Haskell Library 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.

HasChor: Functional Choreographic Programming for All (Functional Pearl)

Choreographic programming is an emerging paradigm for programming distributed systems. In choreographic programming, the programmer describes the behavior of the entire system as a single, unified program -- a choreography -- which is then compiled to individual programs that run on each node, via a compilation step called endpoint projection. We present a new model for functional choreographic programming where choreographies are expressed as computations in a monad. Our model supports cutting-edge choreographic programming features that enable modularity and code reuse: in particular, it supports higher-order choreographies, in which a choreography may be passed as an argument to another choreography, and location-polymorphic choreographies, in which a choreography can abstract over nodes. Our model is implemented in a Haskell library, HasChor , which lets programmers write choreographic programs while using the rich Haskell ecosystem at no cost, bringing choreographic programming within reach of everyday Haskellers. Moreover, thanks to Haskell's abstractions, the implementation of the HasChor library itself is concise and understandable, boiling down endpoint projection to its short and simple essence.

Affine Monads and Lazy Structures for Bayesian Programming

We show that streams and lazy data structures are a natural idiom for programming with infinite-dimensional Bayesian methods such as Poisson processes, Gaussian processes, jump processes, Dirichlet processes, and Beta processes. The crucial semantic idea, inspired by developments in synthetic probability theory, is to work with two separate monads: an affine monad of probability, which supports laziness, and a commutative, non-affine monad of measures, which does not. (Affine means that T (1)≅ 1.) We show that the separation is important from a decidability perspective, and that the recent model of quasi-Borel spaces supports these two monads. To perform Bayesian inference with these examples, we introduce new inference methods that are specially adapted to laziness; they are proven correct by reference to the Metropolis-Hastings-Green method. Our theoretical development is implemented as a Haskell library, LazyPPL.

Searching entangled program spaces

Many problem domains, including program synthesis and rewrite-based optimization, require searching astronomically large spaces of programs. Existing approaches often rely on building specialized data structures—version-space algebras, finite tree automata, or e-graphs—to compactly represent such spaces. At their core, all these data structures exploit independence of subterms; as a result, they cannot efficiently represent more complex program spaces, where the choices of subterms are entangled. We introduce equality-constrained tree automata (ECTAs), a new data structure, designed to compactly represent large spaces of programs with entangled subterms. We present efficient algorithms for extracting programs from ECTAs, implemented in a performant Haskell library, ecta. Using the ecta library, we construct Hectare, a type-driven program synthesizer for Haskell. Hectare significantly outperforms a state-of-the-art synthesizer Hoogle+—providing an average speedup of 8×—despite its implementation being an order of magnitude smaller.

Structure verification of deep neural networks at compilation time

This paper presents TensorSafe , a Haskell library that makes possible the definition and structural validation of deep neural network architectures. Nowadays, the development process of deep learning models has been notably simplified due to the availability of sophisticated tools in the industry. However, most of these tools do not provide any security controls at compilation time, making the developers deal with unexpected run-time errors and uncertainties. In particular, validating the structure of deep neural networks at compilation time is a complex subject that involves the mathematical validation of all operations that a deep learning model will perform. Moreover, this structural checking requires an advanced usage of types systems theories to manipulate abstract type definitions capable of modeling neural network constructions. Many different programming techniques were involved in the specification of TensorSafe. Primarily, the application of the functional programming paradigm and the use of type-level programming were of great importance for the development process and to probe the correctness of the neural network models. The experimental evaluation showed that by using TensorSafe it is possible to correctly create well-known deep neural network architectures, such as AlexNet or ResNet50 . • Review state of the art of deep learning DSLs that provide structural controls at compile time. • Extensible Haskell library that is capable of defining non-sequential deep learning architectures. • Interaction with external deep learning frameworks like TensorFlow for JavaScript or Keras for Python.

