## Universes for Generic Programs and Proofs in Dependent Type Theory (2003)

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Venue: | Nordic Journal of Computing |

Citations: | 42 - 2 self |

### BibTeX

@ARTICLE{Benke03universesfor,

author = {Marcin Benke and Peter Dybjer and Patrik Jansson},

title = {Universes for Generic Programs and Proofs in Dependent Type Theory},

journal = {Nordic Journal of Computing},

year = {2003},

volume = {10},

pages = {2003}

}

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### Abstract

We show how to write generic programs and proofs in MartinL of type theory. To this end we consider several extensions of MartinL of's logical framework for dependent types. Each extension has a universes of codes (signatures) for inductively defined sets with generic formation, introduction, elimination, and equality rules. These extensions are modeled on Dybjer and Setzer's finitely axiomatized theories of inductive-recursive definitions, which also have a universe of codes for sets, and generic formation, introduction, elimination, and equality rules.