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<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>F.33. pg_trgm</title><link rel="stylesheet" type="text/css" href="stylesheet.css" /><link rev="made" href="pgsql-docs@lists.postgresql.org" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="prev" href="pgsurgery.html" title="F.32. pg_surgery" /><link rel="next" href="pgvisibility.html" title="F.34. pg_visibility" /></head><body id="docContent" class="container-fluid col-10"><div xmlns="http://www.w3.org/TR/xhtml1/transitional" class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="5" align="center">F.33. pg_trgm</th></tr><tr><td width="10%" align="left"><a accesskey="p" href="pgsurgery.html" title="F.32. pg_surgery">Prev</a> </td><td width="10%" align="left"><a accesskey="u" href="contrib.html" title="Appendix F. Additional Supplied Modules">Up</a></td><th width="60%" align="center">Appendix F. Additional Supplied Modules</th><td width="10%" align="right"><a accesskey="h" href="index.html" title="PostgreSQL 14.5 Documentation">Home</a></td><td width="10%" align="right"> <a accesskey="n" href="pgvisibility.html" title="F.34. pg_visibility">Next</a></td></tr></table><hr></hr></div><div class="sect1" id="PGTRGM"><div class="titlepage"><div><div><h2 class="title" style="clear: both">F.33. pg_trgm</h2></div></div></div><div class="toc"><dl class="toc"><dt><span class="sect2"><a href="pgtrgm.html#id-1.11.7.42.5">F.33.1. Trigram (or Trigraph) Concepts</a></span></dt><dt><span class="sect2"><a href="pgtrgm.html#id-1.11.7.42.6">F.33.2. Functions and Operators</a></span></dt><dt><span class="sect2"><a href="pgtrgm.html#id-1.11.7.42.7">F.33.3. GUC Parameters</a></span></dt><dt><span class="sect2"><a href="pgtrgm.html#id-1.11.7.42.8">F.33.4. Index Support</a></span></dt><dt><span class="sect2"><a href="pgtrgm.html#id-1.11.7.42.9">F.33.5. Text Search Integration</a></span></dt><dt><span class="sect2"><a href="pgtrgm.html#id-1.11.7.42.10">F.33.6. References</a></span></dt><dt><span class="sect2"><a href="pgtrgm.html#id-1.11.7.42.11">F.33.7. Authors</a></span></dt></dl></div><a id="id-1.11.7.42.2" class="indexterm"></a><p>
The <code class="filename">pg_trgm</code> module provides functions and operators
for determining the similarity of
alphanumeric text based on trigram matching, as
well as index operator classes that support fast searching for similar
strings.
</p><p>
This module is considered <span class="quote">“<span class="quote">trusted</span>”</span>, that is, it can be
installed by non-superusers who have <code class="literal">CREATE</code> privilege
on the current database.
</p><div class="sect2" id="id-1.11.7.42.5"><div class="titlepage"><div><div><h3 class="title">F.33.1. Trigram (or Trigraph) Concepts</h3></div></div></div><p>
A trigram is a group of three consecutive characters taken
from a string. We can measure the similarity of two strings by
counting the number of trigrams they share. This simple idea
turns out to be very effective for measuring the similarity of
words in many natural languages.
</p><div class="note"><h3 class="title">Note</h3><p>
<code class="filename">pg_trgm</code> ignores non-word characters
(non-alphanumerics) when extracting trigrams from a string.
Each word is considered to have two spaces
prefixed and one space suffixed when determining the set
of trigrams contained in the string.
For example, the set of trigrams in the string
<span class="quote">“<span class="quote"><code class="literal">cat</code></span>”</span> is
<span class="quote">“<span class="quote"><code class="literal"> c</code></span>”</span>,
<span class="quote">“<span class="quote"><code class="literal"> ca</code></span>”</span>,
<span class="quote">“<span class="quote"><code class="literal">cat</code></span>”</span>, and
<span class="quote">“<span class="quote"><code class="literal">at </code></span>”</span>.
