The article investigates behavioural equivalence between programs in a call-by-value functional language extended with a signature of (algebraic) effect-triggering operations. Two programs are considered as being behaviourally equivalent if they enjoy the same behavioural properties. To formulate this, we define a logic whose formulas specify behavioural properties. A crucial ingredient is a collection of modalities expressing effect-specific aspects of behaviour. We give a general theory of such modalities. If two conditions, openness and decomposability , are satisfied by the modalities, then the logically specified behavioural equivalence coincides with a modality-defined notion of applicative bisimilarity, which can be proven to be a congruence by a generalisation of Howe’s method. We show that the openness and decomposability conditions hold for several examples of algebraic effects: nondeterminism, probabilistic choice, global store, and input/output.

@article{paperbot698,
  title = {Behavioural Equivalence via Modalities for Algebraic Effects},
  author = {Alex Simpson and Niels Voorneveld},
  journal = {ACM Transactions on Programming Languages and Systems},
  volume = {42},
  number = {1},
  year = {2019},
  doi = {10.1145/3363518}
}