Application of OOP type theory

Abstract

Important strides toward developing expressive yet semantically sound type systems for object-oriented programming languages have recently been made by Cook, Bruce, Mitchell, and others. This paper focusses on how the theoretical work using F-bounded quantification may be brought more into the realm of actual language implementations while preserving rigorous soundness properties. We simultaneously address three of the more significant problems: adding a notion of global state, proving type-checking is decidable, and integrating the more widely implemented view that subclasses correspond to subtypes with the F-bounded view.

A Theory of Class

“…This promoted the use of F-bounded parameters to describe the self-type of recursive objects, in order to show how this type changes when it is inherited. Other researchers have since developed formal languages in which the self-type is described in this way, but type compatibility between object fields is either handled by subtyping (Bruce et al, 1993) or else the field-types match exactly (Eifrig et al, 1994). In another article (Simons, 1995a), we have argued that object-oriented languages now have too many mechanisms to handle type polymorphism: for example, Eiffel has conformance (a kind of pseudo-subtyping), constrained generic and anchored types (both kinds of F-bounded polymorphism); whereas C++ has subtyping and templates (a kind of parametric polymorphism).…”

“…F-bounds were used to constrain the self-types that belong to a class. As a result of this focus, subsequent work has only used F-bounds to characterise the self-type as it evolves under inheritance (Bruce et al, 1993;Eifrig et al, 1994).…”

“…In particular, subtyping is too weak, conformance is incorrect (Cook, 1989), constrained generic parameters and anchored types describe the same kind of polymorphism as class inheritance (Simons, 1995a), which is best described using F-bounds. F-bounds also provide a formal explanation for where-clauses (Day, et al, 1995), matching (Abadi and Cardelli, 1995;Bruce, 1994;Bruce et al, 1993) open types (Eifrig et al, 1994) and similar expressions of constraint upon interfaces.…”