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<!DOCTYPE chapter SYSTEM "chapter.dtd">

<chapter>
  <header>
    <copyright>
      <year>2003</year><year>2017</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>Sequential Programming</title>
    <prepared></prepared>
    <docno></docno>
    <date></date>
    <rev></rev>
    <file>seq_prog.xml</file>
  </header>

  <section>
    <title>The Erlang Shell</title>
    <p>
      Most operating systems have a command interpreter or shell, UNIX
      and Linux have many, Windows has the command prompt. Erlang has
      its own shell where bits of Erlang code can be written directly,
      and be evaluated to see what happens
      (see the <seeerl marker="stdlib:shell">shell(3)</seeerl>
      manual page in STDLIB).
    </p>
    <p>Start
      the Erlang shell (in Linux or UNIX) by starting a shell or
      command interpreter in your operating system and typing
      <c>erl</c>. You will see something like this.</p>
    <pre>
% <input>erl</input>
Erlang R15B (erts-5.9.1) [source] [smp:8:8] [rq:8] [async-threads:0] [hipe] [kernel-poll:false]

Eshell V5.9.1  (abort with ^G)
1></pre>
    <p>Type "2 + 5." in the shell and then press Enter (carriage return).
    Notice that you tell the shell you are done entering code by finishing
    with a full stop "." and a carriage return.</p>
    <pre>
1> <input>2 + 5.</input>
7
2></pre>
    <p>As shown, the Erlang shell numbers the lines that
      can be entered, (as 1&gt; 2&gt;) and that it correctly says
      that 2 + 5 is 7. If you make writing mistakes in the shell,
      you can delete with the backspace key, as in most shells.
      There are many more editing commands in the shell
      (see <seeguide marker="erts:tty">tty - A command line interface</seeguide> in ERTS User's Guide).</p>
    <p>(Notice that many line numbers given by the shell in the
      following examples are out of sequence. This is because this
      tutorial was written and code-tested in separate sessions).</p>
    <p>Here is a bit more complex calculation:</p>
    <pre>
2> <input>(42 + 77) * 66 / 3.</input>
2618.0</pre>
    <p>Notice the use of brackets, the multiplication operator "*",
      and the division operator "/", as in normal arithmetic (see
      <seeguide marker="system/reference_manual:expressions">Expressions</seeguide>).</p>
    <p>Press Control-C to shut down the Erlang system and the Erlang
      shell.</p>
    <p>The following output is shown:</p>
    <pre>
BREAK: (a)bort (c)ontinue (p)roc info (i)nfo (l)oaded
       (v)ersion (k)ill (D)b-tables (d)istribution
<input>a</input>
%</pre>
    <p>Type "a" to leave the Erlang system.</p>
    <p>Another way to shut down the Erlang system is by entering
      <c>halt()</c>:</p>
    <pre>
3> <input>halt().</input>
% </pre>
  </section>

  <section>
    <title>Modules and Functions</title>
    <p>A programming language is not much use if you only can run code
      from the shell. So here is a small Erlang program. Enter it into
      a file named <c>tut.erl</c> using a suitable
      text editor. The file name <c>tut.erl</c> is important, and also
      that it is in the same directory as the one where you started
      <c>erl</c>). If you are lucky your editor has an Erlang mode
      that makes it easier for you to enter and format your code
      nicely (see <seeguide
      marker="tools:erlang_mode_chapter">The Erlang mode for
      Emacs</seeguide> in Tools User's Guide), but you can manage
      perfectly well without. Here is the code to enter:</p>
    <code type="none">
-module(tut).
-export([double/1]).

double(X) ->
    2 * X.</code>
    <p>It is not hard to guess that this program doubles the value of
      numbers. The first two lines of the code are described later.
      Let us compile the program. This can be done in an Erlang shell
      as follows, where <c>c</c> means compile:</p>
    <pre>
3> <input>c(tut).</input>
{ok,tut}</pre>
    <p>The <c>{ok,tut}</c> means that the compilation is OK. If it
      says "error" it means that there is some mistake in the text
      that you entered. Additional error messages gives an idea to
      what is wrong so you can modify the text and then try to compile
      the program again.</p>
    <p>Now run the program:</p>
    <pre>
4> <input>tut:double(10).</input>
20</pre>
    <p>As expected, double of 10 is 20.</p>
    <p>Now let us get back to the first two lines of the code. Erlang
      programs are
      written in files. Each file contains an Erlang
      <em>module</em>. The first line of code in the module is
      the module name (see
      <seeguide marker="system/reference_manual:modules">Modules</seeguide>):</p>
    <code type="none">
-module(tut).</code>
    <p>Thus, the module is called <em>tut</em>. Notice
      the full stop "." at the end of the line. The files which are
      used to store
      the module must have the same name as the module but with
      the extension ".erl". In this case the file name is <c>tut.erl</c>.
      When using a function in another module, the syntax
      <c>module_name:function_name(arguments)</c> is used. So the
      following means call function <c>double</c> in module <c>tut</c>
      with argument "10".</p>
    <pre>
4> <input>tut:double(10).</input></pre>
    <p>The second line says that the module <c>tut</c> contains a
      function called <c>double</c>, which takes one argument
      (<c>X</c> in our example):</p>
    <code type="none">
-export([double/1]).</code>
    <p>The second line also says that this function can be called from
      outside the module <c>tut</c>. More about this later. Again,
      notice the "." at the end of the line.</p>
    <p>Now for a more complicated example, the factorial of a number.
      For example, the factorial of 4 is 4 * 3 * 2 * 1, which equals 24.</p>
    <p>Enter the following code in a file named <c>tut1.erl</c>:</p>
    <code type="none">
-module(tut1).
-export([fac/1]).

fac(1) ->
    1;
fac(N) ->
    N * fac(N - 1).</code>
    <p>So this is a module, called <c>tut1</c> that contains a
      function called <c>fac></c>, which takes one argument,
      <c>N</c>.</p>
    <p>The first part says that the factorial of 1 is 1.:</p>
    <code type="none">
fac(1) ->
    1;</code>
    <p>Notice that this part ends with a semicolon ";" that indicates
      that there is more of the function <c>fac></c> to come.</p>
    <p>The second part says that the factorial of N is N multiplied
      by the factorial of N - 1:</p>
    <code type="none">
fac(N) ->
    N * fac(N - 1).</code>
    <p>Notice that this part ends with a "." saying that there are
      no more parts of this function.</p>
    <p>Compile the file:</p>
    <pre>
5> <input>c(tut1).</input>
{ok,tut1}</pre>
    <p>And now calculate the factorial of 4.</p>
    <pre>
6> <input>tut1:fac(4).</input>
24</pre>
    <p>Here the function <c>fac></c> in module <c>tut1</c> is called
      with argument <c>4</c>.</p>
    <p>A function can have many arguments. Let us expand the module
      <c>tut1</c> with the function to multiply two numbers:</p>
    <code type="none">
-module(tut1).
-export([fac/1, mult/2]).

