Update Programming Examples

Language cleaned up by the technical writers xsipewe and tmanevik
from Combitech. Proofreading and corrections by Björn Gustavsson.

1 files changed, 144 insertions, 136 deletions

diff --git a/system/doc/programming_examples/funs.xmlsrc b/system/doc/programming_examples/funs.xmlsrc
index 7bfac9db8c..e4f5c9c9c9 100644
--- a/system/doc/programming_examples/funs.xmlsrc
+++ b/system/doc/programming_examples/funs.xmlsrc
@@ -30,128 +30,124 @@
   </header>
 
   <section>
-    <title>Example 1 - map</title>
-    <p>If we want to double every element in a list, we could write a
-      function named <c>double</c>:</p>
+    <title>map</title>
+    <p>The following function, <c>double</c>, doubles every element in a list:</p>
     <code type="none">
 double([H|T]) -> [2*H|double(T)];
 double([])    -> [].</code>
-    <p>This function obviously doubles the argument entered as input
-      as follows:</p>
+    <p>Hence, the argument entered as input is doubled as follows:</p>
     <pre>
 > <input>double([1,2,3,4]).</input>
 [2,4,6,8]</pre>
-    <p>We now add the function <c>add_one</c>, which adds one to every
+    <p>The following function, <c>add_one</c>, adds one to every
       element in a list:</p>
     <code type="none">
 add_one([H|T]) -> [H+1|add_one(T)];
 add_one([])    -> [].</code>
-    <p>These functions, <c>double</c> and <c>add_one</c>, have a very
-      similar structure. We can exploit this fact and write a function
-      <c>map</c> which expresses this similarity:</p>
+    <p>The functions <c>double</c> and <c>add_one</c> have a
+      similar structure. This can be used by writing a function
+      <c>map</c> that expresses this similarity:</p>
     <codeinclude file="funs1.erl" tag="%1" type="erl"></codeinclude>
-    <p>We can now express the functions <c>double</c> and
-      <c>add_one</c> in terms of <c>map</c> as follows:</p>
+    <p>The functions <c>double</c> and <c>add_one</c> can now be expressed
+    in terms of <c>map</c> as follows:</p>
     <code type="none">
 double(L)  -> map(fun(X) -> 2*X end, L).
 add_one(L) -> map(fun(X) -> 1 + X end, L).</code>
-    <p><c>map(F, List)</c> is a function which takes a function
-      <c>F</c> and a list <c>L</c> as arguments and returns the new
-      list which is obtained by applying <c>F</c> to each of
+    <p><c>map(F, List)</c> is a function that takes a function
+      <c>F</c> and a list <c>L</c> as arguments and returns a new
+      list, obtained by applying <c>F</c> to each of
       the elements in <c>L</c>.</p>
     <p>The process of abstracting out the common features of a number
-      of different programs is called procedural abstraction.
-      Procedural abstraction can be used in order to write several
-      different functions which have a similar structure, but differ
-      only in some minor detail. This is done as follows:</p>
+      of different programs is called <em>procedural abstraction</em>.
+      Procedural abstraction can be used to write several
+      different functions that have a similar structure, but differ
+      in some minor detail. This is done as follows:</p>
     <list type="ordered">
-      <item>write one function which represents the common features of
-       these functions</item>
-      <item>parameterize the difference in terms of functions which
+      <item><em>Step 1.</em> Write one function that represents the common features of
+       these functions.</item>
+      <item><em>Step 2.</em> Parameterize the difference in terms of functions that
        are passed as arguments to the common function.</item>
     </list>
   </section>
 
