**Project:** LiquidEff

**Title:** Algebraic Foundations for Liquid Effects

**Period:** 1. 10. 2019 - 30. 9. 2021

**Host Institution:** University of Ljubljana, Faculty of Mathematics and Physics

**Principal investigator:** Danel Ahman

**Research activity:** Mathematics

**Project description:**

The goal of the LiquidEff project is to significantly advance the state of the art of type-based reasoning about the correctness of programs that can incorporate computational effects such as accessing memory, raising and handling exceptions, making nondeterministic and probabilistic choices, and communicating over a network---all integral features of modern mainstream programming languages.

The timeliness and importance of this project is demonstrated by the staggering cost of software failure in our increasingly digital world---one recent study put the number at $1.7 trillion worldwide in 2017 alone. While there already exist different approaches to type-based reasoning about the correctness of effectful programs, they all have their notable shortcomings: the approaches might be tied to a specific typing discipline, the supported effects can be limited, and the kind of properties one can reason about may be restricted.

In contrast, the LiquidEff project aims to develop a foundational, uniform, and widely applicable framework for type-based reasoning about effectful programs, based on the highly scalable and modular algebraic approach to modelling computational effects. Specifically, this project will 1) develop an expressive modal logic for reasoning about a wide range of computational effects; 2) show that this logic can express existing effect specification styles; 3) demonstrate that it can be used to design refinement type systems for lightweight type-based reasoning about effectful behaviour, thus giving a general account of the Liquid Effects effect-typing discipline that so far has been restricted to the state effect; 4) study the category-theoretic semantics of these foundations; 5) implement LiquidEff, an extension of the Eff language with a support for lightweight type-level reasoning about programs' behaviour; and 6) use LiquidEff to apply the developed theory in practice to case studies involving big data and asynchronous parallel programming.