Towards a Complete Picture of Lens Laws

Bidirectional transformation, also called lens, has played important roles in maintaining consistency in many fields of applications. A lens is specified by a pair of forward and backward functions which relate to each other in a consistent manner. The relation is formalized as a set of equations called lens laws. This report investigates precise dependencies among lens laws: which law implies another and which combination of laws implies another. The set of such implications forms a complicated graph structure. It would be helpful to check a well-definedness of bidirectional transformation in a lightweight way.