Bidirectionalization for Free with Runtime Recording: Or, a Light-Weight Approach to the View-Update Problem

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 laws. Over the years, a lot of effort has been made to offer better language support for programming such transformations. In particular, a technique known as bidirectionalization is able to analyze and transform unidirectional programs written in general purpose languages, and "bidirectionalize" them. Among others, a technique termed as semantic bidirectionalization proposed by Voigtländer stands out in term of user-friendliness. The unidirectional program can be written using arbitrary language constructs, as long as the function is polymorphic and the language constructs respect parametricity. The free theorems that follow from the polymorphic type of the program allow a kind of forensic examination of the transformation, determining its effect without examining its implementation. This is convenient, in the sense that the programmer is not restricted to using a particular syntax; but it does require the transformation to be polymorphic. In this paper, we lift this polymorphism requirement to improve the applicability of semantic bidirectionalization. Concretely, we provide a type class PackM γ α μ, which intuitively reads "a concrete datatype γ is abstracted to a type α, and the 'observations' made by a transformation on values of type γ are recorded by a monad μ". With PackM, we turn monomorphic transformations into polymorphic ones, that are ready to be bidirectionalized. We demonstrate our technique with a case study of standard XML queries, which were considered beyond semantic bidirectionalization because of their monomorphic nature

How functional programming mattered

In 1989 when functional programming was still considered a niche topic, Hughes wrote a visionary paper arguing convincingly ‘why functional programming matters’. More than two decades have passed. Has functional programming really mattered? Our answer is a resounding ‘Yes!’. Functional programming is now at the forefront of a new generation of programming technologies, and enjoying increasing popularity and influence. In this paper, we review the impact of functional programming, focusing on how it has changed the way we may construct programs, the way we may verify programs, and fundamentally the way we may think about programs

‘do’ unchained: embracing local imperativity in a purely functional language (functional pearl)

Purely functional programming languages pride themselves with reifying effects that are implicit in imperative languages into reusable and composable abstractions such as monads. This reification allows for more exact control over effects as well as the introduction of new or derived effects. However, despite libraries of more and more powerful abstractions over effectful operations being developed, syntactically the common \u27do\u27 notation still lags behind equivalent imperative code it is supposed to mimic regarding verbosity and code duplication. In this paper, we explore extending \u27do\u27 notation with other imperative language features that can be added to simplify monadic code: local mutation, early return, and iteration. We present formal translation rules that compile these features back down to purely functional code, show that the generated code can still be reasoned over using an implementation of the translation in the Lean 4 theorem prover, and formally prove the correctness of the translation rules relative to a simple static and dynamic semantics in Lean

Dynamic IFC Theorems for Free!

We show that noninterference and transparency, the key soundness theorems for dynamic IFC libraries, can be obtained "for free", as direct consequences of the more general parametricity theorem of type abstraction. This allows us to give very short soundness proofs for dynamic IFC libraries such as faceted values and LIO. Our proofs stay short even when fully mechanized for Agda implementations of the libraries in terms of type abstraction.Comment: CSF 2021 final versio

Applicative Bidirectional Programming with Lenses

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 laws. One way to reduce the development and maintenance effort of bidirectional transformations is to have specialized languages in which the resulting programs are bidirectional by construction---giving rise to the paradigm of bidirectional programming. In this paper, we develop a framework for applicative-style and higher-order bidirectional programming, in which we can write bidirectional transformations as unidirectional programs in standard functional languages, opening up access to the bundle of language features previously only available to conventional unidirectional languages. Our framework essentially bridges two very different approaches of bidirectional programming, namely the lens framework and Voigtlander’s semantic bidirectionalization, creating a new programming style that is able to bag benefits from both