Generalized evidence passing for effect handlers: efficient compilation of effect handlers to C

This paper studies compilation techniques for algebraic effect handlers. In particular, we present a sequence of refinements of algebraic effects, going via multi-prompt delimited control, _generalized evidence passing_, yield bubbling, and finally a monadic translation into plain lambda calculus which can be compiled efficiently to many target platforms. Along the way we explore various interesting points in the design space. We provide two implementations of our techniques, one as a library in Haskell, and one as a C backend for the Koka programming language. We show that our techniques are effective, by comparing against three other best-in-class implementations of effect handlers: multi-core OCaml, the _Ev.Eff_ Haskell library, and the libhandler C library. We hope this work can serve as a basis for future designs and implementations of algebraic effects.

Explainable dynamic programming

AbstractIn 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.

Generating Random Well-Typed Featherweight Java Programs Using QuickCheck

Currently, Java is one of the most used programming language, being adopted in many large projects, where applications reach a level of complexity for which manual testing and human inspection are not enough to guarantee quality in software development. Even when using automated unit tests, such tests rarely cover all interesting cases of code, which means that a bug could never be discovered, once the code is tested against the same set of rules over and over again. This paper addresses the problem of generating random well-typed programs in the context of Featherweight Java, a well-known object-oriented calculus, using QuickCheck, a Haskell library for property-based testing.

Language-integrated provenance in Haskell

Scientific progress increasingly depends on data management, particularly to clean and curate data so that it can be systematically analyzed and reused. A wealth of techniques for managing and curating data (and its provenance) have been proposed, largely in the database community. In particular, a number of influential papers have proposed collecting provenance information explaining where a piece of data was copied from, or what other records were used to derive it. Most of these techniques, however, exist only as research prototypes and are not available in mainstream database systems. This means scientists must either implement such techniques themselves or (all too often) go without. This is essentially a code reuse problem: provenance techniques currently cannot be implemented reusably, only as ad hoc, usually unmaintained extensions to standard databases. An alternative, relatively unexplored approach is to support such techniques at a higher abstraction level, using metaprogramming or reflection techniques. Can advanced programming techniques make it easier to transfer provenance research results into practice? We build on a recent approach called language-integrated provenance, which extends language-integrated query techniques with source-to-source query translations that record provenance. In previous work, a proof of concept was developed in a research programming language called Links, which supports sophisticated Web and database programming. In this paper, we show how to adapt this approach to work in Haskell building on top of the Database-Supported Haskell (DSH) library. Even though it seemed clear in principle that Haskell's rich programming features ought to be sufficient, implementing language-integrated provenance in Haskell required overcoming a number of technical challenges due to interactions between these capabilities. Our implementation serves as a proof of concept showing how this combination of metaprogramming features can, for the first time, make data provenance facilities available to programmers as a library in a widely-used, general-purpose language. In our work we were successful in implementing forms of provenance known as where-provenance and lineage. We have tested our implementation using a simple database and query set and established that the resulting queries are executed correctly on the database. Our implementation is publicly available on GitHub. Our work makes provenance tracking available to users of DSH at little cost. Although Haskell is not widely used for scientific database development, our work suggests which languages features are necessary to support provenance as library. We also highlight how combining Haskell's advanced type programming features can lead to unexpected complications, which may motivate further research into type system expressiveness.

Flexible dynamic information flow control in the presence of exceptions

AbstractWe describe a language-based, dynamic information flow control (IFC) system called LIO. Our system presents a new design point for IFC, influenced by the challenge of implementing IFC as a Haskell library, as opposed to the more typical approach of modifying the language runtime system. In particular, we take a coarse-grained, floating-label approach, previously used by IFC Operating Systems, and associate a single, mutable label—thecurrent label—with all the data in a computation's context. This label is always raised to reflect the reading of sensitive information and it is used to restrict the underlying computation's effects. To preserve the flexibility of fine-grained systems, LIO also provides programmers with a means for associating an explicit label with a piece of data. Interestingly, these labeled values can be used to encapsulate the results of sensitive computations which would otherwise lead to the creeping of the current label. Unlike other language-based systems, LIO also bounds the current label with acurrent clearance, providing a form of discretionary access control that LIO programs can use to deal with covert channels. Moreover, LIO provides programmers with mutable references and exceptions. The latter, exceptions, are used in LIO to encode and recover from monitor failures, all while preserving data confidentiality and integrity—this addresses a longstanding concern that dynamic IFC is inherently prone to information leakage due to monitor failure.

