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Lambda Calculus – Rising Entropy
For background on how lambda diagrams work, look HERE. The equivalence of lambda calculus with Turing machine computations, and the logical limitations on computation, combine to give us interesting limitative results on lambda diagrams.
Henceforth, I will assume that a particular reduction strategy has been fixed, and so will only speak of reducibility and irreducibility, no absolutes and contingents. In fact, lambda calculus can be thought of as just one specific highly abstract functional programming language (along the lines of Haskell and Lisp). Every number has a “standard form”: λfx.f (f … (f x))), with N copies of f. The lambda diagram for this looks like an upside down ladder with N steps:
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