erts: Improve the documentation of the abstract format

1 files changed, 131 insertions, 109 deletions

diff --git a/erts/doc/src/absform.xml b/erts/doc/src/absform.xml
index 1c0c3e1319..3f47b3061b 100644
--- a/erts/doc/src/absform.xml
+++ b/erts/doc/src/absform.xml
@@ -4,7 +4,7 @@
 <chapter>
   <header>
     <copyright>
-      <year>2001</year><year>2015</year>
+      <year>2001</year><year>2016</year>
       <holder>Ericsson AB. All Rights Reserved.</holder>
     </copyright>
     <legalnotice>
@@ -80,12 +80,15 @@
        Rep(F) = <c>{attribute,LINE,import,{Mod,[{Fun_1,A_1}, ..., {Fun_k,A_k}]}}</c>.</item>
       <item>If F is an attribute <c>-export_type([Type_1/A_1, ..., Type_k/A_k])</c>, then
        Rep(F) = <c>{attribute,LINE,export_type,[{Type_1,A_1}, ..., {Type_k,A_k}]}</c>.</item>
+      <item>If F is an attribute <c>-optional_callbacks([Fun_1/A_1, ..., Fun_k/A_k])</c>, then
+       Rep(F) = <c>{attribute,LINE,optional_callbacks,[{Fun_1,A_1}, ..., {Fun_k,A_k}]}</c>.</item>
       <item>If F is an attribute <c>-compile(Options)</c>, then
        Rep(F) = <c>{attribute,LINE,compile,Options}</c>.</item>
       <item>If F is an attribute <c>-file(File,Line)</c>, then
        Rep(F) = <c>{attribute,LINE,file,{File,Line}}</c>.</item>
       <item>If F is a record declaration
-       <c>-record(Name,{V_1, ..., V_k})</c>, then Rep(F) =
+       <c>-record(Name,{V_1, ..., V_k})</c>,
+       where each <c>V_i</c> is a record field, then Rep(F) =
        <c>{attribute,LINE,record,{Name,[Rep(V_1), ..., Rep(V_k)]}}</c>.
        For Rep(V), see below.</item>
       <item>If F is a type declaration
@@ -173,12 +176,12 @@
 
   <section>
     <title>Patterns</title>
-    <p>If <c>Ps</c> is a sequence of patterns <c>P_1, ..., P_k</c>, then
+    <p>If Ps is a sequence of patterns <c>P_1, ..., P_k</c>, then
       Rep(Ps) = <c>[Rep(P_1), ..., Rep(P_k)]</c>. Such sequences occur as the
       list of arguments to a function or fun.</p>
     <p>Individual patterns are represented as follows:</p>
     <list type="bulleted">
-      <item>If P is an atomic literal L, then Rep(P) = Rep(L).</item>
+      <item>If P is an atomic literal <c>L</c>, then Rep(P) = Rep(L).</item>
       <item>If P is a compound pattern <c>P_1 = P_2</c>, then
        Rep(P) = <c>{match,LINE,Rep(P_1),Rep(P_2)}</c>.</item>
       <item>If P is a variable pattern <c>V</c>, then
@@ -211,6 +214,10 @@
       <c>{record,LINE,Name,[{record_field,LINE,Rep(Field_1),Rep(P_1)}, ..., {record_field,LINE,Rep(Field_k),Rep(P_k)}]}</c>.</item>
       <item>If P is <c>#Name.Field</c>, then
        Rep(P) = <c>{record_index,LINE,Name,Rep(Field)}</c>.</item>
+      <item>If P is a map pattern <c>#{A_1, ..., A_k}</c>, where each
+       <c>A_i</c> is an association <c>P_i_1 := P_i_2</c>, then Rep(P) =
+       <c>{map,LINE,[Rep(A_1), ..., Rep(A_k)]}</c>. For Rep(A), see
+       below.</item>
       <item>If P is <c>( P_0 )</c>, then
        Rep(P) = <c>Rep(P_0)</c>,
