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24 changes: 13 additions & 11 deletions tutorials/online/sidenote-multiplicity.html
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Original file line number Diff line number Diff line change
Expand Up @@ -7,27 +7,27 @@
<body>
<h2>Multiplicity Markings</h2>

<p>When defining a field of a signature to be a relation, you write something like this:</p>
<p>When defining a field of a signature to be a relation in itself as well , you write something like this:</p>

<pre><b>
sig University {
groupMember: Student -> Professor
}
</b></pre>

<p> Here, each University knows which student is a member of which
professor's research group. That is, there is a relation from
Universities to Students to Professors. By writing multiplicity
markings to the declaration of the relation, we can add additional
constraints in a concise way. For example, </p>
<p> Here, there is a (nameless) relation from Students to Professors, which is
in turn related to some university through the relation <i>groupMember</i>.

By writing multiplicity markings to the declaration of the relation,
we can add additional constraints in a concise way. For example, </p>

<pre><b>
sig University {
groupMember: Student -> one Professor
}
</b></pre>

<p> means that each student is in exactly one professor's research
<p> means that each student is in exactly <b>one</b> professor's research
group. If we instead wrote this,</p>

<pre><b>
Expand All @@ -36,17 +36,19 @@ <h2>Multiplicity Markings</h2>
}
</b></pre>

<p> Then we are saying that some students may be in no research group,
but no student is in more than one. Lastly, we can write</p>
<p> Then we are saying that every student is studying (related) with at most
one professor. Lastly, we can write</p>

<pre><b>
sig University {
groupMember: Student -> some Professor
}
</b></pre>

<p> to say that each student is in one or more research groups. When
no multiplicity markings are present, there are not
<p> to say that each student is in one or more research groups (since the student
can be related with <i>some</i> ie. one or more professors.

When no multiplicity markings are present, there are no
constraints.</p>

<hr WIDTH="50%">
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