path: root/lib/tools/doc/src/xref.xml

<?xml version="1.0" encoding="utf-8" ?>
<!DOCTYPE erlref SYSTEM "erlref.dtd">

<erlref>
  <header>
    <copyright>
      <year>2000</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>xref</title>
    <prepared>Hans Bolinder</prepared>
    <responsible>nobody</responsible>
    <docno></docno>
    <approved>nobody</approved>
    <checked>no</checked>
    <date>2000-08-15</date>
    <rev>PA1</rev>
    <file>xref.sgml</file>
  </header>
  <module since="">xref</module>
  <modulesummary>A Cross Reference Tool for analyzing dependencies between functions, modules, applications and releases.</modulesummary>
  <description>
    <p>Xref is a cross reference tool that can be used for finding
      dependencies between functions, modules, applications and
      releases.
      </p>
    <p>Calls between functions are either       <marker id="local_call"></marker>
<em>local calls</em> like <c>f()</c>, or       <marker id="external_call"></marker>
<em>external calls</em> like
      <c>m:f()</c>.       <marker id="module_data"></marker>
<em>Module data</em>,
      which are extracted from BEAM files, include local functions,
      exported functions, local calls and external calls. By default,
      calls to built-in functions (<term id="BIF"></term>) are ignored, but
      if the option <c>builtins</c>, accepted by some of this
      module's functions, is set to <c>true</c>, calls to BIFs
      are included as well. It is the analyzing OTP version that
      decides what functions are BIFs. Functional objects are assumed
      to be called where they are created (and nowhere else).       <marker id="unresolved_call"></marker>
<em>Unresolved calls</em> are calls to
      <c>apply</c> or <c>spawn</c> with variable module, variable
      function, or variable arguments. Examples are <c>M:F(a)</c>,
      <c>apply(M,&nbsp;f,&nbsp;[a])</c>, and
      <c>spawn(m,&nbsp;f(),&nbsp;Args)</c>. Unresolved calls are
      represented by calls where variable modules have been replaced
      with the atom <c>'$M_EXPR'</c>, variable functions have been
      replaced with the atom <c>'$F_EXPR'</c>, and variable number of
      arguments have been replaced with the number <c>-1</c>. The
      above mentioned examples are represented by calls to
      <c>'$M_EXPR':'$F_EXPR'/1</c>, <c>'$M_EXPR':f/1</c>, and
      <c>m:'$F_EXPR'/-1</c>. The unresolved calls are a subset of the
      external calls.
      </p>
    <warning>
      <p>Unresolved calls make module data incomplete, which
        implies that the results of analyses may be invalid.</p>
    </warning>
    <p><em>Applications</em> are collections of modules. The
      modules' BEAM files are located in the <c>ebin</c>
      subdirectory of the application directory. The name of the
      application directory determines the name and version of the
      application.
      <em>Releases</em> are collections of applications
      located in the <c>lib</c> subdirectory of the release directory. 
      There is more to read about applications and releases in the
      Design Principles book.
      </p>
    <p>      <marker id="xref_server"></marker>
<em>Xref servers</em> are identified
      by names, supplied when creating new servers. Each Xref server
      holds a set of releases, a set of applications, and a set of
      modules with module data. Xref servers are independent of each
      other, and all analyses are evaluated in the context of one
      single Xref server (exceptions are the functions <c>m/1</c> and
      <c>d/1</c> which do not use servers at all). The       <marker id="mode"></marker>
<em>mode</em> of an Xref server determines what module
      data are extracted from BEAM files as modules are added to the
      server. Starting with R7, BEAM files compiled with the option
      <c>debug_info</c> contain so called       <marker id="debug_info"></marker>
debug information, which is an abstract
      representation of the code. In <c>functions</c> mode, which is
      the default mode, function calls and line numbers are extracted
      from debug information. In <c>modules</c> mode, debug
      information is ignored if present, but dependencies between
      modules are extracted from other parts of the BEAM files. The
      <c>modules</c> mode is significantly less time and space
      consuming than the <c>functions</c> mode, but the analyses that
      can be done are limited.
      </p>
    <p>An       <marker id="analyzed_module"></marker>
<em>analyzed module</em> is a
      module that has been added to an Xref server together with its
      module data.
      A       <marker id="library_module"></marker>
<em>library module</em> is a
      module located in some directory mentioned in the       <marker id="library_path"></marker>
<em>library path</em>. 
      A library module is said to be used if some of its exported
      functions are used by some analyzed module.
      An       <marker id="unknown_module"></marker>
<em>unknown module</em> is a
      module that is neither an analyzed module nor a library module,
      but whose exported functions are used by some analyzed module. 
      An       <marker id="unknown_function"></marker>
<em>unknown function</em> is a
      used function that is neither local or exported by any 
      analyzed module nor exported by any library module. 
      An       <marker id="undefined_function"></marker>
<em>undefined function</em> is an externally used function that
      is not exported by any analyzed module or library module. With
      this notion, a local function can be an undefined function, namely
      if it is externally used from some module. All unknown functions
      are also undefined functions; there is a <seealso marker="xref_chapter#venn2">figure</seealso> in the
      User's Guide that illustrates this relationship.
      </p>
    <p>Starting with R9C, the module attribute tag <c>deprecated</c>
      can be used to inform Xref about       <marker id="deprecated_function"></marker>
<em>deprecated functions</em> and
      optionally when functions are planned to be removed. A few
      examples show the idea:
      </p>
    <taglist>
      <tag>-deprecated({f,1}).</tag>
      <item>The exported function <c>f/1</c> is deprecated. Nothing is
       said whether <c>f/1</c> will be removed or not.</item>
      <tag>-deprecated({f,'_'}).</tag>
      <item>All exported functions <c>f/0</c>, <c>f/1</c> and so on are
       deprecated.</item>
      <tag>-deprecated(module).</tag>
      <item>All exported functions in the module are deprecated.
       Equivalent to <c>-deprecated({'_','_'}).</c>.</item>
      <tag>-deprecated([{g,1,next_version}]).</tag>
      <item>The function <c>g/1</c> is deprecated and will be
       removed in next version.</item>
      <tag>-deprecated([{g,2,next_major_release}]).</tag>
      <item>The function <c>g/2</c> is deprecated and will be
       removed in next major release.</item>
      <tag>-deprecated([{g,3,eventually}]).</tag>
      <item>The function <c>g/3</c> is deprecated and will
       eventually be removed.</item>
      <tag>-deprecated({'_','_',eventually}).</tag>
      <item>All exported functions in the module are deprecated and
       will eventually be removed.</item>
    </taglist>
    <p>Before any analysis can take place, module data must be <em>set up</em>. For instance, the cross reference and the unknown
      functions are computed when all module data are known. The
      functions that need complete data (<c>analyze</c>, <c>q</c>,
      <c>variables</c>) take care of setting up data automatically.
      Module data need to be set up (again) after calls to any of the
      <c>add</c>, <c>replace</c>, <c>remove</c>,
      <c>set_library_path</c> or <c>update</c> functions.
      </p>
    <p>The result of setting up module data is the       <marker id="call_graph"></marker>
<em>Call Graph</em>. A (directed) graph
      consists of a set of vertices and a set of (directed) edges. The
      edges represent       <marker id="call"></marker>
<em>calls</em> (From,&nbsp;To)
      between functions, modules, applications or releases. From is
      said to call To, and To is said to be used by From. The vertices
      of the Call Graph are the functions of all module data: local
      and exported functions of analyzed modules; used BIFs; used
      exported functions of library modules; and unknown functions.
      The functions <c>module_info/0,1</c> added by the compiler are
      included among the exported functions, but only when called from
      some module. The edges are the function calls of all module
      data. A consequence of the edges being a set is that there is
      only one edge if a function is locally or externally used
      several times on one and the same line of code.
      </p>
    <p>The Call Graph is       <marker id="representation"></marker>
represented by
      Erlang terms (the sets are lists), which is suitable for many
      analyses. But for analyses that look at chains of calls, a list
      representation is much too
      slow. Instead the representation offered by the <c>digraph</c>
      module is used. The translation of the list representation of
      the Call Graph - or a subgraph thereof - to the <c>digraph</c>
      representation does not
      come for free, so the language used for expressing queries to be
      described below has a special operator for this task and a
      possibility to save the <c>digraph</c> representation for
      subsequent analyses.
      </p>
    <p>In addition to the Call Graph there is a graph called the
            <marker id="inter_call_graph"></marker>
<em>Inter Call Graph</em>. This is
      a graph of calls (From,&nbsp;To) such that there is a chain of
      calls from From to To in the Call Graph, and every From and To
      is an exported function or an unused local function.
      The vertices are the same as for the Call Graph.
      </p>
    <p>Calls between modules, applications and releases are also
      directed graphs. The       <marker id="type"></marker>
<em>types</em>
      of the vertices and edges of these graphs are (ranging from the
      most special to the most general):
      <c>Fun</c> for functions; <c>Mod</c> for modules;
      <c>App</c> for applications; and <c>Rel</c> for releases.
