# Matija Pretnar: Explicit Effect Subtyping

Source: Mathematics and theoretical computing seminar

Joint work with Amr Hany Saleh, Georgios Karachalias, and Tom Schrijvers

**Abstract:** As popularity of algebraic effects and handlers increases, so does a demand for their efficient execution. Eff, an ML-like language with native support for handlers, has a subtyping-based effect system on which an effect-aware optimising compiler could be built. Unfortunately, in our experience, implementing optimisations for Eff is overly error-prone because its core language is implicitly-typed, making code transformations very fragile.

To remedy this, we present an explicitly-typed polymorphic core calculus for algebraic effect handlers with a subtyping-based type-and-effect system. It reifies appeals to subtyping in explicit casts with coercions that witness the subtyping proof, quickly exposing typing bugs in program transformations.

Our typing-directed elaboration comes with a constraint-based inference algorithm that turns an implicitly-typed Eff-like language into our calculus. Moreover, all coercions and effect information can be erased in a straightforward way, demonstrating that coercions have no computational content.