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 observation that program structure follows data structure is a key lesson in introductory programming: good hints for possible program designs can be found by considering the structure of the data concerned. In particular, this lesson is a core message of the influential textbook “How to Design Programs” by Felleisen, Findler, Flatt, and Krishnamurthi. However, that book discusses using only the structure of input data for guiding program design, typically leading towards structurally recursive programs. We argue that novice programmers should also be taught to consider the structure of output data, leading them also towards structurally corecursive programs.

The challenge of reasoning about programs with (multiple) effects such as mutation, jumps, or IO dates back to the inception of program semantics in the works of Strachey and Landin. Using monads to represent individual effects and the associated equational laws to reason about them proved exceptionally effective. Even then it is not always clear what laws are to be associated with a monad—for a good reason, as we show for non-determinism. Combining expressions using different effects brings challenges not just for monads, which do not compose, but also for equational reasoning: the interaction of effects may invalidate their individual laws, as well as induce emerging properties that are not apparent in the semantics of individual effects. Overall, the problems are judging the adequacy of a law; determining if or when a law continues to hold upon addition of new effects; and obtaining and easily verifying emergent laws.

We present a solution relying on the framework of (algebraic, extensible) effects, which already proved itself for writing programs with multiple effects. Equipped with a fairly conventional denotational semantics, this framework turns useful, as we demonstrate, also for reasoning about and optimizing programs with multiple interacting effects. Unlike the conventional approach, equational laws are not imposed on programs/effect handlers, but induced from them: our starting point hence is a program (model), whose denotational semantics, besides being used directly, suggests and justifies equational laws and clarifies side conditions. The main technical result is the introduction of the notion of equivalence modulo handlers (“modulo observation”) or a particular combination of handlers—and proving it to be a congruence. It is hence usable for reasoning in any context, not just evaluation contexts—provided particular conditions are met.

Concretely, we describe several realistic handlers for non-determinism and elucidate their laws (some of which hold in the presence of any other effect). We demonstrate appropriate equational laws of non-determinism in the presence of global state, which have been a challenge to state and prove before.

Distributed systems are hard to get right, model, test, debug, and teach. Their textbook definitions, typically given in a form of replicated state machines, are concise, yet prone to introducing programming errors if naïvely translated into runnable implementations.

In this work, we present Distributed Protocol Combinators (DPC), a declarative programming framework that aims to bridge the gap between specifications and runnable implementations of distributed systems, and facilitate their modeling, testing, and execution. DPC builds on the ideas from the state-of-the art logics for compositional systems verification. The contribution of DPC is a novel family of program-level primitives, which facilitates construction of larger distributed systems from smaller components, streamlining the usage of the most common asynchronous message-passing communication patterns, and providing machinery for testing and user-friendly dynamic verification of systems. This paper describes the main ideas behind the design of the framework and presents its implementation in Haskell. We introduce DPC through a series of characteristic examples and showcase it on a number of distributed protocols from the literature.

This paper extends our preceeding conference publication (Andersen & Sergey, 2019a) with an exploration of randomized testing for protocols and their implementations, and an additional case study demonstrating bounded model checking of protocols.

We present a region-based memory management scheme with support for generational garbage collection. The scheme features a compile-time region inference algorithm, which associates values with logical regions, and builds on a region type system that deploys region types at runtime to avoid the overhead of write barriers and to support partly tag-free garbage collection. The scheme is implemented in the MLKit Standard ML compiler, which generates native x64 machine code. Besides demonstrating a number of important formal properties of the scheme, we measure the scheme’s characteristics, for a number of benchmarks, and compare the performance of the generated executables with the performance of executables generated with the MLton state-of-the-art Standard ML compiler and configurations of the MLKit with and without region inference and generational garbage collection enabled. Although region inference often serves the purpose of generations, combining region inference with generational garbage collection is shown often to be superior to combining region inference with non-generational collection despite the overhead introduced by a larger amount of memory waste, due to region fragmentation.