fac(1) ->
    1;
fac(N) ->
    N * fac(N - 1).

mult(X, Y) ->
    X * Y.</code>
    <p>Notice that it is also required to expand the <c>-export</c> line
      with the information that there is another function <c>mult</c>
      with two arguments.</p>
    <p>Compile:</p>
    <pre>
7> <input>c(tut1).</input>
{ok,tut1}</pre>
    <p>Try out the new function <c>mult</c>:</p>
    <pre>
8> <input>tut1:mult(3,4).</input>
12</pre>
    <p>In this example the numbers are integers and the arguments
      in the functions in the code <c>N</c>, <c>X</c>, and <c>Y</c> are
      called variables. Variables must start with a capital letter
      (see
      <seeguide marker="system/reference_manual:expressions">Variables</seeguide>).
      Examples of variables are
      <c>Number</c>, <c>ShoeSize</c>, and <c>Age</c>.</p>
  </section>

  <section>
    <title>Atoms</title>
    <p>Atom is another data type in Erlang. Atoms start with a small
      letter (see
      <seeguide marker="system/reference_manual:data_types">Atom</seeguide>),
      for example, <c>charles</c>,
      <c>centimeter</c>, and <c>inch</c>. Atoms are simply names, nothing
      else. They are not like variables, which can have a value.</p>
    <p>Enter the next program in a file named <c>tut2.erl</c>). It can be
      useful for converting from inches to centimeters and conversely:</p>
    <code type="none">
-module(tut2).
-export([convert/2]).

convert(M, inch) ->
    M / 2.54;

convert(N, centimeter) ->
    N * 2.54.</code>
    <p>Compile:</p>
    <pre>
9> <input>c(tut2).</input>
{ok,tut2}
</pre>
    <p>Test:</p>
 <pre>
10> <input>tut2:convert(3, inch).</input>
1.1811023622047243
11> <input>tut2:convert(7, centimeter).</input>
17.78</pre>
    <p>Notice the introduction of decimals (floating point numbers)
      without any explanation. Hopefully you can cope with that.</p>
    <p>Let us see what happens if something other than <c>centimeter</c> or
      <c>inch</c> is entered in the <c>convert</c> function:</p>
    <pre>
12> <input>tut2:convert(3, miles).</input>
** exception error: no function clause matching tut2:convert(3,miles) (tut2.erl, line 4)</pre>
    <p>The two parts of the <c>convert</c> function are called its
      clauses. As shown, <c>miles</c> is not part of either of
      the clauses. The Erlang system cannot <em>match</em> either of
      the clauses so an error message <c>function_clause</c> is returned.
      The shell formats the error message nicely, but the error tuple
      is saved in the shell's history list and can be output by the shell
      command <c>v/1</c>:</p>
    <pre>
13> <input>v(12).</input>
{'EXIT',{function_clause,[{tut2,convert,
                                [3,miles],
                                [{file,"tut2.erl"},{line,4}]},
                          {erl_eval,do_apply,6,
                                    [{file,"erl_eval.erl"},{line,677}]},
                          {shell,exprs,7,[{file,"shell.erl"},{line,687}]},
                          {shell,eval_exprs,7,[{file,"shell.erl"},{line,642}]},
                          {shell,eval_loop,3,
                                 [{file,"shell.erl"},{line,627}]}]}}</pre>
  </section>

  <section>
    <title>Tuples</title>
    <p>Now the <c>tut2</c> program is hardly good programming style.
      Consider:</p>
    <code type="none">
tut2:convert(3, inch).</code>
    <p>Does this mean that 3 is in inches? Or does it mean that 3 is
      in centimeters
      and is to be converted to inches? Erlang has a way to group
      things together to make things more understandable. These are called
      <em>tuples</em> and are surrounded by curly brackets, "{" and "}".</p>
    <p>So, <c>{inch,3}</c> denotes 3 inches and
      <c>{centimeter,5}</c> denotes 5 centimeters. Now let us write a
      new program that converts centimeters to inches and conversely.
      Enter the following code in a file called <c>tut3.erl</c>):</p>
    <code type="none">
-module(tut3).
-export([convert_length/1]).

convert_length({centimeter, X}) ->
    {inch, X / 2.54};
convert_length({inch, Y}) ->
    {centimeter, Y * 2.54}.</code>
    <p>Compile and test:</p>
    <pre>
14> <input>c(tut3).</input>
{ok,tut3}
15> <input>tut3:convert_length({inch, 5}).</input>
{centimeter,12.7}
16> <input>tut3:convert_length(tut3:convert_length({inch, 5})).</input>
{inch,5.0}</pre>
    <p>Notice on line 16 that 5 inches is converted to centimeters and back
      again and reassuringly get back to the original value. That is,
      the argument to a function can be the result of another function.
      Consider how line 16 (above) works.
      The argument given to the function <c>{inch,5}</c> is first
      matched against the first head clause of <c>convert_length</c>,
      that is, <c>convert_length({centimeter,X})</c>. It can be seen
      that <c>{centimeter,X}</c> does not match <c>{inch,5}</c>
      (the head is the bit before the "-&gt;"). This having failed,
      let us try
      the head of the next clause that is, <c>convert_length({inch,Y})</c>.
      This matches, and <c>Y</c> gets the value 5.</p>
    <p>Tuples can have more than two parts, in fact
      as many parts as you want, and contain any valid Erlang
      <em>term</em>. For example, to represent the temperature of
      various cities of the world:</p>
    <code type="none">
{moscow, {c, -10}}
{cape_town, {f, 70}}
{paris, {f, 28}}</code>
    <p>Tuples have a fixed number of items in them. Each item in a
      tuple is called an <em>element</em>. In the tuple
      <c>{moscow,{c,-10}}</c>, element 1 is <c>moscow</c> and element
      2 is <c>{c,-10}</c>. Here <c>c</c> represents Celsius and
      <c>f</c> Fahrenheit.</p>
  </section>