      The following paragraphs will describe the different constructs
      of the language used for selecting and analyzing parts of the
      graphs, beginning with the       <marker id="constants"></marker>
<em>constants</em>:
      </p>
    <list type="bulleted">
      <item>Expression ::= Constants</item>
      <item>Constants ::= Consts | Consts <c>:</c> Type | RegExpr</item>
      <item>Consts ::= Constant | <c>[</c>Constant<c>,</c>&nbsp;...<c>]</c>
       | <c>{</c>Constant<c>,</c>&nbsp;...<c>}</c></item>
      <item>Constant ::= Call | Const</item>
      <item>Call ::= FunSpec&nbsp;<c>-></c>&nbsp;FunSpec
       | <c>{</c>MFA<c>,</c>&nbsp;MFA<c>}</c>
       | AtomConst&nbsp;<c>-></c>&nbsp;AtomConst 
       | <c>{</c>AtomConst<c>,</c>&nbsp;AtomConst<c>}</c></item>
      <item>Const ::= AtomConst | FunSpec | MFA</item>
      <item>AtomConst ::= Application | Module | Release</item>
      <item>FunSpec ::= Module <c>:</c> Function <c>/</c> Arity</item>
      <item>MFA ::=
      <c>{</c>Module<c>,</c>&nbsp;Function<c>,</c>&nbsp;Arity<c>}</c></item>
      <item>RegExpr ::= RegString <c>:</c> Type 
       | RegFunc 
       | RegFunc <c>:</c> Type</item>
      <item>RegFunc ::= RegModule <c>:</c> RegFunction <c>/</c> RegArity</item>
      <item>RegModule ::= RegAtom</item>
      <item>RegFunction ::= RegAtom</item>
      <item>RegArity ::= RegString | Number | <c>_</c> | <c>-1</c></item>
      <item>RegAtom ::= RegString | Atom | <c>_</c></item>
      <item>RegString ::= - a regular expression, as described in the 
      <c>re</c> module, enclosed in double quotes -</item>
      <item>Type ::= <c>Fun</c> | <c>Mod</c> | <c>App</c> | <c>Rel</c></item>
      <item>Function ::= Atom</item>
      <item>Application ::= Atom</item>
      <item>Module ::= Atom</item>
      <item>Release ::= Atom</item>
      <item>Arity ::= Number | <c>-1</c></item>
      <item>Atom ::= - same as Erlang atoms -</item>
      <item>Number ::= - same as non-negative Erlang integers -</item>
    </list>
    <p>Examples of constants are: <c>kernel</c>, <c>kernel->stdlib</c>,
      <c>[kernel, sasl]</c>, <c>[pg -> mnesia, {tv, mnesia}] : Mod</c>.
      It is an error if an instance of <c>Const</c> does not match any
      vertex of any graph. 
      If there  are more than one vertex matching an untyped instance
      of <c>AtomConst</c>, then the one of the most general type is
      chosen.
      A list of constants is interpreted as a set of constants, all of
      the same type.
      A tuple of constants constitute a chain of calls (which may,
      but does not have to, correspond to an actual chain of calls of
      some graph).
      Assigning a type to a list or tuple of <c>Constant</c> is
      equivalent to assigning the type to each <c>Constant</c>.
      </p>
    <p><marker id="regexp"></marker><em>Regular expressions</em> are used as a
      means to select some of the vertices of a graph.
      A <c>RegExpr</c> consisting of a <c>RegString</c> and a type -
      an example is <c>"xref_.*" : Mod</c> - is interpreted as those
      modules (or applications or releases, depending on the type)
      that match the expression.
      Similarly, a <c>RegFunc</c> is interpreted as those vertices
      of the Call Graph that match the expression. 
      An example is <c>"xref_.*":"add_.*"/"(2|3)"</c>, which matches
      all <c>add</c> functions of arity two or three of any of the
      xref modules.
      Another example, one that matches all functions of arity 10 or
      more: <c>_:_/"[1-9].+"</c>. Here <c>_</c> is an abbreviation for
      <c>".*"</c>, that is, the regular expression that matches
      anything.
      </p>
    <p>The syntax of       <marker id="variable"></marker>
<em>variables</em> is
      simple:
      </p>
    <list type="bulleted">
      <item>Expression ::= Variable</item>
      <item>Variable ::= - same as Erlang variables -</item>
    </list>
    <p>There are two kinds of variables: predefined variables and user 
      variables. 
            <marker id="predefined_variable"></marker>
<em>Predefined variables</em>
      hold set up module data, and cannot be assigned to but only used 
      in queries. 
            <marker id="user_variable"></marker>
<em>User variables</em> on the other 
      hand can be assigned to, and are typically used for
      temporary results while evaluating a query, and for keeping
      results of queries for use in subsequent queries. 
      The predefined variables are (variables marked with (*) are
      available in <c>functions</c> mode only):
      </p>
    <taglist>
      <tag><c>E</c></tag>
      <item>Call Graph Edges (*).</item>
      <tag><c>V</c></tag>
      <item>Call Graph Vertices (*).
      </item>
      <tag><c>M</c></tag>
      <item>Modules. All modules: analyzed modules, used library
       modules, and unknown modules.</item>
      <tag><c>A</c></tag>
      <item>Applications.</item>
      <tag><c>R</c></tag>
      <item>Releases.
      </item>
      <tag><c>ME</c></tag>
      <item>Module Edges. All module calls.</item>
      <tag><c>AE</c></tag>
      <item>Application Edges. All application calls. </item>
      <tag><c>RE</c></tag>
      <item>Release Edges. All release calls.
      </item>
      <tag><c>L</c></tag>
      <item>Local Functions (*). All local functions of analyzed modules.</item>
      <tag><c>X</c></tag>
      <item>Exported Functions. All exported functions of analyzed 
       modules and all used exported functions of library modules.</item>
      <tag><c>F</c></tag>
      <item>Functions (*).</item>
      <tag><c>B</c></tag>
      <item>Used BIFs. <c>B</c> is empty if <c>builtins</c> is 
      <c>false</c> for all analyzed modules.</item>
      <tag><c>U</c></tag>
      <item>Unknown Functions.</item>
      <tag><c>UU</c></tag>
      <item>Unused Functions (*). All local and exported functions of
       analyzed modules that have not been used. </item>
      <tag><c>XU</c></tag>
      <item>Externally Used Functions. Functions of all modules -
       including local functions - that have been used in some
       external call.</item>
      <tag><c>LU</c></tag>
      <item>Locally Used Functions (*). Functions of all modules that have
       been used in some local call.
      </item>
      <tag><c>OL</c></tag>
      <item>Functions with an attribute tag <c>on_load</c> (*).
      </item>
      <tag><c>LC</c></tag>
      <item>Local Calls (*).</item>
      <tag><c>XC</c></tag>
      <item>External Calls (*).
      </item>
      <tag><c>AM</c></tag>
      <item>Analyzed Modules.</item>
      <tag><c>UM</c></tag>
      <item>Unknown Modules.</item>
      <tag><c>LM</c></tag>
      <item>Used Library Modules.
      </item>
      <tag><c>UC</c></tag>
      <item>Unresolved Calls. Empty in <c>modules</c> mode.
      </item>
      <tag><c>EE</c></tag>
      <item>Inter Call Graph Edges (*).
