Y. Bertot, V. Capretta, and K. D. Barman. Type-theoretic functional semantics. In V. A. Carreno, C. A. Munoz, and S. Tahar, editors, Theorem Proving in Higher Order Logics (TPHOLS'02), volume 2410 of LNCS, pages 83--98. Springer, 2002. Home/Search Document Details and Download
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Modelling General Recursion in Type Theory - Bove, Capretta (2002) (3 citations) Self-citation (Capretta) (Correct)
....purpose. One can adopt a set theoretic approach and see functions as relations. Specifically, the behaviour of a recursive function can be described by an inductive relation giving its operational semantics (see, for example, Win93] Operational semantics has been developed in type theory in [BCB02] and [ZMHH02] However, relations do not have any computational content in type theory. The real challenge consists in representing general recursive programs as elements of some functional type. Using classical logic it is possible to extend every partial function to a total one. This fact is ....
....the well foundedness of the recursive calls when one de nes the algorithms, there is a clear separation between the algorithms and these proofs. In any case, it is not very clear how their methods can be used to formalise partial or nested recursive algorithms. In a recent work, Bertot et al. [BCB02] present a technique to encode the method we describe in [BC01] for partial and nested algorithms in type theo30 ries that do not support Dybjer s schema for simultaneous inductive recursive de nitions. They do so by combining the way we de ne our special accessibility predicate with the ....
Y. Bertot, V. Capretta, and K. Das Barman. Type-theoretic functional semantics. In Carreno et al. [CMT02], pages 83-97.
Inductive Fixpoints in Higher Order Logic - Krstic (2004) (Correct)
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Y. Bertot, V. Capretta, and K. D. Barman. Type-theoretic functional semantics. In V. A. Carreno, C. A. Munoz, and S. Tahar, editors, Theorem Proving in Higher Order Logics (TPHOLS'02), volume 2410 of LNCS, pages 83--98. Springer, 2002.
Inductive Invariants for Nested Recursion - Krstic, Matthews (2003) (Correct)
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Y. Bertot, V. Capretta, and K. D. Barman. Type-theoretic functional semantics. In V. A Carreno, C. A. Munoz, and S. Tahar, editors, Theorem Proving in Higher Order Logics (TPHOLS 2002), volume 2410 of LNCS, pages 83-98. Springer, 2002.
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