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Patterns
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<H2>5.6 Patterns</H2>
<A NAME="@manual.kwd5"></A><DIV ALIGN=center>
<TABLE CELLSPACING=2 CELLPADDING=0>
<TR><TD ALIGN=right NOWRAP>
<TT><I><FONT COLOR=maroon>pattern</FONT></I></TT></TD>
<TD ALIGN=right NOWRAP>::=</TD>
<TD ALIGN=left NOWRAP>
<TT><I><FONT COLOR=maroon>value-name</FONT></I></TT></TD>
</TR>
<TR><TD ALIGN=right NOWRAP> </TD>
<TD ALIGN=right NOWRAP>|</TD>
<TD ALIGN=left NOWRAP> <TT><FONT COLOR=blue>_</FONT></TT></TD>
</TR>
<TR><TD ALIGN=right NOWRAP> </TD>
<TD ALIGN=right NOWRAP>|</TD>
<TD ALIGN=left NOWRAP> <TT><I><FONT COLOR=maroon>constant</FONT></I></TT></TD>
</TR>
<TR><TD ALIGN=right NOWRAP> </TD>
<TD ALIGN=right NOWRAP>|</TD>
<TD ALIGN=left NOWRAP> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT> <TT><FONT COLOR=blue>as</FONT></TT> <TT><I><FONT COLOR=maroon>value-name</FONT></I></TT></TD>
</TR>
<TR><TD ALIGN=right NOWRAP> </TD>
<TD ALIGN=right NOWRAP>|</TD>
<TD ALIGN=left NOWRAP> <TT><FONT COLOR=blue>(</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT> <TT><FONT COLOR=blue>)</FONT></TT></TD>
</TR>
<TR><TD ALIGN=right NOWRAP> </TD>
<TD ALIGN=right NOWRAP>|</TD>
<TD ALIGN=left NOWRAP> <TT><FONT COLOR=blue>(</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT> <TT><FONT COLOR=blue>:</FONT></TT> <TT><I><FONT COLOR=maroon>typexpr</FONT></I></TT> <TT><FONT COLOR=blue>)</FONT></TT></TD>
</TR>
<TR><TD ALIGN=right NOWRAP> </TD>
<TD ALIGN=right NOWRAP>|</TD>
<TD ALIGN=left NOWRAP> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT> <TT><FONT COLOR=blue>|</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT></TD>
</TR>
<TR><TD ALIGN=right NOWRAP> </TD>
<TD ALIGN=right NOWRAP>|</TD>
<TD ALIGN=left NOWRAP> <TT><I><FONT COLOR=maroon>ncconstr</FONT></I></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT></TD>
</TR>
<TR><TD ALIGN=right NOWRAP> </TD>
<TD ALIGN=right NOWRAP>|</TD>
<TD ALIGN=left NOWRAP> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT> { <TT><FONT COLOR=blue>,</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT> }</TD>
</TR>
<TR><TD ALIGN=right NOWRAP> </TD>
<TD ALIGN=right NOWRAP>|</TD>
<TD ALIGN=left NOWRAP> <TT><FONT COLOR=blue>{</FONT></TT> <TT><I><FONT COLOR=maroon>label</FONT></I></TT> <TT><FONT COLOR=blue>=</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT> { <TT><FONT COLOR=blue>;</FONT></TT> <TT><I><FONT COLOR=maroon>label</FONT></I></TT> <TT><FONT COLOR=blue>=</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT> } <TT><FONT COLOR=blue>}</FONT></TT></TD>
</TR>
<TR><TD ALIGN=right NOWRAP> </TD>
<TD ALIGN=right NOWRAP>|</TD>
<TD ALIGN=left NOWRAP> <TT><FONT COLOR=blue>[</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT> { <TT><FONT COLOR=blue>;</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT> } <TT><FONT COLOR=blue>]</FONT></TT></TD>
</TR>
<TR><TD ALIGN=right NOWRAP> </TD>
<TD ALIGN=right NOWRAP>|</TD>
<TD ALIGN=left NOWRAP> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT> <TT><FONT COLOR=blue>::</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT></TD>
</TR></TABLE></DIV><BR>
The table below shows the relative precedences and associativity of
operators and non-closed pattern constructions. The constructions with
higher precedences come first.