        that is, patterns cannot be distinguished from their bodies.</item>
@@ -221,11 +228,11 @@
 
   <section>
     <title>Expressions</title>
-    <p>A body B is a sequence of expressions <c>E_1, ..., E_k</c>, and
-      Rep(B) = <c>[Rep(E_1), ..., Rep(E_k)]</c>.</p>
+    <p>A body B is a nonempty sequence of expressions <c>E_1, ..., E_k</c>,
+      and Rep(B) = <c>[Rep(E_1), ..., Rep(E_k)]</c>.</p>
     <p>An expression E is one of the following alternatives:</p>
     <list type="bulleted">
-      <item>If P is an atomic literal <c>L</c>, then Rep(P) = Rep(L).</item>
+      <item>If E is an atomic literal <c>L</c>, then Rep(E) = Rep(L).</item>
       <item>If E is <c>P = E_0</c>, then
        Rep(E) = <c>{match,LINE,Rep(P),Rep(E_0)}</c>.</item>
       <item>If E is a variable <c>V</c>, then Rep(E) = <c>{var,LINE,A}</c>,
@@ -256,14 +263,16 @@
        Rep(E) = <c>{record_index,LINE,Name,Rep(Field)}</c>.</item>
       <item>If E is <c>E_0#Name.Field</c>, then
        Rep(E) = <c>{record_field,LINE,Rep(E_0),Name,Rep(Field)}</c>.</item>
-      <item>If E is <c>#{W_1, ..., W_k}</c> where each
-       <c>W_i</c> is a map assoc or exact field, then Rep(E) =
-       <c>{map,LINE,[Rep(W_1), ..., Rep(W_k)]}</c>. For Rep(W), see
+      <item>If E is a map creation <c>#{A_1, ..., A_k}</c>,
+       where each <c>A_i</c> is an association <c>E_i_1 => E_i_2</c>
+       or <c>E_i_1 := E_i_2</c>, then Rep(E) =
+       <c>{map,LINE,[Rep(A_1), ..., Rep(A_k)]}</c>. For Rep(A), see
        below.</item>
-      <item>If E is <c>E_0#{W_1, ..., W_k}</c> where
-       <c>W_i</c> is a map assoc or exact field, then Rep(E) =
-       <c>{map,LINE,Rep(E_0),[Rep(W_1), ..., Rep(W_k)]}</c>.
-       For Rep(W), see below.</item>
+      <item>If E is a map update <c>E_0#{A_1, ..., A_k}</c>,
+       where each <c>A_i</c> is an association <c>E_i_1 => E_i_2</c>
+       or <c>E_i_1 := E_i_2</c>, then Rep(E) =
+       <c>{map,LINE,Rep(E_0),[Rep(A_1), ..., Rep(A_k)]}</c>.
+       For Rep(A), see below.</item>
       <item>If E is <c>catch E_0</c>, then
        Rep(E) = <c>{'catch',LINE,Rep(E_0)}</c>.</item>
       <item>If E is <c>E_0(E_1, ..., E_k)</c>, then
@@ -271,15 +280,15 @@
       <item>If E is <c>E_m:E_0(E_1, ..., E_k)</c>, then Rep(E) =
       <c>{call,LINE,{remote,LINE,Rep(E_m),Rep(E_0)},[Rep(E_1), ...,  Rep(E_k)]}</c>.
       </item>
-      <item>If E is a list comprehension <c>[E_0 || W_1, ..., W_k]</c>,
-       where each <c>W_i</c> is a generator or a filter, then Rep(E) =
-       <c>{lc,LINE,Rep(E_0),[Rep(W_1), ..., Rep(W_k)]}</c>. For Rep(W), see
+      <item>If E is a list comprehension <c>[E_0 || Q_1, ..., Q_k]</c>,
+       where each <c>Q_i</c> is a qualifier, then Rep(E) =
+       <c>{lc,LINE,Rep(E_0),[Rep(Q_1), ..., Rep(Q_k)]}</c>. For Rep(Q), see
        below.</item>
       <item>If E is a binary comprehension
-       <c>&lt;&lt;E_0 || W_1, ..., W_k>></c>,
-       where each <c>W_i</c> is a generator or a filter, then
-       Rep(E) = <c>{bc,LINE,Rep(E_0),[Rep(W_1), ..., Rep(W_k)]}</c>.
