Multimethods

In this chapter, we show two important techniques. First, we define methods for built-in generic functions — in this case, for the functions +, <, and =. Second, we define multimethods. We describe how method dispatch works for multimethods.

Methods for the + generic function

We need to make it possible to add one time to another. We could define a method with a name such as add or plus. However, the concept of adding times is the same as the concept of adding numbers. Dylan already provides the + generic function for adding numbers. Instead of inventing a new name for the addition operation, we define new methods on the built-in generic function +. We can extend + by defining new methods for it. In certain languages, this technique is called operator overloading.

Comparison with C++ and Java:

In C++, operator overloading means customizing the action of any built-in operator for classes that you define. In Dylan, operators are just generic functions, and you can add methods to those generic functions for your classes. In C++, the meaning of an overloaded operator is resolved at compile time — the types of the operands must be known at compile time. Because Dylan operators are generic functions, the method is chosen dynamically according to the argument types —at run time, if the types may vary at run time.

Java does not allow operator overloading. The Java designers believe that overloading of operators results in inscrutable code (because the meaning of the operator can vary). Dylan and C++ designers believe that, judiciously used, operator overloading permits clearer, more concise code.

Method for adding two time offsets

We now define a method for +. The method adds two time offsets and returns the sum, which is also a time offset:

// Method on <time-offset>, <time-offset>
define method \+
    (offset1 :: <time-offset>, offset2 :: <time-offset>)
 => (sum :: <time-offset>)
  let sum = offset1.total-seconds + offset2.total-seconds;
  make(<time-offset>, total-seconds: sum);
end method \+;

On line 2, notice that the method is defined on \+, rather than simply on +. When we define a method on + or on another infix function, we need to use a backslash before the function name. The backslash clarifies that we mean the value of the variable + (which is a generic function), and that we are not trying to call the function.

On line 4, we add the values stored in the total-seconds slots of the two instances. On line 5, we make and return a new instance of <time-offset>. We initialize the total-seconds slot to contain the sum calculated in line 4.

To test the method, we need to create two instances of <time-offset>:

define variable *minus-2-hours* =
  make(<time-offset>, total-seconds: - encode-total-seconds (2, 0, 0));

define variable *plus-15-20-45* =
  make(<time-offset>, total-seconds: encode-total-seconds (15, 20, 45));

We can add the time offsets:

? *minus-2-hours* + *plus-15-20-45*;
=> {instance <time-offset>}

The result is a new instance of <time-offset>. We did not save the value returned. (Many environments offer a way to access values returned by the listener.) We can add the time offsets again, and view the total-seconds slot of the result:

? decode-total-seconds(*minus-2-hours* + *plus-15-20-45*);
=> 13
=> 20
=> 45

Methods for adding a time of day to a time offset

These methods implement addition between a time offset and a time of day:

// Method on <time-offset>, <time-of-day>
define method \+
    (offset :: <time-offset>, time-of-day :: <time-of-day>)
 => (sum :: <time-of-day>)
  make(<time-of-day>,
  total-seconds: offset.total-seconds + time-of-day.total-seconds);
end method \+;

The method on <time-offset>, <time-of-day> is invoked when the first argument is a time offset and the second argument is a time of day. It does the work of creating a new <time-of-day> instance with the total-seconds slot initialized to the sum of the total-seconds slots of the two arguments.

// Method on <time-of-day>, <time-offset>
define method \+
    (time-of-day :: <time-of-day>, offset :: <time-offset>)
 => (sum :: <time-of-day>)
  offset + time-of-day;
end method \+;

The method on <time-of-day>, <time-offset> is invoked when the first argument is a time of day and the second argument is a time offset. It simply calls + with the order of the arguments switched — this call invokes the method on <time-offset>, <time-of-day>.

To test these methods, we can use one of the time offsets created in Method for adding two time offsets, and define the *8-30-59* variable, which contains a <time-of-day> instance, which we define as follows:

define variable *8-30-59* =
  make(<time-of-day>, total-seconds: encode-total-seconds(8, 30, 59));

We add the time offset and the time of day:

? decode-total-seconds(*minus-2-hours* + *8-30-59*);
=> 6
=> 30
=> 59

We add the time of day and the time offset:

? decode-total-seconds(*8-30-59* + *minus-2-hours*);
=> 6
=> 30
=> 59

Method for adding other kinds of times

We have already defined methods for adding the kinds of time that it makes sense to add together. It is not logical to add one time of day to another time of day — what would three o’clock plus two o’clock mean? Someone could create another concrete subclass of <time>, without providing any methods for adding that time to other times. If someone tries to add times that we do not intend them to add, the result will be a “No applicable method” error.

