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Higher-order unification, polymorphism, and subsorts

  • Chapter 7 Extension Of Unification And Narrowing Techniques
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Conditional and Typed Rewriting Systems (CTRS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 516))

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Abstract

This paper analyzes the problems that arise in extending Huet's higher-order unification algorithm from the simply typed λ-calculus to one with type variables. A simple, incomplete, but in practice very useful extension to Huet's algorithm is discussed. This extension takes an abstract view of types. As a particular instance we explore a type system with ml-style polymorphism enriched with a notion of sorts. Sorts are partially ordered and classify types, thus giving rise to an order-sorted algebra of types. Type classes in the functional language Haskell can be understood as sorts in this sense. Sufficient conditions on the sort structure to ensure the existence of principal types are discussed. Finally we suggest a new type system for the λ-calculus which may pave the way to a complete unification algorithm for polymorphic terms.

(Extended Abstract)

Research supported by ESPRIT BRA 3245, Logical Frameworks.

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Authors and Affiliations

  1. Computer Laboratory, University of Cambridge, Pembroke Street, CB2 3QG, Cambridge, England

    Tobias Nipkow

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  1. Tobias Nipkow
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S. Kaplan M. Okada

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© 1991 Springer-Verlag Berlin Heidelberg

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Nipkow, T. (1991). Higher-order unification, polymorphism, and subsorts. In: Kaplan, S., Okada, M. (eds) Conditional and Typed Rewriting Systems. CTRS 1990. Lecture Notes in Computer Science, vol 516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54317-1_112

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  • DOI: https://doi.org/10.1007/3-540-54317-1_112

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54317-6

  • Online ISBN: 978-3-540-47558-3

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