the :: operator - Maple Help

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:: - the :: operator

Calling Sequence

x :: T




any expression



a type specification



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 typex,T.


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 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 ::.

Thread Safety


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


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


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

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

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

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






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

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.


Error, assertion failed in assignment, expected integer, got 3.4

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


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

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")
    print("not an integer")
    end if
end proc:


an integer



not an integer


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










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







See Also

boolean, evalb, if, parameter, procedure, while

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