  <section>
    <title>Lists</title>
    <p>Whereas tuples group things together, it is also needed to
      represent lists of things. Lists in Erlang are surrounded by
      square brackets, "[" and "]". For example, a list of the
      temperatures of various cities in the world can be:</p>
    <code type="none">
[{moscow, {c, -10}}, {cape_town, {f, 70}}, {stockholm, {c, -4}},
 {paris, {f, 28}}, {london, {f, 36}}]</code>
    <p>Notice that this list was so long that it did not fit on one line.
      This does not matter, Erlang allows line breaks at all "sensible
      places" but not, for example, in the middle of atoms, integers,
       and others.</p>
    <p>A useful way of looking at parts of lists, is by using "|".
      This is best explained by an example using the shell:</p>
    <pre>
17> <input>[First |TheRest] = [1,2,3,4,5].</input>
[1,2,3,4,5]
18> <input>First.</input>
1
19> <input>TheRest.</input>
[2,3,4,5]</pre>
    <p>To separate the first elements of the list from the rest of the
      list, <c>|</c> is used. <c>First</c> has got value 1 and
      <c>TheRest</c> has got the value [2,3,4,5].</p>
    <p>Another example:</p>
    <pre>
20> <input>[E1, E2 | R] = [1,2,3,4,5,6,7].</input>
[1,2,3,4,5,6,7]
21> <input>E1.</input>
1
22> <input>E2.</input>
2
23> <input>R.</input>
[3,4,5,6,7]</pre>
    <p>Here you see the use of <c>|</c> to get the first two elements from
      the list. If you try to get more elements from the list
      than there are elements in the list, an error is returned. Notice
      also the special case of the list with no elements, []:</p>
    <pre>
24> <input>[A, B | C] = [1, 2].</input>
[1,2]
25> <input>A.</input>
1
26> <input>B.</input>
2
27> <input>C.</input>
[]</pre>
    <p>In the previous examples, new variable names are used, instead of
      reusing the old ones: <c>First</c>, <c>TheRest</c>, <c>E1</c>,
      <c>E2</c>, <c>R</c>, <c>A</c>, <c>B</c>, and <c>C</c>. The reason
      for this is that a variable can only be given a value once in its
      context (scope). More about this later.</p>
    <p>The following example shows how to find the length of a list.
     Enter the following code in a file named <c>tut4.erl</c>):</p>
    <code type="none">
-module(tut4).

-export([list_length/1]).

list_length([]) ->
    0;    
list_length([First | Rest]) ->
    1 + list_length(Rest).</code>
    <p>Compile and test:</p>
    <pre>
28> <input>c(tut4).</input>
{ok,tut4}
29> <input>tut4:list_length([1,2,3,4,5,6,7]).</input>
7</pre>
    <p>Explanation:</p>
    <code type="none">
list_length([]) ->
    0;</code>
    <p>The length of an empty list is obviously 0.</p>
    <code type="none">
list_length([First | Rest]) ->
    1 + list_length(Rest).</code>
    <p>The length of a list with the first element <c>First</c> and
      the remaining elements <c>Rest</c> is 1 + the length of
      <c>Rest</c>.</p>
    <p>(Advanced readers only: This is not tail recursive, there is a
      better way to write this function.)</p>
    <p>In general, tuples are used where "records"
      or "structs" are used in other languages. Also, lists are used when
      representing things with varying sizes, that is, where
      linked lists are used in other languages.</p>
    <p>Erlang does not have a string data type. Instead, strings can be
      represented by lists of Unicode characters. This implies for example that
      the list <c>[97,98,99]</c> is equivalent to "abc". The Erlang shell is
      "clever" and guesses what list you  mean and outputs it
      in what it thinks is the most appropriate form, for example:</p>
    <pre>
30> <input>[97,98,99].</input>
"abc"</pre>
  </section>

  <section>
    <title>Maps</title>
    <p>Maps are a set of key to value associations. These associations
      are encapsulated with "#{" and "}". To create an association
      from "key" to value 42:</p>
<code type="none">
> #{ "key" => 42 }.
#{"key" => 42}</code>
    <p>Let us jump straight into the deep end with an example using some
      interesting features.</p>
    <p>The following example shows how to calculate alpha blending
      using maps to reference color and alpha channels. Enter the code
      in a file named <c>color.erl</c>):</p>
    <code type="none">
-module(color).

-export([new/4, blend/2]).

-define(is_channel(V), (is_float(V) andalso V &gt;= 0.0 andalso V =&lt; 1.0)).

new(R,G,B,A) when ?is_channel(R), ?is_channel(G),
                  ?is_channel(B), ?is_channel(A) ->
    #{red =&gt; R, green =&gt; G, blue =&gt; B, alpha =&gt; A}.

blend(Src,Dst) ->
    blend(Src,Dst,alpha(Src,Dst)).

blend(Src,Dst,Alpha) when Alpha > 0.0 ->
    Dst#{
        red   := red(Src,Dst) / Alpha,
        green := green(Src,Dst) / Alpha,
        blue  := blue(Src,Dst) / Alpha,
        alpha := Alpha
    };
blend(_,Dst,_) ->
    Dst#{
        red   := 0.0,
        green := 0.0,
        blue  := 0.0,
        alpha := 0.0
    }.

alpha(#{alpha := SA}, #{alpha := DA}) ->
    SA + DA*(1.0 - SA).

red(#{red := SV, alpha := SA}, #{red := DV, alpha := DA}) ->
    SV*SA + DV*DA*(1.0 - SA).
green(#{green := SV, alpha := SA}, #{green := DV, alpha := DA}) ->
    SV*SA + DV*DA*(1.0 - SA).
blue(#{blue := SV, alpha := SA}, #{blue := DV, alpha := DA}) ->
    SV*SA + DV*DA*(1.0 - SA).</code>
    <p>Compile and test:</p>
    <pre>
> <input>c(color).</input>
{ok,color}
> <input>C1 = color:new(0.3,0.4,0.5,1.0).</input>
#{alpha => 1.0,blue => 0.5,green => 0.4,red => 0.3}
> <input>C2 = color:new(1.0,0.8,0.1,0.3).</input>
#{alpha => 0.3,blue => 0.1,green => 0.8,red => 1.0}
> <input>color:blend(C1,C2).</input>
#{alpha => 1.0,blue => 0.5,green => 0.4,red => 0.3}
> <input>color:blend(C2,C1).</input>
#{alpha => 1.0,blue => 0.38,green => 0.52,red => 0.51}
</pre>
    <p>This example warrants some explanation:</p>
    <code type="none">
-define(is_channel(V), (is_float(V) andalso V &gt;= 0.0 andalso V =&lt; 1.0)).</code>
    <p>First a macro <c>is_channel</c> is defined to help with the
      guard tests. This is only here for convenience and to reduce
      syntax cluttering. For more information about macros, see
      <seeguide marker="system/reference_manual:macros">
      The Preprocessor</seeguide>.
    </p>
    <code type="none">
new(R,G,B,A) when ?is_channel(R), ?is_channel(G),
                  ?is_channel(B), ?is_channel(A) ->
    #{red =&gt; R, green =&gt; G, blue =&gt; B, alpha =&gt; A}.</code>
    <p>The function <c>new/4</c> creates a new map term and lets the keys
      <c>red</c>, <c>green</c>, <c>blue</c>, and <c>alpha</c> be
      associated with an initial value. In this case, only float
      values between and including 0.0 and 1.0 are allowed, as ensured
      by the <c>?is_channel/1</c> macro for each argument. Only the
      <c>=></c> operator is allowed when creating a new map.
    </p>
    <p>By calling <c>blend/2</c> on any color term created by
      <c>new/4</c>, the resulting color can be calculated as
      determined by the two map terms.
    </p>
    <p>The first thing <c>blend/2</c> does is to calculate the
      resulting alpha channel:
    </p>
    <code type="none">
alpha(#{alpha := SA}, #{alpha := DA}) ->
    SA + DA*(1.0 - SA).</code>
    <p>The value associated with key <c>alpha</c> is fetched for both
      arguments using the <c>:=</c> operator. The other keys in the
      map are ignored, only the key <c>alpha</c> is required and
      checked for.
    </p>
    <p>This is also the case for functions <c>red/2</c>,
      <c>blue/2</c>, and <c>green/2</c>.</p>
    <code type="none">
red(#{red := SV, alpha := SA}, #{red := DV, alpha := DA}) ->
    SV*SA + DV*DA*(1.0 - SA).</code>
    <p>The difference here is that a check is made for two keys in
      each map argument. The other keys are ignored.
    </p>
    <p>Finally, let us return the resulting color in <c>blend/3</c>:
    </p>
    <code type="none">
blend(Src,Dst,Alpha) when Alpha > 0.0 ->
    Dst#{
        red   := red(Src,Dst) / Alpha,
        green := green(Src,Dst) / Alpha,
        blue  := blue(Src,Dst) / Alpha,
        alpha := Alpha
    };</code>
    <p>The <c>Dst</c> map is updated with new channel values. The
      syntax for updating an existing key with a new value is with the
      <c>:=</c> operator.
    </p>
  </section>