The set of trigrams in the string
<span class="quote">“<span class="quote"><code class="literal">foo|bar</code></span>”</span> is
<span class="quote">“<span class="quote"><code class="literal"> f</code></span>”</span>,
<span class="quote">“<span class="quote"><code class="literal"> fo</code></span>”</span>,
<span class="quote">“<span class="quote"><code class="literal">foo</code></span>”</span>,
<span class="quote">“<span class="quote"><code class="literal">oo </code></span>”</span>,
<span class="quote">“<span class="quote"><code class="literal"> b</code></span>”</span>,
<span class="quote">“<span class="quote"><code class="literal"> ba</code></span>”</span>,
<span class="quote">“<span class="quote"><code class="literal">bar</code></span>”</span>, and
<span class="quote">“<span class="quote"><code class="literal">ar </code></span>”</span>.
</p></div></div><div class="sect2" id="id-1.11.7.42.6"><div class="titlepage"><div><div><h3 class="title">F.33.2. Functions and Operators</h3></div></div></div><p>
The functions provided by the <code class="filename">pg_trgm</code> module
are shown in <a class="xref" href="pgtrgm.html#PGTRGM-FUNC-TABLE" title="Table F.25. pg_trgm Functions">Table F.25</a>, the operators
in <a class="xref" href="pgtrgm.html#PGTRGM-OP-TABLE" title="Table F.26. pg_trgm Operators">Table F.26</a>.
</p><div class="table" id="PGTRGM-FUNC-TABLE"><p class="title"><strong>Table F.25. <code class="filename">pg_trgm</code> Functions</strong></p><div class="table-contents"><table class="table" summary="pg_trgm Functions" border="1"><colgroup><col /></colgroup><thead><tr><th class="func_table_entry"><p class="func_signature">
Function
</p>
<p>
Description
</p></th></tr></thead><tbody><tr><td class="func_table_entry"><p class="func_signature">
<a id="id-1.11.7.42.6.3.2.2.1.1.1.1" class="indexterm"></a>
<code class="function">similarity</code> ( <code class="type">text</code>, <code class="type">text</code> )
→ <code class="returnvalue">real</code>
</p>
<p>
Returns a number that indicates how similar the two arguments are.
The range of the result is zero (indicating that the two strings are
completely dissimilar) to one (indicating that the two strings are
identical).
</p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
<a id="id-1.11.7.42.6.3.2.2.2.1.1.1" class="indexterm"></a>
<code class="function">show_trgm</code> ( <code class="type">text</code> )
→ <code class="returnvalue">text[]</code>
</p>
<p>
Returns an array of all the trigrams in the given string.
(In practice this is seldom useful except for debugging.)
</p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
<a id="id-1.11.7.42.6.3.2.2.3.1.1.1" class="indexterm"></a>
<code class="function">word_similarity</code> ( <code class="type">text</code>, <code class="type">text</code> )
→ <code class="returnvalue">real</code>
</p>
<p>
Returns a number that indicates the greatest similarity between
the set of trigrams in the first string and any continuous extent
of an ordered set of trigrams in the second string. For details, see
the explanation below.
</p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
<a id="id-1.11.7.42.6.3.2.2.4.1.1.1" class="indexterm"></a>
<code class="function">strict_word_similarity</code> ( <code class="type">text</code>, <code class="type">text</code> )
→ <code class="returnvalue">real</code>
</p>
<p>
Same as <code class="function">word_similarity</code>, but forces
extent boundaries to match word boundaries. Since we don't have
cross-word trigrams, this function actually returns greatest similarity
between first string and any continuous extent of words of the second
string.
</p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
<a id="id-1.11.7.42.6.3.2.2.5.1.1.1" class="indexterm"></a>
<code class="function">show_limit</code> ()
→ <code class="returnvalue">real</code>
</p>
<p>
Returns the current similarity threshold used by the <code class="literal">%</code>
operator. This sets the minimum similarity between
two words for them to be considered similar enough to
be misspellings of each other, for example.
(<span class="emphasis"><em>Deprecated</em></span>; instead use <code class="command">SHOW</code>
<code class="varname">pg_trgm.similarity_threshold</code>.)
