A Game-Theoretic, Concurrent and Fair Model of the Typed Lambda-calculus, with Full Recursion

This paper, and the talk on which it is based, were strongly influenced by two, contradictory words of advice. First, there is Gian-Carlo Rota’s eloquent injunction in [17] to “publish the same result often”; and so I will take some time to describe again and (I hope) motivate and explain better the game-theoretic model of concurrency, with fair merge and full recursion introduced in [7] and further studied in [9, 8, 10, 12]. Second, there is this young computer scientist friend of mine, who complaints about conferences in which “everyone presents a finished, polished paper on what they did the year before, so that the talks are stylized and do not lead to meaningful interaction among the participants”; and so I put off writing the paper until after the meeting, and I spent all my time up to it perfecting as best I could the new theorem I wanted to present. Still not quite what I would like to prove, this result adds products and function spaces to the constructions of [7, 9], which then yield a concurrent model of the typed λ-calculus which still accommodates fairness and full recursion. As it happened, game-theoretic semantics of higher-type languages were featured prominently in this conference, quite different from mine, to be sure, but, still, not entirely unrelated, and so my unconventional choice for structuring the talk and this paper made good sense in the end.