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Publications (385)
Functional logic languages have a rich literature, but it is tricky to give them a satisfying semantics. In this paper we describe the Verse calculus, VC, a new core calculus for deterministic functional logic programming. Our main contribution is to equip VC with a small-step rewrite semantics, so that we can reason about a VC program in the same...
The trie data structure is a good choice for finite maps whose keys are data structures (trees) rather than atomic values. But what if we want the keys to be patterns, each of which matches many lookup keys? Efficient matching of this kind is well studied in the theorem prover community, but much less so in the context of statically typed functiona...
Automatic differentiation (AD) is a technique for computing the derivative of a function represented by a program. This technique is considered as the de-facto standard for computing the differentiation in many machine learning and optimisation software tools. Despite the practicality of this technique, the performance of the differentiated program...
In this paper, we give a simple and efficient implementation of reverse-mode automatic differentiation, which both extends easily to higher-order functions, and has run time and memory consumption linear in the run time of the original program. In addition to a formal description of the translation, we also describe an implementation of this algori...
Type inference for parametric polymorphism is wildly successful, but has always suffered from an embarrassing flaw: polymorphic types are themselves not first class. We present Quick Look, a practical, implemented, and deployable design for impredicative type inference. To demonstrate our claims, we have modified GHC, a production-quality Haskell c...
A compiler should warn if a function defined by pattern matching does not cover its inputs—that is, if there are missing or redundant patterns. Generating such warnings accurately is difficult for modern languages due to the myriad of language features that interact with pattern matching. This is especially true in Haskell, a language with a compli...
A language supporting polymorphism is a boon to programmers: they can express complex ideas once and reuse functions in a variety of situations. However, polymorphism is pain for compilers tasked with producing efficient code that manipulates concrete values.
This paper presents a new intermediate language that allows for efficient static compilati...
Build systems are awesome, terrifying – and unloved. They are used by every developer around the world, but are rarely the object of study. In this paper, we offer a systematic, and executable, framework for developing and comparing build systems, viewing them as related points in a landscape rather than as isolated phenomena. By teasing apart exis...
For many years, GHC has implemented an extension to Haskell that allows type variables to be bound in type signatures and patterns, and to scope over terms. This extension was never properly specified. We rectify that oversight here. With the formal specification in hand, the otherwise-labyrinthine path toward a design for binding type variables in...
For many years, GHC has implemented an extension to Haskell that allows type variables to be bound in type signatures and patterns, and to scope over terms. This extension was never properly specified. We rectify that oversight here. With the formal specification in hand, the otherwise-labyrinthine path toward a design for binding type variables in...
Build systems are awesome, terrifying -- and unloved. They are used by every developer around the world, but are rarely the object of study. In this paper we offer a systematic, and executable, framework for developing and comparing build systems, viewing them as related points in landscape rather than as isolated phenomena. By teasing apart existi...
The design space for type systems that support impredicative instantiation is extremely complicated. One needs to strike a balance between expressiveness, simplicity for both the end programmer and the type system implementor, and how easily the system can be integrated with other advanced type system concepts. In this paper, we propose a new point...
For many years, GHC has implemented an extension to Haskell that allows type variables to be bound in type signatures and patterns, and to scope over terms. This extension was never properly specified. We rectify that oversight here. With the formal specification in hand, the otherwise-labyrinthine path toward a design for binding type variables in...
We present a system for the automatic differentiation of a higher-order functional array-processing language. The core functional language underlying this system simultaneously supports both source-to-source automatic differentiation and global optimizations such as loop transformations. Thanks to this feature, we demonstrate how for some real-worl...
We show how to compile high-level functional array-processing programs, drawn from image processing and machine learning, into C code that runs as fast as hand-written C. The key idea is to transform the program to destination-passing style, which in turn enables a highly-efficient stack-like memory allocation discipline.
We introduce a general way to locate programmer mistakes that are detected by static analyses. The program analysis is expressed in a general constraint language that is powerful enough to model type checking, information flow analysis, dataflow analysis, and points-to analysis. Mistakes in program analysis result in unsatisfiable constraints. Give...
Parametric polymorphism is one of the linchpins of modern typed programming, but it comes with a real performance penalty. We describe this penalty; offer a principled way to reason about it (kinds as calling conventions); and propose levity polymorphism. This new form of polymorphism allows abstractions over calling conventions; we detail and veri...
Many fields of study in compilers give rise to the concept of a join point—a place where different execution paths come together. Join points are often treated as functions or continuations, but we believe it is time to study them in their own right. We show that adding join points to a direct-style functional intermediate language is a simple but...
