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Lambda Calculus and Lisp, part 1

The first of a series of envisioned blog posts on lambda calculus, and Lisp. It’s unclear exactly where to start: there is a whole heap of interesting issues, both theoretical and in terms of concrete implementations, which tangle and interconnect. A particular application of lambda calculus is a very salient part of my “day job” as a formal semanticist of natural language. And my interests in Emacs and lisp(s) feel like they tie in here as well—though that’s a question in itself which is probably as good of a starting point into this (planned) series of posts as any.

There is much to explore: origins of John McCarthy ‘s Lisp and Alonzo Church ‘s lambda calculus; encodings of the simple made complex by restriction to a limited set of tools; recursion, fixed points, and paradoxes; infinities, philosophy, and engineering. McCarthy’s initial aim for LISP was more akin that of the Turing Machine: as a formal abstraction describing a mathematical model whose components were simple and few but yet was capable of performing any (and all) arbitrary computational operation: The entities of formal logic are abstractions, invented because of their use in describing and systematizing facts of experience or observation, and their properties, determined in rough outline by this intended use, depend for their exact character on the arbitrary choice of the inventor.

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