what a class is

what a class is

In Macaulay 2 the behavior of a function depends heavily on the types of the arguments it's presented with. For example, the expression x+y means the sum if x and y are integers, but it means the union if x and y are sets. To implement this in a clean fashion, we store the code for doing things with sets in something called Set and store the code for doing things with integers in something called ZZ. We say that each integer is an instance of ZZ, and ZZ is the class (or type) of each integer. The function class provides the class of an object, and the function instance tells whether an given object is an instance of a given class, or a subclass of it, and so on.

i1 : class 33



o1 = ZZ



o1 : Ring



  --  the class of all integers

i2 : instance(33,ZZ)



o2 = true

i3 : instance(33,String)



o3 = false

The corresponding mathematical idea is that ZZ is the set of all integers.

The class of all classes or types is called Type.

i4 : instance(ZZ,Type)



o4 = true

i5 : instance(33,Type)



o5 = false

The class of all objects in the system is Thing.

i6 : instance(33,Thing)



o6 = true

Everything has a class, and every class has a parent. The parent class represents a broader class of objects, and is used to contain code that applies to the broader class. For example, ZZ is a ring, and every ring is also a type.

i7 : class ZZ



o7 = Ring



o7 : Type



  --  the class of all rings

i8 : parent class ZZ



o8 = Type



o8 : Type



  --  the class of all types

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.

For more details, see one of the topics below.

class -- class of an object

parent

instance -- whether something has a certain type

ancestor -- whether one type is an ancestor of another

newClass -- copy an object, changing the class

new -- new objects of various types

For related topics, see one of the following.

uniform -- test whether elements of a list are of the same class

Thing -- the class of all things

Nothing -- the empty class

Type -- the class of all types

MutableList -- the class of all mutable lists

MutableHashTable -- the class of all mutable hash tables

SelfInitializingType -- the class of all self initializing types