Parametric polymorphism is one of the linchpins of modern typed programming, but it comes with a real performance penalty. We describe this penalty; offer a principled way to reason about it (kinds as calling conventions); and propose levity polymorphism. This new form of polymorphism allows abstractions over calling conventions; we detail and veri...
Many fields of study in compilers give rise to the concept of a join point—a place where different execution paths come together. Join points are often treated as functions or continuations, but we believe it is time to study them in their own right. We show that adding join points to a direct-style functional intermediate language is a simple but...
Ideally, a program written as a composition of concise, self-contained components should perform as well as the equivalent hand-written version where the functionality of what was many components has been manually combined into a monolithic implementation. That is, programmers should not have to sacrifice code clarity or good software engineering p...
We study the notion of extensibility in functional data types, as a new approach to the problem of decorating abstract syntax trees with additional sets of information. We observed the need for such extensibility while redesigning the data types representing Haskell abstract syntax inside GHC. Specifically, we describe our approach to the tree-deco...
Pattern matching has proven to be a convenient, expressive way of inspecting data. Yet this language feature, in its traditional form, is limited: patterns must be data constructors of concrete data types. No computation or abstraction is allowed. The data type in question must be concrete, with no ability to enforce any invariants. Any change in t...
Monads have taken the world by storm, and are supported by do-notation (at least in Haskell). Programmers are increasingly waking up to the usefulness and ubiquity of Applicatives, but they have so far been hampered by the absence of supporting notation. In this paper we show how to re-use the very same do-notation to work for Applicatives as well,...
Monads have taken the world by storm, and are supported by do-notation (at least in Haskell). Programmers are increasingly waking up to the usefulness and ubiquity of Applicatives, but they have so far been hampered by the absence of supporting notation. In this paper we show how to re-use the very same do-notation to work for Applicatives as well,...
Pattern matching has proven to be a convenient, expressive way of inspecting data. Yet this language feature, in its traditional form, is limited: patterns must be data constructors of concrete data types. No computation or abstraction is allowed. The data type in question must be concrete, with no ability to enforce any invariants. Any change in t...
Most build systems start small and simple, but over time grow into hairy monsters that few dare to touch. As we demonstrate in this paper, there are a few issues that cause build systems major scalability challenges, and many pervasively used build systems (e.g. Make) do not scale well.
This paper presents a solution to the challenges we identify....
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 abst...
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 desig...
The ability to perform type tests at runtime blurs the line between statically-typed and dynamically-checked languages. Recent developments in Haskell’s type system allow even programs that use reflection to themselves be statically typed, using a type-indexed runtime representation of types called \(\textsf {\textit{TypeRep}}\). As a result we can...
For ML and Haskell, accurate warnings when a function definition has redundant or missing patterns are mission critical. But to-day's compilers generate bogus warnings when the programmer uses guards (even simple ones), GADTs, pattern guards, or view patterns. We give the first algorithm that handles all these cases in a single, uniform framework,...
Haskell, as implemented by the Glasgow Haskell Compiler (GHC), allows expressive type-level programming. The most popular typelevel programming extension is TypeFamilies, which allows users to write functions on types. Yet, using type functions can cripple type inference in certain situations. In particular, lack of injectivity in type functions me...
Type inference engines often give terrible error messages, and the more sophisticated the type system the worse the problem. We show that even with the highly expressive type system implemented by the Glasgow Haskell Compiler (GHC)-including type classes, GADTs, and type families-it is possible to identify the most likely source of the type error,...
SMT-based checking of refinement types for call-by-value languages is a well-studied subject. Unfortunately, the classical translation of refinement types to verification conditions is unsound under lazy evaluation. When checking an expression, such systems implicitly assume that all the free variables in the expression are bound to values. This pr...
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 ab...
Since the mid '80s, compiler writers for functional languages (es-pecially lazy ones) have been writing papers about identifying and exploiting thunks and lambdas that are used only once. However it has proved difficult to achieve both power and simplicity in prac-tice. We describe a new, modular analysis for a higher-order lan-guage, which is both...
Open, type-level functions are a recent innovation in Haskell that move Haskell towards the expressiveness of dependent types, while retaining the look and feel of a practical programming language. This paper shows how to increase expressiveness still further, by adding closed type functions whose equations may overlap, and may have non-linear patt...
Module systems like that of Haskell permit only a weak form of modularity in which module implementations depend directly on other implementations and must be processed in dependency order. Module systems like that of ML, on the other hand, permit a stronger form of modularity in which explicit interfaces express assumptions about dependencies, and...
