merged
authorwenzelm
Sat, 01 Mar 2014 23:48:55 +0100
changeset 55830 eebefb9a2b01
parent 55819 e21d83c8e1c7 (current diff)
parent 55829 b7bdea5336dd (diff)
child 55831 3a9386b32211
merged
--- a/src/Doc/antiquote_setup.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Doc/antiquote_setup.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -86,7 +86,9 @@
         then txt1 ^ ": " ^ txt2
         else txt1 ^ " : " ^ txt2;
       val txt' = if kind = "" then txt else kind ^ " " ^ txt;
-      val _ = ML_Context.eval_text_in (SOME ctxt) false Position.none (ml (txt1, txt2));  (* ML_Lex.read (!?) *)
+      val _ =  (* ML_Lex.read (!?) *)
+        ML_Context.eval_source_in (SOME ctxt) false
+          {delimited = false, text = ml (txt1, txt2), pos = Position.none};
       val kind' = if kind = "" then "ML" else "ML " ^ kind;
     in
       "\\indexdef{}{" ^ kind' ^ "}{" ^ clean_string (ml_name txt1) ^ "}" ^
--- a/src/HOL/Library/BigO.thy	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/HOL/Library/BigO.thy	Sat Mar 01 23:48:55 2014 +0100
@@ -19,7 +19,7 @@
 \item We have eliminated the @{text O} operator on sets. (Most uses of this seem
   to be inessential.)
 \item We no longer use @{text "+"} as output syntax for @{text "+o"}
-\item Lemmas involving @{text "sumr"} have been replaced by more general lemmas 
+\item Lemmas involving @{text "sumr"} have been replaced by more general lemmas
   involving `@{text "setsum"}.
 \item The library has been expanded, with e.g.~support for expressions of
   the form @{text "f < g + O(h)"}.
@@ -34,14 +34,12 @@
 
 subsection {* Definitions *}
 
-definition
-  bigo :: "('a => 'b::linordered_idom) => ('a => 'b) set"  ("(1O'(_'))") where
-  "O(f::('a => 'b)) =
-      {h. EX c. ALL x. abs (h x) <= c * abs (f x)}"
+definition bigo :: "('a \<Rightarrow> 'b::linordered_idom) \<Rightarrow> ('a \<Rightarrow> 'b) set"  ("(1O'(_'))")
+  where "O(f:: 'a \<Rightarrow> 'b) = {h. \<exists>c. \<forall>x. abs (h x) \<le> c * abs (f x)}"
 
-lemma bigo_pos_const: "(EX (c::'a::linordered_idom). 
-    ALL x. (abs (h x)) <= (c * (abs (f x))))
-      = (EX c. 0 < c & (ALL x. (abs(h x)) <= (c * (abs (f x)))))"
+lemma bigo_pos_const:
+  "(\<exists>c::'a::linordered_idom. \<forall>x. abs (h x) \<le> c * abs (f x)) \<longleftrightarrow>
+    (\<exists>c. 0 < c \<and> (\<forall>x. abs (h x) \<le> c * abs (f x)))"
   apply auto
   apply (case_tac "c = 0")
   apply simp
@@ -49,7 +47,7 @@
   apply simp
   apply (rule_tac x = "abs c" in exI)
   apply auto
-  apply (subgoal_tac "c * abs(f x) <= abs c * abs (f x)")
+  apply (subgoal_tac "c * abs (f x) \<le> abs c * abs (f x)")
   apply (erule_tac x = x in allE)
   apply force
   apply (rule mult_right_mono)
@@ -57,42 +55,40 @@
   apply (rule abs_ge_zero)
   done
 
-lemma bigo_alt_def: "O(f) = 
-    {h. EX c. (0 < c & (ALL x. abs (h x) <= c * abs (f x)))}"
+lemma bigo_alt_def: "O(f) = {h. \<exists>c. 0 < c \<and> (\<forall>x. abs (h x) \<le> c * abs (f x))}"
   by (auto simp add: bigo_def bigo_pos_const)
 
-lemma bigo_elt_subset [intro]: "f : O(g) ==> O(f) <= O(g)"
+lemma bigo_elt_subset [intro]: "f \<in> O(g) \<Longrightarrow> O(f) \<le> O(g)"
   apply (auto simp add: bigo_alt_def)
   apply (rule_tac x = "ca * c" in exI)
   apply (rule conjI)
   apply (rule mult_pos_pos)
-  apply (assumption)+
+  apply assumption+
   apply (rule allI)
   apply (drule_tac x = "xa" in spec)+
-  apply (subgoal_tac "ca * abs(f xa) <= ca * (c * abs(g xa))")
+  apply (subgoal_tac "ca * abs (f xa) \<le> ca * (c * abs (g xa))")
   apply (erule order_trans)
   apply (simp add: mult_ac)
   apply (rule mult_left_mono, assumption)
   apply (rule order_less_imp_le, assumption)
   done
 
-lemma bigo_refl [intro]: "f : O(f)"
+lemma bigo_refl [intro]: "f \<in> O(f)"
   apply(auto simp add: bigo_def)
   apply(rule_tac x = 1 in exI)
   apply simp
   done
 
-lemma bigo_zero: "0 : O(g)"
+lemma bigo_zero: "0 \<in> O(g)"
   apply (auto simp add: bigo_def func_zero)
   apply (rule_tac x = 0 in exI)
   apply auto
   done
 
-lemma bigo_zero2: "O(%x.0) = {%x.0}"
-  by (auto simp add: bigo_def) 
+lemma bigo_zero2: "O(\<lambda>x. 0) = {\<lambda>x. 0}"
+  by (auto simp add: bigo_def)
 
-lemma bigo_plus_self_subset [intro]: 
-  "O(f) + O(f) <= O(f)"
+lemma bigo_plus_self_subset [intro]: "O(f) + O(f) \<subseteq> O(f)"
   apply (auto simp add: bigo_alt_def set_plus_def)
   apply (rule_tac x = "c + ca" in exI)
   apply auto
@@ -102,30 +98,29 @@
   apply (rule add_mono)
   apply force
   apply force
-done
+  done
 
 lemma bigo_plus_idemp [simp]: "O(f) + O(f) = O(f)"
   apply (rule equalityI)
   apply (rule bigo_plus_self_subset)
-  apply (rule set_zero_plus2) 
+  apply (rule set_zero_plus2)
   apply (rule bigo_zero)
   done
 
-lemma bigo_plus_subset [intro]: "O(f + g) <= O(f) + O(g)"
+lemma bigo_plus_subset [intro]: "O(f + g) \<subseteq> O(f) + O(g)"
   apply (rule subsetI)
   apply (auto simp add: bigo_def bigo_pos_const func_plus set_plus_def)
   apply (subst bigo_pos_const [symmetric])+
-  apply (rule_tac x = 
-    "%n. if abs (g n) <= (abs (f n)) then x n else 0" in exI)
+  apply (rule_tac x = "\<lambda>n. if abs (g n) \<le> (abs (f n)) then x n else 0" in exI)
   apply (rule conjI)
   apply (rule_tac x = "c + c" in exI)
   apply (clarsimp)
   apply (auto)
-  apply (subgoal_tac "c * abs (f xa + g xa) <= (c + c) * abs (f xa)")
+  apply (subgoal_tac "c * abs (f xa + g xa) \<le> (c + c) * abs (f xa)")
   apply (erule_tac x = xa in allE)
   apply (erule order_trans)
   apply (simp)
-  apply (subgoal_tac "c * abs (f xa + g xa) <= c * (abs (f xa) + abs (g xa))")
+  apply (subgoal_tac "c * abs (f xa + g xa) \<le> c * (abs (f xa) + abs (g xa))")
   apply (erule order_trans)
   apply (simp add: ring_distribs)
   apply (rule mult_left_mono)
@@ -133,16 +128,15 @@
   apply (simp add: order_less_le)
   apply (rule mult_nonneg_nonneg)
   apply auto
-  apply (rule_tac x = "%n. if (abs (f n)) <  abs (g n) then x n else 0" 
-     in exI)
+  apply (rule_tac x = "\<lambda>n. if (abs (f n)) < abs (g n) then x n else 0" in exI)
   apply (rule conjI)
   apply (rule_tac x = "c + c" in exI)
   apply auto
-  apply (subgoal_tac "c * abs (f xa + g xa) <= (c + c) * abs (g xa)")
+  apply (subgoal_tac "c * abs (f xa + g xa) \<le> (c + c) * abs (g xa)")
   apply (erule_tac x = xa in allE)
   apply (erule order_trans)
-  apply (simp)
-  apply (subgoal_tac "c * abs (f xa + g xa) <= c * (abs (f xa) + abs (g xa))")
+  apply simp
+  apply (subgoal_tac "c * abs (f xa + g xa) \<le> c * (abs (f xa) + abs (g xa))")
   apply (erule order_trans)
   apply (simp add: ring_distribs)
   apply (rule mult_left_mono)
@@ -153,41 +147,39 @@
   apply simp
   done
 
-lemma bigo_plus_subset2 [intro]: "A <= O(f) ==> B <= O(f) ==> A + B <= O(f)"
-  apply (subgoal_tac "A + B <= O(f) + O(f)")
+lemma bigo_plus_subset2 [intro]: "A \<subseteq> O(f) \<Longrightarrow> B \<subseteq> O(f) \<Longrightarrow> A + B \<subseteq> O(f)"
+  apply (subgoal_tac "A + B \<subseteq> O(f) + O(f)")
   apply (erule order_trans)
   apply simp
   apply (auto del: subsetI simp del: bigo_plus_idemp)
   done
 
-lemma bigo_plus_eq: "ALL x. 0 <= f x ==> ALL x. 0 <= g x ==> 
-    O(f + g) = O(f) + O(g)"
+lemma bigo_plus_eq: "\<forall>x. 0 \<le> f x \<Longrightarrow> \<forall>x. 0 \<le> g x \<Longrightarrow> O(f + g) = O(f) + O(g)"
   apply (rule equalityI)
   apply (rule bigo_plus_subset)
   apply (simp add: bigo_alt_def set_plus_def func_plus)
   apply clarify
   apply (rule_tac x = "max c ca" in exI)
   apply (rule conjI)
-  apply (subgoal_tac "c <= max c ca")
+  apply (subgoal_tac "c \<le> max c ca")
   apply (erule order_less_le_trans)
   apply assumption
   apply (rule max.cobounded1)
   apply clarify
   apply (drule_tac x = "xa" in spec)+
-  apply (subgoal_tac "0 <= f xa + g xa")
+  apply (subgoal_tac "0 \<le> f xa + g xa")
   apply (simp add: ring_distribs)
-  apply (subgoal_tac "abs(a xa + b xa) <= abs(a xa) + abs(b xa)")
-  apply (subgoal_tac "abs(a xa) + abs(b xa) <= 
-      max c ca * f xa + max c ca * g xa")
-  apply (force)
+  apply (subgoal_tac "abs (a xa + b xa) \<le> abs (a xa) + abs (b xa)")
+  apply (subgoal_tac "abs (a xa) + abs (b xa) \<le> max c ca * f xa + max c ca * g xa")
+  apply force
   apply (rule add_mono)
-  apply (subgoal_tac "c * f xa <= max c ca * f xa")
-  apply (force)
+  apply (subgoal_tac "c * f xa \<le> max c ca * f xa")
+  apply force
   apply (rule mult_right_mono)
   apply (rule max.cobounded1)
   apply assumption
-  apply (subgoal_tac "ca * g xa <= max c ca * g xa")
-  apply (force)
+  apply (subgoal_tac "ca * g xa \<le> max c ca * g xa")
+  apply force
   apply (rule mult_right_mono)
   apply (rule max.cobounded2)
   apply assumption
@@ -196,8 +188,7 @@
   apply assumption+
   done
 
-lemma bigo_bounded_alt: "ALL x. 0 <= f x ==> ALL x. f x <= c * g x ==> 
-    f : O(g)" 
+lemma bigo_bounded_alt: "\<forall>x. 0 \<le> f x \<Longrightarrow> \<forall>x. f x \<le> c * g x \<Longrightarrow> f \<in> O(g)"
   apply (auto simp add: bigo_def)
   apply (rule_tac x = "abs c" in exI)
   apply auto
@@ -205,14 +196,12 @@
   apply (simp add: abs_mult [symmetric])
   done
 
-lemma bigo_bounded: "ALL x. 0 <= f x ==> ALL x. f x <= g x ==> 
-    f : O(g)" 
+lemma bigo_bounded: "\<forall>x. 0 \<le> f x \<Longrightarrow> \<forall>x. f x \<le> g x \<Longrightarrow> f \<in> O(g)"
   apply (erule bigo_bounded_alt [of f 1 g])
   apply simp
   done
 
-lemma bigo_bounded2: "ALL x. lb x <= f x ==> ALL x. f x <= lb x + g x ==>
-    f : lb +o O(g)"
+lemma bigo_bounded2: "\<forall>x. lb x \<le> f x \<Longrightarrow> \<forall>x. f x \<le> lb x + g x \<Longrightarrow> f \<in> lb +o O(g)"
   apply (rule set_minus_imp_plus)
   apply (rule bigo_bounded)
   apply (auto simp add: fun_Compl_def func_plus)
@@ -222,21 +211,21 @@
   apply force
   done
 
-lemma bigo_abs: "(%x. abs(f x)) =o O(f)" 
+lemma bigo_abs: "(\<lambda>x. abs (f x)) =o O(f)"
   apply (unfold bigo_def)
   apply auto
   apply (rule_tac x = 1 in exI)
   apply auto
   done
 
-lemma bigo_abs2: "f =o O(%x. abs(f x))"
+lemma bigo_abs2: "f =o O(\<lambda>x. abs (f x))"
   apply (unfold bigo_def)
   apply auto
   apply (rule_tac x = 1 in exI)
   apply auto
   done
 
-lemma bigo_abs3: "O(f) = O(%x. abs(f x))"
+lemma bigo_abs3: "O(f) = O(\<lambda>x. abs (f x))"
   apply (rule equalityI)
   apply (rule bigo_elt_subset)
   apply (rule bigo_abs2)
@@ -244,65 +233,63 @@
   apply (rule bigo_abs)
   done
 
-lemma bigo_abs4: "f =o g +o O(h) ==> 
-    (%x. abs (f x)) =o (%x. abs (g x)) +o O(h)"
+lemma bigo_abs4: "f =o g +o O(h) \<Longrightarrow> (\<lambda>x. abs (f x)) =o (\<lambda>x. abs (g x)) +o O(h)"
   apply (drule set_plus_imp_minus)
   apply (rule set_minus_imp_plus)
   apply (subst fun_diff_def)
 proof -
-  assume a: "f - g : O(h)"
-  have "(%x. abs (f x) - abs (g x)) =o O(%x. abs(abs (f x) - abs (g x)))"
+  assume a: "f - g \<in> O(h)"
+  have "(\<lambda>x. abs (f x) - abs (g x)) =o O(\<lambda>x. abs (abs (f x) - abs (g x)))"
     by (rule bigo_abs2)
-  also have "... <= O(%x. abs (f x - g x))"
+  also have "\<dots> \<subseteq> O(\<lambda>x. abs (f x - g x))"
     apply (rule bigo_elt_subset)
     apply (rule bigo_bounded)
     apply force
     apply (rule allI)
     apply (rule abs_triangle_ineq3)
     done
-  also have "... <= O(f - g)"
+  also have "\<dots> \<subseteq> O(f - g)"
     apply (rule bigo_elt_subset)
     apply (subst fun_diff_def)
     apply (rule bigo_abs)
     done
-  also from a have "... <= O(h)"
+  also from a have "\<dots> \<subseteq> O(h)"
     by (rule bigo_elt_subset)
-  finally show "(%x. abs (f x) - abs (g x)) : O(h)".
+  finally show "(\<lambda>x. abs (f x) - abs (g x)) \<in> O(h)".
 qed
 
-lemma bigo_abs5: "f =o O(g) ==> (%x. abs(f x)) =o O(g)" 
+lemma bigo_abs5: "f =o O(g) \<Longrightarrow> (\<lambda>x. abs (f x)) =o O(g)"
   by (unfold bigo_def, auto)
 
