Folds and unfolds have been understood as fundamental building blocks for total programming, and have been extended to form an entire zoo of specialised structured recursion schemes. A great number of these schemes were unified by the introduction of adjoint folds, but more exotic beasts such as recursion schemes from comonads proved to be elusive. In this paper, we show how the two canonical derivations of adjunctions from (co)monads yield recursion schemes of significant computational importance: monadic catamorphisms come from the Kleisli construction, and more astonishingly, the elusive recursion schemes from comonads come from the Eilenberg–Moore construction. Thus, we demonstrate that adjoint folds are more unifying than previously believed.

In this paper, we study strong normalization of a core language based on System ${\mathsf{F}_\omega}$ which supports programming with finite and infinite structures. Finite data such as finite lists and trees is defined via constructors and manipulated via pattern matching, while infinite data such as streams and infinite trees is defined by observations and synthesized via copattern matching. Taking a type-based approach to strong normalization, we track size information about finite and infinite data in the type. We exploit the duality of pattern and copatterns to give a unifying semantic framework which allows us to elegantly and uniformly support both well-founded induction and coinduction by rewriting. The strong normalization proof is structured around Girard's reducibility candidates. As such, our system allows for non-determinism and does not rely on coverage. Since System ${\mathsf{F}_\omega}$ is general enough that it can be the target of compilation for the Calculus of Constructions, this work is a significant step towards representing observation-based infinite data in proof assistants such as Coq and Agda.

This paper proposes a new typed lambda-encoding for inductive types which, for Peano numerals, has the expected time complexities for basic operations like addition and multiplication, has a constant-time predecessor function, and requires only quadratic space to encode a numeral. This improves on the exponential space required by the Parigot encoding. Like the Parigot encoding, the new encoding is typable in System F-omega plus positive-recursive type definitions, a total type theory. The new encoding is compared with previous ones through a significant case study: mergesort using Braun trees. The practical runtime efficiency of the new encoding, and the Church and Parigot encodings, are compared by two translations, one to Racket and one to Haskell, on a small suite of benchmarks.

Information-flow control mechanisms are difficult both to design and to prove correct. To reduce the time wasted on doomed proof attempts due to broken definitions, we advocate modern random-testing techniques for finding counterexamples during the design process. We show how to use QuickCheck, a property-based random-testing tool, to guide the design of increasingly complex information-flow abstract machines, leading up to a sophisticated register machine with a novel and highly permissive flow-sensitive dynamic enforcement mechanism that is sound in the presence of first-class public labels. We find that both sophisticated strategies for generating well-distributed random programs and readily falsifiable formulations of noninterference properties are critically important for efficient testing. We propose several approaches and evaluate their effectiveness on a collection of injected bugs of varying subtlety. We also present an effective technique for shrinking large counterexamples to minimal, easily comprehensible ones. Taken together, our best methods enable us to quickly and automatically generate simple counterexamples for more than 45 bugs. Moreover, we show how testing guides the discovery of the sophisticated invariants needed for the noninterference proof of our most complex machine.

Reliability is set to become a major concern on emergent large-scale architectures. While there are many parallel languages, and indeed many parallel functional languages, very few address reliability. The notable exception is the widely emulated Erlang distributed actor model that provides explicit supervision and recovery of actors with isolated state. We investigate scalable transparent fault tolerant functional computation with automatic supervision and recovery of tasks. We do so by developing HdpH-RS, a variant of the Haskell distributed parallel Haskell (HdpH) DSL with Reliable Scheduling. Extending the distributed work stealing protocol of HdpH for task supervision and recovery is challenging. To eliminate elusive concurrency bugs, we validate the HdpH-RS work stealing protocol using the SPIN model checker. HdpH-RS differs from the actor model in that its principal entities are tasks, i.e. independent stateless computations, rather than isolated stateful actors. Thanks to statelessness, fault recovery can be performed automatically and entirely hidden in the HdpH-RS runtime system. Statelessness is also key for proving a crucial property of the semantics of HdpH-RS: fault recovery does not change the result of the program, akin to deterministic parallelism. HdpH-RS provides a simple distributed fork/join-style programming model, with minimal exposure of fault tolerance at the language level, and a library of higher level abstractions such as algorithmic skeletons. In fact, the HdpH-RS DSL is exactly the same as the HdpH DSL, hence users can opt in or out of fault tolerant execution without any refactoring. Computations in HdpH-RS are always as reliable as the root node, no matter how many nodes and cores are actually used. We benchmark HdpH-RS on conventional clusters and an High Performance Computing platform: all benchmarks survive Chaos Monkey random fault injection; the system scales well e.g. up to 1,400 cores on the High Performance Computing; reliability and recovery overheads are consistently low even at scale.