Good tools can bring mechanical verification to programs written in mainstream functional languages. We use hs-to-coq to translate significant portions of Haskell’s containers library into Coq, and verify it against specifications that we derive from a variety of sources including type class laws, the library’s test suite, and interfaces from Coq’s standard library. Our work shows that it is feasible to verify mature, widely used, highly optimized, and unmodified Haskell code. We also learn more about the theory of weight-balanced trees, extend hs-to-coq to handle partiality, and – since we found no bugs – attest to the superb quality of well-tested functional 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).

Parallel reduction is a major component of parallel programming and widely used for summarisation and aggregation. It is not well understood, however, what sorts of non-trivial summarisations can be implemented as parallel reductions. This paper develops a calculus named λAS, a simply typed lambda calculus with algebraic simplification. This calculus provides a foundation for studying a parallelisation of complex reductions by equational reasoning. Its key feature is δ abstraction. A δ abstraction is observationally equivalent to the standard λ abstraction, but its body is simplified before the arrival of its arguments using algebraic properties such as associativity and commutativity. In addition, the type system of λAS guarantees that simplifications due to δ abstractions do not lead to serious overheads. The usefulness of λAS is demonstrated on examples of developing complex parallel reductions, including those containing more than one reduction operator, loops with conditional jumps, prefix sum patterns and even tree manipulations.

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.

We propose and study StkTokens: a new calling convention that provably enforces well-bracketed control flow and local state encapsulation on a capability machine. The calling convention is based on linear capabilities: a type of capabilities that are prevented from being duplicated by the hardware. In addition to designing and formalizing this new calling convention, we also contribute a new way to formalize and prove that it effectively enforces well-bracketed control flow and local state encapsulation using what we call a fully abstract overlay semantics.

In this paper, we present a method for explaining the results produced by dynamic programming (DP) algorithms. Our approach is based on retaining a granular representation of values that are aggregated during program execution. The explanations that are created from the granular representations can answer questions of why one result was obtained instead of another and therefore can increase the confidence in the correctness of program results.

Our focus on dynamic programming is motivated by the fact that dynamic programming offers a systematic approach to implementing a large class of optimization algorithms which produce decisions based on aggregated value comparisons. It is those decisions that the granular representation can help explain. Moreover, the fact that dynamic programming can be formalized using semirings supports the creation of a Haskell library for dynamic programming that has two important features. First, it allows programmers to specify programs by recurrence relationships from which efficient implementations are derived automatically. Second, the dynamic programs can be formulated generically (as type classes), which supports the smooth transition from programs that only produce result to programs that can run with granular representation and also produce explanations. Finally, we also demonstrate how to anticipate user questions about program results and how to produce corresponding explanations automatically in advance.

Extending Martín Escardó’s effectful forcing technique, we give a new proof of a well-known result: Brouwer’s monotone bar theorem holds for any bar that can be realized by a functional of type (ℕ→ℕ)→ℕ in Gödel’s System T. Effectful forcing is an elementary alternative to standard sheaf-theoretic forcing arguments, using ideas from programming languages, including computational effects, monads, the algebra interpretation of call-by-name λ-calculus, and logical relations.

Our argument proceeds by interpreting System T programs as well-founded dialogue trees whose nodes branch on a query to an oracle of type ℕ→ℕ, lifted to higher type along a call-by-name translation. To connect this interpretation to the bar theorem, we then show that Brouwer’s famous “mental constructions” of barhood constitute an invariant form of these dialogue trees in which queries to the oracle are made maximally and in order.

We show how to systematically derive an efficient regular expression (regex) matcher using a variety of program transformation techniques, but very little specialized formal language and automata theory. Starting from the standard specification of the set-theoretic semantics of regular expressions, we proceed via a continuation-based backtracking matcher, to a classical, table-driven state machine. All steps of the development are supported by self-contained (and machine-verified) equational correctness proofs.

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.

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 recently renamed our “education” track’s papers from Education Pearl to Education Matters. This would be a good time to explain our vision for the track as a whole, as well as this specific renaming.

The algebraic properties of the combination of probabilistic choice and nondeterministic choice have long been a research topic in program semantics. This paper explains a formalization in the Coq proof assistant of a monad equipped with both choices: the geometrically convex monad. This formalization has an immediate application: it provides a model for a monad that implements a nontrivial interface, which allows for proofs by equational reasoning using probabilistic and nondeterministic effects. We explain the technical choices we made to go from the literature to a complete Coq formalization, from which we identify reusable theories about mathematical structures such as convex spaces and concrete categories, and that we integrate in a framework for monadic equational reasoning.

Proving only over source code that programs do not leak sensitive data leaves a gap between reasoning and reality that can only be filled by accounting for the behaviour of the compiler. Furthermore, software does not always have the luxury of limiting itself to single-threaded computation with resources statically dedicated to each user to ensure the confidentiality of their data. This results in mixed-sensitivity concurrent programs, which might reuse memory shared between their threads to hold data of different sensitivity levels at different times; for such programs, a compiler must preserve the value-dependent coordination of such mixed-sensitivity reuse despite the impact of concurrency. Here we demonstrate, using Isabelle/HOL, that it is feasible to verify that a compiler preserves noninterference, the strictest kind of confidentiality property, for mixed-sensitivity concurrent programs. First, we present notions of refinement that preserve a concurrent value-dependent notion of noninterference that we have designed to support such programs. As proving noninterference-preserving refinement can be considerably more complex than the standard refinements typically used to verify semantics-preserving compilation, our notions include a decomposition principle that separates the semantics preservation from security preservation concerns. Second, we demonstrate that these refinement notions are applicable to verified secure compilation, by exercising them on a single-pass compiler for mixed-sensitivity concurrent programs that synchronise using mutex locks, from a generic imperative language to a generic RISC-style assembly language. Finally, we execute our compiler on a non-trivial mixed-sensitivity concurrent program modelling a real-world use case, thus preserving its source-level noninterference properties down to an assembly-level model automatically. All results are formalised and proved in the Isabelle/HOL interactive proof assistant. Our work paves the way for more fully featured compilers to offer verified secure compilation support to developers of multithreaded software that must handle data of multiple sensitivity levels.

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.

C#, Dart, Pyret, Racket, TypeScript, VB: many recent languages integrate dynamic and static types via gradual typing. We systematically develop four calculi for gradual typing and the relations between them, building on and strengthening previous work. The calculi are as follows: $\lambda{B}$ , based on the blame calculus of Wadler and Findler (2009); $\lambda{C}$ , inspired by the coercion calculus of Henglein (1994); $\lambda{S}$ inspired by the space-efficient calculus of Herman, Tomb, and Flanagan (2006); and $\lambda{T}$ based on the threesome calculus of Siek and Wadler (2010). While $\lambda{B}$ and $\lambda{T}$ are little changed from previous work, $\lambda{C}$ and $\lambda{S}$ are new. Together, $\lambda{B}$ , $\lambda{C}$ , $\lambda{S}$ , and $\lambda{T}$ provide a coherent foundation for design, implementation, and optimization of gradual types. We define translations from $\lambda{B}$ to $\lambda{C}$ , from $\lambda{C}$ to $\lambda{S}$ , and from $\lambda{S}$ to $\lambda{T}$ . Much previous work lacked proofs of correctness or had weak correctness criteria; here we demonstrate the strongest correctness criterion one could hope for, that each of the translations is fully abstract. Each of the calculi reinforces the design of the others: $\lambda{C}$ has a particularly simple definition, and the subtle definition of blame safety for $\lambda{B}$ is justified by the simple definition of blame safety for $\lambda{C}$ . Our calculus $\lambda{S}$ is implementation-ready: the first space-efficient calculus that is both straightforward to implement and easy to understand. We give two applications: first, using full abstraction from $\lambda{C}$ to $\lambda{S}$ to establish an equational theory of coercions; and second, using full abstraction from $\lambda{B}$ to $\lambda{S}$ to easily establish the Fundamental Property of Casts, which required a custom bisimulation and six lemmas in earlier work.