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Arrays and streams seem to be fundamentally at odds: arrays require their size to be known in advance, streams are dynamically growing; arrays offer direct access to all of their elements, streams provide direct access to the front elements only; the list goes on. Despite these differences, many computational problems at some point require shifting from one paradigm to the other. The driving forces for such a shift can be manifold. Typically, it is a shift in the task requirements at hand or it is motivated by efficiency considerations. In this talk, we present a basis for a unified framework for dealing with arrays and streams alike. We introduce an applied lambda calculus whose fundamental data structure is a new form of array, named "Transfinite Array". Transfinite arrays maintain properties from finite array calculi yet incorporate support for infinite arrays. As it turns out, it is even possible to maintain recursive specifications as they are typically found in a traditional stream / list-based setting.

An arxiv paper as well as an implementation of an interpreter in Ocaml are available here