A Lisp Way to Type Theory and Formal Proofs

Frederic Peschanski (1)

1 APR - Algorithmes, Programmes et Résolution

In this paper we describe the LaTTe proof assistant, a software that promotes the Lisp notation for the formalization of and reasoning about mathematical contents. LaTTe is based on type theory and implemented as a Clojure library with top-level forms for specifying axioms, definitions, theorems and proofs. As a pure library, LaTTe can exploit the advanced interactive coding experience provided by modern development environments. Moreover, LaTTe enables a form of proving in the large by leveraging the Clojar/Maven ecosystem. It also introduces a very simple and concise domain-specific proof language that is deeply rooted in natural deduction proof theory. And when pure logic is not enough, the system allows to take advantage of the host language: a Lisp way to proof automation.

Mots clés: Type theory; Logic; Proof Assistant; Clojure

Domaines: Langage de programmation [cs.PL]

Frederic Peschanski. A Lisp Way to Type Theory and Formal Proofs. 10th European Lisp Symposium (ELS 2017), Apr 2017, Bruxelles, Belgium. ⟨10.1145/1235⟩. ⟨hal-01563373⟩