path: root/system/doc/reference_manual/expressions.xml

<?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>Expressions</title>
    <prepared></prepared>
    <docno></docno>
    <date></date>
    <rev></rev>
    <file>expressions.xml</file>
  </header>
  <p>In this chapter, all valid Erlang expressions are listed.
    When writing Erlang programs, it is also allowed to use macro-
    and record expressions. However, these expressions are expanded
    during compilation and are in that sense not true Erlang
    expressions. Macro- and record expressions are covered in
    separate chapters: <seealso marker="macros">Macros</seealso> and
    <seealso marker="records">Records</seealso>.</p>

  <section>
    <title>Expression Evaluation</title>
    <p>All subexpressions are evaluated before an expression itself is
      evaluated, unless explicitly stated otherwise. For example,
      consider the expression:</p>
    <code type="none">
Expr1 + Expr2</code>
    <p><c>Expr1</c> and <c>Expr2</c>, which are also expressions, are
      evaluated first - in any order - before the addition is
      performed.</p>
    <p>Many of the operators can only be applied to arguments of a
      certain type. For example, arithmetic operators can only be
      applied to numbers. An argument of the wrong type will cause
      a <c>badarg</c> run-time error.</p>
  </section>

  <section>
    <marker id="term"></marker>
    <title>Terms</title>
    <p>The simplest form of expression is a term, that is an integer,
      float, atom, string, list or tuple.
      The return value is the term itself.</p>
  </section>

  <section>
    <title>Variables</title>
    <p>A variable is an expression. If a variable is bound to a value,
      the return value is this value. Unbound variables are only
      allowed in patterns.</p>
    <p>Variables start with an uppercase letter or underscore (_)
      and may contain alphanumeric characters, underscore and @.
      Examples:</p>
    <pre>
X
Name1
PhoneNumber
Phone_number
_
_Height</pre>
    <p>Variables are bound to values using
      <seealso marker="patterns">pattern matching</seealso>. Erlang
      uses <em>single assignment</em>, a variable can only be bound
      once.</p>
    <p>The <em>anonymous variable</em> is denoted by underscore (_) and
      can be used when a variable is required but its value can be
      ignored. Example:</p>
    <pre>
[H|_] = [1,2,3]</pre>
    <p>Variables starting with underscore (_), for example
      <c>_Height</c>, are normal variables, not anonymous. They are
      however ignored by the compiler in the sense that they will not
      generate any warnings for unused variables. Example: The following
      code</p>
    <pre>
member(_, []) ->
    [].</pre>
    <p>can be rewritten to be more readable:</p>
    <pre>
member(Elem, []) ->
    [].</pre>
    <p>This will however cause a warning for an unused variable
      <c>Elem</c>, if the code is compiled with the flag
      <c>warn_unused_vars</c> set. Instead, the code can be rewritten
      to:</p>
    <pre>
member(_Elem, []) ->
    [].</pre>
    <p>Note that since variables starting with an underscore are
      not anonymous, this will match:</p>
    <pre>
{_,_} = {1,2}</pre>
    <p>But this will fail:</p>
    <pre>
{_N,_N} = {1,2}</pre>
    <p>The scope for a variable is its function clause.
      Variables bound in a branch of an <c>if</c>, <c>case</c>, 
      or <c>receive</c> expression must be bound in all branches 
      to have a value outside the expression, otherwise they
      will be regarded as 'unsafe' outside the expression.</p>
    <p>For the <c>try</c> expression introduced in 
      Erlang 5.4/OTP-R10B, variable scoping is limited so that 
      variables bound in the expression are always 'unsafe' outside 
      the expression. This will be improved.</p>
  </section>

  <section>
    <marker id="pattern"></marker>
    <title>Patterns</title>
    <p>A pattern has the same structure as a term but may contain
      unbound variables. Example:</p>
    <pre>
Name1
[H|T]
{error,Reason}</pre>
    <p>Patterns are allowed in clause heads, <c>case</c> and
      <c>receive</c> expressions, and match expressions.</p>

    <section>
      <title>Match Operator = in Patterns</title>
      <p>If <c>Pattern1</c> and <c>Pattern2</c> are valid patterns,
        then the following is also a valid pattern:</p>
      <pre>
Pattern1 = Pattern2</pre>
      <p>When matched against a term, both <c>Pattern1</c> and
        <c>Pattern2</c> will be matched against the term. The idea
        behind this feature is to avoid reconstruction of terms.
        Example:</p>
      <pre>
f({connect,From,To,Number,Options}, To) ->
    Signal = {connect,From,To,Number,Options},
    ...;
f(Signal, To) ->
    ignore.</pre>
      <p>can instead be written as</p>
      <pre>
f({connect,_,To,_,_} = Signal, To) ->
    ...;
f(Signal, To) ->
    ignore.</pre>
    </section>

    <section>
      <title>String Prefix in Patterns</title>
      <p>When matching strings, the following is a valid pattern:</p>
      <pre>
f("prefix" ++ Str) -> ...</pre>
      <p>This is syntactic sugar for the equivalent, but harder to
        read</p>
      <pre>
f([$p,$r,$e,$f,$i,$x | Str]) -> ...</pre>
    </section>

    <section>
      <title>Expressions in Patterns</title>
      <p>An arithmetic expression can be used within a pattern, if
        it uses only numeric or bitwise operators, and if its value
        can be evaluated to a constant at compile-time. Example:</p>
      <pre>
case {Value, Result} of
    {?THRESHOLD+1, ok} -> ...</pre>
      <p>This feature was added in Erlang 5.0/OTP R7.</p>
    </section>
  </section>

  <section>
    <title>Match</title>
    <pre>
Expr1 = Expr2</pre>
    <p>Matches <c>Expr1</c>, a pattern, against <c>Expr2</c>.
      If the matching succeeds, any unbound variable in the pattern
      becomes bound and the value of <c>Expr2</c> is returned.</p>
    <p>If the matching fails, a <c>badmatch</c> run-time error will
      occur.</p>
    <p>Examples:</p>
    <pre>
1> <input>{A, B} = {answer, 42}.</input>
{answer,42}
2> <input>A.</input>
answer
3> <input>{C, D} = [1, 2].</input>
** exception error: no match of right hand side value [1,2]</pre>
  </section>

  <section>
    <marker id="calls"></marker>
    <title>Function Calls</title>
    <pre>
ExprF(Expr1,...,ExprN)
ExprM:ExprF(Expr1,...,ExprN)</pre>
    <p>In the first form of function calls,
      <c>ExprM:ExprF(Expr1,...,ExprN)</c>, each of <c>ExprM</c> and
      <c>ExprF</c> must be an atom or an expression that evaluates to
      an atom. The function is said to be called by using the
      <em>fully qualified function name</em>. This is often referred
      to as a <em>remote</em> or <em>external function call</em>.
      Example:</p>
    <code type="none">
lists:keysearch(Name, 1, List)</code>
    <p>In the second form of function calls,
      <c>ExprF(Expr1,...,ExprN)</c>, <c>ExprF</c> must be an atom or
      evaluate to a fun.</p>

