diff --git a/doc/transform_iterator_ref.rst b/doc/transform_iterator_ref.rst
index bb59c1e..2a6cd58 100644
--- a/doc/transform_iterator_ref.rst
+++ b/doc/transform_iterator_ref.rst
@@ -1,6 +1,6 @@
 ::
 
-  template <class AdaptableUnaryFunction,
+  template <class UnaryFunction,
             class Iterator, 
             class Reference = use_default, 
             class Value = use_default>
@@ -10,50 +10,48 @@
     friend class iterator_core_access;
   public:
     transform_iterator();
-    transform_iterator(Iterator const& x, AdaptableUnaryFunction f);
+    transform_iterator(Iterator const& x, UnaryFunction f);
 
     template<class OtherIterator, class R2, class V2>
     transform_iterator(
-          transform_iterator<AdaptableUnaryFunction, OtherIterator, R2, V2> const& t
+          transform_iterator<UnaryFunction, OtherIterator, R2, V2> const& t
         , typename enable_if_convertible<OtherIterator, Iterator>::type* = 0 // exposition
     );
 
-    AdaptableUnaryFunction functor() const;
+    UnaryFunction functor() const;
   private:
     typename transform_iterator::value_type dereference() const;
-    AdaptableUnaryFunction m_f;
+    UnaryFunction m_f;
   };
 
 
 ``transform_iterator`` requirements
 ...................................
 
-The type ``AdaptableUnaryFunction`` must be Assignable, Copy
-Constructible, and the expression ``f(x)`` must be valid where ``f``
-is an object of type ``AdaptableUnaryFunction``, ``x`` is an object of
-type ``AdaptableUnaryFunction::argument_type``, and where the type of
-``f(x)`` must be ``AdaptableUnaryFunction::result_type``.
+The type ``UnaryFunction`` must be Assignable, Copy Constructible, and
+the expression ``f(*i)`` must be valid where ``f`` is an object of
+type ``UnaryFunction``, ``i`` is an object of type ``Iterator``, and
+where the type of ``f(*i)`` must be
+``result_of<UnaryFunction(iterator_traits<Iterator>::reference)>::type``.
 
 The type ``Iterator`` must at least model Readable Iterator.  The
 resulting ``transform_iterator`` models the most refined of the
 following options that is also modeled by ``Iterator``.
 
-  * Writable Lvalue Iterator if the ``result_type`` of the
-    ``AdaptableUnaryFunction`` is a non-const reference. 
+  * Writable Lvalue Iterator if ``result_of<UnaryFunction(iterator_traits<Iterator>::reference)>::type`` is a non-const reference. 
 
-  * Readable Lvalue Iterator if the ``result_type`` is a const
+  * Readable Lvalue Iterator if ``result_of<UnaryFunction(iterator_traits<Iterator>::reference)>::type`` is a const
     reference.
 
   * Readable Iterator otherwise. 
 
 
-The ``transform_iterator`` models the most refined standard traversal
+The ``transform_iterator`` models the traversal
 concept that is modeled by ``Iterator``.
 
-The ``value_type`` of ``transform_iterator`` is
-``remove_reference<result_type>::type``. The ``reference`` type is
-``result_type``.
-
+The ``reference`` type of ``transform_iterator`` is
+``result_of<UnaryFunction(iterator_traits<Iterator>::reference)>::type``.
+The ``value_type`` is ``remove_cv<remove_reference<reference> >::type``.
 
 ``transform_iterator`` public operations
 ........................................
@@ -65,7 +63,7 @@ The ``value_type`` of ``transform_iterator`` is
   and ``m_iterator`` default constructed.
 
 
-``transform_iterator(Iterator const& x, AdaptableUnaryFunction f);``
+``transform_iterator(Iterator const& x, UnaryFunction f);``
 
 :Returns: An instance of ``transform_iterator`` with ``m_f``
   initialized to ``f`` and ``m_iterator`` initialized to ``x``.
@@ -75,14 +73,14 @@ The ``value_type`` of ``transform_iterator`` is
 
     template<class OtherIterator, class R2, class V2>
     transform_iterator(
-          transform_iterator<AdaptableUnaryFunction, OtherIterator, R2, V2> const& t
+          transform_iterator<UnaryFunction, OtherIterator, R2, V2> const& t
         , typename enable_if_convertible<OtherIterator, Iterator>::type* = 0 // exposition
     );
 
 :Returns: An instance of ``transform_iterator`` that is a copy of ``t``.
 :Requires: ``OtherIterator`` is implicitly convertible to ``Iterator``.
 
-``AdaptableUnaryFunction functor() const;``
+``UnaryFunction functor() const;``
 
 :Returns: ``m_f``