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Semantics of constructions (I) — The traditional approach

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Abstract

It is well known that impredicative type systems do not have set theoretical semantics. This paper takes a look at semantics of inductive types in impredicative type systems. A generalized inductive type is interpreted as an omega set generated by effectivizing a certain rule set. The result provides a semantic justification of inductive types in the calculus of constructions.

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Authors and Affiliations

  1. Department of Computer Science, Shanghai Jiaotong University, 200030, Shanghai, P. R. China

    Fu Yuxi

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  1. Fu Yuxi
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Correspondence to Fu Yuxi.

Additional information

This work is funded by the National Natural Science Foundation of China (No. 69973030). It is also supported by BASICS, Center of Basic Studies in Computing Science, sponsored by Shanghai Education Committee. BASICS is affiliated to the Department of Computer Science at Shanghai Jiaotong University.

FU Yuxi is a professor at the Department of Computer Science of Shanghai Jiaotong University. He received his Ph.D. degree in 1992 from Manchester University, England. His current research interest covers concurrency theory, type theory and semantics.

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Fu, Y. Semantics of constructions (I) — The traditional approach. J. Comput. Sci. & Technol. 16, 13–24 (2001). https://doi.org/10.1007/BF02948849

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