :: "'a fps" show "0 + a = a "
-    by (simp add: fps_ext)
+  fix a :: "'a fps"
+  show "0 + a = a" by (simp add: fps_ext)
 qed
 
 instance fps :: (semiring_1) monoid_mult
 proof
-  fix a :: "'a fps" show "1 * a = a"
+  fix a :: "'a fps"
+  show "1 * a = a"
     by (simp add: fps_ext fps_mult_nth mult_delta_left setsum_delta)
-next
-  fix a :: "'a fps" show "a * 1 = a"
+  show "a * 1 = a"
     by (simp add: fps_ext fps_mult_nth mult_delta_right setsum_delta')
 qed
 
 instance fps :: (cancel_semigroup_add) cancel_semigroup_add
 proof
   fix a b c :: "'a fps"
-  assume "a + b = a + c" then show "b = c"
-    by (simp add: expand_fps_eq)
-next
-  fix a b c :: "'a fps"
-  assume "b + a = c + a" then show "b = c"
-    by (simp add: expand_fps_eq)
+  { assume "a + b = a + c" then show "b = c" by (simp add: expand_fps_eq) }
+  { assume "b + a = c + a" then show "b = c" by (simp add: expand_fps_eq) }
 qed
 
 instance fps :: (cancel_ab_semigroup_add) cancel_ab_semigroup_add
 proof
   fix a b c :: "'a fps"
-  assume "a + b = a + c" then show "b = c"
-    by (simp add: expand_fps_eq)
+  assume "a + b = a + c"
+  then show "b = c" by (simp add: expand_fps_eq)
 qed
 
 instance fps :: (cancel_comm_monoid_add) cancel_comm_monoid_add ..
 
 instance fps :: (group_add) group_add
 proof
-  fix a :: "'a fps" show "- a + a = 0"
-    by (simp add: fps_ext)
-next
-  fix a b :: "'a fps" show "a - b = a + - b"
-    by (simp add: fps_ext diff_minus)
+  fix a b :: "'a fps"
+  show "- a + a = 0" by (simp add: fps_ext)
+  show "a - b = a + - b" by (simp add: fps_ext diff_minus)
 qed
 
 instance fps :: (ab_group_add) ab_group_add
 proof
-  fix a :: "'a fps"
-  show "- a + a = 0"
-    by (simp add: fps_ext)
-next
   fix a b :: "'a fps"
-  show "a - b = a + - b"
-    by (simp add: fps_ext)
+  show "- a + a = 0" by (simp add: fps_ext)
+  show "a - b = a + - b" by (simp add: fps_ext)
 qed
 
 instance fps :: (zero_neq_one) zero_neq_one
@@ -261,19 +253,15 @@
   fix a b c :: "'a fps"
   show "(a + b) * c = a * c + b * c"
     by (simp add: expand_fps_eq fps_mult_nth distrib_right setsum_addf)
-next
-  fix a b c :: "'a fps"
   show "a * (b + c) = a * b + a * c"
     by (simp add: expand_fps_eq fps_mult_nth distrib_left setsum_addf)
 qed
 
 instance fps :: (semiring_0) semiring_0
 proof
-  fix a:: "'a fps" show "0 * a = 0"
-    by (simp add: fps_ext fps_mult_nth)
-next
-  fix a:: "'a fps" show "a * 0 = 0"
-    by (simp add: fps_ext fps_mult_nth)
+  fix a:: "'a fps"
+  show "0 * a = 0" by (simp add: fps_ext fps_mult_nth)
+  show "a * 0 = 0" by (simp add: fps_ext fps_mult_nth)
 qed
 
 instance fps :: (semiring_0_cancel) semiring_0_cancel ..
@@ -284,7 +272,7 @@
   by (simp add: expand_fps_eq)
 
 lemma fps_nonzero_nth_minimal:
-  "f \<noteq> 0 \<longleftrightarrow> (\<exists>n. f $ n \<noteq> 0 \<and> (\<forall>m<n. f $ m = 0))"
+  "f \<noteq> 0 \<longleftrightarrow> (\<exists>n. f $ n \<noteq> 0 \<and> (\<forall>m < n. f $ m = 0))"
 proof
   let ?n = "LEAST n. f $ n \<noteq> 0"
   assume "f \<noteq> 0"
@@ -304,18 +292,18 @@
 lemma fps_eq_iff: "f = g \<longleftrightarrow> (\<forall>n. f $ n = g $n)"
   by (rule expand_fps_eq)
 
-lemma fps_setsum_nth: "(setsum f S) $ n = setsum (\<lambda>k. (f k) $ n) S"
+lemma fps_setsum_nth: "setsum f S $ n = setsum (\<lambda>k. (f k) $ n) S"
 proof (cases "finite S")
-  assume "\<not> finite S" then show ?thesis by simp
+  case True
+  then show ?thesis by (induct set: finite) auto
 next
-  assume "finite S"
-  then show ?thesis by (induct set: finite) auto
+  case False
+  then show ?thesis by simp
 qed
 
 subsection{* Injection of the basic ring elements and multiplication by scalars *}
 
-definition
-  "fps_const c = Abs_fps (\<lambda>n. if n = 0 then c else 0)"
+definition "fps_const c = Abs_fps (\<lambda>n. if n = 0 then c else 0)"
 
 lemma fps_nth_fps_const [simp]: "fps_const c $ n = (if n = 0 then c else 0)"
   unfolding fps_const_def by simp
@@ -331,8 +319,10 @@
 
 lemma fps_const_add [simp]: "fps_const (c::'a\<Colon>monoid_add) + fps_const d = fps_const (c + d)"
   by (simp add: fps_ext)
+
 lemma fps_const_sub [simp]: "fps_const (c::'a\<Colon>group_add) - fps_const d = fps_const (c - d)"
   by (simp add: fps_ext)
+
 lemma fps_const_mult[simp]: "fps_const (c::'a\<Colon>ring) * fps_const d = fps_const (c * d)"
   by (simp add: fps_eq_iff fps_mult_nth setsum_0')
 
@@ -429,18 +419,20 @@
   case 0 thus ?case by (simp add: X_def fps_eq_iff)
 next
   case (Suc k)
-  {fix m
+  {
+    fix m
     have "(X^Suc k) $ m = (if m = 0 then (0::'a) else (X^k) $ (m - 1))"
-      by (simp add: power_Suc del: One_nat_def)
-    then     have "(X^Suc k) $ m = (if m = Suc k then (1::'a) else 0)"
-      using Suc.hyps by (auto cong del: if_weak_cong)}
+      by (simp del: One_nat_def)
+    then have "(X^Suc k) $ m = (if m = Suc k then (1::'a) else 0)"
+      using Suc.hyps by (auto cong del: if_weak_cong)
+  }
   then show ?case by (simp add: fps_eq_iff)
 qed
 
 lemma X_power_mult_nth:
     "(X^k * (f :: ('a::comm_ring_1) fps)) $n = (if n < k then 0 else f $ (n - k))"
   apply (induct k arbitrary: n)
-  apply (simp)
+  apply simp
   unfolding power_Suc mult_assoc
   apply (case_tac n)
   apply auto
@@ -452,7 +444,7 @@
 
 
 
-  
+
 subsection{* Formal Power series form a metric space *}
 
 definition (in dist) ball_def: "ball x r = {y. dist y x < r}"
@@ -460,8 +452,9 @@
 instantiation fps :: (comm_ring_1) dist
 begin
 
-definition dist_fps_def:
-  "dist (a::'a fps) b = (if (\<exists>n. a$n \<noteq> b$n) then inverse (2 ^ The (leastP (\<lambda>n. a$n \<noteq> b$n))) else 0)"
+definition
+  dist_fps_def: "dist (a::'a fps) b =
+    (if (\<exists>n. a$n \<noteq> b$n) then inverse (2 ^ The (leastP (\<lambda>n. a$n \<noteq> b$n))) else 0)"
 
 lemma dist_fps_ge0: "dist (a::'a fps) b \<ge> 0"
   by (simp add: dist_fps_def)
@@ -479,18 +472,22 @@
 
 lemma fps_nonzero_least_unique: assumes a0: "a \<noteq> 0"
   shows "\<exists>! n. leastP (\<lambda>n. a$n \<noteq> 0) n"
-proof-
-  from fps_nonzero_nth_minimal[of a] a0
-  obtain n where n: "a$n \<noteq> 0" "\<forall>m < n. a$m = 0" by blast
-  from n have ln: "leastP (\<lambda>n. a$n \<noteq> 0) n" 
-    by (auto simp add: leastP_def setge_def not_le[symmetric])
+proof -
+  from fps_nonzero_nth_minimal [of a] a0
+  obtain n where "a$n \<noteq> 0" "\<forall>m < n. a$m = 0" by blast
+  then have ln: "leastP (\<lambda>n. a$n \<noteq> 0) n"
+    by (auto simp add: leastP_def setge_def not_le [symmetric])
   moreover
-  {fix m assume "leastP (\<lambda>n. a$n \<noteq> 0) m"
+  {
+    fix m
+    assume "leastP (\<lambda>n. a $ n \<noteq> 0) m"
     then have "m = n" using ln
       apply (auto simp add: leastP_def setge_def)
       apply (erule allE[where x=n])
       apply (erule allE[where x=m])
-      by simp}
+      apply simp
+      done
+  }
   ultimately show ?thesis by blast
 qed
 
@@ -507,21 +504,21 @@
 
 instance
 proof
-  fix S :: "'a fps set" 
+  fix S :: "'a fps set"
   show "open S = (\<forall>x\<in>S. \<exists>e>0. \<forall>y. dist y x < e \<longrightarrow> y \<in> S)"
     by (auto simp add: open_fps_def ball_def subset_eq)
 next
   {
     fix a b :: "'a fps"
     {
-      assume ab: "a = b"
-      then have "\<not> (\<exists>n. a$n \<noteq> b$n)" by simp
+      assume "a = b"
+      then have "\<not> (\<exists>n. a $ n \<noteq> b $ n)" by simp
       then have "dist a b = 0" by (simp add: dist_fps_def)
     }
     moreover
     {
       assume d: "dist a b = 0"
-      then have "\<forall>n. a$n = b$n" 
+      then have "\<forall>n. a$n = b$n"
         by - (rule ccontr, simp add: dist_fps_def)
       then have "a = b" by (simp add: fps_eq_iff)
     }
@@ -531,23 +528,25 @@
   from th have th'[simp]: "\<And>a::'a fps. dist a a = 0" by simp
   fix a b c :: "'a fps"
   {
-    assume ab: "a = b" then have d0: "dist a b = 0"  unfolding th .
-    then have "dist a b \<le> dist a c + dist b c" 
-      using dist_fps_ge0[of a c] dist_fps_ge0[of b c] by simp
+    assume "a = b"
+    then have "dist a b = 0" unfolding th .
+    then have "dist a b \<le> dist a c + dist b c"
+      using dist_fps_ge0 [of a c] dist_fps_ge0 [of b c] by simp
   }
   moreover
   {
-    assume c: "c = a \<or> c = b"
+    assume "c = a \<or> c = b"
     then have "dist a b \<le> dist a c + dist b c"
-      by (cases "c=a") (simp_all add: th dist_fps_sym)
+      by (cases "c = a") (simp_all add: th dist_fps_sym)
   }
   moreover
-  {assume ab: "a \<noteq> b" and ac: "a \<noteq> c" and bc: "b \<noteq> c"
+  {
+    assume ab: "a \<noteq> b" and ac: "a \<noteq> c" and bc: "b \<noteq> c"
     let ?P = "\<lambda>a b n. a$n \<noteq> b$n"
-    from fps_eq_least_unique[OF ab] fps_eq_least_unique[OF ac] 
+    from fps_eq_least_unique[OF ab] fps_eq_least_unique[OF ac]
       fps_eq_least_unique[OF bc]
-    obtain nab nac nbc where nab: "leastP (?P a b) nab" 
-      and nac: "leastP (?P a c) nac" 
+    obtain nab nac nbc where nab: "leastP (?P a b) nab"
+      and nac: "leastP (?P a c) nac"
       and nbc: "leastP (?P b c) nbc" by blast
     from nab have nab': "\<And>m. m < nab \<Longrightarrow> a$m = b$m" "a$nab \<noteq> b$nab"
       by (auto simp add: leastP_def setge_def)
@@ -558,41 +557,46 @@
 
     have th0: "\<And>(a::'a fps) b. a \<noteq> b \<longleftrightarrow> (\<exists>n. a$n \<noteq> b$n)"
       by (simp add: fps_eq_iff)
-    from ab ac bc nab nac nbc 
-    have dab: "dist a b = inverse (2 ^ nab)" 
-      and dac: "dist a c = inverse (2 ^ nac)" 
+    from ab ac bc nab nac nbc
+    have dab: "dist a b = inverse (2 ^ nab)"
+      and dac: "dist a c = inverse (2 ^ nac)"
       and dbc: "dist b c = inverse (2 ^ nbc)"
       unfolding th0
       apply (simp_all add: dist_fps_def)
       apply (erule the1_equality[OF fps_eq_least_unique[OF ab]])
       apply (erule the1_equality[OF fps_eq_least_unique[OF ac]])
-      by (erule the1_equality[OF fps_eq_least_unique[OF bc]])
+      apply (erule the1_equality[OF fps_eq_least_unique[OF bc]])
+      done
     from ab ac bc have nz: "dist a b \<noteq> 0" "dist a c \<noteq> 0" "dist b c \<noteq> 0"
       unfolding th by simp_all
     from nz have pos: "dist a b > 0" "dist a c > 0" "dist b c > 0"
-      using dist_fps_ge0[of a b] dist_fps_ge0[of a c] dist_fps_ge0[of b c] 
+      using dist_fps_ge0[of a b] dist_fps_ge0[of a c] dist_fps_ge0[of b c]
       by auto
     have th1: "\<And>n. (2::real)^n >0" by auto
-    {assume h: "dist a b > dist a c + dist b c"
+    {
+      assume h: "dist a b > dist a c + dist b c"
       then have gt: "dist a b > dist a c" "dist a b > dist b c"
         using pos by auto
       from gt have gtn: "nab < nbc" "nab < nac"
         unfolding dab dbc dac by (auto simp add: th1)
       from nac'(1)[OF gtn(2)] nbc'(1)[OF gtn(1)]
-      have "a$nab = b$nab" by simp
-      with nab'(2) have False  by simp}
+      have "a $ nab = b $ nab" by simp
+      with nab'(2) have False  by simp
+    }
     then have "dist a b \<le> dist a c + dist b c"
-      by (auto simp add: not_le[symmetric]) }
+      by (auto simp add: not_le[symmetric])
+  }
   ultimately show "dist a b \<le> dist a c + dist b c" by blast
 qed
-  
+
 end
 
