erts: Correct the types section in The Abstract Format document

The Types section is more consistent with Kostis' text in The
Reference Manual.

1 files changed, 178 insertions, 197 deletions

diff --git a/erts/doc/src/absform.xml b/erts/doc/src/absform.xml
index df2553ced3..8584898a9d 100644
--- a/erts/doc/src/absform.xml
+++ b/erts/doc/src/absform.xml
@@ -61,7 +61,7 @@
     </p>
 
   <section>
-    <title>Module declarations and forms</title>
+    <title>Module Declarations and Forms</title>
     <p>A module declaration consists of a sequence of forms that are either
       function declarations or attributes.</p>
     <list type="bulleted">
@@ -78,204 +78,87 @@
        Rep(F) = <c><![CDATA[{attribute,LINE,export,[{Fun_1,A_1}, ..., {Fun_k,A_k}]}]]></c>.</item>
       <item>If F is an attribute <c><![CDATA[-import(Mod,[Fun_1/A_1, ..., Fun_k/A_k])]]></c>, then
        Rep(F) = <c><![CDATA[{attribute,LINE,import,{Mod,[{Fun_1,A_1}, ..., {Fun_k,A_k}]}}]]></c>.</item>
+      <item>If F is an attribute <c><![CDATA[-export_type([Type_1/A_1, ..., Type_k/A_k])]]></c>, then
+       Rep(F) = <c><![CDATA[{attribute,LINE,export_type,[{Type_1,A_1}, ..., {Type_k,A_k}]}]]></c>.</item>
       <item>If F is an attribute <c><![CDATA[-compile(Options)]]></c>, then
        Rep(F) = <c><![CDATA[{attribute,LINE,compile,Options}]]></c>.</item>
       <item>If F is an attribute <c><![CDATA[-file(File,Line)]]></c>, then
        Rep(F) = <c><![CDATA[{attribute,LINE,file,{File,Line}}]]></c>.</item>
-      <item>If F is a record declaration <c><![CDATA[-record(Name,{V_1, ..., V_k})]]></c>, then
-       Rep(F) =
-      <c><![CDATA[{attribute,LINE,record,{Name,[Rep(V_1), ..., Rep(V_k)]}}]]></c>. For Rep(V), see below.</item>
-      <item>If F is a type attribute (i.e. <c><![CDATA[opaque]]></c> or
-       <c><![CDATA[type]]></c>)
-       <c><![CDATA[-Attr Name(A_1, ..., A_k) :: T]]></c> where each
-       <c><![CDATA[A_i]]></c> is a variable, then Rep(F) =
-       <c><![CDATA[{attribute,LINE,Attr,{Name,Rep(T),[Rep(A_1), ..., Rep(A_k)]}}]]></c>.
-       For Rep(T), see below.</item>
-      <item>If F is a type spec (i.e. <c><![CDATA[callback]]></c> or
-       <c><![CDATA[spec]]></c>)
-       <c><![CDATA[-Attr F Tc_1; ...; Tc_k]]></c>,
-       where each <c><![CDATA[Tc_i]]></c> is a fun type clause with an
-       argument sequence of the same length <c><![CDATA[Arity]]></c>, then
-       Rep(F) =
-       <c><![CDATA[{Attr,LINE,{{F,Arity},[Rep(Tc_1), ..., Rep(Tc_k)]}}]]></c>.
-       For Rep(Tc_i), see below.</item>
-      <item>If F is a type spec (i.e. <c><![CDATA[callback]]></c> or
-       <c><![CDATA[spec]]></c>)
-       <c><![CDATA[-Attr Mod:F Tc_1; ...; Tc_k]]></c>,
-       where each <c><![CDATA[Tc_i]]></c> is a fun type clause with an
-       argument sequence of the same length <c><![CDATA[Arity]]></c>, then
-       Rep(F) =
-       <c><![CDATA[{Attr,LINE,{{Mod,F,Arity},[Rep(Tc_1), ..., Rep(Tc_k)]}}]]></c>.
