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A lambda-calculus with patterns. (English) Zbl 1070.03506

Proceedings of the international conference on algebra and its applications (ICAA 2002), Chulalongkorn University, Bangkok, Thailand, March 18–20, 2002. Bangkog: Chulalongkorn University, Department of Mathematics (ISBN 970-13-2182-1). 266-277 (2002).
Summary: There are some functions that cannot be represented by \(\lambda\)-terms in the original \(\lambda\)-calculus. By adding patterns, which will be used to specify the form of the argument accepted and to extract subterms of the argument, and by modifying the definition of terms to allow a kind of “definition by cases”, we can construct a new \(\lambda\)-calculus. This new \(\lambda\)-calculus can describe a larger class of functions, yet still satisfies all the basic properties of the original \(\lambda\)-calculus, including the Church-Rosser theorem.
For the entire collection see [Zbl 1058.16501].

MSC:

03B40 Combinatory logic and lambda calculus
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