      </item>
      <tag><c>DF</c></tag>
      <item>Deprecated Functions. All deprecated exported 
       functions and all used deprecated BIFs.</item>
      <tag><c>DF_1</c></tag>
      <item>Deprecated Functions. All deprecated functions 
       to be removed in next version.</item>
      <tag><c>DF_2</c></tag>
      <item>Deprecated Functions. All deprecated functions 
       to be removed in next version or next major release.</item>
      <tag><c>DF_3</c></tag>
      <item>Deprecated Functions. All deprecated functions to be
       removed in next version, next major release, or later.</item>
    </taglist>
    <p>These are a few       <marker id="simple_facts"></marker>
facts about the
      predefined variables (the set operators <c>+</c> (union) and
      <c>-</c> (difference) as well as the cast operator
      <c>(</c>Type<c>)</c> are described below):
      </p>
    <list type="bulleted">
      <item><c>F</c> is equal to  <c>L + X</c>.</item>
      <item><c>V</c> is equal to <c>X + L + B + U</c>, where <c>X</c>,
      <c>L</c>, <c>B</c> and <c>U</c> are pairwise disjoint (that
       is, have no elements in common).</item>
      <item><c>UU</c> is equal to <c>V - (XU + LU)</c>, where
      <c>LU</c> and <c>XU</c> may have elements in common. Put in
       another way:</item>
      <item><c>V</c> is equal to <c>UU + XU + LU</c>.</item>
      <item><c>OL</c> is a subset of <c>F</c>.</item>
      <item><c>E</c> is equal to <c>LC + XC</c>. Note that <c>LC</c>
       and <c>XC</c> may have elements in common, namely if some
       function is locally and externally used from one and the same
       function.</item>
      <item><c>U</c> is a subset of <c>XU</c>.</item>
      <item><c>B</c> is a subset of <c>XU</c>.</item>
      <item><c>LU</c> is equal to <c>range LC</c>.</item>
      <item><c>XU</c> is equal to <c>range XC</c>.</item>
      <item><c>LU</c> is a subset of <c>F</c>.</item>
      <item><c>UU</c> is a subset of <c>F</c>. </item>
      <item><c>range UC</c> is a subset of <c>U</c>.</item>
      <item><c>M</c> is equal to <c>AM + LM + UM</c>, where <c>AM</c>,
      <c>LM</c> and <c>UM</c> are pairwise disjoint. </item>
      <item><c>ME</c> is equal to <c>(Mod) E</c>.</item>
      <item><c>AE</c> is equal to <c>(App) E</c>.</item>
      <item><c>RE</c> is equal to <c>(Rel) E</c>.</item>
      <item><c>(Mod) V</c> is a subset of <c>M</c>. Equality holds
       if all analyzed modules have some local, exported, or unknown 
       function.</item>
      <item><c>(App) M</c> is a subset of <c>A</c>. Equality holds
       if all applications have some module.</item>
      <item><c>(Rel) A</c> is a subset of <c>R</c>. Equality holds
       if all releases have some application.</item>
      <item><c>DF_1</c> is a subset of <c>DF_2</c>.</item>
      <item><c>DF_2</c> is a subset of <c>DF_3</c>.</item>
      <item><c>DF_3</c> is a subset of <c>DF</c>.</item>
      <item><c>DF</c> is a subset of <c>X + B</c>.</item>
    </list>
    <p>An important notion is that of       <marker id="conversion"></marker>
<em>conversion</em> of expressions. The syntax of
      a cast expression is:
      </p>
    <list type="bulleted">
      <item>Expression ::= <c>(</c> Type <c>)</c> Expression</item>
    </list>
    <p>The interpretation of the cast operator depends on the named
      type <c>Type</c>, the type of <c>Expression</c>, and the
      structure of the elements of the interpretation of <c>Expression</c>. 
      If the named type is equal to the
      expression type, no conversion is done. Otherwise, the
      conversion is done one step at a time;
      <c>(Fun)&nbsp;(App)&nbsp;RE</c>, for instance, is equivalent to
      <c>(Fun)&nbsp;(Mod)&nbsp;(App)&nbsp;RE</c>. Now assume that the
      interpretation of <c>Expression</c> is a set of constants
      (functions, modules, applications or releases). If the named
      type is more general than the expression type, say <c>Mod</c>
      and <c>Fun</c> respectively, then the interpretation of the cast
      expression is the set of modules that have at least one
      of their functions mentioned in the interpretation of the
      expression. If the named
      type is more special than the expression type, say <c>Fun</c>
      and <c>Mod</c>, then the interpretation is the set of all the
      functions of the modules (in <c>modules</c> mode, the conversion
      is partial since the local functions are not known).
      The conversions to and from applications and releases
      work analogously. For instance, <c>(App) "xref_.*" : Mod</c>
      returns all applications containing at least one module
      such that <c>xref_</c> is a prefix of the module name.
      </p>
    <p>Now assume that the interpretation of <c>Expression</c> is a
      set of calls. If the named type is more general than the
      expression type, say <c>Mod</c> and <c>Fun</c> respectively,
      then the interpretation of the cast expression is the set of
      calls (M1,&nbsp;M2) such that the interpretation of the 
      expression contains a call from some function
      of M1 to some function of M2. If the named type is more special
      than the expression type, say <c>Fun</c> and <c>Mod</c>, then
      the interpretation is the set of all function calls
      (F1,&nbsp;F2) such that the interpretation of the expression
      contains a call (M1,&nbsp;M2) and F1 is
      a function of M1 and F2 is a function of M2 (in <c>modules</c>
      mode, there are no functions calls, so a cast to <c>Fun</c>
      always yields an empty set). Again, the conversions to and from
      applications and releases work analogously.
      </p>
    <p>The interpretation of constants and variables are sets, and
      those sets can be used as the basis for forming new sets by the
      application of       <marker id="set_operator"></marker>
<em>set operators</em>.
      The syntax:
      </p>
    <list type="bulleted">
      <item>Expression ::= Expression BinarySetOp Expression</item>
      <item>BinarySetOp ::= <c>+</c> | <c>*</c> | <c>-</c></item>
    </list>
    <p><c>+</c>, <c>*</c> and <c>-</c> are interpreted as union,
      intersection and difference respectively: the union of two sets
      contains the elements of both sets; the intersection of two sets
      contains the elements common to both sets; and the difference of
      two sets contains the elements of the first set that are not
      members of the second set. The elements of the two sets must be
      of the same structure; for instance, a function call cannot be
      combined with a function. But if a cast operator can make the
      elements compatible, then the more general elements are
      converted to the less general element type. For instance,
      <c>M&nbsp;+&nbsp;F</c> is equivalent to
      <c>(Fun)&nbsp;M&nbsp;+&nbsp;F</c>, and <c>E&nbsp;-&nbsp;AE</c>
      is equivalent to <c>E&nbsp;-&nbsp;(Fun)&nbsp;AE</c>. One more
      example: <c>X * xref : Mod</c> is interpreted as the set of
      functions exported by the module <c>xref</c>; <c>xref : Mod</c>
      is converted to the more special type of <c>X</c> (<c>Fun</c>,
      that is) yielding all functions of <c>xref</c>, and the
      intersection with <c>X</c> (all functions exported by analyzed 
      modules and library modules) is interpreted as those functions
      that are exported by some module <em>and</em> functions of 
      <c>xref</c>. 
      </p>
    <p>There are also unary set operators:
      </p>
    <list type="bulleted">
      <item>Expression ::= UnarySetOp Expression</item>
      <item>UnarySetOp ::= <c>domain</c> | <c>range</c> | <c>strict</c></item>
    </list>
    <p>Recall that a call is a pair (From,&nbsp;To). <c>domain</c>
      applied to a set of calls is interpreted as the set of all
      vertices From, and <c>range</c> as the set of all vertices To.
      The interpretation of the <c>strict</c> operator is the operand
      with all calls on the form (A,&nbsp;A) removed. 
      </p>
    <p>The interpretation of the       <marker id="restriction"></marker>
<em>restriction operators</em> is a 
      subset of the first operand, a set of calls. The second operand,
      a set of vertices, is converted to the type of the first operand.
      The syntax of the restriction operators:
      </p>
    <list type="bulleted">
      <item>Expression ::= Expression RestrOp Expression</item>
      <item>RestrOp ::= <c>|</c></item>
      <item>RestrOp ::= <c>||</c></item>
      <item>RestrOp ::= <c>|||</c></item>
    </list>
    <p>The interpretation in some detail for the three operators:
      </p>
    <taglist>
      <tag><c>|</c></tag>
      <item>The subset of calls from any of the vertices.</item>
      <tag><c>||</c></tag>
      <item>The subset of calls to any of the vertices.</item>
      <tag><c>|||</c></tag>
      <item>The subset of calls to and from any of the vertices.
       For all sets of calls <c>CS</c> and all sets of vertices
      <c>VS</c>, <c>CS&nbsp;|||&nbsp;VS&nbsp;</c> is equivalent to
      <c>CS&nbsp;|&nbsp;VS&nbsp;*&nbsp;CS&nbsp;||&nbsp;VS</c>.</item>
    </taglist>
    <p>      <marker id="graph_analyses"></marker>
Two functions (modules,
      applications, releases) belong to the same strongly connected
      component if they call each other (in)directly. The
      interpretation of the <c>components</c> operator is the set of
      strongly connected components of a set of calls. The
      <c>condensation</c> of a set of calls is a new set of calls
      between the strongly connected components such that there is an
      edge between two components if there is some constant of the first
      component that calls some constant of the second component.
      </p>
    <p>The interpretation of the <c>of</c> operator is a chain of
      calls of the second operand (a set of calls) that passes throw
      all of the vertices of the first operand (a tuple of
      constants), in the given order. The second operand
      is converted to the type of the first operand.
      For instance, the <c>of</c> operator can be used for finding out
      whether a function calls another function indirectly, and the
      chain of calls demonstrates how. The syntax of the graph
      analyzing operators:
      </p>
    <list type="bulleted">
      <item>Expression ::= Expression BinaryGraphOp Expression</item>
      <item>Expression ::= UnaryGraphOp Expression</item>
      <item>UnaryGraphOp ::= <c>components</c> | <c>condensation</c></item>
      <item>BinaryGraphOp ::= <c>of</c></item>
    </list>
    <p>As was mentioned before, the graph analyses operate on
      the <c>digraph</c> representation of graphs.
      By default, the <c>digraph</c> representation is created when
      needed (and deleted when no longer used), but it can also be
      created explicitly by use of the <c>closure</c> operator:
      </p>
    <list type="bulleted">
      <item>Expression ::= ClosureOp Expression</item>
      <item>ClosureOp ::= <c>closure</c></item>
    </list>
    <p>The interpretation of the <c>closure</c> operator is the
      transitive closure of the operand. 
