Haskell Implementation Research Articles

Parallel Algebraic Effect Handlers

Algebraic effect handlers support composable and structured control-flow abstraction. However, existing designs of algebraic effects often require effects to be executed sequentially. This paper studies parallel algebraic effect handlers. In particular, we formalize λ p , a lambda calculus which models two key features, effect handlers and parallelizable computations, the latter of which takes the form of a for expression, inspired by the Dex programming language. We present various interesting examples expressible in our calculus. To show that our design can be implemented in a type-safe way, we present a higher-order polymorphic lambda calculus F p that extends λ p with a lightweight value dependent type system, and prove that F p preserves the semantics of λ p and enjoys syntactic type soundness. Lastly, we provide an implementation of the language design as a Haskell library, which mirrors both λ p and F p and reveals new connections to free applicative functors. All examples presented can be encoded in the Haskell implementation. We believe this paper is the first to study the combination of user-defined effect handlers and parallel computations, and it is our hope that it provides a basis for future designs and implementations of parallel algebraic effect handlers.

Profunctor Optics, a Categorical Update

Optics are bidirectional data accessors that capture data transformation patterns such as accessing subfields or iterating over containers. Profunctor optics are a particular choice of representation supporting modularity, meaning that we can construct accessors for complex structures by combining simpler ones. Profunctor optics have previously been studied only in an unenriched and non-mixed setting, in which both directions of access are modelled in the same category. However, functional programming languages are arguably better described by enriched categories; and we have found that some structures in the literature are actually mixed optics, with access directions modelled in different categories. Our work generalizes a classic result by Pastro and Street on Tambara theory and uses it to describe mixed V-enriched profunctor optics and to endow them with V-category structure. We provide some original families of optics and derivations, including an elementary one for traversals. Finally, we discuss a Haskell implementation.

Monadic Expressions and Their Derivatives

There are several well-known ways to compute derivatives of regular expressions due to Brzozowski, Antimirov or Lombardy and Sakarovitch. We propose another one which abstracts the underlying data structures (e.g. sets or linear combinations) using the notion of monad. As an example of this generalization advantage, we first introduce a new derivation technique based on the graded module monad and then show an application of this technique to generalize the parsing of expressions with capture groups and back references. We also extend operators defining expressions to any n-ary functions over value sets, such as classical operations (like negation or intersection for Boolean weights) or more exotic ones (like algebraic mean for rational weights). Moreover, we present how to compute a (non-necessarily finite) automaton from such an extended expression, using the Colcombet and Petrisan categorical definition of automata. These category theory concepts allow us to perform this construction in a unified way, whatever the underlying monad. Finally, to illustrate our work, we present a Haskell implementation of these notions using advanced techniques of functional programming, and we provide a web interface to manipulate concrete examples.

Normalization by evaluation for modal dependent type theory

Abstract We present the Kripke-style modal type theory, Mint, which combines dependent types and the necessity modality. It extends the Kripke-style modal lambda-calculus by Pfenning and Davies to the full Martin-Löf type theory. As such it encompasses dependently typed variants of system K, T, K4, and S4. Further, Mint seamlessly supports a full universe hierarchy, usual inductive types, and large eliminations. In this paper, we give a modular sound and complete normalization-by-evaluation (NbE) proof for Mint based on an untyped domain model, which applies to all four aforementioned modal systems without modification. This NbE proof yields a normalization algorithm for Mint, which can be directly implemented. To further strengthen our results, our models and the NbE proof are fully mechanized in Agda and we extract a Haskell implementation of our NbE algorithm from it.

Safe couplings: coupled refinement types

We enhance refinement types with mechanisms to reason about relational properties of probabilistic computations. Our mechanisms, which are inspired from probabilistic couplings, are applicable to a rich set of probabilistic properties, including expected sensitivity, which ensures that the distance between outputs of two probabilistic computations can be controlled from the distance between their inputs. We implement our mechanisms in the type system of Liquid Haskell and we use them to formally verify Haskell implementations of two classic machine learning algorithms: Temporal Difference (TD) reinforcement learning and stochastic gradient descent (SGD). We formalize a fragment of our system for discrete distributions and we prove soundness with respect to a set-theoretical semantics.

