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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
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.

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.

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.

Object Modules can be added directly under the Objects node in the Document Explorer, directly under any of the Library nodes or under any folder node in the Document Explorer tree. To add an Object Module in any of these locations:

In the Document Explorer window, right-click any the appropriate parent node for the new Object Module.
Select Add object module from the context menu.
Name the new module and press the Enter key.

Object definitions are always created inside of a namespace. To insert a namespace:

Right-click anywhere within the module and select Insert namespace from the context menu.
Type the name of the namespace object.
Select a namespace from the autocomplete popup window and press the Enter key.

An object module can contain multiple namespaces. To add an additional namespace to the same module, highlight the existing namespace and press the Enter key to insert a new namespace below the existing namespace, or press the Insert key to insert the new namespace above the existing namespace. Both options are also available by right-clicking the highlighted namespace and selecting the appropriate option from the context menu.