Module systems like that of Haskell permit only a weak form of modularity in which module implementations depend directly on other implementations and must be processed in dependency order. Module systems like that of ML, on the other hand, permit a stronger form of modularity in which explicit interfaces express assumptions about dependencies, and...
Open, type-level functions are a recent innovation in Haskell that move Haskell towards the expressiveness of dependent types, while retaining the look and feel of a practical programming language. This paper shows how to increase expressiveness still further, by adding closed type functions whose equations may overlap, and may have non-linear patt...
Stream fusion is a powerful technique for automatically transforming high-level sequence-processing functions into efficient implementations. It has been used to great effect in Haskell libraries for manipulating byte arrays, Unicode text, and unboxed vectors. However, some operations, like vector append, still do not perform well within the standa...
Computer science is one of the richest, most exciting disciplines on the planet, yet any teenager will tell you that ICT (as it is called in UK schools --- "information and communication technology") is focused almost entirely on the use and application of computers, and in practice covers nothing about how computers work, nor programming, nor anyt...
Computer science is one of the richest, most exciting disciplines on the planet, yet any teenager will tell you that ICT (as it is called in UK schools --- "information and communication technology") is focused almost entirely on the use and application of computers, and in practice covers nothing about how computers work, nor programming, nor anyt...
Stream fusion is a powerful technique for automatically transforming high-level sequence-processing functions into efficient implementations. It has been used to great effect in Haskell libraries for manipulating byte arrays, Unicode text, and unboxed vectors. However, some operations, like vector append, still do not perform well within the standa...
The Computing at School (CAS) Working Group aims to promote the teaching of computer science at school. CAS was born out of our excitement with our discipline, combined with a serious concern that many students are being "turned off" computing by a combination of factors that have conspired to make the subject seem dull and pedestrian. Our goal is...
Computer science in UK schools is a subject in decline: the ratio of Computing to Maths A-Level students (i.e. ages 16--18) has fallen from 1:2 in 2003 to 1:20 in 2011 and in 2012. In 2011 and again in 2012, the ratio for female students was 1:100, with less than 300 female students taking Computing A-Level in the whole of the UK each year. Similar...
Even well-typed programs can go wrong in modern functional languages, by encountering a pattern-match failure, or simply returning the wrong answer. An increasingly-popular response is to allow programmers to write contracts that express semantic properties, such as crash-freedom or some useful post-condition. We study the static verification of su...
Even well-typed programs can go wrong in modern functional languages, by encountering a pattern-match failure, or simply returning the wrong answer. An increasingly-popular response is to allow programmers to write contracts that express semantic properties, such as crash-freedom or some useful post-condition. We study the static verification of su...
Stream fusion [6] is a powerful technique for automatically transforming high-level sequence-processing functions into efficient implementations. It has been used to great effect in Haskell libraries for manipulating byte arrays, Unicode text, and unboxed vectors. However, some operations, like vector append, still do not perform well within the st...
We propose a programming style for incremental stream pro-cessing based on typed simple generators. It promotes modularity and decoupling of producers and consumers just like lazy evaluation. Simple generators, however, expose the implicit suspension and resumption in-herent in lazy evaluation as computational effects, and hence are robust in the p...
Flattening nested parallelism is a vectorising code transform that converts irregular nested parallelism into flat data parallelism. Although the result has good asymptotic performance, flattening thoroughly restructures the code. Many intermediate data structures and traversals are introduced, which may or may not be eliminated by subsequent optim...
We present a refined approach to parallel array fusion that uses indexed types to specify the internal representation of each array. Our approach aids the client programmer in reasoning about the performance of their program in terms of the source code. It also makes the intermediate code easier to transform at compile-time, resulting in faster com...
Supercompilation is a powerful technique for program optimisation and theorem proving. In this paper we describe and evaluate three improvements to the Cambridge Haskell Supercompiler (CHSC). We reduce supercompiled program size by the use of a weak nor-maliser and aggressive rollback, and we improve the performance of supercompiled programs by hea...
The Glasgow Haskell Compiler is an optimizing compiler that expresses and manipulates first-class equality proofs in its intermediate language. We describe a simple, elegant technique that exploits these equality proofs to support deferred type errors. The technique requires us to treat equality proofs as possibly-divergent terms; we show how to do...
Existing approaches to higher-order vectorisation, also known as flattening nested data parallelism, do not preserve the asymptotic work complexity of the source program. Straightforward examples, such as sparse matrix-vector multiplication, can suffer a severe blow-up in both time and space, which limits the practicality of this method. We discuss...
