Calchylus - Lambda Calculus with Hy
Project description
calchylus is a Hy module that is used to evaluate, and furthermore through this documentation, shine light to the basics of Lambda calculus (also written as λ-calculus).
Lambda calculus is a formal system in mathematical logic for expressing computation that is based on function abstraction and application using variable binding and substitution. -wikipedia.org
Intended audience is those who:
are interested in the theory and the history of the programming languages,
may have some experience in Python and/or Lisp,
but also those, who wants to narrow the gap between mathematical notation and programming languages, especially by means of logic.
Andrew Bayer writes in his blog post in 2016/08:
Traditional logic, and to some extent also type theory, hides computation behind equality.
Lambda calculus, on the other hand, reveals how the computation is made by manipulation of the lambda terms.
calchylus can also serve as a starting point for a mini programming language. Via custom macros representing well known Lambda forms, calchylus provides all necessary elements for boolean, integer, and list data types as well as conditionals, loops, variable setters, mathematical operators, and exemplary arithmetic functions like, summation, factorial, and fibonacci. Finally, one can expect to get a good understanding of combinatory logic, not the least of the fixed point combinator or ϒ combinator:
$$\Large ϒ = 𝜆x.(𝜆y.x \space (y \space y)) \space (𝜆y.x \space (y \space y))$$
Quick start
$ pip install hy calchylus
$ hy
(require [calchylus.lambdas [*]])
(with-alpha-conversion-and-macros L ,)
(L x y , (x (x (x (x (x y))))) a b) ; output: (a (a (a (a (a b)))))
(FIBONACCI FIVE) ; output: (x (x (x (x (x (x (x (x y))))))))
Project details
Release history Release notifications | RSS feed
Download files
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.