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<html>
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<head>
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<title>Mapping-Semantics Genericity</title>
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<meta name="GENERATOR" content="Microsoft Visual Studio .NET 7.1">
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<meta name="vs_targetSchema" content="http://schemas.microsoft.com/intellisense/ie5">
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<body bgcolor = "white">
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<h1>Mapping-Semantics</h1>
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<p>
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This section describes genericity over different mapping-semantics. It is organized as follows.
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</p>
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<ol>
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<li><a href = "#intro">Introduction</a></li>
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<li><a href = "#ds_policy">Data Types as a Policy</a></li>
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<li><a href = "#problem">The Basic Problem</a></li>
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<li><a href = "#mapping_level">Mapping Levels</a></li>
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<li><a href = "#ms_traits">Tags and Traits</a></li>
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<li><a href = "#drawbacks">Drawbacks</a></li>
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</ol>
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<h2><a name = "intro">Introduction</a></h2>
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<p>
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<a href = "motivation.html#mapping_semantics">Motivation::Mapping Semantics</a> discussed scalability issues with the STL's non-unique-mapping associative containers; non-unique association inherently embeds linked-lists in associative containers resulting in scalability problems and other problems.
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</p>
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<p>
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In <tt>pb_assoc</tt>, all containers have unique-key semantics. Each key is uniquely mapped to "something".
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</p>
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<h2><a name = "ds_policy">Data Types as a Policy</a></h2>
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<p>
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All associative-containers in <tt>pb_assoc</tt> are parameterized by a data type.
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<i>E.g.,</i> <a href = "cc_hash_assoc_cntnr.html">cc_hash_assoc_cntnr</a> is parameterized as
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</p>
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<pre>
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<b>template</b><
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<b>typename</b> Key,
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<b>typename</b> Data,
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...>
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<b>class</b> <a href = "cc_hash_assoc_cntnr.html">cc_hash_assoc_cntnr</a>;
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</pre>
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<p>
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There are no separate classes for maps, sets, multimaps, and multisets (as the STL has). Rather, the mapping-semantic is set by specifying the <tt>Key</tt> parameter.
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</p>
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<ol>
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<li> If <tt>Data</tt> is any type (<i>e.g.</i>, <tt><b>int</b></tt> or
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<tt>std::string</tt>), then the container is a "map" - it maps each <tt>Key</tt> object to a <tt>Data</tt> object.
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</li>
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<li> If <tt>Data</tt> is
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<a href = "null_data_type.html"><tt>null_data_type</tt></a>,
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then the container is a "set" - it stores each <tt>Key</tt> object. In this case, each <tt>Key</tt> object is not really mapped to anything (except, implicitly, to the fact that it is stored in the container object).
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</li>
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<li>
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If <tt>Data</tt> is
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<a href = "compound_data_type.html">compound_data_type</a><tt><Cntnr></tt>,
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then the container is a "multimap" - it maps each <tt>Key</tt> object into a <tt>Cntnr</tt> object. This structure is recursive - <tt>Cntnr</tt> itself can be a "map", "set", "multimap", and so forth.
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</li>
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</ol>
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<p>
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Each container derives from one of the three containers
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in the oval of Figure
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<a href = "#ms_cd">
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Data-types as a policy
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</a>.
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</p>
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<ol>
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<li><a href = "basic_assoc_cntnr.html"><tt>basic_assoc_cntnr</tt></a>
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is the base for most instantiations of a container's <tt>Data</tt> paramter. This
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base includes the definition of <tt>data_type</tt>, and supports
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<tt><b>operator</b>[]</tt>.
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</li>
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<li><a href = "basic_assoc_cntnr_no_data.html"><tt>basic_assoc_cntnr</tt></a> is the base for a
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<a href = "null_data_type"><tt>null_data_type</tt></a> instantiation of a container's <tt>Data</tt> paramter. This
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base lacks the definition of <tt>data_type</tt>, and does not support
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<tt><b>operator</b>[]</tt>.