The Glasgow Haskell Compiler is an optimizing compiler that expresses and manipulates first-class equality proofs in its intermediate language. We describe a simple, elegant technique that exploits these equality proofs to support deferred type errors. The technique requires us to treat equality proofs as possibly-divergent terms; we show how to do...
Though Haskell is predominantly type-safe, implementations contain a few loopholes through which code can bypass typing and module encapsulation. This paper presents Safe Haskell, a language extension that closes these loopholes. Safe Haskell makes it possible to confine and safely execute untrusted, possibly malicious code. By strictly enforcing t...
Static type systems strive to be richly expressive while still being simple enough for programmers to use. We describe an experiment that enriches Haskell's kind system with two features promoted from its type system: data types and polymorphism. The new system has a very good power-to-weight ratio: it offers a significant improvement in expressive...
We describe a library-based approach to constructing termination tests suitable for controlling termination of symbolic methods such as partial evaluation, supercompilation and theorem proving. With our combinators, all termination tests are correct by construction. We show how the library can be designed to embody various optimisations of the term...
We present Cloud Haskell, a domain-specific language for developing programs for a distributed computing environment. Implemented as a shallow embedding in Haskell, it provides a message-passing communication model, inspired by Erlang, without introducing incompatibility with Haskell's established shared-memory concurrency. A key contribution is a...
We present a new programming model for deterministic parallel computation in a pure functional language. The model is monadic and has explicit granularity, but allows dynamic construction of dataflow networks that are scheduled at runtime, while remaining deterministic and pure. The implementation is based on monadic concurrency, which has until no...
In a parallel, shared-memory, language with a garbage collected heap, it is desirable for each processor to perform minor garbage collections independently. Although obvious, it is difficult to make this idea pay off in practice, especially in languages where mutation is common. We present several techniques that substantially improve the state of...
We present Cloud Haskell, a domain-specific language for developing programs for a distributed computing environment. Implemented as a shallow embedding in Haskell, it provides a message-passing communication model, inspired by Erlang, without introducing incompatibility with Haskell's established shared-memory concurrency. A key contribution is a...
Advanced type system features, such as GADTs, type classes and type families, have proven to be invaluable language extensions for ensuring data invariants and program correctness. Unfortunately, they pose a tough problem for type inference when they are used as local type assumptions. Local type assumptions often result in the lack of principal ty...
Languages with rich type systems are beginning to employ a blend of type inference and type checking, so that the type inference engine is guided by programmer-supplied type annotations. In this paper we show, for the first time, how to combine the virtues of two well-established ideas: unification-based inference, and bidirectional propagation of...
Modular languages support generative type abstraction, ensuring that an abstract type is distinct from its representation, except inside the implementation where the two are synonymous. We show that this well-established feature is in tension with the non-parametric features of newer type systems, such as indexed type families and GADTs. In this pa...
System FC is an explicitly typed language that serves as the tar-get language for Haskell source programs. System FC is based on System F with the addition of erasable but explicit type equality proof witnesses. This paper improves FC in two directions: The first contribution is extending term-level functions with the ability to return equality pro...
Modular languages support generative type abstraction, ensuring that an abstract type is distinct from its representation, except inside the implementation where the two are synonymous. We show that this well-established feature is in tension with the non-parametric features of newer type systems, such as indexed type families and GADTs. In this pa...
Dataflow analysis and transformation of control-flow graphs is pervasive in optimizing compilers, but it is typically entangled with the details of a particular compiler. We describe Hoopl, a reusable library that makes it unusually easy to define new analyses and transformations for any compiler written in Haskell. Hoopl's interface is modular and...
Supercompilation is a technique due to Turchin [1] which allows for the construction of program optimisers that are both simple and extremely powerful. Supercompilation is capable of achieving transformations such as deforestation [2], function specialisation and constructor specialisation [3]. Inspired by Mitchell’s promising results [4], we show...
Dataflow analysis and transformation of control-flow graphs is pervasive in optimizing compilers, but it is typically entangled with the details of a particular compiler. We describe Hoopl, a reusable library that makes it unusually easy to define new analyses and transformations for any compiler written in Haskell. Hoopl's interface is modular and...
Tony Hoare has always been a leader in writing down and proving properties of programs. To prove properties of programs automatically,
the most widely used technology today is the ubiquitous type checker. Alas, static type systems inevitably exclude some good
programs and allow some bad ones. Thus motivated, we describe some fun we have been having...
We present a novel approach to regular, multi-dimensional arrays in Haskell. The main highlights of our approach are that it (1) is purely functional, (2) supports reuse through shape polymorphism, (3) avoids unnecessary intermediate structures rather than relying on subsequent loop fusion, and (4) supports transparent parallelisation.