    <p>If <c>ExprF</c> is an atom the function is said to be called by
      using the <em>implicitly qualified function name</em>.  If the
      function <c>ExprF</c> is locally defined, it is called.
      Alternatively if <c>ExprF</c> is explicitly imported from module
      <c>M</c>, <c>M:ExprF(Expr1,...,ExprN)</c> is called. If
      <c>ExprF</c> is neither declared locally nor explicitly
      imported, <c>ExprF</c> must be the name of an automatically
      imported BIF. Examples:</p>

    <code type="none">
handle(Msg, State)
spawn(m, init, [])</code>
    <p>Examples where ExprF is a fun:</p>
    <code type="none">
Fun1 = fun(X) -> X+1 end
Fun1(3)
=> 4

fun lists:append/2([1,2], [3,4])
=> [1,2,3,4]</code>

    <p>Note that when calling a local function, there is a difference
    between using the implicitly or fully qualified function name, as
    the latter always refers to the latest version of the module. See
    <seealso marker="code_loading">Compilation and Code Loading</seealso>.</p>

    <p>See also the chapter about
      <seealso marker="functions#eval">Function Evaluation</seealso>.</p>

    <section>
      <title>Local Function Names Clashing With  Auto-imported BIFs</title>
    <p>If a local function has the same name as an auto-imported BIF,
    the semantics is that implicitly qualified function calls are
    directed to the locally defined function, not to the BIF. To avoid
    confusion, there is a compiler directive available,
    <c>-compile({no_auto_import,[F/A]})</c>, that makes a BIF not
    being auto-imported. In certain situations, such a compile-directive
    is mandatory.</p>

    <warning><p>Before OTP R14A (ERTS version 5.8), an implicitly
    qualified function call to a function having the same name as an
    auto-imported BIF always resulted in the BIF being called. In
    newer versions of the compiler the local function is instead
    called. The change is there to avoid that future additions to the
    set of auto-imported BIFs does not silently change the behavior
    of old code.</p>

    <p>However, to avoid that old (pre R14) code changed its
    behavior when compiled with OTP version R14A or later, the
    following restriction applies: If you override the name of a BIF
    that was auto-imported in OTP versions prior to R14A (ERTS version
    5.8) and have an implicitly qualified call to that function in
    your code, you either need to explicitly remove the auto-import
    using a compiler directive, or replace the call with a fully
    qualified function call, otherwise you will get a compilation
    error. See example below:</p> </warning>

    <code type="none">
-export([length/1,f/1]).

-compile({no_auto_import,[length/1]}). % erlang:length/1 no longer autoimported

length([]) ->
    0;
length([H|T]) ->
    1 + length(T). %% Calls the local funtion length/1

f(X) when erlang:length(X) > 3 -> %% Calls erlang:length/1,
                                  %% which is allowed in guards
    long.</code>

    <p>The same logic applies to explicitly imported functions from
    other modules as to locally defined functions. To both import a
    function from another module and have the function declared in the
    module at the same time is not allowed.</p>

    <code type="none">
-export([f/1]).

-compile({no_auto_import,[length/1]}). % erlang:length/1 no longer autoimported

-import(mod,[length/1]).

f(X) when erlang:length(X) > 33 -> %% Calls erlang:lenght/1,
                                   %% which is allowed in guards

    erlang:length(X);              %% Explicit call to erlang:length in body

f(X) ->
    length(X).                     %% mod:length/1 is called</code>


    <p>For auto-imported BIFs added to Erlang in release R14A and thereafter,
    overriding the name with a local function or explicit import is always
    allowed. However, if the <c>-compile({no_auto_import,[F/A])</c>
    directive is not used, the compiler will issue a warning whenever
    the function is called in the module using the implicitly qualified
    function name.</p>
    </section>
  </section>

  <section>
    <title>If</title>
    <pre>
if
    GuardSeq1 ->
        Body1;
    ...;
    GuardSeqN ->
        BodyN
end</pre>
    <p>The branches of an <c>if</c>-expression are scanned sequentially
      until a guard sequence <c>GuardSeq</c> which evaluates to true is
      found. Then the corresponding <c>Body</c> (sequence of expressions
      separated by ',') is evaluated.</p>
    <p>The return value of <c>Body</c> is the return value of
      the <c>if</c> expression.</p>
    <p>If no guard sequence is true, an <c>if_clause</c> run-time error
      will occur. If necessary, the guard expression <c>true</c> can be
      used in the last branch, as that guard sequence is always true.</p>
    <p>Example:</p>
    <pre>
is_greater_than(X, Y) ->
    if
        X>Y ->
            true;
        true -> % works as an 'else' branch
            false
    end</pre>
  </section>

  <section>
    <marker id="case"></marker>
    <title>Case</title>
    <pre>
case Expr of
    Pattern1 [when GuardSeq1] ->
        Body1;
    ...;
    PatternN [when GuardSeqN] ->
        BodyN
end</pre>
    <p>The expression <c>Expr</c> is evaluated and the patterns
      <c>Pattern</c> are sequentially matched against the result. If a
      match succeeds and the optional guard sequence <c>GuardSeq</c> is
      true, the corresponding <c>Body</c> is evaluated.</p>
    <p>The return value of <c>Body</c> is the return value of
      the <c>case</c> expression.</p>
    <p>If there is no matching pattern with a true guard sequence,
      a <c>case_clause</c> run-time error will occur.</p>
    <p>Example:</p>
    <pre>
is_valid_signal(Signal) ->
    case Signal of
        {signal, _What, _From, _To} ->
            true;
        {signal, _What, _To} ->
            true;
        _Else ->
            false
    end.</pre>
  </section>

  <section>
    <marker id="send"></marker>
    <title>Send</title>
    <pre>
Expr1 ! Expr2</pre>
    <p>Sends the value of <c>Expr2</c> as a message to the process
      specified by <c>Expr1</c>. The value of <c>Expr2</c> is also
      the return value of the expression.</p>
    <p><c>Expr1</c> must evaluate to a pid, a registered name (atom) or
      a tuple <c>{Name,Node}</c>, where <c>Name</c> is an atom and
      <c>Node</c> a node name, also an atom.</p>
    <list type="bulleted">
      <item>If <c>Expr1</c> evaluates to a name, but this name is not
       registered, a <c>badarg</c> run-time error will occur.</item>
      <item>Sending a message to a pid never fails, even if the pid
       identifies a non-existing process.</item>
      <item>Distributed message sending, that is if <c>Expr1</c>
       evaluates to a tuple <c>{Name,Node}</c> (or a pid located at
       another node), also never fails.</item>
    </list>
  </section>