-lemma bigo_elt_subset2 [intro]: "f : g +o O(h) ==> O(f) <= O(g) + O(h)"
+lemma bigo_elt_subset2 [intro]: "f \<in> g +o O(h) \<Longrightarrow> O(f) \<subseteq> O(g) + O(h)"
 proof -
-  assume "f : g +o O(h)"
-  also have "... <= O(g) + O(h)"
+  assume "f \<in> g +o O(h)"
+  also have "\<dots> \<subseteq> O(g) + O(h)"
     by (auto del: subsetI)
-  also have "... = O(%x. abs(g x)) + O(%x. abs(h x))"
+  also have "\<dots> = O(\<lambda>x. abs (g x)) + O(\<lambda>x. abs (h x))"
     apply (subst bigo_abs3 [symmetric])+
     apply (rule refl)
     done
-  also have "... = O((%x. abs(g x)) + (%x. abs(h x)))"
-    by (rule bigo_plus_eq [symmetric], auto)
-  finally have "f : ...".
-  then have "O(f) <= ..."
+  also have "\<dots> = O((\<lambda>x. abs (g x)) + (\<lambda>x. abs (h x)))"
+    by (rule bigo_plus_eq [symmetric]) auto
+  finally have "f \<in> \<dots>" .
+  then have "O(f) \<subseteq> \<dots>"
     by (elim bigo_elt_subset)
-  also have "... = O(%x. abs(g x)) + O(%x. abs(h x))"
+  also have "\<dots> = O(\<lambda>x. abs (g x)) + O(\<lambda>x. abs (h x))"
     by (rule bigo_plus_eq, auto)
   finally show ?thesis
     by (simp add: bigo_abs3 [symmetric])
 qed
 
-lemma bigo_mult [intro]: "O(f)*O(g) <= O(f * g)"
+lemma bigo_mult [intro]: "O(f)*O(g) \<subseteq> O(f * g)"
   apply (rule subsetI)
   apply (subst bigo_def)
   apply (auto simp add: bigo_alt_def set_times_def func_times)
   apply (rule_tac x = "c * ca" in exI)
-  apply(rule allI)
-  apply(erule_tac x = x in allE)+
-  apply(subgoal_tac "c * ca * abs(f x * g x) = 
-      (c * abs(f x)) * (ca * abs(g x))")
-  apply(erule ssubst)
+  apply (rule allI)
+  apply (erule_tac x = x in allE)+
+  apply (subgoal_tac "c * ca * abs (f x * g x) = (c * abs (f x)) * (ca * abs (g x))")
+  apply (erule ssubst)
   apply (subst abs_mult)
   apply (rule mult_mono)
   apply assumption+
@@ -311,24 +298,24 @@
   apply (simp add: mult_ac abs_mult)
   done
 
-lemma bigo_mult2 [intro]: "f *o O(g) <= O(f * g)"
+lemma bigo_mult2 [intro]: "f *o O(g) \<subseteq> O(f * g)"
   apply (auto simp add: bigo_def elt_set_times_def func_times abs_mult)
   apply (rule_tac x = c in exI)
   apply auto
   apply (drule_tac x = x in spec)
-  apply (subgoal_tac "abs(f x) * abs(b x) <= abs(f x) * (c * abs(g x))")
+  apply (subgoal_tac "abs (f x) * abs (b x) \<le> abs (f x) * (c * abs (g x))")
   apply (force simp add: mult_ac)
   apply (rule mult_left_mono, assumption)
   apply (rule abs_ge_zero)
   done
 
-lemma bigo_mult3: "f : O(h) ==> g : O(j) ==> f * g : O(h * j)"
+lemma bigo_mult3: "f \<in> O(h) \<Longrightarrow> g \<in> O(j) \<Longrightarrow> f * g \<in> O(h * j)"
   apply (rule subsetD)
   apply (rule bigo_mult)
   apply (erule set_times_intro, assumption)
   done
 
-lemma bigo_mult4 [intro]:"f : k +o O(h) ==> g * f : (g * k) +o O(g * h)"
+lemma bigo_mult4 [intro]: "f \<in> k +o O(h) \<Longrightarrow> g * f \<in> (g * k) +o O(g * h)"
   apply (drule set_plus_imp_minus)
   apply (rule set_minus_imp_plus)
   apply (drule bigo_mult3 [where g = g and j = g])
@@ -336,110 +323,117 @@
   done
 
 lemma bigo_mult5:
-  assumes "ALL x. f x ~= 0"
-  shows "O(f * g) <= (f::'a => ('b::linordered_field)) *o O(g)"
+  fixes f :: "'a \<Rightarrow> 'b::linordered_field"
+  assumes "\<forall>x. f x \<noteq> 0"
+  shows "O(f * g) \<subseteq> f *o O(g)"
 proof
   fix h
-  assume "h : O(f * g)"
-  then have "(%x. 1 / (f x)) * h : (%x. 1 / f x) *o O(f * g)"
+  assume "h \<in> O(f * g)"
+  then have "(\<lambda>x. 1 / (f x)) * h \<in> (\<lambda>x. 1 / f x) *o O(f * g)"
     by auto
-  also have "... <= O((%x. 1 / f x) * (f * g))"
+  also have "\<dots> \<subseteq> O((\<lambda>x. 1 / f x) * (f * g))"
     by (rule bigo_mult2)
-  also have "(%x. 1 / f x) * (f * g) = g"
-    apply (simp add: func_times) 
+  also have "(\<lambda>x. 1 / f x) * (f * g) = g"
+    apply (simp add: func_times)
     apply (rule ext)
     apply (simp add: assms nonzero_divide_eq_eq mult_ac)
     done
-  finally have "(%x. (1::'b) / f x) * h : O(g)" .
-  then have "f * ((%x. (1::'b) / f x) * h) : f *o O(g)"
+  finally have "(\<lambda>x. (1::'b) / f x) * h \<in> O(g)" .
+  then have "f * ((\<lambda>x. (1::'b) / f x) * h) \<in> f *o O(g)"
     by auto
-  also have "f * ((%x. (1::'b) / f x) * h) = h"
-    apply (simp add: func_times) 
+  also have "f * ((\<lambda>x. (1::'b) / f x) * h) = h"
+    apply (simp add: func_times)
     apply (rule ext)
     apply (simp add: assms nonzero_divide_eq_eq mult_ac)
     done
-  finally show "h : f *o O(g)" .
+  finally show "h \<in> f *o O(g)" .
 qed
 
-lemma bigo_mult6: "ALL x. f x ~= 0 ==>
-    O(f * g) = (f::'a => ('b::linordered_field)) *o O(g)"
+lemma bigo_mult6:
+  fixes f :: "'a \<Rightarrow> 'b::linordered_field"
+  shows "\<forall>x. f x \<noteq> 0 \<Longrightarrow> O(f * g) = f *o O(g)"
   apply (rule equalityI)
   apply (erule bigo_mult5)
   apply (rule bigo_mult2)
   done
 
-lemma bigo_mult7: "ALL x. f x ~= 0 ==>
-    O(f * g) <= O(f::'a => ('b::linordered_field)) * O(g)"
+lemma bigo_mult7:
+  fixes f :: "'a \<Rightarrow> 'b::linordered_field"
+  shows "\<forall>x. f x \<noteq> 0 \<Longrightarrow> O(f * g) \<subseteq> O(f) * O(g)"
   apply (subst bigo_mult6)
   apply assumption
   apply (rule set_times_mono3)
   apply (rule bigo_refl)
   done
 
-lemma bigo_mult8: "ALL x. f x ~= 0 ==>
-    O(f * g) = O(f::'a => ('b::linordered_field)) * O(g)"
+lemma bigo_mult8:
+  fixes f :: "'a \<Rightarrow> 'b::linordered_field"
+  shows "\<forall>x. f x \<noteq> 0 \<Longrightarrow> O(f * g) = O(f) * O(g)"
   apply (rule equalityI)
   apply (erule bigo_mult7)
   apply (rule bigo_mult)
   done
 
-lemma bigo_minus [intro]: "f : O(g) ==> - f : O(g)"
+lemma bigo_minus [intro]: "f \<in> O(g) \<Longrightarrow> - f \<in> O(g)"
   by (auto simp add: bigo_def fun_Compl_def)
 
-lemma bigo_minus2: "f : g +o O(h) ==> -f : -g +o O(h)"
+lemma bigo_minus2: "f \<in> g +o O(h) \<Longrightarrow> - f \<in> -g +o O(h)"
   apply (rule set_minus_imp_plus)
   apply (drule set_plus_imp_minus)
   apply (drule bigo_minus)
   apply simp
   done
 
-lemma bigo_minus3: "O(-f) = O(f)"
+lemma bigo_minus3: "O(- f) = O(f)"
   by (auto simp add: bigo_def fun_Compl_def)
 
-lemma bigo_plus_absorb_lemma1: "f : O(g) ==> f +o O(g) <= O(g)"
+lemma bigo_plus_absorb_lemma1: "f \<in> O(g) \<Longrightarrow> f +o O(g) \<subseteq> O(g)"
 proof -
-  assume a: "f : O(g)"
-  show "f +o O(g) <= O(g)"
+  assume a: "f \<in> O(g)"
+  show "f +o O(g) \<subseteq> O(g)"
   proof -
-    have "f : O(f)" by auto
-    then have "f +o O(g) <= O(f) + O(g)"
+    have "f \<in> O(f)" by auto
+    then have "f +o O(g) \<subseteq> O(f) + O(g)"
       by (auto del: subsetI)
-    also have "... <= O(g) + O(g)"
+    also have "\<dots> \<subseteq> O(g) + O(g)"
     proof -
-      from a have "O(f) <= O(g)" by (auto del: subsetI)
+      from a have "O(f) \<subseteq> O(g)" by (auto del: subsetI)
       thus ?thesis by (auto del: subsetI)
     qed
-    also have "... <= O(g)" by simp
+    also have "\<dots> \<subseteq> O(g)" by simp
     finally show ?thesis .
   qed
 qed
 
-lemma bigo_plus_absorb_lemma2: "f : O(g) ==> O(g) <= f +o O(g)"
+lemma bigo_plus_absorb_lemma2: "f \<in> O(g) \<Longrightarrow> O(g) \<subseteq> f +o O(g)"
 proof -
-  assume a: "f : O(g)"
-  show "O(g) <= f +o O(g)"
+  assume a: "f \<in> O(g)"
+  show "O(g) \<subseteq> f +o O(g)"
   proof -
-    from a have "-f : O(g)" by auto
-    then have "-f +o O(g) <= O(g)" by (elim bigo_plus_absorb_lemma1)
-    then have "f +o (-f +o O(g)) <= f +o O(g)" by auto
-    also have "f +o (-f +o O(g)) = O(g)"
+    from a have "- f \<in> O(g)"
+      by auto
+    then have "- f +o O(g) \<subseteq> O(g)"
+      by (elim bigo_plus_absorb_lemma1)
+    then have "f +o (- f +o O(g)) \<subseteq> f +o O(g)"
+      by auto
+    also have "f +o (- f +o O(g)) = O(g)"
       by (simp add: set_plus_rearranges)
     finally show ?thesis .
   qed
 qed
 
-lemma bigo_plus_absorb [simp]: "f : O(g) ==> f +o O(g) = O(g)"
+lemma bigo_plus_absorb [simp]: "f \<in> O(g) \<Longrightarrow> f +o O(g) = O(g)"
   apply (rule equalityI)
   apply (erule bigo_plus_absorb_lemma1)
   apply (erule bigo_plus_absorb_lemma2)
   done
 
-lemma bigo_plus_absorb2 [intro]: "f : O(g) ==> A <= O(g) ==> f +o A <= O(g)"
-  apply (subgoal_tac "f +o A <= f +o O(g)")
+lemma bigo_plus_absorb2 [intro]: "f \<in> O(g) \<Longrightarrow> A \<subseteq> O(g) \<Longrightarrow> f +o A \<subseteq> O(g)"
+  apply (subgoal_tac "f +o A \<subseteq> f +o O(g)")
   apply force+
   done
 
-lemma bigo_add_commute_imp: "f : g +o O(h) ==> g : f +o O(h)"
+lemma bigo_add_commute_imp: "f \<in> g +o O(h) \<Longrightarrow> g \<in> f +o O(h)"
   apply (subst set_minus_plus [symmetric])
   apply (subgoal_tac "g - f = - (f - g)")
   apply (erule ssubst)
@@ -449,63 +443,88 @@
   apply (simp add: add_ac)
   done
 
-lemma bigo_add_commute: "(f : g +o O(h)) = (g : f +o O(h))"
+lemma bigo_add_commute: "f \<in> g +o O(h) \<longleftrightarrow> g \<in> f +o O(h)"
   apply (rule iffI)
   apply (erule bigo_add_commute_imp)+
   done
 
-lemma bigo_const1: "(%x. c) : O(%x. 1)"
+lemma bigo_const1: "(\<lambda>x. c) \<in> O(\<lambda>x. 1)"
   by (auto simp add: bigo_def mult_ac)
 
-lemma bigo_const2 [intro]: "O(%x. c) <= O(%x. 1)"
+lemma bigo_const2 [intro]: "O(\<lambda>x. c) \<subseteq> O(\<lambda>x. 1)"
   apply (rule bigo_elt_subset)
   apply (rule bigo_const1)
   done
 
-lemma bigo_const3: "(c::'a::linordered_field) ~= 0 ==> (%x. 1) : O(%x. c)"
+lemma bigo_const3:
+  fixes c :: "'a::linordered_field"
+  shows "c \<noteq> 0 \<Longrightarrow> (\<lambda>x. 1) \<in> O(\<lambda>x. c)"
   apply (simp add: bigo_def)
-  apply (rule_tac x = "abs(inverse c)" in exI)
+  apply (rule_tac x = "abs (inverse c)" in exI)
   apply (simp add: abs_mult [symmetric])
   done
 
-lemma bigo_const4: "(c::'a::linordered_field) ~= 0 ==> O(%x. 1) <= O(%x. c)"
-  by (rule bigo_elt_subset, rule bigo_const3, assumption)
+lemma bigo_const4:
+  fixes c :: "'a::linordered_field"
+  shows "c \<noteq> 0 \<Longrightarrow> O(\<lambda>x. 1) \<subseteq> O(\<lambda>x. c)"
+  apply (rule bigo_elt_subset)
+  apply (rule bigo_const3)
+  apply assumption
+  done
 
-lemma bigo_const [simp]: "(c::'a::linordered_field) ~= 0 ==> 
-    O(%x. c) = O(%x. 1)"
-  by (rule equalityI, rule bigo_const2, rule bigo_const4, assumption)
+lemma bigo_const [simp]:
+  fixes c :: "'a::linordered_field"
+  shows "c \<noteq> 0 \<Longrightarrow> O(\<lambda>x. c) = O(\<lambda>x. 1)"
+  apply (rule equalityI)
+  apply (rule bigo_const2)
+  apply (rule bigo_const4)
+  apply assumption
+  done
 
-lemma bigo_const_mult1: "(%x. c * f x) : O(f)"
+lemma bigo_const_mult1: "(\<lambda>x. c * f x) \<in> O(f)"
   apply (simp add: bigo_def)
-  apply (rule_tac x = "abs(c)" in exI)
+  apply (rule_tac x = "abs c" in exI)
   apply (auto simp add: abs_mult [symmetric])
   done
 
-lemma bigo_const_mult2: "O(%x. c * f x) <= O(f)"
-  by (rule bigo_elt_subset, rule bigo_const_mult1)
+lemma bigo_const_mult2: "O(\<lambda>x. c * f x) \<subseteq> O(f)"
+  apply (rule bigo_elt_subset)
+  apply (rule bigo_const_mult1)
+  done
 
-lemma bigo_const_mult3: "(c::'a::linordered_field) ~= 0 ==> f : O(%x. c * f x)"
+lemma bigo_const_mult3:
+  fixes c :: "'a::linordered_field"
+  shows "c \<noteq> 0 \<Longrightarrow> f \<in> O(\<lambda>x. c * f x)"
   apply (simp add: bigo_def)
-  apply (rule_tac x = "abs(inverse c)" in exI)
+  apply (rule_tac x = "abs (inverse c)" in exI)
   apply (simp add: abs_mult [symmetric] mult_assoc [symmetric])
   done
 