  <section>
    <title>Standard Modules and Manual Pages</title>
    <p>Erlang has many standard modules to help you do things. For
      example, the module <c>io</c> contains many functions that help
      in doing formatted input/output. To look up information about
      standard modules, the command <c>erl -man</c> can be used at the
      operating shell or command prompt (the same place as you started
      <c>erl</c>). Try the operating system shell command:</p>
    <pre>
% <input>erl -man io</input>
ERLANG MODULE DEFINITION                                    io(3)

MODULE
     io - Standard I/O Server Interface Functions

DESCRIPTION
     This module provides an  interface  to  standard  Erlang  IO
     servers. The output functions all return ok if they are suc-
     ...</pre>
    <p>If this does not work on your system, the documentation is
      included as HTML in the Erlang/OTP release. You can also read
      the documentation as HTML or download it as PDF from either of
      the sites www.erlang.se (commercial Erlang) or www.erlang.org
      (open source). For example, for Erlang/OTP release R9B:</p>
    <code type="none">
http://www.erlang.org/doc/r9b/doc/index.html</code>
  </section>

  <section>
    <title>Writing Output to a Terminal</title>
    <p>It is nice to be able to do formatted output in examples, so
      the next example shows a simple way to use the <c>io:format</c>
      function. Like all other exported functions, you can test the
      <c>io:format</c> function in the shell:</p>
    <pre>
31> <input>io:format("hello world~n", []).</input>
hello world
ok
32> <input>io:format("this outputs one Erlang term: ~w~n", [hello]).</input>
this outputs one Erlang term: hello
ok
33> <input>io:format("this outputs two Erlang terms: ~w~w~n", [hello, world]).</input>
this outputs two Erlang terms: helloworld
ok
34> <input>io:format("this outputs two Erlang terms: ~w ~w~n", [hello, world]).</input>
this outputs two Erlang terms: hello world
ok</pre>
    <p>The function <c>format/2</c> (that is, <c>format</c> with two
      arguments) takes two lists. The first one is nearly always a list
      written between " ". This list is printed out as it is,
      except that each ~w is replaced by a term taken in order from
      the second list. Each ~n is replaced by a new line.
      The <c>io:format/2</c> function itself returns the atom <c>ok</c>
      if everything goes as planned. Like other functions in Erlang, it
      crashes if an error occurs. This is not a fault in Erlang, it is
      a deliberate policy. Erlang has sophisticated mechanisms to
      handle errors which are shown later. As an exercise, try to
      make <c>io:format</c> crash, it should not be difficult. But
      notice that although <c>io:format</c> crashes, the Erlang shell
      itself does not crash.</p>
  </section>

  <section>
    <title>A Larger Example</title>
    <p>Now for a larger example to consolidate what you have learnt so
      far. Assume that you have a list of temperature readings from a number
      of cities in the world. Some of them are in Celsius
      and some in Fahrenheit (as in the previous list). First let us
      convert them all to Celsius, then let us print the data neatly.</p>
    <code type="none">
%% This module is in file tut5.erl

-module(tut5).
-export([format_temps/1]).

%% Only this function is exported
format_temps([])->                        % No output for an empty list
    ok;
format_temps([City | Rest]) ->
    print_temp(convert_to_celsius(City)),
    format_temps(Rest).

convert_to_celsius({Name, {c, Temp}}) ->  % No conversion needed
    {Name, {c, Temp}};
convert_to_celsius({Name, {f, Temp}}) ->  % Do the conversion
    {Name, {c, (Temp - 32) * 5 / 9}}.

print_temp({Name, {c, Temp}}) ->
    io:format("~-15w ~w c~n", [Name, Temp]).</code>
    <pre>
35> <input>c(tut5).</input>
{ok,tut5}
36> <input>tut5:format_temps([{moscow, {c, -10}}, {cape_town, {f, 70}},</input>
<input>{stockholm, {c, -4}}, {paris, {f, 28}}, {london, {f, 36}}]).</input>
moscow          -10 c
cape_town       21.11111111111111 c
stockholm       -4 c
paris           -2.2222222222222223 c
london          2.2222222222222223 c
ok</pre>
    <p>Before looking at how this program works, notice that
      a few comments are added to the code. A comment starts with a
      %-character and goes on to the end of the line. Notice also that
      the <c>-export([format_temps/1]).</c> line only includes
      the function <c>format_temps/1</c>. The other functions are
      <em>local</em> functions, that is, they are not visible from outside
      the module <c>tut5</c>.</p>
    <p>Notice also that when testing the program from the shell,
      the input is spread over two lines as the line was too long.</p>
    <p>When <c>format_temps</c> is called the first time, <c>City</c>
      gets the value <c>{moscow,{c,-10}}</c> and <c>Rest</c> is
      the rest of the list. So the function
      <c>print_temp(convert_to_celsius({moscow,{c,-10}}))</c> is called.</p>
    <p>Here is a function call as
      <c>convert_to_celsius({moscow,{c,-10}})</c> as the argument to
      the function <c>print_temp</c>. When function calls are <em>nested</em>
      like this, they execute (evaluate) from the inside out.
      That is, first <c>convert_to_celsius({moscow,{c,-10}})</c> is evaluated,
      which gives the value <c>{moscow,{c,-10}}</c> as the temperature
      is already in Celsius. Then <c>print_temp({moscow,{c,-10}})</c>
      is evaluated.
      The function <c>convert_to_celsius</c> works in a similar way to
      the <c>convert_length</c> function in the previous example.</p>
    <p><c>print_temp</c> simply calls <c>io:format</c> in a similar way
      to what has been described above. Notice that ~-15w says to print
      the "term" with a field length (width) of 15 and left justify it.
      (see the <seemfa marker="stdlib:io#fwrite/1">io(3)</seemfa>) manual page in STDLIB.</p>
    <p>Now <c>format_temps(Rest)</c> is called with the rest of the list
      as an argument. This way of doing things is similar to the loop
      constructs in other languages. (Yes, this is recursion, but do not
      let that worry you.) So the same <c>format_temps</c> function is
      called again, this time <c>City</c> gets the value
      <c>{cape_town,{f,70}}</c> and the same procedure is repeated as
      before. This is done until the list becomes empty, that is [],
      which causes the first clause <c>format_temps([])</c> to match.
      This simply returns (results in) the atom <c>ok</c>, so
      the program ends.</p>
  </section>

