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<title>Mapping-Semantics Genericity</title>
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<h1>Mapping-Semantics</h1>
<p>
This section describes genericity over different mapping-semantics. It is organized as follows.
</p>
<ol>
<li><a href = "#intro">Introduction</a></li>
<li><a href = "#ds_policy">Data Types as a Policy</a></li>
<li><a href = "#problem">The Basic Problem</a></li>
<li><a href = "#mapping_level">Mapping Levels</a></li>
<li><a href = "#ms_traits">Tags and Traits</a></li>
<li><a href = "#drawbacks">Drawbacks</a></li>
</ol>
<h2><a name = "intro">Introduction</a></h2>
<p>
<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.
</p>
<p>
In <tt>pb_assoc</tt>, all containers have unique-key semantics. Each key is uniquely mapped to "something".
</p>
<h2><a name = "ds_policy">Data Types as a Policy</a></h2>
<p>
All associative-containers in <tt>pb_assoc</tt> are parameterized by a data type.
<i>E.g.,</i> <a href = "cc_hash_assoc_cntnr.html">cc_hash_assoc_cntnr</a> is parameterized as
</p>
<pre>
<b>template</b><
<b>typename</b> Key,
<b>typename</b> Data,
...>
<b>class</b> <a href = "cc_hash_assoc_cntnr.html">cc_hash_assoc_cntnr</a>;
</pre>
<p>
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.
</p>
<ol>
<li> If <tt>Data</tt> is any type (<i>e.g.</i>, <tt><b>int</b></tt> or
<tt>std::string</tt>), then the container is a "map" - it maps each <tt>Key</tt> object to a <tt>Data</tt> object.
</li>
<li> If <tt>Data</tt> is
<a href = "null_data_type.html"><tt>null_data_type</tt></a>,
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).
</li>
<li>
If <tt>Data</tt> is
<a href = "compound_data_type.html">compound_data_type</a><tt><Cntnr></tt>,
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.
</li>
</ol>
<p>
Each container derives from one of the three containers
in the oval of Figure
<a href = "#ms_cd">
Data-types as a policy
</a>.
</p>
<ol>
<li><a href = "basic_assoc_cntnr.html"><tt>basic_assoc_cntnr</tt></a>
is the base for most instantiations of a container's <tt>Data</tt> paramter. This
base includes the definition of <tt>data_type</tt>, and supports
<tt><b>operator</b>[]</tt>.
</li>
<li><a href = "basic_assoc_cntnr_no_data.html"><tt>basic_assoc_cntnr</tt></a> is the base for a
<a href = "null_data_type"><tt>null_data_type</tt></a> instantiation of a container's <tt>Data</tt> paramter. This
base lacks the definition of <tt>data_type</tt>, and does not support
<tt><b>operator</b>[]</tt>.
<li><a href = "basic_assoc_cntnr_compound_data.html"><tt>basic_assoc_cntnr</tt></a> is the base for a
<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
base includes the definition of <tt>data_type</tt>, and supports
<tt><b>operator</b>[]</tt>. It further supports some advanced functionality described in the remainder of this section.
</ol>
<h6 align = "center">
<a name = "ms_cd">
<img src = "ms_cd.jpg" width = "70%" alt = "no image">
</h6>
</a>
<h6 align = "center">
Data-types as a policy.
</h6>
<h2><a name = "problem">The Basic Problem</a></h2>
<p>
Consider a <tt>pb_assoc</tt> "multimap" mapping integers to characters.
Since a <tt>pb_assoc</tt> "multimap" is a "map" of "sets",
if <tt>m</tt> is an object of this type, it is not possible to directly use
<tt>m.insert(std::make_pair(2, 'b')</tt> (however, it is possible to directly use
<tt>m[2].insert('b')</tt>). In would be nice if this method whould be supported.
</p>
<p>
Put differently, while the <tt>pb_assoc</tt> "multimap" can be viewed logically as the collection
</p>
<p>
{ <tt><b>int</b></tt> → {<tt><b>char</b></tt>} },
</p>
<p>
It would be nice if it could simultaneously be viewed as the collection
</p>
<p>
{ (<tt><b>int</b></tt>, <tt><b>char</b></tt>) },
</p>
<p><i>i.e.</i>, a "set" of pairs.</p>
<p>
In more general terms, it would be nice to be able to simultaneously
view a collection
</p>
<p>
{ key_type_0 → { key_type_1 → { key_type_2 → { key_type_3 → { ... }}}}}
</p>
<p>
as each of the following:
</p>
<p>
{ (key_type_0, key_type_1) → { key_type_2 &rarr { key_type_e → { ... }}}},
</p>
<p>
{ (key_type_0, key_type_1, key_type_2) &rarr { key_type_3 → { ... }}}
</p>
<p>
{ (key_type_0, key_type_1, key_type_2, key_type_3 ) &rarr { }}
</p>
<p>
...
