Safe and decidable type checking in an object-oriented language

Abstract

Over the last several years, much interesting work has been done in modelling object-oriented programming languages in terms of extensions of the bounded second-order lambda calculus, Fr. Unfortunately, it has recently been shown by Pierce ([Pie92]) that type checking F< is undecidable. Moreover, he showed that the undecidability arises in t,he seemingly simpler problem of determining whether one type is a subtype of another.In [Bru93a, Bru93b], the fist author introduced a statically-typed, functional, object-oriented programming language, TOOPL, which supports classes, objects, methods, instance variables, subtypes, and inheritance.The semantics of TOOPL is based on F<, so the question arises whether type checking in this language is decidable. In this paper we show that type checking for TOOPLE, a minor variant of TOOPL (Typed Object-OrientedProgramming Language), is decidable. The proof proceeds by showing that subtyping is decidable, that all terms of TOOPLE have minimum types (which are in fact computable), and then using these two results to show that type checking is decidable.Our algorithm fails to be polynomial in the size of the term because the size of its type can be exponential in the size of the term. Nevertheless, it performs well in practice.

Type Inference with Selftype

“…For example, when comparing the type rules of Abadi and Cardelli [4] with those of Bruce et al [5,6], we find both striking similarities, such as in the rules for message send, and significant differences, such as Bruce's use of the ≤ meth relation on types. Both these type systems have been proved sound, and for Bruce's language TOOPLE, type checking is decidable [6].…”

“…Typing self in the presence of inheritance has been studied by Abadi and Cardelli [3,2,1,4], Bruce [5,6], Palsberg and Schwartzbach [11,12], and others. These developments all identify a need to give self a special treatment, as illustrated by the following standard example.…”

“…Selftype has been studied by Abadi and Cardelli [4], Bruce [5,6], and others, and used in for example Eiffel [9] (Eiffel uses the syntax like Current for selftype). In the example with Point and ColorPoint, we can annotate the move method with selftype as the return type.…”

The Theory of Classification Part 20: Modular Checking of Classtypes.

“…Bruce and his co-workers started building type-safe experimental objectoriented languages in the early 1990s. TOOPL and TOOPLE were functional-style object languages (rather like the λ-calculus models we have used in this series), which supported both simple subtyping and a new treatment of the self-type using a distinguished type variable called MyType [11]. Originally, the motivation for MyType arose from considering the same problems with subtyping in the presence of recursive types that led Cook to devise F-bounded quantification [5]; and Bruce's early treatments relied on an F-bounded explanation.…”

Class-graph inference for adaptive programs

“…The key difference between the first and the last two problems is that in the former case the subclass relationships are known, but in the latter case they are not. All published algorithms on type checking and type inference for object-oriented programs, for example [5,6,15,20,18,19,1,14,7], rely on knowing the subclass relationships, and if there is a separate notion of typing and subtyping, then, of course, the algorithms rely on knowing the definition of subtyping. Hence, they do not apply to the typability and class-graph inference problems that we study in this paper.…”