</p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
<a id="id-1.11.7.42.6.3.2.2.6.1.1.1" class="indexterm"></a>
<code class="function">set_limit</code> ( <code class="type">real</code> )
→ <code class="returnvalue">real</code>
</p>
<p>
Sets the current similarity threshold that is used by the <code class="literal">%</code>
operator. The threshold must be between 0 and 1 (default is 0.3).
Returns the same value passed in.
(<span class="emphasis"><em>Deprecated</em></span>; instead use <code class="command">SET</code>
<code class="varname">pg_trgm.similarity_threshold</code>.)
</p></td></tr></tbody></table></div></div><br class="table-break" /><p>
Consider the following example:
</p><pre class="programlisting">
# SELECT word_similarity('word', 'two words');
word_similarity
-----------------
0.8
(1 row)
</pre><p>
In the first string, the set of trigrams is
<code class="literal">{" w"," wo","wor","ord","rd "}</code>.
In the second string, the ordered set of trigrams is
<code class="literal">{" t"," tw","two","wo "," w"," wo","wor","ord","rds","ds "}</code>.
The most similar extent of an ordered set of trigrams in the second string
is <code class="literal">{" w"," wo","wor","ord"}</code>, and the similarity is
<code class="literal">0.8</code>.
</p><p>
This function returns a value that can be approximately understood as the
greatest similarity between the first string and any substring of the second
string. However, this function does not add padding to the boundaries of
the extent. Thus, the number of additional characters present in the
second string is not considered, except for the mismatched word boundaries.
</p><p>
At the same time, <code class="function">strict_word_similarity</code>
selects an extent of words in the second string. In the example above,
<code class="function">strict_word_similarity</code> would select the
extent of a single word <code class="literal">'words'</code>, whose set of trigrams is
<code class="literal">{" w"," wo","wor","ord","rds","ds "}</code>.
</p><pre class="programlisting">
# SELECT strict_word_similarity('word', 'two words'), similarity('word', 'words');
strict_word_similarity | similarity
------------------------+------------
0.571429 | 0.571429
(1 row)
</pre><p>
</p><p>
Thus, the <code class="function">strict_word_similarity</code> function
is useful for finding the similarity to whole words, while
<code class="function">word_similarity</code> is more suitable for
finding the similarity for parts of words.
</p><div class="table" id="PGTRGM-OP-TABLE"><p class="title"><strong>Table F.26. <code class="filename">pg_trgm</code> Operators</strong></p><div class="table-contents"><table class="table" summary="pg_trgm Operators" border="1"><colgroup><col /></colgroup><thead><tr><th class="func_table_entry"><p class="func_signature">
Operator
</p>
<p>
Description
</p></th></tr></thead><tbody><tr><td class="func_table_entry"><p class="func_signature">
<code class="type">text</code> <code class="literal">%</code> <code class="type">text</code>
→ <code class="returnvalue">boolean</code>
</p>
<p>
Returns <code class="literal">true</code> if its arguments have a similarity
that is greater than the current similarity threshold set by
<code class="varname">pg_trgm.similarity_threshold</code>.
</p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
<code class="type">text</code> <code class="literal"><%</code> <code class="type">text</code>
→ <code class="returnvalue">boolean</code>
</p>
<p>
Returns <code class="literal">true</code> if the similarity between the trigram
set in the first argument and a continuous extent of an ordered trigram
set in the second argument is greater than the current word similarity
threshold set by <code class="varname">pg_trgm.word_similarity_threshold</code>
parameter.
</p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
<code class="type">text</code> <code class="literal">%></code> <code class="type">text</code>
→ <code class="returnvalue">boolean</code>
</p>
<p>
Commutator of the <code class="literal"><%</code> operator.
</p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
<code class="type">text</code> <code class="literal"><<%</code> <code class="type">text</code>
→ <code class="returnvalue">boolean</code>
</p>
<p>
Returns <code class="literal">true</code> if its second argument has a continuous
extent of an ordered trigram set that matches word boundaries,
and its similarity to the trigram set of the first argument is greater
than the current strict word similarity threshold set by the
<code class="varname">pg_trgm.strict_word_similarity_threshold</code> parameter.
