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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.
Special Objects
The "At" Object
The At object in the Core namespace is used to specify the location of child term inside of a parent expression. The At object is capable of defining the location of any term in an expression no matter how many levels down in the expression tree it's located. The At object is commonly used with commands that act on the highlighted term in an expression.

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
  - Objects Used in Code
    Objects that are commonly used in clauses in function are listed below.
  - Property Objects
  - Special Objects
    - Numbers and Scientific Notation
      The Num object is used any time a number is created in an expression. The SciNum object is used to create scientific notation.
    - Text Objects
      Text can be added to a module or text can be created inside an expression. In both cases, a Text object in the Text namespace is used to hold the text.
    - Objects with Values
      Objects can have a value property attached to the object definition. Physical constants or objects that represent specific values (pi for example) are created with object definitions that have Value properties attached. The Value property is in the Core namespace.
    - The "At" Object
      The At object in the Core namespace is used to specify the location of child term inside of a parent expression. The At object is capable of defining the location of any term in an expression no matter how many levels down in the expression tree it's located. The At object is commonly used with commands that act on the highlighted term in an expression.
    - Autocomplete Objects
      An autocomplete object is an object that appears in the autocomplete pop-up menu when text is typed into an empty box. The purpose of an autocomplete object is to create a group of objects that appear in the autocomplete popup. An autocomplete object can also be used to get an object to appear in the autocomplete popup under more than one name.
    - Color Objects
      A standard set of colors are defined in the Autogenerated Objects library. In addition, in the Basics library, an ARGB object is defined that allows creating an arbitrary color.
    - Command Parameter Objects
      When a command is executed the command parameters property determines what expressions are passed into the parameters of the function called by the command.
    - Declaration Objects
      It's often the case when doing a calculation that you need to specify one or more properties of particular variable used in the calculation. For example, you may want to specify that certain variables are constants or that a variable is greater than zero. Declarations allow you to define these kinds of properties.
    - Namespace Objects
      The full name of every object consists of a namespace and an object name. Including a namespace in the object name makes it less likely that creating a new object definition in a new library will result in a name collision with another object definition.
    - Notation Objects
      The renderings of an Object define how it appears on the screen. Object renderings are tied to a notation, which determine which object rendering is used in a document section.
    - Space and Ctrl + Space objects
      The Space and CtrlSpace objects are used to edit and create expressions. They are placeholders during the editing process and are not normally left in the final expression.
    - Display Settings
      The display settings are attached to instances of objects where properties are attached to object definitions. The display settings only affect how an object is rendered, changing a display setting doesn't change whether a pattern match succeeds or fails.
  - 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.

The "At" Object

The At object in the Core namespace is used to specify the location of child term inside of a parent expression. The At object is capable of defining the location of any term in an expression no matter how many levels down in the expression tree it's located. The At object is commonly used with commands that act on the highlighted term in an expression.

The At object is normally rendered as @[a, b, …] and the parameters of the At object are Integers. Each parameter of the At object corresponds to one more level down in the tree. The parameter numbers are zero based, so the location of the first parameter in an expression is always @[0].

In the expression "| x + y |", the following locations are valid:


Location	Expression
@[ ]	\| x + y \|
@[0]	x + y
@[0, 0]	x
@[0, 1]	y

The GetTerm function can be used to get the term at a specified location. So in the example above, GetTerm[ | x + y |, @[0]] will return the expression "x + y". For the expression in the example, the GetTerm function will return null for any location other than the ones in the table.

The At object is a monoid. This means that in an expression like:

{ @[0, 0, 0] => @[m..., n] }

are valid and the variable "m" is bound to @[0, 0], which is the parent of the term identified by the original location expression. Patterns like this allow construction of functionality that recursively walks up the expression tree. The Move command uses this approach to go up the expression tree looking for an Equal object so it can move the highlight to the other side of the equality.

In the pattern match:

{ @[0, 0] => @[k, m, n...] }

the variable "n" is bound to @[], the zero parameter At object, which refers to location of the whole expression. The result from calling GetTerm[expr, @[]] is always just "expr".