 text{* The infinite sums and justification of the notation in textbooks*}
 
-lemma reals_power_lt_ex: assumes xp: "x > 0" and y1: "(y::real) > 1"
+lemma reals_power_lt_ex:
+  assumes xp: "x > 0" and y1: "(y::real) > 1"
   shows "\<exists>k>0. (1/y)^k < x"
-proof-
+proof -
   have yp: "y > 0" using y1 by simp
   from reals_Archimedean2[of "max 0 (- log y x) + 1"]
   obtain k::nat where k: "real k > max 0 (- log y x) + 1" by blast
@@ -605,62 +609,72 @@
   then have "exp (real k * ln y + ln x) > exp 0"
     by (simp add: mult_ac)
   then have "y ^ k * x > 1"
-    unfolding exp_zero exp_add exp_real_of_nat_mult
-    exp_ln[OF xp] exp_ln[OF yp] by simp
-  then have "x > (1/y)^k" using yp 
+    unfolding exp_zero exp_add exp_real_of_nat_mult exp_ln [OF xp] exp_ln [OF yp]
+    by simp
+  then have "x > (1 / y)^k" using yp
     by (simp add: field_simps nonzero_power_divide)
   then show ?thesis using kp by blast
 qed
+
 lemma X_nth[simp]: "X$n = (if n = 1 then 1 else 0)" by (simp add: X_def)
+
 lemma X_power_nth[simp]: "(X^k) $n = (if n = k then 1 else (0::'a::comm_ring_1))"
   by (simp add: X_power_iff)
- 
+
 
 lemma fps_sum_rep_nth: "(setsum (%i. fps_const(a$i)*X^i) {0..m})$n =
     (if n \<le> m then a$n else (0::'a::comm_ring_1))"
-  apply (auto simp add: fps_eq_iff fps_setsum_nth X_power_nth cond_application_beta cond_value_iff
-    cong del: if_weak_cong)
+  apply (auto simp add: fps_setsum_nth cond_value_iff cong del: if_weak_cong)
   apply (simp add: setsum_delta')
   done
-  
-lemma fps_notation: 
+
+lemma fps_notation:
   "(%n. setsum (%i. fps_const(a$i) * X^i) {0..n}) ----> a" (is "?s ----> a")
-proof-
-    {fix r:: real
-      assume rp: "r > 0"
-      have th0: "(2::real) > 1" by simp
-      from reals_power_lt_ex[OF rp th0] 
-      obtain n0 where n0: "(1/2)^n0 < r" "n0 > 0" by blast
-      {fix n::nat
-        assume nn0: "n \<ge> n0"
-        then have thnn0: "(1/2)^n <= (1/2 :: real)^n0"
+proof -
+  {
+    fix r:: real
+    assume rp: "r > 0"
+    have th0: "(2::real) > 1" by simp
+    from reals_power_lt_ex[OF rp th0]
+    obtain n0 where n0: "(1/2)^n0 < r" "n0 > 0" by blast
+    {
+      fix n::nat
+      assume nn0: "n \<ge> n0"
+      then have thnn0: "(1/2)^n <= (1/2 :: real)^n0"
+        by (auto intro: power_decreasing)
+      {
+        assume "?s n = a"
+        then have "dist (?s n) a < r"
+          unfolding dist_eq_0_iff[of "?s n" a, symmetric]
+          using rp by (simp del: dist_eq_0_iff)
+      }
+      moreover
+      {
+        assume neq: "?s n \<noteq> a"
+        from fps_eq_least_unique[OF neq]
+        obtain k where k: "leastP (\<lambda>i. ?s n $ i \<noteq> a$i) k" by blast
+        have th0: "\<And>(a::'a fps) b. a \<noteq> b \<longleftrightarrow> (\<exists>n. a$n \<noteq> b$n)"
+          by (simp add: fps_eq_iff)
+        from neq have dth: "dist (?s n) a = (1/2)^k"
+          unfolding th0 dist_fps_def
+          unfolding the1_equality[OF fps_eq_least_unique[OF neq], OF k]
+          by (auto simp add: inverse_eq_divide power_divide)
+
+        from k have kn: "k > n"
+          by (simp add: leastP_def setge_def fps_sum_rep_nth split:split_if_asm)
+        then have "dist (?s n) a < (1/2)^n" unfolding dth
+          by (auto intro: power_strict_decreasing)
+        also have "\<dots> <= (1/2)^n0" using nn0
           by (auto intro: power_decreasing)
-        {assume "?s n = a" then have "dist (?s n) a < r" 
-            unfolding dist_eq_0_iff[of "?s n" a, symmetric]
-            using rp by (simp del: dist_eq_0_iff)}
-        moreover
-        {assume neq: "?s n \<noteq> a"
-          from fps_eq_least_unique[OF neq] 
-          obtain k where k: "leastP (\<lambda>i. ?s n $ i \<noteq> a$i) k" by blast
-          have th0: "\<And>(a::'a fps) b. a \<noteq> b \<longleftrightarrow> (\<exists>n. a$n \<noteq> b$n)"
-            by (simp add: fps_eq_iff)
-          from neq have dth: "dist (?s n) a = (1/2)^k"
-            unfolding th0 dist_fps_def
-            unfolding the1_equality[OF fps_eq_least_unique[OF neq], OF k]
-            by (auto simp add: inverse_eq_divide power_divide)
-
-          from k have kn: "k > n"
-            by (simp add: leastP_def setge_def fps_sum_rep_nth split:split_if_asm)
-          then have "dist (?s n) a < (1/2)^n" unfolding dth
-            by (auto intro: power_strict_decreasing)
-          also have "\<dots> <= (1/2)^n0" using nn0
-            by (auto intro: power_decreasing)
-          also have "\<dots> < r" using n0 by simp
-          finally have "dist (?s n) a < r" .}
-        ultimately have "dist (?s n) a < r" by blast}
-      then have "\<exists>n0. \<forall> n \<ge> n0. dist (?s n) a < r " by blast}
-    then show ?thesis  unfolding  LIMSEQ_def by blast
-  qed
+        also have "\<dots> < r" using n0 by simp
+        finally have "dist (?s n) a < r" .
+      }
+      ultimately have "dist (?s n) a < r" by blast
+    }
+    then have "\<exists>n0. \<forall> n \<ge> n0. dist (?s n) a < r " by blast
+  }
+  then show ?thesis unfolding LIMSEQ_def by blast
+qed
 
 subsection{* Inverses of formal power series *}
 
@@ -669,52 +683,58 @@
 instantiation fps :: ("{comm_monoid_add, inverse, times, uminus}") inverse
 begin
 
-fun natfun_inverse:: "'a fps \<Rightarrow> nat \<Rightarrow> 'a" where
+fun natfun_inverse:: "'a fps \<Rightarrow> nat \<Rightarrow> 'a"
+where
   "natfun_inverse f 0 = inverse (f$0)"
 | "natfun_inverse f n = - inverse (f$0) * setsum (\<lambda>i. f$i * natfun_inverse f (n - i)) {1..n}"
 
-definition fps_inverse_def:
-  "inverse f = (if f $ 0 = 0 then 0 else Abs_fps (natfun_inverse f))"
-
-definition fps_divide_def: "divide = (\<lambda>(f::'a fps) g. f * inverse g)"
+definition
+  fps_inverse_def: "inverse f = (if f $ 0 = 0 then 0 else Abs_fps (natfun_inverse f))"
+
+definition
+  fps_divide_def: "divide = (\<lambda>(f::'a fps) g. f * inverse g)"
 
 instance ..
 
 end
 
-lemma fps_inverse_zero[simp]:
+lemma fps_inverse_zero [simp]:
   "inverse (0 :: 'a::{comm_monoid_add,inverse, times, uminus} fps) = 0"
   by (simp add: fps_ext fps_inverse_def)
 
-lemma fps_inverse_one[simp]: "inverse (1 :: 'a::{division_ring,zero_neq_one} fps) = 1"
+lemma fps_inverse_one [simp]: "inverse (1 :: 'a::{division_ring,zero_neq_one} fps) = 1"
   apply (auto simp add: expand_fps_eq fps_inverse_def)
-  by (case_tac n, auto)
-
-lemma inverse_mult_eq_1 [intro]: assumes f0: "f$0 \<noteq> (0::'a::field)"
+  apply (case_tac n)
+  apply auto
+  done
+
+lemma inverse_mult_eq_1 [intro]:
+  assumes f0: "f$0 \<noteq> (0::'a::field)"
   shows "inverse f * f = 1"
-proof-
+proof -
   have c: "inverse f * f = f * inverse f" by (simp add: mult_commute)
   from f0 have ifn: "\<And>n. inverse f $ n = natfun_inverse f n"
     by (simp add: fps_inverse_def)
   from f0 have th0: "(inverse f * f) $ 0 = 1"
     by (simp add: fps_mult_nth fps_inverse_def)
-  {fix n::nat assume np: "n >0 "
+  {
+    fix n :: nat
+    assume np: "n > 0"
     from np have eq: "{0..n} = {0} \<union> {1 .. n}" by auto
     have d: "{0} \<inter> {1 .. n} = {}" by auto
-    from f0 np have th0: "- (inverse f$n) =
+    from f0 np have th0: "- (inverse f $ n) =
       (setsum (\<lambda>i. f$i * natfun_inverse f (n - i)) {1..n}) / (f$0)"
-      by (cases n, simp, simp add: divide_inverse fps_inverse_def)
+      by (cases n) (simp_all add: divide_inverse fps_inverse_def)
     from th0[symmetric, unfolded nonzero_divide_eq_eq[OF f0]]
-    have th1: "setsum (\<lambda>i. f$i * natfun_inverse f (n - i)) {1..n} =
-      - (f$0) * (inverse f)$n"
+    have th1: "setsum (\<lambda>i. f$i * natfun_inverse f (n - i)) {1..n} = - (f$0) * (inverse f)$n"
       by (simp add: field_simps)
     have "(f * inverse f) $ n = (\<Sum>i = 0..n. f $i * natfun_inverse f (n - i))"
       unfolding fps_mult_nth ifn ..
-    also have "\<dots> = f$0 * natfun_inverse f n
-      + (\<Sum>i = 1..n. f$i * natfun_inverse f (n-i))"
+    also have "\<dots> = f$0 * natfun_inverse f n + (\<Sum>i = 1..n. f$i * natfun_inverse f (n-i))"
       by (simp add: eq)
     also have "\<dots> = 0" unfolding th1 ifn by simp
-    finally have "(inverse f * f)$n = 0" unfolding c . }
+    finally have "(inverse f * f)$n = 0" unfolding c .
+  }
   with th0 show ?thesis by (simp add: fps_eq_iff)
 qed
 
@@ -722,28 +742,34 @@
   by (simp add: fps_inverse_def nonzero_imp_inverse_nonzero)
 
 lemma fps_inverse_eq_0_iff[simp]: "inverse f = (0:: ('a::field) fps) \<longleftrightarrow> f $0 = 0"
-proof-
-  {assume "f$0 = 0" hence "inverse f = 0" by (simp add: fps_inverse_def)}
+proof -
+  {
+    assume "f$0 = 0"
+    then have "inverse f = 0" by (simp add: fps_inverse_def)
+  }
   moreover
-  {assume h: "inverse f = 0" and c: "f $0 \<noteq> 0"
-    from inverse_mult_eq_1[OF c] h have False by simp}
+  {
+    assume h: "inverse f = 0" and c: "f $0 \<noteq> 0"
+    from inverse_mult_eq_1[OF c] h have False by simp
+  }
   ultimately show ?thesis by blast
 qed
 
 lemma fps_inverse_idempotent[intro]:
   assumes f0: "f$0 \<noteq> (0::'a::field)"
   shows "inverse (inverse f) = f"
-proof-
+proof -
   from f0 have if0: "inverse f $ 0 \<noteq> 0" by simp
   from inverse_mult_eq_1[OF f0] inverse_mult_eq_1[OF if0]
-  have th0: "inverse f * f = inverse f * inverse (inverse f)"   by (simp add: mult_ac)
+  have "inverse f * f = inverse f * inverse (inverse f)"
+    by (simp add: mult_ac)
   then show ?thesis using f0 unfolding mult_cancel_left by simp
 qed
 
 lemma fps_inverse_unique:
   assumes f0: "f$0 \<noteq> (0::'a::field)" and fg: "f*g = 1"
   shows "inverse f = g"
-proof-
+proof -
   from inverse_mult_eq_1[OF f0] fg
   have th0: "inverse f * f = g * f" by (simp add: mult_ac)
   then show ?thesis using f0  unfolding mult_cancel_right
@@ -755,8 +781,9 @@
   apply (rule fps_inverse_unique)
   apply simp
   apply (simp add: fps_eq_iff fps_mult_nth)
-proof(clarsimp)
-  fix n::nat assume n: "n > 0"
+proof clarsimp
+  fix n :: nat
+  assume n: "n > 0"
   let ?f = "\<lambda>i. if n = i then (1\<Colon>'a) else if n - i = 1 then - 1 else 0"
   let ?g = "\<lambda>i. if i = n then 1 else if i=n - 1 then - 1 else 0"
   let ?h = "\<lambda>i. if i=n - 1 then - 1 else 0"
@@ -771,7 +798,8 @@
     unfolding th1
     apply (simp add: setsum_Un_disjoint[OF f d, unfolded eq[symmetric]] del: One_nat_def)
     unfolding th2
-    by(simp add: setsum_delta)
+    apply (simp add: setsum_delta)
+    done
 qed
 