Learning nominal automata

We present an Angluin-style algorithm to learn nominal automata, which are acceptors of languages over infinite (structured) alphabets. The abstract approach we take allows us to seamlessly extend known variations of the algorithm to this new setting. In particular we can learn a subclass of nominal non-deterministic automata. An implementation using a recently developed Haskell library for nominal computation is provided for preliminary experiments.

Lazy graph processing in Haskell

This paper presents a Haskell library for graph processing: DeltaGraph. One unique feature of this system is that intentions to perform graph updates can be memoized in-graph in a decentralized fashion, and the propagation of these intentions within the graph can be decoupled from the realization of the updates. As a result, DeltaGraph can respond to updates in constant time and work elegantly with parallelism support. We build a Twitter-like application on top of DeltaGraph to demonstrate its effectiveness and explore parallelism and opportunistic computing optimizations.

Generalising tree traversals and tree transformations to DAGs: Exploiting sharing without the pain

We present a recursion scheme based on attribute grammars that can be transparently applied to trees and acyclic graphs. Our recursion scheme allows the programmer to implement a tree traversal or a tree transformation and then apply it to compact graph representations of trees instead. The resulting graph traversal or graph transformation avoids recomputation of intermediate results for shared nodes – even if intermediate results are used in different contexts. Consequently, this approach leads to asymptotic speedup proportional to the compression provided by the graph representation. In general, however, this sharing of intermediate results is not sound. Therefore, we complement our implementation of the recursion scheme with a number of correspondence theorems that ensure soundness for various classes of traversals. We illustrate the practical applicability of the implementation as well as the complementing theory with a number of examples. • We give a method for defining traversals that run seamlessly on trees and DAGs. • We extend the method to sharing-preserving transformations. • Correspondence theorems characterise the semantics of traversals on trees vs. DAGs. • The method is based on attribute grammars, implemented as a Haskell library. • We demonstrate the technique on a number of example algorithms.

Combinators for impure yet hygienic code generation

Code generation is the leading approach to making high-performance software reusable. Effects are indispensable in code generators, whether to report failures or to insert let-statements and if-guards. Extensive painful experience shows that unrestricted effects interact with generated binders in undesirable ways to produce unexpectedly unbound variables, or worse, unexpectedly bound ones. These subtleties hinder domain experts in using and extending the generator. A pressing problem is thus to express the desired effects while regulating them so that the generated code is correct, or at least correctly scoped, by construction.We present a code-combinator framework that lets us express arbitrary monadic effects, including mutable references and delimited control, that move open code across generated binders. The static types of our generator expressions not only ensure that a well-typed generator produces well-typed and well-scoped code. They also express the lexical scopes of generated binders and prevent mixing up variables with different scopes. For the first time ever we demonstrate statically safe and well-scoped loop interchange and constant factoring from arbitrarily nested loops.Our framework is implemented as a Haskell library that embeds an extensible typed higher-order domain-specific language. It may be regarded as ‘staged Haskell.’ To become practical, the library relies on higher-order abstract syntax and polymorphism over generated type environments, and is written in a mature language.

The remote monad design pattern

Remote Procedure Calls are expensive. This paper demonstrates how to reduce the cost of calling remote procedures from Haskell by using the remote monad design pattern, which amortizes the cost of remote calls. This gives the Haskell community access to remote capabilities that are not directly supported, at a surprisingly inexpensive cost. We explore the remote monad design pattern through six models of remote execution patterns, using a simulated Internet of Things toaster as a running example. We consider the expressiveness and optimizations enabled by each remote execution model, and assess the feasibility of our approach. We then present a full-scale case study: a Haskell library that provides a Foreign Function Interface to the JavaScript Canvas API. Finally, we discuss existing instances of the remote monad design pattern found in Haskell libraries.

