# Verified instances for parallel functional programming

### Ryan Scott

# Abstract

LVish is a Haskell library that claims to offer deterministic parallelism. However, LVish is only deterministic up to a certain point, as several parts of the API rely on type class instances to check for equality, provide an ordering for keys in a map, and other operations. A rogue user can define “bad” instances that break invariants that LVish expects to hold true, and consequently, it is possible to violate determinism through this backdoor.

Our work presents a solution to this problem by integrating LVish code with Liquid Haskell’s refinement type–based proof system. With Liquid Haskell, we can require users who write type class instances for LVish to provide proofs that their instances satisfy the properties that we expect—for instance, that a parallel fold operation is actually associative. Equipped with this proof assistant, Haskell emerges as the first practical parallel programming language that also has an integrated proof system. We will demonstrate some examples of how one can prove simple properties in this system, and will examine what it takes to fully verify some LVish applications.