# A logic of sequentiality

Martin Churchill, James Laird

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Citations (Scopus)
45 Downloads (Pure)

## Abstract

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 \emph{core} proof in the system. We then use this result to derive an explicit cut-elimination procedure.
Original language English Computer Science Logic (Lecture Notes in Computer Science) A Dawar, H Veith Springer 215-229 15 6247/2 https://doi.org/10.1007/978-3-642-15205-4_19 Published - 24 Aug 2010

### Publication series

Name Lecture Notes in Computer Science Springer Verlag

## Keywords

• full completeness
• sequentiality
• Game semantics

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