Since the late 1990s, numerous proposals have emerged for type systems that describe the topology of objects — that is, how objects are connected through references in memory, or which objects or closures may read/write/call other objects. By encoding such properties into types, these systems provide powerful guarantees that can be leveraged across a wide range of critical concerns, such as garbage collection, concurrency, mutable concurrent sharing, program architecture, program verification, capabilities tracking, and security.

These ideas have since moved beyond theory, finding their way — in various forms — into several mainstream and research programming languages, including Rust, Scala 3, X10, and Pony, among others.

In this tutorial, we survey the landscape of these proposals, with a deliberate focus on the invariants they guarantee rather than the mechanisms by which those invariants are enforced (whether statically or dynamically). We carefully distinguish between the different kinds of restrictions each system imposes — such as uniqueness, immutability, isolation, domination, or articulation points — and examine the concrete benefits each restriction unlocks for the concerns we listed earlier. This tutorial is intended to build intuition across the design space, and assumes no prior familiarity with any one specific language.

Sophia Drossopoulou is a Professor of Programming Languages at Imperial College London. She obtained her PhD at KIT (Karlsruhe), and has held positions at KIT, Microsoft Research, and Meta. Her research spans programming language specification, design, and implementation, with contributions across a broad range of topics: ownership types, session types, concurrency, wildcard types, traits, garbage collection, dynamic linking, object reclassification (a precursor to type state), object to class based transition (a precursor to gradual types), program verification, and object capabilities.