Rotprover

Rotprover is an automated theorem prover designed to reason about rotational symmetries and geometric constructions. It aims to formalize and verify theorems in Euclidean geometry in which rotations and circular relations are central. The system provides a domain-specific language for geometric objects and a proof engine that combines symbolic computation with decision procedures for algebraic and trigonometric relations.

Rotprover's core language supports definitions of points, lines, circles, and transformations, with explicit syntax for rotations, rotation compositions, and fixed-angle relationships. The underlying logic blends first-order geometry with constructive reasoning, enabling both automated proof search and interactive tactics. The engine uses a combination of rewriting rules, geometric invariants, and algebraic solvers to handle congruence, angle chasing, and symmetry arguments.

Architecture includes a geometry kernel that maintains a symbolic model of a figure; a tactic layer for proof automation; a checker that produces a verified proof object; and backends that connect to external solvers. The project emphasizes modularity, allowing new rotation-based rules, transformation libraries, and geometry solvers to be plugged in.

Rotprover is used in research and education to explore automated reasoning about geometry and to assist in teaching geometric problem solving. It supports interactive proof development, automated discharge of routine theorems, and exporting of proofs to readable formats. Visualizations of constructions and proof steps aid comprehension.

Limitations include scalability challenges for large or highly nonlinear configurations, and the need for user guidance when working with synthetic or non-standard geometries. The project remains under active development, with ongoing work on expanding the rotation toolkit, improving solver integration, and enhancing proof tracing.