Is logical theory of computable functions.

Lambda calculus is a formal language capable of expressing arbitrary computable functions. In combination with types it forms a compact way to denote on the one hand functional programs and on the other hand mathematical proofs.

Lambda calculus is Turing complete, meaning you can express everything computable in a regular computer in lambda calculus.

You can formalize the entire lambda calculus inside of category theory via cartesian closed categories.

Caramel - Set of bidirectional, Haskell-inspired syntax-sugars that are expanded to, and contracted from, λ-Calculus terms.

LICK - Correct-by-construction implementation of the simply-typed lamba calculus' expressions, beta-reduction, and evaluation.

minitt-rs - Rust implementation of Mini-TT, a simple dependently-typed lambda calculus.

Mikrokosmosai - Educational λ-calculus interpreter.

path - Lambda calculus to explore type-directed program synthesis.

Lambda Zero - Minimalist pure lazy functional programming language.

Dedukti - Implementation of the λΠ-calculus modulo rewriting.

pLam - Interpreter for learning and exploring pure λ-calculus.