We’ll write τabs for the type inside the existential. The function new takes a class name and instance data for that class and constructs an object, while the function send takes an object and a method name and produces an element of the method’s result type. Given a dispatch matrix edm : τdm, there are two natural ways of implementing ∃tobj.τabs. The first, which is analogous to the traditiona...

We’ll write τabs for the type inside the existential. The function new takes a class name and instance data for that class and constructs an object, while the function send takes an object and a method name and produces an element of the method’s result type. Given a dispatch matrix edm : τdm, there are two natural ways of implementing ∃tobj.τabs. The first, which is analogous to the traditiona...

Let S be some type system. A typing in S for a typable term M is the collection of all of the information other than M which appears in the final judgement of a proof derivation showing that M is typable. For example, suppose there is a derivation in S ending with the judgement A ` M : τ meaning that M has result type τ when assuming the types of free variables are given by A. Then (A, τ ) is a...