Translation Correctness for First-Order Object-Oriented Pattern Matching

Abstract

Pattern matching makes ML programs more concise and readable, and these qualities are also sought in object-oriented settings. However, objects and classes come with open class hierarchies, extensibility requirements and the need for data abstraction, which all conflict with matching on concrete data types. Extractor-based pattern matching has been proposed to address this conflict. Extractors are user-defined methods that perform the task of value discrimination and deconstruction during pattern matching. In this paper, we give the first formalization of extractor-based matching, using a first-order object-oriented calculus. We give a direct operational semantics and prove it sound. We then present an optimizing translation to a target language without matching, and prove a correctness result stating that an expression is equivalent to its translation.

Algebraic Pattern Matching in Join Calculus

“…A simulation relation is demonstrated from target code to source code by induction on evaluation derivation and case study over the last applied evaluation rule. Closer to our work, [12] shows the correctness of an optimizing translation that compiles away pattern matching in Scala. Proof techniques analogous with ours are applied, i.e.…”

Static Type Analysis of Pattern Matching by Abstract Interpretation

“…Thus type cases in pattern matching are translated into type tests and casts. For instance, the body of method extract in Figure 1 is translated into the code in Figure 2 by the Scala compiler [13]. Note that information about generics is erased.…”