Data refinement by calculation
Acta Informatica
Algebra of programming
Update semantics of relational views
ACM Transactions on Database Systems (TODS)
Communications of the ACM
Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire
Proceedings of the 5th ACM Conference on Functional Programming Languages and Computer Architecture
Calculating functional programs
Algebraic and coalgebraic methods in the mathematics of program construction
Relational lenses: a language for updatable views
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Combinators for bidirectional tree transformations: A linguistic approach to the view-update problem
ACM Transactions on Programming Languages and Systems (TOPLAS) - Special issue on POPL 2005
Strongly Typed Rewriting For Coupled Software Transformation
Electronic Notes in Theoretical Computer Science (ENTCS)
Bidirectionalization transformation based on automatic derivation of view complement functions
ICFP '07 Proceedings of the 12th ACM SIGPLAN international conference on Functional programming
Boomerang: resourceful lenses for string data
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A programmable editor for developing structured documents based on bidirectional transformations
Higher-Order and Symbolic Computation
Semantic subtyping: Dealing set-theoretically with function, union, intersection, and negation types
Journal of the ACM (JACM)
Algebraic Models for Bidirectional Model Synchronization
MoDELS '08 Proceedings of the 11th international conference on Model Driven Engineering Languages and Systems
Bidirectionalization for free! (Pearl)
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Recursive coalgebras from comonads
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Transformation of structure-shy programs with application to XPath queries and strategic functions
Science of Computer Programming
Type-safe two-level data transformation
FM'06 Proceedings of the 14th international conference on Formal Methods
A framework for point-free program transformation
IFL'05 Proceedings of the 17th international conference on Implementation and Application of Functional Languages
Coupled schema transformation and data conversion for XML and SQL
PADL'07 Proceedings of the 9th international conference on Practical Aspects of Declarative Languages
Bidirectional model transformations in QVT: semantic issues and open questions
MODELS'07 Proceedings of the 10th international conference on Model Driven Engineering Languages and Systems
Matching lenses: alignment and view update
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
Calculating with lenses: optimising bidirectional transformations
Proceedings of the 20th ACM SIGPLAN workshop on Partial evaluation and program manipulation
Incremental updates for efficient bidirectional transformations
Proceedings of the 16th ACM SIGPLAN international conference on Functional programming
Multifocal: a strategic bidirectional transformation language for XML schemas
ICMT'12 Proceedings of the 5th international conference on Theory and Practice of Model Transformations
Three complementary approaches to bidirectional programming
SSGIP'10 Proceedings of the 2010 international spring school conference on Generic and Indexed Programming
Relations as executable specifications: taming partiality and non-determinism using invariants
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
Programming language approaches to bidirectional transformation
Proceedings of the Twelfth Workshop on Language Descriptions, Tools, and Applications
Science of Computer Programming
Monadic combinators for "Putback" style bidirectional programming
Proceedings of the ACM SIGPLAN 2014 Workshop on Partial Evaluation and Program Manipulation
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Lenses are one the most popular approaches to define bidirectional transformations between data models. A bidirectional transformation with view-update, denoted a lens, encompasses the definition of a forward transformation projecting concrete models into abstract views, together with a backward transformation instructing how to translate an abstract view to an update over concrete models. In this paper we show that most of the standard point-free combinators can be lifted to lenses with suitable backward semantics, allowing us to use the point-free style to define powerful bidirectional transformations by composition. We also demonstrate how to define generic lenses over arbitrary inductive data types by lifting standard recursion patterns, like folds or unfolds. To exemplify the power of this approach, we "lensify" some standard functions over naturals and lists, which are tricky to define directly "by-hand" using explicit recursion.