lambdaPi

lambdapi is a proof assistant and interactive theorem prover designed for formalizing mathematics within a dependent type theory. It is based on the lambda-Pi calculus modulo rewriting, a framework that extends the standard dependent lambda calculus with user-defined rewrite rules integrated into type-checking. This design enables compact formalizations and flexible reasoning while maintaining soundness through a trusted kernel.

Its core features include a dependent type system with Pi-types, universes, and higher-order abstraction, together with a rewriting mechanism that allows definitions to be simplified by specified rules. The system provides an interactive top-level for building definitions, theorems, and proofs, and it supports modular development with components and scopes. A kernel enforces type correctness and reduces terms to normal forms under rewriting.

lambdapi is used in research on type theory and the formalization of mathematics. It is associated with the Dedukti family of proof systems and can interface with the Dedukti kernel for checking and sharing proofs across systems. Documentation and source code are available through public repositories, and the project is developed by researchers in the type-theory community.