-       For Rep(W), see below.</item>
+       <c>&lt;&lt;E_0 || Q_1, ..., Q_k>></c>,
+       where each <c>Q_i</c> is a qualifier, then
+       Rep(E) = <c>{bc,LINE,Rep(E_0),[Rep(Q_1), ..., Rep(Q_k)]}</c>.
+       For Rep(Q), see below.</item>
       <item>If E is <c>begin B end</c>, where <c>B</c> is a body, then
        Rep(E) = <c>{block,LINE,Rep(B)}</c>.</item>
       <item>If E is <c>if Ic_1 ; ... ; Ic_k  end</c>,
@@ -311,7 +320,7 @@
       <c>{'try',LINE,Rep(B),[],[Rep(Tc_1), ..., Rep(Tc_k)],Rep(A)}</c>.</item>
       <item>If E is <c>try B of Cc_1 ; ... ; Cc_k  catch Tc_1 ; ... ; Tc_n after A end</c>,
        where <c>B</c> and <c>A</c> are a bodies,
-       each <c>Cc_i</c> is a case clause and
+       each <c>Cc_i</c> is a case clause, and
        each <c>Tc_j</c> is a catch clause then
        Rep(E) =
       <c>{'try',LINE,Rep(B),[Rep(Cc_1), ..., Rep(Cc_k)],[Rep(Tc_1),  ..., Rep(Tc_n)],Rep(A)}</c>.</item>
@@ -328,10 +337,10 @@
        <c>{'fun',LINE,{function,Rep(Module),Rep(Name),Rep(Arity)}}</c>.
        (Before the R15 release: Rep(E) =
        <c>{'fun',LINE,{function,Module,Name,Arity}}</c>.)</item>
-      <item>If E is <c>fun Fc_1 ; ... ; Fc_k end</c>
+      <item>If E is <c>fun Fc_1 ; ... ; Fc_k end</c>,
        where each <c>Fc_i</c> is a function clause then Rep(E) =
       <c>{'fun',LINE,{clauses,[Rep(Fc_1), ..., Rep(Fc_k)]}}</c>.</item>
-      <item>If E is <c>fun Name Fc_1 ; ... ; Name Fc_k end</c>
+      <item>If E is <c>fun Name Fc_1 ; ... ; Name Fc_k end</c>,
        where <c>Name</c> is a variable and each
        <c>Fc_i</c> is a function clause then Rep(E) =
        <c>{named_fun,LINE,Name,[Rep(Fc_1), ..., Rep(Fc_k)]}</c>.
@@ -342,46 +351,43 @@
     </list>
 
     <section>
-      <title>Generators and Filters</title>
-      <p>When W is a generator or a filter (in the body of a list or
-       binary comprehension), then:</p>
+      <title>Qualifiers</title>
+      <p>A qualifier Q is one of the following alternatives:</p>
       <list type="bulleted">
-        <item>If W is a generator <c>P &lt;- E</c>, where <c>P</c> is
+        <item>If Q is a generator <c>P &lt;- E</c>, where <c>P</c> is
 	 a pattern and <c>E</c> is an expression, then
-         Rep(W) = <c>{generate,LINE,Rep(P),Rep(E)}</c>.</item>
-        <item>If W is a generator <c>P &lt;= E</c>, where <c>P</c> is
+         Rep(Q) = <c>{generate,LINE,Rep(P),Rep(E)}</c>.</item>
+        <item>If Q is a generator <c>P &lt;= E</c>, where <c>P</c> is
 	 a pattern and <c>E</c> is an expression, then
-         Rep(W) = <c>{b_generate,LINE,Rep(P),Rep(E)}</c>.</item>
-        <item>If W is a filter <c>E</c>, which is an expression, then
-         Rep(W) = <c>Rep(E)</c>.</item>
+         Rep(Q) = <c>{b_generate,LINE,Rep(P),Rep(E)}</c>.</item>
+        <item>If Q is a filter <c>E</c>, where <c>E</c> is an expression, then
+         Rep(Q) = <c>Rep(E)</c>.</item>
       </list>
     </section>
 
     <section>
       <title>Binary Element Type Specifiers</title>
       <p>A type specifier list TSL for a binary element is a sequence of type
-        specifiers <c>TS_1 - ... - TS_k</c>.