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<li><a href = "basic_assoc_cntnr_compound_data.html"><tt>basic_assoc_cntnr</tt></a> is the base for a
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<a href = "compound_data_type.html"><tt>compound_data_type</tt></a><tt><Cntnr></tt> instantiation of a container's <tt>Data</tt> paramter. This
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base includes the definition of <tt>data_type</tt>, and supports
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<tt><b>operator</b>[]</tt>. It further supports some advanced functionality described in the remainder of this section.
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</ol>
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<h6 align = "center">
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<a name = "ms_cd">
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<img src = "ms_cd.jpg" width = "70%" alt = "no image">
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</h6>
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</a>
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<h6 align = "center">
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Data-types as a policy.
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</h6>
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<h2><a name = "problem">The Basic Problem</a></h2>
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<p>
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Consider a <tt>pb_assoc</tt> "multimap" mapping integers to characters.
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Since a <tt>pb_assoc</tt> "multimap" is a "map" of "sets",
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if <tt>m</tt> is an object of this type, it is not possible to directly use
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<tt>m.insert(std::make_pair(2, 'b')</tt> (however, it is possible to directly use
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<tt>m[2].insert('b')</tt>). In would be nice if this method whould be supported.
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</p>
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<p>
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Put differently, while the <tt>pb_assoc</tt> "multimap" can be viewed logically as the collection
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</p>
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<p>
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{ <tt><b>int</b></tt> → {<tt><b>char</b></tt>} },
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</p>
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<p>
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It would be nice if it could simultaneously be viewed as the collection
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</p>
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<p>
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{ (<tt><b>int</b></tt>, <tt><b>char</b></tt>) },
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</p>
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<p><i>i.e.</i>, a "set" of pairs.</p>
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<p>
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In more general terms, it would be nice to be able to simultaneously
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view a collection
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</p>
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<p>
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{ key_type_0 → { key_type_1 → { key_type_2 → { key_type_3 → { ... }}}}}
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</p>
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<p>
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as each of the following:
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</p>
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<p>
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{ (key_type_0, key_type_1) → { key_type_2 &rarr { key_type_e → { ... }}}},
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</p>
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<p>
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{ (key_type_0, key_type_1, key_type_2) &rarr { key_type_3 → { ... }}}
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</p>
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<p>
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{ (key_type_0, key_type_1, key_type_2, key_type_3 ) &rarr { }}
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</p>
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<p>
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...
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</p>
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<p>
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<a href = #mapping_level">Mapping_Levels</a> discusses the mechanism
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for these multiple views in <tt>pb_assoc</tt>
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</p>
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<h2><a name = "mapping_level">Mapping Levels</a></h2>
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<p>
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Each associative container in <tt>pb_assoc</tt> has
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a <i>mapping level</i>. The mapping level is defined by
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the instantiation of a container's <tt>Data</tt>
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parameter:
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</p>
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<ol>
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<li> If the <tt>Data</tt> parameter is instantiated
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by
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<a href = "null_data_type.html"><tt>null_data_type</tt></a> (<i>i.e.</i>,
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the container is a "set"), then the mapping level is 1.
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</li>
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<li> If the <tt>Data</tt> parameter is instantiated
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by
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<a href = "compound_data_type.html">compound_data_type</a><tt><Cntnr></tt>
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(<i>i.e.</i>, the container is a "multimap"), then the mapping level
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is 1 + the mapping level of <tt>Cntnr</tt>.
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</li>
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<li> If the <tt>Data</tt> parameter is instantiated
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by any other type, <i>e.g.</i>, <tt><b>char</b></tt> (<i>i.e.</i>,
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the container is a "map"), then the mapping level is 1.
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</li>
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</ol>
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<p>
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Containers can be rebound, at compile time, to different mapping levels.