  <section>
    <marker id="receive"></marker>
    <title>Receive</title>
    <pre>
receive
    Pattern1 [when GuardSeq1] ->
        Body1;
    ...;
    PatternN [when GuardSeqN] ->
        BodyN
end</pre>
    <p>Receives messages sent to the process using the send operator
      (!). The patterns <c>Pattern</c> are sequentially matched
      against the first message in time order in the mailbox, then
      the second, and so on. If a match succeeds and the optional
      guard sequence <c>GuardSeq</c> is true, the corresponding
      <c>Body</c> is evaluated. The matching message is consumed, that
      is removed from the mailbox, while any other messages in
      the mailbox remain unchanged.</p>
    <p>The return value of <c>Body</c> is the return value of
      the <c>receive</c> expression.</p>
    <p><c>receive</c> never fails. Execution is suspended, possibly
      indefinitely, until a message arrives that does match one of
      the patterns and with a true guard sequence. </p>
    <p>Example:</p>
    <pre>
wait_for_onhook() ->
    receive
        onhook ->
            disconnect(),
            idle();
        {connect, B} ->
            B ! {busy, self()},
            wait_for_onhook()
    end.</pre>
    <p>It is possible to augment the <c>receive</c> expression with a
      timeout:</p>
    <pre>
receive
    Pattern1 [when GuardSeq1] ->
        Body1;
    ...;
    PatternN [when GuardSeqN] ->
        BodyN
after
    ExprT ->
        BodyT
end</pre>
    <p><c>ExprT</c> should evaluate to an integer. The highest allowed
      value is 16#ffffffff, that is, the value must fit in 32 bits.
      <c>receive..after</c> works exactly as <c>receive</c>, except
      that if no matching message has arrived within <c>ExprT</c>
      milliseconds, then <c>BodyT</c> is evaluated instead and its
      return value becomes the return value of the <c>receive..after</c>
      expression.</p>
    <p>Example:</p>
    <pre>
wait_for_onhook() ->
    receive
        onhook ->
            disconnect(),
            idle();
        {connect, B} ->
            B ! {busy, self()},
            wait_for_onhook()
    after
        60000 ->
            disconnect(),
            error()
    end.</pre>
    <p>It is legal to use a <c>receive..after</c> expression with no
      branches:</p>
    <pre>
receive
after
    ExprT ->
        BodyT
end</pre>
    <p>This construction will not consume any messages, only suspend
      execution in the process for <c>ExprT</c> milliseconds and can be
      used to implement simple timers.</p>
    <p>Example:</p>
    <pre>
timer() ->
    spawn(m, timer, [self()]).

timer(Pid) ->
    receive
    after
        5000 ->
            Pid ! timeout
    end.</pre>
    <p>There are two special cases for the timeout value <c>ExprT</c>:</p>
    <taglist>
      <tag><c>infinity</c></tag>
      <item>The process should wait indefinitely for a matching message
       -- this is the same as not using a timeout. Can be
       useful for timeout values that are calculated at run-time.</item>
      <tag>0</tag>
      <item>If there is no matching message in the mailbox, the timeout
       will occur immediately.</item>
    </taglist>
  </section>

  <section>
    <title>Term Comparisons</title>
    <pre>
Expr1 <input>op</input> Expr2</pre>
    <table>
      <row>
        <cell align="left" valign="middle"><em>op</em></cell>
        <cell align="left" valign="middle"><em>Description</em></cell>
      </row>
      <row>
        <cell align="left" valign="middle">==</cell>
        <cell align="left" valign="middle">equal to</cell>
      </row>
      <row>
        <cell align="left" valign="middle">/=</cell>
        <cell align="left" valign="middle">not equal to</cell>
      </row>
      <row>
        <cell align="left" valign="middle">=&lt;</cell>
        <cell align="left" valign="middle">less than or equal to</cell>
      </row>
      <row>
        <cell align="left" valign="middle">&lt;</cell>
        <cell align="left" valign="middle">less than</cell>
      </row>
      <row>
        <cell align="left" valign="middle">&gt;=</cell>
        <cell align="left" valign="middle">greater than or equal to</cell>
      </row>
      <row>
        <cell align="left" valign="middle">&gt;</cell>
        <cell align="left" valign="middle">greater than</cell>
      </row>
      <row>
        <cell align="left" valign="middle">=:=</cell>
        <cell align="left" valign="middle">exactly equal to</cell>
      </row>
      <row>
        <cell align="left" valign="middle">=/=</cell>
        <cell align="left" valign="middle">exactly not equal to</cell>
      </row>
      <tcaption>Term Comparison Operators.</tcaption>
    </table>
    <p>The arguments may be of different data types. The following
      order is defined:</p>
    <pre>
number &lt; atom &lt; reference &lt; fun &lt; port &lt; pid &lt; tuple &lt; list &lt; bit string</pre>
    <p>Lists are compared element by element. Tuples are ordered by
      size, two tuples with the same size are compared element by
      element.</p>
      <p>When comparing an integer to a float, the term with the lesser
      precision will be converted into the other term's type, unless the
      operator is one of =:= or =/=. A float is more precise than
      an integer until all significant figures of the float are to the left of
      the decimal point. This happens when the float is larger/smaller than
      +/-9007199254740992.0. The conversion strategy is changed
      depending on the size of the float because otherwise comparison of large
      floats and integers would lose their transitivity.</p>

    <p>Returns the Boolean value of the expression, <c>true</c> or
      <c>false</c>.</p>
    <p>Examples:</p>
    <pre>
1> <input>1==1.0.</input>
true
2> <input>1=:=1.0.</input>
false
3> <input>1 > a.</input>
false</pre>
  </section>