+        specifiers <c>TS_1 - ... - TS_k</c>, and
         Rep(TSL) = <c>[Rep(TS_1), ..., Rep(TS_k)]</c>.</p>
-      <p>When TS is a type specifier for a binary element, then:</p>
       <list type="bulleted">
-        <item>If TS is an atom <c>A</c>, then Rep(TS) = <c>A</c>.</item>
-        <item>If TS is a couple <c>A:Value</c> where <c>A</c> is an atom
-	 and <c>Value</c> is an integer, then Rep(TS) =
-	 <c>{A,Value}</c>.</item>
+        <item>If TS is a type specifier <c>A</c>, where <c>A</c> is an atom,
+	 then Rep(TS) = <c>A</c>.</item>
+        <item>If TS is a type specifier <c>A:Value</c>,
+	 where <c>A</c> is an atom and <c>Value</c> is an integer,
+	 then Rep(TS) = <c>{A,Value}</c>.</item>
       </list>
     </section>
 
     <section>
-      <title>Map Assoc and Exact Fields</title>
-      <p>When W is an assoc or exact field (in the body of a map), then:</p>
+      <title>Associations</title>
+      <p>An association A is one of the following alternatives:</p>
       <list type="bulleted">
-        <item>If W is an assoc field <c>K => V</c>, where
-         <c>K</c> and <c>V</c> are both expressions,
-         then Rep(W) = <c>{map_field_assoc,LINE,Rep(K),Rep(V)}</c>.
+	<item>If A is an association <c>K => V</c>,
+	 then Rep(A) = <c>{map_field_assoc,LINE,Rep(K),Rep(V)}</c>.
          </item>
-        <item>If W is an exact field <c>K := V</c>, where
-         <c>K</c> and <c>V</c> are both expressions,
-         then Rep(W) = <c>{map_field_exact,LINE,Rep(K),Rep(V)}</c>.
+	<item>If A is an association <c>K := V</c>,
+         then Rep(A) = <c>{map_field_exact,LINE,Rep(K),Rep(V)}</c>.
