Abstract
We show that infinite objects can be constructively understood without the consideration of partial elements, or greatest fixed-points, through the explicit consideration of proof objects. We present then a proof system based on these explanations. According to this analysis, the proof expressions should have the same structure as the program expressions of a pure functional lazy language: variable, constructor, application, abstraction, case expressions, and local let expressions.
This research has been done within the ESPRIT Basic Research Action “Types for Proofs and Programs”. It has been paid by NUTEK, Chalmers and the University of Göteborg.
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Coquand, T. (1994). Infinite objects in type theory. In: Barendregt, H., Nipkow, T. (eds) Types for Proofs and Programs. TYPES 1993. Lecture Notes in Computer Science, vol 806. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58085-9_72
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DOI: https://doi.org/10.1007/3-540-58085-9_72
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