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The compound data-type specialization <a href = "basic_assoc_cntnr_compound_data.html"><tt>basic_assoc_cntnr</tt></a>
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defines internally
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</p>
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<pre>
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<b>template</b><
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<b>int</b> Mapping_Level>
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<b>struct</b> rebind
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{
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<b>typedef</b>
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...
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other;
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};
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</pre>
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<p>
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(which is similar to the STL's allocator rebind mechanism).
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the type <tt>other</tt> is the view of the container with mapping
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level <tt>Mapping_Level</tt>. The container can be safely cast
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to <tt>other</tt>.
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</p>
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<p>
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As an example, consider the type
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</p>
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<pre>
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<b>typedef</b>
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<a href = "cc_hash_assoc_cntnr.html">cc_hash_assoc_cntnr</a><
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<b>int</b>,
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<a href = "compound_data_type.html">compound_data_type</a><
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<a href = "tree_assoc_cntnr.html">tree_assoc_cntnr</a><
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<b>char</b>,
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<a href = "null_data_type.html"><tt>null_data_type</tt></a>> > >
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cntnr_t;
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</pre>
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<p>
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which is a "map" mapping each <tt><b>int</b></tt> to
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a "set" of <tt><b>char</b></tt>s. In this case, <tt>cntnr_t</tt> has mapping level 2.
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</p>
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<p>
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An object of type <tt>cntnr_t</tt> cannot support <tt>insert(std::make_pair(2, 'b'));</tt>. On the other hand, the following code snippet shows how to do so:
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</p>
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<pre>
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cntnr_t c;
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<b>typedef</b>
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t::rebind<1>::other
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t_;
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((t_ &)c).insert(std::make_pair(2, 'b'));
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</pre>
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<p>
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<a href = "../example/mapping_level_example.cpp"><tt>mapping_level_example.cpp</tt></a> shows a more detailed example.
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</p>
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<h2><a name = "ms_traits">Tags and Traits</a></h2>
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<p>
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It is, of course, beneficial to query types for their mapping semantics.
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</p>
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<p>
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Each container defines internally the type <tt>ms_category</tt>
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as its mapping-semantics tag (hopefully this name is not copyrighted
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by some major corporation). The possible tags, shown in Figure
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are the following:
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</p>
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<ol>
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<li>
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<a href = "basic_ms_tag.html"><tt>basic_ms_tag</tt></a>
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is a basic mapping-semantics tag. It is the type defined by "set"s.
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</li>
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<li>
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<a href = "data_enabled_ms_tag.html"><tt>data_enabled_ms_tag</tt></a>
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is a mapping-semantics tag of types that have data. It is the type defined by "map"s.
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</li>
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<li>
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<a href = "compound_data_enabled_ms_tag.html"><tt>compound_data_enabled_ms_tag</tt></a>
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is a mapping-semantics tag of types that have compound data. It is the type defined by "multimap"s.
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</li>
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</ol>
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<p>
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Additionally, a container's mapping semantics can be queried by traits. For any
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container <tt>Cntnr</tt>,
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</p>
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<pre>
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<a href = "ms_traits.html">ms_traits</a><Cntnr>::mapping_level
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</pre>
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<p>
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indicates the mapping level of the container, for example.
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</p>
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<h2><a name = "drawbacks">Drawbacks</a></h2>
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<tt>pb_assoc</tt>'s mapping-semantics design has some drawbacks compared to that of the STL.
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<h3>Equivalent, Non-Identical Keys</h3>
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<p>
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The STL's multimaps and multisets allow storing equivalent, non-identical keys
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[<a href = "references.html#kleft00sets">kleft00sets</a>]. For example, assume a bank maintains a data structure monitoring the accounts opened by each person. This could be modeled as the following:
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</p>
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<pre>
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<i>// Name type.</i>
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<b>typedef</b>
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std::string
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name;
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<i>// Account-id type.</i>
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<b>typedef</b>
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<b>unsigned long</b>
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account_id;
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<i>// Association between a name and an account id.</i>
|
| 318 |
|
|
<b>class</b> opened_info
|
| 319 |
|
|
{
|
| 320 |
|
|
<b>public</b>:
|
| 321 |
|
|
...
