## Paper: A Logic for Algebraic Effects (at LICS 2008)

**Gordon D. Plotkin Matija Pretnar**

### Abstract

We present a logic for algebraic effects, based on the algebraic representation of computational effects by operations and equations. We begin with the a-calculus, a minimal calculus which separates values, effects, and computations and thereby canonises the order of evaluation. This is extended to obtain the logic, which is a classical first-order multi-sorted logic with higher-order value and computation types, as in Levy's call-by-push-value, a principle of induction over computations, a free algebra principle, and predicate fixed points. This logic embraces Moggi's computational lambda calculus, and also, via definable modalities, Hennessy-Milner logic, and evaluation logic, though Hoare logic presents difficulties.

### BibTeX

@InProceedings{PlotkinPretnar-ALogicforAlgebraicE, author = {Gordon D. Plotkin and Matija Pretnar}, title = {A Logic for Algebraic Effects}, booktitle = {Proceedings of the Twenty-Third Annual IEEE Symposium on Logic in Computer Science (LICS 2008)}, year = {2008}, month = {June}, pages = {118--129}, location = {Pittsburgh, PA, USA}, publisher = {IEEE Computer Society Press} }