          </item>
       </list>
     </section>
@@ -393,37 +399,37 @@
       and catch clauses.</p>
     <p>A clause <c>C</c> is one of the following alternatives:</p>
     <list type="bulleted">
-      <item>If C is a function clause <c>( Ps ) -> B</c>
+      <item>If C is a function clause <c>( Ps ) -> B</c>,
        where <c>Ps</c> is a pattern sequence and <c>B</c> is a body, then
        Rep(C) = <c>{clause,LINE,Rep(Ps),[],Rep(B)}</c>.</item>
-      <item>If C is a function clause <c>( Ps ) when Gs -> B</c>
+      <item>If C is a function clause <c>( Ps ) when Gs -> B</c>,
        where <c>Ps</c> is a pattern sequence,
       <c>Gs</c> is a guard sequence and <c>B</c> is a body, then
        Rep(C) = <c>{clause,LINE,Rep(Ps),Rep(Gs),Rep(B)}</c>.</item>
-      <item>If C is an if clause <c>Gs -> B</c>
+      <item>If C is an if clause <c>Gs -> B</c>,
        where <c>Gs</c> is a guard sequence and <c>B</c> is a body, then
        Rep(C) = <c>{clause,LINE,[],Rep(Gs),Rep(B)}</c>.</item>
-      <item>If C is a case clause <c>P -> B</c>
+      <item>If C is a case clause <c>P -> B</c>,
        where <c>P</c> is a pattern and <c>B</c> is a body, then
        Rep(C) = <c>{clause,LINE,[Rep(P)],[],Rep(B)}</c>.</item>
-      <item>If C is a case clause <c>P when Gs -> B</c>
+      <item>If C is a case clause <c>P when Gs -> B</c>,
        where <c>P</c> is a pattern,
       <c>Gs</c> is a guard sequence and <c>B</c> is a body, then
        Rep(C) = <c>{clause,LINE,[Rep(P)],Rep(Gs),Rep(B)}</c>.</item>
-      <item>If C is a catch clause <c>P -> B</c>
+      <item>If C is a catch clause <c>P -> B</c>,
        where <c>P</c> is a pattern and <c>B</c> is a body, then
        Rep(C) = <c>{clause,LINE,[Rep({throw,P,_})],[],Rep(B)}</c>.</item>
-      <item>If C is a catch clause <c>X : P -> B</c>
+      <item>If C is a catch clause <c>X : P -> B</c>,
        where <c>X</c> is an atomic literal or a variable pattern,
-      <c>P</c> is a pattern and <c>B</c> is a body, then
+      <c>P</c> is a pattern, and <c>B</c> is a body, then
        Rep(C) = <c>{clause,LINE,[Rep({X,P,_})],[],Rep(B)}</c>.</item>
-      <item>If C is a catch clause <c>P when Gs -> B</c>
-       where <c>P</c> is a pattern, <c>Gs</c> is a guard sequence
+      <item>If C is a catch clause <c>P when Gs -> B</c>,
+       where <c>P</c> is a pattern, <c>Gs</c> is a guard sequence,
        and <c>B</c> is a body, then
        Rep(C) = <c>{clause,LINE,[Rep({throw,P,_})],Rep(Gs),Rep(B)}</c>.</item>
-      <item>If C is a catch clause <c>X : P when Gs -> B</c>
+      <item>If C is a catch clause <c>X : P when Gs -> B</c>,
        where <c>X</c> is an atomic literal or a variable pattern,
-      <c>P</c> is a pattern, <c>Gs</c> is a guard sequence
+      <c>P</c> is a pattern, <c>Gs</c> is a guard sequence,
        and <c>B</c> is a body, then
        Rep(C) = <c>{clause,LINE,[Rep({X,P,_})],Rep(Gs),Rep(B)}</c>.</item>
     </list>
@@ -439,7 +445,7 @@
       <c>[Rep(Gt_1), ..., Rep(Gt_k)]</c>.</p>
     <p>A guard test <c>Gt</c> is one of the following alternatives:</p>
     <list type="bulleted">
-      <item>If Gt is an atomic literal L, then Rep(Gt) = Rep(L).</item>
+      <item>If Gt is an atomic literal <c>L</c>, then Rep(Gt) = Rep(L).</item>
       <item>If Gt is a variable pattern <c>V</c>, then
        Rep(Gt) = <c>{var,LINE,A}</c>, where A is an atom with
        a printname consisting of the same characters as <c>V</c>.</item>
@@ -467,15 +473,21 @@
        Rep(Gt) = <c>{record_index,LINE,Name,Rep(Field)}</c>.</item>
       <item>If Gt is <c>Gt_0#Name.Field</c>, then
        Rep(Gt) = <c>{record_field,LINE,Rep(Gt_0),Name,Rep(Field)}</c>.</item>
+      <item>If Gt is a map creation <c>#{A_1, ..., A_k}</c>,
+       where each <c>A_i</c> is an association <c>Gt_i_1 => Gt_i_2</c>
+       or <c>Gt_i_1 := Gt_i_2</c>, then Rep(Gt) =
+       <c>{map,LINE,[Rep(A_1), ..., Rep(A_k)]}</c>. For Rep(A), see
+       above.</item>
+      <item>If Gt is a map update <c>Gt_0#{A_1, ..., A_k}</c>, where each
+       <c>A_i</c> is an association <c>Gt_i_1 => Gt_i_2</c>
+       or <c>Gt_i_1 := Gt_i_2</c>, then Rep(Gt) =
+       <c>{map,LINE,Rep(Gt_0),[Rep(A_1), ..., Rep(A_k)]}</c>.