<A NAME="@manual.kwd6"></A>
<BR>
<BR>
<DIV ALIGN=center>
<TABLE BORDER=1 CELLSPACING=0 CELLPADDING=1 WIDTH="80%">
<TR><TD ALIGN=center NOWRAP><B>Operator</B></TD>
<TD ALIGN=center NOWRAP><B>Associativity</B></TD>
</TR>
<TR><TD ALIGN=left NOWRAP>
Constructor application</TD>
<TD ALIGN=left NOWRAP>--</TD>
</TR>
<TR><TD ALIGN=left NOWRAP><TT>::</TT></TD>
<TD ALIGN=left NOWRAP>right</TD>
</TR>
<TR><TD ALIGN=left NOWRAP><TT>,</TT></TD>
<TD ALIGN=left NOWRAP>--</TD>
</TR>
<TR><TD ALIGN=left NOWRAP><TT>|</TT></TD>
<TD ALIGN=left NOWRAP>left</TD>
</TR>
<TR><TD ALIGN=left NOWRAP><TT>as</TT></TD>
<TD ALIGN=left NOWRAP>--</TD>
</TR></TABLE></DIV><BR>
Patterns are templates that allow selecting data structures of a
given shape, and binding identifiers to components of the data
structure. This selection operation is called pattern matching; its
outcome is either ``this value does not match this pattern'', or
``this value matches this pattern, resulting in the following bindings
of names to values''.<BR>
<BR>
<H4>Variable patterns</H4>A pattern that consists in a value name matches any value,
binding the name to the value. The pattern <TT><FONT COLOR=blue>_</FONT></TT> also matches
any value, but does not bind any name.<BR>
<BR>
Patterns are <EM>linear</EM>: a variable cannot appear several times in
a given pattern. In particular, there is no way to test for equality
between two parts of a data structure using only a pattern (but
<TT><FONT COLOR=blue>when</FONT></TT> guards can be used for this purpose).<BR>
<BR>
<H4>Constant patterns</H4>A pattern consisting in a constant matches the values that
are equal to this constant.<BR>
<BR>
<H4>Alias patterns</H4>
<A NAME="@manual.kwd7"></A>The pattern <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> <TT><FONT COLOR=blue>as</FONT></TT> <TT><I><FONT COLOR=maroon>value-name</FONT></I></TT> matches the same values as
<TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB>. If the matching against <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> is successful,
the name <TT><I><FONT COLOR=maroon>name</FONT></I></TT> is bound to the matched value, in addition to the
bindings performed by the matching against <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB>.<BR>
<BR>
<H4>Parenthesized patterns</H4>The pattern <TT><FONT COLOR=blue>(</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> <TT><FONT COLOR=blue>)</FONT></TT> matches the same values as
<TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB>. A type constraint can appear in a
parenthesized pattern, as in <TT><FONT COLOR=blue>(</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> <TT><FONT COLOR=blue>:</FONT></TT> <TT><I><FONT COLOR=maroon>typexpr</FONT></I></TT> <TT><FONT COLOR=blue>)</FONT></TT>. This
constraint forces the type of <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> to be compatible with
<TT><I><FONT COLOR=maroon>type</FONT></I></TT>.<BR>
<BR>
<H4>``Or'' patterns</H4>The pattern <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> <TT><FONT COLOR=blue>|</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>2</FONT></SUB> represents the logical ``or'' of
the two patterns <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> and <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>2</FONT></SUB>. A value matches
<TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> <TT><FONT COLOR=blue>|</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>2</FONT></SUB> either if it matches <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> or if it
matches <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>2</FONT></SUB>. The two sub-patterns <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> and <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>2</FONT></SUB>
must contain no identifiers. Hence no bindings are returned by
matching against an ``or'' pattern.<BR>
<BR>
<H4>Variant patterns</H4>The pattern <TT><I><FONT COLOR=maroon>ncconstr</FONT></I></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> matches all variants whose