 subsection{* Formal Derivatives, and the MacLaurin theorem around 0*}
@@ -789,9 +817,9 @@
 lemma fps_deriv_mult[simp]:
   fixes f :: "('a :: comm_ring_1) fps"
   shows "fps_deriv (f * g) = f * fps_deriv g + fps_deriv f * g"
-proof-
+proof -
   let ?D = "fps_deriv"
-  {fix n::nat
+  { fix n::nat
     let ?Zn = "{0 ..n}"
     let ?Zn1 = "{0 .. n + 1}"
     let ?f = "\<lambda>i. i + 1"
@@ -801,25 +829,33 @@
         of_nat (i+1)* f $ (i+1) * g $ (n - i)"
     let ?h = "\<lambda>i. of_nat i * g $ i * f $ ((n+1) - i) +
         of_nat i* f $ i * g $ ((n + 1) - i)"
-    {fix k assume k: "k \<in> {0..n}"
-      have "?h (k + 1) = ?g k" using k by auto}
+    {
+      fix k
+      assume k: "k \<in> {0..n}"
+      have "?h (k + 1) = ?g k" using k by auto
+    }
     note th0 = this
     have eq': "{0..n +1}- {1 .. n+1} = {0}" by auto
-    have s0: "setsum (\<lambda>i. of_nat i * f $ i * g $ (n + 1 - i)) ?Zn1 = setsum (\<lambda>i. of_nat (n + 1 - i) * f $ (n + 1 - i) * g $ i) ?Zn1"
+    have s0: "setsum (\<lambda>i. of_nat i * f $ i * g $ (n + 1 - i)) ?Zn1 =
+      setsum (\<lambda>i. of_nat (n + 1 - i) * f $ (n + 1 - i) * g $ i) ?Zn1"
       apply (rule setsum_reindex_cong[where f="\<lambda>i. n + 1 - i"])
       apply (simp add: inj_on_def Ball_def)
       apply presburger
       apply (rule set_eqI)
       apply (presburger add: image_iff)
-      by simp
-    have s1: "setsum (\<lambda>i. f $ i * g $ (n + 1 - i)) ?Zn1 = setsum (\<lambda>i. f $ (n + 1 - i) * g $ i) ?Zn1"
+      apply simp
+      done
+    have s1: "setsum (\<lambda>i. f $ i * g $ (n + 1 - i)) ?Zn1 =
+      setsum (\<lambda>i. f $ (n + 1 - i) * g $ i) ?Zn1"
       apply (rule setsum_reindex_cong[where f="\<lambda>i. n + 1 - i"])
       apply (simp add: inj_on_def Ball_def)
       apply presburger
       apply (rule set_eqI)
       apply (presburger add: image_iff)
-      by simp
-    have "(f * ?D g + ?D f * g)$n = (?D g * f + ?D f * g)$n" by (simp only: mult_commute)
+      apply simp
+      done
+    have "(f * ?D g + ?D f * g)$n = (?D g * f + ?D f * g)$n"
+      by (simp only: mult_commute)
     also have "\<dots> = (\<Sum>i = 0..n. ?g i)"
       by (simp add: fps_mult_nth setsum_addf[symmetric])
     also have "\<dots> = setsum ?h {1..n+1}"
@@ -829,14 +865,17 @@
       apply simp
       apply (simp add: subset_eq)
       unfolding eq'
-      by simp
+      apply simp
+      done
     also have "\<dots> = (fps_deriv (f * g)) $ n"
       apply (simp only: fps_deriv_nth fps_mult_nth setsum_addf)
       unfolding s0 s1
       unfolding setsum_addf[symmetric] setsum_right_distrib
       apply (rule setsum_cong2)
-      by (auto simp add: of_nat_diff field_simps)
-    finally have "(f * ?D g + ?D f * g) $ n = ?D (f*g) $ n" .}
+      apply (auto simp add: of_nat_diff field_simps)
+      done
+    finally have "(f * ?D g + ?D f * g) $ n = ?D (f*g) $ n" .
+  }
   then show ?thesis unfolding fps_eq_iff by auto
 qed
 
@@ -845,6 +884,7 @@
 
 lemma fps_deriv_neg[simp]: "fps_deriv (- (f:: ('a:: comm_ring_1) fps)) = - (fps_deriv f)"
   by (simp add: fps_eq_iff fps_deriv_def)
+
 lemma fps_deriv_add[simp]: "fps_deriv ((f:: ('a::comm_ring_1) fps) + g) = fps_deriv f + fps_deriv g"
   using fps_deriv_linear[of 1 f 1 g] by simp
 
@@ -871,11 +911,14 @@
 lemma fps_deriv_setsum:
   "fps_deriv (setsum f S) = setsum (\<lambda>i. fps_deriv (f i :: ('a::comm_ring_1) fps)) S"
 proof-
-  { assume "\<not> finite S" hence ?thesis by simp }
+  {
+    assume "\<not> finite S"
+    then have ?thesis by simp
+  }
   moreover
   {
     assume fS: "finite S"
-    have ?thesis  by (induct rule: finite_induct[OF fS]) simp_all
+    have ?thesis by (induct rule: finite_induct [OF fS]) simp_all
   }
   ultimately show ?thesis by blast
 qed
@@ -883,23 +926,29 @@
 lemma fps_deriv_eq_0_iff[simp]:
   "fps_deriv f = 0 \<longleftrightarrow> (f = fps_const (f$0 :: 'a::{idom,semiring_char_0}))"
 proof-
-  {assume "f= fps_const (f$0)" hence "fps_deriv f = fps_deriv (fps_const (f$0))" by simp
-    hence "fps_deriv f = 0" by simp }
+  {
+    assume "f = fps_const (f$0)"
+    then have "fps_deriv f = fps_deriv (fps_const (f$0))" by simp
+    then have "fps_deriv f = 0" by simp
+  }
   moreover
-  {assume z: "fps_deriv f = 0"
-    hence "\<forall>n. (fps_deriv f)$n = 0" by simp
-    hence "\<forall>n. f$(n+1) = 0" by (simp del: of_nat_Suc of_nat_add One_nat_def)
-    hence "f = fps_const (f$0)"
+  {
+    assume z: "fps_deriv f = 0"
+    then have "\<forall>n. (fps_deriv f)$n = 0" by simp
+    then have "\<forall>n. f$(n+1) = 0" by (simp del: of_nat_Suc of_nat_add One_nat_def)
+    then have "f = fps_const (f$0)"
       apply (clarsimp simp add: fps_eq_iff fps_const_def)
       apply (erule_tac x="n - 1" in allE)
-      by simp}
+      apply simp
+      done
+  }
   ultimately show ?thesis by blast
 qed
 
 lemma fps_deriv_eq_iff:
   fixes f:: "('a::{idom,semiring_char_0}) fps"
   shows "fps_deriv f = fps_deriv g \<longleftrightarrow> (f = fps_const(f$0 - g$0) + g)"
-proof-
+proof -
   have "fps_deriv f = fps_deriv g \<longleftrightarrow> fps_deriv (f - g) = 0" by simp
   also have "\<dots> \<longleftrightarrow> f - g = fps_const ((f-g)$0)" unfolding fps_deriv_eq_0_iff ..
   finally show ?thesis by (simp add: field_simps)
@@ -907,7 +956,8 @@
 
 lemma fps_deriv_eq_iff_ex:
   "(fps_deriv f = fps_deriv g) \<longleftrightarrow> (\<exists>(c::'a::{idom,semiring_char_0}). f = fps_const c + g)"
-  apply auto unfolding fps_deriv_eq_iff
+  apply auto
+  unfolding fps_deriv_eq_iff
   apply blast
   done
 
@@ -957,12 +1007,15 @@
 
 lemma fps_nth_deriv_setsum:
   "fps_nth_deriv n (setsum f S) = setsum (\<lambda>i. fps_nth_deriv n (f i :: ('a::comm_ring_1) fps)) S"
-proof-
-  { assume "\<not> finite S" hence ?thesis by simp }
+proof -
+  {
+    assume "\<not> finite S"
+    then have ?thesis by simp
+  }
   moreover
   {
     assume fS: "finite S"
-    have ?thesis  by (induct rule: finite_induct[OF fS]) simp_all
+    have ?thesis by (induct rule: finite_induct[OF fS]) simp_all
   }
   ultimately show ?thesis by blast
 qed
@@ -977,13 +1030,15 @@
   by (induct n) (auto simp add: expand_fps_eq fps_mult_nth)
 
 lemma fps_power_first_eq: "(a:: 'a::comm_ring_1 fps)$0 =1 \<Longrightarrow> a^n $ 1 = of_nat n * a$1"
-proof(induct n)
-  case 0 thus ?case by simp
+proof (induct n)
+  case 0
+  then show ?case by simp
 next
   case (Suc n)
   note h = Suc.hyps[OF `a$0 = 1`]
   show ?case unfolding power_Suc fps_mult_nth
-    using h `a$0 = 1`  fps_power_zeroth_eq_one[OF `a$0=1`] by (simp add: field_simps)
+    using h `a$0 = 1` fps_power_zeroth_eq_one[OF `a$0=1`]
+    by (simp add: field_simps)
 qed
 
 lemma startsby_one_power:"a $ 0 = (1::'a::comm_ring_1) \<Longrightarrow> a^n $ 0 = 1"
@@ -993,44 +1048,56 @@
   by (induct n) (auto simp add: fps_mult_nth)
 
 lemma startsby_power:"a $0 = (v::'a::{comm_ring_1}) \<Longrightarrow> a^n $0 = v^n"
-  by (induct n) (auto simp add: fps_mult_nth power_Suc)
-
-lemma startsby_zero_power_iff[simp]:
-  "a^n $0 = (0::'a::{idom}) \<longleftrightarrow> (n \<noteq> 0 \<and> a$0 = 0)"
-apply (rule iffI)
-apply (induct n)
-apply (auto simp add: fps_mult_nth)
-apply (rule startsby_zero_power, simp_all)
-done
+  by (induct n) (auto simp add: fps_mult_nth)
+
+lemma startsby_zero_power_iff[simp]: "a^n $0 = (0::'a::{idom}) \<longleftrightarrow> (n \<noteq> 0 \<and> a$0 = 0)"
+  apply (rule iffI)
+  apply (induct n)
+  apply (auto simp add: fps_mult_nth)
+  apply (rule startsby_zero_power, simp_all)
+  done
 
 lemma startsby_zero_power_prefix:
   assumes a0: "a $0 = (0::'a::idom)"
   shows "\<forall>n < k. a ^ k $ n = 0"
   using a0
 proof(induct k rule: nat_less_induct)
-  fix k assume H: "\<forall>m<k. a $0 =  0 \<longrightarrow> (\<forall>n<m. a ^ m $ n = 0)" and a0: "a $0 = (0\<Colon>'a)"
+  fix k
+  assume H: "\<forall>m<k. a $0 =  0 \<longrightarrow> (\<forall>n<m. a ^ m $ n = 0)" and a0: "a $0 = (0\<Colon>'a)"
   let ?ths = "\<forall>m<k. a ^ k $ m = 0"
-  {assume "k = 0" then have ?ths by simp}
+  { assume "k = 0" then have ?ths by simp }
   moreover
-  {fix l assume k: "k = Suc l"
-    {fix m assume mk: "m < k"
-      {assume "m=0" hence "a^k $ m = 0" using startsby_zero_power[of a k] k a0
-          by simp}
+  {
+    fix l
+    assume k: "k = Suc l"
+    {
+      fix m
+      assume mk: "m < k"
+      {
+        assume "m = 0"
+        then have "a^k $ m = 0"
+          using startsby_zero_power[of a k] k a0 by simp
+      }
       moreover
-      {assume m0: "m \<noteq> 0"
-        have "a ^k $ m = (a^l * a) $m" by (simp add: k power_Suc mult_commute)
+      {
+        assume m0: "m \<noteq> 0"
+        have "a ^k $ m = (a^l * a) $m" by (simp add: k mult_commute)
         also have "\<dots> = (\<Sum>i = 0..m. a ^ l $ i * a $ (m - i))" by (simp add: fps_mult_nth)
-        also have "\<dots> = 0" apply (rule setsum_0')
+        also have "\<dots> = 0"
+          apply (rule setsum_0')
           apply auto
           apply (case_tac "x = m")
-          using a0
-          apply simp
+          using a0 apply simp
           apply (rule H[rule_format])
-          using a0 k mk by auto
-        finally have "a^k $ m = 0" .}
-    ultimately have "a^k $ m = 0" by blast}
-    hence ?ths by blast}
-  ultimately show ?ths by (cases k, auto)
+          using a0 k mk apply auto
+          done
+        finally have "a^k $ m = 0" .
+      }
+      ultimately have "a^k $ m = 0" by blast
+    }
+    then have ?ths by blast
+  }
+  ultimately show ?ths by (cases k) auto
 qed
 
 lemma startsby_zero_setsum_depends:
@@ -1039,16 +1106,20 @@
   apply (rule setsum_mono_zero_right)
   using kn apply auto
   apply (rule startsby_zero_power_prefix[rule_format, OF a0])
-  by arith
-
-lemma startsby_zero_power_nth_same: assumes a0: "a$0 = (0::'a::{idom})"
+  apply arith
+  done
+
+lemma startsby_zero_power_nth_same:
+  assumes a0: "a$0 = (0::'a::{idom})"
   shows "a^n $ n = (a$1) ^ n"
-proof(induct n)
-  case 0 thus ?case by (simp add: power_0)
+proof (induct n)
+  case 0
+  then show ?case by (simp add: power_0)
 next
   case (Suc n)
-  have "a ^ Suc n $ (Suc n) = (a^n * a)$(Suc n)" by (simp add: field_simps power_Suc)
-  also have "\<dots> = setsum (\<lambda>i. a^n$i * a $ (Suc n - i)) {0.. Suc n}" by (simp add: fps_mult_nth)
+  have "a ^ Suc n $ (Suc n) = (a^n * a)$(Suc n)" by (simp add: field_simps)
+  also have "\<dots> = setsum (\<lambda>i. a^n$i * a $ (Suc n - i)) {0.. Suc n}"
+    by (simp add: fps_mult_nth)
   also have "\<dots> = setsum (\<lambda>i. a^n$i * a $ (Suc n - i)) {n .. Suc n}"
     apply (rule setsum_mono_zero_right)
     apply simp
@@ -1058,23 +1129,28 @@
     apply arith
     done
   also have "\<dots> = a^n $ n * a$1" using a0 by simp
-  finally show ?case using Suc.hyps by (simp add: power_Suc)
+  finally show ?case using Suc.hyps by simp
 qed
 