Monadic Expressions and their Derivatives

We propose another interpretation of well-known derivatives computations from regular expressions, due to Brzozowski, Antimirov or Lombardy and Sakarovitch, in order to abstract the underlying data structures (e.g. sets or linear combinations) using the notion of monad. As an example of this generalization advantage, we introduce a new derivation technique based on the graded module monad. We also extend operators defining expressions to any n-ary functions over value sets, such as classical operations (like negation or intersection for Boolean weights) or more exotic ones (like algebraic mean for rational weights). Moreover, we present how to compute a (non-necessarily finite) automaton from such an extended expression, using the Colcombet and Petrisan categorical definition of automata. These category theory concepts allow us to perform this construction in a unified way, whatever the underlying monad. Finally, to illustrate our work, we present a Haskell implementation of these notions using advanced techniques of functional programming, and we provide a web interface to manipulate concrete examples.

On Structuring Functional Programs with Monoidal Profunctors

We study monoidal profunctors as a tool to reason and structure pure functional programs both from a categorical perspective and as a Haskell implementation. From the categorical point of view we approach them as monoids in a certain monoidal category of profunctors. We study properties of this monoidal category and construct and implement the free monoidal profunctor. We study the relationship of the monoidal construction to optics, and introduce a promising generalization of the implementation which we illustrate by introducing effectful monoidal profunctors.

Branching processes for QuickCheck generators

In QuickCheck (or, more generally, random testing), it is challenging to control random data generators' distributions---specially when it comes to user-defined algebraic data types (ADT). In this paper, we adapt results from an area of mathematics known as branching processes, and show how they help to analytically predict (at compile-time) the expected number of generated constructors, even in the presence of mutually recursive or composite ADTs. Using our probabilistic formulas, we design heuristics capable of automatically adjusting probabilities in order to synthesize generators which distributions are aligned with users' demands. We provide a Haskell implementation of our mechanism in a tool called DRaGeN and perform case studies with real-world applications. When generating random values, our synthesized QuickCheck generators show improvements in code coverage when compared with those automatically derived by state-of-the-art tools.

Functional programming for modular Bayesian inference

We present an architectural design of a library for Bayesian modelling and inference in modern functional programming languages. The novel aspect of our approach are modular implementations of existing state-of-the-art inference algorithms. Our design relies on three inherently functional features: higher-order functions, inductive data-types, and support for either type-classes or an expressive module system. We provide a performant Haskell implementation of this architecture, demonstrating that high-level and modular probabilistic programming can be added as a library in sufficiently expressive languages. We review the core abstractions in this architecture: inference representations, inference transformations, and inference representation transformers. We then implement concrete instances of these abstractions, counterparts to particle filters and Metropolis-Hastings samplers, which form the basic building blocks of our library. By composing these building blocks we obtain state-of-the-art inference algorithms: Resample-Move Sequential Monte Carlo, Particle Marginal Metropolis-Hastings, and Sequential Monte Carlo Squared. We evaluate our implementation against existing probabilistic programming systems and find it is already competitively performant, although we conjecture that existing functional programming optimisation techniques could reduce the overhead associated with the abstractions we use. We show that our modular design enables deterministic testing of inherently stochastic Monte Carlo algorithms. Finally, we demonstrate using OCaml that an expressive module system can also implement our design.

Deadlock-Free Typestate-Oriented Programming

Context. TypeState-Oriented Programming (TSOP) is a paradigm intended to help developers in the implementation and use of mutable objects whose public interface depends on their private state. Under this paradigm, well-typed programs are guaranteed to conform with the protocol of the objects they use. Inquiry. Previous works have investigated TSOP for both sequential and concurrent objects. However, an important difference between the two settings still remains. In a sequential setting, a well-typed program either progresses indefinitely or terminates eventually. In a concurrent setting, protocol conformance is no longer enough to avoid deadlocks, a situation in which the execution of the program halts because two or more objects are involved in mutual dependencies that prevent any further progress. Approach. In this work, we put forward a refinement of TSOP for concurrent objects guaranteeing that well-typed programs not only conform with the protocol of the objects they use, but are also deadlock free. The key ingredients of the type system are behavioral types, used to specify and enforce object protocols, and dependency relations, used to represent abstract descriptions of the dependencies between objects and detect circularities that might cause deadlocks. Knowledge. The proposed approach stands out for two features. First, the approach is fully compositional and therefore scalable: the objects of a large program can be type checked in isolation; deadlock freedom of an object composition solely depends on the types of the objects being composed; any modification/refactoring of an object that does not affect its public interface does not affect other objects either. Second, we provide the first deadlock analysis technique for join patterns, a high-level concurrency abstraction with which programmers can express complex synchronizations in a succinct and declarative form. Grounding. We detail the proposed typing discipline for a core programming language blending concurrent objects, asynchronous message passing and join patterns. We prove that the type system is sound and give non-trivial examples of programs that can be successfully analyzed. A Haskell implementation of the type system that demonstrates the feasibility of the approach is publicly available. Importance. The static analysis technique described in this work can be used to certify programs written in a core language for concurrent TSOP with proven correctness guarantees. This is an essential first step towards the integration and application of the technique in a real-world developer toolchain, making programming of such systems more productive and less frustrating.