   <section>
-    <title>Example 2 - foreach</title>
-    <p>This example illustrates procedural abstraction. Initially, we
-      show the following two examples written as conventional
-      functions:</p>
-    <list type="ordered">
-      <item>all elements of a list are printed onto a stream</item>
-      <item>a message is broadcast to a list of processes.</item>
-    </list>
+    <title>foreach</title>
+    <p>This section illustrates procedural abstraction. Initially,
+    the following two examples are written as conventional
+      functions.</p>
+      <p>This function prints all elements of a list onto a stream:</p>
     <code type="none">
 print_list(Stream, [H|T]) ->
     io:format(Stream, "~p~n", [H]),
     print_list(Stream, T);
 print_list(Stream, []) ->
     true.</code>
+     <p>This function broadcasts a message to a list of processes:</p>
     <code type="none">
 broadcast(Msg, [Pid|Pids]) ->
     Pid ! Msg,
     broadcast(Msg, Pids);
 broadcast(_, []) ->
     true.</code>
-    <p>Both these functions have a very similar structure. They both
-      iterate over a list doing something to each element in the list.
-      The "something" has to be carried round as an extra argument to
-      the function which does this.</p>
+    <p>These two functions have a similar structure. They both
+      iterate over a list and do something to each element in the list.
+      The "something" is passed on as an extra argument to
+      the function that does this.</p>
     <p>The function <c>foreach</c> expresses this similarity:</p>
     <codeinclude file="funs1.erl" tag="%2" type="erl"></codeinclude>
-    <p>Using <c>foreach</c>, <c>print_list</c> becomes:</p>
+    <p>Using the function <c>foreach</c>, the function <c>print_list</c> becomes:</p>
     <code type="none">
 foreach(fun(H) -> io:format(S, "~p~n",[H]) end, L)</code>
-    <p><c>broadcast</c> becomes:</p>
+     <p>Using the function <c>foreach</c>, the function <c>broadcast</c> becomes:</p>
     <code type="none">
 foreach(fun(Pid) -> Pid ! M end, L)</code>
     <p><c>foreach</c> is evaluated for its side-effect and not its
       value. <c>foreach(Fun ,L)</c> calls <c>Fun(X)</c> for each
       element <c>X</c> in <c>L</c> and the processing occurs in
-      the order in which the elements were defined in <c>L</c>.
+      the order that the elements were defined in <c>L</c>.
       <c>map</c> does not define the order in which its elements are
       processed.</p>
   </section>
 
   <section>
-    <title>The Syntax of Funs</title>
-    <p>Funs are written with the syntax:</p>
+    <title>Syntax of Funs</title>
+    <p>Funs are written with the following syntax:</p>
     <code type="none">
 F = fun (Arg1, Arg2, ... ArgN) ->
         ...
     end</code>
     <p>This creates an anonymous function of <c>N</c> arguments and
       binds it to the variable <c>F</c>.</p>
-    <p>If we have already written a function in the same module and
-      wish to pass this function as an argument, we can use
-      the following syntax:</p>
+    <p>Another function, <c>FunctionName</c>, written in the same module,
+    can be passed as an argument, using the following syntax:</p>
     <code type="none">
 F = fun FunctionName/Arity</code>
-    <p>With this form of function reference, the function which is
+    <p>With this form of function reference, the function that is
       referred to does not need to be exported from the module.</p>
-    <p>We can also refer to a function defined in a different module
+    <p>It is also possible to refer to a function defined in a different module,
       with the following syntax:</p>
     <code type="none">
 F = {Module, FunctionName}</code>
     <p>In this case, the function must be exported from the module in
       question.</p>
-    <p>The follow program illustrates the different ways of creating
+    <p>The following program illustrates the different ways of creating
       funs:</p>
     <codeinclude file="fun_test.erl" tag="%1" type="erl"></codeinclude>
-    <p>We can evaluate the fun <c>F</c> with the syntax:</p>
+    <p>The fun <c>F</c> can be evaluated with the following syntax:</p>
     <code type="none">
 F(Arg1, Arg2, ..., Argn)</code>
     <p>To check whether a term is a fun, use the test
-      <c>is_function/1</c> in a guard. Example:</p>
+      <c>is_function/1</c> in a guard.</p>
+      <p><em>Example:</em></p>
     <code type="none">
 f(F, Args) when is_function(F) ->
    apply(F, Args);
 f(N, _) when is_integer(N) ->
    N.</code>
-    <p>Funs are a distinct type. The BIFs erlang:fun_info/1,2 can
+    <p>Funs are a distinct type. The BIFs <c>erlang:fun_info/1,2</c> can
       be used to retrieve information about a fun, and the BIF
-      erlang:fun_to_list/1 returns a textual representation of a fun.
-      The check_process_code/2 BIF returns true if the process
+      <c>erlang:fun_to_list/1</c> returns a textual representation of a fun.
+      The <c>check_process_code/2</c> BIF returns <c>true</c> if the process
       contains funs that depend on the old version of a module.</p>
     <note>
       <p>In OTP R5 and earlier releases, funs were represented using
@@ -161,15 +157,15 @@ f(N, _) when is_integer(N) ->
 