We could provide a method whose sole purpose is to give more information to the user than “No applicable method” when + is called on two times that cannot be added, because there is no applicable method for adding them. We define such a method here:

// Method on <time>, <time>
define method \+ (time1 :: <time>, time2 :: <time>)
  error("Sorry, we can't add a %s to a %s.",
        object-class(time1), object-class(time2));
end method \+;

This method is called only when the arguments are both general instances of <time>, and none of the more specific methods are applicable to the arguments. The error function signals an error. For more information about signaling and handling errors, see Exceptions.

Note: This method is useful for explaining how method dispatch works for multimethods, but it does not really give the user any more useful information than that supplied by the “No applicable method” error. Therefore, we define the method in this chapter, but do not include it as part of the final library.

Method dispatch for multimethods

A method is specialized on the required parameters that have explicit types. The type of the required parameter is called that parameter’s specializer. A multimethod is a method that specializes more than one of its parameters. The methods that we defined in Methods for the + generic function specialize two required parameters, and therefore are multimethods.

Comparison with C++ and Java:

Neither C++ nor Java supports multimethods. In both languages, method dispatch is based on the first argument of virtual functions.

The method dispatch considers all the required parameters, and sorts the applicable methods by specificity as follows: For each required parameter, construct a separate list of the applicable methods, sorted from most specific to least specific for that parameter. Then, combine the separate sorted lists into an overall list of methods, sorted by specificity. In the overall method ordering, a method is more specific than another if it satisfies two constraints:

1. The method is no less specific than the other method for all required parameters. (The two methods might have the same types for some parameters.)

2. The method is more specific than the other method for some required parameter.

One method might be more specific than another for one parameter, but less specific for another parameter. These two methods are ambiguous in specificity and cannot be ordered. If the method-dispatch procedure cannot find any method that is more specific than all other methods, Dylan signals an error.

Applicable methods for different arguments to +, ordered by specificity.

Type of first argument	Type of second argument	Applicable methods, ordered by specificity
<time-offset>	<time-offset>	# method on <time-offset>, <time-offset> # method on <time>, <time>
<time-of-day>	<time-offset>	# method on <time-of-day>, <time-offset> # method on <time>, <time>
<time-offset>	<time-of-day>	# method on <time-offset>, <time-of-day> # method on <time>, <time>
<time-of-day>	<time-of-day>	# method on <time>, <time>
<integer>	<time-offset>	none

Applicable methods for different arguments to +, ordered by specificity. shows the applicable methods for various arguments to +. If two methods are applicable, we number the more specific method 1, and the less specific method 2.

We call + on two instances of <time-offset>:

? *minus-2-hours* + *plus-15-20-45*;
=> {instance of <time-offset>}

When both arguments are instances of <time-offset>, the first row of the table applies. Two methods are applicable. The method on <time-offset>, <time-offset> is more specific than the method on <time>, <time>. The parameter specializers of the method on <time-offset>, <time-offset> are subtypes of the parameter specializers of the method on <time>, <time>. That is, for the first parameter, <time-offset> is a subtype of <time>; for the second parameter, <time-offset> is a subtype of <time>.

Methods for comparison of times

We need to compare times to see whether they are the same, and to see whether one is greater (later) than another. These methods do the comparisons we need:

define method \<
    (time1 :: <time-of-day>, time2 :: <time-of-day>)
 => (boolean :: <boolean>)
  time1.total-seconds < time2.total-seconds;
end method \<;

define method \<
    (time1 :: <time-offset>, time2 :: <time-offset>)
 => (boolean :: <boolean>)
  time1.total-seconds < time2.total-seconds;
end method \<;

define method \=
    (time1 :: <time-of-day>, time2 :: <time-of-day>)
 => (boolean :: <boolean>)
  time1.total-seconds = time2.total-seconds;
end method \=;

define method \=
    (time1 :: <time-offset>, time2 :: <time-offset>)
 => (boolean :: <boolean>)
  time1.total-seconds = time2.total-seconds;
end method \=;

We can call these methods:

? *plus-15-20-45* = *minus-2-hours*;
=> #f

To compare times, we need only to define methods for < and =. All other numerical comparisons in Dylan are based on these two methods. So, we can call >, >=, <=, and ~= (the not-equal-to function). Here are examples:

? *plus-15-20-45* ~= *minus-2-hours*;
=> #t

? *plus-15-20-45* > *minus-2-hours*;
=> #t

Summary

In this chapter, we covered the following:

• We defined new methods on the built-in generic functions +, <, and =.

• We discussed how method dispatch works for multimethods.