-lemma bigo_const_mult4: "(c::'a::linordered_field) ~= 0 ==> 
-    O(f) <= O(%x. c * f x)"
-  by (rule bigo_elt_subset, rule bigo_const_mult3, assumption)
+lemma bigo_const_mult4:
+  fixes c :: "'a::linordered_field"
+  shows "c \<noteq> 0 \<Longrightarrow> O(f) \<subseteq> O(\<lambda>x. c * f x)"
+  apply (rule bigo_elt_subset)
+  apply (rule bigo_const_mult3)
+  apply assumption
+  done
 
-lemma bigo_const_mult [simp]: "(c::'a::linordered_field) ~= 0 ==> 
-    O(%x. c * f x) = O(f)"
-  by (rule equalityI, rule bigo_const_mult2, erule bigo_const_mult4)
+lemma bigo_const_mult [simp]:
+  fixes c :: "'a::linordered_field"
+  shows "c \<noteq> 0 \<Longrightarrow> O(\<lambda>x. c * f x) = O(f)"
+  apply (rule equalityI)
+  apply (rule bigo_const_mult2)
+  apply (erule bigo_const_mult4)
+  done
 
-lemma bigo_const_mult5 [simp]: "(c::'a::linordered_field) ~= 0 ==> 
-    (%x. c) *o O(f) = O(f)"
+lemma bigo_const_mult5 [simp]:
+  fixes c :: "'a::linordered_field"
+  shows "c \<noteq> 0 \<Longrightarrow> (\<lambda>x. c) *o O(f) = O(f)"
   apply (auto del: subsetI)
   apply (rule order_trans)
   apply (rule bigo_mult2)
   apply (simp add: func_times)
   apply (auto intro!: simp add: bigo_def elt_set_times_def func_times)
-  apply (rule_tac x = "%y. inverse c * x y" in exI)
+  apply (rule_tac x = "\<lambda>y. inverse c * x y" in exI)
   apply (simp add: mult_assoc [symmetric] abs_mult)
   apply (rule_tac x = "abs (inverse c) * ca" in exI)
   apply (rule allI)
@@ -515,11 +534,11 @@
   apply force
   done
 
-lemma bigo_const_mult6 [intro]: "(%x. c) *o O(f) <= O(f)"
+lemma bigo_const_mult6 [intro]: "(\<lambda>x. c) *o O(f) \<subseteq> O(f)"
   apply (auto intro!: simp add: bigo_def elt_set_times_def func_times)
-  apply (rule_tac x = "ca * (abs c)" in exI)
+  apply (rule_tac x = "ca * abs c" in exI)
   apply (rule allI)
-  apply (subgoal_tac "ca * abs(c) * abs(f x) = abs(c) * (ca * abs(f x))")
+  apply (subgoal_tac "ca * abs c * abs (f x) = abs c * (ca * abs (f x))")
   apply (erule ssubst)
   apply (subst abs_mult)
   apply (rule mult_left_mono)
@@ -528,33 +547,34 @@
   apply(simp add: mult_ac)
   done
 
-lemma bigo_const_mult7 [intro]: "f =o O(g) ==> (%x. c * f x) =o O(g)"
+lemma bigo_const_mult7 [intro]: "f =o O(g) \<Longrightarrow> (\<lambda>x. c * f x) =o O(g)"
 proof -
   assume "f =o O(g)"
-  then have "(%x. c) * f =o (%x. c) *o O(g)"
+  then have "(\<lambda>x. c) * f =o (\<lambda>x. c) *o O(g)"
     by auto
-  also have "(%x. c) * f = (%x. c * f x)"
+  also have "(\<lambda>x. c) * f = (\<lambda>x. c * f x)"
     by (simp add: func_times)
-  also have "(%x. c) *o O(g) <= O(g)"
+  also have "(\<lambda>x. c) *o O(g) \<subseteq> O(g)"
     by (auto del: subsetI)
   finally show ?thesis .
 qed
 
-lemma bigo_compose1: "f =o O(g) ==> (%x. f(k x)) =o O(%x. g(k x))"
-by (unfold bigo_def, auto)
+lemma bigo_compose1: "f =o O(g) \<Longrightarrow> (\<lambda>x. f (k x)) =o O(\<lambda>x. g (k x))"
+  unfolding bigo_def by auto
 
-lemma bigo_compose2: "f =o g +o O(h) ==> (%x. f(k x)) =o (%x. g(k x)) +o 
-    O(%x. h(k x))"
+lemma bigo_compose2: "f =o g +o O(h) \<Longrightarrow>
+    (\<lambda>x. f (k x)) =o (\<lambda>x. g (k x)) +o O(\<lambda>x. h(k x))"
   apply (simp only: set_minus_plus [symmetric] fun_Compl_def func_plus)
-  apply (drule bigo_compose1) apply (simp add: fun_diff_def)
+  apply (drule bigo_compose1)
+  apply (simp add: fun_diff_def)
   done
 
 
 subsection {* Setsum *}
 
-lemma bigo_setsum_main: "ALL x. ALL y : A x. 0 <= h x y ==> 
-    EX c. ALL x. ALL y : A x. abs(f x y) <= c * (h x y) ==>
-      (%x. SUM y : A x. f x y) =o O(%x. SUM y : A x. h x y)"  
+lemma bigo_setsum_main: "\<forall>x. \<forall>y \<in> A x. 0 \<le> h x y \<Longrightarrow>
+    \<exists>c. \<forall>x. \<forall>y \<in> A x. abs (f x y) \<le> c * (h x y) \<Longrightarrow>
+      (\<lambda>x. \<Sum>y \<in> A x. f x y) =o O(\<lambda>x. \<Sum>y \<in> A x. h x y)"
   apply (auto simp add: bigo_def)
   apply (rule_tac x = "abs c" in exI)
   apply (subst abs_of_nonneg) back back
@@ -571,14 +591,14 @@
   apply assumption+
   apply (drule bspec)
   apply assumption+
-  apply (rule mult_right_mono) 
+  apply (rule mult_right_mono)
   apply (rule abs_ge_self)
   apply force
   done
 
-lemma bigo_setsum1: "ALL x y. 0 <= h x y ==> 
-    EX c. ALL x y. abs(f x y) <= c * (h x y) ==>
-      (%x. SUM y : A x. f x y) =o O(%x. SUM y : A x. h x y)"
+lemma bigo_setsum1: "\<forall>x y. 0 \<le> h x y \<Longrightarrow>
+    \<exists>c. \<forall>x y. abs (f x y) \<le> c * h x y \<Longrightarrow>
+      (\<lambda>x. \<Sum>y \<in> A x. f x y) =o O(\<lambda>x. \<Sum>y \<in> A x. h x y)"
   apply (rule bigo_setsum_main)
   apply force
   apply clarsimp
@@ -586,14 +606,13 @@
   apply force
   done
 
-lemma bigo_setsum2: "ALL y. 0 <= h y ==> 
-    EX c. ALL y. abs(f y) <= c * (h y) ==>
-      (%x. SUM y : A x. f y) =o O(%x. SUM y : A x. h y)"
-  by (rule bigo_setsum1, auto)  
+lemma bigo_setsum2: "\<forall>y. 0 \<le> h y \<Longrightarrow>
+    \<exists>c. \<forall>y. abs (f y) \<le> c * (h y) \<Longrightarrow>
+      (\<lambda>x. \<Sum>y \<in> A x. f y) =o O(\<lambda>x. \<Sum>y \<in> A x. h y)"
+  by (rule bigo_setsum1) auto
 
-lemma bigo_setsum3: "f =o O(h) ==>
-    (%x. SUM y : A x. (l x y) * f(k x y)) =o
-      O(%x. SUM y : A x. abs(l x y * h(k x y)))"
+lemma bigo_setsum3: "f =o O(h) \<Longrightarrow>
+    (\<lambda>x. \<Sum>y \<in> A x. l x y * f (k x y)) =o O(\<lambda>x. \<Sum>y \<in> A x. abs (l x y * h (k x y)))"
   apply (rule bigo_setsum1)
   apply (rule allI)+
   apply (rule abs_ge_zero)
@@ -608,10 +627,10 @@
   apply (rule abs_ge_zero)
   done
 
-lemma bigo_setsum4: "f =o g +o O(h) ==>
-    (%x. SUM y : A x. l x y * f(k x y)) =o
-      (%x. SUM y : A x. l x y * g(k x y)) +o
-        O(%x. SUM y : A x. abs(l x y * h(k x y)))"
+lemma bigo_setsum4: "f =o g +o O(h) \<Longrightarrow>
+    (\<lambda>x. \<Sum>y \<in> A x. l x y * f (k x y)) =o
+      (\<lambda>x. \<Sum>y \<in> A x. l x y * g (k x y)) +o
+        O(\<lambda>x. \<Sum>y \<in> A x. abs (l x y * h (k x y)))"
   apply (rule set_minus_imp_plus)
   apply (subst fun_diff_def)
   apply (subst setsum_subtractf [symmetric])
@@ -621,12 +640,12 @@
   apply (erule set_plus_imp_minus)
   done
 
-lemma bigo_setsum5: "f =o O(h) ==> ALL x y. 0 <= l x y ==> 
-    ALL x. 0 <= h x ==>
-      (%x. SUM y : A x. (l x y) * f(k x y)) =o
-        O(%x. SUM y : A x. (l x y) * h(k x y))" 
-  apply (subgoal_tac "(%x. SUM y : A x. (l x y) * h(k x y)) = 
-      (%x. SUM y : A x. abs((l x y) * h(k x y)))")
+lemma bigo_setsum5: "f =o O(h) \<Longrightarrow> \<forall>x y. 0 \<le> l x y \<Longrightarrow>
+    \<forall>x. 0 \<le> h x \<Longrightarrow>
+      (\<lambda>x. \<Sum>y \<in> A x. l x y * f (k x y)) =o
+        O(\<lambda>x. \<Sum>y \<in> A x. l x y * h (k x y))"
+  apply (subgoal_tac "(\<lambda>x. \<Sum>y \<in> A x. l x y * h (k x y)) =
+      (\<lambda>x. \<Sum>y \<in> A x. abs (l x y * h (k x y)))")
   apply (erule ssubst)
   apply (erule bigo_setsum3)
   apply (rule ext)
@@ -636,11 +655,11 @@
   apply auto
   done
 
-lemma bigo_setsum6: "f =o g +o O(h) ==> ALL x y. 0 <= l x y ==>
-    ALL x. 0 <= h x ==>
-      (%x. SUM y : A x. (l x y) * f(k x y)) =o
-        (%x. SUM y : A x. (l x y) * g(k x y)) +o
-          O(%x. SUM y : A x. (l x y) * h(k x y))" 
+lemma bigo_setsum6: "f =o g +o O(h) \<Longrightarrow> \<forall>x y. 0 \<le> l x y \<Longrightarrow>
+    \<forall>x. 0 \<le> h x \<Longrightarrow>
+      (\<lambda>x. \<Sum>y \<in> A x. l x y * f (k x y)) =o
+        (\<lambda>x. \<Sum>y \<in> A x. l x y * g (k x y)) +o
+          O(\<lambda>x. \<Sum>y \<in> A x. l x y * h (k x y))"
   apply (rule set_minus_imp_plus)
   apply (subst fun_diff_def)
   apply (subst setsum_subtractf [symmetric])
@@ -654,33 +673,32 @@
 
 subsection {* Misc useful stuff *}
 
-lemma bigo_useful_intro: "A <= O(f) ==> B <= O(f) ==>
-  A + B <= O(f)"
+lemma bigo_useful_intro: "A \<subseteq> O(f) \<Longrightarrow> B \<subseteq> O(f) \<Longrightarrow> A + B \<subseteq> O(f)"
   apply (subst bigo_plus_idemp [symmetric])
   apply (rule set_plus_mono2)
   apply assumption+
   done
 
-lemma bigo_useful_add: "f =o O(h) ==> g =o O(h) ==> f + g =o O(h)"
+lemma bigo_useful_add: "f =o O(h) \<Longrightarrow> g =o O(h) \<Longrightarrow> f + g =o O(h)"
   apply (subst bigo_plus_idemp [symmetric])
   apply (rule set_plus_intro)
   apply assumption+
   done
-  
-lemma bigo_useful_const_mult: "(c::'a::linordered_field) ~= 0 ==> 
-    (%x. c) * f =o O(h) ==> f =o O(h)"
+
+lemma bigo_useful_const_mult:
+  fixes c :: "'a::linordered_field"
+  shows "c \<noteq> 0 \<Longrightarrow> (\<lambda>x. c) * f =o O(h) \<Longrightarrow> f =o O(h)"
   apply (rule subsetD)
-  apply (subgoal_tac "(%x. 1 / c) *o O(h) <= O(h)")
+  apply (subgoal_tac "(\<lambda>x. 1 / c) *o O(h) \<subseteq> O(h)")
   apply assumption
   apply (rule bigo_const_mult6)
-  apply (subgoal_tac "f = (%x. 1 / c) * ((%x. c) * f)")
+  apply (subgoal_tac "f = (\<lambda>x. 1 / c) * ((\<lambda>x. c) * f)")
   apply (erule ssubst)
   apply (erule set_times_intro2)
   apply (simp add: func_times)
   done
 
-lemma bigo_fix: "(%x. f ((x::nat) + 1)) =o O(%x. h(x + 1)) ==> f 0 = 0 ==>
-    f =o O(h)"
+lemma bigo_fix: "(\<lambda>x::nat. f (x + 1)) =o O(\<lambda>x. h (x + 1)) \<Longrightarrow> f 0 = 0 \<Longrightarrow> f =o O(h)"
   apply (simp add: bigo_alt_def)
   apply auto
   apply (rule_tac x = c in exI)
@@ -696,9 +714,9 @@
   apply simp
   done
 
-lemma bigo_fix2: 
-    "(%x. f ((x::nat) + 1)) =o (%x. g(x + 1)) +o O(%x. h(x + 1)) ==> 
-       f 0 = g 0 ==> f =o g +o O(h)"
+lemma bigo_fix2:
+    "(\<lambda>x. f ((x::nat) + 1)) =o (\<lambda>x. g(x + 1)) +o O(\<lambda>x. h(x + 1)) \<Longrightarrow>
+       f 0 = g 0 \<Longrightarrow> f =o g +o O(h)"
   apply (rule set_minus_imp_plus)
   apply (rule bigo_fix)
   apply (subst fun_diff_def)
@@ -711,13 +729,10 @@
 
 subsection {* Less than or equal to *}
 
-definition
-  lesso :: "('a => 'b::linordered_idom) => ('a => 'b) => ('a => 'b)"
-    (infixl "<o" 70) where
-  "f <o g = (%x. max (f x - g x) 0)"
+definition lesso :: "('a \<Rightarrow> 'b::linordered_idom) \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'b"  (infixl "<o" 70)
+  where "f <o g = (\<lambda>x. max (f x - g x) 0)"
 
-lemma bigo_lesseq1: "f =o O(h) ==> ALL x. abs (g x) <= abs (f x) ==>
-    g =o O(h)"
+lemma bigo_lesseq1: "f =o O(h) \<Longrightarrow> \<forall>x. abs (g x) \<le> abs (f x) \<Longrightarrow> g =o O(h)"
   apply (unfold bigo_def)
   apply clarsimp
   apply (rule_tac x = c in exI)
@@ -726,8 +741,7 @@
   apply (erule spec)+
   done
 
-lemma bigo_lesseq2: "f =o O(h) ==> ALL x. abs (g x) <= f x ==>
-      g =o O(h)"
+lemma bigo_lesseq2: "f =o O(h) \<Longrightarrow> \<forall>x. abs (g x) \<le> f x \<Longrightarrow> g =o O(h)"
   apply (erule bigo_lesseq1)
   apply (rule allI)
   apply (drule_tac x = x in spec)
@@ -736,26 +750,24 @@
   apply (rule abs_ge_self)
   done
 
-lemma bigo_lesseq3: "f =o O(h) ==> ALL x. 0 <= g x ==> ALL x. g x <= f x ==>
-    g =o O(h)"
+lemma bigo_lesseq3: "f =o O(h) \<Longrightarrow> \<forall>x. 0 \<le> g x \<Longrightarrow> \<forall>x. g x \<le> f x \<Longrightarrow> g =o O(h)"
   apply (erule bigo_lesseq2)
   apply (rule allI)
   apply (subst abs_of_nonneg)
   apply (erule spec)+
   done
 
