Abstract
This paper is a companion of [S89, S90b] and it demonstrates that FBO is powerful enough to axiomatize CC-Iike calculi [HHP87, CH88] (where FBO is short for a Framework for Binding Operators [589, S90b], and CC stands for the Calculus of Constructions). More specifically, we introduce an extra universe kind above the original universe type in CC. But we allow neither quantification over kind nor introduction of y: kind. Another operator ⇒ is added for typing Π types in FBO, since we are only considering a single-sorted FBO. Also, every CC term is typed in FBO. For example, Πx: M.N in CC is translated as Πy.u ∶ t ⇒ v in FBO, where x, M and N correspond to y, t and u respectively under the translation.
Hence, as a result of our axiomatization of CC in FBO, we know that a countably infinite hierarchy of type universes for CC may be not necessary.
The author would like to thank M. O'Donnell and the other attendants of the Symposium on Constructivity in Computer Science (Trinity University, San Antonio, Texas, USA, June 19–22, 1991) for their comments; to thank M. Atkins and A. Dix for proof-readings and helpful comments on the presentation of this paper; to thank the Department of Computer Science, University of York (UK), for providing a part of travel expense to attend the Symposium.
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Sun, Y. (1992). Axiomatization of calculus of constructions. In: Myers, J.P., O'Donnell, M.J. (eds) Constructivity in Computer Science. Constructivity in CS 1991. Lecture Notes in Computer Science, vol 613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021086
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DOI: https://doi.org/10.1007/BFb0021086
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