   <section>
     <title>Variable Bindings Within a Fun</title>
-    <p>The scope rules for variables which occur in funs are as
+    <p>The scope rules for variables that occur in funs are as
       follows:</p>
     <list type="bulleted">
-      <item>All variables which occur in the head of a fun are assumed
+      <item>All variables that occur in the head of a fun are assumed
        to be "fresh" variables.</item>
-      <item>Variables which are defined before the fun, and which
+      <item>Variables that are defined before the fun, and that
        occur in function calls or guard tests within the fun, have
        the values they had outside the fun.</item>
-      <item>No variables may be exported from a fun.</item>
+      <item>Variables cannot be exported from a fun.</item>
     </list>
     <p>The following examples illustrate these rules:</p>
     <code type="none">
@@ -177,12 +173,13 @@ print_list(File, List) ->
     {ok, Stream} = file:open(File, write),
     foreach(fun(X) -> io:format(Stream,"~p~n",[X]) end, List),
     file:close(Stream).</code>
-    <p>In the above example, the variable <c>X</c> which is defined in
-      the head of the fun is a new variable. The value of the variable
-      <c>Stream</c> which is used within within the fun gets its value
+    <p>Here, the variable <c>X</c>, defined in
+      the head of the fun, is a new variable. The variable
+      <c>Stream</c>, which is used within the fun, gets its value
       from the <c>file:open</c> line.</p>
-    <p>Since any variable which occurs in the head of a fun is
-      considered a new variable it would be equally valid to write:</p>
+    <p>As any variable that occurs in the head of a fun is
+      considered a new variable, it is equally valid to write
+      as follows:</p>
     <code type="none">
 print_list(File, List) ->
     {ok, Stream} = file:open(File, write),
@@ -190,21 +187,21 @@ print_list(File, List) ->
                 io:format(Stream,"~p~n",[File]) 
             end, List),
     file:close(Stream).</code>
-    <p>In this example, <c>File</c> is used as the new variable
-      instead of <c>X</c>. This is rather silly since code in the body
-      of the fun cannot refer to the variable <c>File</c> which is
-      defined outside the fun. Compiling this example will yield
-      the diagnostic:</p>
+    <p>Here, <c>File</c> is used as the new variable
+      instead of <c>X</c>. This is not so wise because code in the fun
+      body cannot refer to the variable <c>File</c>, which is
+      defined outside of the fun. Compiling this example gives
+      the following diagnostic:</p>
     <code type="none">
 ./FileName.erl:Line: Warning: variable 'File' 
       shadowed in 'lambda head'</code>
-    <p>This reminds us that the variable <c>File</c> which is defined
-      inside the fun collides with the variable <c>File</c> which is
+    <p>This indicates that the variable <c>File</c>, which is defined
+      inside the fun, collides with the variable <c>File</c>, which is
       defined outside the fun.</p>
     <p>The rules for importing variables into a fun has the consequence
-      that certain pattern matching operations have to be moved into
+      that certain pattern matching operations must be moved into
       guard expressions and cannot be written in the head of the fun.
-      For example, we might write the following code if we intend
+      For example, you might write the following code if you intend
       the first clause of <c>F</c> to be evaluated when the value of
       its argument is <c>Y</c>:</p>
     <code type="none">
@@ -216,7 +213,7 @@ f(...) ->
              ...
         end, ...)
     ...</code>
-    <p>instead of</p>
+    <p>instead of writng the following code:</p>
     <code type="none">
 f(...) ->
     Y = ...
@@ -229,35 +226,37 @@ f(...) ->
   </section>
 
