Abstract
A typechecker for a typed λ-calculus having implicit arguments is presented. The typechecker works in such a way that the uniqueness of implicit arguments is always preserved during reduction. Consequently, when it compares two terms by reduction, it can reduce them without inferring implicit arguments. Before describing the typechecker, we analyze various situations where the uniqueness of implicit arguments is not preserved by naïvely defined reduction.
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References
H. Barendregt. Introduction to generalised type systems. Journal of Functional Programming, Vol.1, No.2, pp.124–154, 1991.
V. Breazu-Tannen, T. Coquand, C. A. Gunter and A. Scedrov. Inheritance as Implicit Coercion. Information and Computation, Vol.93, No.1, pp.172–221, 1991.
R. Harper and J. C. Mitchell. On the type structure of standard ML. ACM Transactions on Programming Languages and Systems, Vol.15, No.2, pp.211–252, 1993.
Z. Luo and R. Pollack. LEGO proof development system: User's manual. Technical Report ECS-LFCS-92-211, LFCS, Computer Science Department, University of Edinburgh, 1992.
D. Miller. A logic programming language with lambda-abstraction, function variables, and simple unification. Journal of Logic and Computation, Vol.1, No.4, pp.497–536, 1991.
D. Miller. Unification of simply typed lambda-terms as logic programming. In K. Furukawa, editor, In Proceedings of the Eighth International Conference on Logic Programming, MIT Press, 1991.
D. Miller. Unification under a mixed prefix. Journal of Symbolic Computation, Vol.14, No.4, pp.321–358, 1992.
F. Pfenning. Elf: A language for logic definition and verified metaprogramming. In Proceedings of the Fourth Annual Symposium on Logic in Computer Science, Asilomar, California, 1989.
F. Pfenning. Logic programming in the LF logical Framework, In Proceedings of the First Workshop on Logical Frameworks, 1991.
R. Pollack. Implicit syntax. LFCS, Computer Science Department, University of Edinburgh, 1992.
M. H. Takahashi. Parallel Reductions in λ-Calculus. Journal of Symbolic Computation, Vol.7, pp.113–123, 1989.
H. Tsuiki. A normalizing calculus with subtyping and overloading. Theoretical Aspects of Computer Software 94, Lecture Notes in Computer Science, to appear.
L. S. van Benthem Jutting. Typing in pure type systems. Information and Computation, Vol.105, pp.30–41, 1993.
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© 1994 Springer-Verlag Berlin Heidelberg
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Hagiya, M., Toda, Y. (1994). On implicit arguments. In: Jones, N.D., Hagiya, M., Sato, M. (eds) Logic, Language and Computation. Lecture Notes in Computer Science, vol 792. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032392
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DOI: https://doi.org/10.1007/BFb0032392
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