Computer Science Logic

Volume 6247 of the series Lecture Notes in Computer Science pp 215-229

A Logic of Sequentiality

  • Martin ChurchillAffiliated withUniversity of Bath
  • , James LairdAffiliated withUniversity of Bath

* Final gross prices may vary according to local VAT.

Get Access


Game semantics has been used to interpret both proofs and functional programs: an important further development on the programming side has been to model higher-order programs with state by allowing strategies with ”history-sensitive” behaviour. In this paper, we develop a detailed analysis of the structure of these strategies from a logical perspective by showing that they correspond to proofs in a new kind of affine logic.

We describe the semantics of our logic formally by giving a notion of categorical model and an instance based on a simple category of games. Using further categorical properties of this model, we prove a full completeness result: each total strategy is the semantics of a unique cut-free core proof in the system. We then use this result to derive an explicit cut-elimination procedure.


Game semantics sequentiality full completeness