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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="___The_sp__Macaulay2_splanguage.html" title="">The Macaulay2 language</a> > <a href="_what_spa_spclass_spis.html" title="">what a class is</a></div>
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<div><h1>what a class is</h1>
<div>In Macaulay2 the behavior of a function depends heavily on the types of the arguments it's presented with. For example, the expression <tt>x+y</tt> means the sum if <tt>x</tt> and <tt>y</tt> are integers, but it means the union if <tt>x</tt> and <tt>y</tt> are sets. To implement this in a clean fashion, we store the code for doing things with sets in something called <a href="___Set.html" title="the class of all sets">Set</a> and we store the code for doing things with integers in something called <a href="___Z__Z.html" title="the class of all integers">ZZ</a>. We say that each integer is an <a href="_instance.html" title="whether something has a certain type">instance</a> of <a href="___Z__Z.html" title="the class of all integers">ZZ</a>, and <a href="___Z__Z.html" title="the class of all integers">ZZ</a> is the <a href="_class.html" title="class of an object">class</a> (or type) of each integer. The function <a href="_class.html" title="class of an object">class</a> provides the class of an object, and the function <a href="_instance.html" title="whether something has a certain type">instance</a> tells whether a given object is an instance of a given class, or a subclass of it, and so on.<p/>
<table class="examples"><tr><td><pre>i1 : class 33
o1 = ZZ
o1 : Ring</pre>
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<tr><td><pre>i2 : instance(33,ZZ)
o2 = true</pre>
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<tr><td><pre>i3 : instance(33,String)
o3 = false</pre>
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The corresponding mathematical idea is that <a href="___Z__Z.html" title="the class of all integers">ZZ</a> is the set of all integers.<p/>
The class of all classes or types is called <a href="___Type.html" title="the class of all types">Type</a>.<table class="examples"><tr><td><pre>i4 : instance(ZZ,Type)
o4 = true</pre>
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<tr><td><pre>i5 : instance(33,Type)
o5 = false</pre>
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The class of all objects in the system is <a href="___Thing.html" title="the class of all things">Thing</a>.<table class="examples"><tr><td><pre>i6 : instance(33,Thing)
o6 = true</pre>
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Everything has a class, and every class has a <a href="_parent.html" title="parent type of an object">parent</a>. The parent class represents a broader class of objects, and is used to contain code that applies to the broader class. For example, <a href="___Z__Z.html" title="the class of all integers">ZZ</a> is a ring, and every ring is also a type.<table class="examples"><tr><td><pre>i7 : class ZZ
o7 = Ring
o7 : Type</pre>
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<tr><td><pre>i8 : parent class ZZ
o8 = Type
o8 : Type</pre>
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Types are implemented as hash tables -- it's a versatile way of storing bits of code that are needed in various situations; the keys for the hash table are constructed in a certain way from the function and the types of its arguments whose details the user doesn't need to know.<p/>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_uniform.html" title="test whether elements of a list are of the same class">uniform</a> -- test whether elements of a list are of the same class</span></li>
<li><span><a href="___Thing.html" title="the class of all things">Thing</a> -- the class of all things</span></li>
<li><span><a href="___Nothing.html" title="the empty class">Nothing</a> -- the empty class</span></li>
<li><span><a href="___Type.html" title="the class of all types">Type</a> -- the class of all types</span></li>
<li><span><a href="___Mutable__List.html" title="the class of all mutable lists">MutableList</a> -- the class of all mutable lists</span></li>
<li><span><a href="___Mutable__Hash__Table.html" title="the class of all mutable hash tables">MutableHashTable</a> -- the class of all mutable hash tables</span></li>
<li><span><a href="___Self__Initializing__Type.html" title="the class of all self initializing types">SelfInitializingType</a> -- the class of all self initializing types</span></li>
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<div><h3>Menu</h3>
<ul><li><span><a href="_class.html" title="class of an object">class</a> -- class of an object</span></li>
<li><span><a href="_parent.html" title="parent type of an object">parent</a> -- parent type of an object</span></li>
<li><span><a href="_instance.html" title="whether something has a certain type">instance</a> -- whether something has a certain type</span></li>
<li><span>ancestor, see <span><a href="_ancestor_lp__Type_cm__Type_rp.html" title="whether one type is an ancestor of another">ancestor(Type,Type)</a> -- whether one type is an ancestor of another</span></span></li>
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