4.5.5 Languages Based on Covariant Redefinition

Some languages support bounded polymorphic classes through covariant redefinition of types or operations: a polymorphic class is defined as a regular class that has an "anchor" type member initialized to the upper bound of the type parameter, and instances are made by defining subclasses that redefine some anchor types to selected subtypes. Instances may themselves be further subclassed and their anchor types narrowed. Eiffel supports covariant overriding of methods and instance variables, and uses the like construct to refer to anchors [Meyer 92]; Eiffel also supports unbounded parameterized classes as well. Beta supports virtual patterns as anchor classes [Madsen & Møller-Pedersen 89, Madsen et al. 93], and Thorup adapted this idea in his proposed virtual types extension to Java [Thorup 97]. While all of these mechanisms seem natural to programmers in many cases and are syntactically concise, they suffer from a loss of static type safety. In contrast, Cecil can directly support all of the standard examples used to justify such mechanisms (including binary methods and the model-view example), for instance using one or more mutually recursive F-bounded type parameters, without sacrificing static type safety. We are working on syntactic support for the general pattern of mutually recursive F-bounded type parameters, in hopes of achieving the same syntactic conciseness and programmer comprehensibility as well.