-lemma bigo_lesseq4: "f =o O(h) ==>
-    ALL x. 0 <= g x ==> ALL x. g x <= abs (f x) ==>
-      g =o O(h)"
+lemma bigo_lesseq4: "f =o O(h) \<Longrightarrow>
+    \<forall>x. 0 \<le> g x \<Longrightarrow> \<forall>x. g x \<le> abs (f x) \<Longrightarrow> g =o O(h)"
   apply (erule bigo_lesseq1)
   apply (rule allI)
   apply (subst abs_of_nonneg)
   apply (erule spec)+
   done
 
-lemma bigo_lesso1: "ALL x. f x <= g x ==> f <o g =o O(h)"
+lemma bigo_lesso1: "\<forall>x. f x \<le> g x \<Longrightarrow> f <o g =o O(h)"
   apply (unfold lesso_def)
-  apply (subgoal_tac "(%x. max (f x - g x) 0) = 0")
+  apply (subgoal_tac "(\<lambda>x. max (f x - g x) 0) = 0")
   apply (erule ssubst)
   apply (rule bigo_zero)
   apply (unfold func_zero)
@@ -763,9 +775,8 @@
   apply (simp split: split_max)
   done
 
-lemma bigo_lesso2: "f =o g +o O(h) ==>
-    ALL x. 0 <= k x ==> ALL x. k x <= f x ==>
-      k <o g =o O(h)"
+lemma bigo_lesso2: "f =o g +o O(h) \<Longrightarrow>
+    \<forall>x. 0 \<le> k x \<Longrightarrow> \<forall>x. k x \<le> f x \<Longrightarrow> k <o g =o O(h)"
   apply (unfold lesso_def)
   apply (rule bigo_lesseq4)
   apply (erule set_plus_imp_minus)
@@ -773,7 +784,7 @@
   apply (rule max.cobounded2)
   apply (rule allI)
   apply (subst fun_diff_def)
-  apply (case_tac "0 <= k x - g x")
+  apply (case_tac "0 \<le> k x - g x")
   apply simp
   apply (subst abs_of_nonneg)
   apply (drule_tac x = x in spec) back
@@ -781,15 +792,14 @@
   apply (subst diff_conv_add_uminus)+
   apply (rule add_right_mono)
   apply (erule spec)
-  apply (rule order_trans) 
+  apply (rule order_trans)
   prefer 2
   apply (rule abs_ge_zero)
   apply (simp add: algebra_simps)
   done
 
-lemma bigo_lesso3: "f =o g +o O(h) ==>
-    ALL x. 0 <= k x ==> ALL x. g x <= k x ==>
-      f <o k =o O(h)"
+lemma bigo_lesso3: "f =o g +o O(h) \<Longrightarrow>
+    \<forall>x. 0 \<le> k x \<Longrightarrow> \<forall>x. g x \<le> k x \<Longrightarrow> f <o k =o O(h)"
   apply (unfold lesso_def)
   apply (rule bigo_lesseq4)
   apply (erule set_plus_imp_minus)
@@ -797,7 +807,7 @@
   apply (rule max.cobounded2)
   apply (rule allI)
   apply (subst fun_diff_def)
-  apply (case_tac "0 <= f x - k x")
+  apply (case_tac "0 \<le> f x - k x")
   apply simp
   apply (subst abs_of_nonneg)
   apply (drule_tac x = x in spec) back
@@ -806,14 +816,15 @@
   apply (rule add_left_mono)
   apply (rule le_imp_neg_le)
   apply (erule spec)
-  apply (rule order_trans) 
+  apply (rule order_trans)
   prefer 2
   apply (rule abs_ge_zero)
   apply (simp add: algebra_simps)
   done
 
-lemma bigo_lesso4: "f <o g =o O(k::'a=>'b::linordered_field) ==>
-    g =o h +o O(k) ==> f <o h =o O(k)"
+lemma bigo_lesso4:
+  fixes k :: "'a \<Rightarrow> 'b::linordered_field"
+  shows "f <o g =o O(k) \<Longrightarrow> g =o h +o O(k) \<Longrightarrow> f <o h =o O(k)"
   apply (unfold lesso_def)
   apply (drule set_plus_imp_minus)
   apply (drule bigo_abs5) back
@@ -822,25 +833,22 @@
   apply assumption
   apply (erule bigo_lesseq2) back
   apply (rule allI)
-  apply (auto simp add: func_plus fun_diff_def algebra_simps
-    split: split_max abs_split)
+  apply (auto simp add: func_plus fun_diff_def algebra_simps split: split_max abs_split)
   done
 
-lemma bigo_lesso5: "f <o g =o O(h) ==>
-    EX C. ALL x. f x <= g x + C * abs(h x)"
+lemma bigo_lesso5: "f <o g =o O(h) \<Longrightarrow> \<exists>C. \<forall>x. f x \<le> g x + C * abs (h x)"
   apply (simp only: lesso_def bigo_alt_def)
   apply clarsimp
   apply (rule_tac x = c in exI)
   apply (rule allI)
   apply (drule_tac x = x in spec)
-  apply (subgoal_tac "abs(max (f x - g x) 0) = max (f x - g x) 0")
-  apply (clarsimp simp add: algebra_simps) 
+  apply (subgoal_tac "abs (max (f x - g x) 0) = max (f x - g x) 0")
+  apply (clarsimp simp add: algebra_simps)
   apply (rule abs_of_nonneg)
   apply (rule max.cobounded2)
   done
 
-lemma lesso_add: "f <o g =o O(h) ==>
-      k <o l =o O(h) ==> (f + k) <o (g + l) =o O(h)"
+lemma lesso_add: "f <o g =o O(h) \<Longrightarrow> k <o l =o O(h) \<Longrightarrow> (f + k) <o (g + l) =o O(h)"
   apply (unfold lesso_def)
   apply (rule bigo_lesseq3)
   apply (erule bigo_useful_add)
@@ -849,7 +857,7 @@
   apply (auto split: split_max simp add: func_plus)
   done
 
-lemma bigo_LIMSEQ1: "f =o O(g) ==> g ----> 0 ==> f ----> (0::real)"
+lemma bigo_LIMSEQ1: "f =o O(g) \<Longrightarrow> g ----> 0 \<Longrightarrow> f ----> (0::real)"
   apply (simp add: LIMSEQ_iff bigo_alt_def)
   apply clarify
   apply (drule_tac x = "r / c" in spec)
@@ -866,21 +874,20 @@
   apply (rule order_le_less_trans)
   apply assumption
   apply (rule order_less_le_trans)
-  apply (subgoal_tac "c * abs(g n) < c * (r / c)")
+  apply (subgoal_tac "c * abs (g n) < c * (r / c)")
   apply assumption
   apply (erule mult_strict_left_mono)
   apply assumption
   apply simp
-done
+  done
 
-lemma bigo_LIMSEQ2: "f =o g +o O(h) ==> h ----> 0 ==> f ----> a 
-    ==> g ----> (a::real)"
+lemma bigo_LIMSEQ2: "f =o g +o O(h) \<Longrightarrow> h ----> 0 \<Longrightarrow> f ----> a \<Longrightarrow> g ----> (a::real)"
   apply (drule set_plus_imp_minus)
   apply (drule bigo_LIMSEQ1)
   apply assumption
   apply (simp only: fun_diff_def)
   apply (erule LIMSEQ_diff_approach_zero2)
   apply assumption
-done
+  done
 
 end
--- a/src/HOL/ex/Cartouche_Examples.thy	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/HOL/ex/Cartouche_Examples.thy	Sat Mar 01 23:48:55 2014 +0100
@@ -114,13 +114,13 @@
 setup -- "document antiquotation"
 {*
   Thy_Output.antiquotation @{binding ML_cartouche}
-    (Scan.lift Args.cartouche_source_position) (fn {context, ...} => fn (txt, pos) =>
+    (Scan.lift Args.cartouche_source_position) (fn {context, ...} => fn source =>
       let
         val toks =
           ML_Lex.read Position.none "fn _ => (" @
-          ML_Lex.read pos txt @
+          ML_Lex.read_source source @
           ML_Lex.read Position.none ");";
-        val _ = ML_Context.eval_in (SOME context) false pos toks;
+        val _ = ML_Context.eval_in (SOME context) false (#pos source) toks;
       in "" end);
 *}
 
@@ -177,19 +177,19 @@
 structure ML_Tactic:
 sig
   val set: (Proof.context -> tactic) -> Proof.context -> Proof.context
-  val ml_tactic: string * Position.T -> Proof.context -> tactic
+  val ml_tactic: Symbol_Pos.source -> Proof.context -> tactic
 end =
 struct
   structure Data = Proof_Data(type T = Proof.context -> tactic fun init _ = K no_tac);
 
   val set = Data.put;
 
-  fun ml_tactic (txt, pos) ctxt =
+  fun ml_tactic source ctxt =
     let
       val ctxt' = ctxt |> Context.proof_map
-        (ML_Context.expression pos
+        (ML_Context.expression (#pos source)
           "fun tactic (ctxt : Proof.context) : tactic"
-          "Context.map_proof (ML_Tactic.set tactic)" (ML_Lex.read pos txt));
+          "Context.map_proof (ML_Tactic.set tactic)" (ML_Lex.read_source source));
     in Data.get ctxt' ctxt end;
 end;
 *}
--- a/src/Pure/General/symbol_pos.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/General/symbol_pos.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -40,6 +40,8 @@
   val implode: T list -> text
   val implode_range: Position.T -> Position.T -> T list -> text * Position.range
   val explode: text * Position.T -> T list
+  type source = {delimited: bool, text: text, pos: Position.T}
+  val source_content: source -> string * Position.T
   val scan_ident: T list -> T list * T list
   val is_identifier: string -> bool
 end;
@@ -255,6 +257,14 @@
   in fold (fn (s, p) => if s = Symbol.DEL then I else cons (s, p)) res [] end;
 
 
+(* full source information *)
+
+type source = {delimited: bool, text: text, pos: Position.T};
+
+fun source_content {delimited = _, text, pos} =
+  let val syms = explode (text, pos) in (content syms, pos) end;
+
+
 (* identifiers *)
 
 local
--- a/src/Pure/Isar/args.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/Isar/args.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -30,9 +30,9 @@
   val mode: string -> bool parser
   val maybe: 'a parser -> 'a option parser
   val cartouche_inner_syntax: string parser
-  val cartouche_source_position: (Symbol_Pos.text * Position.T) parser
+  val cartouche_source_position: Symbol_Pos.source parser
   val name_inner_syntax: string parser
-  val name_source_position: (Symbol_Pos.text * Position.T) parser
+  val name_source_position: Symbol_Pos.source parser
   val name: string parser
   val binding: binding parser
   val alt_name: string parser
--- a/src/Pure/Isar/attrib.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/Isar/attrib.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -35,8 +35,7 @@
     Context.generic -> (string * thm list) list * Context.generic
   val eval_thms: Proof.context -> (Facts.ref * src list) list -> thm list
   val setup: Binding.binding -> attribute context_parser -> string -> theory -> theory
-  val attribute_setup: bstring * Position.T -> Symbol_Pos.text * Position.T -> string ->
-    theory -> theory
+  val attribute_setup: bstring * Position.T -> Symbol_Pos.source -> string -> theory -> theory
   val internal: (morphism -> attribute) -> src
   val add_del: attribute -> attribute -> attribute context_parser
   val thm_sel: Facts.interval list parser
@@ -185,12 +184,12 @@
   add_attribute name
     (fn src => fn (ctxt, th) => let val (a, ctxt') = syntax scan src ctxt in a (ctxt', th) end);
 
-fun attribute_setup name (txt, pos) cmt =
-  Context.theory_map (ML_Context.expression pos
+fun attribute_setup name source cmt =
+  Context.theory_map (ML_Context.expression (#pos source)
     "val (name, scan, comment): binding * attribute context_parser * string"
     "Context.map_theory (Attrib.setup name scan comment)"
     (ML_Lex.read Position.none ("(" ^ ML_Syntax.make_binding name ^ ", ") @
-      ML_Lex.read pos txt @
+      ML_Lex.read_source source @
       ML_Lex.read Position.none (", " ^ ML_Syntax.print_string cmt ^ ")")));
 
 
--- a/src/Pure/Isar/isar_cmd.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/Isar/isar_cmd.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -6,20 +6,20 @@
 
 signature ISAR_CMD =
 sig
-  val global_setup: Symbol_Pos.text * Position.T -> theory -> theory
-  val local_setup: Symbol_Pos.text * Position.T -> Proof.context -> Proof.context
-  val parse_ast_translation: Symbol_Pos.text * Position.T -> theory -> theory
-  val parse_translation: Symbol_Pos.text * Position.T -> theory -> theory
-  val print_translation: Symbol_Pos.text * Position.T -> theory -> theory
-  val typed_print_translation: Symbol_Pos.text * Position.T -> theory -> theory
-  val print_ast_translation: Symbol_Pos.text * Position.T -> theory -> theory
+  val global_setup: Symbol_Pos.source -> theory -> theory
+  val local_setup: Symbol_Pos.source -> Proof.context -> Proof.context
+  val parse_ast_translation: Symbol_Pos.source -> theory -> theory
+  val parse_translation: Symbol_Pos.source -> theory -> theory
+  val print_translation: Symbol_Pos.source -> theory -> theory
+  val typed_print_translation: Symbol_Pos.source -> theory -> theory
+  val print_ast_translation: Symbol_Pos.source -> theory -> theory
   val translations: (xstring * string) Syntax.trrule list -> theory -> theory
   val no_translations: (xstring * string) Syntax.trrule list -> theory -> theory
-  val oracle: bstring * Position.T -> Symbol_Pos.text * Position.T -> theory -> theory
+  val oracle: bstring * Position.T -> Symbol_Pos.source -> theory -> theory
   val add_defs: (bool * bool) * ((binding * string) * Attrib.src list) list -> theory -> theory
   val declaration: {syntax: bool, pervasive: bool} ->
-    Symbol_Pos.text * Position.T -> local_theory -> local_theory
-  val simproc_setup: string * Position.T -> string list -> Symbol_Pos.text * Position.T ->
+    Symbol_Pos.source -> local_theory -> local_theory
+  val simproc_setup: string * Position.T -> string list -> Symbol_Pos.source ->
     string list -> local_theory -> local_theory
   val hide_class: bool -> xstring list -> theory -> theory
   val hide_type: bool -> xstring list -> theory -> theory
@@ -36,7 +36,7 @@
   val immediate_proof: Toplevel.transition -> Toplevel.transition
   val done_proof: Toplevel.transition -> Toplevel.transition
   val skip_proof: Toplevel.transition -> Toplevel.transition
-  val ml_diag: bool -> Symbol_Pos.text * Position.T -> Toplevel.transition -> Toplevel.transition
+  val ml_diag: bool -> Symbol_Pos.source -> Toplevel.transition -> Toplevel.transition
   val diag_state: Proof.context -> Toplevel.state
   val diag_goal: Proof.context -> {context: Proof.context, facts: thm list, goal: thm}
   val print_theorems: bool -> Toplevel.transition -> Toplevel.transition
@@ -56,10 +56,10 @@
   val print_term: (string list * string) -> Toplevel.transition -> Toplevel.transition
   val print_type: (string list * (string * string option)) ->
     Toplevel.transition -> Toplevel.transition
-  val header_markup: Symbol_Pos.text * Position.T -> Toplevel.transition -> Toplevel.transition
-  val local_theory_markup: (xstring * Position.T) option * (Symbol_Pos.text * Position.T) ->
+  val header_markup: Symbol_Pos.source -> Toplevel.transition -> Toplevel.transition
+  val local_theory_markup: (xstring * Position.T) option * (Symbol_Pos.source) ->
     Toplevel.transition -> Toplevel.transition
-  val proof_markup: Symbol_Pos.text * Position.T -> Toplevel.transition -> Toplevel.transition
+  val proof_markup: Symbol_Pos.source -> Toplevel.transition -> Toplevel.transition
 end;
 
 structure Isar_Cmd: ISAR_CMD =
@@ -70,50 +70,50 @@
 
 (* generic setup *)
 
-fun global_setup (txt, pos) =
-  ML_Lex.read pos txt
-  |> ML_Context.expression pos "val setup: theory -> theory" "Context.map_theory setup"
+fun global_setup source =
+  ML_Lex.read_source source
+  |> ML_Context.expression (#pos source) "val setup: theory -> theory" "Context.map_theory setup"
   |> Context.theory_map;
 
