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<chapter>
  <header>
    <copyright>
      <year>2003</year><year>2016</year>
      <holder>Ericsson AB. All Rights Reserved.</holder>
    </copyright>
    <legalnotice>
      Licensed under the Apache License, Version 2.0 (the "License");
      you may not use this file except in compliance with the License.
      You may obtain a copy of the License at
 
          http://www.apache.org/licenses/LICENSE-2.0

      Unless required by applicable law or agreed to in writing, software
      distributed under the License is distributed on an "AS IS" BASIS,
      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
      See the License for the specific language governing permissions and
      limitations under the License.
    
    </legalnotice>

    <title>Funs</title>
    <prepared></prepared>
    <docno></docno>
    <date></date>
    <rev></rev>
    <file>funs.xml</file>
  </header>

  <section>
    <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>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>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>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>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 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 <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><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>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>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 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>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 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>Syntax of Funs</title>
    <p>Funs are written with the following syntax (see <seeguide
      marker="system/reference_manual:expressions#funs">Fun Expressions
      </seeguide> for full description):</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>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 that is
      referred to does not need to be exported from the module.</p>
    <p>It is also possible to refer to a function defined in a different module,
      with the following syntax:</p>
    <code type="none">
F = fun Module:FunctionName/Arity</code>
    <p>In this case, the function must be exported from the module in
      question.</p>
    <p>The following program illustrates the different ways of creating
      funs:</p>
    <codeinclude file="fun_test.erl" tag="%1" type="erl"></codeinclude>
    <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.</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 <c>erlang:fun_info/1,2</c> can
      be used to retrieve information about a fun, and the BIF
      <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>
  </section>

  <section>
    <title>Variable Bindings Within a Fun</title>
    <p>The scope rules for variables that occur in funs are as
      follows:</p>
    <list type="bulleted">
      <item>All variables that occur in the head of a fun are assumed
       to be "fresh" variables.</item>
      <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>Variables cannot be exported from a fun.</item>
    </list>
    <p>The following examples illustrate these rules:</p>
    <code type="none">
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>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>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),
    foreach(fun(File) -> 
                io:format(Stream,"~p~n",[File]) 
            end, List),
    file:close(Stream).</code>
    <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 'fun'</code>
    <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 must be moved into
      guard expressions and cannot be written in the head of the fun.
      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">
f(...) ->
    Y = ...
    map(fun(X) when X == Y ->
             ;
           (_) ->
             ...
        end, ...)
    ...</code>
    <p>instead of writing the following code:</p>
    <code type="none">
f(...) ->
    Y = ...
    map(fun(Y) ->
             ;
           (_) ->
             ...
        end, ...)
    ...</code>
  </section>

  <section>
    <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>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>

    </section>

    <section>
      <title>any</title>
      <p><c>any</c> takes a predicate <c>P</c> of one argument and a
        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;
> <input>lists:any(Big, [1,2,3,4]).</input>
false
> <input>lists:any(Big, [1,2,3,12,5]).</input>
true</pre>
    </section>

    <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>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
> <input>lists:all(Big, [12,13,14,15]).</input>       
true</pre>
    </section>

    <section>
      <title>foreach</title>
      <p><c>foreach</c> takes a function of one argument and a list of
        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
2
3
4
ok</pre>
    </section>

    <section>
      <title>foldl</title>
      <p><c>foldl</c> takes a function of two arguments, an
        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 function is called.</p>
      <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>
["I","like","Erlang"]
10> <input>lists:foldl(fun(X, Sum) -> length(X) + Sum end, 0, L).</input>                    
11</pre>
      <p><c>foldl</c> works like a <c>while</c> loop in an imperative
        language:</p>
      <code type="none">
L =  ["I","like","Erlang"],
Sum = 0,
while( L != []){
    Sum += length(head(L)),
    L = tail(L)
end</code>
    </section>

    <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>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> 
<input>end.</input>
#Fun&lt;erl_eval.6.72228031&gt;
> <input>Upcase_word =</input> 
<input>fun(X) -></input> 
<input>lists:map(Upcase, X)</input> 
<input>end.</input>
#Fun&lt;erl_eval.6.72228031&gt;
> <input>Upcase_word("Erlang").</input>
"ERLANG"
> <input>lists:map(Upcase_word, L).</input>
["I","LIKE","ERLANG"]</pre>
      <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>
<input>end, 0, L).</input>
{["I","LIKE","ERLANG"],11}</pre>
    </section>

    <section>
      <title>filter</title>
      <p><c>filter</c> takes a predicate of one argument and a list
        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>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>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>
    </section>

    <section>
      <title>takewhile</title>
      <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>
      <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>
    </section>

    <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>
      <pre>
> <input>lists:dropwhile(Big, [200,500,45,5,3,45,6]).</input>
[5,3,45,6]</pre>
    </section>

    <section>
      <title>splitwith</title>
      <p><c>splitwith(P, L)</c> splits the list <c>L</c> into the two
        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>
    </section>
  </section>

  <section>
    <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 that given <c>X</c>, returns
        a new function <c>G</c> such that <c>G(K)</c> returns
        <c>K + X</c>:</p>
      <pre>
> <input>Adder = fun(X) -> fun(Y) -> X + Y end end.</input>
#Fun&lt;erl_eval.6.72228031&gt;
> <input>Add6 = Adder(6).</input>
#Fun&lt;erl_eval.6.72228031&gt;
> <input>Add6(10).</input>
16</pre>
    </section>

    <section>
      <title>Infinite Lists</title>
      <p>The idea is to write something like:</p>
      <code type="none">
-module(lazy).
-export([ints_from/1]).
ints_from(N) ->
    fun() ->
            [N|ints_from(N+1)]
    end.</code>
      <p>Then proceed as follows:</p>
      <pre>
> <input>XX = lazy:ints_from(1).</input>
#Fun&lt;lazy.0.29874839&gt;
> <input>XX().</input>
[1|#Fun&lt;lazy.0.29874839&gt;]
> <input>hd(XX()).</input>
1
> <input>Y = tl(XX()).</input>
#Fun&lt;lazy.0.29874839&gt;
> <input>hd(Y()).</input>
2</pre>
      <p>And so on. This is an example of "lazy embedding".</p>
    </section>

    <section>
      <title>Parsing</title>
      <p>The following examples show parsers of the following type:</p>
      <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>.</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 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>
> <input>P1 = funparse:pconst(a).</input>
#Fun&lt;funparse.0.22674075&gt;
> <input>P1([a,b,c]).</input>
{ok,{const,a},[b,c]}
> <input>P1([x,y,z]).</input>     
fail</pre>
      <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
        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>
      <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
        problem:</p>
      <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>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}}}}
> <input>funparse:parse([a,d]).</input> 
{ok,{'and',{'or',1,{const,a}},{'or',2,{const,d}}}}
> <input>funparse:parse([b,c]).</input>   
{ok,{'and',{'or',2,{const,b}},{'or',1,{const,c}}}}
> <input>funparse:parse([b,d]).</input> 
{ok,{'and',{'or',2,{const,b}},{'or',2,{const,d}}}}
> <input>funparse:parse([a,b]).</input>   
fail</pre>
    </section>
  </section>
</chapter>

