Concept-based design is a new emerging formalism that uses concepts to facilitate the construction of modular and reusable software. Concepts are independent and generic units of functionality that can be composed to form complex applications. This work presents Conceptual, a domain-specific language for defining and composing concepts. A compiler from this language to Alloy6 is implemented, establishing a way to model and validate concept specifications of software formally. The practical application of Conceptual is examined qualitatively by leveraging Alloy’s analysis tools to reason about existing concept specifications in the literature.