-       For Rep(Tc_i), see below.</item>
+      <item>If F is a record declaration
+       <c>-record(Name,{V_1, ..., V_k})</c>, 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
+       <c>-Type Name(V_1, ..., V_k) :: T</c>, where
+       <c>Type</c> is either the atom <c>type</c> or the atom <c>opaque</c>,
+       each <c>V_i</c> is a variable, and <c>T</c> is a type, then Rep(F) =
+       <c>{attribute,LINE,Type,{Name,Rep(T),[Rep(V_1), ..., Rep(V_k)]}}</c>.
+      </item>
+      <item>If F is a function specification
+       <c>-Spec Name Ft_1; ...; Ft_k</c>,
+       where <c>Spec</c> is either the atom <c>spec</c> or the atom
+       <c>callback</c>, and each <c>Ft_i</c> is a possibly constrained
+       function type with an argument sequence of the same length
+       <c>Arity</c>, then Rep(F) =
+       <c>{attribute,Line,Spec,{{Name,Arity},[Rep(Ft_1), ..., Rep(Ft_k)]}}</c>.
+      </item>
+      <item>If F is a function specification
+       <c>-spec Mod:Name Ft_1; ...; Ft_k</c>,
+       where each <c>Ft_i</c> is a possibly constrained
+       function type with an argument sequence of the same length
+       <c>Arity</c>, then Rep(F) =
+       <c>{attribute,Line,spec,{{Mod,Name,Arity},[Rep(Ft_1), ..., Rep(Ft_k)]}}</c>.
+      </item>
       <item>If F is a wild attribute <c><![CDATA[-A(T)]]></c>, then
        Rep(F) = <c><![CDATA[{attribute,LINE,A,T}]]></c>.
       <br></br></item>
-      <item>If F is a function declaration <c><![CDATA[Name Fc_1 ; ... ; Name Fc_k]]></c>, 
-       where each <c><![CDATA[Fc_i]]></c> is a function clause with a
-       pattern sequence of the same length <c><![CDATA[Arity]]></c>, then
-       Rep(F) = <c><![CDATA[{function,LINE,Name,Arity,[Rep(Fc_1), ...,Rep(Fc_k)]}]]></c>.</item>
+      <item>If F is a function declaration
+       <c>Name Fc_1 ; ... ; Name Fc_k</c>,
+       where each <c>Fc_i</c> is a function clause with a
+       pattern sequence of the same length <c>Arity</c>, then
+       Rep(F) = <c>{function,LINE,Name,Arity,[Rep(Fc_1), ...,Rep(Fc_k)]}</c>.
+      </item>
     </list>
 
     <section>
-      <title>Type clauses</title>
-      <list type="bulleted">
-       <item>If T is a fun type clause
-        <c><![CDATA[(A_1, ..., A_n) -> Ret]]></c>, where each
-        <c><![CDATA[A_i]]></c> and <c><![CDATA[Ret]]></c> are types, then
-        Rep(T) =
-        <c><![CDATA[{type,LINE,'fun',[{type,LINE,product,[Rep(A_1), ..., Rep(A_n)]},Rep(Ret)]}]]></c>.
-        </item>
-       <item>If T is a bounded fun type clause <c><![CDATA[Tc when Tg]]></c>,
-        where <c><![CDATA[Tc]]></c> is an unbounded fun type clause and
-        <c><![CDATA[Tg]]></c> is a type guard sequence, then Rep(T) =
-        <c><![CDATA[{type,LINE,bounded_fun,[Rep(Tc),Rep(Tg)]}]]></c>.</item>
-      </list>
-    </section>
-
-    <section>
-      <title>Type guards</title>
-      <list type="bulleted">
-       <item>If G is a constraint <c><![CDATA[F(A_1, ..., A_k)]]></c>, where
-        <c><![CDATA[F]]></c> is an atom and each <c><![CDATA[A_i]]></c> is a
-        type, then Rep(G) =
-        <c><![CDATA[{type,LINE,constraint,[Rep(F),[Rep(A_1), ..., Rep(A_k)]]}]]></c>.
