Coalgebraic Aspects of Bidirectional Computation

Faris Abou-Saleh, James McKinna, Jeremy Gibbons

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We have previously (Bx, 2014; MPC, 2015) shown that several state-based bx formalisms can be captured using monadic functional programming, using the state monad together with possibly other monadic effects, giving rise to structures we have called monadic bx (mbx). In this paper, we develop a coalgebraic theory of state-based bx, and relate the resulting coalgebraic structures (cbx) to mbx. We show that cbx support a notion of composition coherent with, but conceptually simpler than, our previous mbx definition. Coalgebraic bisimulation yields a natural notion of behavioural equivalence on cbx, which respects composition, and essentially includes symmetric lens equivalence as a special case. Finally, we speculate on the applications of this coalgebraic perspective to other bx constructions and formalisms.
Original languageEnglish
Title of host publicationProceedings of the 4th International Workshop on Bidirectional Transformations co-located with Software Technologies: Applications and Foundations (STAF 2015)
EditorsAlcino Cunha, Ekkart Kindler
PublisherCEUR Workshop Proceedings
Number of pages15
Publication statusPublished - 2015

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