   <section>
-    <title>Funs and the Module Lists</title>
+    <title>Funs and Module Lists</title>
     <p>The following examples show a dialogue with the Erlang shell.
       All the higher order functions discussed are exported from
       the module <c>lists</c>.</p>
 
     <section>
       <title>map</title>
+      <p><c>map</c> takes a function of one argument and a list of terms:</p>
       <codeinclude file="funs1.erl" tag="%1" type="erl"></codeinclude>
-      <p><c>map</c> takes a function of one argument and a list of
-        terms. It returns the list obtained by applying the function
+      <p>It returns the list obtained by applying the function
         to every argument in the list.</p>
+	<p>When a new fun is defined in the shell, the value of the fun
+        is printed as <c><![CDATA[Fun#<erl_eval>]]></c>:</p>
       <pre>
 > <input>Double = fun(X) -> 2 * X end.</input>
 #Fun&lt;erl_eval.6.72228031&gt;
 > <input>lists:map(Double, [1,2,3,4,5]).</input>
 [2,4,6,8,10]</pre>
-      <p>When a new fun is defined in the shell, the value of the Fun
-        is printed as <c><![CDATA[Fun#<erl_eval>]]></c>.</p>
+
     </section>
 
     <section>
       <title>any</title>
-      <codeinclude file="funs1.erl" tag="%4" type="erl"></codeinclude>
       <p><c>any</c> takes a predicate <c>P</c> of one argument and a
-        list of terms. A predicate is a function which returns
-        <c>true</c> or <c>false</c>. <c>any</c> is true if there is a
-        term <c>X</c> in the list such that <c>P(X)</c> is <c>true</c>.</p>
-      <p>We define a predicate <c>Big(X)</c> which is <c>true</c> if
-        its argument is greater that 10.</p>
+        list of terms:</p>
+      <codeinclude file="funs1.erl" tag="%4" type="erl"></codeinclude>
+      <p>A predicate is a function that returns <c>true</c> or <c>false</c>.
+      <c>any</c> is <c>true</c> if there is a term <c>X</c> in the list such that
+      <c>P(X)</c> is <c>true</c>.</p>
+      <p>A predicate <c>Big(X)</c> is defined, which is <c>true</c> if
+        its argument is greater that 10:</p>
       <pre>
 > <input>Big =  fun(X) -> if X > 10 -> true; true -> false end end.</input>
 #Fun&lt;erl_eval.6.72228031&gt;
@@ -269,9 +268,10 @@ true</pre>
 
     <section>
       <title>all</title>
+      <p><c>all</c> has the same arguments as <c>any</c>:</p>
       <codeinclude file="funs1.erl" tag="%3" type="erl"></codeinclude>
-      <p><c>all</c> has the same arguments as <c>any</c>. It is true
-        if the predicate applied to all elements in the list is true.</p>
+      <p>It is <c>true</c>
+        if the predicate applied to all elements in the list is <c>true</c>.</p>
       <pre>
 > <input>lists:all(Big, [1,2,3,4,12,6]).</input>   
 false
@@ -281,11 +281,12 @@ true</pre>
 
     <section>
       <title>foreach</title>
-      <codeinclude file="funs1.erl" tag="%2" type="erl"></codeinclude>
       <p><c>foreach</c> takes a function of one argument and a list of
-        terms. The function is applied to each argument in the list.
-        <c>foreach</c> returns <c>ok</c>. It is used for its
-        side-effect only.</p>
+        terms:</p>
+      <codeinclude file="funs1.erl" tag="%2" type="erl"></codeinclude>
+      <p>The function is applied to each argument in the list.
+        <c>foreach</c> returns <c>ok</c>. It is only used for its
+        side-effect:</p>
       <pre>
 > <input>lists:foreach(fun(X) -> io:format("~w~n",[X]) end, [1,2,3,4]).</input> 
 1
@@ -297,15 +298,16 @@ ok</pre>
 