 lemma fps_inverse_power:
   fixes a :: "('a::{field}) fps"
   shows "inverse (a^n) = inverse a ^ n"
-proof-
-  {assume a0: "a$0 = 0"
-    hence eq: "inverse a = 0" by (simp add: fps_inverse_def)
-    {assume "n = 0" hence ?thesis by simp}
+proof -
+  {
+    assume a0: "a$0 = 0"
+    then have eq: "inverse a = 0" by (simp add: fps_inverse_def)
+    { assume "n = 0" hence ?thesis by simp }
     moreover
-    {assume n: "n > 0"
+    {
+      assume n: "n > 0"
       from startsby_zero_power[OF a0 n] eq a0 n have ?thesis
-        by (simp add: fps_inverse_def)}
-    ultimately have ?thesis by blast}
+        by (simp add: fps_inverse_def)
+    }
+    ultimately have ?thesis by blast
+  }
   moreover
-  {assume a0: "a$0 \<noteq> 0"
+  {
+    assume a0: "a$0 \<noteq> 0"
     have ?thesis
       apply (rule fps_inverse_unique)
       apply (simp add: a0)
@@ -1082,16 +1158,18 @@
       apply (rule ssubst[where t = "a * inverse a" and s= 1])
       apply simp_all
       apply (subst mult_commute)
-      by (rule inverse_mult_eq_1[OF a0])}
+      apply (rule inverse_mult_eq_1[OF a0])
+      done
+  }
   ultimately show ?thesis by blast
 qed
 
 lemma fps_deriv_power:
     "fps_deriv (a ^ n) = fps_const (of_nat n :: 'a:: comm_ring_1) * fps_deriv a * a ^ (n - 1)"
   apply (induct n)
-  apply (auto simp add: power_Suc field_simps fps_const_add[symmetric] simp del: fps_const_add)
+  apply (auto simp add: field_simps fps_const_add[symmetric] simp del: fps_const_add)
   apply (case_tac n)
-  apply (auto simp add: power_Suc field_simps)
+  apply (auto simp add: field_simps)
   done
 
 lemma fps_inverse_deriv:
@@ -1379,7 +1457,7 @@
       apply (rule bexI[where x = "?m"])
       apply (rule exI[where x = "?xs"])
       apply (rule exI[where x = "?ys"])
-      using ls l 
+      using ls l
       apply (auto simp add: natpermute_def l_take_drop simp del: append_take_drop_id)
       apply simp
       done
@@ -1719,7 +1797,7 @@
       ultimately  show "?r ^ Suc k $ n = a $n" by (cases n, auto)
     qed }
   then have ?thesis using r0 by (simp add: fps_eq_iff)}
-moreover 
+moreover
 { assume h: "(fps_radical r (Suc k) a) ^ (Suc k) = a"
   hence "((fps_radical r (Suc k) a) ^ (Suc k))$0 = a$0" by simp
   then have "(r (Suc k) (a$0)) ^ Suc k = a$0"
@@ -1998,15 +2076,15 @@
 
   {assume ?rhs
     then have "?r (a/b) $ 0 = (?r a / ?r b)$0" by simp
-    then have ?lhs using k a0 b0 rb0' 
+    then have ?lhs using k a0 b0 rb0'
       by (simp add: fps_divide_def fps_mult_nth fps_inverse_def divide_inverse) }
   moreover
   {assume h: ?lhs
-    from a0 b0 have ab0[simp]: "(a/b)$0 = a$0 / b$0" 
+    from a0 b0 have ab0[simp]: "(a/b)$0 = a$0 / b$0"
       by (simp add: fps_divide_def fps_mult_nth divide_inverse fps_inverse_def)
     have th0: "r k ((a/b)$0) ^ k = (a/b)$0"
       by (simp add: h nonzero_power_divide[OF rb0'] ra0 rb0 del: k)
-    from a0 b0 ra0' rb0' kp h 
+    from a0 b0 ra0' rb0' kp h
     have th1: "r k ((a / b) $ 0) = (fps_radical r k a / fps_radical r k b) $ 0"
       by (simp add: fps_divide_def fps_mult_nth fps_inverse_def divide_inverse del: k)
     from a0 b0 ra0' rb0' kp have ab0': "(a / b) $ 0 \<noteq> 0"
@@ -2360,7 +2438,7 @@
 
 then have "(?ia oo b) *  (a oo b) * ?iab  = 1 * ?iab" by simp
 then have "(?ia oo b) *  (?iab * (a oo b))  = ?iab" by simp
-then show ?thesis 
+then show ?thesis
   unfolding inverse_mult_eq_1[OF ab0] by simp
 qed
 
@@ -2374,11 +2452,11 @@
   shows "(Abs_fps (\<lambda>n. 1)) oo a = 1/(1 - a)" (is "?one oo a = _")
 proof-
   have o0: "?one $ 0 \<noteq> 0" by simp
-  have th0: "(1 - X) $ 0 \<noteq> (0::'a)" by simp  
+  have th0: "(1 - X) $ 0 \<noteq> (0::'a)" by simp
   from fps_inverse_gp[where ?'a = 'a]
   have "inverse ?one = 1 - X" by (simp add: fps_eq_iff)
   hence "inverse (inverse ?one) = inverse (1 - X)" by simp
-  hence th: "?one = 1/(1 - X)" unfolding fps_inverse_idempotent[OF o0] 
+  hence th: "?one = 1/(1 - X)" unfolding fps_inverse_idempotent[OF o0]
     by (simp add: fps_divide_def)
   show ?thesis unfolding th
     unfolding fps_divide_compose[OF a0 th0]
@@ -2402,8 +2480,8 @@
     by (simp add: ab0 fps_compose_def)
   have th0: "(?r a oo b) ^ (Suc k) = a  oo b"
     unfolding fps_compose_power[OF b0]
-    unfolding iffD1[OF power_radical[of a r k], OF a0 ra0]  .. 
-  from iffD1[OF radical_unique[where r=r and k=k and b= ?ab and a = "?r a oo b", OF rab0(2) th00 rab0(1)], OF th0] show ?thesis  . 
+    unfolding iffD1[OF power_radical[of a r k], OF a0 ra0]  ..
+  from iffD1[OF radical_unique[where r=r and k=k and b= ?ab and a = "?r a oo b", OF rab0(2) th00 rab0(1)], OF th0] show ?thesis  .
 qed
 
 lemma fps_const_mult_apply_left:
@@ -2485,7 +2563,7 @@
   show "?dia = inverse ?d" by simp
 qed
 
-lemma fps_inv_idempotent: 
+lemma fps_inv_idempotent:
   assumes a0: "a$0 = 0" and a1: "a$1 \<noteq> 0"
   shows "fps_inv (fps_inv a) = a"
 proof-
@@ -2495,7 +2573,7 @@
   have X0: "X$0 = 0" by simp
   from fps_inv[OF ra0 ra1] have "?r (?r a) oo ?r a = X" .
   then have "?r (?r a) oo ?r a oo a = X oo a" by simp
-  then have "?r (?r a) oo (?r a oo a) = a" 
+  then have "?r (?r a) oo (?r a oo a) = a"
     unfolding X_fps_compose_startby0[OF a0]
     unfolding fps_compose_assoc[OF a0 ra0, symmetric] .
   then show ?thesis unfolding fps_inv[OF a0 a1] by simp
@@ -2509,7 +2587,7 @@
   let ?r = "fps_ginv"
   from c0 have rca0: "?r c a $0 = 0" by (simp add: fps_ginv_def)
   from a1 c1 have rca1: "?r c a $ 1 \<noteq> 0" by (simp add: fps_ginv_def field_simps)
-  from fps_ginv[OF rca0 rca1] 
+  from fps_ginv[OF rca0 rca1]
   have "?r b (?r c a) oo ?r c a = b" .
   then have "?r b (?r c a) oo ?r c a oo a = b oo a" by simp
   then have "?r b (?r c a) oo (?r c a oo a) = b oo a"
@@ -2537,7 +2615,7 @@
   from fps_ginv[OF a0 a1, of b] have "?d (?ia oo a) = fps_deriv b" by simp
   then have "(?d ?ia oo a) * ?d a = ?d b" unfolding fps_compose_deriv[OF a0] .
   then have "(?d ?ia oo a) * ?d a * inverse (?d a) = ?d b * inverse (?d a)" by simp
-  then have "(?d ?ia oo a) * (inverse (?d a) * ?d a) = ?d b / ?d a" 
+  then have "(?d ?ia oo a) * (inverse (?d a) * ?d a) = ?d b / ?d a"
     by (simp add: fps_divide_def)
   then have "(?d ?ia oo a) oo ?iXa =  (?d b / ?d a) oo ?iXa "
     unfolding inverse_mult_eq_1[OF da0] by simp
@@ -2649,7 +2727,7 @@
   by (induct n) (auto simp add: field_simps E_add_mult power_Suc)
 
 lemma radical_E:
-  assumes r: "r (Suc k) 1 = 1" 
+  assumes r: "r (Suc k) 1 = 1"
   shows "fps_radical r (Suc k) (E (c::'a::{field_char_0})) = E (c / of_nat (Suc k))"
 proof-
   let ?ck = "(c / of_nat (Suc k))"
@@ -2660,24 +2738,24 @@
   have th: "r (Suc k) (E c $0) ^ Suc k = E c $ 0"
     "r (Suc k) (E c $ 0) = E ?ck $ 0" "E c $ 0 \<noteq> 0" using r by simp_all
   from th0 radical_unique[where r=r and k=k, OF th]
-  show ?thesis by auto 
+  show ?thesis by auto
 qed
 
-lemma Ec_E1_eq: 
+lemma Ec_E1_eq:
   "E (1::'a::{field_char_0}) oo (fps_const c * X) = E c"
   apply (auto simp add: fps_eq_iff E_def fps_compose_def power_mult_distrib)
   by (simp add: cond_value_iff cond_application_beta setsum_delta' cong del: if_weak_cong)
 
 text{* The generalized binomial theorem as a  consequence of @{thm E_add_mult} *}
 
-lemma gbinomial_theorem: 
+lemma gbinomial_theorem:
   "((a::'a::{field_char_0, field_inverse_zero})+b) ^ n = (\<Sum>k=0..n. of_nat (n choose k) * a^k * b^(n-k))"
 proof-
-  from E_add_mult[of a b] 
+  from E_add_mult[of a b]
   have "(E (a + b)) $ n = (E a * E b)$n" by simp
   then have "(a + b) ^ n = (\<Sum>i\<Colon>nat = 0\<Colon>nat..n. a ^ i * b ^ (n - i)  * (of_nat (fact n) / of_nat (fact i * fact (n - i))))"
     by (simp add: field_simps fps_mult_nth of_nat_mult[symmetric] setsum_right_distrib)
-  then show ?thesis 
+  then show ?thesis
     apply simp
     apply (rule setsum_cong2)
     apply simp
@@ -2693,11 +2771,11 @@
 
 subsubsection{* Logarithmic series *}
 
-lemma Abs_fps_if_0: 
+lemma Abs_fps_if_0:
   "Abs_fps(%n. if n=0 then (v::'a::ring_1) else f n) = fps_const v + X * Abs_fps (%n. f (Suc n))"
   by (auto simp add: fps_eq_iff)
 
-definition L:: "'a::{field_char_0} \<Rightarrow> 'a fps" where 
+definition L:: "'a::{field_char_0} \<Rightarrow> 'a fps" where
   "L c \<equiv> fps_const (1/c) * Abs_fps (\<lambda>n. if n = 0 then 0 else (- 1) ^ (n - 1) / of_nat n)"
 
 lemma fps_deriv_L: "fps_deriv (L c) = fps_const (1/c) * inverse (1 + X)"
@@ -2722,7 +2800,7 @@
   finally have eq: "fps_deriv (E a - 1) oo fps_inv (E a - 1) = fps_const a * (X + 1)" .
   from fps_inv_deriv[OF b0 b1, unfolded eq]
   have "fps_deriv (fps_inv ?b) = fps_const (inverse a) / (X + 1)"
-    using a 
+    using a
     by (simp add: fps_const_inverse eq fps_divide_def fps_inverse_mult)
   hence "fps_deriv ?l = fps_deriv ?r"
     by (simp add: fps_deriv_L add_commute fps_divide_def divide_inverse)
@@ -2730,7 +2808,7 @@
     by (simp add: L_nth fps_inv_def)
 qed
 