Graphics Processing Units (GPUs) offer potential for very high performance; they are also rapidly evolving. Obsidian is an embedded language (in Haskell) for implementing high performance kernels to be run on GPUs. We would like to have our cake and eat it too; we want to raise the level of abstraction beyond CUDA code and still give the programmer control over the details relevant to kernel performance. To that end, Obsidian provides array representations that guarantee elimination of intermediate arrays while also using the type system to model the hierarchy of the GPU. Operations are compiled very differently depending on what level of the GPU they target, and as a result, the user is gently constrained to write code that matches the capabilities of the GPU. Thus, we implement not Nested Data Parallelism, but a more limited form that we call Hierarchical Data Parallelism. We walk through case-studies that demonstrate how to use Obsidian for rapid design exploration or auto-tuning, resulting in performance that compares well to the hand-tuned kernels used in Accelerate and NVIDIA Thrust.

This article presents how the compiler from the OCaml-Java project generates Java bytecode from OCaml sources. Targeting the Java Virtual Machine (JVM) is a technological challenge, but gives access to a platform where OCaml can leverage multiple cores and access numerous libraries. We present the main design choices regarding the runtime and the various optimizations performed by the compiler that are crucial to get decent performance on a JVM. The challenge is indeed not only to generate bytecode but to generate efficient bytecode, and to provide a runtime library whose memory footprint does not impede the efficiency of the garbage collector. We focus on the strategies that differ from the original OCaml compiler, as the constraints are quite different on the JVM when compared to native code. The level of performance reached by the OCaml-Java compiler is assessed through benchmarks, comparing with both the original OCaml implementation and the Scala language.

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

The runtime for a modern, concurrent, garbage collected language like Java or Haskell is like an operating system: sophisticated, complex, performant, but alas very hard to change. If more of the runtime system were in the high-level language, it would be far more modular and malleable. In this paper, we describe a novel concurrency substrate design for the Glasgow Haskell Compiler that allows multicore schedulers for concurrent and parallel Haskell programs to be safely and modularly described as libraries in Haskell. The approach relies on abstracting the interface to the user-implemented schedulers through scheduler activations, together with the use of Software Transactional Memory to promote safety in a multicore context.

Over time, several competing approaches to parallel Haskell programming have emerged. Different approaches support parallelism at various different scales, ranging from small multicores to massively parallel high-performance computing systems. They also provide varying degrees of control, ranging from completely implicit approaches to ones providing full programmer control. Most current designs assume a shared memory model at the programmer, implementation and hardware levels. This is, however, becoming increasingly divorced from the reality at the hardware level. It also imposes significant unwanted runtime overheads in the form of garbage collection synchronisation etc. What is needed is an easy way to abstract over the implementation and hardware levels, while presenting a simple parallelism model to the programmer. The PArallEl shAred Nothing runtime system design aims to provide a portable and high-level shared-nothing implementation platform for parallel Haskell dialects. It abstracts over major issues such as work distribution and data serialisation, consolidating existing, successful designs into a single framework. It also provides an optional virtual shared-memory programming abstraction for (possibly) shared-nothing parallel machines, such as modern multicore/manycore architectures or cluster/cloud computing systems. It builds on, unifies and extends, existing well-developed support for shared-memory parallelism that is provided by the widely used GHC Haskell compiler. This paper summarises the state-of-the-art in shared-nothing parallel Haskell implementations, introduces the PArallEl shAred Nothing abstractions, shows how they can be used to implement three distinct parallel Haskell dialects, and demonstrates that good scalability can be obtained on recent parallel machines.

We compare two inherently different approaches to implement complex process systems in Eden: stable process systems and a compositional approach. A stable process system is characterised by handling several computation stages in each of the participating processes. Often, processes communicate using streams of data, change behaviour with the different computation phases, and more often than not, exactly one process is allocated to each processor element. In contrast, a complex process system can also be achieved by skeleton composition of a number of elementary skeletons, such as parallel transformation, reduction, or special communication patterns. In a compositional implementation, each computation phase leads to a new set of interacting processes. When implementing complex parallel algorithms, skeleton composition is usually easier and more flexible, but has a larger overhead from additional process creation and communication. We present case studies of different parallel application kernels implemented as stable systems and using composition in Eden, including a comprehensive description of Eden's features. Our results show that the compositional performance loss can be alleviated by co-locating processes which directly communicate, and by using Eden's remote data concept to enable such direct communication. Moreover, Eden's parallel runtime system handles communication between co-located processes in an optimised way. EdenTV visualisations of execution traces are invaluable to analyse program characteristics and for targeted optimisations towards better process placement and communication avoidance.