-        </item>
-       <item>If G is a type definition <c><![CDATA[Name :: Type]]></c>,
-        where <c><![CDATA[Name]]></c> is a variable and
-        <c><![CDATA[Type]]></c> is a type, then Rep(G) =
-        <c><![CDATA[{type,LINE,constraint,[{atom,LINE,is_subtype},[Rep(Name),Rep(Type)]]}]]></c>.</item>
-      </list>
-    </section>
-
-    <section>
-      <title>Types</title>
-      <list type="bulleted">
-       <item>If T is a type definition <c><![CDATA[Name :: Type]]></c>,
-        where <c><![CDATA[Name]]></c> is a variable and
-        <c><![CDATA[Type]]></c> is a type, then Rep(T) =
-        <c><![CDATA[{ann_type,LINE,[Rep(Name),Rep(Type)]}]]></c>.</item>
-       <item>If T is a type union <c><![CDATA[A_1 | ... | A_k]]></c>,
-        where each <c><![CDATA[A_i]]></c> is a type, then Rep(T) =
-        <c><![CDATA[{type,LINE,union,[Rep(A_1), ..., Rep(A_k)]}]]></c>.</item>
-       <item>If T is a type range <c><![CDATA[L .. R]]></c>,
-        where <c><![CDATA[L]]></c> and <c><![CDATA[R]]></c> are types, then
-        Rep(T) = <c><![CDATA[{type,LINE,range,[Rep(L), Rep(R)]}]]></c>.</item>
-       <item>If T is a binary operation <c><![CDATA[L Op R]]></c>,
-        where <c><![CDATA[Op]]></c> is an arithmetic or bitwise binary operator
-        and <c><![CDATA[L]]></c> and <c><![CDATA[R]]></c> are types, then
-        Rep(T) = <c><![CDATA[{op,LINE,Op,Rep(L),Rep(R)}]]></c>.</item>
-       <item>If T is <c><![CDATA[Op A]]></c>, where <c><![CDATA[Op]]></c> is an
-        arithmetic or bitwise unary operator and <c><![CDATA[A]]></c> is a
-        type, then Rep(T) = <c><![CDATA[{op,LINE,Op,Rep(A)}]]></c>.</item>
-       <item>If T is a fun type <c><![CDATA[fun()]]></c>, then Rep(T) =
-        <c><![CDATA[{type,LINE,'fun',[]}]]></c>.</item>
-       <item>If T is a variable <c><![CDATA[V]]></c>, then Rep(T) =
-        <c><![CDATA[{var,LINE,A}]]></c>, where <c><![CDATA[A]]></c> is an atom
-        with a printname consisting of the same characters as
-        <c><![CDATA[V]]></c>.</item>
-       <item>If T is an atomic literal L and L is not a string literal, then
-        Rep(T) = Rep(L).</item>
-       <item>If T is a tuple or map type <c><![CDATA[F()]]></c> (i.e.
-        <c><![CDATA[tuple]]></c> or <c><![CDATA[map]]></c>), then Rep(T) =
-        <c><![CDATA[{type,LINE,F,any}]]></c>.</item>
-       <item>If T is a type <c><![CDATA[F(A_1, ..., A_k)]]></c>, where each
-        <c><![CDATA[A_i]]></c> is a type, then Rep(T) =
-        <c><![CDATA[{user_type,LINE,F,[Rep(A_1), ..., Rep(A_k)]}]]></c>.</item>
-       <item>If T is a remote type <c><![CDATA[M:F(A_1, ..., A_k)]]></c>, where
-        each <c><![CDATA[A_i]]></c> is a type and <c><![CDATA[M]]></c> and
-        <c><![CDATA[F]]></c>, then Rep(T) =
-        <c><![CDATA[{remote_type,LINE,[Rep(M),Rep(F),[Rep(A_1), ..., Rep(A_k)]]}]]></c>.
