Linguistic foundations for bidirectional transformations: invited tutorial

Computing is full of situations where two different structures must be "connected" in such a way that updates to each can be propagated to the other. This is a generalization of the classical view update problem, which has been studied for decades in the database community [11, 2, 22]; more recently, related problems have attracted considerable interest in other areas, including programming languages [42, 28, 34, 39, 4, 7, 33, 16, 1, 37, 35, 47, 49] software model transformation [43, 50, 44, 45, 12, 13, 14, 24, 25, 10, 51], user interfaces [38] and system configuration [36]. See [18, 17, 10, 30] for recent surveys. Among the fruits of this cross-pollination has been the development of a linguistic perspective on the problem. Rather than taking some view definition language as fixed (e.g., choosing some subset of relational algebra) and looking for tractable ways of "inverting" view definitions to propagate updates from view to source [9], we can directly design new bidirectional programming languages in which every expression defines a pair of functions mapping updates on one structure to updates on the other. Such structures are often called lenses [18]. The foundational theory of lenses has been studied extensively [20, 47, 26, 32, 48, 40, 15, 31, 46, 41, 21, 27], and lens-based language designs have been developed in several domains, including strings [5, 19, 3, 36], trees [18, 28, 39, 35, 29], relations [6], graphs [23], and software models [43, 50, 44, 12, 13, 14, 24, 25, 8]. These languages share some common elements with modern functional languages---in particular, they come with very expressive type systems. In other respects, they are rather novel and surprising. This tutorial surveys recent developments in the theory of lenses and the practice of bidirectional programming languages.