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In mathematical logic and computer science, lambda calculus, also written as λ-calculus, is a formal system for function definition, function application and recursion. It was introduced by Alonzo Church in the 1930s as part of an investigation into the foundations of mathematics. After the original system was shown to be logically inconsistent (the Kleene–Rosser paradox), Church isolated and published in 1936 just the portion relevant to computation, what is now called the untyped lambda calculus. In 1940, he also introduced a computationally weaker but logically consistent system, known as the simply typed lambda calculus. In both typed and untyped versions, ideas from lambda calculus have found application in the fields of logic, recursion theory (computability), and linguistics, and have played an important role in the development of the theory of programming languages (with untyped lambda calculus being the original inspiration for functional programming, in particular Lisp, and typed lambda calculus serving as the foundation for modern type systems). This article deals primarily with the untyped lambda calculus. Informal descriptionFrom Wikipedia under the
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