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Lambda Calculus Expressions Reduced with REGEX

Last modified: 2016-09-25

#### Abstract

The paper aim is to demonstrate the usefulness of the lambda calculus in programming. In this respect we used javascript alongside with regular expressions to accomplish the substitutions. Firstly there are presented the structure and syntax of the lambda calculus. After that, we provided examples of substitutions on the most popular lambda functions: successor, plus, multiply and the Y combinator. For each example we provided the equivalent code in javascript for each rule of substitution we had used.

#### Keywords

lambda, redex, regex, alpha/beta reduction.

#### References

[1] Church, A. (1932), A set of postulates for the foundation of logic part I, Annals of Mathematics 33 pp. 346–366, http://www.jstor.org/stable/1968702 Electronic Edition. URL http://www.jstor.org/stable/1968702

[www1, 2016] Lambda calculus, https://en.wikipedia.org/wiki/Lambda_calculus

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[www3, 2013] Mathematics Stack Exchange, http://math.stackexchange.com/questions/595518/how-to-multiply-in-lambda-calculus

[www4, 2011] Rehno Lindeque, PLT: Lambda Calculus - Basics 3 (Operations on church numerals), https://www.youtube.com/watch?v=j6lkjd9woMw

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