We propose a novel approach to the view-update problem for tree-structured data: a domain-specific programming language in which all expressions denote bidirectional transformations on trees. In one direction, these transformations---dubbed lenses---map ...
Bidirectional Programming Languages
The need to edit source data through a view arises in a host of applications across many different areas of computing. Unfortunately, few existing systems provide support for updatable views. In practice, when they are needed, updatable views are usually implemented using two separate programs: one that computes the view from the source and another that handles updates. This rudimentary design is tedious for programmers, difficult to reason about, and a nightmare to maintain. This dissertation presents bidirectional programming languages, which provide an elegant and effective mechanism for describing updatable views. Unlike programs written in an ordinary language, which only work in one direction, programs in a bidirectional language can be run both forwards and backwards: from left to right, they describe functions that map sources to views, and from right to left, they describe functions that map updated views back to updated sources. Besides eliminating redundancy, these languages can be designed to ensure correctness, guaranteeing by construction that the two functions work well together. Starting from the foundations, we define a general semantic space of well-behaved bidirectional transformations called lenses. Then, building on this foundation, we describe a particular language for defining lenses on strings with syntax based on the familiar regular operators (union, concatenation, and Kleene star). We present extensions to the basic framework that address the subtle complications that arise when lenses are used to manipulate, data containing unimportant details, ordered data, and confidential data.
Boomerang | Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Bidirectional programming languages are a practical approach to the view update problem. Programs in these languages, called lenses, define both a view and an update policy - i.e., every program can be read as a function mapping sources to views as well ...
Quotient lenses | Proceedings of the 13th ACM SIGPLAN international conference on Functional programming
Bidirectional programming languages are a practical approach to the view update problem. Programs in these languages, called lenses, define both a view and an update policy - i.e., every program can be read as a function mapping sources to views as well ...
Bidirectionalization for free! (Pearl) | Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A bidirectional transformation consists of a function get that takes a source (document or value) to a view and a function put that takes an updated view and the original source back to an updated source, governed by certain consistency conditions ...
Categorical Data Structures for Technical Computing
Many mathematical objects can be represented as functors from finitely-presented categories $\mathsf{C}$ to $\mathsf{Set}$. For instance, graphs are functors to $\mathsf{Set}$ from the category with two parallel arrows. Such functors are known informally as $\mathsf{C}$-sets. In this paper, we describe and implement an extension of $\mathsf{C}$-sets having data attributes with fixed types, such as graphs with labeled vertices or real-valued edge weights. We call such structures "acsets," short for "attributed $\mathsf{C}$-sets." Derived from previous work on algebraic databases, acsets are a joint generalization of graphs and data frames. They also encompass more elaborate graph-like objects such as wiring diagrams and Petri nets with rate constants. We develop the mathematical theory of acsets and then describe a generic implementation in the Julia programming language, which uses advanced language features to achieve performance comparable with specialized data structures.
Introduction - Tree-sitter
Tree-sitter is a parser generator tool and an incremental parsing library. It can build a concrete syntax tree for a source file and efficiently update the syntax tree as the source file is edited. Tree-sitter aims to be:
An Algebraic Approach to Bi-directional Updating
In many occasions would one encounter the task of maintaining the consistency of two pieces of structured data that are related by some transform — synchronising bookmarks in different web browsers, the source and the view in an editor, or views in databases, to name a few. This paper proposes a formal model of such tasks, basing on a programming language allowing injective functions only. The programmer designs the transformation as if she is writing a functional program, while the synchronisation behaviour is automatically derived by algebraic reasoning. The main advantage is being able to deal with duplication and structural changes. The result will be integrated to our structure XML editor in the Programmable Structured Document project.
Delta 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 develop a point-free delta lens language with an explicit separation of shape and data.In contrast with the already known issue of data alignment, we identify the new problem of shape alignment and solve it by lifting standard recursion patterns such as folds and unfolds to delta lenses that use alignment to infer meaningful shape updates.