constructor is equal to <TT><I><FONT COLOR=maroon>ncconstr</FONT></I></TT>, and whose argument matches
<TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB>.<BR>
<BR>
The pattern <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> <TT><FONT COLOR=blue>::</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>2</FONT></SUB> matches non-empty lists whose
heads match <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB>, and whose tails match <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>2</FONT></SUB>. This
pattern behaves like <TT><FONT COLOR=blue>(</FONT></TT> <TT><FONT COLOR=blue>::</FONT></TT> <TT><FONT COLOR=blue>)</FONT></TT> <TT><FONT COLOR=blue>(</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> <TT><FONT COLOR=blue>,</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>2</FONT></SUB> <TT><FONT COLOR=blue>)</FONT></TT>.<BR>
<BR>
The pattern <TT><FONT COLOR=blue>[</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> <TT><FONT COLOR=blue>;</FONT></TT> ... <TT><FONT COLOR=blue>;</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2><I>n</I></FONT></SUB> <TT><FONT COLOR=blue>]</FONT></TT> matches lists
of length <I>n</I> whose elements match <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> ...<TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2><I>n</I></FONT></SUB>,
respectively. This pattern behaves like
<TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> <TT><FONT COLOR=blue>::</FONT></TT> ... <TT><FONT COLOR=blue>::</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2><I>n</I></FONT></SUB> <TT><FONT COLOR=blue>::</FONT></TT> <TT><FONT COLOR=blue>[]</FONT></TT>.<BR>
<BR>
<H4>Tuple patterns</H4>The pattern <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> <TT><FONT COLOR=blue>,</FONT></TT> ... <TT><FONT COLOR=blue>,</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2><I>n</I></FONT></SUB> matches <I>n</I>-tuples
whose components match the patterns <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> through <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2><I>n</I></FONT></SUB>. That
is, the pattern matches the tuple values (<TT><I><FONT COLOR=maroon>v</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB>, ..., <TT><I><FONT COLOR=maroon>v</FONT></I></TT><SUB><FONT SIZE=2><I>n</I></FONT></SUB>) such that
<TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2><I>i</I></FONT></SUB> matches <TT><I><FONT COLOR=maroon>v</FONT></I></TT><SUB><FONT SIZE=2><I>i</I></FONT></SUB> for <I>i</I> = 1,... , <I>n</I>.<BR>
<BR>
<H4>Record patterns</H4>The pattern <TT><FONT COLOR=blue>{</FONT></TT> <TT><I><FONT COLOR=maroon>label</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> <TT><FONT COLOR=blue>=</FONT></TT> <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> <TT><FONT COLOR=blue>;</FONT></TT> ... <TT><FONT COLOR=blue>;</FONT></TT> <TT><I><FONT COLOR=maroon>label</FONT></I></TT><SUB><FONT SIZE=2><I>n</I></FONT></SUB> <TT><FONT COLOR=blue>=</FONT></TT>
<TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2><I>n</I></FONT></SUB> <TT><FONT COLOR=blue>}</FONT></TT> matches records that define at least the labels
<TT><I><FONT COLOR=maroon>label</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> through <TT><I><FONT COLOR=maroon>label</FONT></I></TT><SUB><FONT SIZE=2><I>n</I></FONT></SUB>, and such that the value associated to
<TT><I><FONT COLOR=maroon>label</FONT></I></TT><SUB><FONT SIZE=2><I>i</I></FONT></SUB> match the pattern <TT><I><FONT COLOR=maroon>pattern</FONT></I></TT><SUB><FONT SIZE=2><I>i</I></FONT></SUB>, for <I>i</I> = 1,... , <I>n</I>.
The record value can define more labels than <TT><I><FONT COLOR=maroon>label</FONT></I></TT><SUB><FONT SIZE=2>1</FONT></SUB> ...<TT><I><FONT COLOR=maroon>label</FONT></I></TT><SUB><FONT SIZE=2><I>n</I></FONT></SUB>; the values associated to these extra labels are not taken
into account for matching.<BR>
<BR>
<BR>
<BR>
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