      </p>
    <p>The restriction operators are defined for closures as well;
      <c>closure&nbsp;E&nbsp;|&nbsp;xref&nbsp;:&nbsp;Mod</c> is
      interpreted as the direct or indirect function calls from the
      <c>xref</c> module, while the interpretation of
      <c>E&nbsp;|&nbsp;xref&nbsp;:&nbsp;Mod</c> is the set of direct
      calls from <c>xref</c>. 
      If some graph is to be used in several graph analyses, it saves
      time to assign the <c>digraph</c> representation of the graph
      to a user variable, 
      and then make sure that every graph analysis operates on that
      variable instead of the list representation of the graph.
      </p>
    <p>The lines where functions are defined (more precisely: where
      the first clause begins) and the lines where functions are used
      are available in <c>functions</c> mode. The line numbers refer
      to the files where the functions are defined. This holds also for
      files included with the <c>-include</c> and <c>-include_lib</c>
      directives, which may result in functions defined apparently in
      the same line. The <em>line operators</em> are used for assigning
      line numbers to functions and for assigning sets of line numbers
      to function calls. 
      The syntax is similar to the one of the cast operator:
      </p>
    <list type="bulleted">
      <item>Expression ::= <c>(</c> LineOp<c>)</c> Expression</item>
      <item>Expression ::= <c>(</c> XLineOp<c>)</c> Expression</item>
      <item>LineOp ::= <c>Lin</c> | <c>ELin</c> | <c>LLin</c> | <c>XLin</c></item>
      <item>XLineOp ::= <c>XXL</c></item>
    </list>
    <p>The interpretation of the <c>Lin</c> operator applied to a set
      of functions assigns to each function the line number where the
      function is defined. Unknown functions and functions of library
      modules are assigned the number 0.
      </p>
    <p>The interpretation of some LineOp operator applied to a
      set of function calls assigns to each call the set of line
      numbers where the first function calls the second function. Not
      all calls are assigned line numbers by all operators:
      </p>
    <list type="bulleted">
      <item>the <c>Lin</c> operator is defined for Call Graph Edges;</item>
      <item>the <c>LLin</c> operator is defined for Local Calls.</item>
      <item>the <c>XLin</c> operator is defined for External Calls.</item>
      <item>the <c>ELin</c> operator is defined for Inter Call Graph Edges.</item>
    </list>
    <p>The <c>Lin</c> (<c>LLin</c>, <c>XLin</c>) operator assigns
      the lines where calls (local calls, external calls) are made.
      The <c>ELin</c> operator assigns to each call (From,&nbsp;To),
      for which it is defined, every line L such that there is
      a chain of calls from From to To beginning with a call on line
      L.
      </p>
    <p>The <c>XXL</c> operator is defined for the interpretation of
      any of the LineOp operators applied to a set of function
      calls. The result is that of replacing the function call with
      a line numbered function call, that is, each of the two
      functions of the call is replaced by a pair of the function and
      the line where the function is defined. The effect of the
      <c>XXL</c> operator can be undone by the LineOp operators. For
      instance, <c>(Lin)&nbsp;(XXL)&nbsp;(Lin)&nbsp;E</c> is
      equivalent to <c>(Lin)&nbsp;E</c>.
      </p>
    <p>The <c>+</c>, <c>-</c>, <c>*</c> and <c>#</c> operators are
      defined for line number expressions, provided the operands are
      compatible. The LineOp operators are also defined for
      modules, applications, and releases; the operand is implicitly
      converted to functions. Similarly, the cast operator is defined
      for the interpretation of the LineOp operators.
      </p>
    <p>The interpretation of the       <marker id="count"></marker>
<em>counting operator</em> is the number of elements of a set. The operator
      is undefined for closures. The <c>+</c>, <c>-</c> and <c>*</c>
      operators are interpreted as the obvious arithmetical operators
      when applied to numbers. The syntax of the counting operator:
      </p>
    <list type="bulleted">
      <item>Expression ::= CountOp Expression</item>
      <item>CountOp ::= <c>#</c></item>
    </list>
    <p>All binary operators are left associative; for instance,
      <c>A&nbsp;|&nbsp;B &nbsp;||&nbsp;C</c> is equivalent to
      <c>(A&nbsp;|&nbsp;B)&nbsp;||&nbsp;C</c>. The following is a list
      of all operators, in increasing order of       <marker id="precedence"></marker>
<em>precedence</em>:
      </p>
    <list type="bulleted">
      <item><c>+</c>, <c>-</c></item>
      <item><c>*</c></item>
      <item><c>#</c></item>
      <item><c>|</c>, <c>||</c>, <c>|||</c></item>
      <item><c>of</c></item>
      <item><c>(</c>Type<c>)</c></item>
      <item><c>closure</c>, <c>components</c>, <c>condensation</c>,
      <c>domain</c>, <c>range</c>, <c>strict</c></item>
    </list>
    <p>Parentheses are used for grouping, either to make an expression
      more readable or to override the default precedence of operators:
      </p>
    <list type="bulleted">
      <item>Expression ::= <c>(</c> Expression <c>)</c></item>
    </list>
    <p>A       <marker id="query"></marker>
<em>query</em> is a non-empty sequence of
      statements. A statement is either an assignment of a user
      variable or an expression. The value of an assignment is the
      value of the right hand side expression. It makes no sense to
      put a plain expression anywhere else but last in queries. The
      syntax of queries is summarized by these productions:
      </p>
    <list type="bulleted">
      <item>Query ::= Statement<c>,</c>&nbsp;...</item>
      <item>Statement ::= Assignment | Expression</item>
      <item>Assignment ::= Variable <c>:=</c> Expression 
       | Variable <c>=</c> Expression</item>
    </list>
    <p>A variable cannot be assigned a new value unless first removed.
      Variables assigned to by the <c>=</c> operator are removed at
      the end of the query, while variables assigned to by the
      <c>:=</c> operator can only be removed by calls to
      <c>forget</c>. There are no user variables when module data
      need to be set up again; if any of the functions that make it
      necessary to set up module data again is called, all user
      variables are forgotten.
      </p>
    <p><em>Types</em></p>
    <pre>
application() = atom()
arity() = int() | -1
bool() = true | false
call() = {atom(), atom()} | funcall()
constant() = mfa() | module() | application() | release()
directory() = string()
file() = string()
funcall() = {mfa(), mfa()}
function() = atom()
int() = integer() >= 0
library() = atom()
library_path() = path() | code_path
mfa() = {module(), function(), arity()}
mode() = functions | modules
module() = atom()
release() = atom()
string_position() = int() | at_end
variable() = atom()
xref() = atom() | pid()  </pre>
  </description>
  <funcs>
    <func>
      <name since="">add_application(Xref, Directory [, Options]) ->  {ok, application()} | Error</name>
      <fsummary>Add the modules of an application.</fsummary>
      <type>
        <v>Directory = directory()</v>
        <v>Error = {error, module(), Reason}</v>
        <v>Options = [Option] | Option</v>
        <v>Option = {builtins, bool()} | {name, application()}  | {verbose, bool()} | {warnings, bool()}</v>
        <v>Reason =  {application_clash, {application(), directory(), directory()}} | {file_error, file(), error()} | {invalid_filename, term()} | {invalid_options, term()} | -&nbsp;see&nbsp;also&nbsp;add_directory&nbsp;-</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Adds an application, the modules of the application and <seealso marker="#module_data">module data</seealso> of the
          modules to an <seealso marker="#xref_server">Xref server</seealso>.
          The modules will be members of the application.
          The default is to use the base name of the
          directory with the version removed as application name, but
          this can be overridden by the <c>name</c> option. Returns the
          name of the application.
          </p>
        <p>If the given directory has a subdirectory named
          <c>ebin</c>, modules (BEAM files) are searched for in that
          directory, otherwise modules are searched for in the given
          directory.
          </p>
        <p>If the <seealso marker="#mode">mode</seealso> of the Xref
          server is <c>functions</c>, BEAM files that contain no
          <seealso marker="#debug_info">debug information</seealso> are
          ignored.
          </p>
      </desc>
    </func>
    <func>
      <name since="">add_directory(Xref, Directory [, Options]) ->  {ok, Modules} | Error</name>
      <fsummary>Add the modules in a directory.</fsummary>
      <type>
        <v>Directory = directory()</v>
        <v>Error = {error, module(), Reason}</v>
        <v>Modules = [module()]</v>
        <v>Options = [Option] | Option</v>
        <v>Option = {builtins, bool()} | {recurse, bool()}  | {verbose, bool()} | {warnings, bool()}</v>
        <v>Reason = {file_error, file(), error()} | {invalid_filename, term()} | {invalid_options, term()} | {unrecognized_file, file()} | -&nbsp;error from beam_lib:chunks/2&nbsp;-</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Adds the modules found in the given directory and the <seealso marker="#module_data">modules' data</seealso>
          to an <seealso marker="#xref_server">Xref server</seealso>. 