+       For Rep(A), see above.</item>
       <item>If Gt is <c>A(Gt_1, ..., Gt_k)</c>, where <c>A</c> is an atom, then
        Rep(Gt) = <c>{call,LINE,Rep(A),[Rep(Gt_1), ..., Rep(Gt_k)]}</c>.</item>
       <item>If Gt is <c>A_m:A(Gt_1, ..., Gt_k)</c>, where <c>A_m</c> is
        the atom <c>erlang</c> and <c>A</c> is an atom or an operator, then
        Rep(Gt) = <c>{call,LINE,{remote,LINE,Rep(A_m),Rep(A)},[Rep(Gt_1), ..., Rep(Gt_k)]}</c>.</item>
-      <item>If Gt is <c>{A_m,A}(Gt_1, ..., Gt_k)</c>, where <c>A_m</c> is
-       the atom <c>erlang</c> and <c>A</c> is an atom or an operator, then
-       Rep(Gt) = <c>{call,LINE,Rep({A_m,A}),[Rep(Gt_1), ..., Rep(Gt_k)]}</c>.
-      </item>
       <item>If Gt is <c>( Gt_0 )</c>, then
        Rep(Gt) = <c>Rep(Gt_0)</c>, that is, parenthesized
        guard tests cannot be distinguished from their bodies.</item>
@@ -487,21 +499,20 @@
   <section>
     <title>Types</title>
     <list type="bulleted">
-      <item>If T is an annotated type <c>Anno :: Type</c>,
-       where <c>Anno</c> is a variable and
-       <c>Type</c> is a type, then Rep(T) =
-       <c>{ann_type,LINE,[Rep(Anno),Rep(Type)]}</c>.</item>
+      <item>If T is an annotated type <c>A :: T_0</c>,
+       where <c>A</c> is a variable, then Rep(T) =
+       <c>{ann_type,LINE,[Rep(A),Rep(T_0)]}</c>.</item>
       <item>If T is an atom or integer literal L, then Rep(T) = Rep(L).
       </item>
-      <item>If T is <c>L Op R</c>,
-       where <c>Op</c> is a binary operator and <c>L</c> and <c>R</c>
-       are types  (this is an occurrence of an expression that can be
-       evaluated to an integer at compile time), then
-       Rep(T) = <c>{op,LINE,Op,Rep(L),Rep(R)}</c>.</item>
-      <item>If T is <c>Op A</c>, where <c>Op</c> is a
-       unary operator and <c>A</c> is a type (this is an occurrence of
+      <item>If T is an operator type <c>T_1 Op T_2</c>,
+       where <c>Op</c> is a binary operator (this is an occurrence of
+       an expression that can be evaluated to an integer at compile
+       time), then
+       Rep(T) = <c>{op,LINE,Op,Rep(T_1),Rep(T_2)}</c>.</item>
+      <item>If T is an operator type <c>Op T_0</c>, where <c>Op</c> is a
+       unary operator (this is an occurrence of
        an expression that can be evaluated to an integer at compile time),
-       then Rep(T) = <c>{op,LINE,Op,Rep(A)}</c>.</item>
+       then Rep(T) = <c>{op,LINE,Op,Rep(T_0)}</c>.</item>
       <item>If T is a bitstring type <c>&lt;&lt;_:M,_:_*N>></c>,
        where <c>M</c> and <c>N</c> are singleton integer types, then Rep(T) =
        <c>{type,LINE,binary,[Rep(M),Rep(N)]}</c>.</item>
@@ -509,53 +520,44 @@
        <c>{type,Line,nil,[]}</c>.</item>
       <item>If T is a fun type <c>fun()</c>, then Rep(T) =
        <c>{type,LINE,'fun',[]}</c>.</item>
-      <item>If T is a fun type <c>fun((...) -> B)</c>,
-       where <c>B</c> is a type, then
-       Rep(T) = <c>{type,LINE,'fun',[{type,LINE,any},Rep(B)]}</c>.