|
| 322 |
|
|
|
| 323 |
|
|
<i>// Comparison operator.</i>
|
| 324 |
|
|
<b>bool</b>
|
| 325 |
|
|
<b></b>operator<</b>
|
| 326 |
|
|
(<b>const</b> opened_info &r_other)
|
| 327 |
|
|
{
|
| 328 |
|
|
<i>Comparison is defined as the comparison of the names.</i>
|
| 329 |
|
|
<b>return</b> m_name < r_other.m_name;
|
| 330 |
|
|
}
|
| 331 |
|
|
|
| 332 |
|
|
|
| 333 |
|
|
<b>private</b>:
|
| 334 |
|
|
name m_name;
|
| 335 |
|
|
|
| 336 |
|
|
account_id m_acc_id;
|
| 337 |
|
|
};
|
| 338 |
|
|
|
| 339 |
|
|
<i>// A multiset of opened accounts.</i>
|
| 340 |
|
|
<b>typedef</b>
|
| 341 |
|
|
std::multiset<
|
| 342 |
|
|
opened_info>
|
| 343 |
|
|
all_opened_info;
|
| 344 |
|
|
</pre>
|
| 345 |
|
|
|
| 346 |
|
|
<p>
|
| 347 |
|
|
<tt>std::multiset</tt> can accomodate multiple equivalent, non-identical <tt>opened_info</tt> - those with the same name but different account id.
|
| 348 |
|
|
</p>
|
| 349 |
|
|
|
| 350 |
|
|
<p>
|
| 351 |
|
|
In <tt>pb_assoc</tt>, however, non-unique mapping is unsupported. The equivalent to the above could be
|
| 352 |
|
|
</p>
|
| 353 |
|
|
|
| 354 |
|
|
<pre>
|
| 355 |
|
|
<b>typedef</b>
|
| 356 |
|
|
tree_assoc_cntnr<
|
| 357 |
|
|
name,
|
| 358 |
|
|
compound_data_type<
|
| 359 |
|
|
cc_hash_assoc_cntnr<
|
| 360 |
|
|
account_id> > >
|
| 361 |
|
|
all_opened_info;
|
| 362 |
|
|
</pre>
|
| 363 |
|
|
|
| 364 |
|
|
<p>
|
| 365 |
|
|
The drawback lies in the fact that the data stored in
|
| 366 |
|
|
<tt>all_opened_info</tt> is less encapsulated - an <tt>opened_info</tt>
|
| 367 |
|
|
object needs to be constructed when a specific name and account are found, and
|
| 368 |
|
|
an <tt>opened_info</tt> object needs to be decomposed into <tt>name</tt> and
|
| 369 |
|
|
<tt>account_id</tt> objects when it is inserted into a <tt>all_opened_info</tt>
|
| 370 |
|
|
object.
|
| 371 |
|
|
</p>
|
| 372 |
|
|
|
| 373 |
|
|
<p>
|
| 374 |
|
|
It should be noticed however, that the above drawbacks - construction and decomposition are constant-time additive drawbacks. The drawbacks of the
|
| 375 |
|
|
STL's associative containers are in terms of orders of growth.
|
| 376 |
|
|
</p>
|
| 377 |
|
|
|
| 378 |
|
|
<h3>Definition of <tt>value_type</tt></h3>
|
| 379 |
|
|
|
| 380 |
|
|
<p>
|
| 381 |
|
|
The STL's associative containers contain a pleasingly uniform definition of
|
| 382 |
|
|
the <tt>value_type</tt> of a container.
