It captures the features of a wide variety of programming languages. Encode a rational number $q$ as a pair $(k,a)$ where $k$ is an integer, $a$ is natural, and $q = k / (1 a)$. This paper is a concise and painless introduction to the -calculus. Lambda calculus (also written as -calculus or called 'the lambda calculus') is a formal system in mathematical logic and computer science for expressing computation by way of variable binding and substitution.But a more complicated question is how to encode reals. The case of complex numbers is similar in the sense that a complex number is encoded as a pair of reals. Mul = \k m -> (fst k * fst m snd k * snd m, fst k * snd m snd k * fst m) Then you can define the usual operations on integers as (using Haskell notation for $\lambda$-calculus): neg = \k -> (snd k, fst k)Īdd = \k m -> (fst k fst m, snd k snd m) Represent an integer $k$ as a pair of natural numbers $(a,b)$ such that $k = a - b$. Lambda-reduction (also called lambda conversion) refers to all three. Three theorems of lambda calculus are -conversion, -conversion, and -conversion. In the lambda calculus, is defined as the abstraction operator. It is a system for ma-nipulatingfunctions as expressions. First encode natural numbers and pairs, as described by jmad. Lambda Calculus A formal logic developed by Alonzo Church and Stephen Kleene to address the computable number problem. 1.2 The lambda calculus The lambda calculus is a theory of functions as formulas.
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