Notions of bidirectional computation and entangled state monads

Faris Abou-Saleh, James Cheney, Jeremy Gibbons*, James McKinna, Perdita Stevens

*Corresponding author for this work

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

9 Citations (Scopus)


Bidirectional transformations (bx) support principled consistency maintenance between data sources. Each data source corresponds to one perspective on a composite system, manifested by operations to ‘get’ and ‘set’ a view of the whole from that particular perspective. Bx are important in a wide range of settings, including databases, interactive applications, and model-driven development. We show that bx are naturally modelled in terms of mutable state; in particular, the ‘set’ operations are stateful functions. This leads naturally to considering bx that exploit other computational effects too, such as I/O, nondeterminism, and failure, all largely ignored in the bx literature to date. We present a semantic foundation for symmetric bidirectional transformations with effects.We build on the mature theory of monadic encapsulation of effects in functional programming, develop the equational theory and important combinators for effectful bx, and provide a prototype implementation in Haskell along with several illustrative examples.

Original languageEnglish
Title of host publicationMathematics of Program Construction. MPC 2015
EditorsJanis Voigtländer, Ralf Hinze
Number of pages28
ISBN (Electronic)9783319197975
ISBN (Print)9783319197968
Publication statusPublished - 2015
Event12th International Conference on Mathematics of Program Construction 2015 - Konigswinter, Germany
Duration: 29 Jun 20151 Jul 2015

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference12th International Conference on Mathematics of Program Construction 2015
Abbreviated titleMPC 2015

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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