  <section>
    <title>Matching, Guards, and Scope of Variables</title>
    <p>It can be useful to find the maximum and minimum temperature
      in lists like this. Before extending the program to do this,
      let us look at functions for finding the maximum value of
      the elements in a list:</p>
    <code type="none">
-module(tut6).
-export([list_max/1]).

list_max([Head|Rest]) ->
   list_max(Rest, Head).

list_max([], Res) ->
    Res;
list_max([Head|Rest], Result_so_far) when Head > Result_so_far ->
    list_max(Rest, Head);
list_max([Head|Rest], Result_so_far)  ->
    list_max(Rest, Result_so_far).</code>
    <pre>
37> <input>c(tut6).</input>
{ok,tut6}
38> <input>tut6:list_max([1,2,3,4,5,7,4,3,2,1]).</input>
7</pre>
    <p>First notice that two functions have the same name,
      <c>list_max</c>. However, each of these takes a different number
      of arguments (parameters). In Erlang these are regarded as
      completely different functions. Where you need to distinguish
      between these functions, you write Name/Arity, where
      Name is the function name and Arity is
      the number of arguments, in this case <c>list_max/1</c> and
      <c>list_max/2</c>.</p>
    <p>In this example you walk through a list "carrying" a
      value, in this case <c>Result_so_far</c>.
      <c>list_max/1</c> simply assumes that the max value of the list
      is the head of the list and calls <c>list_max/2</c> with the rest
      of the list and the value of the head of the list. In the above
      this would be <c>list_max([2,3,4,5,7,4,3,2,1],1)</c>. If you tried
      to use <c>list_max/1</c> with an empty list or tried to use it
      with something that is not a list at all, you would cause an error.
      Notice that the Erlang philosophy is not to handle errors of this
      type in the function they occur, but to do so elsewhere. More
      about this later.</p>
    <p>In <c>list_max/2</c>, you walk down the list and use <c>Head</c>
      instead of <c>Result_so_far</c> when <c>Head</c> &gt;
      <c>Result_so_far</c>. <c>when</c> is a special word used before
      the -&gt; in the function to say that you only use this part
      of the function if the test that follows is true. A test
      of this type is called <em>guard</em>. If the guard is false (that is,
      the guard fails), the next part of the function is tried. In this
      case, if <c>Head</c> is not greater than <c>Result_so_far</c>, then
      it must be smaller or equal to it. This means that a guard on
      the next part of the function is not needed.</p>
    <p>Some useful operators in guards are:
    </p><list type="bulleted"><item>&lt; less than</item>
    <item>&gt; greater than</item>
    <item>== equal</item>
    <item>&gt;= greater or equal</item>
    <item>=&lt; less or equal</item>
    <item>/= not equal</item></list>
    <p>(see <seeguide marker="system/reference_manual:expressions">Guard Sequences</seeguide>).</p>
    <p>To change the above program to one that works out the minimum
      value of the element in a list, you only need to
      write &lt; instead of &gt;. (But it would be wise to change
      the name of the function to <c>list_min</c>.)</p>
    <p>Earlier it was mentioned that a variable can only be
      given a value once in its scope. In the above you see
      that <c>Result_so_far</c> is given several values. This is
      OK since every time you call <c>list_max/2</c> you create a new
      scope and one can regard <c>Result_so_far</c> as a
      different variable in each scope.</p>
    <p>Another way of creating and giving a variable a value is by using
      the match operator = . So if you write <c>M = 5</c>, a variable
      called <c>M</c> is created with the value 5. If, in
      the same scope, you then write <c>M = 6</c>, an error is returned. Try
      this out in the shell:</p>
    <pre>
39> <input>M = 5.</input>
5
40> <input>M = 6.</input>
** exception error: no match of right hand side value 6
41> <input>M = M + 1.</input>
** exception error: no match of right hand side value 6
42> <input>N = M + 1.</input>
6</pre>
    <p>The use of the match operator is particularly useful for pulling
      apart Erlang terms and creating new ones.</p>
    <pre>
43> <input>{X, Y} = {paris, {f, 28}}.</input>
{paris,{f,28}}
44> <input>X.</input>
paris
45> <input>Y.</input>
{f,28}</pre>
    <p>Here <c>X</c> gets the value <c>paris</c> and
      <c>Y</c><c>{f,28}</c>.</p>
    <p>If you try to do the same again with another city,
      an error is returned:</p>
    <pre>
46> <input>{X, Y} = {london, {f, 36}}.</input>
** exception error: no match of right hand side value {london,{f,36}}</pre>
    <p>Variables can also be used to improve the readability of
      programs. For example, in function <c>list_max/2</c> above,
      you can write:</p>
    <code type="none">
list_max([Head|Rest], Result_so_far) when Head > Result_so_far ->
    New_result_far = Head,
    list_max(Rest, New_result_far);</code>
    <p>This is possibly a little clearer.</p>
  </section>

  <section>
    <title>More About Lists</title>
    <p>Remember that the | operator can be used to get the head of a
      list:</p>
    <pre>
47> <input>[M1|T1] = [paris, london, rome].</input>
[paris,london,rome]
48> <input>M1.</input>
paris
49> <input>T1.</input>
[london,rome]</pre>
    <p>The | operator can also be used to add a head to a list:</p>
    <pre>
50> <input>L1 = [madrid | T1].</input>
[madrid,london,rome]
51> <input>L1.</input>
[madrid,london,rome]</pre>
    <p>Now an example of this when working with lists - reversing
      the order of a list:</p>
    <code type="none">
-module(tut8).