-        </item>
-       <item>If T is the nil type <c><![CDATA[[]]]></c>, then Rep(T) =
-        <c><![CDATA[{type,LINE,nil,[]}]]></c>.</item>
-       <item>If T is a list type <c><![CDATA[[A]]]></c>, where
-        <c><![CDATA[A]]></c> is a type, then Rep(T) =
-        <c><![CDATA[{type,LINE,list,[Rep(A)]}]]></c>.</item>
-       <item>If T is a non-empty list type <c><![CDATA[[A, ...]]]></c>, where
-        <c><![CDATA[A]]></c> is a type, then Rep(T) =
-        <c><![CDATA[{type,LINE,nonempty_list,[Rep(A)]}]]></c>.</item>
-       <item>If T is a map type <c><![CDATA[#{P_1, ..., P_k}]]></c>, where each
-        <c><![CDATA[P_i]]></c> is a map pair type, then Rep(T) =
-        <c><![CDATA[{type,LINE,map,[Rep(P_1), ..., Rep(P_k)]}]]></c>.</item>
-       <item>If T is a map pair type <c><![CDATA[K => V]]></c>, where
-        <c><![CDATA[K]]></c> and <c><![CDATA[V]]></c> are types,
-        then Rep(T) =
-        <c><![CDATA[{type,LINE,map_field_assoc,[Rep(K),Rep(V)]}]]></c>.</item>
-       <item>If T is a tuple type <c><![CDATA[{A_1, ..., A_k}]]></c>, where
-        each <c><![CDATA[A_i]]></c> is a type, then Rep(T) =
-        <c><![CDATA[{type,LINE,tuple,[Rep(A_1), ..., Rep(A_k)]}]]></c>.</item>
-       <item>If T is a record type <c><![CDATA[#Name{}]]></c>, where
-        <c><![CDATA[Name]]></c> is an atom, then Rep(T) =
-        <c><![CDATA[{type,LINE,record,[Rep(Name)]}]]></c>.</item>
-       <item>If T is a record type <c><![CDATA[#Name{F_1, ..., F_k}]]></c>,
-        where <c><![CDATA[Name]]></c> is an atom, then Rep(T) =
-        <c><![CDATA[{type,LINE,record,[Rep(Name),[Rep(F_1), ..., Rep(F_k)]]}]]></c>.
-        </item>
-       <item>If T is a record field type <c><![CDATA[Name :: Type]]></c>,
-        where <c><![CDATA[Name]]></c> is an atom, then Rep(T) =
-        <c><![CDATA[{type,LINE,field_type,[Rep(Name),Rep(Type)]}]]></c>.</item>
-       <item>If T is a record field type <c><![CDATA[<<>>]]></c>, then Rep(T) =
-        <c><![CDATA[{type,LINE,binary,[{integer,LINE,0},{integer,LINE,0}]}]]></c>.
-        </item>
-       <item>If T is a binary type <c><![CDATA[<< _ : B >>]]></c>, where
-        <c><![CDATA[B]]></c> is a type, then Rep(T) =
-        <c><![CDATA[{type,LINE,binary,[Rep(B),{integer,LINE,0}]}]]></c>.</item>
-       <item>If T is a binary type <c><![CDATA[<< _ : _ * U >>]]></c>,
-        where <c><![CDATA[U]]></c> is a type, then Rep(T) =
-        <c><![CDATA[{type,LINE,binary,[{integer,LINE,0},Rep(U)]}]]></c>.</item>
-       <item>If T is a binary type <c><![CDATA[<< _ : B , _ : _ * U >>]]></c>,
-        where <c><![CDATA[B]]></c> and <c><![CDATA[U]]></c> is a type, then
-        Rep(T) =
-        <c><![CDATA[{type,LINE,binary,[Rep(B),Rep(U)]}]]></c>.</item>
-
-       <item>If T is a fun type <c><![CDATA[fun((...) -> Ret)]]></c>, then
-        Rep(T) = <c><![CDATA[{type,LINE,'fun',[{type,LINE,product,[]},Rep(Ret)]}]]></c>.
-        </item>
-       <item>If T is a fun type <c><![CDATA[fun(Tc)]]></c>, where
-        <c><![CDATA[Tc]]></c> is an unbounded fun type clause,
-        then Rep(T) = <c><![CDATA[Rep(Tc)]]></c>.</item>
-      </list>
-    </section>
-
-    <section>
-      <title>Record fields</title>
+      <title>Record Fields</title>
       <p>Each field in a record declaration may have an optional
-        explicit default initializer expression</p>
+        explicit default initializer expression, as well as an
+        optional type.</p>
       <list type="bulleted">
         <item>If V is <c><![CDATA[A]]></c>, then
          Rep(V) = <c><![CDATA[{record_field,LINE,Rep(A)}]]></c>.</item>
-        <item>If V is <c><![CDATA[A = E]]></c>, then
+        <item>If V is <c><![CDATA[A = E]]></c>,
+	 where <c>E</c> is an expression, then
          Rep(V) = <c><![CDATA[{record_field,LINE,Rep(A),Rep(E)}]]></c>.</item>
-        <item>If V is <c><![CDATA[A :: T]]></c>, where <c><![CDATA[A]]></c> is
-         an atom and <c><![CDATA[T]]></c> is a type and it does not contain
-         <c><![CDATA[undefined]]></c> syntactically, then Rep(V) =
-         <c><![CDATA[{typed_record_field,{record_field,LINE,Rep(A)},Rep(undefined | T)}]]></c>.
