### Abstract

Language | English |
---|---|

Title of host publication | 26th Annual IEEE Symposium on Logic in Computer Science (LICS) 2011 |

Publisher | IEEE |

Pages | 65-74 |

Number of pages | 10 |

ISBN (Electronic) | 9780769544120 |

ISBN (Print) | 9781457704512 |

DOIs | |

Status | Published - 2011 |

Event | 26th Annual IEEE Symposium on Logic in Computer Science - Toronto, ON, Canada Duration: 21 Jun 2011 → 24 Jun 2011 |

### Publication series

Name | Annual Symposium on Logic in Computer Science |
---|---|

Publisher | IEEE |

ISSN (Print) | 1043-6871 |

### Conference

Conference | 26th Annual IEEE Symposium on Logic in Computer Science |
---|---|

Abbreviated title | LICS 2011 |

Country | Canada |

City | Toronto, ON |

Period | 21/06/11 → 24/06/11 |

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### Cite this

*26th Annual IEEE Symposium on Logic in Computer Science (LICS) 2011*(pp. 65-74). (Annual Symposium on Logic in Computer Science). IEEE. https://doi.org/10.1109/LICS.2011.19

**Imperative programs as proofs via game semantics.** / Churchill, Martin; Laird, James; McCusker, Guy.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*26th Annual IEEE Symposium on Logic in Computer Science (LICS) 2011.*Annual Symposium on Logic in Computer Science, IEEE, pp. 65-74, 26th Annual IEEE Symposium on Logic in Computer Science, Toronto, ON, Canada, 21/06/11. https://doi.org/10.1109/LICS.2011.19

}

TY - GEN

T1 - Imperative programs as proofs via game semantics

AU - Churchill, Martin

AU - Laird, James

AU - McCusker, Guy

PY - 2011

Y1 - 2011

N2 - Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this paper we describe a logical counterpart to this extension, in which proofs denote such strategies. We can embed intuitionistic first-order linear logic into this system, as well as an imperative total programming language. The logic makes explicit use of the fact that in the game semantics the exponential can be expressed as a final co algebra. We establish a full completeness theorem for our logic, showing that every bounded strategy is the denotation of a proof.

AB - Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this paper we describe a logical counterpart to this extension, in which proofs denote such strategies. We can embed intuitionistic first-order linear logic into this system, as well as an imperative total programming language. The logic makes explicit use of the fact that in the game semantics the exponential can be expressed as a final co algebra. We establish a full completeness theorem for our logic, showing that every bounded strategy is the denotation of a proof.

UR - http://www.scopus.com/inward/record.url?scp=80052172689&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1109/LICS.2011.19

U2 - 10.1109/LICS.2011.19

DO - 10.1109/LICS.2011.19

M3 - Conference contribution

SN - 9781457704512

T3 - Annual Symposium on Logic in Computer Science

SP - 65

EP - 74

BT - 26th Annual IEEE Symposium on Logic in Computer Science (LICS) 2011

PB - IEEE

ER -