  <section>
    <title>Arithmetic Expressions</title>
    <pre>
<input>op</input> Expr
Expr1 <input>op</input> Expr2</pre>
    <table>
      <row>
        <cell align="left" valign="middle"><em>op</em></cell>
        <cell align="left" valign="middle"><em>Description</em></cell>
        <cell align="left" valign="middle"><em>Argument type</em></cell>
      </row>
      <row>
        <cell align="left" valign="middle">+</cell>
        <cell align="left" valign="middle">unary +</cell>
        <cell align="left" valign="middle">number</cell>
      </row>
      <row>
        <cell align="left" valign="middle">-</cell>
        <cell align="left" valign="middle">unary -</cell>
        <cell align="left" valign="middle">number</cell>
      </row>
      <row>
        <cell align="left" valign="middle">+</cell>
        <cell align="left" valign="middle">&nbsp;</cell>
        <cell align="left" valign="middle">number</cell>
      </row>
      <row>
        <cell align="left" valign="middle">-</cell>
        <cell align="left" valign="middle">&nbsp;</cell>
        <cell align="left" valign="middle">number</cell>
      </row>
      <row>
        <cell align="left" valign="middle">*</cell>
        <cell align="left" valign="middle">&nbsp;</cell>
        <cell align="left" valign="middle">number</cell>
      </row>
      <row>
        <cell align="left" valign="middle">/</cell>
        <cell align="left" valign="middle">floating point division</cell>
        <cell align="left" valign="middle">number</cell>
      </row>
      <row>
        <cell align="left" valign="middle">bnot</cell>
        <cell align="left" valign="middle">unary bitwise not</cell>
        <cell align="left" valign="middle">integer</cell>
      </row>
      <row>
        <cell align="left" valign="middle">div</cell>
        <cell align="left" valign="middle">integer division</cell>
        <cell align="left" valign="middle">integer</cell>
      </row>
      <row>
        <cell align="left" valign="middle">rem</cell>
        <cell align="left" valign="middle">integer remainder of X/Y</cell>
        <cell align="left" valign="middle">integer</cell>
      </row>
      <row>
        <cell align="left" valign="middle">band</cell>
        <cell align="left" valign="middle">bitwise and</cell>
        <cell align="left" valign="middle">integer</cell>
      </row>
      <row>
        <cell align="left" valign="middle">bor</cell>
        <cell align="left" valign="middle">bitwise or</cell>
        <cell align="left" valign="middle">integer</cell>
      </row>
      <row>
        <cell align="left" valign="middle">bxor</cell>
        <cell align="left" valign="middle">arithmetic bitwise xor</cell>
        <cell align="left" valign="middle">integer</cell>
      </row>
      <row>
        <cell align="left" valign="middle">bsl</cell>
        <cell align="left" valign="middle">arithmetic bitshift left</cell>
        <cell align="left" valign="middle">integer</cell>
      </row>
      <row>
        <cell align="left" valign="middle">bsr</cell>
        <cell align="left" valign="middle">bitshift right</cell>
        <cell align="left" valign="middle">integer</cell>
      </row>
      <tcaption>Arithmetic Operators.</tcaption>
    </table>

    <p>Examples:</p>
    <pre>
1> <input>+1.</input>
1
2> <input>-1.</input>
-1
3> <input>1+1.</input>
2
4> <input>4/2.</input>
2.0
5> <input>5 div 2.</input>
2
6> <input>5 rem 2.</input>
1
7> <input>2#10 band 2#01.</input>
0
8> <input>2#10 bor 2#01.</input>
3
9> <input>a + 10.</input>
** exception error: an error occurred when evaluating an arithmetic expression
     in operator  +/2
        called as a + 10
10> <input>1 bsl (1 bsl 64).</input>
** exception error: a system limit has been reached
     in operator  bsl/2
        called as 1 bsl 18446744073709551616</pre>
  </section>

  <section>
    <title>Boolean Expressions</title>
    <pre>
<input>op</input> Expr
Expr1 <input>op</input> Expr2</pre>
    <table>
      <row>
        <cell align="left" valign="middle"><em>op</em></cell>
        <cell align="left" valign="middle"><em>Description</em></cell>
      </row>
      <row>
        <cell align="left" valign="middle">not</cell>
        <cell align="left" valign="middle">unary logical not</cell>
      </row>
      <row>
        <cell align="left" valign="middle">and</cell>
        <cell align="left" valign="middle">logical and</cell>
      </row>
      <row>
        <cell align="left" valign="middle">or</cell>
        <cell align="left" valign="middle">logical or</cell>
      </row>
      <row>
        <cell align="left" valign="middle">xor</cell>
        <cell align="left" valign="middle">logical xor</cell>
      </row>
      <tcaption>Logical Operators.</tcaption>
    </table>
    <p>Examples:</p>
    <pre>
1> <input>not true.</input>
false
2> <input>true and false.</input>
false
3> <input>true xor false.</input>
true
4> <input>true or garbage.</input>
** exception error: bad argument
     in operator  or/2
        called as true or garbage</pre>
  </section>

  <section>
    <title>Short-Circuit Expressions</title>
    <pre>
Expr1 orelse Expr2
Expr1 andalso Expr2</pre>
    <p>Expressions where <c>Expr2</c> is evaluated only if
      necessary. That is, <c>Expr2</c> is evaluated only if <c>Expr1</c>
      evaluates to <c>false</c> in an <c>orelse</c> expression, or only
      if <c>Expr1</c> evaluates to <c>true</c> in an <c>andalso</c>
      expression. Returns either the value of <c>Expr1</c> (that is,
      <c>true</c> or <c>false</c>) or the value of <c>Expr2</c>
      (if <c>Expr2</c> was evaluated).</p>

    <p>Example 1:</p>
    <pre>
case A >= -1.0 andalso math:sqrt(A+1) > B of</pre>
    <p>This will work even if <c>A</c> is less than <c>-1.0</c>,
      since in that case, <c>math:sqrt/1</c> is never evaluated.</p>
    <p>Example 2:</p>
    <pre>
OnlyOne = is_atom(L) orelse
         (is_list(L) andalso length(L) == 1),</pre>

    <p>From R13A, <c>Expr2</c> is no longer required to evaluate to a
    boolean value. As a consequence, <c>andalso</c> and <c>orelse</c>
    are now tail-recursive.  For instance, the following function is
    tail-recursive in R13A and later:</p>

    <pre>
all(Pred, [Hd|Tail]) ->
    Pred(Hd) andalso all(Pred, Tail);
all(_, []) ->
    true.</pre>
  </section>

  <section>
    <title>List Operations</title>
    <pre>
Expr1 ++ Expr2
Expr1 -- Expr2</pre>
    <p>The list concatenation operator <c>++</c> appends its second
      argument to its first and returns the resulting list.</p>
    <p>The list subtraction operator <c>--</c> produces a list which
      is a copy of the first argument, subjected to the following
      procedure: for each element in the second argument, the first
      occurrence of this element (if any) is removed.</p>
    <p>Example:</p>
    <pre>
1> <input>[1,2,3]++[4,5].</input>
[1,2,3,4,5]
2> <input>[1,2,3,2,1,2]--[2,1,2].</input>
[3,1,2]</pre>

     <warning><p>The complexity of <c>A -- B</c> is
     proportional to <c>length(A)*length(B)</c>, meaning that it
     will be very slow if both <c>A</c> and <c>B</c> are
     long lists.</p></warning>
   </section>

  <section>
    <marker id="bit_syntax"></marker>
    <title>Bit Syntax Expressions</title>
    <code type="none"><![CDATA[<<>>
<<E1,...,En>>]]></code>
    <p>Each element <c>Ei</c> specifies a <em>segment</em> of
      the bit string. Each element <c>Ei</c> is a value, followed by an
      optional <em>size expression</em> and an optional <em>type specifier list</em>.</p>
    <pre>
Ei = Value |
     Value:Size |
     Value/TypeSpecifierList |
     Value:Size/TypeSpecifierList</pre>
    <p>Used in a bit string construction, <c>Value</c> is an expression
    which should evaluate to an integer, float or bit string.  If the
    expression is something else than a single literal or variable, it
    should be enclosed in parenthesis.</p>