-lemma L_mult_add: 
+lemma L_mult_add:
   assumes c0: "c\<noteq>0" and d0: "d\<noteq>0"
   shows "L c + L d = fps_const (c+d) * L (c*d)"
   (is "?r = ?l")
@@ -2768,12 +2846,12 @@
     by (simp add: field_simps)
   finally have eq: "?l = ?r \<longleftrightarrow> ?lhs" by simp
   moreover
-  {assume h: "?l = ?r" 
+  {assume h: "?l = ?r"
     {fix n
       from h have lrn: "?l $ n = ?r$n" by simp
-      
-      from lrn 
-      have "a$ Suc n = ((c - of_nat n) / of_nat (Suc n)) * a $n" 
+
+      from lrn
+      have "a$ Suc n = ((c - of_nat n) / of_nat (Suc n)) * a $n"
         apply (simp add: field_simps del: of_nat_Suc)
         by (cases n, simp_all add: field_simps del: of_nat_Suc)
     }
@@ -2796,7 +2874,7 @@
   moreover
   {assume h: ?rhs
   have th00:"\<And>x y. x * (a$0 * y) = a$0 * (x*y)" by (simp add: mult_commute)
-    have "?l = ?r" 
+    have "?l = ?r"
       apply (subst h)
       apply (subst (2) h)
       apply (clarsimp simp add: fps_eq_iff field_simps)
@@ -2856,10 +2934,10 @@
 
 lemma binomial_Vandermonde: "setsum (\<lambda>k. (a choose k) * (b choose (n - k))) {0..n} = (a + b) choose n"
   using gbinomial_Vandermonde[of "(of_nat a)" "of_nat b" n]
-  
+
   apply (simp only: binomial_gbinomial[symmetric] of_nat_mult[symmetric] of_nat_setsum[symmetric] of_nat_add[symmetric])
   by simp
-  
+
 lemma binomial_Vandermonde_same: "setsum (\<lambda>k. (n choose k)^2) {0..n} = (2*n) choose n"
   using binomial_Vandermonde[of n n n,symmetric]
   unfolding mult_2 apply (simp add: power2_eq_square)
@@ -2879,22 +2957,22 @@
     {assume c:"pochhammer (b - of_nat n + 1) n = 0"
       then obtain j where j: "j < n" "b - of_nat n + 1 = - of_nat j"
         unfolding pochhammer_eq_0_iff by blast
-      from j have "b = of_nat n - of_nat j - of_nat 1" 
+      from j have "b = of_nat n - of_nat j - of_nat 1"
         by (simp add: algebra_simps)
-      then have "b = of_nat (n - j - 1)" 
+      then have "b = of_nat (n - j - 1)"
         using j kn by (simp add: of_nat_diff)
       with b have False using j by auto}
-    then have nz: "pochhammer (1 + b - of_nat n) n \<noteq> 0" 
+    then have nz: "pochhammer (1 + b - of_nat n) n \<noteq> 0"
       by (auto simp add: algebra_simps)
-    
-    from nz kn [simplified] have nz': "pochhammer (1 + b - of_nat n) k \<noteq> 0" 
+
+    from nz kn [simplified] have nz': "pochhammer (1 + b - of_nat n) k \<noteq> 0"
       by (rule pochhammer_neq_0_mono)
-    {assume k0: "k = 0 \<or> n =0" 
-      then have "b gchoose (n - k) = (?m1 n * ?p b n * ?m1 k * ?p (of_nat n) k) / (?f n * pochhammer (b - of_nat n + 1) k)" 
+    {assume k0: "k = 0 \<or> n =0"
+      then have "b gchoose (n - k) = (?m1 n * ?p b n * ?m1 k * ?p (of_nat n) k) / (?f n * pochhammer (b - of_nat n + 1) k)"
         using kn
         by (cases "k=0", simp_all add: gbinomial_pochhammer)}
     moreover
-    {assume n0: "n \<noteq> 0" and k0: "k \<noteq> 0" 
+    {assume n0: "n \<noteq> 0" and k0: "k \<noteq> 0"
       then obtain m where m: "n = Suc m" by (cases n, auto)
       from k0 obtain h where h: "k = Suc h" by (cases k, auto)
       {assume kn: "k = n"
@@ -2905,27 +2983,27 @@
           by (simp add: field_simps power_add[symmetric])}
       moreover
       {assume nk: "k \<noteq> n"
-        have m1nk: "?m1 n = setprod (%i. - 1) {0..m}" 
+        have m1nk: "?m1 n = setprod (%i. - 1) {0..m}"
           "?m1 k = setprod (%i. - 1) {0..h}"
           by (simp_all add: setprod_constant m h)
         from kn nk have kn': "k < n" by simp
         have bnz0: "pochhammer (b - of_nat n + 1) k \<noteq> 0"
-          using bn0 kn 
+          using bn0 kn
           unfolding pochhammer_eq_0_iff
           apply auto
           apply (erule_tac x= "n - ka - 1" in allE)
           by (auto simp add: algebra_simps of_nat_diff)
-        have eq1: "setprod (%k. (1::'a) + of_nat m - of_nat k) {0 .. h} = setprod of_nat {Suc (m - h) .. Suc m}"        
+        have eq1: "setprod (%k. (1::'a) + of_nat m - of_nat k) {0 .. h} = setprod of_nat {Suc (m - h) .. Suc m}"
           apply (rule strong_setprod_reindex_cong[where f="%k. Suc m - k "])
           using kn' h m
           apply (auto simp add: inj_on_def image_def)
           apply (rule_tac x="Suc m - x" in bexI)
           apply (simp_all add: of_nat_diff)
           done
-        
+
         have th1: "(?m1 k * ?p (of_nat n) k) / ?f n = 1 / of_nat(fact (n - k))"
-          unfolding m1nk 
-          
+          unfolding m1nk
+
           unfolding m h pochhammer_Suc_setprod
           apply (simp add: field_simps del: fact_Suc id_def minus_one)
           unfolding fact_altdef_nat id_def
@@ -2939,21 +3017,21 @@
           apply auto
           done
         have th20: "?m1 n * ?p b n = setprod (%i. b - of_nat i) {0..m}"
-          unfolding m1nk 
+          unfolding m1nk
           unfolding m h pochhammer_Suc_setprod
           unfolding setprod_timesf[symmetric]
           apply (rule setprod_cong)
           apply auto
           done
         have th21:"pochhammer (b - of_nat n + 1) k = setprod (%i. b - of_nat i) {n - k .. n - 1}"
-          unfolding h m 
+          unfolding h m
           unfolding pochhammer_Suc_setprod
           apply (rule strong_setprod_reindex_cong[where f="%k. n - 1 - k"])
           using kn
           apply (auto simp add: inj_on_def m h image_def)
           apply (rule_tac x= "m - x" in bexI)
           by (auto simp add: of_nat_diff)
-        
+
         have "?m1 n * ?p b n = pochhammer (b - of_nat n + 1) k * setprod (%i. b - of_nat i) {0.. n - k - 1}"
           unfolding th20 th21
           unfolding h m
@@ -2963,24 +3041,24 @@
           apply (rule setprod_cong)
           apply auto
           done
-        then have th2: "(?m1 n * ?p b n)/pochhammer (b - of_nat n + 1) k = setprod (%i. b - of_nat i) {0.. n - k - 1}" 
+        then have th2: "(?m1 n * ?p b n)/pochhammer (b - of_nat n + 1) k = setprod (%i. b - of_nat i) {0.. n - k - 1}"
           using nz' by (simp add: field_simps)
         have "(?m1 n * ?p b n * ?m1 k * ?p (of_nat n) k) / (?f n * pochhammer (b - of_nat n + 1) k) = ((?m1 k * ?p (of_nat n) k) / ?f n) * ((?m1 n * ?p b n)/pochhammer (b - of_nat n + 1) k)"
           using bnz0
           by (simp add: field_simps)
-        also have "\<dots> = b gchoose (n - k)" 
+        also have "\<dots> = b gchoose (n - k)"
           unfolding th1 th2
           using kn' by (simp add: gbinomial_def)
         finally have "b gchoose (n - k) = (?m1 n * ?p b n * ?m1 k * ?p (of_nat n) k) / (?f n * pochhammer (b - of_nat n + 1) k)" by simp}
       ultimately have "b gchoose (n - k) = (?m1 n * ?p b n * ?m1 k * ?p (of_nat n) k) / (?f n * pochhammer (b - of_nat n + 1) k)"
         by (cases "k =n", auto)}
     ultimately have "b gchoose (n - k) = (?m1 n * ?p b n * ?m1 k * ?p (of_nat n) k) / (?f n * pochhammer (b - of_nat n + 1) k)" "pochhammer (1 + b - of_nat n) k \<noteq> 0 "
-      using nz' 
+      using nz'
       apply (cases "n=0", auto)
       by (cases "k", auto)}
   note th00 = this
   have "?r = ((a + b) gchoose n) * (of_nat (fact n)/ (?m1 n * pochhammer (- b) n))"
-    unfolding gbinomial_pochhammer 
+    unfolding gbinomial_pochhammer
     using bn0 by (auto simp add: field_simps)
   also have "\<dots> = ?l"
     unfolding gbinomial_Vandermonde[symmetric]
@@ -2991,9 +3069,9 @@
     apply (drule th00(2))
     by (simp add: field_simps power_add[symmetric])
   finally show ?thesis by simp
-qed 
-
-    
+qed
+
+
 lemma Vandermonde_pochhammer:
    fixes a :: "'a::field_char_0"
   assumes c: "ALL i : {0..< n}. c \<noteq> - of_nat i"
@@ -3211,17 +3289,17 @@
 proof-
   {fix n::nat
     {assume en: "even n"
-      from en obtain m where m: "n = 2*m" 
+      from en obtain m where m: "n = 2*m"
         unfolding even_mult_two_ex by blast
-      
-      have "?l $n = ?r$n" 
+
+      have "?l $n = ?r$n"
         by (simp add: m fps_sin_def fps_cos_def power_mult_distrib
           power_mult power_minus)}
     moreover
     {assume on: "odd n"
-      from on obtain m where m: "n = 2*m + 1" 
-        unfolding odd_nat_equiv_def2 by (auto simp add: mult_2)  
-      have "?l $n = ?r$n" 
+      from on obtain m where m: "n = 2*m + 1"
+        unfolding odd_nat_equiv_def2 by (auto simp add: mult_2)
+      have "?l $n = ?r$n"
         by (simp add: m fps_sin_def fps_cos_def power_mult_distrib
           power_mult power_minus)}
     ultimately have "?l $n = ?r$n"  by blast}
@@ -3240,7 +3318,7 @@
 lemma fps_cos_Eii:
   "fps_cos c = (E (ii * c) + E (- ii * c)) / fps_const 2"
 proof-
-  have th: "fps_cos c + fps_cos c = fps_cos c * fps_const 2" 
+  have th: "fps_cos c + fps_cos c = fps_cos c * fps_const 2"
     by (simp add: numeral_fps_const)
   show ?thesis
   unfolding Eii_sin_cos minus_mult_commute
@@ -3251,7 +3329,7 @@
 lemma fps_sin_Eii:
   "fps_sin c = (E (ii * c) - E (- ii * c)) / fps_const (2*ii)"
 proof-
-  have th: "fps_const \<i> * fps_sin c + fps_const \<i> * fps_sin c = fps_sin c * fps_const (2 * ii)" 
+  have th: "fps_const \<i> * fps_sin c + fps_const \<i> * fps_sin c = fps_sin c * fps_const (2 * ii)"
     by (simp add: fps_eq_iff numeral_fps_const)
   show ?thesis
   unfolding Eii_sin_cos minus_mult_commute
@@ -3287,7 +3365,7 @@
     foldr (\<lambda>b r. r * pochhammer b n) bs (of_nat (fact n))"
   by (simp add: foldl_mult_start foldr_mult_foldl)
 
-lemma F_E[simp]: "F [] [] c = E c" 
+lemma F_E[simp]: "F [] [] c = E c"
   by (simp add: fps_eq_iff)
 
 lemma F_1_0[simp]: "F [1] [] c = 1/(1 - fps_const c * X)"
@@ -3340,7 +3418,7 @@
 lemma XDp_fps_integral[simp]:"XDp 0 (fps_integral a c) = X * a"
   by (simp add: fps_eq_iff fps_integral_def)
 
-lemma F_minus_nat: 
+lemma F_minus_nat:
   "F [- of_nat n] [- of_nat (n + m)] (c::'a::{field_char_0, field_inverse_zero}) $ k = (if k <= n then pochhammer (- of_nat n) k * c ^ k /
     (pochhammer (- of_nat (n + m)) k * of_nat (fact k)) else 0)"
   "F [- of_nat m] [- of_nat (m + n)] (c::'a::{field_char_0, field_inverse_zero}) $ k = (if k <= m then pochhammer (- of_nat m) k * c ^ k /
@@ -3352,19 +3430,19 @@
   apply (subst setsum_insert[symmetric])
   by (auto simp add: not_less setsum_head_Suc)
 
-lemma pochhammer_rec_if: 
+lemma pochhammer_rec_if:
   "pochhammer a n = (if n = 0 then 1 else a * pochhammer (a + 1) (n - 1))"
   by (cases n, simp_all add: pochhammer_rec)
 
-lemma XDp_foldr_nth[simp]: "foldr (%c r. XDp c o r) cs (%c. XDp c a) c0 $ n = 
+lemma XDp_foldr_nth[simp]: "foldr (%c r. XDp c o r) cs (%c. XDp c a) c0 $ n =
   foldr (%c r. (c + of_nat n) * r) cs (c0 + of_nat n) * a$n"
   by (induct cs arbitrary: c0) (auto simp add: algebra_simps)
 
 lemma genric_XDp_foldr_nth:
-  assumes 
+  assumes
   f: "ALL n c a. f c a $ n = (of_nat n + k c) * a$n"
 
-  shows "foldr (%c r. f c o r) cs (%c. g c a) c0 $ n = 
+  shows "foldr (%c r. f c o r) cs (%c. g c a) c0 $ n =
   foldr (%c r. (k c + of_nat n) * r) cs (g c0 a $ n)"
   by (induct cs arbitrary: c0) (auto simp add: algebra_simps f)
 