     <section>
       <title>foldl</title>
-      <codeinclude file="funs1.erl" tag="%8" type="erl"></codeinclude>
       <p><c>foldl</c> takes a function of two arguments, an
-        accumulator and a list. The function is called with two
+        accumulator and a list:</p>
+      <codeinclude file="funs1.erl" tag="%8" type="erl"></codeinclude>
+      <p>The function is called with two
         arguments. The first argument is the successive elements in
-        the list, the second argument is the accumulator. The function
-        must return a new accumulator which is used the next time
+        the list. The second argument is the accumulator. The function
+        must return a new accumulator, which is used the next time
         the function is called.</p>
-      <p>If we have a list of lists <c>L = ["I","like","Erlang"]</c>,
-        then we can sum the lengths of all the strings in <c>L</c> as
+      <p>If you have a list of lists <c>L = ["I","like","Erlang"]</c>,
+        then you can sum the lengths of all the strings in <c>L</c> as
         follows:</p>
       <pre>
 > <input>L = ["I","like","Erlang"].</input>
@@ -325,11 +327,11 @@ end</code>
 
     <section>
       <title>mapfoldl</title>
+      <p><c>mapfoldl</c> simultaneously maps and folds over a list:</p>
       <codeinclude file="funs1.erl" tag="%10" type="erl"></codeinclude>
-      <p><c>mapfoldl</c> simultaneously maps and folds over a list.
-        The following example shows how to change all letters in
-        <c>L</c> to upper case and count them.</p>
-      <p>First upcase:</p>
+      <p>The following example shows how to change all letters in
+        <c>L</c> to upper case and then count them.</p>
+      <p>First the change to upper case:</p>
       <pre>
 > <input>Upcase =  fun(X) when $a =&lt; X,  X =&lt; $z -> X + $A - $a;</input>
 <input>(X) -> X</input> 
@@ -344,7 +346,7 @@ end</code>
 "ERLANG"
 > <input>lists:map(Upcase_word, L).</input>
 ["I","LIKE","ERLANG"]</pre>
-      <p>Now we can do the fold and the map at the same time:</p>
+      <p>Now, the fold and the map can be done at the same time:</p>
       <pre>
 > <input>lists:mapfoldl(fun(Word, Sum) -></input>
 <input>{Upcase_word(Word), Sum + length(Word)}</input>
@@ -354,23 +356,24 @@ end</code>
 
     <section>
       <title>filter</title>
-      <codeinclude file="funs1.erl" tag="%9" type="erl"></codeinclude>
       <p><c>filter</c> takes a predicate of one argument and a list
-        and returns all element in the list which satisfy
-        the predicate.</p>
+        and returns all elements in the list that satisfy
+        the predicate:</p>
+      <codeinclude file="funs1.erl" tag="%9" type="erl"></codeinclude>
       <pre>
 > <input>lists:filter(Big, [500,12,2,45,6,7]).</input>
 [500,12,45]</pre>
-      <p>When we combine maps and filters we can write very succinct
-        code. For example, suppose we want to define a set difference
-        function. We want to define <c>diff(L1, L2)</c> to be
-        the difference between the lists <c>L1</c> and <c>L2</c>.
-        This is the list of all elements in L1 which are not contained
-        in L2. This code can be written as follows:</p>
+      <p>Combining maps and filters enables writing of very succinct
+        code. For example, to define a set difference
+        function <c>diff(L1, L2)</c> to be
+        the difference between the lists <c>L1</c> and <c>L2</c>,
+        the code can be written as follows:</p>
       <code type="none">
 diff(L1, L2) -> 
     filter(fun(X) -> not member(X, L2) end, L1).</code>
-      <p>The AND intersection of the list <c>L1</c> and <c>L2</c> is
+      <p>This gives the list of all elements in L1 that are not contained
+        in L2.</p>
+	<p> The AND intersection of the list <c>L1</c> and <c>L2</c> is
         also easily defined:</p>
       <code type="none">
 intersection(L1,L2) -> filter(fun(X) -> member(X,L1) end, L2).</code>
@@ -378,9 +381,9 @@ intersection(L1,L2) -> filter(fun(X) -> member(X,L1) end, L2).</code>
 