-         Note that if <![CDATA[T]]> is an annotated type, it will be wrapped in
-         parentheses.</item>
-        <item>If V is <c><![CDATA[A :: T]]></c>, where <c><![CDATA[A]]></c> is
-         an atom and <c><![CDATA[T]]></c> is a type, then Rep(V) =
-         <c><![CDATA[{typed_record_field,{record_field,LINE,Rep(A)},Rep(T)}]]></c>.
-         </item>
-        <item>If V is <c><![CDATA[A = E :: T]]></c>, where <c><![CDATA[A]]></c>
-         is an atom, <c><![CDATA[E]]></c> is an expression and
-         <c><![CDATA[T]]></c> is a type, then Rep(V) =
-         <c><![CDATA[{typed_record_field,{record_field,LINE,Rep(A),Rep(E)},Rep(T)}]]></c>.
-         </item>
+        <item>If V is <c>A :: T</c>, where <c>T</c> is a
+          type and it does not contain
+          <c>undefined</c> syntactically, then Rep(V) =
+          <c>{typed_record_field,{record_field,LINE,Rep(A)},Rep(undefined | T)}</c>.
+        </item>
+        <item>If V is <c>A :: T</c>, where <c>T</c> is a type, then Rep(V) =
+          <c>{typed_record_field,{record_field,LINE,Rep(A)},Rep(T)}</c>.
+          </item>
+        <item>If V is <c>A = E :: T</c>, where
+          <c>E</c> is an expression and <c>T</c> is a type, then Rep(V) =
+          <c>{typed_record_field,{record_field,LINE,Rep(A),Rep(E)},Rep(T)}</c>.
+        </item>
       </list>
     </section>
 
     <section>
-      <title>Representation of parse errors and end of file</title>
+      <title>Representation of Parse Errors and End-of-file</title>
       <p>In addition to the representations of forms, the list that represents
-        a module declaration (as returned by functions in <c><![CDATA[erl_parse]]></c> and
-        <c><![CDATA[epp]]></c>) may contain tuples <c><![CDATA[{error,E}]]></c> and <c><![CDATA[{warning,W}]]></c>, denoting
-        syntactically incorrect forms and warnings, and <c><![CDATA[{eof,LINE}]]></c>, denoting an end
-        of stream encountered before a complete form had been parsed.</p>
+        a module declaration (as returned by functions in <c>erl_parse</c> and
+        <c>epp</c>) may contain tuples <c>{error,E}</c> and
+	<c>{warning,W}</c>, denoting syntactically incorrect forms and
+	warnings, and <c>{eof,LINE}</c>, denoting an end-of-stream
+	encountered before a complete form had been parsed.</p>
     </section>
   </section>
 
   <section>
-    <title>Atomic literals</title>
+    <title>Atomic Literals</title>
     <p>There are five kinds of atomic literals, which are represented in the
       same way in patterns, expressions and guards:</p>
     <list type="bulleted">
@@ -330,12 +213,12 @@
        time), then Rep(P) = <c><![CDATA[{op,LINE,Op,Rep(P_0)}]]></c>.</item>
       <item>If P is a record pattern <c><![CDATA[#Name{Field_1=P_1, ..., Field_k=P_k}]]></c>,
        then Rep(P) =
-      <c><![CDATA[{record,LINE,Name, [{record_field,LINE,Rep(Field_1),Rep(P_1)}, ..., {record_field,LINE,Rep(Field_k),Rep(P_k)}]}]]></c>.</item>
+      <c><![CDATA[{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><![CDATA[#Name.Field]]></c>, then
        Rep(P) = <c><![CDATA[{record_index,LINE,Name,Rep(Field)}]]></c>.</item>