Algebraic data integration
In this paper, we develop an algebraic approach to data integration by combining techniques from functional programming, category theory, and database theory. In our formalism, database schemas and instances are algebraic (multi-sorted equational) theories of a certain form. Schemas denote categories, and instances denote their initial (term) algebras. The instances on a schema S form a category, S–Inst, and a morphism of schemas F : S → T induces three adjoint data migration functors: ΣF : S–Inst → T–Inst, defined by substitution along F, which has a right adjoint ΔF : T–Inst → S–Inst, which in turn has a right adjoint ΠF : S–Inst → T–Inst. We present a query language based on for/where/return syntax where each query denotes a sequence of data migration functors; a pushout-based design pattern for performing data integration using our formalism; and describe the implementation of our formalism in a tool we call AQL (Algebraic Query Language).
Bidirectional model transformations in QVT: semantic issues and open questions
We consider the OMG’s queries, views and transformations standard as applied to the specification of bidirectional transformations between models. We discuss what is meant by bidirectional transformations, and the model-driven development scenarios in which they are needed. We analyse the fundamental requirements on tools which support such transformations, and discuss some semantic issues which arise. In particular, we show that any transformation language sufficient to the needs of model-driven development would have to be able to express non-bijective transformations. We argue that a considerable amount of basic research is needed before suitable tools will be fully realisable, and suggest directions for this future research.
Symmetric lenses | Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A lens is a bidirectional transformation between a pair of connected data structures, capable of translating an edit on one structure into an appropriate edit on the other. Many varieties of lenses have been studied, but none, to date, has offered a ...
Functorial data migration
In this paper we present a simple database definition language: that of categories and functors. A database schema is a small category and an instance is a set-valued functor on it. We show that morphisms of schemas induce three “data migration functors”, which translate instances from one schema to the other in canonical ways. These functors parameterize projections, unions, and joins over all tables simultaneously and can be used in place of conjunctive and disjunctive queries. We also show how to connect a database and a functional programming language by introducing a functorial connection between the schema and the category of types for that language. We begin the paper with a multitude of examples to motivate the definitions, and near the end we provide a dictionary whereby one can translate database concepts into category-theoretic concepts and vice versa.
Relational foundations for functorial data migration | Proceedings of the 15th Symposium on Database Programming Languages
In this paper we present a simple database definition language: that of categories and functors. A database schema is a small category and an instance is a set-valued functor on it. We show that morphisms of schemas induce three ''data migration ...
Edit lenses
A lens is a bidirectional transformation between a pair of connected data structures, capable of translating an edit on one structure into an appropriate edit on the other. Many varieties of lenses have been studied, but none, to date, has offered a satisfactory treatment of how edits are represented. Many foundational accounts only consider edits of the form "overwrite the whole structure," leading to poor behavior in many situations by failing to track the associations between corresponding parts of the structures when elements are inserted and deleted in ordered lists, for example. Other theories of lenses do maintain these associations, either by annotating the structures themselves with change information or using auxiliary data structures, but every extant theory assumes that the entire original source structure is part of the information passed to the lens.We offer a general theory of edit lenses, which work with descriptions of changes to structures, rather than with the structures themselves. We identify 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. We show how a range of constructions from earlier papers on "state-based" lenses can be carried out in this space, including composition, products, sums, list operations, etc. Further, we show how to construct edit lenses for arbitrary containers in the sense of Abbott, Altenkirch, and Ghani. Finally, we show that edit lenses refine a well-known formulation of state-based lenses, in the sense that every state-based lens gives rise to an edit lens over structures with a simple overwrite-only edit language, and conversely every edit lens on such structures gives rise to a state-based lens.
Profunctor Optics, a Categorical Update
Optics are bidirectional data accessors that capture data transformation patterns such as accessing subfields or iterating over containers. Profunctor optics are a particular choice of representation supporting modularity, meaning that we can construct accessors for complex structures by combining simpler ones. Profunctor optics have previously been studied only in an unenriched and non-mixed setting, in which both directions of access are modelled in the same category. However, functional programming languages are arguably better described by enriched categories; and we have found that some structures in the literature are actually mixed optics, with access directions modelled in different categories. Our work generalizes a classic result by Pastro and Street on Tambara theory and uses it to describe mixed V-enriched profunctor optics and to endow them with V-category structure. We provide some original families of optics and derivations, including an elementary one for traversals. Finally, we discuss a Haskell implementation.
Generic deriving of generic traversals | Proceedings of the ACM on Programming Languages
Functional programmers have an established tradition of using traversals as a design pattern to work with recursive data structures. The technique is so prolific that a whole host of libraries have been designed to help in the task of automatically ...