</p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
<code class="type">text</code> <code class="literal">%>></code> <code class="type">text</code>
→ <code class="returnvalue">boolean</code>
</p>
<p>
Commutator of the <code class="literal"><<%</code> operator.
</p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
<code class="type">text</code> <code class="literal"><-></code> <code class="type">text</code>
→ <code class="returnvalue">real</code>
</p>
<p>
Returns the <span class="quote">“<span class="quote">distance</span>”</span> between the arguments, that is
one minus the <code class="function">similarity()</code> value.
</p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
<code class="type">text</code> <code class="literal"><<-></code> <code class="type">text</code>
→ <code class="returnvalue">real</code>
</p>
<p>
Returns the <span class="quote">“<span class="quote">distance</span>”</span> between the arguments, that is
one minus the <code class="function">word_similarity()</code> value.
</p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
<code class="type">text</code> <code class="literal"><->></code> <code class="type">text</code>
→ <code class="returnvalue">real</code>
</p>
<p>
Commutator of the <code class="literal"><<-></code> operator.
</p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
<code class="type">text</code> <code class="literal"><<<-></code> <code class="type">text</code>
→ <code class="returnvalue">real</code>
</p>
<p>
Returns the <span class="quote">“<span class="quote">distance</span>”</span> between the arguments, that is
one minus the <code class="function">strict_word_similarity()</code> value.
</p></td></tr><tr><td class="func_table_entry"><p class="func_signature">
<code class="type">text</code> <code class="literal"><->>></code> <code class="type">text</code>
→ <code class="returnvalue">real</code>
</p>
<p>
Commutator of the <code class="literal"><<<-></code> operator.
</p></td></tr></tbody></table></div></div><br class="table-break" /></div><div class="sect2" id="id-1.11.7.42.7"><div class="titlepage"><div><div><h3 class="title">F.33.3. GUC Parameters</h3></div></div></div><div class="variablelist"><dl class="variablelist"><dt id="GUC-PGTRGM-SIMILARITY-THRESHOLD"><span class="term">
<code class="varname">pg_trgm.similarity_threshold</code> (<code class="type">real</code>)
<a id="id-1.11.7.42.7.2.1.1.3" class="indexterm"></a>
</span></dt><dd><p>
Sets the current similarity threshold that is used by the <code class="literal">%</code>
operator. The threshold must be between 0 and 1 (default is 0.3).
</p></dd><dt id="GUC-PGTRGM-WORD-SIMILARITY-THRESHOLD"><span class="term">
<code class="varname">pg_trgm.word_similarity_threshold</code> (<code class="type">real</code>)
<a id="id-1.11.7.42.7.2.2.1.3" class="indexterm"></a>
</span></dt><dd><p>
Sets the current word similarity threshold that is used by the
<code class="literal"><%</code> and <code class="literal">%></code> operators. The threshold
must be between 0 and 1 (default is 0.6).
</p></dd><dt id="GUC-PGTRGM-STRICT-WORD-SIMILARITY-THRESHOLD"><span class="term">
<code class="varname">pg_trgm.strict_word_similarity_threshold</code> (<code class="type">real</code>)
<a id="id-1.11.7.42.7.2.3.1.3" class="indexterm"></a>
</span></dt><dd><p>
Sets the current strict word similarity threshold that is used by the
<code class="literal"><<%</code> and <code class="literal">%>></code> operators. The threshold
must be between 0 and 1 (default is 0.5).
</p></dd></dl></div></div><div class="sect2" id="id-1.11.7.42.8"><div class="titlepage"><div><div><h3 class="title">F.33.4. Index Support</h3></div></div></div><p>
The <code class="filename">pg_trgm</code> module provides GiST and GIN index
operator classes that allow you to create an index over a text column for
the purpose of very fast similarity searches. These index types support
the above-described similarity operators, and additionally support
trigram-based index searches for <code class="literal">LIKE</code>, <code class="literal">ILIKE</code>,
<code class="literal">~</code>, <code class="literal">~*</code> and <code class="literal">=</code> queries.
