Symmetry and interactivity in Programming

We recall some of the early occurrences of the notions of interac-tivity and symmetry in the operational and denotational semantics of programming languages. We suggest some connections with ludics. Proof theory and programming are deeply intertwinned research areas. This short paper will address and compare ideas from both sides, so it seems appropriate to begin by recalling what this general interplay is about, before we enter into the more specific topic we have in mind here, namely symmetry and interactivity of computation. First, a disclaimer is in order: the encounter of logic and programming is by far not limited to what is commonly called logic programming. This expression refers to a programming style in which computation is proof search. I am speaking here of the larger match between two kinds of wide-range activities: • writing programs, or any piece of structured software, proving their correctness with respect to a specification, designing a language, implementing it via a compiler into another programming language, which may be itself amenable to the same kind of analysis, etc...;