Quantitative Logics for Equivalence of Effectful Programs
Abstract
In order to reason about effects, we can define quantitative formulas to describe behavioural aspects of effectful programs. These formulas can for example express probabilities that (or sets of correct starting states for which) a program satisfies a property. Fundamental to this approach is the notion of quantitative modality, which is used to lift a property on values to a property on computations. Taking all formulas together, we say that two terms are equivalent if they satisfy all formulas to the same quantitative degree. Under sufficient conditions on the quantitative modalities, this equivalence is equal to a notion of Abramsky's applicative bisimilarity, and is moreover a congruence. We investigate these results in the context of Levy's callbypushvalue with general recursion and algebraic effects. In particular, the results apply to (combinations of) nondeterministic choice, probabilistic choice, and global store.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.11771
 Bibcode:
 2019arXiv190411771V
 Keywords:

 Computer Science  Logic in Computer Science
 EPrint:
 Submitted to MFPS 2019, 20 pages