The  operator serves several purposes in Maple, all related to types.

When used in a procedure parameter declaration, the left-hand side of the operator specifies the parameter name, and the right-hand side specifies the expected type of the argument.

The return type of a procedure can be declared by following the procedure's parameter declaration sequence by . In this context,  serves as an assertion that the procedure returns a value of the specified type, T. If assertions are enabled, returning a value not matching the type will raise an exception.

When used as the left-hand side of an assignment statement or as the first argument to the assign function,  asserts that the value being assigned to x is of type T.

A local variable can be declared with a type by using the  operator. Within the procedure in which the variable is declared, any assignment made to it are treated as if the left-hand side of the assignment were written using the  declaration.

In the condition of an if or while statement,  serves as a type testing operator. In this context,  is equivalent to .

The  operator also acts as a type test when used as an argument to any of the Boolean operators, and, or, not, xor, implies, or the  function.

In any other context,  evaluates its arguments, but does not itself evaluate any further. Thus, it can be used as a data structure or part of a larger data structure. Although it is not required, it is customary to use  as a data structure only when the right-hand side represents a type or a type-like concept. For example, see RealRange.

An expression using the  operator is of type .

The :: operator is thread-safe as of Maple 15.

For more information on thread safety, see index/threadsafe.

f := proc( x::integer ) x^2 end proc:

Error, invalid input: f expects its 1st argument, x, to be of type integer, but received 3.4

f := proc( x::integer ) :: odd; x^2 end proc:

Error, (in f) assertion failed: f expects its return value to be of type odd, but computed 16

Error, (in myassign) assertion failed in assignment, expected integer, got 3.4

f := proc( x ) local y::integer;
    y := x
end proc:

Error, (in myassign) assertion failed in assignment, expected integer, got 4.5

f := proc( x )
    if x::integer then
    print("an integer")
    else
    print("not an integer")
    end if
end proc: