Sequent Calculus and Equational Programming

Nicolas Guenot
(IT University of Copenhagen)
Daniel Gustafsson
(IT University of Copenhagen)

Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.

In Iliano Cervesato and Kaustuv Chaudhuri: Proceedings Tenth International Workshop on Logical Frameworks and Meta Languages: Theory and Practice (LFMTP 2015), Berlin, Germany, 1 August 2015, Electronic Proceedings in Theoretical Computer Science 185, pp. 102–109.
Published: 27th July 2015.

ArXived at: http://dx.doi.org/10.4204/EPTCS.185.7 bibtex PDF

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