[2606.19936] Prismriver: Formalization of Music Theory and Algorithmic Composition in Lean 4 (opens in new tab)

Music theory obeys a rich set of mathematical rules and symmetries. These symmetries follow mathematical structure which can be verified and expressioned in the precise language of a proof assistant. In this paper, we present Prismriver, a formalization of music theory in Lean 4. By formalizing music theory in Lean 4, we open the door to verifiable algorithmic composition and accompaniment generation. We also enable the analysis of monadic analysis of structures in music.