Download PDFOpen PDF in browserCyclic Proofs and Coinductive Principles7 pages•Published: May 15, 2012AbstractIt 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.Keyphrases: coinductive, constructive, inductive, transition systems, types In: Ekaterina Komendantskaya, Ana Bove and Milad Niqui (editors). PAR-10. Partiality and Recursion in Interactive Theorem Provers, vol 5, pages 107-113.
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