A Tangled Web of 12 Lens Laws

摘要

Bidirectional transformation has played important roles in broad areas, database management, programming language, and model-driven development after Foster et al. revisited view updating problems introduced by Bancilhon and Spyratos. They introduced the concept of (asymmetric) lens as a pair of a forward get and a backward put functions to synchronize a source data and its view consistently. For the get and put functions to be consistent, they should satisfy several lens laws such as the (STRONGGETPUT), (GETPUT), (PUTGET) and (PUTPUT) laws. By combining some of these lens laws, we can represent how consistent a lens satisfying the laws is. Fischer et al. has introduced nine meaningful weaker lens laws to give a "clear picture" of the laws where they show relations among lens laws, for example, that one law implies another and combination of two laws is equivalent to combination of the other three laws. This paper gives more precise relationship among 12 lens laws that have been presented in literature. The relationship makes an intertwined implication diagram like a tangled web. The results can be used for easily verifying the desirable lens laws.