## Induction and co-induction in sequent calculus (2003)

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Venue: | Post-proceedings of TYPES 2003, number 3085 in LNCS |

Citations: | 23 - 8 self |

### BibTeX

@INPROCEEDINGS{Tiu03inductionand,

author = {Alwen Tiu and Alberto Momigliano},

title = {Induction and co-induction in sequent calculus},

booktitle = {Post-proceedings of TYPES 2003, number 3085 in LNCS},

year = {2003},

pages = {293--308}

}

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### Abstract

Abstract. Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles are based on a proof theoretic (rather than set-theoretic) notion of definition [13, 20, 25, 51]. Definitions are akin to (stratified) logic programs, where the left and right rules for defined atoms allow one to view theories as “closed ” or defining fixed points. The use of definitions makes it possible to reason intensionally about syntax, in particular enforcing free equality via unification. We add in a consistent way rules for pre and post fixed points, thus allowing the user to reason inductively and co-inductively about properties of computational system making full use of higher-order abstract syntax. Consistency is guaranteed via cut-elimination, where we give the first, to our knowledge, cut-elimination procedure in the presence of general inductive and co-inductive definitions. 1