It is well known that simply typed λ-terms can be used to represent numbers, as well as some other data types. We show that λ-terms of each fixed (but possibly very complicated) type can be described by a finite piece of information (a set of appropriately defined intersection types) and by a vector of natural numbers. On the one hand, the description is compositional: having only the finite piece of information for two closed λ-terms M and N, we can determine its counterpart for MN, and a linear transformation that applied to the vectors of numbers for M and N gives us the vector for MN. On the other hand, when a λ-term represents a natural number, then this number is approximated by a number in the vector corresponding to this λ-term. As a consequence, we prove that in a λ-term of a fixed type, we can store only a fixed number of natural numbers, in such a way that they can be extracted using λ-terms. More precisely, while representing k numbers in a closed λ-term of some type, we only require that there are k closed λ-terms M1,. . .,Mk such that Mi takes as argument the λ-term representing the k-tuple, and returns the i-th number in the tuple (we do not require that, using λ-calculus, one can construct the representation of the k-tuple out of the k numbers in the tuple). Moreover, the same result holds when we allow that the numbers can be extracted approximately, up to some error (even when we only want to know whether a set is bounded or not). All the results remain true when we allow the Y combinator (recursion) in our λ-terms, as well as uninterpreted constants.

Current systems for safely manipulating values containing names only support simple binding structures for those names. As a result, few tools exist to safely manipulate code in those languages for which name problems are the most challenging. We address this problem with Romeo, a language that respects α-equivalence on its values, and which has access to a rich specification language for binding, inspired by attribute grammars. Our work has the complex-binding support of David Herman's λm, but is a full-fledged binding-safe language like Pure FreshML.

The 12th International Symposium on Functional and Logic Programming was held in Kanazawa, Japan, June 4–6, 2014. The aim of the Functional and Logic Programming series of conferences is to bring together researchers interested in declarative programming including functional programming and logic programming. The series aims to promote cross-fertilization and integration between the two paradigms and it is traditionally organized and held in Japan.

Generative type abstractions – present in Haskell, OCaml, and other languages – are useful concepts to help prevent programmer errors. They serve to create new types that are distinct at compile time but share a run-time representation with some base type. We present a new mechanism that allows for zero-cost conversions between generative type abstractions and their representations, even when such types are deeply nested. We prove type safety in the presence of these conversions and have implemented our work in GHC.

Dependent pattern matching is an intuitive way to write programs and proofs in dependently typed languages. It is reminiscent of both pattern matching in functional languages and case analysis in on-paper mathematics. However, in general, it is incompatible with new type theories such as homotopy type theory (HoTT). As a consequence, proofs in such theories are typically harder to write and to understand. The source of this incompatibility is the reliance of dependent pattern matching on the so-called K axiom – also known as the uniqueness of identity proofs – which is inadmissible in HoTT. In this paper, we propose a new criterion for dependent pattern matching without K, and prove it correct by a translation to eliminators in the style of Goguen et al. (2006 Algebra, Meaning, and Computation). Our criterion is both less restrictive than existing proposals, and solves a previously undetected problem in the old criterion offered by Agda. It has been implemented in Agda and is the first to be supported by a formal proof. Thus, it brings the benefits of dependent pattern matching to contexts where we cannot assume K, such as HoTT.

Homotopy type theory is an extension of Martin-Löf type theory, based on a correspondence with homotopy theory and higher category theory. In homotopy type theory, the propositional equality type is proof-relevant, and corresponds to paths in a space. This allows for a new class of datatypes, called higher inductive types, which are specified by constructors not only for points but also for paths. In this paper, we consider a programming application of higher inductive types. Version control systems such as Darcs are based on the notion of patches—syntactic representations of edits to a repository. We show how patch theory can be developed in homotopy type theory. Our formulation separates formal theories of patches from their interpretation as edits to repositories. A patch theory is presented as a higher inductive type. Models of a patch theory are given by maps out of that type, which, being functors, automatically preserve the structure of patches. Several standard tools of homotopy theory come into play, demonstrating the use of these methods in a practical programming context.

Effect systems have the potential to help software developers, but their practical adoption has been very limited. We conjecture that this limited adoption is due in part to the difficulty of transitioning from a system where effects are implicit and unrestricted to a system with a static effect discipline, which must settle for conservative checking in order to be decidable. To address this hindrance, we develop a theory of gradual effect checking, which makes it possible to incrementally annotate and statically check effects, while still rejecting statically inconsistent programs. We extend the generic type-and-effect framework of Marino and Millstein with a notion of unknown effects, which turns out to be significantly more subtle than unknown types in traditional gradual typing. We appeal to abstract interpretation to develop and validate the concepts of gradual effect checking. We also demonstrate how an effect system formulated in the framework of Marino and Millstein can be automatically extended to support gradual checking. We use gradual effect checking to develop a fully gradual type-and-effect framework, which permits interaction between static and dynamic checking for both effects and types.

The 19th ACM SIGPLAN International Conference on Functional Programming (ICFP) took place on September 1–3, 2014 in Gothenburg, Sweden. After the conference, the programme committee, chaired by Manuel Chakravarty, selected several outstanding papers and invited their authors to submit to this special issue of JFP. We acted as editors for these submissions. This issue includes the six accepted papers, each of which provides substantial new material beyond the original conference version. The selected papers demonstrate both the quality and the breadth of the conference, with a strong emphasis on types and their applications, and ranging from compilation methods through contract verification to homotopy type theory.