    <p>Used in a bit string matching, <c>Value</c> must be a variable,
    or an integer, float or string.</p>

    <p>Note that, for example, using a string literal as in
    <c><![CDATA[<<"abc">>]]></c> is syntactic sugar for
    <c><![CDATA[<<$a,$b,$c>>]]></c>.</p>

    <p>Used in a bit string construction, <c>Size</c> is an expression
    which should evaluate to an integer.</p>
    
    <p>Used in a bit string matching, <c>Size</c> must be an integer or a 
    variable bound to an integer.</p>

    <p>The value of <c>Size</c> specifies the size of the segment in
    units (see below). The default value depends on the type (see
    below). For <c>integer</c> it is 8, for
    <c>float</c> it is 64, for <c>binary</c> and <c>bitstring</c> it is
    the whole binary or bit string. In matching, this default value is only
    valid for the very last element. All other bit string or binary 
    elements in the matching must have a size specification.</p>

    <p>For the <c>utf8</c>, <c>utf16</c>, and <c>utf32</c> types,
    <c>Size</c> must not be given. The size of the segment is implicitly
    determined by the type and value itself.</p>
    
    <p><c>TypeSpecifierList</c> is a list of type specifiers, in any
    order, separated by hyphens (-). Default values are used for any
    omitted type specifiers.</p>
    <taglist>
      <tag><c>Type</c>= <c>integer</c> | <c>float</c> | <c>binary</c> |
             <c>bytes</c> | <c>bitstring</c> | <c>bits</c> |
	     <c>utf8</c> | <c>utf16</c> | <c>utf32</c> </tag>
      <item>The default is <c>integer</c>. <c>bytes</c> is a shorthand for 
      <c>binary</c> and <c>bits</c> is a shorthand for <c>bitstring</c>.
      See below for more information about the <c>utf</c> types.
      </item>

      <tag><c>Signedness</c>= <c>signed</c> | <c>unsigned</c></tag>
      <item>Only matters for matching and when the type is <c>integer</c>. 
      The default is <c>unsigned</c>.</item>

      <tag><c>Endianness</c>= <c>big</c> | <c>little</c> | <c>native</c></tag>
      <item>Native-endian means that the endianness will be resolved at load
       time to be either big-endian or little-endian, depending on
       what is native for the CPU that the Erlang machine is run on.
       Endianness only matters when the Type is either <c>integer</c>,
       <c>utf16</c>, <c>utf32</c>, or <c>float</c>. The default is <c>big</c>.
       </item>

      <tag><c>Unit</c>= <c>unit:IntegerLiteral</c></tag>
      <item>The allowed range is 1..256. Defaults to 1 for <c>integer</c>,
       <c>float</c> and <c>bitstring</c>, and to 8 for <c>binary</c>.
       No unit specifier must be given for the types 
       <c>utf8</c>, <c>utf16</c>, and <c>utf32</c>.
       </item>
    </taglist>
    <p>The value of <c>Size</c> multiplied with the unit gives
      the number of bits. A segment of type <c>binary</c> must have 
      a size that is evenly divisible by 8.</p>

    <note><p>When constructing binaries, if the size <c>N</c> of an integer
    segment is too small to contain the given integer, the most significant
    bits of the integer will be silently discarded and only the <c>N</c> least
    significant bits will be put into the binary.</p></note>

    <p>The types <c>utf8</c>, <c>utf16</c>, and <c>utf32</c> specifies
    encoding/decoding of the <em>Unicode Transformation Format</em>s UTF-8, UTF-16,
    and UTF-32, respectively.</p>

    <p>When constructing a segment of a <c>utf</c> type, <c>Value</c>
    must be an integer in the range 0..16#D7FF or
    16#E000....16#10FFFF. Construction
    will fail with a <c>badarg</c> exception if <c>Value</c> is
    outside the allowed ranges. The size of the resulting binary
    segment depends on the type and/or <c>Value</c>. For <c>utf8</c>,
    <c>Value</c> will be encoded in 1 through 4 bytes. For
    <c>utf16</c>, <c>Value</c> will be encoded in 2 or 4
    bytes. Finally, for <c>utf32</c>, <c>Value</c> will always be
    encoded in 4 bytes.</p>

    <p>When constructing, a literal string may be given followed
    by one of the UTF types, for example: <c><![CDATA[<<"abc"/utf8>>]]></c>
    which is syntatic sugar for 
    <c><![CDATA[<<$a/utf8,$b/utf8,$c/utf8>>]]></c>.</p>

    <p>A successful match of a segment of a <c>utf</c> type results
    in an integer in the range 0..16#D7FF or  16#E000..16#10FFFF.
    The match will fail if returned value
    would fall outside those ranges.</p>

    <p>A segment of type <c>utf8</c> will match 1 to 4 bytes in the binary,
    if the binary at the match position contains a valid UTF-8 sequence.
    (See RFC-3629 or the Unicode standard.)</p>

    <p>A segment of type <c>utf16</c> may match 2 or 4 bytes in the binary.
    The match will fail if the binary at the match position does not contain
    a legal UTF-16 encoding of a Unicode code point. (See RFC-2781 or
    the Unicode standard.)</p>

    <p>A segment of type <c>utf32</c> may match 4 bytes in the binary in the
    same way as an <c>integer</c> segment matching 32 bits.
    The match will fail if the resulting integer is outside the legal ranges
    mentioned above.</p>

    <p>Examples:</p>
    <pre>
1> <input>Bin1 = &lt;&lt;1,17,42&gt;&gt;.</input>
&lt;&lt;1,17,42&gt;&gt;
2> <input>Bin2 = &lt;&lt;"abc"&gt;&gt;.</input>
&lt;&lt;97,98,99&gt;&gt;
3> <input>Bin3 = &lt;&lt;1,17,42:16&gt;&gt;.</input>
&lt;&lt;1,17,0,42&gt;&gt;
4> <input>&lt;&lt;A,B,C:16&gt;&gt; = &lt;&lt;1,17,42:16&gt;&gt;.</input>
&lt;&lt;1,17,0,42&gt;&gt;
5> <input>C.</input>
42
6> <input>&lt;&lt;D:16,E,F&gt;&gt; = &lt;&lt;1,17,42:16&gt;&gt;.</input>
&lt;&lt;1,17,0,42&gt;&gt;
7> <input>D.</input>
273
8> <input>F.</input>
42
9> <input>&lt;&lt;G,H/binary&gt;&gt; = &lt;&lt;1,17,42:16&gt;&gt;.</input>
&lt;&lt;1,17,0,42&gt;&gt;
10> <input>H.</input>
&lt;&lt;17,0,42&gt;&gt;
11> <input>&lt;&lt;G,H/bitstring&gt;&gt; = &lt;&lt;1,17,42:12&gt;&gt;.</input>
&lt;&lt;1,17,1,10:4&gt;&gt;
12> <input>H.</input>
&lt;&lt;17,1,10:4&gt;&gt;
13> <input>&lt;&lt;1024/utf8&gt;&gt;.</input>
&lt;&lt;208,128&gt;&gt;
</pre>
    <p>Note that bit string patterns cannot be nested.</p>
    <p>Note also that "<c><![CDATA[B=<<1>>]]></c>" is interpreted as
      "<c><![CDATA[B =<<1>>]]></c>" which is a syntax error. The correct way is
      to write a space after '=': "<c><![CDATA[B= <<1>>]]></c>.</p>
    <p>More examples can be found in <em>Programming Examples</em>.</p>
  </section>