-fun local_setup (txt, pos) =
-  ML_Lex.read pos txt
-  |> ML_Context.expression pos "val setup: local_theory -> local_theory" "Context.map_proof setup"
+fun local_setup source =
+  ML_Lex.read_source source
+  |> ML_Context.expression (#pos source) "val setup: local_theory -> local_theory" "Context.map_proof setup"
   |> Context.proof_map;
 
 
 (* translation functions *)
 
-fun parse_ast_translation (txt, pos) =
-  ML_Lex.read pos txt
-  |> ML_Context.expression pos
+fun parse_ast_translation source =
+  ML_Lex.read_source source
+  |> ML_Context.expression (#pos source)
     "val parse_ast_translation: (string * (Proof.context -> Ast.ast list -> Ast.ast)) list"
     "Context.map_theory (Sign.parse_ast_translation parse_ast_translation)"
   |> Context.theory_map;
 
-fun parse_translation (txt, pos) =
-  ML_Lex.read pos txt
-  |> ML_Context.expression pos
+fun parse_translation source =
+  ML_Lex.read_source source
+  |> ML_Context.expression (#pos source)
     "val parse_translation: (string * (Proof.context -> term list -> term)) list"
     "Context.map_theory (Sign.parse_translation parse_translation)"
   |> Context.theory_map;
 
-fun print_translation (txt, pos) =
-  ML_Lex.read pos txt
-  |> ML_Context.expression pos
+fun print_translation source =
+  ML_Lex.read_source source
+  |> ML_Context.expression (#pos source)
     "val print_translation: (string * (Proof.context -> term list -> term)) list"
     "Context.map_theory (Sign.print_translation print_translation)"
   |> Context.theory_map;
 
-fun typed_print_translation (txt, pos) =
-  ML_Lex.read pos txt
-  |> ML_Context.expression pos
+fun typed_print_translation source =
+  ML_Lex.read_source source
+  |> ML_Context.expression (#pos source)
     "val typed_print_translation: (string * (Proof.context -> typ -> term list -> term)) list"
     "Context.map_theory (Sign.typed_print_translation typed_print_translation)"
   |> Context.theory_map;
 
-fun print_ast_translation (txt, pos) =
-  ML_Lex.read pos txt
-  |> ML_Context.expression pos
+fun print_ast_translation source =
+  ML_Lex.read_source source
+  |> ML_Context.expression (#pos source)
     "val print_ast_translation: (string * (Proof.context -> Ast.ast list -> Ast.ast)) list"
     "Context.map_theory (Sign.print_ast_translation print_ast_translation)"
   |> Context.theory_map;
@@ -135,18 +135,19 @@
 
 (* oracles *)
 
-fun oracle (name, pos) (body_txt, body_pos) =
+fun oracle (name, pos) source =
   let
-    val body = ML_Lex.read body_pos body_txt;
+    val body = ML_Lex.read_source source;
     val ants =
       ML_Lex.read Position.none
        ("local\n\
         \  val binding = " ^ ML_Syntax.make_binding (name, pos) ^ ";\n\
         \  val body = ") @ body @ ML_Lex.read Position.none (";\n\
         \in\n\
-        \  val " ^ name ^ " = snd (Context.>>> (Context.map_theory_result (Thm.add_oracle (binding, body))));\n\
+        \  val " ^ name ^
+        " = snd (Context.>>> (Context.map_theory_result (Thm.add_oracle (binding, body))));\n\
         \end;\n");
-  in Context.theory_map (ML_Context.exec (fn () => ML_Context.eval false body_pos ants)) end;
+  in Context.theory_map (ML_Context.exec (fn () => ML_Context.eval false (#pos source) ants)) end;
 
 
 (* old-style defs *)
@@ -161,9 +162,9 @@
 
 (* declarations *)
 
-fun declaration {syntax, pervasive} (txt, pos) =
-  ML_Lex.read pos txt
-  |> ML_Context.expression pos
+fun declaration {syntax, pervasive} source =
+  ML_Lex.read_source source
+  |> ML_Context.expression (#pos source)
     "val declaration: Morphism.declaration"
     ("Context.map_proof (Local_Theory.declaration {syntax = " ^ Bool.toString syntax ^ ", \
       \pervasive = " ^ Bool.toString pervasive ^ "} declaration)")
@@ -172,9 +173,9 @@
 
 (* simprocs *)
 
-fun simproc_setup name lhss (txt, pos) identifier =
-  ML_Lex.read pos txt
-  |> ML_Context.expression pos
+fun simproc_setup name lhss source identifier =
+  ML_Lex.read_source source
+  |> ML_Context.expression (#pos source)
     "val proc: Morphism.morphism -> Proof.context -> cterm -> thm option"
     ("Context.map_proof (Simplifier.def_simproc_cmd {name = " ^ ML_Syntax.make_binding name ^ ", \
       \lhss = " ^ ML_Syntax.print_strings lhss ^ ", proc = proc, \
@@ -253,11 +254,11 @@
   fun init _ = Toplevel.toplevel;
 );
 
-fun ml_diag verbose (txt, pos) = Toplevel.keep (fn state =>
+fun ml_diag verbose source = Toplevel.keep (fn state =>
   let val opt_ctxt =
     try Toplevel.generic_theory_of state
     |> Option.map (Context.proof_of #> Diag_State.put state)
-  in ML_Context.eval_text_in opt_ctxt verbose pos txt end);
+  in ML_Context.eval_source_in opt_ctxt verbose source end);
 
 val diag_state = Diag_State.get;
 
--- a/src/Pure/Isar/isar_syn.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/Isar/isar_syn.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -248,16 +248,17 @@
 
 val _ =
   Outer_Syntax.command @{command_spec "ML"} "ML text within theory or local theory"
-    (Parse.ML_source >> (fn (txt, pos) =>
+    (Parse.ML_source >> (fn source =>
       Toplevel.generic_theory
-        (ML_Context.exec (fn () => ML_Context.eval_text true pos txt) #>
+        (ML_Context.exec (fn () => ML_Context.eval_source true source) #>
           Local_Theory.propagate_ml_env)));
 
 val _ =
   Outer_Syntax.command @{command_spec "ML_prf"} "ML text within proof"
-    (Parse.ML_source >> (fn (txt, pos) =>
+    (Parse.ML_source >> (fn source =>
       Toplevel.proof (Proof.map_context (Context.proof_map
-        (ML_Context.exec (fn () => ML_Context.eval_text true pos txt))) #> Proof.propagate_ml_env)));
+        (ML_Context.exec (fn () => ML_Context.eval_source true source))) #>
+          Proof.propagate_ml_env)));
 
 val _ =
   Outer_Syntax.command @{command_spec "ML_val"} "diagnostic ML text"
--- a/src/Pure/Isar/method.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/Isar/method.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -42,8 +42,8 @@
   val drule: Proof.context -> int -> thm list -> method
   val frule: Proof.context -> int -> thm list -> method
   val set_tactic: (thm list -> tactic) -> Proof.context -> Proof.context
-  val tactic: string * Position.T -> Proof.context -> method
-  val raw_tactic: string * Position.T -> Proof.context -> method
+  val tactic: Symbol_Pos.source -> Proof.context -> method
+  val raw_tactic: Symbol_Pos.source -> Proof.context -> method
   type src = Args.src
   type combinator_info
   val no_combinator_info: combinator_info
@@ -68,8 +68,7 @@
   val check_source: Proof.context -> src -> src
   val syntax: 'a context_parser -> src -> Proof.context -> 'a * Proof.context
   val setup: binding -> (Proof.context -> method) context_parser -> string -> theory -> theory
-  val method_setup: bstring * Position.T -> Symbol_Pos.text * Position.T -> string ->
-    theory -> theory
+  val method_setup: bstring * Position.T -> Symbol_Pos.source -> string -> theory -> theory
   type modifier = (Proof.context -> Proof.context) * attribute
   val section: modifier parser list -> thm list context_parser
   val sections: modifier parser list -> thm list list context_parser
@@ -266,16 +265,16 @@
 
 val set_tactic = ML_Tactic.put;
 
-fun ml_tactic (txt, pos) ctxt =
+fun ml_tactic source ctxt =
   let
     val ctxt' = ctxt |> Context.proof_map
-      (ML_Context.expression pos
+      (ML_Context.expression (#pos source)
         "fun tactic (facts: thm list) : tactic"
-        "Context.map_proof (Method.set_tactic tactic)" (ML_Lex.read pos txt));
+        "Context.map_proof (Method.set_tactic tactic)" (ML_Lex.read_source source));
   in Context.setmp_thread_data (SOME (Context.Proof ctxt)) (ML_Tactic.get ctxt') end;
 
-fun tactic txt ctxt = METHOD (ml_tactic txt ctxt);
-fun raw_tactic txt ctxt = RAW_METHOD (ml_tactic txt ctxt);
+fun tactic source ctxt = METHOD (ml_tactic source ctxt);
+fun raw_tactic source ctxt = RAW_METHOD (ml_tactic source ctxt);
 
 
 
@@ -366,12 +365,12 @@
   add_method name
     (fn src => fn ctxt => let val (m, ctxt') = syntax scan src ctxt in m ctxt' end);
 
-fun method_setup name (txt, pos) cmt =
-  Context.theory_map (ML_Context.expression pos
+fun method_setup name source cmt =
+  Context.theory_map (ML_Context.expression (#pos source)
     "val (name, scan, comment): binding * (Proof.context -> Proof.method) context_parser * string"
     "Context.map_theory (Method.setup name scan comment)"
     (ML_Lex.read Position.none ("(" ^ ML_Syntax.make_binding name ^ ", ") @
-      ML_Lex.read pos txt @
+      ML_Lex.read_source source @
       ML_Lex.read Position.none (", " ^ ML_Syntax.print_string cmt ^ ")")));
 
 
--- a/src/Pure/Isar/parse.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/Isar/parse.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -16,7 +16,7 @@
   val triple_swap: ('a * 'b) * 'c -> ('a * 'c) * 'b
   val not_eof: Token.T parser
   val position: 'a parser -> ('a * Position.T) parser
-  val source_position: 'a parser -> (Symbol_Pos.text * Position.T) parser
+  val source_position: 'a parser -> Symbol_Pos.source parser
   val inner_syntax: 'a parser -> string parser
   val command: string parser
   val keyword: string parser
@@ -93,8 +93,8 @@
   val simple_fixes: (binding * string option) list parser
   val fixes: (binding * string option * mixfix) list parser
   val for_fixes: (binding * string option * mixfix) list parser
-  val ML_source: (Symbol_Pos.text * Position.T) parser
-  val document_source: (Symbol_Pos.text * Position.T) parser
+  val ML_source: Symbol_Pos.source parser
+  val document_source: Symbol_Pos.source parser
   val term_group: string parser
   val prop_group: string parser
   val term: string parser
--- a/src/Pure/Isar/proof_context.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/Isar/proof_context.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -377,8 +377,8 @@
 fun read_class ctxt text =
   let
     val tsig = tsig_of ctxt;
-    val (syms, pos) = Syntax.read_token text;
-    val c = Type.cert_class tsig (Type.intern_class tsig (Symbol_Pos.content syms))
+    val (s, pos) = Symbol_Pos.source_content (Syntax.read_token text);
+    val c = Type.cert_class tsig (Type.intern_class tsig s)
       handle TYPE (msg, _, _) => error (msg ^ Position.here pos);
     val _ = Context_Position.report ctxt pos (Name_Space.markup (Type.class_space tsig) c);
   in c end;
@@ -439,8 +439,6 @@
 
 local
 
-val token_content = Syntax.read_token #>> Symbol_Pos.content;
-
 fun prep_const_proper ctxt strict (c, pos) =
   let
     fun err msg = error (msg ^ Position.here pos);
@@ -461,7 +459,7 @@
 fun read_type_name ctxt strict text =
   let
     val tsig = tsig_of ctxt;
-    val (c, pos) = token_content text;
+    val (c, pos) = Symbol_Pos.source_content (Syntax.read_token text);
   in
     if Lexicon.is_tid c then
      (Context_Position.report ctxt pos Markup.tfree;
@@ -486,11 +484,12 @@
   | T => error ("Not a type constructor: " ^ Syntax.string_of_typ ctxt T));
 
 
-fun read_const_proper ctxt strict = prep_const_proper ctxt strict o token_content;
+fun read_const_proper ctxt strict =
+  prep_const_proper ctxt strict o Symbol_Pos.source_content o Syntax.read_token;
 
 fun read_const ctxt strict ty text =
   let
-    val (c, pos) = token_content text;
+    val (c, pos) = Symbol_Pos.source_content (Syntax.read_token text);
     val _ = no_skolem false c;
   in
     (case (Variable.lookup_fixed ctxt c, Variable.is_const ctxt c) of
--- a/src/Pure/Isar/token.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/Isar/token.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -40,7 +40,7 @@
   val is_blank: T -> bool
   val is_newline: T -> bool
   val inner_syntax_of: T -> string
-  val source_position_of: T -> Symbol_Pos.text * Position.T
+  val source_position_of: T -> Symbol_Pos.source
   val content_of: T -> string
   val markup: T -> Markup.T * string
   val unparse: T -> string
@@ -127,6 +127,8 @@
   | Sync => "sync marker"
   | EOF => "end-of-input";
 
+val delimited_kind = member (op =) [String, AltString, Verbatim, Cartouche, Comment];
+
 
 (* position *)
 
@@ -206,11 +208,16 @@
 
 (* token content *)
 
-fun inner_syntax_of (Token ((source, (pos, _)), (_, x), _)) =
+fun inner_syntax_of (Token ((source, (pos, _)), (kind, x), _)) =
   if YXML.detect x then x
-  else YXML.string_of (XML.Elem (Markup.token (Position.properties_of pos), [XML.Text source]));
+  else
+    let
+      val delimited = delimited_kind kind;
+      val tree = XML.Elem (Markup.token delimited (Position.properties_of pos), [XML.Text source]);
+    in YXML.string_of tree end;
 
-fun source_position_of (Token ((source, (pos, _)), _, _)) = (source, pos);
+fun source_position_of (Token ((source, (pos, _)), (kind, _), _)) =
+  {delimited = delimited_kind kind, text = source, pos = pos};
 
 fun content_of (Token (_, (_, x), _)) = x;
 
--- a/src/Pure/ML/ml_context.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/ML/ml_context.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -31,10 +31,10 @@
   val eval_antiquotes: ML_Lex.token Antiquote.antiquote list * Position.T ->
     Context.generic option -> (ML_Lex.token list * ML_Lex.token list) * Context.generic option
   val eval: bool -> Position.T -> ML_Lex.token Antiquote.antiquote list -> unit
-  val eval_text: bool -> Position.T -> Symbol_Pos.text -> unit
+  val eval_source: bool -> Symbol_Pos.source -> unit
   val eval_in: Proof.context option -> bool -> Position.T ->
     ML_Lex.token Antiquote.antiquote list -> unit
-  val eval_text_in: Proof.context option -> bool -> Position.T -> Symbol_Pos.text -> unit
+  val eval_source_in: Proof.context option -> bool -> Symbol_Pos.source -> unit
   val expression: Position.T -> string -> string -> ML_Lex.token Antiquote.antiquote list ->
     Context.generic -> Context.generic
 end
@@ -208,13 +208,14 @@
 
 (* derived versions *)
 
-fun eval_text verbose pos txt = eval verbose pos (ML_Lex.read pos txt);
+fun eval_source verbose source =
+  eval verbose (#pos source) (ML_Lex.read_source source);
 
 fun eval_in ctxt verbose pos ants =
   Context.setmp_thread_data (Option.map Context.Proof ctxt) (fn () => eval verbose pos ants) ();
 
-fun eval_text_in ctxt verbose pos txt =
-  Context.setmp_thread_data (Option.map Context.Proof ctxt) (fn () => eval_text verbose pos txt) ();
+fun eval_source_in ctxt verbose source =
+  Context.setmp_thread_data (Option.map Context.Proof ctxt) (fn () => eval_source verbose source) ();
 
 fun expression pos bind body ants =
   exec (fn () => eval false pos
--- a/src/Pure/ML/ml_lex.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/ML/ml_lex.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -26,6 +26,7 @@
       Source.source) Source.source
   val tokenize: string -> token list
   val read: Position.T -> Symbol_Pos.text -> token Antiquote.antiquote list
+  val read_source: Symbol_Pos.source -> token Antiquote.antiquote list
 end;
 
 structure ML_Lex: ML_LEX =
@@ -298,10 +299,9 @@
 
 val tokenize = Source.of_string #> Symbol.source #> source #> Source.exhaust;
 
