dhil / phd-dissertation

A summary of my activities during the past four years

Foundations for programming and implementing effect handlers

A copy of my dissertation can be downloaded via my website.

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Submitted on May 30, 2021. Examined on August 13, 2021.

The board of examiners were

• Andrew Kennedy (Facebook London)
• Edwin Brady (University of St Andrews)
• Ohad Kammar (The University of Edinburgh)
• Stephen Gilmore (The University of Edinburgh)

Thesis structure

The dissertation is structured as follows.

Introduction

• Chapter 1 puts forth an argument for why effect handlers matter. Following this argument it provides a basic introduction to several different approaches to effectful programming through the lens of the state effect. In addition, it also declares the scope and contributions of the dissertation, and discusses some related work.

Programming

• Chapter 2 illustrates effect handler oriented programming by example by implementing a small operating system dubbed Tiny UNIX, which captures some essential traits of Ritchie and Thompson's UNIX. The implementation starts with a basic notion of file i/o, and then, it evolves into a feature-rich operating system with full file i/o, multiple user environments, multi-tasking, and more, by composing ever more effect handlers.

• Chapter 3 introduces a polymorphic fine-grain call-by-value core calculus, λ_b, which makes key use of Rémy-style row polymorphism to implement polymorphic variants, structural records, and a structural effect system. The calculus distils the essence of the core of the Links programming language. The chapter also presents three extensions of λ_b, which are λ_h that adds deep handlers, λ^† that adds shallow handlers, and λ^‡ that adds parameterised handlers.

Implementation

• Chapter 4 develops a higher-order continuation passing style translation for effect handlers through a series of step-wise refinements of an initial standard continuation passing style translation for λ_b. Each refinement slightly modifies the notion of continuation employed by the translation. The development ultimately leads to the key invention of generalised continuation, which is used to give a continuation passing style semantics to deep, shallow, and parameterised handlers.

• Chapter 5 demonstrates an application of generalised continuations to abstract machine as we plug generalised continuations into Felleisen and Friedman's CEK machine to obtain an adequate abstract runtime with simultaneous support for deep, shallow, and parameterised handlers.

Expressiveness

• Chapter 6 shows that deep, shallow, and parameterised notions of handlers can simulate one another up to specific notions of administrative reduction.

• Chapter 7 studies the fundamental efficiency of effect handlers. In this chapter, we show that effect handlers enable an asymptotic improvement in runtime complexity for a certain class of functions. Specifically, we consider the generic count problem using a pure PCF-like base language λ_b^→ (a simply typed variation of λ_b) and its extension with effect handlers λ_h^→. We show that λ_h^→ admits an asymptotically more efficient implementation of generic count than any λ_b^→ implementation.

Conclusions

• Chapter 8 concludes and discusses future work.

Appendices

• Appendix A contains a literature survey of continuations and first-class control. I classify continuations according to their operational behaviour and provide an overview of the various first-class sequential control operators that appear in the literature. The application spectrum of continuations is discussed as well as implementation strategies for first-class control.
• Appendix B contains a proof that shows the Get-get equation for state is redundant.
• Appendix C contains the proof details and gadgetry for the complexity of the effectful generic count program.
• Appendix D provides a sample implementation of the Berger count program and discusses it in more detail.

Building

To build the dissertation you need the Informatics thesis LaTeX class with the University of Edinburgh crests. Invoking make on the command line ought to produce a PDF copy of the dissertation named thesis.pdf, e.g.

$ make

Timeline

I submitted my thesis on May 30, 2021. It was examined on August 13, 2021, where I received pass with minor corrections. The revised thesis was submitted on December 22, 2021. It was approved on March 14, 2022. The final revision was submitted on March 23, 2022. I received my PhD award letter on March 24, 2022. My graduation ceremony took place in McEwan Hall on July 11, 2022.