Inequality operators are not supported.
Note that those indexes may not be as efficient as regular B-tree indexes
for equality operator.
</p><p>
Example:
</p><pre class="programlisting">
CREATE TABLE test_trgm (t text);
CREATE INDEX trgm_idx ON test_trgm USING GIST (t gist_trgm_ops);
</pre><p>
or
</p><pre class="programlisting">
CREATE INDEX trgm_idx ON test_trgm USING GIN (t gin_trgm_ops);
</pre><p>
</p><p>
<code class="literal">gist_trgm_ops</code> GiST opclass approximates a set of
trigrams as a bitmap signature. Its optional integer parameter
<code class="literal">siglen</code> determines the
signature length in bytes. The default length is 12 bytes.
Valid values of signature length are between 1 and 2024 bytes. Longer
signatures lead to a more precise search (scanning a smaller fraction of the index and
fewer heap pages), at the cost of a larger index.
</p><p>
Example of creating such an index with a signature length of 32 bytes:
</p><pre class="programlisting">
CREATE INDEX trgm_idx ON test_trgm USING GIST (t gist_trgm_ops(siglen=32));
</pre><p>
At this point, you will have an index on the <code class="structfield">t</code> column that
you can use for similarity searching. A typical query is
</p><pre class="programlisting">
SELECT t, similarity(t, '<em class="replaceable"><code>word</code></em>') AS sml
FROM test_trgm
WHERE t % '<em class="replaceable"><code>word</code></em>'
ORDER BY sml DESC, t;
</pre><p>
This will return all values in the text column that are sufficiently
similar to <em class="replaceable"><code>word</code></em>, sorted from best match to worst. The
index will be used to make this a fast operation even over very large data
sets.
</p><p>
A variant of the above query is
</p><pre class="programlisting">
SELECT t, t <-> '<em class="replaceable"><code>word</code></em>' AS dist
FROM test_trgm
ORDER BY dist LIMIT 10;
</pre><p>
This can be implemented quite efficiently by GiST indexes, but not
by GIN indexes. It will usually beat the first formulation when only
a small number of the closest matches is wanted.
</p><p>
Also you can use an index on the <code class="structfield">t</code> column for word
similarity or strict word similarity. Typical queries are:
</p><pre class="programlisting">
SELECT t, word_similarity('<em class="replaceable"><code>word</code></em>', t) AS sml
FROM test_trgm
WHERE '<em class="replaceable"><code>word</code></em>' <% t
ORDER BY sml DESC, t;
</pre><p>
and
</p><pre class="programlisting">
SELECT t, strict_word_similarity('<em class="replaceable"><code>word</code></em>', t) AS sml
FROM test_trgm
WHERE '<em class="replaceable"><code>word</code></em>' <<% t
ORDER BY sml DESC, t;
</pre><p>
This will return all values in the text column for which there is a
continuous extent in the corresponding ordered trigram set that is
sufficiently similar to the trigram set of <em class="replaceable"><code>word</code></em>,
sorted from best match to worst. The index will be used to make this
a fast operation even over very large data sets.
</p><p>
Possible variants of the above queries are:
</p><pre class="programlisting">
SELECT t, '<em class="replaceable"><code>word</code></em>' <<-> t AS dist
FROM test_trgm
ORDER BY dist LIMIT 10;
</pre><p>
and
</p><pre class="programlisting">
SELECT t, '<em class="replaceable"><code>word</code></em>' <<<-> t AS dist
FROM test_trgm
ORDER BY dist LIMIT 10;
</pre><p>
This can be implemented quite efficiently by GiST indexes, but not
by GIN indexes.
</p><p>
Beginning in <span class="productname">PostgreSQL</span> 9.1, these index types also support
index searches for <code class="literal">LIKE</code> and <code class="literal">ILIKE</code>, for example
</p><pre class="programlisting">
SELECT * FROM test_trgm WHERE t LIKE '%foo%bar';
</pre><p>
The index search works by extracting trigrams from the search string
and then looking these up in the index. The more trigrams in the search
string, the more effective the index search is. Unlike B-tree based
searches, the search string need not be left-anchored.