-fun read pos txt =
+fun read pos text =
   let
-    val _ = Position.report pos Markup.language_ML;
-    val syms = Symbol_Pos.explode (txt, pos);
+    val syms = Symbol_Pos.explode (text, pos);
     val termination =
       if null syms then []
       else
@@ -318,6 +318,9 @@
         |> tap (List.app (fn Antiquote.Text tok => (check_content_of tok; warn tok) | _ => ())));
   in input @ termination end;
 
+fun read_source {delimited, text, pos} =
+  (Position.report pos (Markup.language_ML delimited); read pos text);
+
 end;
 
 end;
--- a/src/Pure/PIDE/command.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/PIDE/command.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -156,14 +156,11 @@
                 if id == command.id || id == alt_id =>
                   command.chunks.get(file_name) match {
                     case Some(chunk) =>
-                      chunk.decode(raw_range).try_restrict(chunk.range) match {
+                      chunk.incorporate(raw_range) match {
                         case Some(range) =>
-                          if (!range.is_singularity) {
-                            val props = Position.purge(atts)
-                            val info = Text.Info(range, XML.Elem(Markup(name, props), args))
-                            state.add_markup(false, file_name, info)
-                          }
-                          else state
+                          val props = Position.purge(atts)
+                          val info = Text.Info(range, XML.Elem(Markup(name, props), args))
+                          state.add_markup(false, file_name, info)
                         case None => bad(); state
                       }
                     case None => bad(); state
@@ -219,7 +216,17 @@
     def file_name: String
     def length: Int
     def range: Text.Range
-    def decode(r: Text.Range): Text.Range
+    def decode(raw_range: Text.Range): Text.Range
+
+    def incorporate(raw_range: Text.Range): Option[Text.Range] =
+    {
+      def inc(r: Text.Range): Option[Text.Range] =
+        range.try_restrict(decode(r)) match {
+          case Some(r1) if !r1.is_singularity => Some(r1)
+          case _ => None
+        }
+     inc(raw_range) orElse inc(raw_range - 1)
+    }
   }
 
   class File(val file_name: String, text: CharSequence) extends Chunk
@@ -227,7 +234,7 @@
     val length = text.length
     val range = Text.Range(0, length)
     private val symbol_index = Symbol.Index(text)
-    def decode(r: Text.Range): Text.Range = symbol_index.decode(r)
+    def decode(raw_range: Text.Range): Text.Range = symbol_index.decode(raw_range)
 
     override def toString: String = "Command.File(" + file_name + ")"
   }
@@ -367,8 +374,8 @@
   def source(range: Text.Range): String = source.substring(range.start, range.stop)
 
   private lazy val symbol_index = Symbol.Index(source)
-  def decode(i: Text.Offset): Text.Offset = symbol_index.decode(i)
-  def decode(r: Text.Range): Text.Range = symbol_index.decode(r)
+  def decode(raw_offset: Text.Offset): Text.Offset = symbol_index.decode(raw_offset)
+  def decode(raw_range: Text.Range): Text.Range = symbol_index.decode(raw_range)
 
 
   /* accumulated results */
--- a/src/Pure/PIDE/document.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/PIDE/document.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -376,8 +376,32 @@
   }
 
 
+  /* markup elements */
 
-  /** global state -- document structure, execution process, editing history **/
+  object Elements
+  {
+    def apply(elems: Set[String]): Elements = new Elements(elems)
+    def apply(elems: String*): Elements = apply(Set(elems: _*))
+    val empty: Elements = apply()
+    val full: Elements = new Full_Elements
+  }
+
+  sealed class Elements private[Document](private val rep: Set[String])
+  {
+    def apply(elem: String): Boolean = rep.contains(elem)
+    def + (elem: String): Elements = new Elements(rep + elem)
+    def ++ (elems: Elements): Elements = new Elements(rep ++ elems.rep)
+    override def toString: String = rep.mkString("Elements(", ",", ")")
+  }
+
+  private class Full_Elements extends Elements(Set.empty)
+  {
+    override def apply(elem: String): Boolean = true
+    override def toString: String = "Full_Elements()"
+  }
+
+
+  /* snapshot */
 
   object Snapshot
   {
@@ -403,17 +427,21 @@
     def cumulate[A](
       range: Text.Range,
       info: A,
-      elements: String => Boolean,
+      elements: Elements,
       result: Command.State => (A, Text.Markup) => Option[A],
       status: Boolean = false): List[Text.Info[A]]
 
     def select[A](
       range: Text.Range,
-      elements: String => Boolean,
+      elements: Elements,
       result: Command.State => Text.Markup => Option[A],
       status: Boolean = false): List[Text.Info[A]]
   }
 
+
+
+  /** global state -- document structure, execution process, editing history **/
+
   type Assign_Update =
     List[(Document_ID.Command, List[Document_ID.Exec])]  // update of exec state assignment
 
@@ -672,7 +700,7 @@
         def cumulate[A](
           range: Text.Range,
           info: A,
-          elements: String => Boolean,
+          elements: Elements,
           result: Command.State => (A, Text.Markup) => Option[A],
           status: Boolean = false): List[Text.Info[A]] =
         {
@@ -708,7 +736,7 @@
 
         def select[A](
           range: Text.Range,
-          elements: String => Boolean,
+          elements: Elements,
           result: Command.State => Text.Markup => Option[A],
           status: Boolean = false): List[Text.Info[A]] =
         {
--- a/src/Pure/PIDE/markup.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/PIDE/markup.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -20,18 +20,21 @@
   val name: string -> T -> T
   val kindN: string
   val instanceN: string
+  val languageN: string
   val symbolsN: string
-  val languageN: string
-  val language: {name: string, symbols: bool, antiquotes: bool} -> T
+  val delimitedN: string
+  val is_delimited: Properties.T -> bool
+  val language: {name: string, symbols: bool, antiquotes: bool, delimited: bool} -> T
+  val language': {name: string, symbols: bool, antiquotes: bool} -> bool -> T
   val language_method: T
-  val language_sort: T
-  val language_type: T
-  val language_term: T
-  val language_prop: T
-  val language_ML: T
-  val language_document: T
+  val language_sort: bool -> T
+  val language_type: bool -> T
+  val language_term: bool -> T
+  val language_prop: bool -> T
+  val language_ML: bool -> T
+  val language_document: bool -> T
   val language_antiquotation: T
-  val language_text: T
+  val language_text: bool -> T
   val language_rail: T
   val bindingN: string val binding: T
   val entityN: string val entity: string -> string -> T
@@ -106,7 +109,7 @@
   val cartoucheN: string val cartouche: T
   val commentN: string val comment: T
   val controlN: string val control: T
-  val tokenN: string val token: Properties.T -> T
+  val tokenN: string val token: bool -> Properties.T -> T
   val keyword1N: string val keyword1: T
   val keyword2N: string val keyword2: T
   val keyword3N: string val keyword3: T
@@ -251,24 +254,36 @@
 
 (* embedded languages *)
 
+val languageN = "language";
 val symbolsN = "symbols";
 val antiquotesN = "antiquotes";
-val languageN = "language";
+val delimitedN = "delimited"
+
+fun is_delimited props =
+  Properties.get props delimitedN = SOME "true";
 
-fun language {name, symbols, antiquotes} =
+fun language {name, symbols, antiquotes, delimited} =
   (languageN,
-    [(nameN, name), (symbolsN, print_bool symbols), (antiquotesN, print_bool antiquotes)]);
+   [(nameN, name),
+    (symbolsN, print_bool symbols),
+    (antiquotesN, print_bool antiquotes),
+    (delimitedN, print_bool delimited)]);
 
-val language_method = language {name = "method", symbols = true, antiquotes = false};
-val language_sort = language {name = "sort", symbols = true, antiquotes = false};
-val language_type = language {name = "type", symbols = true, antiquotes = false};
-val language_term = language {name = "term", symbols = true, antiquotes = false};
-val language_prop = language {name = "prop", symbols = true, antiquotes = false};
-val language_ML = language {name = "ML", symbols = false, antiquotes = true};
-val language_document = language {name = "document", symbols = false, antiquotes = true};
-val language_antiquotation = language {name = "antiquotation", symbols = true, antiquotes = false};
-val language_text = language {name = "text", symbols = true, antiquotes = false};
-val language_rail = language {name = "rail", symbols = true, antiquotes = true};
+fun language' {name, symbols, antiquotes} delimited =
+  language {name = name, symbols = symbols, antiquotes = antiquotes, delimited = delimited};
+
+val language_method =
+  language {name = "method", symbols = true, antiquotes = false, delimited = false};
+val language_sort = language' {name = "sort", symbols = true, antiquotes = false};
+val language_type = language' {name = "type", symbols = true, antiquotes = false};
+val language_term = language' {name = "term", symbols = true, antiquotes = false};
+val language_prop = language' {name = "prop", symbols = true, antiquotes = false};
+val language_ML = language' {name = "ML", symbols = false, antiquotes = true};
+val language_document = language' {name = "document", symbols = false, antiquotes = true};
+val language_antiquotation =
+  language {name = "antiquotation", symbols = true, antiquotes = false, delimited = true};
+val language_text = language' {name = "text", symbols = true, antiquotes = false};
+val language_rail = language {name = "rail", symbols = true, antiquotes = true, delimited = true};
 
 
 (* formal entities *)
@@ -411,7 +426,7 @@
 val (controlN, control) = markup_elem "control";
 
 val tokenN = "token";
-fun token props = (tokenN, props);
+fun token delimited props = (tokenN, (delimitedN, print_bool delimited) :: props);
 
 
 (* timing *)
--- a/src/Pure/PIDE/markup.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/PIDE/markup.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -94,6 +94,7 @@
 
   val Symbols = new Properties.Boolean("symbols")
   val Antiquotes = new Properties.Boolean("antiquotes")
+  val Delimited = new Properties.Boolean("delimited")
 
   val LANGUAGE = "language"
   object Language
@@ -101,12 +102,12 @@
     val ML = "ML"
     val UNKNOWN = "unknown"
 
-    def unapply(markup: Markup): Option[(String, Boolean, Boolean)] =
+    def unapply(markup: Markup): Option[(String, Boolean, Boolean, Boolean)] =
       markup match {
         case Markup(LANGUAGE, props) =>
-          (props, props, props) match {
-            case (Name(name), Symbols(symbols), Antiquotes(antiquotes)) =>
-              Some((name, symbols, antiquotes))
+          (props, props, props, props) match {
+            case (Name(name), Symbols(symbols), Antiquotes(antiquotes), Delimited(delimited)) =>
+              Some((name, symbols, antiquotes, delimited))
             case _ => None
           }
         case _ => None
--- a/src/Pure/PIDE/markup_tree.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/PIDE/markup_tree.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -51,10 +51,10 @@
   {
     def markup: List[XML.Elem] = rev_markup.reverse
 
-    def filter_markup(pred: String => Boolean): List[XML.Elem] =
+    def filter_markup(elements: Document.Elements): List[XML.Elem] =
     {
       var result: List[XML.Elem] = Nil
-      for { elem <- rev_markup; if (pred(elem.name)) }
+      for { elem <- rev_markup; if (elements(elem.name)) }
         result ::= elem
       result.toList
     }
@@ -194,7 +194,7 @@
   def to_XML(text: CharSequence): XML.Body =
     to_XML(Text.Range(0, text.length), text, (_: XML.Elem) => true)
 
-  def cumulate[A](root_range: Text.Range, root_info: A, elements: String => Boolean,
+  def cumulate[A](root_range: Text.Range, root_info: A, elements: Document.Elements,
     result: (A, Text.Markup) => Option[A]): List[Text.Info[A]] =
   {
     def results(x: A, entry: Entry): Option[A] =
--- a/src/Pure/PIDE/protocol.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/PIDE/protocol.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -77,11 +77,11 @@
   def command_status(markups: List[Markup]): Status =
     (Status.init /: markups)(command_status(_, _))
 
-  val command_status_elements: Set[String] =
-    Set(Markup.ACCEPTED, Markup.FORKED, Markup.JOINED, Markup.RUNNING,
+  val command_status_elements =
+    Document.Elements(Markup.ACCEPTED, Markup.FORKED, Markup.JOINED, Markup.RUNNING,
       Markup.FINISHED, Markup.FAILED)
 
-  val status_elements: Set[String] =
+  val status_elements =
     command_status_elements + Markup.WARNING + Markup.ERROR
 
 
@@ -165,7 +165,8 @@
 
   /* result messages */
 
-  private val clean_elements = Set(Markup.REPORT, Markup.NO_REPORT)
+  private val clean_elements =
+    Document.Elements(Markup.REPORT, Markup.NO_REPORT)
 
   def clean_message(body: XML.Body): XML.Body =
     body filter {
@@ -276,7 +277,7 @@
   /* reported positions */
 
   private val position_elements =
-    Set(Markup.BINDING, Markup.ENTITY, Markup.REPORT, Markup.POSITION)
+    Document.Elements(Markup.BINDING, Markup.ENTITY, Markup.REPORT, Markup.POSITION)
 
   def message_positions(
     command_id: Document_ID.Command,
@@ -288,8 +289,8 @@
       props match {
         case Position.Reported(id, file_name, raw_range)
         if (id == command_id || id == alt_id) && file_name == chunk.file_name =>
-          chunk.decode(raw_range).try_restrict(chunk.range) match {
-            case Some(range) if !range.is_singularity => set + range
+          chunk.incorporate(raw_range) match {
+            case Some(range) => set + range
             case _ => set
           }
         case _ => set
--- a/src/Pure/Syntax/syntax.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/Syntax/syntax.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -14,10 +14,10 @@
   val ambiguity_warning: bool Config.T
   val ambiguity_limit_raw: Config.raw
   val ambiguity_limit: int Config.T
-  val read_token: string -> Symbol_Pos.T list * Position.T
   val read_token_pos: string -> Position.T
+  val read_token: string -> Symbol_Pos.source
   val parse_token: Proof.context -> (XML.tree list -> 'a) ->
-    Markup.T -> (Symbol_Pos.T list * Position.T -> 'a) -> string -> 'a
+    (bool -> Markup.T) -> (Symbol_Pos.T list * Position.T -> 'a) -> string -> 'a
   val parse_sort: Proof.context -> string -> sort
   val parse_typ: Proof.context -> string -> typ
   val parse_term: Proof.context -> string -> term
@@ -159,26 +159,33 @@
 
 (* outer syntax token -- with optional YXML content *)
 
+local
+
 fun token_position (XML.Elem ((name, props), _)) =
-      if name = Markup.tokenN then Position.of_properties props
-      else Position.none
-  | token_position (XML.Text _) = Position.none;
+      if name = Markup.tokenN
+      then (Markup.is_delimited props, Position.of_properties props)
+      else (false, Position.none)
+  | token_position (XML.Text _) = (false, Position.none);
 
-fun explode_token tree =
+fun token_source tree =
   let
     val text = XML.content_of [tree];
-    val pos = token_position tree;
-  in (Symbol_Pos.explode (text, pos), pos) end;
+    val (delimited, pos) = token_position tree;
+  in {delimited = delimited, text = text, pos = pos} end;
 
-fun read_token str = explode_token (YXML.parse str handle Fail msg => error msg);
-fun read_token_pos str = token_position (YXML.parse str handle Fail msg => error msg);
+in
+
+fun read_token_pos str = #2 (token_position (YXML.parse str handle Fail msg => error msg));
+
+fun read_token str = token_source (YXML.parse str handle Fail msg => error msg);
 
 fun parse_token ctxt decode markup parse str =
   let
     fun parse_tree tree =
       let
-        val (syms, pos) = explode_token tree;
-        val _ = Context_Position.report ctxt pos markup;
+        val {delimited, text, pos} = token_source tree;
+        val syms = Symbol_Pos.explode (text, pos);
+        val _ = Context_Position.report ctxt pos (markup delimited);
       in parse (syms, pos) end;
   in
     (case YXML.parse_body str handle Fail msg => error msg of
@@ -188,6 +195,8 @@
     | body => decode body)
   end;
 
