Several definitions attached to the same symbol can be used:

Make a declaration and compile a function that uses the definitions:

This calls the definition that uses a condition:

This calls the definition that uses a literal 2:

This calls the last catchall definition:

Definitions attached to a symbol can be used in more than one declaration with different types:

Make two declarations with different types and compile functions that use each:

Call the integer case:

Call the real case:

Definitions attached to a symbol can be declared with a polymorphic type:

Make two declarations with different types and compile functions that use each:

Call the integer case:

Call the real case:

Function declarations that use a symbol definition can call themselves:

Make a declaration and compile a function that uses it:

Call the function:

Function declarations that do not apply to all inputs can use a predicate to strip out:

Make a polymorphic declaration:

This compiles for a Boolean type, but the predicate for the Floor case is known to be False at compile time, so it is stripped out:

This compiles for a real type and uses the branch with the Floor:

Declarations that use symbol definitions are useful if the declaration is used more than once:

A FunctionDeclaration that refers to the symbol:

A function that uses the symbol:

Compiled code for the function:

A vector plot based on the data that was created:

The compiled version is much faster:

An animation of the output:

DownValuesFunction uses the definitions used when the compilation is carried out:

The result uses the definitions in place when the compilation is done:

KernelFunction uses the definitions used when the computation is carried out:

The result uses the definitions in place when the computation is done: