PhD Abstracts

Many students complete PhDs in functional programming each year. As a service to the community, twice per year the Journal of Functional Programming publishes the abstracts from PhD dissertations completed during the previous year. The abstracts are made freely available on the JFP website, i.e. not behind any paywall. They do not require any transfer of copyright, merely a license from the author. A dissertation is eligible for inclusion if parts of it have or could have appeared in JFP, that is, if it is in the general area of functional programming. The abstracts are not reviewed. We are delighted to publish five abstracts in this round and hope that JFP readers will find many interesting dissertations in this collection that they may not otherwise have seen. If a student or advisor would like to submit a dissertation abstract for publication in this series, please contact the series editor for further details. Graham Hutton PhD Abstract Editor

On being a PhD student of Robert Harper

The Robert Harper Festschrift includes articles by three of Bob’s students and colleagues—Karl Crary, Andrzej Filinski, and Jonathan Sterling. Each of these articles touches on themes that are central to Bob’s research: module system design, proof-directed program development, and (to use Bob’s term) “computational trinitarianism”. In this foreword to the Festschrift, we have additionally compiled reminiscences of Bob Harper from his PhD students. We invited them to reflect on their experiences working with and learning from Bob. We believe these reminiscences, presented in chronological order of dissertation date, deliver a most fitting tribute to Bob in honor of his 64th birthday.

Relational cost analysis in a functional-imperative setting

Relational cost analysis aims at formally establishing bounds on the difference in the evaluation costs of two programs. As a particular case, one can also use relational cost analysis to establish bounds on the difference in the evaluation cost of the same program on two different inputs. One way to perform relational cost analysis is to use a relational type-and-effect system that supports reasoning about relations between two executions of two programs. Building on this basic idea, we present a type-and-effect system, called ARel, for reasoning about the relative cost (the difference in the evaluation cost) of array-manipulating, higher order functional-imperative programs. The key ingredient of our approach is a new lightweight type refinement discipline that we use to track relations (differences) between two mutable arrays. This discipline combined with Hoare-style triples built into the types allows us to express and establish precise relative costs of several interesting programs that imperatively update their data. We have implemented ARel using ideas from bidirectional type checking.

Gradual type theory

Gradually typed languages are designed to support both dynamically typed and statically typed programming styles while preserving the benefits of each. Sound gradually typed languages dynamically check types at runtime at the boundary between statically typed and dynamically typed modules. However, there is much disagreement in the gradual typing literature over how to enforce complex types such as tuples, lists, functions and objects. In this paper, we propose a new perspective on the design of runtime gradual type enforcement: runtime type casts exist precisely to ensure the correctness of certain type-based refactorings and optimizations. For instance, for simple types, a language designer might desire that beta-eta equality is valid. We show that this perspective is useful by demonstrating that a cast semantics can be derived from beta-eta equality. We do this by providing an axiomatic account program equivalence in a gradual cast calculus in a logic we call gradual type theory (GTT). Based on Levy’s call-by-push-value, GTT allows us to axiomatize both call-by-value and call-by-name gradual languages. We then show that we can derive the behavior of casts for simple types from the corresponding eta equality principle and the assumption that the language satisfies a property called graduality, also known as the dynamic gradual guarantee. Since we can derive the semantics from the assumption of eta equality, we also receive a useful contrapositive: any observably different cast semantics that satisfies graduality must violate the eta equality. We show the consistency and applicability of our axiomatic theory by proving that a contract-based implementation using the lazy cast semantics gives a logical relations model of our type theory, where equivalence in GTT implies contextual equivalence of the programs. Since GTT also axiomatizes the dynamic gradual guarantee, our model also establishes this central theorem of gradual typing. The model is parameterized by the implementation of the dynamic types, and so gives a family of implementations that validate type-based optimization and the gradual guarantee.

Real-time MLton: A Standard ML runtime for real-time functional programs

There is a growing interest in leveraging functional programming languages in real-time and embedded contexts. Functional languages are appealing as many are strictly typed, amenable to formal methods, have limited mutation, and have simple but powerful concurrency control mechanisms. Although there have been many recent proposals for specialized domain-specific languages for embedded and real-time systems, there has been relatively little progress on adapting more general purpose functional languages for programming embedded and real-time systems. In this paper, we present our current work on leveraging Standard ML (SML) in the embedded and real-time domains. Specifically, we detail our experiences in modifying MLton, a whole-program optimizing compiler for SML, for use in such contexts. We focus primarily on the language runtime, reworking the threading subsystem, object model, and garbage collector. We provide preliminary results over a radar-based aircraft collision detector ported to SML.

Linear capabilities for fully abstract compilation of separation-logic-verified code

Separation logic is a powerful program logic for the static modular verification of imperative programs. However, dynamic checking of separation logic contracts on the boundaries between verified and untrusted modules is hard because it requires one to enforce (among other things) that outcalls from a verified to an untrusted module do not access memory resources currently owned by the verified module. This paper proposes an approach to dynamic contract checking by relying on support for capabilities, a well-studied form of unforgeable memory pointers that enables fine-grained, efficient memory access control. More specifically, we rely on a form of capabilities called linear capabilities for which the hardware enforces that they cannot be copied. We formalize our approach as a fully abstract compiler from a statically verified source language to an unverified target language with support for linear capabilities. The key insight behind our compiler is that memory resources described by spatial separation logic predicates can be represented at run time by linear capabilities. The compiler is separation-logic-proof-directed: it uses the separation logic proof of the source program to determine how memory accesses in the source program should be compiled to linear capability accesses in the target program. The full abstraction property of the compiler essentially guarantees that compiled verified modules can interact with untrusted target language modules as if they were compiled from verified code as well. This article is an extended version of one that was presented at ICFP 2019 (Van Strydonck et al., 2019).

Composable data visualizations

Let’s say we want to create the two charts in Figure 1. The chart on the left is a bar chart that shows two different values for each bar. The chart on the right consists of two line charts that share the x axis with parts of the timeline highlighted using two different colors.

Cubical Agda: A dependently typed programming language with univalence and higher inductive types

Proof assistants based on dependent type theory provide expressive languages for both programming and proving within the same system. However, all of the major implementations lack powerful extensionality principles for reasoning about equality, such as function and propositional extensionality. These principles are typically added axiomatically which disrupts the constructive properties of these systems. Cubical type theory provides a solution by giving computational meaning to Homotopy Type Theory and Univalent Foundations, in particular to the univalence axiom and higher inductive types (HITs). This paper describes an extension of the dependently typed functional programming language Agda with cubical primitives, making it into a full-blown proof assistant with native support for univalence and a general schema of HITs. These new primitives allow the direct definition of function and propositional extensionality as well as quotient types, all with computational content. Additionally, thanks also to copatterns, bisimilarity is equivalent to equality for coinductive types. The adoption of cubical type theory extends Agda with support for a wide range of extensionality principles, without sacrificing type checking and constructivity.

PhD Abstracts

Many students complete PhDs in functional programming each year. As a service to the community, twice per year the Journal of Functional Programming publishes the abstracts from PhD dissertations completed during the previous year.