          The default is not to examine subdirectories, but if the option
          <c>recurse</c> has the value <c>true</c>, modules are searched
          for in subdirectories on all levels as well as in the given 
          directory.
          Returns a sorted list of the names of the added modules.
          </p>
        <p>The modules added will not be members of any applications. 
          </p>
        <p>If the <seealso marker="#mode">mode</seealso> of the Xref
          server is <c>functions</c>, BEAM files that contain no
          <seealso marker="#debug_info">debug information</seealso> are
          ignored.
          </p>
      </desc>
    </func>
    <func>
      <name since="">add_module(Xref, File [, Options]) -> {ok, module()} | Error</name>
      <fsummary>Add a module.</fsummary>
      <type>
        <v>Error = {error, module(), Reason}</v>
        <v>File = file()</v>
        <v>Options = [Option] | Option</v>
        <v>Option = {builtins, bool()} | {verbose, bool()}  | {warnings, bool()}</v>
        <v>Reason = {file_error, file(), error()} | {invalid_filename, term()} | {invalid_options, term()} | {module_clash, {module(), file(), file()}} | {no_debug_info, file()} | -&nbsp;error from beam_lib:chunks/2&nbsp;-</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Adds a module and its <seealso marker="#module_data">module data</seealso> to an <seealso marker="#xref_server">Xref server</seealso>.
          The module will not be member of any application.
          Returns the name of the module.
          </p>
        <p>If the <seealso marker="#mode">mode</seealso> of the Xref
          server is <c>functions</c>, and the BEAM file contains no
          <seealso marker="#debug_info">debug information</seealso>,
          the error message <c>no_debug_info</c> is returned.
          </p>
      </desc>
    </func>
    <func>
      <name since="">add_release(Xref, Directory [, Options]) ->  {ok, release()} | Error</name>
      <fsummary>Add the modules of a release.</fsummary>
      <type>
        <v>Directory = directory()</v>
        <v>Error = {error, module(), Reason}</v>
        <v>Options = [Option] | Option</v>
        <v>Option = {builtins, bool()} | {name, release()}  | {verbose, bool()} | {warnings, bool()}</v>
        <v>Reason =  {application_clash, {application(), directory(), directory()}} | {file_error, file(), error()} | {invalid_filename, term()} | {invalid_options, term()} | {release_clash, {release(), directory(), directory()}} | -&nbsp;see&nbsp;also&nbsp;add_directory&nbsp;-</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Adds a release, the applications of the release, the
          modules of the applications, and <seealso marker="#module_data">module data</seealso> of the
          modules to an <seealso marker="#xref_server">Xref server</seealso>.
          The applications will be members of the release, 
          and the modules will be members of the applications.
          The default is to use the base name of the
          directory as release name, but this can be overridden by the
          <c>name</c> option. Returns the name of the release.
          </p>
        <p>If the given directory has a subdirectory named <c>lib</c>,
          the directories in that directory are assumed to be
          application directories, otherwise all subdirectories of the
          given directory are assumed to be application directories.
          If there are several versions of some application, the one
          with the highest version is chosen.
          </p>
        <p>If the <seealso marker="#mode">mode</seealso> of the Xref
          server is <c>functions</c>, BEAM files that contain no
          <seealso marker="#debug_info">debug information</seealso> are
          ignored.
          </p>
      </desc>
    </func>
    <func>
      <name since="">analyze(Xref, Analysis [, Options]) ->  {ok, Answer} | Error</name>
      <fsummary>Evaluate a predefined analysis.</fsummary>
      <type>
        <v>Analysis = undefined_function_calls  | undefined_functions | locals_not_used | exports_not_used | deprecated_function_calls | {deprecated_function_calls, DeprFlag} | deprecated_functions | {deprecated_functions, DeprFlag} | {call, FuncSpec} | {use, FuncSpec} | {module_call, ModSpec} | {module_use, ModSpec} | {application_call, AppSpec} | {application_use, AppSpec} | {release_call, RelSpec} | {release_use, RelSpec}</v>
        <v>Answer = [term()]</v>
        <v>AppSpec = application() | [application()]</v>
        <v>DeprFlag = next_version | next_major_release | eventually</v>
        <v>Error = {error, module(), Reason}</v>
        <v>FuncSpec = mfa() | [mfa()]</v>
        <v>ModSpec = module() | [module()]</v>
        <v>Options = [Option] | Option</v>
        <v>Option = {verbose, bool()}</v>
        <v>RelSpec = release() | [release()]</v>
        <v>Reason = {invalid_options, term()} | {parse_error, string_position(), term()} | {unavailable_analysis, term()} | {unknown_analysis, term()} | {unknown_constant, string()} | {unknown_variable, variable()}</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>          <marker id="analyze"></marker>
Evaluates a predefined analysis.
          Returns a sorted list without duplicates of <c>call()</c> or
          <c>constant()</c>, depending on the chosen analysis. The
          predefined analyses, which operate on all <seealso marker="#analyzed_module">analyzed modules</seealso>, are
          (analyses marked with (*) are available in <c>functions</c><seealso marker="#mode">mode</seealso> only):</p>
        <taglist>
          <tag><c>undefined_function_calls</c>(*)</tag>
          <item>Returns a list of calls to <seealso marker="#undefined_function">undefined functions</seealso>.</item>
          <tag><c>undefined_functions</c></tag>
          <item>Returns a list of <seealso marker="#undefined_function">undefined functions</seealso>. </item>
          <tag><c>locals_not_used</c>(*)</tag>
          <item>Returns a list of local functions that have not been
           locally used.</item>
          <tag><c>exports_not_used</c></tag>
          <item>Returns a list of exported functions that have not been
           externally used.</item>
          <tag><c>deprecated_function_calls</c>(*)</tag>
          <item>Returns a list of external calls to <seealso marker="#deprecated_function">deprecated functions</seealso>.</item>
          <tag><c>{deprecated_function_calls, DeprFlag}</c>(*)</tag>
          <item>Returns a list of external calls to deprecated
           functions. If <c>DeprFlag</c> is equal to
          <c>next_version</c>, calls to functions to be removed in
           next version are returned. If <c>DeprFlag</c> is equal to
          <c>next_major_release</c>, calls to functions to be
           removed in next major release are returned as well as
           calls to functions to be removed in next version. Finally,
           if <c>DeprFlag</c> is equal to <c>eventually</c>, all
           calls to functions to be removed are returned, including
           calls to functions to be removed in next version or next
           major release.</item>
          <tag><c>deprecated_functions</c></tag>
          <item>Returns a list of externally used deprecated
           functions.</item>
          <tag><c>{deprecated_functions, DeprFlag}</c></tag>
          <item>Returns a list of externally used deprecated
           functions. If <c>DeprFlag</c> is equal to
          <c>next_version</c>, functions to be removed in next
           version are returned. If <c>DeprFlag</c> is equal to
          <c>next_major_release</c>, functions to be removed in next
           major release are returned as well as functions to be
           removed in next version. Finally, if <c>DeprFlag</c> is
           equal to <c>eventually</c>, all functions to be removed
           are returned, including functions to be removed in next
           version or next major release.</item>
          <tag><c>{call, FuncSpec}</c>(*)</tag>
          <item>Returns a list of functions called by some of the given 
           functions.</item>
          <tag><c>{use, FuncSpec}</c>(*)</tag>
          <item>Returns a list of functions that use some of the given 
           functions.</item>
          <tag><c>{module_call, ModSpec}</c></tag>
          <item>Returns a list of modules called by some of the given 
           modules.</item>
          <tag><c>{module_use, ModSpec}</c></tag>
          <item>Returns a list of modules that use some of the given 
           modules.</item>
          <tag><c>{application_call, AppSpec}</c></tag>
          <item>Returns a list of applications called by some of the given 
           applications.</item>
          <tag><c>{application_use, AppSpec}</c></tag>
          <item>Returns a list of applications that use some of the given 
           applications.</item>
          <tag><c>{release_call, RelSpec}</c></tag>
          <item>Returns a list of releases called by some of the given 
           releases.</item>
          <tag><c>{release_use, RelSpec}</c></tag>
          <item>Returns a list of releases that use some of the given 
           releases.</item>
        </taglist>
      </desc>
    </func>
    <func>
      <name since="">d(Directory) -> [DebugInfoResult] | [NoDebugInfoResult] | Error</name>
      <fsummary>Check the modules in a directory using the code path.</fsummary>
      <type>
        <v>Directory = directory()</v>
        <v>DebugInfoResult = {deprecated, [funcall()]} | {undefined, [funcall()]} | {unused, [mfa()]}</v>
        <v>Error = {error, module(), Reason}</v>
        <v>NoDebugInfoResult = {deprecated, [mfa()]} | {undefined, [mfa()]}</v>
        <v>Reason = {file_error, file(), error()} | {invalid_filename, term()} | {unrecognized_file, file()} | -&nbsp;error from beam_lib:chunks/2&nbsp;-</v>
      </type>
      <desc>
        <p>The modules found in the given directory are checked for
          calls to <seealso marker="#deprecated_function">deprecated functions</seealso>, calls to <seealso marker="#undefined_function">undefined functions</seealso>,
          and for unused local functions. The code path is used as
          <seealso marker="#library_path">library path</seealso>.