+      <item>If T is a fun type <c>fun((...) -> T_0)</c>, then
+       Rep(T) = <c>{type,LINE,'fun',[{type,LINE,any},Rep(T_0)]}</c>.
        </item>
       <item>If T is a fun type <c>fun(Ft)</c>, where
        <c>Ft</c> is a function type,
-       then Rep(T) = <c>Rep(Ft)</c>.</item>
+       then Rep(T) = <c>Rep(Ft)</c>. For Rep(Ft), see below.</item>
       <item>If T is an integer range type <c>L .. H</c>,
        where <c>L</c> and <c>H</c> are singleton integer types, then
        Rep(T) = <c>{type,LINE,range,[Rep(L),Rep(H)]}</c>.</item>
       <item>If T is a map type <c>map()</c>, then Rep(T) =
        <c>{type,LINE,map,any}</c>.</item>
-      <item>If T is a map type <c>#{P_1, ..., P_k}</c>, where each
-       <c>P_i</c> is a map pair type, then Rep(T) =
-       <c>{type,LINE,map,[Rep(P_1), ..., Rep(P_k)]}</c>.</item>
-      <item>If T is a map pair type <c>K => V</c>, where
-       <c>K</c> and <c>V</c> are types, then Rep(T) =
-       <c>{type,LINE,map_field_assoc,[Rep(K),Rep(V)]}</c>.</item>
-      <item>If T is a predefined (or built-in) type <c>N(A_1, ..., A_k)</c>,
-       where each <c>A_i</c> is a type, then Rep(T) =
-       <c>{type,LINE,N,[Rep(A_1), ..., Rep(A_k)]}</c>.</item>
+      <item>If T is a map type <c>#{A_1, ..., A_k}</c>, where each
+       <c>A_i</c> is an association type, then Rep(T) =
+       <c>{type,LINE,map,[Rep(A_1), ..., Rep(A_k)]}</c>.
+       For Rep(A), see below.</item>
+      <item>If T is a predefined (or built-in) type <c>N(T_1, ..., T_k)</c>,
+       then Rep(T) =
+       <c>{type,LINE,N,[Rep(T_1), ..., Rep(T_k)]}</c>.</item>
       <item>If T is a record type <c>#Name{F_1, ..., F_k}</c>,
        where each <c>F_i</c> is a record field type, then Rep(T) =
        <c>{type,LINE,record,[Rep(Name),Rep(F_1), ..., Rep(F_k)]}</c>.
-       </item>
-      <item>If T is a record field type <c>Name :: Type</c>,
-       where <c>Type</c> is a type, then Rep(T) =
-       <c>{type,LINE,field_type,[Rep(Name),Rep(Type)]}</c>.</item>
-      <item>If T is a remote type <c>M:N(A_1, ..., A_k)</c>, where
-       each <c>A_i</c> is a type, then Rep(T) =
-       <c>{remote_type,LINE,[Rep(M),Rep(N),[Rep(A_1), ..., Rep(A_k)]]}</c>.
+       For Rep(F), see below.</item>
+      <item>If T is a remote type <c>M:N(T_1, ..., T_k)</c>, then Rep(T) =
+       <c>{remote_type,LINE,[Rep(M),Rep(N),[Rep(T_1), ..., Rep(T_k)]]}</c>.