|
| 383 |
|
|
If a container is parameterized by <tt>key</tt> as its <tt>Key</tt>, and <tt>data</tt> as its <tt>Data</tt>, then its <tt>value_type</tt> is
|
| 384 |
|
|
<tt>std::pair<<b>const</b> key, data></tt>;
|
| 385 |
|
|
for example, the <tt>value_type</tt> of <tt>std::map<<b>int</b>, <b>char</b>></tt> is
|
| 386 |
|
|
<tt>std::pair<<b>const int</b>, <b>char</b>></tt>. Futhermore, the <tt>value_type</tt> of a container and the <tt>value_type</tt> of the container's iterators are identical.
|
| 387 |
|
|
</p>
|
| 388 |
|
|
|
| 389 |
|
|
<p>
|
| 390 |
|
|
In <tt>pb_assoc</tt>, conversely, the rules are more complex.
|
| 391 |
|
|
</p>
|
| 392 |
|
|
|
| 393 |
|
|
<p> For one, a container's
|
| 394 |
|
|
<tt>value_type</tt> is, in general
|
| 395 |
|
|
<tt>std::pair<<b>const</b> Key, Data></tt>,
|
| 396 |
|
|
but if <tt>Data</tt> is <tt>null_data_type</tt>, then the <tt>value_type</tt>
|
| 397 |
|
|
is
|
| 398 |
|
|
<tt>Key</tt>,
|
| 399 |
|
|
and if
|
| 400 |
|
|
<tt>Data</tt> is
|
| 401 |
|
|
<tt>compound_data_type<Cntnr></tt>, then the <tt>value_type</tt> is
|
| 402 |
|
|
<tt>std::pair<<b>const</b> Key, Cntnr></tt>.
|
| 403 |
|
|
</p>
|
| 404 |
|
|
|
| 405 |
|
|
<p>
|
| 406 |
|
|
Futhermore, assume that <tt>Cntnr</tt> is an associative container with more than a single mapping level, and let <tt>Cntnr_</tt> be defined as
|
| 407 |
|
|
</p>
|
| 408 |
|
|
|
| 409 |
|
|
<pre>
|
| 410 |
|
|
<b>typedef</b>
|
| 411 |
|
|
<b>typename</b> Cntnr::<b>template</b> rebind<i>::other</tt>
|
| 412 |
|
|
Cntnr_;
|
| 413 |
|
|
</pre>
|
| 414 |
|
|
<p>
|
| 415 |
|
|
<i>i.e.</i>, the container rebound to a different mapping level.
|
| 416 |
|
|
In this case, the <tt>value_type</tt> of the rebound container is not the <tt>value_type</tt>
|
| 417 |
|
|
of the rebound container's iterators. <i>I.e.</i>, it is <emph>not</emph> true that
|
| 418 |
|
|
<tt><b>typename</b> Cntnr_::value_type</tt> is the same as
|
| 419 |
|
|
<tt><b>typename</b> Cntnr_::iterator::value_type</tt>. This complication never exists for the STL's container.
|
| 420 |
|
|
</p>
|
| 421 |
|
|
|
| 422 |
|
|
<h6 align = "center">
|
| 423 |
|
|
<a name = "reference_iterator">
|
| 424 |
|
|
<img src = "reference_iterator.jpg" width = "70%" alt = "no image">
|
| 425 |
|
|
</h6>
|
| 426 |
|
|
</a>
|
| 427 |
|
|
<h6 align = "center">
|
| 428 |
|
|
Iterator of a rebound type.
|
| 429 |
|
|
</h6>
|
| 430 |
|
|
|
| 431 |
|
|
|
| 432 |
|
|
<h3>Multisets</h3>
|
| 433 |
|
|
|
| 434 |
|
|
<p>
|
| 435 |
|
|
<tt>pb_assoc</tt> does not contain a "multiset" type. The closest equivalent is mapping keys to non-negative integral types, <i>e.g.</i>, <tt>size_t</tt>.
|
| 436 |
|
|
</p>
|
| 437 |
|
|
|
| 438 |
|
|
</body>
|
| 439 |
|
|
|
| 440 |
|
|
</html>
|