  <section>
    <marker id="funs"></marker>
    <title>Fun Expressions</title>
    <pre>
fun
    [Name](Pattern11,...,Pattern1N) [when GuardSeq1] ->
              Body1;
    ...;
    [Name](PatternK1,...,PatternKN) [when GuardSeqK] ->
              BodyK
end</pre>
    <p>A fun expression begins with the keyword <c>fun</c> and ends
      with the keyword <c>end</c>. Between them should be a function
      declaration, similar to a
      <seealso marker="functions#syntax">regular function declaration</seealso>,
      except that the function name is optional and should be a variable if
      any.</p>
    <p>Variables in a fun head shadow the function name and both shadow
      variables in the function clause surrounding the fun expression, and
      variables bound in a fun body are local to the fun body.</p>
    <p>The return value of the expression is the resulting fun.</p>
    <p>Examples:</p>
    <pre>
1> <input>Fun1 = fun (X) -> X+1 end.</input>
#Fun&lt;erl_eval.6.39074546&gt;
2> <input>Fun1(2).</input>
3
3> <input>Fun2 = fun (X) when X>=5 -> gt; (X) -> lt end.</input>
#Fun&lt;erl_eval.6.39074546&gt;
4> <input>Fun2(7).</input>
gt
5> <input>Fun3 = fun Fact(1) -> 1; Fact(X) when X > 1 -> X * Fact(X - 1) end.</input>
#Fun&lt;erl_eval.6.39074546&gt;
6> <input>Fun3(4).</input>
24</pre>
    <p>The following fun expressions are also allowed:</p>
    <pre>
fun Name/Arity
fun Module:Name/Arity</pre>
    <p>In <c>Name/Arity</c>, <c>Name</c> is an atom and <c>Arity</c> is an integer.
      <c>Name/Arity</c> must specify an existing local function. The expression is
      syntactic sugar for:</p>
    <pre>
fun (Arg1,...,ArgN) -> Name(Arg1,...,ArgN) end</pre>
    <p>In <c>Module:Name/Arity</c>, <c>Module</c> and <c>Name</c> are atoms
      and <c>Arity</c> is an integer. Starting from the R15 release,
      <c>Module</c>, <c>Name</c>, and <c>Arity</c> may also be variables.
      A fun defined in this way will refer to the function <c>Name</c>
      with arity <c>Arity</c> in the <em>latest</em> version of module
      <c>Module</c>. A fun defined in this way will not be dependent on
      the code for module in which it is defined.
      </p>
    <p>More examples can be found in <em>Programming Examples</em>.</p>
  </section>

  <section>
    <marker id="catch"></marker>
    <title>Catch and Throw</title>
    <code type="none">
catch Expr</code>
    <p>Returns the value of <c>Expr</c> unless an exception
      occurs during the evaluation. In that case, the exception is
      caught. For exceptions of class <c>error</c>, 
      that is run-time errors: <c>{'EXIT',{Reason,Stack}}</c> 
      is returned. For exceptions of class <c>exit</c>, that is
      the code called <c>exit(Term)</c>: <c>{'EXIT',Term}</c> is returned. 
      For exceptions of class <c>throw</c>, that is
      the code called <c>throw(Term)</c>: <c>Term</c> is returned.</p>
    <p><c>Reason</c> depends on the type of error that occurred, and
      <c>Stack</c> is the stack of recent function calls, see
      <seealso marker="errors#exit_reasons">Errors and Error Handling</seealso>.</p>
    <p>Examples:</p>
    <p></p>
    <pre>
1> <input>catch 1+2.</input>
3
2> <input>catch 1+a.</input>
{'EXIT',{badarith,[...]}}</pre>
    <p>Note that <c>catch</c> has low precedence and catch
      subexpressions often needs to be enclosed in a block
      expression or in parenthesis:</p>
    <pre>
3> <input>A = catch 1+2.</input>
** 1: syntax error before: 'catch' **
4> <input>A = (catch 1+2).</input>
3</pre>
    <p>The BIF <c>throw(Any)</c> can be used for non-local return from
      a function. It must be evaluated within a <c>catch</c>, which will
      return the value <c>Any</c>. Example:</p>
    <pre>
5> <input>catch throw(hello).</input>
hello</pre>
    <p>If <c>throw/1</c> is not evaluated within a catch, a
      <c>nocatch</c> run-time error will occur.</p>
  </section>

