The model-driven development of systems involves multiple models, metamodels and transformations, and relationships between them. A bidirectional transformation (bx) is usually defined as a means of maintaining consistency between “two (or more)” models. This includes cases where one model may be generated from one or more others, as well as more complex (“symmetric”) cases where models record partially overlapping information. In recent years, binary bx, those relating two models, have been extensively studied. Multiary bx, those relating more than two models, have received less attention. In this paper, we consider how a multiary consistency relation may be defined in terms of binary consistency relations and how consistency restoration may be carried out on a network of models and relationships between them. In particular, we consider the circumstances under which we can prove non-interference between several bidirectional transformations that impact on the same model and how the use of a more refined notion of consistency can help in cases where this is not possible. In the process, we develop an abstract theory of parts of a model that are read or modified by a bidirectional transformation. We relate the work to megamodelling and discuss further research that is needed.

/pdf/maintaining-consistency-in-networks-of-models-bidirectional-s1m6mkjg58.pdf

Maintaining consistency in networks of models: bidirectional transformations in the large

Among the frameworks of bidirectional transformations proposed for addressing various synchronisation (consistency maintenance) problems, Foster et al.’s [2007] asymmetric lenses have influenced the design of a generation of bidirectional programming languages. Most of these languages are based on a declarative programming model, and only allow the programmer to describe a consistency specification with ad hoc and/or awkward control over the consistency restoration behaviour. However, synchronisation problems are diverse and require vastly different consistency restoration strategies, and to cope with the diversity, the programmer must have the ability to fully control and reason about the consistency restoration behaviour. The putback-based approach to bidirectional programming aims to provide exactly this ability, and this paper strengthens the putback-based position by proposing the first fully fledged reasoning framework for a bidirectional language — a Hoare-style logic for Ko et al.’s [2016] putback-based language BiGUL. The Hoare-style logic lets the BiGUL programmer precisely characterise the bidirectional behaviour of their programs by reasoning solely in the putback direction, thereby offering a unidirectional programming abstraction that is reasonably straightforward to work with and yet provides full control not achieved by previous approaches. The theory has been formalised and checked in Agda, but this paper presents the Hoare-style logic in a semi-formal way to make it easily understood and usable by the working BiGUL programmer.

An Axiomatic Basis for Bidirectional Programming

Software frequently converts data from one representation to another and vice versa. Naively specifying both conversion directions separately is error prone and introduces conceptual duplication. Instead, bidirectional programming techniques allow programs to be written which can be interpreted in both directions. However, these techniques often employ unfamiliar programming idioms via restricted, specialised combinator libraries. Instead, we introduce a framework for composing bidirectional programs monadically, enabling bidirectional programming with familiar abstractions in functional languages such as Haskell. We demonstrate the generality of our approach applied to parsers/printers, lenses, and generators/predicates. We show how to leverage compositionality and equational reasoning for the verification of round-tripping properties for such monadic bidirectional programs.

/pdf/composing-bidirectional-programs-monadically-1n7nfpeq31.pdf

Composing Bidirectional Programs Monadically

Abstract Invertibility is a fundamental concept in computer science, with various manifestations in software development (serializer/deserializer, parser/printer, redo/undo, compressor/decompressor, and so on). Full invertibility necessarily requires bijectivity, but the direct approach of composing bijective functions to develop invertible programs is too restrictive to be useful. In this paper, we take a different approach by focusing on partially invertible functions—functions that become invertible if some of their arguments are fixed. The simplest example of such is addition, which becomes invertible when fixing one of the operands. More involved examples include entropy-based compression methods (e.g., Huffman coding), which carry the occurrence frequency of input symbols (in certain formats such as Huffman tree), and fixing this frequency information makes the compression methods invertible. We develop a language Sparcl for programming such functions in a natural way, where partial invertibility is the norm and bijectivity is a special case, hence gaining significant expressiveness without compromising correctness. The challenge in designing such a language is to allow ordinary programming (the “partially” part) to interact with the invertible part freely, and yet guarantee invertibility by construction. The language Sparcl is linear-typed and has a type constructor to distinguish data that are subject to invertible computation and those that are not. We present the syntax, type system, and semantics of the language and prove that Sparcl correctly guarantees invertibility for its programs. We demonstrate the expressiveness of Sparcl with examples including tree rebuilding from preorder and inorder traversals, Huffman coding, arithmetic coding, and LZ77 compression. 

pdf/scp-sparcl-scp-a-language-for-partially-invertible-y5gcygnmro.pdf

<scp>Sparcl</scp>: A language for partially invertible computation

https://dl.acm.org/doi/pdf/10.1145/3158129

An axiomatic basis for bidirectional programming

A bidirectional transformation is a pair of mappings between source and view data objects, one in each direction. When the view is modified, the source is updated accordingly with respect to some l...

/pdf/applicative-bidirectional-programming-with-lenses-5e3em6sp81.pdf

Applicative bidirectional programming with lenses

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Applicative bidirectional programming with lenses