</p><p>
Beginning in <span class="productname">PostgreSQL</span> 9.3, these index types also support
index searches for regular-expression matches
(<code class="literal">~</code> and <code class="literal">~*</code> operators), for example
</p><pre class="programlisting">
SELECT * FROM test_trgm WHERE t ~ '(foo|bar)';
</pre><p>
The index search works by extracting trigrams from the regular expression
and then looking these up in the index. The more trigrams that can be
extracted from the regular expression, the more effective the index search
is. Unlike B-tree based searches, the search string need not be
left-anchored.
</p><p>
For both <code class="literal">LIKE</code> and regular-expression searches, keep in mind
that a pattern with no extractable trigrams will degenerate to a full-index
scan.
</p><p>
The choice between GiST and GIN indexing depends on the relative
performance characteristics of GiST and GIN, which are discussed elsewhere.
</p></div><div class="sect2" id="id-1.11.7.42.9"><div class="titlepage"><div><div><h3 class="title">F.33.5. Text Search Integration</h3></div></div></div><p>
Trigram matching is a very useful tool when used in conjunction
with a full text index. In particular it can help to recognize
misspelled input words that will not be matched directly by the
full text search mechanism.
</p><p>
The first step is to generate an auxiliary table containing all
the unique words in the documents:
</p><pre class="programlisting">
CREATE TABLE words AS SELECT word FROM
ts_stat('SELECT to_tsvector(''simple'', bodytext) FROM documents');
</pre><p>
where <code class="structname">documents</code> is a table that has a text field
<code class="structfield">bodytext</code> that we wish to search. The reason for using
the <code class="literal">simple</code> configuration with the <code class="function">to_tsvector</code>
function, instead of using a language-specific configuration,
is that we want a list of the original (unstemmed) words.
</p><p>
Next, create a trigram index on the word column:
</p><pre class="programlisting">
CREATE INDEX words_idx ON words USING GIN (word gin_trgm_ops);
</pre><p>
Now, a <code class="command">SELECT</code> query similar to the previous example can
be used to suggest spellings for misspelled words in user search terms.
A useful extra test is to require that the selected words are also of
similar length to the misspelled word.
</p><div class="note"><h3 class="title">Note</h3><p>
Since the <code class="structname">words</code> table has been generated as a separate,
static table, it will need to be periodically regenerated so that
it remains reasonably up-to-date with the document collection.
Keeping it exactly current is usually unnecessary.
</p></div></div><div class="sect2" id="id-1.11.7.42.10"><div class="titlepage"><div><div><h3 class="title">F.33.6. References</h3></div></div></div><p>
GiST Development Site
<a class="ulink" href="http://www.sai.msu.su/~megera/postgres/gist/" target="_top">http://www.sai.msu.su/~megera/postgres/gist/</a>
</p><p>
Tsearch2 Development Site
<a class="ulink" href="http://www.sai.msu.su/~megera/postgres/gist/tsearch/V2/" target="_top">http://www.sai.msu.su/~megera/postgres/gist/tsearch/V2/</a>
</p></div><div class="sect2" id="id-1.11.7.42.11"><div class="titlepage"><div><div><h3 class="title">F.33.7. Authors</h3></div></div></div><p>
Oleg Bartunov <code class="email"><<a class="email" href="mailto:oleg@sai.msu.su">oleg@sai.msu.su</a>></code>, Moscow, Moscow University, Russia
</p><p>
Teodor Sigaev <code class="email"><<a class="email" href="mailto:teodor@sigaev.ru">teodor@sigaev.ru</a>></code>, Moscow, Delta-Soft Ltd.,Russia
</p><p>
Alexander Korotkov <code class="email"><<a class="email" href="mailto:a.korotkov@postgrespro.ru">a.korotkov@postgrespro.ru</a>></code>, Moscow, Postgres Professional, Russia
</p><p>
Documentation: Christopher Kings-Lynne
</p><p>
This module is sponsored by Delta-Soft Ltd., Moscow, Russia.
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