-export([reverse/1]).

reverse(List) ->
    reverse(List, []).

reverse([Head | Rest], Reversed_List) ->
    reverse(Rest, [Head | Reversed_List]);
reverse([], Reversed_List) ->
    Reversed_List.</code>
    <pre>
52> <input>c(tut8).</input>
{ok,tut8}
53> <input>tut8:reverse([1,2,3]).</input>
[3,2,1]</pre>
    <p>Consider how <c>Reversed_List</c> is built. It starts as [],
      then successively the heads are taken off of the list to be reversed
      and added to the the <c>Reversed_List</c>, as shown in
      the following:</p>
    <code type="none">
reverse([1|2,3], []) =>
    reverse([2,3], [1|[]])

reverse([2|3], [1]) =>
    reverse([3], [2|[1])

reverse([3|[]], [2,1]) =>
    reverse([], [3|[2,1]])

reverse([], [3,2,1]) =>
    [3,2,1]</code>
    <p>The module <c>lists</c> contains many functions for
      manipulating lists, for example, for reversing them. So before
      writing a list-manipulating function it is a good idea to check
      if one not already is written for you
      (see the <seeerl marker="stdlib:lists">lists(3)</seeerl>
      manual page in STDLIB).</p>
    <p>Now let us get back to the cities and temperatures, but take a more
      structured approach this time. First let us convert the whole list
      to Celsius as follows:</p>
    <code type="none">
-module(tut7).
-export([format_temps/1]).

format_temps(List_of_cities) ->
    convert_list_to_c(List_of_cities).

convert_list_to_c([{Name, {f, F}} | Rest]) ->
    Converted_City = {Name, {c, (F -32)* 5 / 9}},
    [Converted_City | convert_list_to_c(Rest)];

convert_list_to_c([City | Rest]) ->
    [City | convert_list_to_c(Rest)];

convert_list_to_c([]) ->
    [].</code>
    <p>Test the function:</p>
    <pre>
54> <input>c(tut7).</input>
{ok, tut7}.
55> <input>tut7:format_temps([{moscow, {c, -10}}, {cape_town, {f, 70}},</input>
<input>{stockholm, {c, -4}}, {paris, {f, 28}}, {london, {f, 36}}]).</input>
[{moscow,{c,-10}},
 {cape_town,{c,21.11111111111111}},
 {stockholm,{c,-4}},
 {paris,{c,-2.2222222222222223}},
 {london,{c,2.2222222222222223}}]</pre>
    <p>Explanation:</p>
    <code type="none">
format_temps(List_of_cities) ->
    convert_list_to_c(List_of_cities).</code>
    <p>Here <c>format_temps/1</c> calls
      <c>convert_list_to_c/1</c>. <c>convert_list_to_c/1</c> takes off
      the head of the <c>List_of_cities</c>, converts it to Celsius if
      needed. The | operator is used to add the (maybe) converted
      to the converted rest of the list:</p>
    <code type="none">
[Converted_City | convert_list_to_c(Rest)];</code>
    <p>or:</p>
    <code type="none">
[City | convert_list_to_c(Rest)];</code>
    <p>This is done until the end of the list is reached, that is,
      the list is empty:</p>
    <code type="none">
convert_list_to_c([]) ->
    [].</code>
    <p>Now when the list is converted, a function to print it is added:</p>
    <code type="none">
-module(tut7).
-export([format_temps/1]).

format_temps(List_of_cities) ->
    Converted_List = convert_list_to_c(List_of_cities),
    print_temp(Converted_List).

convert_list_to_c([{Name, {f, F}} | Rest]) ->
    Converted_City = {Name, {c, (F -32)* 5 / 9}},
    [Converted_City | convert_list_to_c(Rest)];

convert_list_to_c([City | Rest]) ->
    [City | convert_list_to_c(Rest)];

convert_list_to_c([]) ->
    [].

print_temp([{Name, {c, Temp}} | Rest]) ->
    io:format("~-15w ~w c~n", [Name, Temp]),
    print_temp(Rest);
print_temp([]) ->
    ok.</code>
    <pre>
56> <input>c(tut7).</input>
{ok,tut7}
57> <input>tut7:format_temps([{moscow, {c, -10}}, {cape_town, {f, 70}},</input>
<input>{stockholm, {c, -4}}, {paris, {f, 28}}, {london, {f, 36}}]).</input>
moscow          -10 c
cape_town       21.11111111111111 c
stockholm       -4 c
paris           -2.2222222222222223 c
london          2.2222222222222223 c
ok</pre>
    <p>Now a function has to be added to find the cities with
      the maximum and minimum temperatures. The following program is not
      the most efficient way of doing this as you walk through the list
      of cities four times. But it is better to first strive for
      clarity and correctness and to make programs efficient only if
      needed.</p>
    <code type="none"><![CDATA[
-module(tut7).
-export([format_temps/1]).

format_temps(List_of_cities) ->
    Converted_List = convert_list_to_c(List_of_cities),
    print_temp(Converted_List),
    {Max_city, Min_city} = find_max_and_min(Converted_List),
    print_max_and_min(Max_city, Min_city).

convert_list_to_c([{Name, {f, Temp}} | Rest]) ->
    Converted_City = {Name, {c, (Temp -32)* 5 / 9}},
    [Converted_City | convert_list_to_c(Rest)];

convert_list_to_c([City | Rest]) ->
    [City | convert_list_to_c(Rest)];

convert_list_to_c([]) ->
    [].

print_temp([{Name, {c, Temp}} | Rest]) ->
    io:format("~-15w ~w c~n", [Name, Temp]),
    print_temp(Rest);
print_temp([]) ->
    ok.

find_max_and_min([City | Rest]) ->
    find_max_and_min(Rest, City, City).

find_max_and_min([{Name, {c, Temp}} | Rest], 
         {Max_Name, {c, Max_Temp}}, 
         {Min_Name, {c, Min_Temp}}) ->
    if 
        Temp > Max_Temp ->
            Max_City = {Name, {c, Temp}};           % Change
        true -> 
            Max_City = {Max_Name, {c, Max_Temp}} % Unchanged
    end,
    if
         Temp < Min_Temp ->
            Min_City = {Name, {c, Temp}};           % Change
        true -> 
            Min_City = {Min_Name, {c, Min_Temp}} % Unchanged
    end,
    find_max_and_min(Rest, Max_City, Min_City);

find_max_and_min([], Max_City, Min_City) ->
    {Max_City, Min_City}.

print_max_and_min({Max_name, {c, Max_temp}}, {Min_name, {c, Min_temp}}) ->
    io:format("Max temperature was ~w c in ~w~n", [Max_temp, Max_name]),
    io:format("Min temperature was ~w c in ~w~n", [Min_temp, Min_name]).]]></code><pre>
58> <input>c(tut7).</input>
{ok, tut7}
59> <input>tut7:format_temps([{moscow, {c, -10}}, {cape_town, {f, 70}},</input>
<input>{stockholm, {c, -4}}, {paris, {f, 28}}, {london, {f, 36}}]).</input>
moscow          -10 c
cape_town       21.11111111111111 c
stockholm       -4 c
paris           -2.2222222222222223 c
london          2.2222222222222223 c
Max temperature was 21.11111111111111 c in cape_town
Min temperature was -10 c in moscow
ok</pre>
  </section>

