<?xml version="1.0" encoding="utf-8" ?>
<!DOCTYPE chapter SYSTEM "chapter.dtd">
<chapter>
<header>
<copyright>
<year>2003</year><year>2013</year>
<holder>Ericsson AB. All Rights Reserved.</holder>
</copyright>
<legalnotice>
The contents of this file are subject to the Erlang Public License,
Version 1.1, (the "License"); you may not use this file except in
compliance with the License. You should have received a copy of the
Erlang Public License along with this software. If not, it can be
retrieved online at http://www.erlang.org/.
Software distributed under the License is distributed on an "AS IS"
basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See
the License for the specific language governing rights 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 <seealso
marker="doc/reference_manual:expressions#funs">Fun Expressions
</seealso> 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 writng 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<erl_eval.6.72228031>
> <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<erl_eval.6.72228031>
> <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 =< X, X =< $z -> X + $A - $a;</input>
<input>(X) -> X</input>
<input>end.</input>
#Fun<erl_eval.6.72228031>
> <input>Upcase_word =</input>
<input>fun(X) -></input>
<input>lists:map(Upcase, X)</input>
<input>end.</input>
#Fun<erl_eval.6.72228031>
> <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<erl_eval.6.72228031>
> <input>Add6 = Adder(6).</input>
#Fun<erl_eval.6.72228031>
> <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<lazy.0.29874839>
> <input>XX().</input>
[1|#Fun<lazy.0.29874839>]
> <input>hd(XX()).</input>
1
> <input>Y = tl(XX()).</input>
#Fun<lazy.0.29874839>
> <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) & (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<funparse.0.22674075>
> <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>