QuickFuzz: an automatic random fuzzer for common file formats

Fuzzing is a technique that involves testing programs using invalid or erroneous inputs. Most fuzzers require a set of valid inputs as a starting point, in which mutations are then introduced. QuickFuzz is a fuzzer that leverages QuickCheck-style random test-case generationto automatically test programs that manipulate common file formats by fuzzing. We rely on existing Haskell implementations of file-format-handling libraries found on Hackage, the community-driven Haskell code repository. We have tried QuickFuzz in the wild and found that the approach is effective in discovering vulnerabilities in real-world implementations of browsers, image processing utilities and file compressors among others. In addition, we introduce a mechanism to automatically derive random generators for the types representing these formats. QuickFuzz handles most well-known image and media formats, and can be used to test programs and libraries written in any language.

Exploiting diversity in type checkers for better error messages

Producing precise and helpful type error messages has been a challenge for the implementations of functional programming languages for over 3 decades now. Many different approaches and methods have been tried to solve this thorny problem, but current type-error reporting tools still suffer from a lack of precision in many cases. Based on the observation that different approaches work well in different situations, we have studied the question of whether a combination of tools that exploits their diversity can lead to improved accuracy. Specifically, we have studied Helium, a Haskell implementation particularly aimed at producing good type error messages, and Lazy Typing, an approach developed previously by us to address the premature-error-commitment problem in type checkers. By analyzing the respective strengths and weaknesses of the two approaches we were able to identify a strategy to combine both tools that could markedly improve the accuracy of reported errors. Specifically, we report an evaluation of 1069 unique ill-typed programs out of a total of 11,256 Haskell programs that reveals that this combination strategy enjoys a correctness rate of 82%, which is an improvement of 25%/20% compared to using Lazy Typing/Helium alone. In addition to describing this particular case study, we will also report insights we gained into the combination of error-reporting tools in general.

FinPar

Commodity many-core hardware is now mainstream, but parallel programming models are still lagging behind in efficiently utilizing the application parallelism. There are (at least) two principal reasons for this. First, real-world programs often take the form of a deeply nested composition of parallel operators, but mapping the available parallelism to the hardware requires a set of transformations that are tedious to do by hand and beyond the capability of the common user. Second, the best optimization strategy, such as what to parallelize and what to efficiently sequentialize, is often sensitive to the input dataset and therefore requires multiple code versions that are optimized differently, which also raises maintainability problems. This article presents three array-based applications from the financial domain that are suitable for gpgpu execution. Common benchmark-design practice has been to provide the same code for the sequential and parallel versions that are optimized for only one class of datasets. In comparison, we document (1) all available parallelism via nested map-reduce functional combinators, in a simple Haskell implementation that closely resembles the original code structure, (2) the invariants and code transformations that govern the main trade-offs of a data-sensitive optimization space, and (3) report target cpu and multiversion gpgpu code together with an evaluation that demonstrates optimization trade-offs and other difficulties. We believe that this work provides useful insight into the language constructs and compiler infrastructure capable of expressing and optimizing such applications, and we report in-progress work in this direction.

PAEAN: Portable and scalable runtime support for parallel Haskell dialects

AbstractOver 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.

