Web Reference: May 2, 2025 · Programs in the lambda calculus are called lambda expressions (abbreviated \ (\lambda exp\)), of which there are only three kinds. In fact, here is a complete BNF grammar for the lambda calculus: In recent years, there has been a renewed interest in categorical approaches to the \ (\lambda\)-calculus, which have mainly focused on typed versions of the \ (\lambda\)-calculus (see sections 8.2 and 9.1.2 below) but also include the untyped \ (\lambda\)-calculus discussed in this article. The lambda calculus (or λ-calculus) was introduced by Alonzo Church and Stephen Cole Kleene in the 1930s to describe functions in an unambiguous and compact manner.
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