  <section>
    <marker id="try"></marker>
    <title>Try</title>
    <code type="none">
try Exprs
catch
    [Class1:]ExceptionPattern1 [when ExceptionGuardSeq1] ->
        ExceptionBody1;
    [ClassN:]ExceptionPatternN [when ExceptionGuardSeqN] ->
        ExceptionBodyN
end</code>
    <p>This is an enhancement of
      <seealso marker="#catch">catch</seealso> that appeared in
      Erlang 5.4/OTP-R10B. It gives the possibility do distinguish
      between different exception classes, and to choose to handle only
      the desired ones, passing the others on to an enclosing
      <c>try</c> or <c>catch</c> or to default error handling.</p>
    <p>Note that although the keyword <c>catch</c> is used in
      the <c>try</c> expression, there is not a <c>catch</c> expression
      within the <c>try</c> expression.</p>
    <p>Returns the value of <c>Exprs</c> (a sequence of expressions
      <c>Expr1, ..., ExprN</c>) unless an exception occurs during
      the evaluation. In that case the exception is caught and
      the patterns <c>ExceptionPattern</c> with the right exception
      class <c>Class</c> are sequentially matched against the caught
      exception. An omitted <c>Class</c> is shorthand for <c>throw</c>.
      If a match succeeds and the optional guard sequence
      <c>ExceptionGuardSeq</c> is true, the corresponding
      <c>ExceptionBody</c> is evaluated to become the return value.</p>
    <p>If an exception occurs during evaluation of <c>Exprs</c> but
      there is no matching <c>ExceptionPattern</c> of the right
      <c>Class</c> with a true guard sequence, the exception is passed
      on as if <c>Exprs</c> had not been enclosed in a <c>try</c>
      expression.</p>
    <p>If an exception occurs during evaluation of <c>ExceptionBody</c>
      it is not caught.</p>
    <p>The <c>try</c> expression can have an <c>of</c>
      section:
      </p>
    <code type="none">
try Exprs of
    Pattern1 [when GuardSeq1] ->
        Body1;
    ...;
    PatternN [when GuardSeqN] ->
        BodyN
catch
    [Class1:]ExceptionPattern1 [when ExceptionGuardSeq1] ->
        ExceptionBody1;
    ...;
    [ClassN:]ExceptionPatternN [when ExceptionGuardSeqN] ->
        ExceptionBodyN
end</code>
    <p>If the evaluation of <c>Exprs</c> succeeds without an exception,
      the patterns <c>Pattern</c> are sequentially matched against
      the result in the same way as for a
      <seealso marker="#case">case</seealso> expression, except that if
      the matching fails, a <c>try_clause</c> run-time error will occur.</p>
    <p>An exception occurring during the evaluation of <c>Body</c> is
      not caught.</p>
    <p>The <c>try</c> expression can also be augmented with an
      <c>after</c> section, intended to be used for cleanup with side
      effects:</p>
    <code type="none">
try Exprs of
    Pattern1 [when GuardSeq1] ->
        Body1;
    ...;
    PatternN [when GuardSeqN] ->
        BodyN
catch
    [Class1:]ExceptionPattern1 [when ExceptionGuardSeq1] ->
        ExceptionBody1;
    ...;
    [ClassN:]ExceptionPatternN [when ExceptionGuardSeqN] ->
        ExceptionBodyN
after
    AfterBody
end</code>
    <p><c>AfterBody</c> is evaluated after either <c>Body</c> or
      <c>ExceptionBody</c> no matter which one. The evaluated value of
      <c>AfterBody</c> is lost; the return value of the <c>try</c>
      expression is the same with an <c>after</c> section as without.</p>
    <p>Even if an exception occurs during evaluation of <c>Body</c> or
      <c>ExceptionBody</c>, <c>AfterBody</c> is evaluated. In this case
      the exception is passed on after <c>AfterBody</c> has been
      evaluated, so the exception from the <c>try</c> expression is
      the same with an <c>after</c> section as without.</p>
    <p>If an exception occurs during evaluation of <c>AfterBody</c>
      itself it is not caught, so if <c>AfterBody</c> is evaluated after
      an exception in <c>Exprs</c>, <c>Body</c> or <c>ExceptionBody</c>,
      that exception is lost and masked by the exception in
      <c>AfterBody</c>.</p>
    <p>The <c>of</c>, <c>catch</c> and <c>after</c> sections are all
      optional, as long as there is at least a <c>catch</c> or an
      <c>after</c> section, so the following are valid <c>try</c>
      expressions:</p>
    <code type="none">
try Exprs of 
    Pattern when GuardSeq -> 
        Body 
after 
    AfterBody 
end

try Exprs
catch 
    ExpressionPattern -> 
        ExpressionBody
after
    AfterBody
end

try Exprs after AfterBody end</code>
    <p>Example of using <c>after</c>, this code will close the file
      even in the event of exceptions in <c>file:read/2</c> or in
      <c>binary_to_term/1</c>, and exceptions will be the same as
      without the <c>try</c>...<c>after</c>...<c>end</c> expression:</p>
    <code type="none">
termize_file(Name) ->
    {ok,F} = file:open(Name, [read,binary]),
    try
        {ok,Bin} = file:read(F, 1024*1024),
        binary_to_term(Bin)
    after
        file:close(F)
    end.</code>
    <p>Example: Using <c>try</c> to emulate <c>catch Expr</c>.</p>
    <code type="none">
try Expr
catch
    throw:Term -> Term;
    exit:Reason -> {'EXIT',Reason}
    error:Reason -> {'EXIT',{Reason,erlang:get_stacktrace()}}
end</code>
  </section>

  <section>
    <title>Parenthesized Expressions</title>
    <pre>
(Expr)</pre>
    <p>Parenthesized expressions are useful to override
      <seealso marker="#prec">operator precedences</seealso>,
      for example in arithmetic expressions:</p>
    <pre>
1> <input>1 + 2 * 3.</input>
7
2> <input>(1 + 2) * 3.</input>
9</pre>
  </section>

  <section>
    <title>Block Expressions</title>
    <pre>
begin
   Expr1,
   ...,
   ExprN
end</pre>
    <p>Block expressions provide a way to group a sequence of
      expressions, similar to a clause body. The return value is
      the value of the last expression <c>ExprN</c>.</p>
  </section>

  <section>
    <marker id="lcs"></marker>
    <title>List Comprehensions</title>
    <p>List comprehensions are a feature of many modern functional
      programming languages. Subject to certain rules, they provide a
      succinct notation for generating elements in a list.</p>
    <p>List comprehensions are analogous to set comprehensions in
      Zermelo-Frankel set theory and are called ZF expressions in
      Miranda. They are analogous to the <c>setof</c> and
      <c>findall</c> predicates in Prolog.</p>
    <p>List comprehensions are written with the following syntax:</p>
    <pre>
[Expr || Qualifier1,...,QualifierN]</pre>
    <p><c>Expr</c> is an arbitrary expression, and each
      <c>Qualifier</c> is either a generator or a filter.</p>
    <list type="bulleted">
      <item>A <em>generator</em> is written as:      <br></br>

       &nbsp;&nbsp;<c><![CDATA[Pattern <- ListExpr]]></c>.      <br></br>
<c>ListExpr</c> must be an expression which evaluates to a
       list of terms.</item>
<item>A <em>bit string generator</em> is written as:      <br></br>

       &nbsp;&nbsp;<c><![CDATA[BitstringPattern <= BitStringExpr]]></c>.      <br></br>
<c>BitStringExpr</c> must be an expression which evaluates to a
       bitstring.</item>
      <item>A <em>filter</em> is an expression which evaluates to
      <c>true</c> or <c>false</c>.</item>
    </list>
    <p>The variables in the generator patterns shadow variables in the function
    clause surrounding the list comprehensions.</p> <p>A list comprehension
    returns a list, where the elements are the result of evaluating <c>Expr</c>
    for each combination of generator list elements and bit string generator
    elements for which all filters are true.</p> <p></p> <p>Example:</p>
    <pre>
1> <input>[X*2 || X &lt;- [1,2,3]].</input>
[2,4,6]</pre>
    <p>More examples can be found in <em>Programming Examples</em>.</p>
  