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/HOL/ex/Adhoc_Overloading_Examples.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/ex/Adhoc_Overloading_Examples.thy	Wed Aug 07 15:43:58 2013 +0200
@@ -0,0 +1,250 @@
+(*  Title:  HOL/ex/Adhoc_Overloading_Examples.thy
+    Author: Christian Sternagel
+*)
+
+header {* Ad Hoc Overloading *}
+
+theory Adhoc_Overloading_Examples
+imports
+  Main
+  "~~/src/Tools/Adhoc_Overloading"
+  "~~/src/HOL/Library/Infinite_Set"
+begin
+
+text {*Adhoc overloading allows to overload a constant depending on
+its type. Typically this involves to introduce an uninterpreted
+constant (used for input and output) and then add some variants (used
+internally).*}
+
+subsection {* Plain Ad Hoc Overloading *}
+
+text {*Consider the type of first-order terms.*}
+datatype ('a, 'b) "term" =
+  Var 'b |
+  Fun 'a "('a, 'b) term list"
+
+text {*The set of variables of a term might be computed as follows.*}
+fun term_vars :: "('a, 'b) term \<Rightarrow> 'b set" where
+  "term_vars (Var x) = {x}" |
+  "term_vars (Fun f ts) = \<Union>set (map term_vars ts)"
+
+text {*However, also for \emph{rules} (i.e., pairs of terms) and term
+rewrite systems (i.e., sets of rules), the set of variables makes
+sense. Thus we introduce an unspecified constant @{text vars}.*}
+
+consts vars :: "'a \<Rightarrow> 'b set"
+
+text {*Which is then overloaded with variants for terms, rules, and TRSs.*}
+adhoc_overloading
+  vars term_vars
+
+value "vars (Fun ''f'' [Var 0, Var 1])"
+
+fun rule_vars :: "('a, 'b) term \<times> ('a, 'b) term \<Rightarrow> 'b set" where
+  "rule_vars (l, r) = vars l \<union> vars r"
+
+adhoc_overloading
+  vars rule_vars
+
+value "vars (Var 1, Var 0)"
+
+definition trs_vars :: "(('a, 'b) term \<times> ('a, 'b) term) set \<Rightarrow> 'b set" where
+  "trs_vars R = \<Union>(rule_vars ` R)"
+
+adhoc_overloading
+  vars trs_vars
+
+value "vars {(Var 1, Var 0)}"
+
+text {*Sometimes it is necessary to add explicit type constraints
+before a variant can be determined.*}
+(*value "vars R" (*has multiple instances*)*)
+value "vars (R :: (('a, 'b) term \<times> ('a, 'b) term) set)"
+
+text {*It is also possible to remove variants.*}
+no_adhoc_overloading
+  vars term_vars rule_vars 
+
+(*value "vars (Var 1)" (*does not have an instance*)*)
+
+text {*As stated earlier, the overloaded constant is only used for
+input and output. Internally, always a variant is used, as can be
+observed by the configuration option @{text show_variants}.*}
+
+adhoc_overloading
+  vars term_vars
+
+declare [[show_variants]]
+
+term "vars (Var 1)" (*which yields: "term_vars (Var 1)"*)
+
+
+subsection {* Adhoc Overloading inside Locales *}
+
+text {*As example we use permutations that are parametrized over an
+atom type @{typ "'a"}.*}
+
+definition perms :: "('a \<Rightarrow> 'a) set" where
+  "perms = {f. bij f \<and> finite {x. f x \<noteq> x}}"
+
+typedef 'a perm = "perms :: ('a \<Rightarrow> 'a) set"
+  by (default) (auto simp: perms_def)
+
+text {*First we need some auxiliary lemmas.*}
+lemma permsI [Pure.intro]:
+  assumes "bij f" and "MOST x. f x = x"
+  shows "f \<in> perms"
+  using assms by (auto simp: perms_def) (metis MOST_iff_finiteNeg)
+
+lemma perms_imp_bij:
+  "f \<in> perms \<Longrightarrow> bij f"
+  by (simp add: perms_def)
+
+lemma perms_imp_MOST_eq:
+  "f \<in> perms \<Longrightarrow> MOST x. f x = x"
+  by (simp add: perms_def) (metis MOST_iff_finiteNeg)
+
+lemma id_perms [simp]:
+  "id \<in> perms"
+  "(\<lambda>x. x) \<in> perms"
+  by (auto simp: perms_def bij_def)
+
+lemma perms_comp [simp]:
+  assumes f: "f \<in> perms" and g: "g \<in> perms"
+  shows "(f \<circ> g) \<in> perms"
+  apply (intro permsI bij_comp)
+  apply (rule perms_imp_bij [OF g])
+  apply (rule perms_imp_bij [OF f])
+  apply (rule MOST_rev_mp [OF perms_imp_MOST_eq [OF g]])
+  apply (rule MOST_rev_mp [OF perms_imp_MOST_eq [OF f]])
+  by simp
+
+lemma perms_inv:
+  assumes f: "f \<in> perms"
+  shows "inv f \<in> perms"
+  apply (rule permsI)
+  apply (rule bij_imp_bij_inv)
+  apply (rule perms_imp_bij [OF f])
+  apply (rule MOST_mono [OF perms_imp_MOST_eq [OF f]])
+  apply (erule subst, rule inv_f_f)
+  by (rule bij_is_inj [OF perms_imp_bij [OF f]])
+
+lemma bij_Rep_perm: "bij (Rep_perm p)"
+  using Rep_perm [of p] unfolding perms_def by simp
+
+instantiation perm :: (type) group_add
+begin
+
+definition "0 = Abs_perm id"
+definition "- p = Abs_perm (inv (Rep_perm p))"
+definition "p + q = Abs_perm (Rep_perm p \<circ> Rep_perm q)"
+definition "(p1::'a perm) - p2 = p1 + - p2"
+
+lemma Rep_perm_0: "Rep_perm 0 = id"
+  unfolding zero_perm_def by (simp add: Abs_perm_inverse)
+
+lemma Rep_perm_add:
+  "Rep_perm (p1 + p2) = Rep_perm p1 \<circ> Rep_perm p2"
+  unfolding plus_perm_def by (simp add: Abs_perm_inverse Rep_perm)
+
+lemma Rep_perm_uminus:
+  "Rep_perm (- p) = inv (Rep_perm p)"
+  unfolding uminus_perm_def by (simp add: Abs_perm_inverse perms_inv Rep_perm)
+
+instance
+  apply default
+  unfolding Rep_perm_inject [symmetric]
+  unfolding minus_perm_def
+  unfolding Rep_perm_add
+  unfolding Rep_perm_uminus
+  unfolding Rep_perm_0
+  by (simp_all add: o_assoc inv_o_cancel [OF bij_is_inj [OF bij_Rep_perm]])
+
+end
+
+lemmas Rep_perm_simps =
+  Rep_perm_0
+  Rep_perm_add
+  Rep_perm_uminus
+
+
+section {* Permutation Types *}
+
+text {*We want to be able to apply permutations to arbitrary types. To
+this end we introduce a constant @{text PERMUTE} together with
+convenient infix syntax.*}
+
+consts PERMUTE :: "'a perm \<Rightarrow> 'b \<Rightarrow> 'b" (infixr "\<bullet>" 75)
+
+text {*Then we add a locale for types @{typ 'b} that support
+appliciation of permutations.*}
+locale permute =
+  fixes permute :: "'a perm \<Rightarrow> 'b \<Rightarrow> 'b"
+  assumes permute_zero [simp]: "permute 0 x = x"
+    and permute_plus [simp]: "permute (p + q) x = permute p (permute q x)"
+begin
+
+adhoc_overloading
+  PERMUTE permute
+
+end
+
+text {*Permuting atoms.*}
+definition permute_atom :: "'a perm \<Rightarrow> 'a \<Rightarrow> 'a" where
+  "permute_atom p a = (Rep_perm p) a"
+
+adhoc_overloading
+  PERMUTE permute_atom
+
+interpretation atom_permute: permute permute_atom
+  by (default) (simp add: permute_atom_def Rep_perm_simps)+
+
+text {*Permuting permutations.*}
+definition permute_perm :: "'a perm \<Rightarrow> 'a perm \<Rightarrow> 'a perm" where
+  "permute_perm p q = p + q - p"
+
+adhoc_overloading
+  PERMUTE permute_perm
+
+interpretation perm_permute: permute permute_perm
+  by (default) (simp add: diff_minus minus_add add_assoc permute_perm_def)+
+
+text {*Permuting functions.*}
+locale fun_permute =
+  dom: permute perm1 + ran: permute perm2
+  for perm1 :: "'a perm \<Rightarrow> 'b \<Rightarrow> 'b"
+  and perm2 :: "'a perm \<Rightarrow> 'c \<Rightarrow> 'c"
+begin
+
+adhoc_overloading
+  PERMUTE perm1 perm2
+
+definition permute_fun :: "'a perm \<Rightarrow> ('b \<Rightarrow> 'c) \<Rightarrow> ('b \<Rightarrow> 'c)" where
+  "permute_fun p f = (\<lambda>x. p \<bullet> (f (-p \<bullet> x)))"
+
+adhoc_overloading
+  PERMUTE permute_fun
+
+end
+
+sublocale fun_permute \<subseteq> permute permute_fun
+  by (unfold_locales, auto simp: permute_fun_def)
+     (metis dom.permute_plus minus_add)
+
+lemma "(Abs_perm id :: nat perm) \<bullet> Suc 0 = Suc 0"
+  unfolding permute_atom_def
+  by (metis Rep_perm_0 id_apply zero_perm_def)
+
+interpretation atom_fun_permute: fun_permute permute_atom permute_atom
+  by (unfold_locales)
+
+adhoc_overloading
+  PERMUTE atom_fun_permute.permute_fun
+
+lemma "(Abs_perm id :: 'a perm) \<bullet> id = id"
+  unfolding atom_fun_permute.permute_fun_def
+  unfolding permute_atom_def
+  by (metis Rep_perm_0 id_def inj_imp_inv_eq inj_on_id uminus_perm_def zero_perm_def)
+
+end
+
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Pure/General/symbol.scala
--- a/src/Pure/General/symbol.scala	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Pure/General/symbol.scala	Wed Aug 07 15:43:58 2013 +0200
@@ -193,7 +193,7 @@
         if (min <= c && c <= max) {
           matcher.region(i, len).lookingAt
           val x = matcher.group
-          result.append(table.get(x) getOrElse x)
+          result.append(table.getOrElse(x, x))
           i = matcher.end
         }
         else { result.append(c); i += 1 }
@@ -255,7 +255,7 @@
     }
 
     val groups: List[(String, List[Symbol])] =
-      symbols.map({ case (sym, props) => (sym, props.get("group") getOrElse "unsorted") })
+      symbols.map({ case (sym, props) => (sym, props.getOrElse("group", "unsorted")) })
         .groupBy(_._2).toList.map({ case (group, list) => (group, list.map(_._1)) })
         .sortBy(_._1)
 
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Pure/PIDE/document.scala
--- a/src/Pure/PIDE/document.scala	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Pure/PIDE/document.scala	Wed Aug 07 15:43:58 2013 +0200
@@ -15,48 +15,6 @@
 {
   /** document structure **/
 
-  /* overlays -- print functions with arguments */
-
-  type Overlay = (Command, (String, List[String]))
-
-  object Overlays
-  {
-    val empty = new Overlays(Map.empty)
-  }
-
-  final class Overlays private(rep: Map[Command, List[(String, List[String])]])
-  {
-    def commands: Set[Command] = rep.keySet
-    def is_empty: Boolean = rep.isEmpty
-
-    def insert(cmd: Command, fn: (String, List[String])): Overlays =
-    {
-      val fns = rep.get(cmd) getOrElse Nil
-      if (fns.contains(fn)) this
-      else new Overlays(rep + (cmd -> (fn :: fns)))
-    }
-
-    def remove(cmd: Command, fn: (String, List[String])): Overlays =
-      rep.get(cmd) match {
-        case Some(fns) =>
-          if (fns.contains(fn)) {
-            fns.filterNot(_ == fn) match {
-              case Nil => new Overlays(rep - cmd)
-              case fns1 => new Overlays(rep + (cmd -> fns1))
-            }
-          }
-          else this
-        case None => this
-      }
-
-    def dest: List[Overlay] =
-      (for {
-        (cmd, fns) <- rep.iterator
-        fn <- fns
-      } yield (cmd, fn)).toList
-  }
-
-
   /* individual nodes */
 
   type Edit[A, B] = (Node.Name, Node.Edit[A, B])
@@ -65,6 +23,11 @@
 
   object Node
   {
+    val empty: Node = new Node()
+
+
+    /* header and name */
+
     sealed case class Header(
       imports: List[Name],
       keywords: Thy_Header.Keywords,
@@ -84,6 +47,7 @@
         def compare(name1: Name, name2: Name): Int = name1.node compare name2.node
       }
     }
+
     sealed case class Name(node: String, dir: String, theory: String)
     {
       override def hashCode: Int = node.hashCode
@@ -95,6 +59,51 @@
       override def toString: String = theory
     }
 
+
+    /* overlays -- print functions with arguments */
+
+    type Overlay = (Command, (String, List[String]))
+
+    object Overlays
+    {
+      val empty = new Overlays(Map.empty)
+    }
+
+    final class Overlays private(rep: Map[Command, List[(String, List[String])]])
+    {
+      def commands: Set[Command] = rep.keySet
+      def is_empty: Boolean = rep.isEmpty
+
+      def insert(cmd: Command, over: (String, List[String])): Overlays =
+      {
+        val overs = rep.getOrElse(cmd, Nil)
+        if (overs.contains(over)) this
+        else new Overlays(rep + (cmd -> (over :: overs)))
+      }
+
+      def remove(cmd: Command, over: (String, List[String])): Overlays =
+        rep.get(cmd) match {
+          case Some(overs) =>
+            if (overs.contains(over)) {
+              overs.filterNot(_ == over) match {
+                case Nil => new Overlays(rep - cmd)
+                case overs1 => new Overlays(rep + (cmd -> overs1))
+              }
+            }
+            else this
+          case None => this
+        }
+
+      def dest: List[Overlay] =
+        (for {
+          (cmd, overs) <- rep.iterator
+          over <- overs
+        } yield (cmd, over)).toList
+    }
+
+
+    /* edits */
+
     sealed abstract class Edit[A, B]
     {
       def foreach(f: A => Unit)
@@ -112,6 +121,9 @@
     type Perspective_Text = Perspective[Text.Edit, Text.Perspective]
     type Perspective_Command = Perspective[Command.Edit, Command.Perspective]
 
