.TH Matching
.PP
Aka 'where exists'
.SH Signature
.PP
.RS
.nf
matching(left: Relation, right: Relation) \-> Relation
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.RE
.SH Examples
.PP
.RS
.nf
matching(suppliers, supplies)
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.RE
.SH Description
.PP
Computes a relation as a subset of \fB\fCleft\fR tuples for which at least one
\fB\fCright\fR tuple would join on common attributes.
.PP
This operator, also known as semi\-join, can be explained through the
definition below. As shown, it consists in joining \fB\fCleft\fR and \fB\fCright\fR
relations and projecting the result back on \fB\fCleft\fR attributes.
.PP
.RS
.nf
def matching(left, right)
  project(join(left, right), left.attr_list)
end
matching(suppliers, supplies)
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.RE
.PP
Or, in SQL terms:
.PP
.RS
.nf
SELECT left.* FROM left NATURAL JOIN right
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.RE
.PP
The synonym 'where exists' comes from the fact that, since right attributes
are projected away, it may seem more intuitive to think about this operator
as filtering tuples from left where \fIthere exists\fP some tuple at right that
\fIwould\fP join. In SQL terms:
.PP
.RS
.nf
SELECT * FROM left WHERE EXISTS (SELECT * FROM right WHERE [join condition])
.fi
.RE
.SH Implementation notes
.PP
As for (natural) \fB\fCjoin\fR, you must take care of ensuring that the list of
common attributes on which the matching applies corresponds to what you
want. Renamings and projections are worth having at hand when using
matching. Alternatively, shortcuts can be considered. A (advanced) example
below:
.PP
.RS
.nf
# Same as matching(left, right) except that only attributes in `wish`
# are take into account in matching.
def matching_on(left, right, wish)
  matching(left, project(right, wish))
end
# observe here how part names have been discarded to avoid matching them
# with supplier names (empty result guaranteed)
matching_on(suppliers, parts, [:city])
.fi
.RE