  <section>
    <title>If and Case</title>
    <p>The function <c>find_max_and_min</c> works out the maximum and
      minimum temperature. A new construct, <c>if</c>, is introduced here.
      If works as follows:</p>
    <code type="none">
if
    Condition 1 ->
        Action 1;
    Condition 2 ->
        Action 2;
    Condition 3 ->
        Action 3;
    Condition 4 ->
        Action 4
end</code>
    <p>Notice that there is no ";" before <c>end</c>. Conditions do
      the same as guards, that is, tests that succeed or fail. Erlang
      starts at the top
      and tests until it finds a condition that succeeds. Then it evaluates
      (performs) the action following the condition and ignores all
      other conditions and actions before the <c>end</c>. If no
      condition matches, a run-time failure occurs. A condition
      that always succeeds is the atom <c>true</c>. This is
      often used last in an <c>if</c>, meaning, do the action following
      the <c>true</c> if all other conditions have failed.</p>
    <p>The following is a short program to show the workings of
      <c>if</c>.</p>
    <code type="none">
-module(tut9).
-export([test_if/2]).

test_if(A, B) ->
    if 
        A == 5 ->
            io:format("A == 5~n", []),
            a_equals_5;
        B == 6 ->
            io:format("B == 6~n", []),
            b_equals_6;
        A == 2, B == 3 ->                      %That is A equals 2 and B equals 3
            io:format("A == 2, B == 3~n", []),
            a_equals_2_b_equals_3;
        A == 1 ; B == 7 ->                     %That is A equals 1 or B equals 7
            io:format("A == 1 ; B == 7~n", []),
            a_equals_1_or_b_equals_7
    end.</code>
    <p>Testing this program gives:</p>
    <pre>
60> <input>c(tut9).</input>
{ok,tut9}
61> <input>tut9:test_if(5,33).</input>
A == 5
a_equals_5
62> <input>tut9:test_if(33,6).</input>
B == 6
b_equals_6
63> <input>tut9:test_if(2, 3).</input>
A == 2, B == 3
a_equals_2_b_equals_3
64> <input>tut9:test_if(1, 33).</input>
A == 1 ; B == 7
a_equals_1_or_b_equals_7
65> <input>tut9:test_if(33, 7).</input>
A == 1 ; B == 7
a_equals_1_or_b_equals_7
66> <input>tut9:test_if(33, 33).</input>
** exception error: no true branch found when evaluating an if expression
     in function  tut9:test_if/2 (tut9.erl, line 5)</pre>
    <p>Notice that <c>tut9:test_if(33,33)</c> does not cause any
      condition to succeed. This leads to the run time error
      <c>if_clause</c>, here nicely formatted by the shell. See
      <seeguide marker="system/reference_manual:expressions">Guard Sequences</seeguide>
      for details of the many guard tests available.</p>
    <p><c>case</c> is another construct in Erlang. Recall that the
      <c>convert_length</c> function was written as:</p>
    <code type="none">
convert_length({centimeter, X}) ->
    {inch, X / 2.54};
convert_length({inch, Y}) ->
    {centimeter, Y * 2.54}.</code>
    <p>The same program can also be written as:</p>
    <code type="none">
-module(tut10).
-export([convert_length/1]).

convert_length(Length) ->
    case Length of
        {centimeter, X} ->
            {inch, X / 2.54};
        {inch, Y} ->
            {centimeter, Y * 2.54}
    end.</code>
    <pre>
67> <input>c(tut10).</input>
{ok,tut10}
68> <input>tut10:convert_length({inch, 6}).</input>
{centimeter,15.24}
69> <input>tut10:convert_length({centimeter, 2.5}).</input>
{inch,0.984251968503937}</pre>
    <p>Both <c>case</c> and <c>if</c> have <em>return values</em>, that is,
      in the above example <c>case</c> returned
      either <c>{inch,X/2.54}</c> or <c>{centimeter,Y*2.54}</c>.
      The behaviour of <c>case</c> can also be modified by using guards.
      The following example clarifies this. It
      tells us the length of a month, given the year.
      The year must be known, since February has 29 days in a leap year.</p>
    <code type="none">
-module(tut11).
-export([month_length/2]).

month_length(Year, Month) ->
    %% All years divisible by 400 are leap
    %% Years divisible by 100 are not leap (except the 400 rule above)
    %% Years divisible by 4 are leap (except the 100 rule above)
    Leap = if
        trunc(Year / 400) * 400 == Year ->
            leap;
        trunc(Year / 100) * 100 == Year ->
            not_leap;
        trunc(Year / 4) * 4 == Year ->
            leap;
        true ->
            not_leap
    end,  
    case Month of
        sep -> 30;
        apr -> 30;
        jun -> 30;
        nov -> 30;
        feb when Leap == leap -> 29;
        feb -> 28;
        jan -> 31;
        mar -> 31;
        may -> 31;
        jul -> 31;
        aug -> 31;
        oct -> 31;
        dec -> 31
    end.</code>
    <pre>
70> <input>c(tut11).</input>
{ok,tut11}
71> <input>tut11:month_length(2004, feb).</input>
29
72> <input>tut11:month_length(2003, feb).</input>
28
73> <input>tut11:month_length(1947, aug).</input>
31</pre>
  </section>

  <section>
    <title>Built-In Functions (BIFs)</title>
    <p>BIFs are functions that for some reason are
      built-in to the Erlang virtual machine. BIFs often implement
      functionality that is impossible or is too
      inefficient to implement in Erlang. Some BIFs can be called
      using the function name only but they are by default belonging
      to the <c>erlang</c> module. For example, the call to the
      BIF <c>trunc</c>
      below is equivalent to a call to <c>erlang:trunc</c>.</p>
    <p>As shown, first it is checked if a year is leap. If a
      year is divisible by 400, it is a leap year. To determine this,
      first divide the year by 400 and use the BIF
      <c>trunc</c> (more about this later) to cut off any decimals. Then
      multiply by 400 again and see if the same value is returned again.
      For example, year 2004:</p>
    <code type="none">
2004 / 400 = 5.01
trunc(5.01) = 5
5 * 400 = 2000</code>
    <p>2000 is not the same as 2004, so 2004 is not divisible by 400.
    Year 2000:</p>
    <code type="none">
2000 / 400 = 5.0
trunc(5.0) = 5
5 * 400 = 2000</code>
    <p>That is, a leap year. The next two <c>trunc</c>-tests evaluate
      if the year is divisible by 100 or 4 in the same way. The first
      <c>if</c> returns <c>leap</c> or <c>not_leap</c>, which lands up
      in the variable <c>Leap</c>. This variable is used in the guard
      for <c>feb</c> in the following <c>case</c> that tells us how
      long the month is.</p>
    <p>This example showed the use of <c>trunc</c>. It is easier
      to use the Erlang operator <c>rem</c> that gives the remainder
      after division, for example:</p>
    <pre>
74> <input>2004 rem 400.</input>
4</pre>
    <p>So instead of writing:</p>
    <code type="none">
trunc(Year / 400) * 400 == Year ->
    leap;</code>
    <p>it can be written:</p>
    <code type="none">
Year rem 400 == 0 ->
    leap;</code>
    <p>There are many other BIFs such as
      <c>trunc</c>. Only a few BIFs can be used in guards,
      and you cannot use functions you have defined yourself in guards.
      (see
      <seeguide marker="system/reference_manual:expressions">Guard Sequences</seeguide>)
      (For advanced readers: This is to ensure that guards do not have side
      effects.) Let us play with a few of these functions in the shell:</p>
    <pre>
75> <input>trunc(5.6).</input>
5
76> <input>round(5.6).</input>
6
77> <input>length([a,b,c,d]).</input>
4
78> <input>float(5).</input>
5.0
79> <input>is_atom(hello).</input>
true
80> <input>is_atom("hello").</input>
false
81> <input>is_tuple({paris, {c, 30}}).</input>
true
82> <input>is_tuple([paris, {c, 30}]).</input>
false</pre>
    <p>All of these can be used in guards. Now for some BIFs that cannot be
      used in guards:</p>
    <pre>
83> <input>atom_to_list(hello).</input>
"hello"
84> <input>list_to_atom("goodbye").</input>
goodbye
85> <input>integer_to_list(22).</input>
"22"</pre>
    <p>These three BIFs do conversions that would be difficult (or
      impossible) to do in Erlang.</p>
  </section>