        </item>
       <item>If T is a tuple type <c>tuple()</c>, then Rep(T) =
        <c>{type,LINE,tuple,any}</c>.</item>
-      <item>If T is a tuple type <c>{A_1, ..., A_k}</c>, where
-       each <c>A_i</c> is a type, then Rep(T) =
-       <c>{type,LINE,tuple,[Rep(A_1), ..., Rep(A_k)]}</c>.</item>
-      <item>If T is a type union <c>T_1 | ... | T_k</c>,
-       where each <c>T_i</c> is a type, then Rep(T) =
+      <item>If T is a tuple type <c>{T_1, ..., T_k}</c>, then Rep(T) =
+       <c>{type,LINE,tuple,[Rep(T_1), ..., Rep(T_k)]}</c>.</item>
+      <item>If T is a type union <c>T_1 | ... | T_k</c>, then Rep(T) =
        <c>{type,LINE,union,[Rep(T_1), ..., Rep(T_k)]}</c>.</item>
       <item>If T is a type variable <c>V</c>, then Rep(T) =
        <c>{var,LINE,A}</c>, where <c>A</c> is an atom with a printname
        consisting of the same characters as <c>V</c>. A type variable
        is any variable except underscore (<c>_</c>).</item>
-      <item>If T is a user-defined type <c>N(A_1, ..., A_k)</c>,
-       where each <c>A_i</c> is a type, then Rep(T) =
-       <c>{user_type,LINE,N,[Rep(A_1), ..., Rep(A_k)]}</c>.</item>
+      <item>If T is a user-defined type <c>N(T_1, ..., T_k)</c>,
+       then Rep(T) =
+       <c>{user_type,LINE,N,[Rep(T_1), ..., Rep(T_k)]}</c>.</item>
       <item>If T is <c>( T_0 )</c>, then Rep(T) = <c>Rep(T_0)</c>,
        that is, parenthesized types cannot be distinguished from their
        bodies.</item>
@@ -563,15 +565,17 @@
 
     <section>
       <title>Function Types</title>
+      <p>A function type Ft is one of the following alternatives:</p>
       <list type="bulleted">
        <item>If Ft is a constrained function type <c>Ft_1 when Fc</c>,
 	where <c>Ft_1</c> is a function type and
 	<c>Fc</c> is a function constraint, then Rep(T) =
-	<c>{type,LINE,bounded_fun,[Rep(Ft_1),Rep(Fc)]}</c>.</item>
-       <item>If Ft is a function type <c>(A_1, ..., A_n) -> B</c>,
-        where each <c>A_i</c> and <c>B</c> are types, then
-	Rep(Ft) = <c>{type,LINE,'fun',[{type,LINE,product,[Rep(A_1),
-	..., Rep(A_n)]},Rep(B)]}</c>.</item>
+	<c>{type,LINE,bounded_fun,[Rep(Ft_1),Rep(Fc)]}</c>.
+        For Rep(Fc), see below.</item>
+       <item>If Ft is a function type <c>(T_1, ..., T_n) -> T_0</c>,
+        where each <c>T_i</c> is a type, then
+	Rep(Ft) = <c>{type,LINE,'fun',[{type,LINE,product,[Rep(T_1),
+	..., Rep(T_n)]},Rep(T_0)]}</c>.</item>
       </list>
     </section>
 
@@ -587,6 +591,24 @@
        </item>
       </list>
     </section>
+
+    <section>
+      <title>Association Types</title>
+      <list type="bulleted">
+       <item>If A is an association type <c>K => V</c>, where
+        <c>K</c> and <c>V</c> are types, then Rep(A) =
+        <c>{type,LINE,map_field_assoc,[Rep(K),Rep(V)]}</c>.</item>
+      </list>
+    </section>
+
+    <section>
+      <title>Record Field Types</title>
+      <list type="bulleted">
+       <item>If F is a record field type <c>Name :: Type</c>,
+	where <c>Type</c> is a type, then Rep(F) =
+	<c>{type,LINE,field_type,[Rep(Name),Rep(Type)]}</c>.</item>
+      </list>
+    </section>
   </section>
 
   <section>