. We present a general semantic universe of call-by-value computation based on elements of game semantics, and validate its appropriateness as a semantic universe by the full abstraction result for call-by-value PCF, a generic typed programming language with call-by-value evaluation. The key idea is to consider the distinction between call-by-name and call-by-value as that of the structure of information flow, which determines the basic form of games. In this way the call-by-name computation and call-by-value computation arise as two independent instances of sequential functional computation with distinct algebraic structures. We elucidate the type structures of the universe following the standard categorical framework developed in the context of domain theory. Mutual relationship between the presented category of games and the corresponding call-by-name universe is also clarified. 1. Introduction The call-by-value is a mode of calling procedures widely used in imperative and function...

Machine by Curien [Cur86]. It is based upon a weak categorical combinatory logic, viz. lacking surjective pairing and extensionality, that arose as a direct semantic-to-syntactic translation of the lambda calculus of tuples. The computational mode was combinator term reduction through rewriting using a direct left-to-right parse algorithm, initially making the evaluation strategy inefficiently eager 1 . Application is therefore simply juxtaposition, losing the full expressiveness of-reduction that computes via substitution. Its overly strong bias towards the lambda calculus was another factor that limited its expressiveness. On one hand the CAM demanded the existence of categorical products but on the other it had no coproducts for developing many useful data structures. Nevertheless, the high acceptance and efficiency of the CAM-based ML compiler, CAML, gives significant encouragement towards developing a highly-programmable categorical computing paradigm. Some prominent workers in ...