Sequentiality and the π-Calculus

A Process-Model for Linear Programs

“…Linearity for process calculi has already been studied in [4,12,13,25], mainly to ensure properties like determinism and strong normalization. A bounded name occurs exactly once in "input" and exactly once in "output".…”

“…α ::= S ǫ Sorting and (non-neutral) modalities are straightforwardly related to the game-theoretic notions of arenas and player/opponent of game semantics as formalized in [4,10]. If φ is a composite sorting then φ ǫ is a question type whileι ǫ is an answer type.…”

“…A seminal work exploring correspondences between process-calculi and game semantics has been presented in [10], where Hyland-Ong strategies are represented by processes of an appropriately sorted polyadic π-calculus. More recently, such result has been improved by introducing an elaborate type discipline for the π-calculus in [4], where the use of linear modalities [12,13] is crucial. A game-independent process-based language for game strategies has been formalized, where strategies are normalized processes.…”

“…We note that the semantic nature of strategies in [4,10] is explicitly reflected by the use of an infinitary syntax for the π-processes, on which no parallel reductions can be performed. Since we want to study processes induced by programs, our interpretation is actually given on finite processes.…”

“…The encodings given in [10,4] impose deterministic reduction strategies, so they are not faithful. This means that, there are programs M, N translated, respectively, by processes P, Q such that M → β N, but P cannot be process-reduced to Q (although P and Q are observationally equivalents).…”