Codata in Action

Abstract

Computer scientists are well-versed in dealing with data structures. The same cannot be said about their dual: codata. Even though codata is pervasive in category theory, universal algebra, and logic, the use of codata for programming has been mainly relegated to representing infinite objects and processes. Our goal is to demonstrate the benefits of codata as a general-purpose programming abstraction independent of any specific language: eager or lazy, statically or dynamically typed, and functional or object-oriented. While codata is not featured in many programming languages today, we show how codata can be easily adopted and implemented by offering simple intercompilation techniques between data and codata. We believe codata is a common ground between the functional and object-oriented paradigms; ultimately, we hope to utilize the Curry-Howard isomorphism to further bridge the gap.

Decomposition Without Regret

“…The duality of data and codata. There is a line of work studying the duality of data and codata [Binder et al 2019;Downen et al 2019;Laforgue and Régis-Gianas 2017;Ostermann and Jabs 2018;Rendel et al 2015]. In particular, Binder et al [2019]'s work is most closely related and our formalization is greatly inspired by their work.…”

“…How to port their formalization to existing languages remains a problem as there is inadequate support for these features in existing languages. There are other transformation schemes between data to codata with a focus on compositionality [Downen et al 2019;Laforgue and Régis-Gianas 2017]. Unlike FOOD, Downen et al [2019] compile data to codata using the V pattern, which does not switch the dimension of extensibility.…”

“…There are other transformation schemes between data to codata with a focus on compositionality [Downen et al 2019;Laforgue and Régis-Gianas 2017]. Unlike FOOD, Downen et al [2019] compile data to codata using the V pattern, which does not switch the dimension of extensibility.…”

“…To address this issue, we propose a bidirectional transformation between functional and objectoriented decomposition based on the observation that restricted forms of functional and objectoriented decomposition are symmetric. Our bidirectional transformation is greatly inspired by Cook [2009]'s pure object-oriented programming and the line of work on the duality of data and codata [Binder et al 2019;Downen et al 2019;Ostermann and Jabs 2018;Rendel et al 2015]. The main novelty of our work is an automatic, type-directed transformation formalized in the core calculus FOOD, which captures the essence of Functional and Object-Oriented Decomposition.…”