+
+    /* commands */
+
     def command_starts(commands: Iterator[Command], offset: Text.Offset = 0)
       : Iterator[(Command, Text.Offset)] =
     {
@@ -124,14 +136,12 @@
     }
 
     private val block_size = 1024
-
-    val empty: Node = new Node()
   }
 
   final class Node private(
     val header: Node.Header = Node.bad_header("Bad theory header"),
     val perspective: Node.Perspective_Command =
-      Node.Perspective(false, Command.Perspective.empty, Overlays.empty),
+      Node.Perspective(false, Command.Perspective.empty, Node.Overlays.empty),
     val commands: Linear_Set[Command] = Linear_Set.empty)
   {
     def clear: Node = new Node(header = header)
@@ -310,19 +320,19 @@
     val node: Node
     val is_outdated: Boolean
     def convert(i: Text.Offset): Text.Offset
+    def revert(i: Text.Offset): Text.Offset
     def convert(range: Text.Range): Text.Range
-    def revert(i: Text.Offset): Text.Offset
     def revert(range: Text.Range): Text.Range
     def eq_content(other: Snapshot): Boolean
     def cumulate_markup[A](
       range: Text.Range,
       info: A,
       elements: Option[Set[String]],
-      result: Command.State => PartialFunction[(A, Text.Markup), A]): Stream[Text.Info[A]]
+      result: Command.State => (A, Text.Markup) => Option[A]): Stream[Text.Info[A]]
     def select_markup[A](
       range: Text.Range,
       elements: Option[Set[String]],
-      result: Command.State => PartialFunction[Text.Markup, A]): Stream[Text.Info[A]]
+      result: Command.State => Text.Markup => Option[A]): Stream[Text.Info[A]]
   }
 
   type Assign_Update =
@@ -554,33 +564,30 @@
             })
 
         def cumulate_markup[A](range: Text.Range, info: A, elements: Option[Set[String]],
-          result: Command.State => PartialFunction[(A, Text.Markup), A]): Stream[Text.Info[A]] =
+          result: Command.State => (A, Text.Markup) => Option[A]): Stream[Text.Info[A]] =
         {
           val former_range = revert(range)
           for {
             (command, command_start) <- node.command_range(former_range).toStream
             st = state.command_state(version, command)
             res = result(st)
-            Text.Info(r0, a) <- st.markup.
-              cumulate[A]((former_range - command_start).restrict(command.range), info, elements,
-                {
-                  case (a, Text.Info(r0, b))
-                  if res.isDefinedAt((a, Text.Info(convert(r0 + command_start), b))) =>
-                    res((a, Text.Info(convert(r0 + command_start), b)))
-                })
+            Text.Info(r0, a) <- st.markup.cumulate[A](
+              (former_range - command_start).restrict(command.range), info, elements,
+              { case (a, Text.Info(r0, b)) => res(a, Text.Info(convert(r0 + command_start), b)) })
           } yield Text.Info(convert(r0 + command_start), a)
         }
 
         def select_markup[A](range: Text.Range, elements: Option[Set[String]],
-          result: Command.State => PartialFunction[Text.Markup, A]): Stream[Text.Info[A]] =
+          result: Command.State => Text.Markup => Option[A]): Stream[Text.Info[A]] =
         {
-          def result1(st: Command.State) =
+          def result1(st: Command.State): (Option[A], Text.Markup) => Option[Option[A]] =
           {
             val res = result(st)
-            new PartialFunction[(Option[A], Text.Markup), Option[A]] {
-              def isDefinedAt(arg: (Option[A], Text.Markup)): Boolean = res.isDefinedAt(arg._2)
-              def apply(arg: (Option[A], Text.Markup)): Option[A] = Some(res(arg._2))
-            }
+            (_: Option[A], x: Text.Markup) =>
+              res(x) match {
+                case None => None
+                case some => Some(some)
+              }
           }
           for (Text.Info(r, Some(x)) <- cumulate_markup(range, None, elements, result1))
             yield Text.Info(r, x)
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Pure/PIDE/markup_tree.scala
--- a/src/Pure/PIDE/markup_tree.scala	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Pure/PIDE/markup_tree.scala	Wed Aug 07 15:43:58 2013 +0200
@@ -223,7 +223,7 @@
     to_XML(Text.Range(0, text.length), text, (_: XML.Elem) => true)
 
   def cumulate[A](root_range: Text.Range, root_info: A, result_elements: Option[Set[String]],
-    result: PartialFunction[(A, Text.Markup), A]): Stream[Text.Info[A]] =
+    result: (A, Text.Markup) => Option[A]): Stream[Text.Info[A]] =
   {
     val notable: Elements => Boolean =
       result_elements match {
@@ -233,15 +233,12 @@
 
     def results(x: A, entry: Entry): Option[A] =
     {
-      val (y, changed) =
-        // FIXME proper cumulation order (including status markup) (!?)
-        ((x, false) /: entry.rev_markup)((res, info) =>
-          {
-            val (y, changed) = res
-            val arg = (y, Text.Info(entry.range, info))
-            if (result.isDefinedAt(arg)) (result(arg), true)
-            else res
-          })
+      var y = x
+      var changed = false
+      for {
+        info <- entry.rev_markup // FIXME proper cumulation order (including status markup) (!?)
+        y1 <- result(y, Text.Info(entry.range, info))
+      } { y = y1; changed = true }
       if (changed) Some(y) else None
     }
 
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Pure/PIDE/xml.scala
--- a/src/Pure/PIDE/xml.scala	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Pure/PIDE/xml.scala	Wed Aug 07 15:43:58 2013 +0200
@@ -22,6 +22,9 @@
 
   sealed abstract class Tree { override def toString = string_of_tree(this) }
   case class Elem(markup: Markup, body: List[Tree]) extends Tree
+  {
+    def name: String = markup.name
+  }
   case class Text(content: String) extends Tree
 
   def elem(name: String, body: List[Tree]) = Elem(Markup(name, Nil), body)
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Pure/Thy/thy_syntax.scala
--- a/src/Pure/Thy/thy_syntax.scala	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Pure/Thy/thy_syntax.scala	Wed Aug 07 15:43:58 2013 +0200
@@ -95,7 +95,7 @@
   def command_perspective(
       node: Document.Node,
       perspective: Text.Perspective,
-      overlays: Document.Overlays): (Command.Perspective, Command.Perspective) =
+      overlays: Document.Node.Overlays): (Command.Perspective, Command.Perspective) =
   {
     if (perspective.is_empty && overlays.is_empty)
       (Command.Perspective.empty, Command.Perspective.empty)
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Pure/Tools/ml_statistics.scala
--- a/src/Pure/Tools/ml_statistics.scala	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Pure/Tools/ml_statistics.scala	Wed Aug 07 15:43:58 2013 +0200
@@ -85,7 +85,7 @@
       // rising edges -- relative speed
       val speeds =
         for ((key, value) <- props; a <- Library.try_unprefix("time", key)) yield {
-          val (x0, y0, s0) = last_edge.get(a) getOrElse (0.0, 0.0, 0.0)
+          val (x0, y0, s0) = last_edge.getOrElse(a, (0.0, 0.0, 0.0))
 
           val x1 = time
           val y1 = java.lang.Double.parseDouble(value)
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Tools/Adhoc_Overloading.thy
--- a/src/Tools/Adhoc_Overloading.thy	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Tools/Adhoc_Overloading.thy	Wed Aug 07 15:43:58 2013 +0200
@@ -2,7 +2,7 @@
    Author: Christian Sternagel, University of Innsbruck
 *)
 
-header {* Ad-hoc overloading of constants based on their types *}
+header {* Adhoc overloading of constants based on their types *}
 
 theory Adhoc_Overloading
 imports Pure
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Tools/adhoc_overloading.ML
--- a/src/Tools/adhoc_overloading.ML	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Tools/adhoc_overloading.ML	Wed Aug 07 15:43:58 2013 +0200
@@ -1,7 +1,7 @@
 (* Author: Alexander Krauss, TU Muenchen
    Author: Christian Sternagel, University of Innsbruck
 
-Ad-hoc overloading of constants based on their types.
+Adhoc overloading of constants based on their types.
 *)
 
 signature ADHOC_OVERLOADING =
@@ -41,7 +41,7 @@
       "in term " ::
       quote (Syntax.string_of_term ctxt' t) ::
       (if null instances then "no instances" else "multiple instances:") ::
-    map (Syntax.string_of_term ctxt') instances)
+    map (Markup.markup Markup.item o Syntax.string_of_term ctxt') instances)
     |> error
   end;
 
@@ -227,12 +227,12 @@
 
 val _ =
   Outer_Syntax.local_theory @{command_spec "adhoc_overloading"}
-    "add ad-hoc overloading for constants / fixed variables"
+    "add adhoc overloading for constants / fixed variables"
     (Parse.and_list1 (Parse.const -- Scan.repeat Parse.term) >> adhoc_overloading_cmd true);
 
 val _ =
   Outer_Syntax.local_theory @{command_spec "no_adhoc_overloading"}
-    "add ad-hoc overloading for constants / fixed variables"
+    "add adhoc overloading for constants / fixed variables"
     (Parse.and_list1 (Parse.const -- Scan.repeat Parse.term) >> adhoc_overloading_cmd false);
 
 end;
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Tools/jEdit/src/document_model.scala
--- a/src/Tools/jEdit/src/document_model.scala	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Tools/jEdit/src/document_model.scala	Wed Aug 07 15:43:58 2013 +0200
@@ -79,7 +79,7 @@
 
   /* overlays */
 
-  private var overlays = Document.Overlays.empty
+  private var overlays = Document.Node.Overlays.empty
 
   def insert_overlay(command: Command, name: String, args: List[String]): Unit =
     Swing_Thread.require { overlays = overlays.insert(command, (name, args)) }
@@ -104,7 +104,7 @@
   }
 
   val empty_perspective: Document.Node.Perspective_Text =
-    Document.Node.Perspective(false, Text.Perspective.empty, Document.Overlays.empty)
+    Document.Node.Perspective(false, Text.Perspective.empty, Document.Node.Overlays.empty)
 
   def node_perspective(): Document.Node.Perspective_Text =
   {
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Tools/jEdit/src/find_dockable.scala
--- a/src/Tools/jEdit/src/find_dockable.scala	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Tools/jEdit/src/find_dockable.scala	Wed Aug 07 15:43:58 2013 +0200
@@ -15,10 +15,10 @@
 import scala.swing.event.ButtonClicked
 
 import java.awt.BorderLayout
-import java.awt.event.{ComponentEvent, ComponentAdapter}
+import java.awt.event.{ComponentEvent, ComponentAdapter, KeyEvent}
 
 import org.gjt.sp.jedit.View
-import org.gjt.sp.jedit.gui.HistoryTextArea
+import org.gjt.sp.jedit.gui.HistoryTextField
 
 
 class Find_Dockable(view: View, position: String) extends Dockable(view, position)
@@ -91,17 +91,23 @@
 
   /* controls */
 
-  private val query = new HistoryTextArea("isabelle-find-theorems") {
+  private def clicked { find_theorems.apply_query(List(query.getText)) }
+
+  private val query = new HistoryTextField("isabelle-find-theorems") {
+    override def processKeyEvent(evt: KeyEvent)
+    {
+      if (evt.getID == KeyEvent.KEY_PRESSED && evt.getKeyCode == KeyEvent.VK_ENTER) clicked
+      super.processKeyEvent(evt)
+    }
     { val max = getPreferredSize; max.width = Integer.MAX_VALUE; setMaximumSize(max) }
-    setColumns(25)
-    setRows(1)
+    setColumns(40)
   }
 
   private val query_wrapped = Component.wrap(query)
 
   private val apply_query = new Button("Apply") {
     tooltip = "Find theorems meeting specified criteria"
-    reactions += { case ButtonClicked(_) => find_theorems.apply_query(List(query.getText)) }
+    reactions += { case ButtonClicked(_) => clicked }
   }
 
   private val locate_query = new Button("Locate") {
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Tools/jEdit/src/query_operation.scala
--- a/src/Tools/jEdit/src/query_operation.scala	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Tools/jEdit/src/query_operation.scala	Wed Aug 07 15:43:58 2013 +0200
@@ -141,7 +141,7 @@
     /* status */
 
     def get_status(name: String, status: Status.Value): Option[Status.Value] =
-      results.collectFirst({ case List(XML.Elem(m, _)) if m.name == name => status })
+      results.collectFirst({ case List(elem: XML.Elem) if elem.name == name => status })
 
     val new_status =
       get_status(Markup.FINISHED, Status.FINISHED) orElse
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Tools/jEdit/src/rendering.scala
--- a/src/Tools/jEdit/src/rendering.scala	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Tools/jEdit/src/rendering.scala	Wed Aug 07 15:43:58 2013 +0200
@@ -154,11 +154,12 @@
         snapshot.cumulate_markup[(Protocol.Status, Int)](
           range, (Protocol.Status.init, 0), Some(overview_include), _ =>
           {
-            case ((status, pri), Text.Info(_, XML.Elem(markup, _)))
-            if overview_include(markup.name) =>
-              if (markup.name == Markup.WARNING || markup.name == Markup.ERROR)
-                (status, pri max Rendering.message_pri(markup.name))
-              else (Protocol.command_status(status, markup), pri)
+            case ((status, pri), Text.Info(_, elem)) =>
+              if (elem.name == Markup.WARNING || elem.name == Markup.ERROR)
+                Some((status, pri max Rendering.message_pri(elem.name)))
+              else if (overview_include(elem.name))
+                Some((Protocol.command_status(status, elem.markup), pri))
+              else None
           })
       if (results.isEmpty) None
       else {
@@ -188,8 +189,10 @@
   {
     snapshot.select_markup(range, Some(highlight_include), _ =>
         {
-          case Text.Info(info_range, XML.Elem(Markup(name, _), _)) if highlight_include(name) =>
-            Text.Info(snapshot.convert(info_range), highlight_color)
+          case Text.Info(info_range, elem) =>
+            if (highlight_include(elem.name))
+              Some(Text.Info(snapshot.convert(info_range), highlight_color))
+            else None
         }) match { case Text.Info(_, info) #:: _ => Some(info) case _ => None }
   }
 
@@ -203,7 +206,8 @@
           case (links, Text.Info(info_range, XML.Elem(Markup.Path(name), _)))
           if Path.is_ok(name) =>
             val jedit_file = PIDE.thy_load.append(snapshot.node_name.dir, Path.explode(name))
-            Text.Info(snapshot.convert(info_range), Hyperlink(jedit_file, 0, 0)) :: links
+            val link = Text.Info(snapshot.convert(info_range), Hyperlink(jedit_file, 0, 0))
+            Some(link :: links)
 
           case (links, Text.Info(info_range, XML.Elem(Markup(Markup.ENTITY, props), _)))
           if !props.exists(
@@ -216,8 +220,10 @@
                 Isabelle_System.source_file(Path.explode(name)) match {
                   case Some(path) =>
                     val jedit_file = Isabelle_System.platform_path(path)
-                    Text.Info(snapshot.convert(info_range), Hyperlink(jedit_file, line, 0)) :: links
-                  case None => links
+                    val link =
+                      Text.Info(snapshot.convert(info_range), Hyperlink(jedit_file, line, 0))
+                    Some(link :: links)
+                  case None => None
                 }
 
               case Position.Def_Id_Offset(id, offset) =>
@@ -227,13 +233,17 @@
                       node.commands.iterator.takeWhile(_ != command).map(_.source) ++
                         Iterator.single(command.source(Text.Range(0, command.decode(offset))))
                     val (line, column) = ((1, 1) /: sources)(Symbol.advance_line_column)
-                    Text.Info(snapshot.convert(info_range),
-                      Hyperlink(command.node_name.node, line, column)) :: links
-                  case None => links
+                    val link =
+                      Text.Info(snapshot.convert(info_range),
+                        Hyperlink(command.node_name.node, line, column))
+                    Some(link :: links)
+                  case None => None
                 }
 