Modular reifiable matching: a list-of-functors approach to two-level types

This paper presents Modular Reifiable Matching (MRM): a new approach to two level types using a fixpoint of list-of-functors representation. MRM allows the modular definition of datatypes and functions by pattern matching, using a style similar to the widely popular Datatypes a la Carte (DTC) approach. However, unlike DTC, MRM uses a fixpoint of list-of-functors approach to two-level types. This approach has advantages that help with various aspects of extensibility, modularity and reuse. Firstly, modular pattern matching definitions are collected using a list of matches that is fully reifiable. This allows for extensible pattern matching definitions to be easily reused/inherited, and particular matches to be overridden. Such flexibility is used, among other things, to implement extensible generic traversals . Secondly, the subtyping relation between lists of functors is quite simple, does not require backtracking, and is easy to model in languages like Haskell. MRM is implemented as a Haskell library, and its use and applicability are illustrated through various examples in the paper.

Practical principled FRP: forget the past, change the future, FRPNow!

We present a new interface for practical Functional Reactive Programming (FRP) that (1) is close in spirit to the original FRP ideas, (2) does not have the original space-leak problems, without using arrows or advanced types, and (3) provides a simple and expressive way for performing IO actions from FRP code. We also provide a denotational semantics for this new interface, and a technique (using Kripke logical relations) for reasoning about which FRP functions may "forget their past", i.e. which functions do not have an inherent space-leak. Finally, we show how we have implemented this interface as a Haskell library called FRPNow.

Fast splittable pseudorandom number generators

We describe a new algorithm SplitMix for an object-oriented and splittable pseudorandom number generator (PRNG) that is quite fast: 9 64-bit arithmetic/logical operations per 64 bits generated. A conventional linear PRNG object provides a generate method that returns one pseudorandom value and updates the state of the PRNG, but a splittable PRNG object also has a second operation, split , that replaces the original PRNG object with two (seemingly) independent PRNG objects, by creating and returning a new such object and updating the state of the original object. Splittable PRNG objects make it easy to organize the use of pseudorandom numbers in multithreaded programs structured using fork-join parallelism. No locking or synchronization is required (other than the usual memory fence immediately after object creation). Because the generate method has no loops or conditionals, it is suitable for SIMD or GPU implementation. We derive SplitMix from the DotMix algorithm of Leiserson, Schardl, and Sukha by making a series of program transformations and engineering improvements. The end result is an object-oriented version of the purely functional API used in the Haskell library for over a decade, but SplitMix is faster and produces pseudorandom sequences of higher quality; it is also far superior in quality and speed to java.util.Random, and has been included in Java JDK8 as the class java.util.SplittableRandom. We have tested the pseudorandom sequences produced by SplitMix using two standard statistical test suites (DieHarder and TestU01) and they appear to be adequate for "everyday" use, such as in Monte Carlo algorithms and randomized data structures where speed is important.

A seamless, client-centric programming model for type safe web applications

We propose a new programming model for web applications which is (1) seamless; one program and one language is used to produce code for both client and server, (2) client-centric; the programmer takes the viewpoint of the client that runs code on the server rather than the other way around, (3) functional and type-safe, and (4) portable; everything is implemented as a Haskell library that implicitly takes care of all networking code. Our aim is to improve the painful and error-prone experience of today's standard development methods, in which clients and servers are coded in different languages and communicate with each other using ad-hoc protocols. We present the design of our library called Haste.App, an example web application that uses it, and discuss the implementation and the compiler technology on which it depends.

Attribute grammar macros

Having extensible languages is appealing, but raises the question of how to construct extensible compilers and how to compose compilers out of a collection of pre-compiled components. We show how having attribute grammar fragments as first-class values can be put into good use to answer this question; the approach leads naturally to a plug-in architecture, in which a core compiler can be constructed out of a (collection of) pre-compiled component(s), to which extra components can safely be added as the need arises.We extend AspectAG, our Haskell library for building strongly typed first-class attribute grammars, with a set of combinators that make it easy to describe new semantics in terms of already existing semantics, just as syntax macros extend the syntax of a language. We especially show how semantics thus defined can be redefined, thus adapting some aspects of the behavior as defined by the macro system only.