       <item>If P is <c><![CDATA[( P_0 )]]></c>, then
        Rep(P) = <c><![CDATA[Rep(P_0)]]></c>,
-       i.e., patterns cannot be distinguished from their bodies.</item>
+       that is, patterns cannot be distinguished from their bodies.</item>
     </list>
     <p>Note that every pattern has the same source form as some expression, and is
       represented the same way as the corresponding expression.</p>
@@ -372,10 +255,10 @@
        Rep(E) = <c><![CDATA[{op,LINE,Op,Rep(E_0)}]]></c>.</item>
       <item>If E is <c><![CDATA[#Name{Field_1=E_1, ..., Field_k=E_k}]]></c>, then
        Rep(E) =
-      <c><![CDATA[{record,LINE,Name,  [{record_field,LINE,Rep(Field_1),Rep(E_1)}, ..., {record_field,LINE,Rep(Field_k),Rep(E_k)}]}]]></c>.</item>
+      <c><![CDATA[{record,LINE,Name,[{record_field,LINE,Rep(Field_1),Rep(E_1)}, ..., {record_field,LINE,Rep(Field_k),Rep(E_k)}]}]]></c>.</item>
       <item>If E is <c><![CDATA[E_0#Name{Field_1=E_1, ..., Field_k=E_k}]]></c>, then
        Rep(E) =
-      <c><![CDATA[{record,LINE,Rep(E_0),Name,  [{record_field,LINE,Rep(Field_1),Rep(E_1)}, ..., {record_field,LINE,Rep(Field_k),Rep(E_k)}]}]]></c>.</item>
+      <c><![CDATA[{record,LINE,Rep(E_0),Name,[{record_field,LINE,Rep(Field_1),Rep(E_1)}, ..., {record_field,LINE,Rep(Field_k),Rep(E_k)}]}]]></c>.</item>
       <item>If E is <c><![CDATA[#Name.Field]]></c>, then
        Rep(E) = <c><![CDATA[{record_index,LINE,Name,Rep(Field)}]]></c>.</item>
       <item>If E is <c><![CDATA[E_0#Name.Field]]></c>, then
@@ -466,20 +349,13 @@
        <c><![CDATA[Fc_i]]></c> is a function clause then Rep(E) =
        <c><![CDATA[{named_fun,LINE,Name,[Rep(Fc_1), ..., Rep(Fc_k)]}]]></c>.
        </item>
-      <item>If E is <c><![CDATA[query [E_0 || W_1, ..., W_k] end]]></c>,
-       where each <c><![CDATA[W_i]]></c> is a generator or a filter, then
-       Rep(E) = <c><![CDATA[{'query',LINE,{lc,LINE,Rep(E_0),[Rep(W_1), ..., Rep(W_k)]}}]]></c>.
-       For Rep(W), see below.</item>
-      <item>If E is <c><![CDATA[E_0.Field]]></c>, a Mnesia record access
-       inside a query, then
-       Rep(E) = <c><![CDATA[{record_field,LINE,Rep(E_0),Rep(Field)}]]></c>.</item>
       <item>If E is <c><![CDATA[( E_0 )]]></c>, then
-       Rep(E) = <c><![CDATA[Rep(E_0)]]></c>,
-       i.e., parenthesized expressions cannot be distinguished from their bodies.</item>
+       Rep(E) = <c>Rep(E_0)</c>, that is, parenthesized
+       expressions cannot be distinguished from their bodies.</item>
     </list>
 
     <section>
-      <title>Generators and filters</title>
+      <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>
       <list type="bulleted">
         <item>If W is a generator <c><![CDATA[P <- E]]></c>, where <c><![CDATA[P]]></c> is a pattern and <c><![CDATA[E]]></c>
@@ -494,20 +370,20 @@
     </section>
 
     <section>
-      <title>Binary element type specifiers</title>
+      <title>Binary Element Type Specifiers</title>
       <p>A type specifier list TSL for a binary element is a sequence of type
         specifiers <c><![CDATA[TS_1 - ... - TS_k]]></c>.
