Towards improved GADT reasoning in Scala

Abstract

Generalized algebraic data types (GADT) have been notoriously difficult to implement correctly in Scala. Both major Scala compilers, Scalac and Dotty, are currently known to have type soundness holes related to them. In particular, covariant GADTs have exposed paradoxes due to Scala's inheritance model. We informally explore foundations for GADTs within Scala's core type system, to guide a principled understanding and implementation of GADTs in Scala.CCS Concepts • Software and its engineering → Data types and structures; Classes and objects;

A Theory of Higher-Order Subtyping with Type Intervals (Extended Version)

“…Intervals with unconstrained bounds are useful, e.g. to encode generalized algebraic datatypes (GADTs) via first-class inequality constraints [Cretin and Rémy 2014;Parreaux et al 2019]. Consistency of such constraints cannot be established when a GADT is defined, only when it is instantiated.…”