-              case _ => links
+              case _ => None
             }
+
+          case _ => None
         }) match { case Text.Info(_, info :: _) #:: _ => Some(info) case _ => None }
   }
 
@@ -246,10 +256,13 @@
         {
           case Text.Info(info_range, elem @ Protocol.Dialog(_, serial, _))
           if !command_state.results.defined(serial) =>
-            Text.Info(snapshot.convert(info_range), elem)
-          case Text.Info(info_range, elem @ XML.Elem(Markup(name, _), _))
-          if name == Markup.BROWSER || name == Markup.GRAPHVIEW || name == Markup.SENDBACK =>
-            Text.Info(snapshot.convert(info_range), elem)
+            Some(Text.Info(snapshot.convert(info_range), elem))
+          case Text.Info(info_range, elem) =>
+            if (elem.name == Markup.BROWSER ||
+                elem.name == Markup.GRAPHVIEW ||
+                elem.name == Markup.SENDBACK)
+              Some(Text.Info(snapshot.convert(info_range), elem))
+            else None
         }) match { case Text.Info(_, info) #:: _ => Some(info) case _ => None }
 
 
@@ -257,7 +270,7 @@
   {
     val results =
       snapshot.select_markup[Command.Results](range, None, command_state =>
-        { case _ => command_state.results }).map(_.info)
+        { case _ => Some(command_state.results) }).map(_.info)
     (Command.Results.empty /: results)(_ ++ _)
   }
 
@@ -272,12 +285,14 @@
           if name == Markup.WRITELN || name == Markup.WARNING || name == Markup.ERROR =>
             val entry: Command.Results.Entry =
               (serial -> XML.Elem(Markup(Markup.message(name), props), body))
-            Text.Info(snapshot.convert(info_range), entry) :: msgs
+            Some(Text.Info(snapshot.convert(info_range), entry) :: msgs)
 
           case (msgs, Text.Info(info_range, msg @ XML.Elem(Markup(Markup.BAD, _), body)))
           if !body.isEmpty =>
             val entry: Command.Results.Entry = (Document_ID.make(), msg)
-            Text.Info(snapshot.convert(info_range), entry) :: msgs
+            Some(Text.Info(snapshot.convert(info_range), entry) :: msgs)
+
+          case _ => None
         }).toList.flatMap(_.info)
     if (results.isEmpty) None
     else {
@@ -328,7 +343,7 @@
         range, Text.Info(range, (Timing.zero, Nil)), Some(tooltip_elements), _ =>
         {
           case (Text.Info(r, (t1, info)), Text.Info(_, XML.Elem(Markup.Timing(t2), _))) =>
-            Text.Info(r, (t1 + t2, info))
+            Some(Text.Info(r, (t1 + t2, info)))
           case (prev, Text.Info(r, XML.Elem(Markup.Entity(kind, name), _))) =>
             val kind1 = space_explode('_', kind).mkString(" ")
             val txt1 = kind1 + " " + quote(name)
@@ -337,19 +352,20 @@
               if (kind == Markup.COMMAND && t.elapsed.seconds >= timing_threshold)
                 "\n" + t.message
               else ""
-            add(prev, r, (true, XML.Text(txt1 + txt2)))
+            Some(add(prev, r, (true, XML.Text(txt1 + txt2))))
           case (prev, Text.Info(r, XML.Elem(Markup.Path(name), _)))
           if Path.is_ok(name) =>
             val jedit_file = PIDE.thy_load.append(snapshot.node_name.dir, Path.explode(name))
-            add(prev, r, (true, XML.Text("file " + quote(jedit_file))))
+            Some(add(prev, r, (true, XML.Text("file " + quote(jedit_file)))))
           case (prev, Text.Info(r, XML.Elem(Markup(name, _), body)))
           if name == Markup.SORTING || name == Markup.TYPING =>
-            add(prev, r, (true, pretty_typing("::", body)))
+            Some(add(prev, r, (true, pretty_typing("::", body))))
           case (prev, Text.Info(r, XML.Elem(Markup(Markup.ML_TYPING, _), body))) =>
-            add(prev, r, (false, pretty_typing("ML:", body)))
-          case (prev, Text.Info(r, XML.Elem(Markup(name, _), _)))
-          if tooltips.isDefinedAt(name) =>
-            add(prev, r, (true, XML.Text(tooltips(name))))
+            Some(add(prev, r, (false, pretty_typing("ML:", body))))
+          case (prev, Text.Info(r, XML.Elem(Markup(name, _), _))) =>
+            if (tooltips.isDefinedAt(name))
+              Some(add(prev, r, (true, XML.Text(tooltips(name)))))
+            else None
         }).toList.map(_.info)
 
     results.map(_.info).flatMap(_._2) match {
@@ -383,15 +399,17 @@
         {
           case (pri, Text.Info(_, XML.Elem(Markup(Markup.WRITELN, _),
               List(XML.Elem(Markup(Markup.INFORMATION, _), _))))) =>
-            pri max Rendering.information_pri
+            Some(pri max Rendering.information_pri)
           case (pri, Text.Info(_, XML.Elem(Markup(Markup.WARNING, _), body))) =>
             body match {
               case List(XML.Elem(Markup(Markup.LEGACY, _), _)) =>
-                pri max Rendering.legacy_pri
-              case _ => pri max Rendering.warning_pri
+                Some(pri max Rendering.legacy_pri)
+              case _ =>
+                Some(pri max Rendering.warning_pri)
             }
           case (pri, Text.Info(_, XML.Elem(Markup(Markup.ERROR, _), _))) =>
-            pri max Rendering.error_pri
+            Some(pri max Rendering.error_pri)
+          case _ => None
         })
     val pri = (0 /: results) { case (p1, Text.Info(_, p2)) => p1 max p2 }
     gutter_icons.get(pri)
@@ -404,19 +422,19 @@
     Rendering.warning_pri -> warning_color,
     Rendering.error_pri -> error_color)
 
-  private val squiggly_elements = Set(Markup.WRITELN, Markup.WARNING, Markup.ERROR)
+  private val squiggly_include = Set(Markup.WRITELN, Markup.WARNING, Markup.ERROR)
 
   def squiggly_underline(range: Text.Range): Stream[Text.Info[Color]] =
   {
     val results =
-      snapshot.cumulate_markup[Int](range, 0, Some(squiggly_elements), _ =>
+      snapshot.cumulate_markup[Int](range, 0, Some(squiggly_include), _ =>
         {
-          case (pri, Text.Info(_, msg @ XML.Elem(Markup(name, _), _)))
-          if name == Markup.WRITELN ||
-            name == Markup.WARNING ||
-            name == Markup.ERROR =>
-              if (Protocol.is_information(msg)) pri max Rendering.information_pri
-              else pri max Rendering.message_pri(name)
+          case (pri, Text.Info(_, elem)) =>
+            if (Protocol.is_information(elem))
+              Some(pri max Rendering.information_pri)
+            else if (squiggly_include.contains(elem.name))
+              Some(pri max Rendering.message_pri(elem.name))
+            else None
         })
     for {
       Text.Info(r, pri) <- results
@@ -441,20 +459,22 @@
     val results =
       snapshot.cumulate_markup[Int](range, 0, Some(line_background_elements), _ =>
         {
-          case (pri, Text.Info(_, XML.Elem(Markup(Markup.INFORMATION, _), _))) =>
-            pri max Rendering.information_pri
-          case (pri, Text.Info(_, XML.Elem(Markup(name, _), _)))
-          if name == Markup.WRITELN_MESSAGE ||
-            name == Markup.TRACING_MESSAGE ||
-            name == Markup.WARNING_MESSAGE ||
-            name == Markup.ERROR_MESSAGE => pri max Rendering.message_pri(name)
+          case (pri, Text.Info(_, elem)) =>
+            val name = elem.name
+            if (name == Markup.INFORMATION)
+              Some(pri max Rendering.information_pri)
+            else if (name == Markup.WRITELN_MESSAGE || name == Markup.TRACING_MESSAGE ||
+                elem.name == Markup.WARNING_MESSAGE || name == Markup.ERROR_MESSAGE)
+              Some(pri max Rendering.message_pri(name))
+            else None
         })
     val pri = (0 /: results) { case (p1, Text.Info(_, p2)) => p1 max p2 }
 
     val is_separator = pri > 0 &&
       snapshot.cumulate_markup[Boolean](range, false, Some(Set(Markup.SEPARATOR)), _ =>
         {
-          case (_, Text.Info(_, XML.Elem(Markup(Markup.SEPARATOR, _), _))) => true
+          case (_, Text.Info(_, elem)) =>
+            if (elem.name == Markup.SEPARATOR) Some(true) else None
         }).exists(_.info)
 
     message_colors.get(pri).map((_, is_separator))
@@ -483,20 +503,21 @@
             {
               case (((Some(status), color), Text.Info(_, XML.Elem(markup, _))))
               if (Protocol.command_status_markup(markup.name)) =>
-                (Some(Protocol.command_status(status, markup)), color)
+                Some((Some(Protocol.command_status(status, markup)), color))
               case (_, Text.Info(_, XML.Elem(Markup(Markup.BAD, _), _))) =>
-                (None, Some(bad_color))
+                Some((None, Some(bad_color)))
               case (_, Text.Info(_, XML.Elem(Markup(Markup.INTENSIFY, _), _))) =>
-                (None, Some(intensify_color))
+                Some((None, Some(intensify_color)))
               case (acc, Text.Info(_, Protocol.Dialog(_, serial, result))) =>
                 command_state.results.get(serial) match {
                   case Some(Protocol.Dialog_Result(res)) if res == result =>
-                    (None, Some(active_result_color))
+                    Some((None, Some(active_result_color)))
                   case _ =>
-                    (None, Some(active_color))
+                    Some((None, Some(active_color)))
                 }
-              case (_, Text.Info(_, XML.Elem(markup, _))) if active_include(markup.name) =>
-                (None, Some(active_color))
+              case (_, Text.Info(_, elem)) =>
+                if (active_include(elem.name)) Some((None, Some(active_color)))
+                else None
             })
         color <-
           (result match {
@@ -513,27 +534,29 @@
   def background2(range: Text.Range): Stream[Text.Info[Color]] =
     snapshot.select_markup(range, Some(Set(Markup.TOKEN_RANGE)), _ =>
       {
-        case Text.Info(_, XML.Elem(Markup(Markup.TOKEN_RANGE, _), _)) => light_color
+        case Text.Info(_, elem) =>
+          if (elem.name == Markup.TOKEN_RANGE) Some(light_color) else None
       })
 
 
   def bullet(range: Text.Range): Stream[Text.Info[Color]] =
     snapshot.select_markup(range, Some(Set(Markup.BULLET)), _ =>
       {
-        case Text.Info(_, XML.Elem(Markup(Markup.BULLET, _), _)) => bullet_color
+        case Text.Info(_, elem) =>
+          if (elem.name == Markup.BULLET) Some(bullet_color) else None
       })
 
 
-  private val foreground_elements =
+  private val foreground_include =
     Set(Markup.STRING, Markup.ALTSTRING, Markup.VERBATIM, Markup.ANTIQ)
 
   def foreground(range: Text.Range): Stream[Text.Info[Color]] =
-    snapshot.select_markup(range, Some(foreground_elements), _ =>
+    snapshot.select_markup(range, Some(foreground_include), _ =>
       {
-        case Text.Info(_, XML.Elem(Markup(Markup.STRING, _), _)) => quoted_color
-        case Text.Info(_, XML.Elem(Markup(Markup.ALTSTRING, _), _)) => quoted_color
-        case Text.Info(_, XML.Elem(Markup(Markup.VERBATIM, _), _)) => quoted_color
-        case Text.Info(_, XML.Elem(Markup(Markup.ANTIQ, _), _)) => antiquoted_color
+        case Text.Info(_, elem) =>
+          if (elem.name == Markup.ANTIQ) Some(antiquoted_color)
+          else if (foreground_include.contains(elem.name)) Some(quoted_color)
+          else None
       })
 
 
@@ -570,8 +593,7 @@
     else
       snapshot.cumulate_markup(range, color, Some(text_color_elements), _ =>
         {
-          case (_, Text.Info(_, XML.Elem(Markup(m, _), _)))
-          if text_colors.isDefinedAt(m) => text_colors(m)
+          case (_, Text.Info(_, elem)) => text_colors.get(elem.name)
         })
   }
 
@@ -583,7 +605,7 @@
   def fold_depth(range: Text.Range): Stream[Text.Info[Int]] =
     snapshot.cumulate_markup[Int](range, 0, Some(fold_depth_include), _ =>
       {
-        case (depth, Text.Info(_, XML.Elem(Markup(name, _), _)))
-        if fold_depth_include(name) => depth + 1
+        case (depth, Text.Info(_, elem)) =>
+          if (fold_depth_include(elem.name)) Some(depth + 1) else None
       })
 }
diff -r 34c47bc771f2 -r 3695ce0f9f96 src/Tools/jEdit/src/timing_dockable.scala
--- a/src/Tools/jEdit/src/timing_dockable.scala	Wed Aug 07 15:40:59 2013 +0200
+++ b/src/Tools/jEdit/src/timing_dockable.scala	Wed Aug 07 15:43:58 2013 +0200
@@ -167,7 +167,7 @@
         case None => Document.Node.Name.empty
         case Some(doc_view) => doc_view.model.name
       }
-    val timing = nodes_timing.get(name) getOrElse Protocol.empty_node_timing
+    val timing = nodes_timing.getOrElse(name, Protocol.empty_node_timing)
 
     val theories =
       (for ((node_name, node_timing) <- nodes_timing.toList if !node_timing.commands.isEmpty)