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An introduction to the Lambda Calculus
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Lambda Calculus

Build Status

Lambda Calculus is a tiny functional language for expressing computation based on function abstraction and application.

This project is intended to be an educational resource for learning and implementing functional programming languages.

Introduction to Lambda Calculus

Introductory material is provided. They can be found at

Extended Examples

More examples can be found in the test-suite, located at



A simple implementation of the untyped lambda calculus is included. It is written in Haskell and is implemented to be as easy to follow, at the possible expense of performance.


In order to build, you will need

  • GHC >= 8
  • stack


stack build

Then install:

stack install


Once the program is installed, you simply run it:


This will open a repl (read-eval-print loop) prompt

Lambda Calculator (0.5.0)
Type :h for help

You can start typing lambda calculus expressions and the program will evaluate them and print the result. Here are a few examples:

Lambda Calculator (0.5.0)
Type :h for help
λ > \x. x
λx. x
λ > (\x. x) n
λ > (\n f x. f (n f x)) (\f x. f (f x))
λf x. f (f (f x))
λ > :q

You can exit by typing the command :q.

Running Tests

In order to run the testsuite, run

stack test


Sean Gillespie


This project is licensed under the MIT License. See LICENSE

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