Certified symbolic management of financial multi-party contracts

Domain-specific languages (DSLs) for complex financial contracts are in practical use in many banks and financial institutions today. Given the level of automation and pervasiveness of software in the sector, the financial domain is immensely sensitive to software bugs. At the same time, there is an increasing need to analyse (and report on) the interaction between multiple parties. In this paper, we present a multi-party contract language that rigorously relegates any artefacts of simulation and computation from its core, which leads to favourable algebraic properties, and therefore allows for formalising domain-specific analyses and transformations using a proof assistant. At the centre of our formalisation is a simple denotational semantics independent of any stochastic aspects. Based on this semantics, we devise certified contract analyses and transformations. In particular, we give a type system, with an accompanying type inference procedure, that statically ensures that contracts follow the principle of causality. Moreover, we devise a reduction semantics that allows us to evolve contracts over time, in accordance with the denotational semantics. From the verified Coq definitions, we automatically extract a Haskell implementation of an embedded contract DSL along with the formally verified contract management functionality. This approach opens a road map towards more reliable contract management software, including the possibility of analysing contracts based on symbolic instead of numeric methods.

Structural Induction Principles for Functional Programmers

User defined recursive types are a fundamental feature of modern functional programming languages like Haskell, Clean, and the ML family of languages. Properties of programs defined by recursion on the structure of recursive types are generally proved by structural induction on the type. It is well known in the theorem proving community how to generate structural induction principles from data type declarations. These methods deserve to be better know in the functional programming community. Existing functional programming textbooks gloss over this material. And yet, if functional programmers do not know how to write down the structural induction principle for a new type - how are they supposed to reason about it? In this paper we describe an algorithm to generate structural induction principles from data type declarations. We also discuss how these methods are taught in the functional programming course at the University of Wyoming. A Haskell implementation of the algorithm is included in an appendix.

Handlers in action

Plotkin and Pretnar's handlers for algebraic effects occupy a sweet spot in the design space of abstractions for effectful computation. By separating effect signatures from their implementation, algebraic effects provide a high degree of modularity, allowing programmers to express effectful programs independently of the concrete interpretation of their effects. A handler is an interpretation of the effects of an algebraic computation. The handler abstraction adapts well to multiple settings: pure or impure, strict or lazy, static types or dynamic types. This is a position paper whose main aim is to popularise the handler abstraction. We give a gentle introduction to its use, a collection of illustrative examples, and a straightforward operational semantics. We describe our Haskell implementation of handlers in detail, outline the ideas behind our OCaml, SML, and Racket implementations, and present experimental results comparing handlers with existing code.

Correctness of an STM Haskell implementation

A concurrent implementation of software transactional memory in Concurrent Haskell using a call-by-need functional language with processes and futures is given. The description of the small-step operational semantics is precise and explicit, and employs an early abort of conflicting transactions. A proof of correctness of the implementation is given for a contextual semantics with may- and should-convergence. This implies that our implementation is a correct evaluator for an abstract specification equipped with a big-step semantics.

Formalizing workflows partitioning over federated clouds: multi-level security and costs

This paper presents an formalization of federated cloud workflows using the Z notation. It is an abstract specification with properties of interest being observed by the possible deployments, which are symbolically calculated by the Z/EVES theorem prover. Mathematical rules are used to define these properties by restricting valid options for security, cost, dependability, etc. A Haskell implementation of these proved properties is also presented. We have a Haskell implementation of the approach that is used to generate valid workflow deployment options, given the user workflow input and the security and cost properties of interest. The result is a set of (sub)-workflows as GraphWiz files respecting these properties.

Wormholes

Functional reactive programming (FRP) is a useful model for programming real-time and reactive systems in which one defines a signal function to process a stream of input values into a stream of output values. However, performing side effects (e.g. memory mutation or input/output) in this model is tricky and typically unsafe. In previous work, Winograd-Cort et al. [2012] introduced resource types and wormholes to address this problem. This paper better motivates, expands upon, and formalizes the notion of a wormhole to fully unlock its potential. We show, for example, that wormholes can be used to define the concept of causality. This in turn allows us to provide behaviors such as looping, a core component of most languages, without building it directly into the language. We also improve upon our previous design by making wormholes less verbose and easier to use. To formalize the notion of a wormhole, we define an extension to the simply typed lambda calculus, complete with typing rules and operational semantics. In addition, we present a new form of semantic transition that we call a temporal transition to specify how an FRP program behaves over time and to allow us to better reason about causality. As our model is designed for a Haskell implementation, the semantics are lazy. Finally, with the language defined, we prove that our wormholes indeed allow side effects to be performed safely in an FRP framework.