Automated generation of pattern destructors for ADTs

19. June 2008 11:36 by CarlosLoria in General  //  Tags:   //   Comments (0)

 As a continuation of our previous posts on ADTs, rules and pattern-matching, we go on with our work studying some alternatives to pattern extensibility and generation (see post 1 and post 2). For the extensibility case, we considered delegation by inheritance as an alternative, where we are currently using the programming language Scala for our illustration. In our previous post, we supported the claim the Scala compiler could be able to help in this aspect. In this post we consider pattern generation out from classes, once again, we identify a potential requirement for the programming languages under our study.

In general, we recall our goal is to discover features or their eventual absence in programming languages that give support to an ADT modeling style within a OOP environment. Our motivation and justification comes from the field of automated software transformation (as understood in and specifically exploring features in languages that properly help to specify transformation rules in a modular and reusable way. The ability to write rules is certainly a central and distinctive element of software transformation tools; especially in the case the feature is available to the final user in order to customize his/her own transformation tasks (as approached for instance in ).

We have already seen how a pattern can be associated with a class in Scala which provides a very natural bridge between rules based programming and OOP. Patterns are views of objects that allow an easy access to its relevant subparts in a particular context, as we know. However, it is programmer’s responsibility to manually build the pattern, in the general case. And knowledge about the set of relevant destructors of the object is required, obviously. And this is usually a matter of domain specific semantics, thus we cope with a task that is difficult to automate.

The notion of destructor is central to ADTs and very particularly when compiling pattern matching. In OOP, destructors are usually implemented as so-called getters (or properties) but, interestingly, neither particular syntax nor semantics in mainstream OOP languages distinguishes them as such from other kind of methods, as we do have for the (class) constructors. In Scala, however, destructors can be automatically generated in some cases which is a fine feature. For instance, consider a simple model for symbolic expressions, defined as follows:

trait ISexp
class Sexp(val car:ISexp, val cdr:ISexp) extends ISexp{
class Atom(val value:String) extends ISexp

In this case Scala injects methods for accessing car and cdr fields, thus, in this case destructors are easily recognized. In the case the class would be a case-class the corresponding pattern is indeed generated as indicated by the constructor declaration. But what happens when the class specification is not Scala code or is not given by this explicit way, as in example.

Thus, an interesting question arises if we would want to support semi automated generation of patterns out of classes which are not available in a form that clearly exhibits its destructors.
In ADTs, a destructor is an operator (functor) f that gives access to one parameter of a constructor c. In other words, following invariant should hold in the ADT theory:

Forall x:T: f(c(…, x, ….)) = x

Or if we prefer using an OOP notation:

(new c(…,x,…)).f() = x

In terms of the type system we should have f: () => T where T is the declared type of formal parameter position where x occurs in c.
This provides us with a criterion for guessing candidates for destructors given a class. However, in order to generate code for a pattern, we would need to query the class implementing the ADT looking for such kind of candidates. However, in the case of Scala, we only have reflection as an alternative to perform the required query because there is no code model exposed as class model. Fortunately, the reflection facilities of Java fill the gap. The nice thing is the full interoperability of Scala with Java. The flaw is that we have to generate source code, only.

In order to evaluate the concept, we have developed a very simple Scala prototype that suggests destructors for Java and Scala classes and for generating patterns for such candidates.  
For instance, for the classes of the Sexp model given above we automatically get as expected
object Atom {
    def unapply(x:sexps.Atom)=Some(x.value)
object Sexp {
    def unapply(x:sexps.Sexp)=Some(, x.cdr)
For a class like java.lang.Integer we get something unexpected:
object Integer {
    def unapply(x:java.lang.Integer)=Some(x.intValue, x.toString, x.hashCode)
Likewise for the class java.lang.String:
object String {
 def unapply(x:java.lang.String)=
   Some(x.toCharArray, x.length, x.getBytes, x.hashCode)
The overloading of constructors plays at this time an important role on the results. Unfortunately, Scala pattern abstraction does not correctly work if we use overloading for the unapply method. Thus, we have to pack all the possibilities in just one definition. Essential was actually, that we have identified additional requirements which are interesting to get attention as a potential language features.