  </section>

<section>
    <title>Bit String Comprehensions</title> 
   
    <p>Bit string comprehensions are
    analogous to List Comprehensions. They are used to generate bit strings
    efficiently and succinctly.</p> 
    <p>Bit string comprehensions are written with
    the following syntax:</p>
    <pre>
&lt;&lt; BitString || Qualifier1,...,QualifierN &gt;&gt;</pre>
    <p><c>BitString</c> is a bit string expression, and each
      <c>Qualifier</c> is either a generator, a bit string generator or a filter.</p>
    <list type="bulleted">
 <item>A <em>generator</em> is written as:      <br></br>
      &nbsp;&nbsp;<c><![CDATA[Pattern <- ListExpr]]></c>.      <br></br>
       <c>ListExpr</c> must be an expression which evaluates to a
       list of terms.</item>
      <item>A <em>bit string generator</em> is written as:      <br></br>

       &nbsp;&nbsp;<c><![CDATA[BitstringPattern <= BitStringExpr]]></c>.      <br></br>
<c>BitStringExpr</c> must be an expression which evaluates to a
       bitstring.</item>
      <item>A <em>filter</em> is an expression which evaluates to
      <c>true</c> or <c>false</c>.</item>
    </list>
    <p>The variables in the generator patterns shadow variables in
      the function clause surrounding the bit string comprehensions.</p>
    <p>A bit string comprehension returns a bit string, which is 
      created by concatenating the results of evaluating <c>BitString</c> 
      for each combination of bit string generator elements for which all 
      filters are true.</p>
    <p></p>
    <p>Example:</p>
    <pre>
1> <input>&lt;&lt; &lt;&lt; (X*2) &gt;&gt; || 
&lt;&lt;X&gt;&gt; &lt;= &lt;&lt; 1,2,3 &gt;&gt; &gt;&gt;.</input>
&lt;&lt;2,4,6&gt;&gt;</pre>
    <p>More examples can be found in <em>Programming Examples</em>.</p>
  </section>

  <section>
    <marker id="guards"></marker>
    <title>Guard Sequences</title>

    <p>A <em>guard sequence</em> is a sequence of guards, separated
      by semicolon (;). The guard sequence is true if at least one of
      the guards is true. (The remaining guards, if any, will not be
      evaluated.)<br></br>
<c>Guard1;...;GuardK</c></p>
    <p>A <em>guard</em> is a sequence of guard expressions, separated
      by comma (,). The guard is true if all guard expressions
      evaluate to <c>true</c>.<br></br>
<c>GuardExpr1,...,GuardExprN</c></p>
    <p>The set of valid <em>guard expressions</em> (sometimes called
      guard tests) is a subset of the set of valid Erlang expressions.
      The reason for restricting the set of valid expressions is that
      evaluation of a guard expression must be guaranteed to be free
      of side effects. Valid guard expressions are:</p>
    <list type="bulleted">
      <item>the atom <c>true</c>,</item>
      <item>other constants (terms and bound variables), all regarded
       as false,</item>
      <item>calls to the BIFs specified below,</item>
      <item>term comparisons,</item>
      <item>arithmetic expressions,</item>
      <item>boolean expressions, and</item>
      <item>short-circuit expressions (<c>andalso</c>/<c>orelse</c>).</item>
    </list>
    <table>
      <row>
        <cell align="left" valign="middle"><c>is_atom/1</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_binary/1</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_bitstring/1</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_boolean/1</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_float/1</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_function/1</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_function/2</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_integer/1</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_list/1</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_number/1</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_pid/1</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_port/1</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_record/2</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_record/3</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_reference/1</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>is_tuple/1</c></cell>
      </row>
      <tcaption>Type Test BIFs.</tcaption>
    </table>
    <p>Note that most type test BIFs have older equivalents, without
      the <c>is_</c> prefix. These old BIFs are retained for backwards
      compatibility only and should not be used in new code. They are
      also only allowed at top level. For example, they are not allowed
      in boolean expressions in guards.</p>
    <table>
      <row>
        <cell align="left" valign="middle"><c>abs(Number)</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>bit_size(Bitstring)</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>byte_size(Bitstring)</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>element(N, Tuple)</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>float(Term)</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>hd(List)</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>length(List)</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>node()</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>node(Pid|Ref|Port)</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>round(Number)</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>self()</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>size(Tuple|Bitstring)</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>tl(List)</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>trunc(Number)</c></cell>
      </row>
      <row>
        <cell align="left" valign="middle"><c>tuple_size(Tuple)</c></cell>
      </row>
      <tcaption>Other BIFs Allowed in Guard Expressions.</tcaption>
    </table>

    <p>If an arithmetic expression, a boolean expression, a
    short-circuit expression, or a call to a guard BIF fails (because
    of invalid arguments), the entire guard fails. If the guard was
    part of a guard sequence, the next guard in the sequence (that is,
    the guard following the next semicolon) will be evaluated.</p>

  </section>

  <section>
    <marker id="prec"></marker>
    <title>Operator Precedence</title>
    <p>Operator precedence in falling priority:</p>
    <table>
      <row>
        <cell align="left" valign="middle">:</cell>
        <cell align="left" valign="middle">&nbsp;</cell>
      </row>
      <row>
        <cell align="left" valign="middle">#</cell>
        <cell align="left" valign="middle">&nbsp;</cell>
      </row>
      <row>
        <cell align="left" valign="middle">Unary + - bnot not</cell>
        <cell align="left" valign="middle">&nbsp;</cell>
      </row>
      <row>
        <cell align="left" valign="middle">/ * div rem band and</cell>
        <cell align="left" valign="middle">Left associative</cell>
      </row>
      <row>
        <cell align="left" valign="middle">+ - bor bxor bsl bsr or xor</cell>
        <cell align="left" valign="middle">Left associative</cell>
      </row>
      <row>
        <cell align="left" valign="middle">++ --</cell>
        <cell align="left" valign="middle">Right associative</cell>
      </row>
      <row>
        <cell align="left" valign="middle">== /= =&lt; &lt; >= > =:= =/=</cell>
        <cell align="left" valign="middle">&nbsp;</cell>
      </row>
      <row>
        <cell align="left" valign="middle">andalso</cell>
        <cell align="left" valign="middle">&nbsp;</cell>
      </row>
      <row>
        <cell align="left" valign="middle">orelse</cell>
        <cell align="left" valign="middle">&nbsp;</cell>
      </row>
      <row>
        <cell align="left" valign="middle">= !</cell>
        <cell align="left" valign="middle">Right associative</cell>
      </row>
      <row>
        <cell align="left" valign="middle">catch</cell>
        <cell align="left" valign="middle">&nbsp;</cell>
      </row>
      <tcaption>Operator Precedence.</tcaption>
    </table>
    <p>When evaluating an expression, the operator with the highest
      priority is evaluated first. Operators with the same priority
      are evaluated according to their associativity. Example:
      The left associative arithmetic operators are evaluated left to
      right:</p>
    <pre>
<input>6 + 5 * 4 - 3 / 2</input> evaluates to
<input>6 + 20 - 1.5</input> evaluates to
<input>26 - 1.5</input> evaluates to
<input>24.5</input></pre>
  </section>
</chapter>