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::

the :: operator

 Calling Sequence x :: T

Parameters

 x - any expression T - a type specification

Description

 • 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 $::T$. 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, $x::T$ 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, $x::T$ is equivalent to $\mathrm{type}\left(x,T\right)$.
 • 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 $\mathrm{evalb}$ 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 $\mathrm{::}$.

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

Examples

A common use of :: is to declare the type of procedure parameters.

 > f := proc( x::integer ) x^2 end proc:
 > $f\left(2\right)$
 ${4}$ (1)
 > $f\left(3.4\right)$

The :: operator can assert the return type of a procedure.

 > f := proc( x::integer ) :: odd; x^2 end proc:
 > $\mathrm{kernelopts}\left(\mathrm{assertlevel}=2\right):$
 > $f\left(3\right)$
 ${9}$ (2)
 > $f\left(4\right)$

Using :: on the left-hand side of an assignment or declaring a local variable with :: asserts that the value being assigned is of the specified type.

 > $x::\mathrm{integer}≔3.4$
 > f := proc( x ) local y::integer;     y := x end proc:
 > $f\left(4.5\right)$

In the condition of an if (or while) statement, the :: operator is equivalent to using the type function.

 > f := proc( x )     if x::integer then     print("an integer")     else     print("not an integer")     end if end proc:
 > $f\left(2\right)$
 ${"an integer"}$ (3)
 > $f\left(3.4\right)$
 ${"not an integer"}$ (4)

The :: operator is inert if used out of context.

 > $x≔2$
 ${x}{:=}{2}$ (5)
 > $x::\mathrm{integer}$
 ${2}{::}{\mathrm{integer}}$ (6)
 > $x::\mathrm{integer}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{and}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}x<3$
 ${\mathrm{true}}$ (7)

Expressions involving the :: operator are of type ::.

 > $\mathrm{type}\left(x::\mathrm{symbol},\mathrm{::}\right)$
 ${\mathrm{true}}$ (8)
 > $\mathrm{evalb}\left(\left(x::\mathrm{string}\right)::\mathrm{::}\right)$
 ${\mathrm{true}}$ (9)