  <section>
    <title>Higher-Order Functions (Funs)</title>
    <p>Erlang, like most modern functional programming languages, has
      higher-order functions. Here is an example using the shell:</p>
    <pre>
86> <input>Xf = fun(X) -> X * 2 end.</input>
#Fun&lt;erl_eval.5.123085357&gt;
87> <input>Xf(5).</input>
10</pre>
    <p>Here is defined a function that doubles
      the value of a number and assigned this function to a variable. Thus
      <c>Xf(5)</c> returns value 10. Two useful functions when
      working with lists are <c>foreach</c> and <c>map</c>, which are
      defined as follows:</p>
    <code type="none">
foreach(Fun, [First|Rest]) ->
    Fun(First),
    foreach(Fun, Rest);
foreach(Fun, []) ->
    ok.

map(Fun, [First|Rest]) -> 
    [Fun(First)|map(Fun,Rest)];
map(Fun, []) -> 
    [].</code>
    <p>These two functions are provided in the standard module
      <c>lists</c>. <c>foreach</c> takes a list and applies a fun to
      every element in the list. <c>map</c> creates a new list by
      applying a fun to every element in a list. Going back to
      the shell, <c>map</c> is used and a fun to add 3 to
      every element of a list:</p>
    <pre>
88> <input>Add_3 = fun(X) -> X + 3 end.</input>
#Fun&lt;erl_eval.5.123085357&gt;
89> <input>lists:map(Add_3, [1,2,3]).</input>
[4,5,6]</pre>
    <p>Let us (again) print the temperatures in a list of cities:</p>
    <pre>
90> <input>Print_City = fun({City, {X, Temp}}) -> io:format("~-15w ~w ~w~n",</input>
<input>[City, X, Temp]) end.</input>
#Fun&lt;erl_eval.5.123085357&gt;
91> <input>lists:foreach(Print_City, [{moscow, {c, -10}}, {cape_town, {f, 70}},</input>
<input>{stockholm, {c, -4}}, {paris, {f, 28}}, {london, {f, 36}}]).</input>
moscow          c -10
cape_town       f 70
stockholm       c -4
paris           f 28
london          f 36
ok</pre>
    <p>Let us now define a fun that can be used to go through a list
      of cities and temperatures and transform them all to Celsius.</p>
    <code type="none">
-module(tut13).

-export([convert_list_to_c/1]).

convert_to_c({Name, {f, Temp}}) ->
    {Name, {c, trunc((Temp - 32) * 5 / 9)}};
convert_to_c({Name, {c, Temp}}) ->
    {Name, {c, Temp}}.

convert_list_to_c(List) ->
    lists:map(fun convert_to_c/1, List).</code>
    <pre>
92> <input>tut13:convert_list_to_c([{moscow, {c, -10}}, {cape_town, {f, 70}},</input>
<input>{stockholm, {c, -4}}, {paris, {f, 28}}, {london, {f, 36}}]).</input>
[{moscow,{c,-10}},
 {cape_town,{c,21}},
 {stockholm,{c,-4}},
 {paris,{c,-2}},
 {london,{c,2}}]</pre>
    <p>The <c>convert_to_c</c> function is the same as before, but here
      it is used as a fun:</p>
    <code type="none">
lists:map(fun convert_to_c/1, List)</code>
    <p>When a function defined elsewhere is used as a fun, it can be referred
      to as <c>Function/Arity</c> (remember that <c>Arity</c> =
      number of arguments). So in the <c>map</c>-call
      <c>lists:map(fun convert_to_c/1, List)</c> is written. As shown,
      <c>convert_list_to_c</c> becomes much shorter and easier to
      understand.</p>
    <p>The standard module <c>lists</c> also contains a function
      <c>sort(Fun, List)</c> where <c>Fun</c> is a fun with two
      arguments. This fun returns <c>true</c> if the first
      argument is less than the second argument, or else <c>false</c>.
      Sorting is added to the <c>convert_list_to_c</c>:</p>
    <code type="none"><![CDATA[
-module(tut13).

-export([convert_list_to_c/1]).

convert_to_c({Name, {f, Temp}}) ->
    {Name, {c, trunc((Temp - 32) * 5 / 9)}};
convert_to_c({Name, {c, Temp}}) ->
    {Name, {c, Temp}}.

convert_list_to_c(List) ->
    New_list = lists:map(fun convert_to_c/1, List),
    lists:sort(fun({_, {c, Temp1}}, {_, {c, Temp2}}) ->
                       Temp1 < Temp2 end, New_list).]]></code>
    <pre>
93> <input>c(tut13).</input>
{ok,tut13}
94> <input>tut13:convert_list_to_c([{moscow, {c, -10}}, {cape_town, {f, 70}},</input>
<input>{stockholm, {c, -4}}, {paris, {f, 28}}, {london, {f, 36}}]).</input>
[{moscow,{c,-10}},
 {stockholm,{c,-4}},
 {paris,{c,-2}},
 {london,{c,2}},
 {cape_town,{c,21}}]</pre>
    <p>In <c>sort</c> the fun is used:</p>
    <code type="none"><![CDATA[
fun({_, {c, Temp1}}, {_, {c, Temp2}}) -> Temp1 < Temp2 end,]]></code>
    <p>Here the concept of an <em>anonymous variable</em>
      "_" is introduced. This is simply shorthand for a variable that
      gets a value, but the value is ignored. This can be used
      anywhere suitable, not just in funs. <c><![CDATA[Temp1 < Temp2]]></c>
      returns <c>true</c> if <c>Temp1</c> is less than <c>Temp2</c>.</p>
  </section>
</chapter>