     <section>
       <title>takewhile</title>
-      <codeinclude file="funs1.erl" tag="%5" type="erl"></codeinclude>
       <p><c>takewhile(P, L)</c> takes elements <c>X</c> from a list
-        <c>L</c> as long as the predicate <c>P(X)</c> is true.</p>
+        <c>L</c> as long as the predicate <c>P(X)</c> is true:</p>
+      <codeinclude file="funs1.erl" tag="%5" type="erl"></codeinclude>
       <pre>
 > <input>lists:takewhile(Big, [200,500,45,5,3,45,6]).</input>  
 [200,500,45]</pre>
@@ -388,8 +391,8 @@ intersection(L1,L2) -> filter(fun(X) -> member(X,L1) end, L2).</code>
 
     <section>
       <title>dropwhile</title>
+      <p><c>dropwhile</c> is the complement of <c>takewhile</c>:</p>
       <codeinclude file="funs1.erl" tag="%6" type="erl"></codeinclude>
-      <p><c>dropwhile</c> is the complement of <c>takewhile</c>.</p>
       <pre>
 > <input>lists:dropwhile(Big, [200,500,45,5,3,45,6]).</input>
 [5,3,45,6]</pre>
@@ -397,10 +400,10 @@ intersection(L1,L2) -> filter(fun(X) -> member(X,L1) end, L2).</code>
 
     <section>
       <title>splitwith</title>
-      <codeinclude file="funs1.erl" tag="%7" type="erl"></codeinclude>
       <p><c>splitwith(P, L)</c> splits the list <c>L</c> into the two
-        sub-lists <c>{L1, L2}</c>, where <c>L = takewhile(P, L)</c>
-        and <c>L2 = dropwhile(P, L)</c>.</p>
+        sublists <c>{L1, L2}</c>, where <c>L = takewhile(P, L)</c>
+        and <c>L2 = dropwhile(P, L)</c>:</p>
+      <codeinclude file="funs1.erl" tag="%7" type="erl"></codeinclude>
       <pre>
 > <input>lists:splitwith(Big, [200,500,45,5,3,45,6]).</input>
 {[200,500,45],[5,3,45,6]}</pre>
@@ -408,17 +411,17 @@ intersection(L1,L2) -> filter(fun(X) -> member(X,L1) end, L2).</code>
   </section>
 
   <section>
-    <title>Funs Which Return Funs</title>
-    <p>So far, this section has only described functions which take
-      funs as arguments. It is also possible to write more powerful
-      functions which themselves return funs. The following examples
-      illustrate these type of functions.</p>
+    <title>Funs Returning Funs</title>
+    <p>So far, only functions that take
+      funs as arguments have been described. More powerful
+      functions, that themselves return funs, can also be written. The following
+      examples illustrate these type of functions.</p>
 
     <section>
       <title>Simple Higher Order Functions</title>
-      <p><c>Adder(X)</c> is a function which, given <c>X</c>, returns
+      <p><c>Adder(X)</c> is a function that given <c>X</c>, returns
         a new function <c>G</c> such that <c>G(K)</c> returns
-        <c>K + X</c>.</p>
+        <c>K + X</c>:</p>
       <pre>
 > <input>Adder = fun(X) -> fun(Y) -> X + Y end end.</input>
 #Fun&lt;erl_eval.6.72228031&gt;
@@ -438,7 +441,7 @@ ints_from(N) ->
     fun() ->
             [N|ints_from(N+1)]
     end.</code>
-      <p>Then we can proceed as follows:</p>
+      <p>Then proceed as follows:</p>
       <pre>
 > <input>XX = lazy:ints_from(1).</input>
 #Fun&lt;lazy.0.29874839&gt;
@@ -450,7 +453,7 @@ ints_from(N) ->
 #Fun&lt;lazy.0.29874839&gt;
 > <input>hd(Y()).</input>
 2</pre>
-      <p>etc. - this is an example of "lazy embedding".</p>
+      <p>And so on. This is an example of "lazy embedding".</p>
     </section>
 
