Functional Programming in Lean

by David Thrane Christiansen

This is an in-progress book on using Lean 4 as a programming language. The most recent release is found at, and it will be updated monthly. This version of the text is written for Lean 4 release nightly-2023-03-11.

Release history

March, 2023

This release adds a chapter on programming with dependent types and indexed families.

January, 2023

This release adds a chapter on monad transformers that includes a description of the imperative features that are available in do-notation.

December, 2022

This release adds a chapter on applicative functors that additionally describes structures and type classes in more detail. This is accompanied with improvements to the description of monads. The December 2022 release was delayed until January 2023 due to winter holidays.

November, 2022

This release adds a chapter on programming with monads. Additionally, the example of using JSON in the coercions section has been updated to include the complete code.

October, 2022

This release completes the chapter on type classes. In addition, a short interlude introducing propositions, proofs, and tactics has been added just before the chapter on type classes, because a small amount of familiarity with the concepts helps to understand some of the standard library type classes.

September, 2022

This release adds the first half of a chapter on type classes, which are Lean's mechanism for overloading operators and an important means of organizing code and structuring libraries. Additionally, the second chapter has been updated to account for changes in Lean's stream API.

August, 2022

This third public release adds a second chapter, which describes compiling and running programs along with Lean's model for side effects.

July, 2022

The second public release completes the first chapter.

June, 2022

This was the first public release, consisting of an introduction and part of the first chapter.

About the Author

David Thrane Christiansen has been using functional languages for twenty years, and dependent types for ten. Together with Daniel P. Friedman, he wrote The Little Typer, an introduction to the key ideas of dependent type theory. He has a Ph.D. from the IT University of Copenhagen. During his studies, he was a major contributor to the first version of the Idris language. Since leaving academia, he has worked at Galois in Portland, Oregon and Deon Digital in Copenhagen, Denmark. At the time of writing, he is the Executive Director of the Haskell Foundation.