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Concepts
This section of the documentation covers the use of Objects, Libraries and References, Notations, Styles and Types and how each is created, edited and used in the Sym application.
Objects
An object is the basic building block of all of the symbolic content contained in a document - every term in every symbolic expression in Sym is an instance of an object. Many of the objects used in Sym have an object definition that specifies how the object looks and behaves, but it's also possible to create objects that don't have object definitions. All objects are identified by their name and object names are always defined in a specific namespace. All object definitions contain a type definition. Optionally, objects can also contain Properties, Clauses, Renderings, and a Description.
Creating and Editing Objects
Extending Object Definitions
When we are building libraries, we often run into situations where we would like to add functionality to an object that was originally created in a different library. We do this by "extending" the object definition. Typically, we extend an object definition either to add additional clauses to the object or to add additional renderings.

Concepts
This section of the documentation covers the use of Objects, Libraries and References, Notations, Styles and Types and how each is created, edited and used in the Sym application.
- Objects
  An object is the basic building block of all of the symbolic content contained in a document - every term in every symbolic expression in Sym is an instance of an object. Many of the objects used in Sym have an object definition that specifies how the object looks and behaves, but it's also possible to create objects that don't have object definitions. All objects are identified by their name and object names are always defined in a specific namespace. All object definitions contain a type definition. Optionally, objects can also contain Properties, Clauses, Renderings, and a Description.
  - Object Modules
    An Object Module contains object definitions. Object definitions contain the name, type definition, renderings, code and properties that define the functionality of every object. Object Modules are created, edited and managed using the Document Explorer.
  - Creating and Editing Objects
    - Creating an Object Module
      Object Modules are the containers for the object definitions that provide both the objects and the functionality available in a document.
    - Creating an Object Definition
      An object is the basic building block of all of the symbolic content contained in a document. After an Object Module has been created and a namespace has been defined, object definitions can be added.
    - Adding Clauses to an Object Definition
      When you add clauses to an object definition, the object becomes an executable function. A function is executed by processing each of the clauses in the object definition in the order that they appear. If the execution of a clause produces a result that is not null, that result is the expression returned by the function. Otherwise, execution continues with the next clause in the object definition. If none of the clauses produce a result other than null, then execution of the function returns null.
    - Extending Object Definitions
      When we are building libraries, we often run into situations where we would like to add functionality to an object that was originally created in a different library. We do this by "extending" the object definition. Typically, we extend an object definition either to add additional clauses to the object or to add additional renderings.
  - Objects Used in Code
    Objects that are commonly used in clauses in function are listed below.
  - Property Objects
  - Special Objects
  - Autogenerated Objects
  - Monoids
    Monoids are typically defined as a binary mapping that has an identity element and is associative. In the construction of the Sym application, we have taken an equivalent, but different approach to defining and handling monoids. It may be surprising to see something so fundamental defined in a non-standard way, so the reasoning for taking this approach is explained below.
- Library Locations and References
  Locations are used to manage groups of libraries and documents. The purpose of locations is to make documents portable from one machine to another. To do that, locations can be online as well as on your local machine. If a document references online libraries, the required libraries will be downloaded automatically when the document is opened.
- Notations and Rendering
  The purpose of notations is to make it possible to easily change the way expressions are displayed. Notations are assigned to Document Modules, Unit Test Modules and Object Modules. The notation assigned determines which renderings are selected for each expression in the module.
- Styles
  Each notation refers to a stylesheet. Stylesheets define Styles. Styles are used in two places. First, they can be used to style text. Second, they can be used to style parts of an expression in a rendering. You can create new style and new stylesheets.
- Types
  Every term in every expression in a Sym document has a type assigned to it. Every object definition has a type definition as one of its components. Since type definitions can include things like type variables, Sym uses a type inferencing process to determine the explicit types assigned to each term in every expression.

Extending Object Definitions

When we are building libraries, we often run into situations where we would like to add functionality to an object that was originally created in a different library. We do this by "extending" the object definition. Typically, we extend an object definition either to add additional clauses to the object or to add additional renderings.

Suppose we have defined an object named MyCommute in a library named Library1.

Now we create a new library named Library2 and a new object named MyObject. With MyObject defined as:

We want MyObject to be commutative and we want to use the MyCommute function to implement that functionality .

To do this, we create an Object Module in Library2. Add the Math namespace and then create an object named MyCommute with the same type definition as the definition of MyCommute in Library1 where the object was originally defined. Next add a clause to MyCommute in the module in Library2:

Note that the MyCommute object has an entry listed under Extensions. The entry refers to the module in Library1 that has the original definition of the MyCommute object. The object definition in Library1 also has an extension that refers to the module in Library2.

Extensions are only shown for object definitions where both the name and the type definitions are identical.

After we build the document, we will be able to use the MyCommute function on MyObject. We can see this be creating a unit test in Library2. To do this, create a new unit test module in Library2 and edit the unit test to look like this:

When an object definition has extensions and more than one of them contains clauses, the clauses are added in the reverse order to the order that the libraries appear in the Object Explorer. So in this case, the clause in Library2 is executed before any clauses in Library1.

In exactly the same way, we can extend an object definition to add a rendering. Any object definition can be extended, not just those that are functions.