On the Ubiquity of Certain Total Type Structures: (Extended Abstract)

We consider a simple and well-known category of alternating games (also known as sequential data structures) and several categories derived from it. In each case, we present an extension of Plotkin’s language FPC (or a suitable linearization thereof) which defines all computable strategies of appropriate types. The quest for such languages results in a novel selection of language primitives for state encapsulation, coroutining and backtracking.