         Rep(TSL) = <c><![CDATA[[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><![CDATA[A]]></c>, Rep(TS) = <c><![CDATA[A]]></c>.</item>
+        <item>If TS is an atom <c><![CDATA[A]]></c>, then Rep(TS) = <c><![CDATA[A]]></c>.</item>
         <item>If TS is a couple <c><![CDATA[A:Value]]></c> where <c><![CDATA[A]]></c> is an atom and <c><![CDATA[Value]]></c>
-         is an integer, Rep(TS) = <c><![CDATA[{A, Value}]]></c>.</item>
+         is an integer, then Rep(TS) = <c>{A,Value}</c>.</item>
       </list>
     </section>
 
     <section>
-      <title>Map assoc and exact fields</title>
+      <title>Map Assoc and Exact Fields</title>
       <p>When W is an assoc or exact field (in the body of a map), then:</p>
       <list type="bulleted">
         <item>If W is an assoc field <c><![CDATA[K => V]]></c>, where
@@ -595,7 +471,7 @@
        Rep(Gt) = <c><![CDATA[{op,LINE,Op,Rep(Gt_0)}]]></c>.</item>
       <item>If Gt is <c><![CDATA[#Name{Field_1=Gt_1, ..., Field_k=Gt_k}]]></c>, then
        Rep(E) =
-      <c><![CDATA[{record,LINE,Name,  [{record_field,LINE,Rep(Field_1),Rep(Gt_1)}, ..., {record_field,LINE,Rep(Field_k),Rep(Gt_k)}]}]]></c>.</item>
+      <c><![CDATA[{record,LINE,Name,[{record_field,LINE,Rep(Field_1),Rep(Gt_1)}, ..., {record_field,LINE,Rep(Field_k),Rep(Gt_k)}]}]]></c>.</item>
       <item>If Gt is <c><![CDATA[#Name.Field]]></c>, then
        Rep(Gt) = <c><![CDATA[{record_index,LINE,Name,Rep(Field)}]]></c>.</item>
       <item>If Gt is <c><![CDATA[Gt_0#Name.Field]]></c>, then
@@ -609,15 +485,120 @@
        the atom <c><![CDATA[erlang]]></c> and <c><![CDATA[A]]></c> is an atom or an operator, then
        Rep(Gt) = <c><![CDATA[{call,LINE,Rep({A_m,A}),[Rep(Gt_1), ..., Rep(Gt_k)]}]]></c>.</item>
       <item>If Gt is <c><![CDATA[( Gt_0 )]]></c>, then
-       Rep(Gt) = <c><![CDATA[Rep(Gt_0)]]></c>,
-       i.e., parenthesized guard tests cannot be distinguished from their bodies.</item>
+       Rep(Gt) = <c><![CDATA[Rep(Gt_0)]]></c>, that is, parenthesized
+       guard tests cannot be distinguished from their bodies.</item>
     </list>
     <p>Note that every guard test has the same source form as some expression,
       and is represented the same way as the corresponding expression.</p>
   </section>
 
   <section>
-    <title>The abstract format after preprocessing</title>
+    <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 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
+       an expression that can be evaluated to an integer at compile time),
+       then Rep(T) = <c>{op,LINE,Op,Rep(A)}</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>
+      <item>If T is the empty list type <c>[]</c>, then Rep(T) =
+       <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>
+      <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>
+      <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 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>.
+       </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) =
+       <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 <c>( T_0 )</c>, then Rep(T) = <c>Rep(T_0)</c>,
+       that is, parenthesized types cannot be distinguished from their
+       bodies.</item>
+    </list>
+
+    <section>
+      <title>Function Types</title>
+      <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>
+      </list>
+    </section>
+
+    <section>
+      <title>Function Constraints</title>
+      <p>A function constraint Fc is a nonempty sequence of constraints
+	<c>C_1, ..., C_k</c>, and
+	Rep(Fc) = <c>[Rep(C_1), ..., Rep(C_k)]</c>.</p>
+      <list type="bulleted">
+       <item>If C is a constraint <c>is_subtype(V, T)</c> or <c>V :: T</c>,
+        where <c>V</c> is a type variable and <c>T</c> is a type, then
+        Rep(C) = <c>{type,LINE,constraint,[Rep(F),[Rep(V),Rep(T)]]}</c>.
+       </item>
+      </list>
+    </section>
+  </section>
+
+  <section>
+    <title>The Abstract Format After Preprocessing</title>
     <p>The compilation option <c><![CDATA[debug_info]]></c> can be given to the
       compiler to have the abstract code stored in 
       the <c><![CDATA[abstract_code]]></c> chunk in the BEAM file