Spans of Delta Lenses
نویسندگان
چکیده
As part of an ongoing project to unify the treatment of symmetric lenses (of various kinds) as equivalence classes of spans of asymmetric lenses (of corresponding kinds) we relate the symmetric delta lenses of Diskin et al, with spans of asymmetric delta lenses. Because delta lenses are based on state spaces which are categories rather than sets there is further structure that needs to be accounted for and one of the main findings in this paper is that the required equivalence relation among spans is compatible with, but coarser than, the one expected. The main result is an isomorphism of categories between a category whose morphisms are equivalence classes of symmetric delta lenses (here called fb-lenses) and the category of spans of delta lenses modulo the new equivalence.
منابع مشابه
Unifying Set-Based, Delta-Based and Edit-Based Lenses
There are many different types of lenses, but largely they fall into the three classes of the title: set-based, delta-based and edit-based lenses. This paper develops some of the general relationships between those classes. The main results are that a category of set-based lenses is a full subcategory of a category of delta-based lenses determined by sending sets to codiscrete categories; that ...
متن کاملUniversal Updates for Symmetric Lenses
Asymmetric c-lenses are the special cases of asymmetric d-lenses (also called delta lenses) whose updates satisfy a universal property which in many applications ensures “least-change”. There has therefore been hope that symmetric c-lenses might characterize those symmetric dlenses which satisfy a similar universal property. This paper begins an analysis of symmetric c-lenses and their relation...
متن کاملSpans of lenses
Corresponding to the variety of notions of asymmetric lens, various notions of symmetric lens have been proposed. A common theory of the various asymmetric and symmetric lenses should result from a study of spans of asymmetric lenses. In order to define a category whose arrows are spans of asymmetric lenses, the fact that a cospan of asymmetric lenses may not have a pullback must be dealt with....
متن کاملDelta Lenses and Opfibrations
We compare the delta lenses, also known as d-lenses, of Diskin et al. with the c-lenses, known to be equivalent to opfibrations, already studied by the authors. Contrary to expectation a c-lens is a d-lens but not conversely. This result is surprising because d-lenses appear to provide the same information as c-lenses, and some more besides, suggesting that the implication would be the reverse ...
متن کاملDelta Lenses over Inductive Types
Existing bidirectional languages are either state-based or operation-based, depending on whether they represent updates as mere states or as sequences of edit operations. In-between both worlds are delta-based frameworks, where updates are represented using alignment relationships between states. In this paper, we formalize delta lenses over inductive types using dependent type theory and devel...
متن کامل