Rationalising Eiffel's Type System

forbidding the redefinition of attribute types, inverting the routine argument redefinition rule to observe contravariance (redefined arguments should have more general types), judging type compatibility between parameterised types after replacing the type parameters and introducing an explicit type attribute scheme to handle Eiffel's anchored types. Contravariance is a counterintuitive finding for subtyping models of inheritance because it prevents the uniform specialisation of function arguments and results. It forbids the replacement of a function f:τ→τ closed over a type τ by a function f:σ→σ closed over a subtype σ ⊆ τ [Cardelli 86]. While insisting that Eiffel should obey the contravariant rule, Cook ruefully admits that: Eiffel has too many polymorphic type mechanisms: conformance, generic and anchored types, some of which are flawed and others redundant. Cook's suggested 1989 corrections to Eiffel's type rules, most notably to make inheritance obey subtyping, were not accepted by Meyer, Eiffel's designer, who found them too restrictive. F-bounded polymorphism has since been widely proposed as an alternative to subtyping for describing the inherited self-type. Here, we adopt F-bounds for all polymorphic types in Eiffel, giving the flexibility Meyer wants. We analyse the intended expressiveness of conformance, anchored and generic types and show how these can all be replaced by a single, elegant parametric mechanism. "[Contravariance] has the unfortunate effect of making argument type redefinition almost useless, since it is usually not very useful to allow a redefined method to accept a larger class of arguments" [Cook 89b, p62].