     <section>
@@ -459,17 +462,21 @@ ints_from(N) ->
       <pre>
 Parser(Toks) -> {ok, Tree, Toks1} | fail</pre>
       <p><c>Toks</c> is the list of tokens to be parsed. A successful
-        parse returns <c>{ok, Tree, Toks1}</c>, where <c>Tree</c> is a
-        parse tree and <c>Toks1</c> is a tail of <c>Tree</c> which
-        contains symbols encountered after the structure which was
-        correctly parsed. Otherwise <c>fail</c> is returned.</p>
-      <p>The example which follows illustrates a simple, functional
-        parser which parses the grammar:</p>
+        parse returns <c>{ok, Tree, Toks1}</c>.</p>
+	<list type="bulleted">
+       <item><c>Tree</c> is a parse tree.</item>
+       <item><c>Toks1</c> is a tail of <c>Tree</c> that
+        contains symbols encountered after the structure that was
+        correctly parsed.</item>
+     </list>
+      <p>An unsuccessful parse returns <c>fail</c>.</p>
+      <p>The following example illustrates a simple, functional
+        parser that parses the grammar:</p>
       <pre>
 (a | b) &amp; (c | d)</pre>
       <p>The following code defines a function <c>pconst(X)</c> in
-        the module <c>funparse</c>, which returns a fun which parses a
-        list of tokens.</p>
+        the module <c>funparse</c>, which returns a fun that parses a
+        list of tokens:</p>
       <codeinclude file="funparse.erl" tag="%14" type="erl"></codeinclude>
       <p>This function can be used as follows:</p>
       <pre>
@@ -479,17 +486,18 @@ Parser(Toks) -> {ok, Tree, Toks1} | fail</pre>
 {ok,{const,a},[b,c]}
 > <input>P1([x,y,z]).</input>     
 fail</pre>
-      <p>Next, we define the two higher order functions <c>pand</c>
-        and <c>por</c> which combine primitive parsers to produce more
-        complex parsers. Firstly <c>pand</c>:</p>
+      <p>Next, the two higher order functions <c>pand</c>
+        and <c>por</c> are defined. They combine primitive parsers to produce more
+        complex parsers.</p>
+	<p>First <c>pand</c>:</p>
       <codeinclude file="funparse.erl" tag="%16" type="erl"></codeinclude>
       <p>Given a parser <c>P1</c> for grammar <c>G1</c>, and a parser
         <c>P2</c> for grammar <c>G2</c>, <c>pand(P1, P2)</c> returns a
-        parser for the grammar which consists of sequences of tokens
-        which satisfy <c>G1</c> followed by sequences of tokens which
+        parser for the grammar, which consists of sequences of tokens
+        that satisfy <c>G1</c>, followed by sequences of tokens that
         satisfy <c>G2</c>.</p>
       <p><c>por(P1, P2)</c> returns a parser for the language
-        described by the grammar <c>G1</c> or <c>G2</c>.</p>
+        described by the grammar <c>G1</c> or <c>G2</c>:</p>
       <codeinclude file="funparse.erl" tag="%15" type="erl"></codeinclude>
       <p>The original problem was to parse the grammar
         <c><![CDATA[(a | b) & (c | d)]]></c>. The following code addresses this
@@ -497,7 +505,7 @@ fail</pre>
       <codeinclude file="funparse.erl" tag="%13" type="erl"></codeinclude>
       <p>The following code adds a parser interface to the grammar:</p>
       <codeinclude file="funparse.erl" tag="%12" type="erl"></codeinclude>
-      <p>We can test this parser as follows:</p>
+      <p>The parser can be tested as follows:</p>
       <pre>
 > <input>funparse:parse([a,c]).</input>
 {ok,{'and',{'or',1,{const,a}},{'or',1,{const,c}}}}