+end;
+
 
 (* (un)parsing *)
 
--- a/src/Pure/Syntax/syntax_phases.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/Syntax/syntax_phases.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -440,7 +440,8 @@
           else decode_appl ps asts
       | decode ps (Ast.Appl asts) = decode_appl ps asts;
 
-    val (syms, pos) = Syntax.read_token str;
+    val {text, pos, ...} = Syntax.read_token str;
+    val syms = Symbol_Pos.explode (text, pos);
     val ast =
       parse_asts ctxt true root (syms, pos)
       |> uncurry (report_result ctxt pos)
@@ -749,8 +750,8 @@
 
 in
 
-val unparse_sort = unparse_t sort_to_ast Printer.pretty_typ_ast Markup.language_sort;
-val unparse_typ = unparse_t typ_to_ast Printer.pretty_typ_ast Markup.language_type;
+val unparse_sort = unparse_t sort_to_ast Printer.pretty_typ_ast (Markup.language_sort false);
+val unparse_typ = unparse_t typ_to_ast Printer.pretty_typ_ast (Markup.language_type false);
 
 fun unparse_term ctxt =
   let
@@ -760,7 +761,7 @@
   in
     unparse_t (term_to_ast idents (is_some o Syntax.lookup_const syn))
       (Printer.pretty_term_ast (not (Pure_Thy.old_appl_syntax thy)))
-      Markup.language_term ctxt
+      (Markup.language_term false) ctxt
   end;
 
 end;
--- a/src/Pure/Thy/latex.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/Thy/latex.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -121,8 +121,8 @@
       enclose "{\\isacharbackquoteopen}" "{\\isacharbackquoteclose}" (output_syms s)
     else if Token.is_kind Token.Verbatim tok then
       let
-        val (txt, pos) = Token.source_position_of tok;
-        val ants = Antiquote.read (Symbol_Pos.explode (txt, pos), pos);
+        val {text, pos, ...} = Token.source_position_of tok;
+        val ants = Antiquote.read (Symbol_Pos.explode (text, pos), pos);
         val out = implode (map output_syms_antiq ants);
       in enclose "{\\isacharverbatimopen}" "{\\isacharverbatimclose}" out end
     else if Token.is_kind Token.Cartouche tok then
--- a/src/Pure/Thy/thy_output.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/Thy/thy_output.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -25,7 +25,7 @@
   datatype markup = Markup | MarkupEnv | Verbatim
   val eval_antiq: Scan.lexicon -> Toplevel.state -> Antiquote.antiq -> string
   val eval_antiquote: Scan.lexicon -> Toplevel.state -> Symbol_Pos.text * Position.T -> string
-  val check_text: Symbol_Pos.text * Position.T -> Toplevel.state -> unit
+  val check_text: Symbol_Pos.source -> Toplevel.state -> unit
   val present_thy: Scan.lexicon -> (string -> string list) -> (markup -> string -> bool) ->
     (Toplevel.transition * Toplevel.state) list -> Token.T list -> Buffer.T
   val pretty_text: Proof.context -> string -> Pretty.T
@@ -184,10 +184,10 @@
   end;
 
 
-fun check_text (txt, pos) state =
- (Position.report pos Markup.language_document;
+fun check_text {delimited, text, pos} state =
+ (Position.report pos (Markup.language_document delimited);
   if Toplevel.is_skipped_proof state then ()
-  else ignore (eval_antiquote (#1 (Keyword.get_lexicons ())) state (txt, pos)));
+  else ignore (eval_antiquote (#1 (Keyword.get_lexicons ())) state (text, pos)));
 
 
 
@@ -360,9 +360,9 @@
         Parse.position (Scan.one (Token.is_command andf is_markup mark o Token.content_of)) --
       Scan.repeat tag --
       Parse.!!!! ((improper -- locale -- improper) |-- Parse.document_source --| improper_end)
-      >> (fn (((tok, pos), tags), txt) =>
+      >> (fn (((tok, pos'), tags), {text, pos, ...}) =>
         let val name = Token.content_of tok
-        in (SOME (name, pos, tags), (mk (name, txt), (flag, d))) end));
+        in (SOME (name, pos', tags), (mk (name, (text, pos)), (flag, d))) end));
 
     val command = Scan.peek (fn d =>
       Parse.position (Scan.one (Token.is_command)) --
@@ -373,7 +373,7 @@
 
     val cmt = Scan.peek (fn d =>
       Parse.$$$ "--" |-- Parse.!!!! (improper |-- Parse.document_source)
-      >> (fn txt => (NONE, (MarkupToken ("cmt", txt), ("", d)))));
+      >> (fn {text, pos, ...} => (NONE, (MarkupToken ("cmt", (text, pos)), ("", d)))));
 
     val other = Scan.peek (fn d =>
        Parse.not_eof >> (fn tok => (NONE, (BasicToken tok, ("", d)))));
@@ -467,8 +467,12 @@
 fun pretty_text ctxt =
   Pretty.chunks o map Pretty.str o map (tweak_line ctxt) o split_lines;
 
-fun pretty_text_report ctxt (s, pos) =
-  (Context_Position.report ctxt pos Markup.language_text; pretty_text ctxt s);
+fun pretty_text_report ctxt source =
+  let
+    val {delimited, pos, ...} = source;
+    val _ = Context_Position.report ctxt pos (Markup.language_text delimited);
+    val (s, _) = Symbol_Pos.source_content source;
+  in pretty_text ctxt s end;
 
 fun pretty_term ctxt t = Syntax.pretty_term (Variable.auto_fixes t ctxt) t;
 
@@ -574,7 +578,7 @@
   basic_entity (Binding.name "typ") Args.typ_abbrev Syntax.pretty_typ #>
   basic_entity (Binding.name "class") (Scan.lift Args.name_inner_syntax) pretty_class #>
   basic_entity (Binding.name "type") (Scan.lift Args.name) pretty_type #>
-  basic_entity (Binding.name "text") (Scan.lift (Parse.position Args.name)) pretty_text_report #>
+  basic_entity (Binding.name "text") (Scan.lift Args.name_source_position) pretty_text_report #>
   basic_entities (Binding.name "prf") Attrib.thms (pretty_prf false) #>
   basic_entities (Binding.name "full_prf") Attrib.thms (pretty_prf true) #>
   basic_entity (Binding.name "theory") (Scan.lift (Parse.position Args.name)) pretty_theory);
@@ -638,15 +642,18 @@
 local
 
 fun ml_text name ml = antiquotation name (Scan.lift Args.name_source_position)
-  (fn {context, ...} => fn (txt, pos) =>
-   (ML_Context.eval_in (SOME context) false pos (ml pos txt);
-    Symbol_Pos.content (Symbol_Pos.explode (txt, pos))
+  (fn {context, ...} => fn source =>
+   (ML_Context.eval_in (SOME context) false (#pos source) (ml source);
+    Symbol_Pos.source_content source
+    |> #1
     |> (if Config.get context quotes then quote else I)
     |> (if Config.get context display then enclose "\\begin{verbatim}\n" "\n\\end{verbatim}"
         else verb_text)));
 
-fun ml_enclose bg en pos txt =
-  ML_Lex.read Position.none bg @ ML_Lex.read pos txt @ ML_Lex.read Position.none en;
+fun ml_enclose bg en source =
+  ML_Lex.read Position.none bg @
+  ML_Lex.read_source source @
+  ML_Lex.read Position.none en;
 
 in
 
@@ -658,11 +665,11 @@
     (ml_enclose "functor XXX() = struct structure XX = " " end;") #>
 
   ml_text (Binding.name "ML_functor")   (* FIXME formal treatment of functor name (!?) *)
-    (fn pos => fn txt =>
+    (fn source =>
       ML_Lex.read Position.none ("ML_Env.check_functor " ^
-        ML_Syntax.print_string (Symbol_Pos.content (Symbol_Pos.explode (txt, pos))))) #>
+        ML_Syntax.print_string (#1 (Symbol_Pos.source_content source)))) #>
 
-  ml_text (Binding.name "ML_text") (K (K [])));
+  ml_text (Binding.name "ML_text") (K []));
 
 end;
 
--- a/src/Pure/Thy/thy_syntax.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/Thy/thy_syntax.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -44,14 +44,15 @@
 
 fun reports_of_token tok =
   let
+    val {text, pos, ...} = Token.source_position_of tok;
     val malformed_symbols =
-      Symbol_Pos.explode (Token.source_position_of tok)
+      Symbol_Pos.explode (text, pos)
       |> map_filter (fn (sym, pos) =>
           if Symbol.is_malformed sym
           then SOME ((pos, Markup.bad), "Malformed symbolic character") else NONE);
     val is_malformed = Token.is_error tok orelse not (null malformed_symbols);
-    val (markup, txt) = Token.markup tok;
-    val reports = ((Token.pos_of tok, markup), txt) :: malformed_symbols;
+    val (markup, msg) = Token.markup tok;
+    val reports = ((Token.pos_of tok, markup), msg) :: malformed_symbols;
   in (is_malformed, reports) end;
 
 in
--- a/src/Pure/Tools/rail.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/Tools/rail.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -192,10 +192,11 @@
 
 in
 
-fun read ctxt (s, pos) =
+fun read ctxt (source: Symbol_Pos.source) =
   let
+    val {text, pos, ...} = source;
     val _ = Context_Position.report ctxt pos Markup.language_rail;
-    val toks = tokenize (Symbol_Pos.explode (s, pos));
+    val toks = tokenize (Symbol_Pos.explode (text, pos));
     val _ = Context_Position.reports ctxt (maps reports_of_token toks);
   in #1 (Scan.error (Scan.finite stopper (rules --| !!! (Scan.ahead (Scan.one is_eof)))) toks) end;
 
--- a/src/Pure/pure_syn.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Pure/pure_syn.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -24,9 +24,10 @@
         let
           val [{src_path, lines, digest, pos}] = files (Context.theory_of gthy);
           val provide = Thy_Load.provide (src_path, digest);
+          val source = {delimited = true, text = cat_lines lines, pos = pos};
         in
           gthy
-          |> ML_Context.exec (fn () => ML_Context.eval_text true pos (cat_lines lines))
+          |> ML_Context.exec (fn () => ML_Context.eval_source true source)
           |> Local_Theory.propagate_ml_env
           |> Context.mapping provide (Local_Theory.background_theory provide)
         end)));
--- a/src/Tools/Code/code_thingol.ML	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/Code/code_thingol.ML	Sat Mar 01 23:48:55 2014 +0100
@@ -882,7 +882,7 @@
       (fn thy'' => not (Sign.declared_const thy'' c)) (Theory.parents_of thy');
     fun consts_of_select thy' = filter (belongs_here thy') (consts_of thy');
     fun read_const_expr str =
-      (case Syntax.parse_token ctxt (K NONE) Markup.empty (SOME o Symbol_Pos.implode o #1) str of
+      (case Syntax.parse_token ctxt (K NONE) (K Markup.empty) (SOME o Symbol_Pos.implode o #1) str of
         SOME "_" => ([], consts_of thy)
       | SOME s =>
           if String.isSuffix "._" s
--- a/src/Tools/jEdit/lib/Tools/jedit	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/lib/Tools/jedit	Sat Mar 01 23:48:55 2014 +0100
@@ -16,6 +16,7 @@
   "src/documentation_dockable.scala"
   "src/find_dockable.scala"
   "src/fold_handling.scala"
+  "src/font_info.scala"
   "src/graphview_dockable.scala"
   "src/info_dockable.scala"
   "src/isabelle.scala"
--- a/src/Tools/jEdit/src/actions.xml	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/actions.xml	Sat Mar 01 23:48:55 2014 +0100
@@ -34,27 +34,27 @@
 	</ACTION>
 	<ACTION NAME="isabelle.reset-font-size">
 	  <CODE>
-	    isabelle.jedit.Isabelle.reset_font_size(view);
+	    isabelle.jedit.Isabelle.reset_font_size();
 	  </CODE>
 	</ACTION>
 	<ACTION NAME="isabelle.increase-font-size">
 	  <CODE>
-	    isabelle.jedit.Isabelle.increase_font_size(view);
+	    isabelle.jedit.Isabelle.increase_font_size();
 	  </CODE>
 	</ACTION>
 	<ACTION NAME="isabelle.increase-font-size2">
 	  <CODE>
-	    isabelle.jedit.Isabelle.increase_font_size(view);
+	    isabelle.jedit.Isabelle.increase_font_size();
 	  </CODE>
 	</ACTION>
 	<ACTION NAME="isabelle.decrease-font-size">
 	  <CODE>
-	    isabelle.jedit.Isabelle.decrease_font_size(view);
+	    isabelle.jedit.Isabelle.decrease_font_size();
 	  </CODE>
 	</ACTION>
 	<ACTION NAME="isabelle.decrease-font-size2">
 	  <CODE>
-	    isabelle.jedit.Isabelle.decrease_font_size(view);
+	    isabelle.jedit.Isabelle.decrease_font_size();
 	  </CODE>
 	</ACTION>
 	<ACTION NAME="isabelle.complete">
--- a/src/Tools/jEdit/src/completion_popup.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/completion_popup.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -150,7 +150,7 @@
           val context =
             (opt_rendering orElse PIDE.document_view(text_area).map(_.get_rendering()) match {
               case Some(rendering) =>
-                rendering.language_context(before_caret_range(rendering))
+                rendering.completion_language(before_caret_range(rendering))
               case None => None
             }) getOrElse syntax.language_context
 
@@ -196,7 +196,8 @@
       def open_popup(result: Completion.Result)
       {
         val font =
-          painter.getFont.deriveFont(Rendering.font_size("jedit_popup_font_scale"))
+          painter.getFont.deriveFont(
+            Font_Info.main_size(PIDE.options.real("jedit_popup_font_scale")))
 
         val range = result.range
         def invalidate(): Unit = JEdit_Lib.invalidate_range(text_area, range)
--- a/src/Tools/jEdit/src/find_dockable.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/find_dockable.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -56,8 +56,8 @@
   {
     Swing_Thread.require()
 
-    pretty_text_area.resize(Rendering.font_family(),
-      (Rendering.font_size("jedit_font_scale") * zoom_factor / 100).round)
+    pretty_text_area.resize(
+      Font_Info.main(PIDE.options.real("jedit_font_scale") * zoom_factor / 100))
   }
 
   private val delay_resize =
@@ -121,7 +121,7 @@
     { val max = getPreferredSize; max.width = Integer.MAX_VALUE; setMaximumSize(max) }
     setColumns(40)
     setToolTipText(query_label.tooltip)
-    setFont(GUI.imitate_font(Rendering.font_family(), getFont, 1.2))
+    setFont(GUI.imitate_font(Font_Info.main_family(), getFont, 1.2))
   }
 
   private case class Context_Entry(val name: String, val description: String)
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Tools/jEdit/src/font_info.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -0,0 +1,94 @@
+/*  Title:      Tools/jEdit/src/font_info.scala
+    Author:     Makarius
+
+Font information, derived from main jEdit view font.
+*/
+
+package isabelle.jedit
+
+
+import isabelle._
+
+
+import java.awt.Font
+
+import org.gjt.sp.jedit.{jEdit, View}
+
+
+object Font_Info
+{
+  /* size range */
+
+  val min_size = 5
+  val max_size = 250
+
+  def restrict_size(size: Float): Float = size max min_size min max_size
+
+
+  /* main jEdit font */
+
+  def main_family(): String = jEdit.getProperty("view.font")
+
+  def main_size(scale: Double = 1.0): Float =
+    restrict_size(jEdit.getIntegerProperty("view.fontsize", 16).toFloat * scale.toFloat)
+
+  def main(scale: Double = 1.0): Font_Info =
+    Font_Info(main_family(), main_size(scale))
+
+
+  /* incremental size change */
+
+  object main_change
+  {
+    private def change_size(change: Float => Float)
+    {
+      Swing_Thread.require()
+
+      val size0 = main_size()
+      val size = restrict_size(change(size0)).round
+      if (size != size0) {
+        jEdit.setIntegerProperty("view.fontsize", size)
+        jEdit.propertiesChanged()
+        jEdit.saveSettings()
+        jEdit.getActiveView().getStatus.setMessageAndClear("Text font size: " + size)
+      }
+    }
+
+    // owned by Swing thread
+    private var steps = 0
+    private val delay = Swing_Thread.delay_last(PIDE.options.seconds("editor_input_delay"))
+    {
+      change_size(size =>
+        {
+          var i = size.round
+          while (steps != 0 && i > 0) {
+            if (steps > 0)
+              { i += (i / 10) max 1; steps -= 1 }
+            else
+              { i -= (i / 10) max 1; steps += 1 }
+          }
+          steps = 0
+          i.toFloat
+        })
+    }
+
+    def step(i: Int)
+    {
+      steps += i
+      delay.invoke()
+    }
+
+    def reset(size: Float)
+    {
+      delay.revoke()
+      steps = 0
+      change_size(_ => size)
+    }
+  }
+}
+
+sealed case class Font_Info(family: String, size: Float)
+{
+  def font: Font = new Font(family, Font.PLAIN, size.round)
+}
+
--- a/src/Tools/jEdit/src/info_dockable.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/info_dockable.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -76,8 +76,8 @@
   {
     Swing_Thread.require()
 
