Typed Applicative Structures and Normalization by Evaluation for System F ω

Abel, Andreas

doi:10.1007/978-3-642-04027-6_6

Cited by 3 publications

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References 16 publications

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“…The use of System F typing allows us to ensure that transitions can be found for any term. Our term language will follow closely on the one used by Abel [2].…”

Section: Languagementioning

confidence: 99%

Cyclic Proofs and Coinductive Principles

Mendel-Gleason¹,

Hamilton²

EPiC Series in Computing

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It is possible to provide a proof for a coinductive type using a corecursive function coupled with a guardedness condition. The guardedness condition, however, is quite restrictive and many programs which are in fact productive and do not compromise soundness will be rejected. We present a system of cyclic proof for an extension of System F extended with sums, products and (co)inductive types. Using program transformation techniques we are able to take some programs whose productivity is suspected and transform them, using a suitable theory of equivalence, into programs for which guardedness is syntactically apparent. The equivalence of the proof prior and subsequent to transformation is given by a bisimulation relation.

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