          </p>
        <p>If some of the found BEAM files contain <seealso marker="#debug_info">debug information</seealso>, then those
          modules are checked and a list of tuples is returned. The
          first element of each tuple is one of:
          </p>
        <list type="bulleted">
          <item><c>deprecated</c>, the second element is a sorted list
           of calls to deprecated functions;</item>
          <item><c>undefined</c>, the second element is a sorted list
           of calls to undefined functions;</item>
          <item><c>unused</c>, the second element is a sorted list of
           unused local functions.</item>
        </list>
        <p>If no BEAM file contains debug information, then a list of
          tuples is returned. The first element of each tuple is one
          of:
          </p>
        <list type="bulleted">
          <item><c>deprecated</c>, the second element is a sorted list
           of externally used deprecated functions;</item>
          <item><c>undefined</c>, the second element is a sorted list
           of undefined functions.</item>
        </list>
      </desc>
    </func>
    <func>
      <name since="">forget(Xref) -> ok</name>
      <name since="">forget(Xref, Variables) -> ok | Error</name>
      <fsummary>Remove user variables and their values.</fsummary>
      <type>
        <v>Error = {error, module(), Reason}</v>
        <v>Reason = {not_user_variable, term()}</v>
        <v>Variables = [variable()] | variable()</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p><c>forget/1</c> and <c>forget/2</c> remove all or some of
          the <seealso marker="#user_variable">user variables</seealso> of an <seealso marker="#xref_server">xref server</seealso>.</p>
      </desc>
    </func>
    <func>
      <name since="">format_error(Error) -> Chars</name>
      <fsummary>Return an English description of an Xref error reply.</fsummary>
      <type>
        <v>Error = {error, module(), term()}</v>
        <v>Chars = [char() | Chars]</v>
      </type>
      <desc>
        <p>Given the error returned by any function of this module, 
          the function <c>format_error</c> returns a descriptive string
          of the error in English. For file errors, the function 
          <c>format_error/1</c> in the <c>file</c> module is called.</p>
      </desc>
    </func>
    <func>
      <name since="">get_default(Xref) -> [{Option, Value}]</name>
      <name since="">get_default(Xref, Option) -> {ok, Value} | Error</name>
      <fsummary>Return the default values of options.</fsummary>
      <type>
        <v>Error = {error, module(), Reason}</v>
        <v>Option = builtins | recurse | verbose | warnings</v>
        <v>Reason = {invalid_options, term()}</v>
        <v>Value = bool()</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Returns the default values of one or more options.</p>
      </desc>
    </func>
    <func>
      <name since="">get_library_path(Xref) -> {ok, LibraryPath}</name>
      <fsummary>Return the library path.</fsummary>
      <type>
        <v>LibraryPath = library_path()</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Returns the <seealso marker="#library_path">library path</seealso>.</p>
      </desc>
    </func>
    <func>
      <name since="">info(Xref) -> [Info]</name>
      <name since="">info(Xref, Category) -> [{Item, [Info]}]</name>
      <name since="">info(Xref, Category, Items) ->  [{Item, [Info]}]</name>
      <fsummary>Return information about an Xref server.</fsummary>
      <type>
        <v>Application = [] | [application()]</v>
        <v>Category = modules | applications | releases | libraries</v>
        <v>Info = {application, Application} | {builtins, bool()} | {directory, directory()} | {library_path, library_path()} | {mode, mode()} | {no_analyzed_modules, int()} | {no_applications, int()} | {no_calls, {NoResolved, NoUnresolved}} | {no_function_calls, {NoLocal, NoResolvedExternal, NoUnresolved}} | {no_functions, {NoLocal, NoExternal}} | {no_inter_function_calls, int()} | {no_releases, int()} | {release, Release} | {version, Version}</v>
        <v>Item = module() | application() | release() | library()</v>
        <v>Items = Item | [Item]</v>
        <v>NoLocal = NoExternal = NoResolvedExternal, NoResolved = NoUnresolved = int()</v>
        <v>Release = [] | [release()]</v>
        <v>Version = [int()]</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>The <c>info</c> functions return information as a list of
          pairs {Tag,&nbsp;term()} in some order about the state and the 
          <seealso marker="#module_data">module data</seealso> of an <seealso marker="#xref_server">Xref server</seealso>.
          </p>
        <p><c>info/1</c> returns information with the following tags
          (tags  marked with (*) are available in <c>functions</c>
          mode only):</p>
        <list type="bulleted">
          <item><c>library_path</c>, the <seealso marker="#library_path">library path</seealso>;</item>
          <item><c>mode</c>, the <seealso marker="#mode">mode</seealso>;</item>
          <item><c>no_releases</c>, number of releases;</item>
          <item><c>no_applications</c>, total number of applications
           (of all releases);</item>
          <item><c>no_analyzed_modules</c>, total number of <seealso marker="#analyzed_module">analyzed modules</seealso>;</item>
          <item><c>no_calls</c> (*), total number of calls (in all
           modules), regarding instances of one function call in 
           different lines as separate calls;</item>
          <item><c>no_function_calls</c> (*), total number of <seealso marker="#local_call">local calls</seealso>, resolved <seealso marker="#external_call">external calls</seealso> and 
          <seealso marker="#unresolved_call">unresolved calls</seealso>;</item>
          <item><c>no_functions</c> (*), total number of local and exported
           functions;</item>
          <item><c>no_inter_function_calls</c> (*), total number of
           calls of the <seealso marker="#inter_call_graph">Inter Call Graph</seealso>.</item>
        </list>
        <p><c>info/2</c> and <c>info/3</c> return information about
          all or some of the analyzed modules, applications, releases
          or library modules of an Xref server. 
          The following information is returned for every analyzed module:</p>
        <list type="bulleted">
          <item><c>application</c>, an empty list if the module does 
           not belong to any application, otherwise a list of 
           the application name;</item>
          <item><c>builtins</c>, whether calls to BIFs are included
           in the module's data;</item>
          <item><c>directory</c>, the directory where the
           module's BEAM file is located;</item>
          <item><c>no_calls</c> (*), number of calls, regarding
           instances of one function call in different lines as
           separate calls;</item>
          <item><c>no_function_calls</c> (*), number of local
           calls, resolved external calls and unresolved calls;</item>
          <item><c>no_functions</c> (*), number of local and exported
           functions;</item>
          <item><c>no_inter_function_calls</c> (*), number of calls
           of the Inter Call Graph;</item>
        </list>
        <p>The following information is returned for every application:</p>
        <list type="bulleted">
          <item><c>directory</c>, the directory where the
           modules' BEAM files are located;</item>
          <item><c>no_analyzed_modules</c>, number of analyzed
           modules;</item>
          <item><c>no_calls</c> (*), number of calls of the
           application's modules, regarding instances of
           one function call in different lines as separate calls;</item>
          <item><c>no_function_calls</c> (*), number of local
           calls, resolved external calls and unresolved calls of the
           application's modules;</item>
          <item><c>no_functions</c> (*), number of local and exported
           functions of the application's modules;</item>
          <item><c>no_inter_function_calls</c> (*), number of calls
           of the Inter Call Graph of the
           application's modules;</item>
          <item><c>release</c>, an empty list if the application does not
           belong to any release, otherwise a list of the release name;</item>
          <item><c>version</c>, the application's version as
           a list of numbers. For instance, the directory "kernel-2.6"
           results in the application name <c>kernel</c> and the
           application version [2,6]; "kernel" yields the name
          <c>kernel</c> and the version [].</item>
        </list>
        <p>The following information is returned for every release:</p>
        <list type="bulleted">
          <item><c>directory</c>, the release directory;</item>
          <item><c>no_analyzed_modules</c>, number of analyzed
           modules;</item>
          <item><c>no_applications</c>, number of applications;</item>
          <item><c>no_calls</c> (*), number of calls of the
           release's modules, regarding
           instances of one function call in different lines as
           separate calls;</item>
          <item><c>no_function_calls</c> (*), number of local
           calls, resolved external calls and unresolved
           calls of the release's modules;</item>
          <item><c>no_functions</c> (*), number of local and exported
           functions of the release's modules;</item>
          <item><c>no_inter_function_calls</c> (*), number of calls
           of the Inter Call Graph of the release's modules.</item>
        </list>
        <p>The following information is returned for every library module:</p>
        <list type="bulleted">
          <item><c>directory</c>, the directory where the <seealso marker="#library_module">library module's</seealso> BEAM file is located.</item>
        </list>
        <p>For every number of calls, functions etc. returned by the
          <c>no_</c> tags, there is a query returning the same number.
