It is shown how the methods of universal algebra can be applied to build iterator lenses for structured data such as lists and trees, yielding lenses for operations like mapping, filtering, and concatenation from first principles.Expand

This work identifies a simple notion of "editable structure"--a set of states plus a monoid of edits with a partial monoid action on the states--and construct a semantic space of lenses between such structures, with natural laws governing their behavior.Expand

It is argued that existing work on differential privacy and type systems can be leveraged to build a programmable query mechanism that can express a wide range of queries while limiting what can be learned about individual customers.Expand

This work constructs a semantic space of edit lenses between “editable structures”—monoids of edits with a partial monoid action for applying edits—with natural laws governing their behavior, and presents a new symmetric formulation which works with descriptions of changes to structures, rather than with the structures themselves.Expand

The sheaves automata from Foster et al's "A Logic Your Typechecker Can Count On" are used and are based on Dal Zilio et al and provide an algorithm for deciding whether a complex edit preserves membership in a tree language.Expand

We consider a simple set of edit operations for unordered, edge-labeled trees, called information trees by Dal Zilio et al [DLM04]. We define tree languages using the sheaves automata from [FPS07]… Expand

We consider a simple set of edit operations for unordered, edge-labeled trees, called information trees by Dal Zilio et al [DLM04]. We define tree languages using the sheaves automata from [FPS07]… Expand

Lenses—bidirectional transformations between pairs of connected structures—have been extensively studied and are beginning to find their way into industrial practice. However, some aspects of their… Expand