</p>
<p>
<a href = #mapping_level">Mapping_Levels</a> discusses the mechanism
for these multiple views in <tt>pb_assoc</tt>
</p>
<h2><a name = "mapping_level">Mapping Levels</a></h2>
<p>
Each associative container in <tt>pb_assoc</tt> has
a <i>mapping level</i>. The mapping level is defined by
the instantiation of a container's <tt>Data</tt>
parameter:
</p>
<ol>
<li> If the <tt>Data</tt> parameter is instantiated
by
<a href = "null_data_type.html"><tt>null_data_type</tt></a> (<i>i.e.</i>,
the container is a "set"), then the mapping level is 1.
</li>
<li> If the <tt>Data</tt> parameter is instantiated
by
<a href = "compound_data_type.html">compound_data_type</a><tt><Cntnr></tt>
(<i>i.e.</i>, the container is a "multimap"), then the mapping level
is 1 + the mapping level of <tt>Cntnr</tt>.
</li>
<li> If the <tt>Data</tt> parameter is instantiated
by any other type, <i>e.g.</i>, <tt><b>char</b></tt> (<i>i.e.</i>,
the container is a "map"), then the mapping level is 1.
</li>
</ol>
<p>
Containers can be rebound, at compile time, to different mapping levels.
The compound data-type specialization <a href = "basic_assoc_cntnr_compound_data.html"><tt>basic_assoc_cntnr</tt></a>
defines internally
</p>
<pre>
<b>template</b><
<b>int</b> Mapping_Level>
<b>struct</b> rebind
{
<b>typedef</b>
...
other;
};
</pre>
<p>
(which is similar to the STL's allocator rebind mechanism).
the type <tt>other</tt> is the view of the container with mapping
level <tt>Mapping_Level</tt>. The container can be safely cast
to <tt>other</tt>.
</p>
<p>
As an example, consider the type
</p>
<pre>
<b>typedef</b>
<a href = "cc_hash_assoc_cntnr.html">cc_hash_assoc_cntnr</a><
<b>int</b>,
<a href = "compound_data_type.html">compound_data_type</a><
<a href = "tree_assoc_cntnr.html">tree_assoc_cntnr</a><
<b>char</b>,
<a href = "null_data_type.html"><tt>null_data_type</tt></a>> > >
cntnr_t;
</pre>
<p>
which is a "map" mapping each <tt><b>int</b></tt> to
a "set" of <tt><b>char</b></tt>s. In this case, <tt>cntnr_t</tt> has mapping level 2.
</p>
<p>
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:
</p>
<pre>
cntnr_t c;
<b>typedef</b>
t::rebind<1>::other
t_;
((t_ &)c).insert(std::make_pair(2, 'b'));
</pre>
<p>
<a href = "../example/mapping_level_example.cpp"><tt>mapping_level_example.cpp</tt></a> shows a more detailed example.
</p>
<h2><a name = "ms_traits">Tags and Traits</a></h2>
<p>
It is, of course, beneficial to query types for their mapping semantics.
</p>
<p>
Each container defines internally the type <tt>ms_category</tt>
as its mapping-semantics tag (hopefully this name is not copyrighted
by some major corporation). The possible tags, shown in Figure
are the following:
</p>
<ol>
<li>
<a href = "basic_ms_tag.html"><tt>basic_ms_tag</tt></a>
is a basic mapping-semantics tag. It is the type defined by "set"s.
</li>
<li>
<a href = "data_enabled_ms_tag.html"><tt>data_enabled_ms_tag</tt></a>
is a mapping-semantics tag of types that have data. It is the type defined by "map"s.
</li>
<li>
<a href = "compound_data_enabled_ms_tag.html"><tt>compound_data_enabled_ms_tag</tt></a>
is a mapping-semantics tag of types that have compound data. It is the type defined by "multimap"s.