          Listed below are examples of such queries. Some of the
          queries return the sum of a two or more of the <c>no_</c>
          tags numbers. <c>mod</c> (<c>app</c>, <c>rel</c>) refers to
          any module (application, release).
          </p>
        <list type="bulleted">
          <item>
            <p><c>no_analyzed_modules</c></p>
            <list type="bulleted">
              <item><c>"# AM"</c> (info/1)</item>
              <item><c>"# (Mod) app:App"</c> 
               (application)</item>
              <item><c>"# (Mod) rel:Rel"</c> (release)</item>
            </list>
          </item>
          <item>
            <p><c>no_applications</c></p>
            <list type="bulleted">
              <item><c>"# A"</c> (info/1)</item>
            </list>
          </item>
          <item>
            <p><c>no_calls</c>. The sum of the number of resolved and
              unresolved calls:</p>
            <list type="bulleted">
              <item><c>"# (XLin) E + # (LLin) E"</c> (info/1)</item>
              <item><c>"T = E | mod:Mod, # (LLin) T + # (XLin) T"</c> 
               (module)</item>
              <item><c>"T = E | app:App, # (LLin) T + # (XLin) T"</c> 
               (application)</item>
              <item><c>"T = E | rel:Rel, # (LLin) T + # (XLin) T"</c> 
               (release)</item>
            </list>
          </item>
          <item>
            <p><c>no_functions</c>. Functions in library modules and
              the functions <c>module_info/0,1</c> are not counted by
              <c>info</c>. Assuming that <c>"Extra := _:module_info/\"(0|1)\" + LM"</c> has been evaluated, the
              sum of the number of local and exported functions are:</p>
            <list type="bulleted">
              <item><c>"# (F - Extra)"</c> (info/1)</item>
              <item><c>"# (F * mod:Mod - Extra)"</c> (module)</item>
              <item><c>"# (F * app:App - Extra)"</c> (application)</item>
              <item><c>"# (F * rel:Rel - Extra)"</c> (release)</item>
            </list>
          </item>
          <item>
            <p><c>no_function_calls</c>. The sum of the number of
              local calls, resolved external calls and unresolved calls:</p>
            <list type="bulleted">
              <item><c>"# LC + # XC"</c> (info/1)</item>
              <item><c>"# LC | mod:Mod + # XC | mod:Mod"</c> (module)</item>
              <item><c>"# LC | app:App + # XC | app:App"</c> (application)</item>
              <item><c>"# LC | rel:Rel + # XC | mod:Rel"</c> (release)</item>
            </list>
          </item>
          <item>
            <p><c>no_inter_function_calls</c></p>
            <list type="bulleted">
              <item><c>"# EE"</c> (info/1)</item>
              <item><c>"# EE | mod:Mod"</c> (module)</item>
              <item><c>"# EE | app:App"</c> (application)</item>
              <item><c>"# EE | rel:Rel"</c> (release)</item>
            </list>
          </item>
          <item>
            <p><c>no_releases</c></p>
            <list type="bulleted">
              <item><c>"# R"</c> (info/1)</item>
            </list>
          </item>
        </list>
      </desc>
    </func>
    <func>
      <name since="">m(Module) -> [DebugInfoResult] | [NoDebugInfoResult] | Error</name>
      <name since="">m(File) -> [DebugInfoResult] | [NoDebugInfoResult] | Error</name>
      <fsummary>Check a module using the code path.</fsummary>
      <type>
        <v>DebugInfoResult = {deprecated, [funcall()]} | {undefined, [funcall()]} | {unused, [mfa()]}</v>
        <v>Error = {error, module(), Reason}</v>
        <v>File = file()</v>
        <v>Module = module()</v>
        <v>NoDebugInfoResult = {deprecated, [mfa()]} | {undefined, [mfa()]}</v>
        <v>Reason = {file_error, file(), error()} | {interpreted, module()} | {invalid_filename, term()} | {cover_compiled, module()} | {no_such_module, module()}  | -&nbsp;error from beam_lib:chunks/2&nbsp;-</v>
      </type>
      <desc>
        <p>The given BEAM file (with or without the <c>.beam</c>
          extension) or the file found by calling
          <c>code:which(Module)</c> is checked for calls to <seealso marker="#deprecated_function">deprecated functions</seealso>, calls to <seealso marker="#undefined_function">undefined functions</seealso>,
          and for unused local functions. The code path is used as
          <seealso marker="#library_path">library path</seealso>.
          </p>
        <p>If the BEAM file contains <seealso marker="#debug_info">debug information</seealso>, then a
          list of tuples is returned. The first element of each tuple
          is one of:
          </p>
        <list type="bulleted">
          <item><c>deprecated</c>, the second element is a sorted list
           of calls to deprecated functions;</item>
          <item><c>undefined</c>, the second element is a sorted list
           of calls to undefined functions;</item>
          <item><c>unused</c>, the second element is a sorted list of
           unused local functions.</item>
        </list>
        <p>If the BEAM file does not contain debug information, then a
          list of tuples is returned. The first element of each tuple
          is one of:
          </p>
        <list type="bulleted">
          <item><c>deprecated</c>, the second element is a sorted list
           of externally used deprecated functions;</item>
          <item><c>undefined</c>, the second element is a sorted list
           of undefined functions.</item>
        </list>
      </desc>
    </func>
    <func>
      <name since="">q(Xref, Query [, Options]) -> {ok, Answer} | Error</name>
      <fsummary>Evaluate a query.</fsummary>
      <type>
        <v>Answer = false | [constant()] | [Call] | [Component] | int() | [DefineAt] | [CallAt] | [AllLines]</v>
        <v>Call = call() | ComponentCall</v>
        <v>ComponentCall = {Component, Component}</v>
        <v>Component = [constant()]</v>
        <v>DefineAt = {mfa(), LineNumber}</v>
        <v>CallAt = {funcall(), LineNumbers}</v>
        <v>AllLines = {{DefineAt, DefineAt}, LineNumbers}</v>
        <v>Error = {error, module(), Reason}</v>
        <v>LineNumbers = [LineNumber]</v>
        <v>LineNumber = int()</v>
        <v>Options = [Option] | Option</v>
        <v>Option = {verbose, bool()}</v>
        <v>Query = string() | atom()</v>
        <v>Reason = {invalid_options, term()} | {parse_error, string_position(), term()} | {type_error, string()} | {type_mismatch, string(), string()} | {unknown_analysis, term()} | {unknown_constant, string()} | {unknown_variable, variable()} | {variable_reassigned, string()}</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Evaluates a <seealso marker="#query">query</seealso> in the
          context of an <seealso marker="#xref_server">Xref server</seealso>, and returns the value of the last
          statement. The syntax of the value depends on the
          expression:
          </p>
        <list type="bulleted">
          <item>A set of calls is represented by a sorted list without
           duplicates of <c>call()</c>.</item>
          <item>A set of constants is represented by a sorted list
           without duplicates of <c>constant()</c>.</item>
          <item>A set of strongly connected components is a sorted list
           without duplicates of <c>Component</c>.</item>
          <item>A set of calls between strongly connected components is
           a sorted list without duplicates of <c>ComponentCall</c>.</item>
          <item>A chain of calls is represented by a list of
          <c>constant()</c>. The list contains the From vertex of every
           call and the To vertex of the last call.</item>
          <item>The <c>of</c> operator returns <c>false</c> if no chain
           of calls between the given constants can be found.</item>
          <item>The value of the <c>closure</c> operator (the
          <c>digraph</c> representation) is represented by the atom
          <c>'closure()'</c>.</item>
          <item>A set of line numbered functions is represented by a sorted
           list without duplicates of <c>DefineAt</c>.</item>
          <item>A set of line numbered function calls is represented by
           a sorted list without duplicates of <c>CallAt</c>.</item>
          <item>A set of line numbered functions and function calls is
           represented by a sorted list without duplicates of
          <c>AllLines</c>.</item>
        </list>
        <p>For both <c>CallAt</c> and <c>AllLines</c> it holds that for
          no list element is <c>LineNumbers</c> an empty list; such
          elements have been removed. The constants of <c>component</c>
          and the integers of <c>LineNumbers</c> are sorted and without
          duplicates.