-    pretty_text_area.resize(Rendering.font_family(),
-      (Rendering.font_size("jedit_font_scale") * zoom_factor / 100).round)
+    pretty_text_area.resize(
+      Font_Info.main(PIDE.options.real("jedit_font_scale") * zoom_factor / 100))
   }
 
 
--- a/src/Tools/jEdit/src/isabelle.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/isabelle.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -186,14 +186,11 @@
 
   /* font size */
 
-  def reset_font_size(view: View): Unit =
-    Rendering.font_size_change(view, _ => PIDE.options.int("jedit_reset_font_size"))
-
-  def increase_font_size(view: View): Unit =
-    Rendering.font_size_change(view, i => i + ((i / 10) max 1))
-
-  def decrease_font_size(view: View): Unit =
-    Rendering.font_size_change(view, i => i - ((i / 10) max 1))
+  def reset_font_size() {
+    Font_Info.main_change.reset(PIDE.options.int("jedit_reset_font_size").toFloat)
+  }
+  def increase_font_size() { Font_Info.main_change.step(1) }
+  def decrease_font_size() { Font_Info.main_change.step(-1) }
 
 
   /* structured edits */
--- a/src/Tools/jEdit/src/isabelle_sidekick.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/isabelle_sidekick.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -30,7 +30,7 @@
     protected var _end = int_to_pos(end)
     override def getIcon: Icon = null
     override def getShortString: String =
-      "<html><span style=\"font-family: " + Rendering.font_family() + ";\">" +
+      "<html><span style=\"font-family: " + Font_Info.main_family() + ";\">" +
       HTML.encode(_name) + "</span></html>"
     override def getLongString: String = _name
     override def getName: String = _name
--- a/src/Tools/jEdit/src/jedit_editor.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/jedit_editor.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -156,7 +156,7 @@
   override def hyperlink_file(name: String, line: Int = 0, column: Int = 0): Hyperlink =
     new Hyperlink { def follow(view: View) = goto(view, name, line, column) }
 
-  override def hyperlink_command(snapshot: Document.Snapshot, command: Command, offset: Int = 0)
+  override def hyperlink_command(snapshot: Document.Snapshot, command: Command, raw_offset: Int = 0)
     : Option[Hyperlink] =
   {
     if (snapshot.is_outdated) None
@@ -167,8 +167,8 @@
           val file_name = command.node_name.node
           val sources =
             node.commands.iterator.takeWhile(_ != command).map(_.source) ++
-              (if (offset == 0) Iterator.empty
-               else Iterator.single(command.source(Text.Range(0, command.decode(offset)))))
+              (if (raw_offset == 0) Iterator.empty
+               else Iterator.single(command.source(Text.Range(0, command.decode(raw_offset)))))
           val (line, column) = ((1, 1) /: sources)(Symbol.advance_line_column)
           Some(new Hyperlink { def follow(view: View) { goto(view, file_name, line, column) } })
       }
--- a/src/Tools/jEdit/src/output_dockable.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/output_dockable.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -41,8 +41,8 @@
   {
     Swing_Thread.require()
 
-    pretty_text_area.resize(Rendering.font_family(),
-      (Rendering.font_size("jedit_font_scale") * zoom_factor / 100).round)
+    pretty_text_area.resize(
+      Font_Info.main(PIDE.options.real("jedit_font_scale") * zoom_factor / 100))
   }
 
   private def handle_update(follow: Boolean, restriction: Option[Set[Command]])
--- a/src/Tools/jEdit/src/pretty_text_area.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/pretty_text_area.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -61,8 +61,7 @@
 
   Swing_Thread.require()
 
-  private var current_font_family = "Dialog"
-  private var current_font_size: Int = 12
+  private var current_font_info: Font_Info = Font_Info.main()
   private var current_body: XML.Body = Nil
   private var current_base_snapshot = Document.Snapshot.init
   private var current_base_results = Command.Results.empty
@@ -80,18 +79,19 @@
   {
     Swing_Thread.require()
 
-    val font = new Font(current_font_family, Font.PLAIN, current_font_size)
+    val font = current_font_info.font
     getPainter.setFont(font)
     getPainter.setAntiAlias(new AntiAlias(jEdit.getProperty("view.antiAlias")))
     getPainter.setFractionalFontMetricsEnabled(jEdit.getBooleanProperty("view.fracFontMetrics"))
-    getPainter.setStyles(SyntaxUtilities.loadStyles(current_font_family, current_font_size))
+    getPainter.setStyles(
+      SyntaxUtilities.loadStyles(current_font_info.family, current_font_info.size.round))
 
     val fold_line_style = new Array[SyntaxStyle](4)
     for (i <- 0 to 3) {
       fold_line_style(i) =
         SyntaxUtilities.parseStyle(
           jEdit.getProperty("view.style.foldLine." + i),
-          current_font_family, current_font_size, true)
+          current_font_info.family, current_font_info.size.round, true)
     }
     getPainter.setFoldLineStyle(fold_line_style)
 
@@ -139,12 +139,11 @@
     }
   }
 
-  def resize(font_family: String, font_size: Int)
+  def resize(font_info: Font_Info)
   {
     Swing_Thread.require()
 
-    current_font_family = font_family
-    current_font_size = font_size
+    current_font_info = font_info
     refresh()
   }
 
--- a/src/Tools/jEdit/src/pretty_tooltip.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/pretty_tooltip.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -199,8 +199,7 @@
     }
   })
 
-  pretty_text_area.resize(Rendering.font_family(),
-    Rendering.font_size("jedit_popup_font_scale").round)
+  pretty_text_area.resize(Font_Info.main(PIDE.options.real("jedit_popup_font_scale")))
 
 
   /* main content */
--- a/src/Tools/jEdit/src/rendering.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/rendering.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -41,27 +41,6 @@
     Markup.ERROR -> error_pri, Markup.ERROR_MESSAGE -> error_pri)
 
 
-  /* jEdit font */
-
-  def font_family(): String = jEdit.getProperty("view.font")
-
-  private def view_font_size(): Int = jEdit.getIntegerProperty("view.fontsize", 16)
-  private val font_size0 = 5
-  private val font_size1 = 250
-
-  def font_size(scale: String): Float =
-    (view_font_size() * PIDE.options.real(scale)).toFloat max font_size0 min font_size1
-
-  def font_size_change(view: View, change: Int => Int)
-  {
-    val size = change(view_font_size()) max font_size0 min font_size1
-    jEdit.setIntegerProperty("view.fontsize", size)
-    jEdit.propertiesChanged()
-    jEdit.saveSettings()
-    view.getStatus.setMessageAndClear("Text font size: " + size)
-  }
-
-
   /* popup window bounds */
 
   def popup_bounds: Double = (PIDE.options.real("jedit_popup_bounds") max 0.2) min 0.8
@@ -150,28 +129,29 @@
 
   /* markup elements */
 
-  private val completion_names_elements = Set(Markup.COMPLETION)
+  private val completion_names_elements =
+    Document.Elements(Markup.COMPLETION)
 
-  private val language_context_elements =
-    Set(Markup.STRING, Markup.ALTSTRING, Markup.VERBATIM,
+  private val completion_language_elements =
+    Document.Elements(Markup.STRING, Markup.ALTSTRING, Markup.VERBATIM,
       Markup.CARTOUCHE, Markup.COMMENT, Markup.LANGUAGE,
       Markup.ML_STRING, Markup.ML_COMMENT)
 
   private val highlight_elements =
-    Set(Markup.LANGUAGE, Markup.ML_TYPING, Markup.TOKEN_RANGE,
+    Document.Elements(Markup.LANGUAGE, Markup.ML_TYPING, Markup.TOKEN_RANGE,
       Markup.ENTITY, Markup.PATH, Markup.URL, Markup.SORTING,
       Markup.TYPING, Markup.FREE, Markup.SKOLEM, Markup.BOUND,
       Markup.VAR, Markup.TFREE, Markup.TVAR)
 
   private val hyperlink_elements =
-    Set(Markup.ENTITY, Markup.PATH, Markup.POSITION, Markup.URL)
+    Document.Elements(Markup.ENTITY, Markup.PATH, Markup.POSITION, Markup.URL)
 
   private val active_elements =
-    Set(Markup.DIALOG, Markup.BROWSER, Markup.GRAPHVIEW,
+    Document.Elements(Markup.DIALOG, Markup.BROWSER, Markup.GRAPHVIEW,
       Markup.SENDBACK, Markup.SIMP_TRACE)
 
   private val tooltip_message_elements =
-    Set(Markup.WRITELN, Markup.WARNING, Markup.ERROR, Markup.BAD)
+    Document.Elements(Markup.WRITELN, Markup.WARNING, Markup.ERROR, Markup.BAD)
 
   private val tooltip_descriptions =
     Map(
@@ -184,22 +164,23 @@
       Markup.TVAR -> "schematic type variable")
 
   private val tooltip_elements =
-    Set(Markup.LANGUAGE, Markup.TIMING, Markup.ENTITY, Markup.SORTING,
+    Document.Elements(Markup.LANGUAGE, Markup.TIMING, Markup.ENTITY, Markup.SORTING,
       Markup.TYPING, Markup.ML_TYPING, Markup.PATH, Markup.URL) ++
-      tooltip_descriptions.keys
+    Document.Elements(tooltip_descriptions.keySet)
 
   private val gutter_elements =
-    Set(Markup.WRITELN, Markup.WARNING, Markup.ERROR)
+    Document.Elements(Markup.WRITELN, Markup.WARNING, Markup.ERROR)
 
   private val squiggly_elements =
-    Set(Markup.WRITELN, Markup.WARNING, Markup.ERROR)
+    Document.Elements(Markup.WRITELN, Markup.WARNING, Markup.ERROR)
 
   private val line_background_elements =
-    Set(Markup.WRITELN_MESSAGE, Markup.TRACING_MESSAGE,
+    Document.Elements(Markup.WRITELN_MESSAGE, Markup.TRACING_MESSAGE,
       Markup.WARNING_MESSAGE, Markup.ERROR_MESSAGE,
       Markup.INFORMATION)
 
-  private val separator_elements = Set(Markup.SEPARATOR)
+  private val separator_elements =
+    Document.Elements(Markup.SEPARATOR)
 
   private val background_elements =
     Protocol.command_status_elements + Markup.WRITELN_MESSAGE +
@@ -208,13 +189,14 @@
       active_elements
 
   private val foreground_elements =
-    Set(Markup.STRING, Markup.ALTSTRING, Markup.VERBATIM,
+    Document.Elements(Markup.STRING, Markup.ALTSTRING, Markup.VERBATIM,
       Markup.CARTOUCHE, Markup.ANTIQUOTED)
 
-  private val bullet_elements = Set(Markup.BULLET)
+  private val bullet_elements =
+    Document.Elements(Markup.BULLET)
 
   private val fold_depth_elements =
-    Set(Markup.TEXT_FOLD, Markup.GOAL, Markup.SUBGOAL)
+    Document.Elements(Markup.TEXT_FOLD, Markup.GOAL, Markup.SUBGOAL)
 }
 
 
@@ -285,11 +267,12 @@
         }).headOption.map(_.info)
     }
 
-  def language_context(range: Text.Range): Option[Completion.Language_Context] =
-    snapshot.select(range, Rendering.language_context_elements, _ =>
+  def completion_language(range: Text.Range): Option[Completion.Language_Context] =
+    snapshot.select(range, Rendering.completion_language_elements, _ =>
       {
-        case Text.Info(_, XML.Elem(Markup.Language(language, symbols, antiquotes), _)) =>
-          Some(Completion.Language_Context(language, symbols, antiquotes))
+        case Text.Info(_, XML.Elem(Markup.Language(language, symbols, antiquotes, delimited), _)) =>
+          if (delimited) Some(Completion.Language_Context(language, symbols, antiquotes))
+          else None
         case Text.Info(_, elem)
         if elem.name == Markup.ML_STRING || elem.name == Markup.ML_COMMENT =>
           Some(Completion.Language_Context.ML_inner)
@@ -421,7 +404,7 @@
   def command_results(range: Text.Range): Command.Results =
   {
     val results =
-      snapshot.select[Command.Results](range, _ => true, command_state =>
+      snapshot.select[Command.Results](range, Document.Elements.full, command_state =>
         { case _ => Some(command_state.results) }).map(_.info)
     (Command.Results.empty /: results)(_ ++ _)
   }
@@ -503,7 +486,7 @@
             Some(add(prev, r, (true, pretty_typing("::", body))))
           case (prev, Text.Info(r, XML.Elem(Markup(Markup.ML_TYPING, _), body))) =>
             Some(add(prev, r, (false, pretty_typing("ML:", body))))
-          case (prev, Text.Info(r, XML.Elem(Markup.Language(language, _, _), _))) =>
+          case (prev, Text.Info(r, XML.Elem(Markup.Language(language, _, _, _), _))) =>
             Some(add(prev, r, (true, XML.Text("language: " + language))))
           case (prev, Text.Info(r, XML.Elem(Markup(name, _), _))) =>
             Rendering.tooltip_descriptions.get(name).
@@ -703,7 +686,8 @@
       Markup.ML_STRING -> inner_quoted_color,
       Markup.ML_COMMENT -> inner_comment_color)
 
-  private lazy val text_color_elements = text_colors.keySet
+  private lazy val text_color_elements =
+    Document.Elements(text_colors.keySet)
 
   def text_color(range: Text.Range, color: Color): List[Text.Info[Color]] =
   {
--- a/src/Tools/jEdit/src/simplifier_trace_dockable.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/simplifier_trace_dockable.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -84,7 +84,7 @@
   private def do_paint()
   {
     Swing_Thread.later {
-        text_area.resize(Rendering.font_family(), Rendering.font_size("jedit_font_scale").round)
+      text_area.resize(Font_Info.main(PIDE.options.real("jedit_font_scale")))
     }
   }
 
--- a/src/Tools/jEdit/src/simplifier_trace_window.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/simplifier_trace_window.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -181,7 +181,7 @@
   def do_paint()
   {
     Swing_Thread.later {
-      area.resize(Rendering.font_family(), Rendering.font_size("jedit_font_scale").round)
+      area.resize(Font_Info.main(PIDE.options.real("jedit_font_scale")))
     }
   }
 
--- a/src/Tools/jEdit/src/sledgehammer_dockable.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/sledgehammer_dockable.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -57,8 +57,8 @@
   {
     Swing_Thread.require()
 
-    pretty_text_area.resize(Rendering.font_family(),
-      (Rendering.font_size("jedit_font_scale") * zoom_factor / 100).round)
+    pretty_text_area.resize(
+      Font_Info.main(PIDE.options.real("jedit_font_scale") * zoom_factor / 100))
   }
 
   private val delay_resize =
--- a/src/Tools/jEdit/src/symbols_dockable.scala	Sat Mar 01 20:40:31 2014 +0100
+++ b/src/Tools/jEdit/src/symbols_dockable.scala	Sat Mar 01 23:48:55 2014 +0100
@@ -26,7 +26,7 @@
   private class Symbol_Component(val symbol: String) extends Button
   {
     private val decoded = Symbol.decode(symbol)
-    private val font_size = Rendering.font_size("jedit_font_scale").round
+    private val font_size = Font_Info.main_size(PIDE.options.real("jedit_font_scale")).round
 
     font =
       Symbol.fonts.get(symbol) match {