Abstract
This paper consists of two parts. In the first part we argue that an appropriate “naive type theory” should replace naive set theory (as understood in Halmos’ book) in everyday mathematical practice, especially in teaching mathematics to Computer Science students. In the second part we make the first step towards developing such a theory: we discuss a certain pure type system with powerset types. While the system only covers very initial aspects of the intended theory, we believe it can be used as an initial formalism to be further developed. The consistency of this basic system is established by proving strong normalization.
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Partly supported by the Polish Government Grant 3 T11C 002 27, and by the EU Coordination Action 510996 “Types for Proofs and Programs”.
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Kozubek, A., Urzyczyn, P. (2008). In the Search of a Naive Type Theory. In: Miculan, M., Scagnetto, I., Honsell, F. (eds) Types for Proofs and Programs. TYPES 2007. Lecture Notes in Computer Science, vol 4941. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68103-8_8
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DOI: https://doi.org/10.1007/978-3-540-68103-8_8
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