Computation-by-Interaction with Effects
A successful approach in the semantics of programming languages is to model programs by interaction dialogues. While dialogues are most often considered abstract mathematical objects, it has also been argued that they are useful for actual computation. A manual implementation of interaction dialogues can be complicated, however. To address this issue, we consider a general method for extending a given language with a metalanguage that supports the implementation of dialogues. This method is based on the construction by Dal Lago and the author of the programming language intml, which applies interaction dialogues to sublinear space computation. We show that only few assumptions on the programming languages are needed to implement a useful intml-like metalanguage. We identify a weak variant of the Enriched Effect Calculus (EEC) of Egger, Møgelberg & Simpson as a convenient setting for capturing the structure needed for the construction of the metalanguage. In particular, function types are not needed for the construction and iteration by means of a Conway operator is sufficient. By using EEC we show how computational effects can be accounted for in the implementation of interaction dialogues.
KeywordsGame Model Computation Type Typing Rule Base Language Monoidal Structure
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