</li>
</ol>
<p>
Additionally, a container's mapping semantics can be queried by traits. For any
container <tt>Cntnr</tt>,
</p>
<pre>
<a href = "ms_traits.html">ms_traits</a><Cntnr>::mapping_level
</pre>
<p>
indicates the mapping level of the container, for example.
</p>
<h2><a name = "drawbacks">Drawbacks</a></h2>
<tt>pb_assoc</tt>'s mapping-semantics design has some drawbacks compared to that of the STL.
<h3>Equivalent, Non-Identical Keys</h3>
<p>
The STL's multimaps and multisets allow storing equivalent, non-identical keys
[<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:
</p>
<pre>
<i>// Name type.</i>
<b>typedef</b>
std::string
name;
<i>// Account-id type.</i>
<b>typedef</b>
<b>unsigned long</b>
account_id;
<i>// Association between a name and an account id.</i>
<b>class</b> opened_info
{
<b>public</b>:
...
<i>// Comparison operator.</i>
<b>bool</b>
<b></b>operator<</b>
(<b>const</b> opened_info &r_other)
{
<i>Comparison is defined as the comparison of the names.</i>
<b>return</b> m_name < r_other.m_name;
}
<b>private</b>:
name m_name;
account_id m_acc_id;
};
<i>// A multiset of opened accounts.</i>
<b>typedef</b>
std::multiset<
opened_info>
all_opened_info;
</pre>
<p>
<tt>std::multiset</tt> can accomodate multiple equivalent, non-identical <tt>opened_info</tt> - those with the same name but different account id.
</p>
<p>
In <tt>pb_assoc</tt>, however, non-unique mapping is unsupported. The equivalent to the above could be
</p>
<pre>
<b>typedef</b>
tree_assoc_cntnr<
name,
compound_data_type<
cc_hash_assoc_cntnr<
account_id> > >
all_opened_info;
</pre>
<p>
The drawback lies in the fact that the data stored in
<tt>all_opened_info</tt> is less encapsulated - an <tt>opened_info</tt>
object needs to be constructed when a specific name and account are found, and
an <tt>opened_info</tt> object needs to be decomposed into <tt>name</tt> and
<tt>account_id</tt> objects when it is inserted into a <tt>all_opened_info</tt>
object.
</p>
<p>
It should be noticed however, that the above drawbacks - construction and decomposition are constant-time additive drawbacks. The drawbacks of the
STL's associative containers are in terms of orders of growth.
</p>
<h3>Definition of <tt>value_type</tt></h3>
<p>
The STL's associative containers contain a pleasingly uniform definition of
the <tt>value_type</tt> of a container.
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
<tt>std::pair<<b>const</b> key, data></tt>;
for example, the <tt>value_type</tt> of <tt>std::map<<b>int</b>, <b>char</b>></tt> is
<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.
</p>
<p>
In <tt>pb_assoc</tt>, conversely, the rules are more complex.
</p>
<p> For one, a container's
<tt>value_type</tt> is, in general
<tt>std::pair<<b>const</b> Key, Data></tt>,
but if <tt>Data</tt> is <tt>null_data_type</tt>, then the <tt>value_type</tt>
is
<tt>Key</tt>,
and if
<tt>Data</tt> is
<tt>compound_data_type<Cntnr></tt>, then the <tt>value_type</tt> is
<tt>std::pair<<b>const</b> Key, Cntnr></tt>.
</p>
<p>
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
</p>
<pre>
<b>typedef</b>
<b>typename</b> Cntnr::<b>template</b> rebind<i>::other</tt>
Cntnr_;
</pre>
<p>
<i>i.e.</i>, the container rebound to a different mapping level.
In this case, the <tt>value_type</tt> of the rebound container is not the <tt>value_type</tt>
of the rebound container's iterators. <i>I.e.</i>, it is <emph>not</emph> true that
<tt><b>typename</b> Cntnr_::value_type</tt> is the same as
<tt><b>typename</b> Cntnr_::iterator::value_type</tt>. This complication never exists for the STL's container.
</p>
<h6 align = "center">
<a name = "reference_iterator">
<img src = "reference_iterator.jpg" width = "70%" alt = "no image">
</h6>
</a>
<h6 align = "center">
Iterator of a rebound type.
</h6>
<h3>Multisets</h3>
<p>
<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>.
</p>
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