          </p>
      </desc>
    </func>
    <func>
      <name since="">remove_application(Xref, Applications) -> ok | Error</name>
      <fsummary>Remove applications and their modules.</fsummary>
      <type>
        <v>Applications = application() | [application()]</v>
        <v>Error = {error, module(), Reason}</v>
        <v>Reason = {no_such_application, application()}</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Removes applications and their modules and <seealso marker="#module_data">module data</seealso> from an <seealso marker="#xref_server">Xref server</seealso>.</p>
      </desc>
    </func>
    <func>
      <name since="">remove_module(Xref, Modules) -> ok | Error</name>
      <fsummary>Remove analyzed modules.</fsummary>
      <type>
        <v>Error = {error, module(), Reason}</v>
        <v>Modules = module() | [module()]</v>
        <v>Reason = {no_such_module, module()}</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Removes <seealso marker="#analyzed_module">analyzed modules</seealso> and <seealso marker="#module_data">module data</seealso> from an <seealso marker="#xref_server">Xref server</seealso>.</p>
      </desc>
    </func>
    <func>
      <name since="">remove_release(Xref, Releases) -> ok | Error</name>
      <fsummary>Remove releases and their applications and modules.</fsummary>
      <type>
        <v>Error = {error, module(), Reason}</v>
        <v>Reason = {no_such_release, release()}</v>
        <v>Releases = release() | [release()]</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Removes releases and their applications, modules and
          <seealso marker="#module_data">module data</seealso> from an
          <seealso marker="#xref_server">Xref server</seealso>.</p>
      </desc>
    </func>
    <func>
      <name since="">replace_application(Xref, Application,  Directory [, Options]) -> {ok, application()} | Error</name>
      <fsummary>Replace an application's modules.</fsummary>
      <type>
        <v>Application = application()</v>
        <v>Directory = directory()</v>
        <v>Error = {error, module(), Reason}</v>
        <v>Options = [Option] | Option</v>
        <v>Option = {builtins, bool()} | {verbose, bool()}  | {warnings, bool()}</v>
        <v>Reason = {no_such_application, application()} | -&nbsp;see&nbsp;also&nbsp;add_application&nbsp;-</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Replaces the modules of an application with other modules
          read from an application directory. Release membership of the
          application is retained. Note that the name of the
          application is kept; the name of the given directory is not
          used.
          </p>
      </desc>
    </func>
    <func>
      <name since="">replace_module(Xref, Module, File [, Options]) ->  {ok, module()} | Error</name>
      <fsummary>Replace an analyzed module.</fsummary>
      <type>
        <v>Error = {error, module(), Reason}</v>
        <v>File = file()</v>
        <v>Module = module()</v>
        <v>Options = [Option] | Option</v>
        <v>Option = {verbose, bool()} | {warnings, bool()}</v>
        <v>ReadModule = module()</v>
        <v>Reason = {module_mismatch, module(), ReadModule} | {no_such_module, module()}  | -&nbsp;see&nbsp;also&nbsp;add_module&nbsp;-</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Replaces <seealso marker="#module_data">module data</seealso> of an <seealso marker="#analyzed_module">analyzed module</seealso> with
          data read from a BEAM file. Application membership of the
          module is retained, and so is the value of the
          <c>builtins</c> option of the module. An error is returned
          if the name of the read module differs from the given
          module.
          </p>
        <p>The <c>update</c> function is an alternative for updating
          module data of recompiled modules.</p>
      </desc>
    </func>
    <func>
      <name since="">set_default(Xref, Option, Value) -> {ok, OldValue} | Error</name>
      <name since="">set_default(Xref, OptionValues) -> ok | Error</name>
      <fsummary>Set the default values of options.</fsummary>
      <type>
        <v>Error = {error, module(), Reason}</v>
        <v>OptionValues = [OptionValue] | OptionValue</v>
        <v>OptionValue = {Option, Value}</v>
        <v>Option = builtins | recurse | verbose | warnings</v>
        <v>Reason = {invalid_options, term()}</v>
        <v>Value = bool()</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Sets the default value of one or more options. 
          The options that can be set this way are:</p>
        <list type="bulleted">
          <item><c>builtins</c>, with initial default value <c>false</c>;</item>
          <item><c>recurse</c>, with initial default value <c>false</c>;</item>
          <item><c>verbose</c>, with initial default value <c>false</c>;</item>
          <item><c>warnings</c>, with initial default value <c>true</c>.</item>
        </list>
        <p>The initial default values are set when creating an <seealso marker="#xref_server">Xref server</seealso>. 
          </p>
      </desc>
    </func>
    <func>
      <name since="">set_library_path(Xref, LibraryPath [, Options]) ->  ok | Error</name>
      <fsummary>Set the library path and finds the library modules.</fsummary>
      <type>
        <v>Error = {error, module(), Reason}</v>
        <v>LibraryPath = library_path()</v>
        <v>Options = [Option] | Option</v>
        <v>Option = {verbose, bool()}</v>
        <v>Reason = {invalid_options, term()} | {invalid_path, term()}</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Sets the <seealso marker="#library_path">library path</seealso>. If the given path is a list of
          directories, the set of <seealso marker="#library_module">library modules</seealso> is
          determined by choosing the first module
          encountered while traversing the directories in
          the given order, for those modules that occur in more than
          one directory. By default, the library path is an empty list.
          </p>
        <p>The library path           <marker id="code_path"></marker>
<c>code_path</c> is
          used by the functions
          <c>m/1</c> and <c>d/1</c>, but can also be set explicitly.
          Note however that the code path will be traversed once for
          each used <seealso marker="#library_module">library module</seealso> while setting up module data.
          On the other hand, if there are only a few modules that are
          used but not analyzed, using <c>code_path</c> may be faster
          than setting the library path to <c>code:get_path()</c>.
          </p>
        <p>If the library path is set to <c>code_path</c>, the set of
          library modules is not determined, and the <c>info</c>
          functions will return empty lists of library modules.</p>
      </desc>
    </func>
    <func>
      <name since="">start(NameOrOptions) -> Return</name>
      <fsummary>Create an Xref server.</fsummary>
      <type>
        <v>NameOrOptions = Name | Options</v>
        <v>Name = atom()</v>
        <v>Options = [Option] | Option</v>
        <v>Option = {xref_mode, mode()} | term()</v>
        <v>Return = {ok, pid()}  | {error, {already_started, pid()}}</v>
      </type>
      <desc>
        <p>Creates an <seealso marker="#xref_server">Xref server</seealso>.
          The process may optionally be given a name.
          The default <seealso marker="#mode">mode</seealso> is <c>functions</c>.
          Options that are not recognized by Xref
          are passed on to <c>gen_server:start/4</c>.</p>
      </desc>
    </func>
    <func>
      <name since="">start(Name, Options) -> Return</name>
      <fsummary>Create an Xref server.</fsummary>
      <type>
        <v>Name = atom()</v>
        <v>Options = [Option] | Option</v>
        <v>Option = {xref_mode, mode()} | term()</v>
        <v>Return = {ok, pid()}  | {error, {already_started, pid()}}</v>
      </type>
      <desc>
        <p>Creates an <seealso marker="#xref_server">Xref server</seealso>
          with a given name. 
          The default <seealso marker="#mode">mode</seealso> is <c>functions</c>.
          Options that are not recognized by Xref
          are passed on to <c>gen_server:start/4</c>.</p>
      </desc>
    </func>
    <func>
      <name since="">stop(Xref)</name>
      <fsummary>Delete an Xref server.</fsummary>
      <type>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Stops an <seealso marker="#xref_server">Xref server</seealso>.</p>
      </desc>
    </func>
    <func>
      <name since="">update(Xref [, Options]) -> {ok, Modules} | Error</name>
      <fsummary>Replace newly compiled analyzed modules.</fsummary>
      <type>
        <v>Error = {error, module(), Reason}</v>
        <v>Modules = [module()]</v>
        <v>Options = [Option] | Option</v>
        <v>Option = {verbose, bool()} | {warnings, bool()}</v>
        <v>Reason = {invalid_options, term()} | {module_mismatch, module(), ReadModule} | -&nbsp;see&nbsp;also&nbsp;add_module&nbsp;-</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Replaces the <seealso marker="#module_data">module data</seealso> of all <seealso marker="#analyzed_module">analyzed modules</seealso> the BEAM
          files of which have been modified since last read by an
          <c>add</c> function or <c>update</c>. Application membership
          of the modules is retained, and so is the value of the
          <c>builtins</c> option. Returns a sorted list
          of the names of the replaced modules.</p>
      </desc>
    </func>
    <func>
      <name since="">variables(Xref [, Options]) -> {ok, [VariableInfo]}</name>
      <fsummary>Return the names of variables.</fsummary>
      <type>
        <v>Options = [Option] | Option</v>
        <v>Option = predefined | user | {verbose, bool()}</v>
        <v>Reason = {invalid_options, term()}</v>
        <v>VariableInfo = {predefined, [variable()]} | {user, [variable()]}</v>
        <v>Xref = xref()</v>
      </type>
      <desc>
        <p>Returns a sorted lists of the names of the variables of an
          <seealso marker="#xref_server">Xref server</seealso>. 
          The default is to return the <seealso marker="#user_variable">user variables</seealso> only.</p>
      </desc>
    </func>
  </funcs>

  <section>
    <title>See Also</title><p>
      <seealso marker="stdlib:beam_lib">beam_lib(3)</seealso>,
      <seealso marker="stdlib:digraph">digraph(3)</seealso>,
      <seealso marker="stdlib:digraph_utils">digraph_utils(3)</seealso>,
      <seealso marker="stdlib:re">re(3)</seealso>,
      <seealso marker="xref_chapter">TOOLS User's Guide</seealso></p>
  </section>
</erlref>