Representing Molecules with Algebraic Data Types: Beyond SMILES and SELFIES
Oliver Goldstein, Samuel March
TL;DR
This work argues that string-based molecular representations (e.g., SMILES, SELFIES) fail to capture essential structure, symmetry, and 3D information needed for robust learning. It proposes a typed molecular representation built on Algebraic Data Types (ADTs) that encode Dietz-style constitution, 3D coordinates, and optional electronic structure via dedicated ADTs, enabling explicit invariants and deterministic edits. The approach is implemented in Haskell, with type-driven composition, and extended to probabilistic programming (LazyPPL) to support Bayesian design and symmetry-aware learning, including reaction representations. The contribution provides a principled, extensible semantic substrate for chemistry in ML pipelines, aiming to improve validity, interpretability, and integration with geometric deep learning and Bayesian inference. This ADT-based representation acts as a rigorous foundation for future interoperability, empirical evaluation, and extensions to complex bonding, polymers, and quantum descriptors, potentially enabling more reliable inverse design and molecular optimization workflows.
Abstract
Algebraic data types (ADTs) let a representation specify at the type level what molecular values are valid and what transformations are meaningful. We propose a molecular representation as a family of typed ADTs that separates (i) constitution (Dietz style bonding systems), (ii) 3D coordinates and stereochemistry, and (iii) electronic structure annotations. This separation makes invariants explicit, supports deterministic local edits, and provides hooks for symmetry aware and Bayesian modeling. These data structures allow us to consider how the representation constrains operations which may be performed over them. Types make invalid manipulations unrepresentable and make it easier to define meaningful priors/likelihoods over generative models (programs with sample and score operations). Unlike string based formats, the ADT exposes chemical structure directly; validity conditions (e.g., valence and symmetry constraints) can be enforced by construction and checked deterministically during transformations. We optionally attach electronic structure annotations (shell/subshell/orbital metadata) to atoms when such information is available; we do not attempt to compute orbitals in this work. We sketch Bayesian probabilistic programming via an integration with LazyPPL, a lazy probabilistic programming library; molecules can be made instances of a group under rotation to support geometric learning settings where molecular properties are invariant under rigid motions and relabellings; and the framework's flexibility is demonstrated through an extension to represent chemical reactions. We provide a Haskell library implementing the representation, released under an OSI approved open source license and archived with a DOI.