Abstract
Partial type theories allow reasoning about recursively- defined computations using fixed-point induction. However, fixed-point induction is only sound for admissible types and not all types are admissible in sufficiently expressive dependent type theories.
Previous solutions have either introduced explicit admissibility conditions on the use of fixed points, or limited the underlying type theory. In this paper we propose a third approach, which supports Hoare-style partial correctness reasoning, without admissibility conditions, but at a tradeoff that one cannot reason equationally about effectful computations. The resulting system is still quite expressive and useful in practice, which we confirm by an implementation as an extension of Coq.
This research has been partially supported by MICINN Project TIN2010-20639 Paran10; AMAROUT grant PCOFUND-GA-2008-229599; and Ramon y Cajal grant RYC-2010-0743.
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Svendsen, K., Birkedal, L., Nanevski, A.: Partiality, State and Dependent Types. Technical report, IT University of Copenhagen (2011), http://www.itu.dk/people/kasv/ihtt-adm-tr.pdf
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Svendsen, K., Birkedal, L., Nanevski, A. (2011). Partiality, State and Dependent Types. In: Ong, L. (eds) Typed Lambda Calculi and Applications. TLCA 2011. Lecture Notes in Computer Science, vol 6690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21691-6_17
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DOI: https://doi.org/10.1007/978-3-642-21691-6_17
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