## Abstract

The standard proof theory for logics with equality and fixpoints suffers from limitations of the sequent calculus, where reasoning is separated from computational tasks such as unification or rewriting. We propose in this paper an extension of the calculus of structures, a deep inference formalism, that supports incremental and contextual reasoning with equality and fixpoints in the setting of linear logic.

This system allows deductive and computational steps to mix freely in a continuum which integrates smoothly into the usual versatile rules of multiplicative-additive linear logic in deep inference.

This system allows deductive and computational steps to mix freely in a continuum which integrates smoothly into the usual versatile rules of multiplicative-additive linear logic in deep inference.

Original language | English |
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Title of host publication | Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), CSL-LICS '14, Vienna, Austria, July 14 - 18, 2014 |

Editors | Thomas A. Henzinger, Dale Miller |

Number of pages | 10 |

Publisher | Association for Computing Machinery |

Publication date | 12 Sept 2014 |

Pages | 30-40 |

ISBN (Print) | 978-1-4503-2886-9 |

DOIs | |

Publication status | Published - 12 Sept 2014 |

Series | Annual Symposium on Logic in Computer Science |
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ISSN | 1043-6871 |

## Keywords

- Deep inference
- Unification
- Fixed points
- Linear logic