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Multilevel functions in Martin-Löf's type theory

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Programs as Data Objects

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 217))

Abstract

Multilevel arrays have been used in the VDL and VDM projects for representing abstract syntax trees. In the same way as the function type can be seen as a generalization of the array type, it is possible to generalize multilevel arrays to multilevel functions. They are general trees with finite depth but arbitrary branching. In this paper, a definition of multilevel functions is given in the framework of Martin-Löf's type theory. The formal rules associated with the new data type is given and justified using the semantics of type theory. The paper contains some programs for manipulating the functions and some data types (vectors, natural numbers, lists, binary trees and functions) are seen as special cases of multilevel functions.

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9. References

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Authors and Affiliations

  1. Programming Methodology Group Department of Computer Sciences, University of Göteborg Chalmers University of Technology, S-412 96, Göteborg, Sweden

    Bengt Nordström

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  1. Bengt Nordström
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Harald Ganzinger Neil D. Jones

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© 1986 Springer-Verlag Berlin Heidelberg

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Nordström, B. (1986). Multilevel functions in Martin-Löf's type theory. In: Ganzinger, H., Jones, N.D. (eds) Programs as Data Objects. Lecture Notes in Computer Science, vol 217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16446-4_12

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  • DOI: https://doi.org/10.1007/3-540-16446-4_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16446-3

  • Online ISBN: 978-3-540-39786-1

  • eBook Packages: Springer Book Archive

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