We show how...
From the dawn of time, all derivatives of the classic Hindley-Milner type system have supported implicit generalisation of local let- bindings. Yet, as we will show, for more sophisticated type systems implicit let-generalisation imposes a disproportionate complex- ity burden. Moreover, it turns out that the feature is very seldom used, so we propo...
We present Hoopl, a Haskell library that makes it easy for compiler writers to implement program transformations based on dataflow analyses. The compiler writer must identify (a) logical assertions on which the transformation will be based; (b) a representation of such assertions, which should form a lattice of finite height; (c) transfer functions...
It is common for compilers to derive the calling convention of a function from its type. Doing so is simple and modular but misses many optimisation opportunities, particularly in lazy, higher-order functional languages with extensive use of currying. We restore the lost opportunities by defining Strict Core, a new intermediate lan- guage whose typ...
Even Haskell programs can occasionally go wrong. Programs calling head on an empty list, and incomplete patterns in function definitions can cause program crashes, reporting little more than the precise location where error was ultimately called. Being told that one application of the head function in your program went wrong, without knowing which...
Purely functional programs should run well on parallel hardware because of the absence of side effects, but it has proved hard to realise this potential in practice. Plenty of papers describe promis- ing ideas, but vastly fewer describe real implementations with good wall-clock performance. We describe just such an implementation, and quantitativel...
GADTs have proven to be an invaluable language extension, for ensuring data invariants and program correctness among others. Unfortunately, they pose a tough problem for type inference: we lose the principal-type property, which is necessary for modular type inference.
We present a novel and simplified type inference approach for local type assumpt...
GADTs have proven to be an invaluable language extension, for ensuring data invariants and program correctness among others. Unfortunately, they pose a tough problem for type inference: we lose the principal-type property, which is necessary for modular type inference.
We present a novel and simplified type inference approach for local type assumpt...
Haskell is now quite widely used, but its most important contributions are the ideas that it embodies. In this talk I will focus on one of these ideas, namely type classes, with a few anecdotes and reflections along the way about the process of developing the language.
Type classes are probably Haskell’s most distinctive feature. The original idea...
Program errors are hard to detect and are costly both to programmers who spend significant efforts in debugging, and for systems that are guarded by runtime checks. Static verification techniques have been applied to imperative and object-oriented languages, like Java and C#, but few have been applied to a higher-order lazy functional language, lik...
If you want to program a parallel computer, a purely functional language like Haskell is a promising starting point. Since the language is pure, it is by-default safe for parallel evaluation, whereas imperative languages are by-default unsafe. But that doesn’t make it easy! Indeed it has proved quite difficult to get robust, scalable performance in...
We report on an extension of Haskell with open type-level func- tions and equality constraints that unifies earlier work on G ADTs, functional dependencies, and associated types. The contribution of the paper is that we identify and characterise the key techni- cal challenge of entailment checking; and we give a novel, decid- able, sound, and compl...
Abstract Languages supporting polymorphism,typically have ad-hoc restric- tions on where,polymorphic,types may,occur. Supporting “first- class” polymorphism, by lifting those restrictions, is obviously de- sirable, but it is hard to achieve this without sacrificing type infer- ence. We present a new,type system for higher-rank and impred- icative p...
Languages supporting polymorphism typically have ad-hoc restric- tions on where polymorphic types may occur. Supporting "first- class" polymorphism, by lifting those restrictions, is obviously de- sirable, but it is hard to achieve this without sacrificing type infer- ence. We present a new type system for higher-rank and impred- icative polymorphi...
Haskell has a sophisticated mechanism for overloading identifiers with multiple definitions at distinct types. Object-oriented programming has a similar notion of overriding and overloading for methods names. Unfortunately, it is not possible to encode object-oriented overloading directly using Haskell overloading. This deficiency becomes particula...
System F is ubiquitous in logic, theorem proving, language meta-theory, compiler intermediate languages, and elsewhere. Along with its type abstractions come type applications, but these often appear redundant. This redundancy is both distracting and costly for type-directed compilers.
We introduce System IF, for implicit System F, in which many ty...
We present a parallel generational-copying garbage collector im- plemented for the Glasgow Haskell Compiler. We use a block- structured memory allocator, which provides a natural granularity for dividing the work of GC between many threads, leading to a simple yet effective method for parallelising copying GC. The re- sults are encouraging: we demo...
This practical tutorial introduces the features available in Haskell for writing parallel and concurrent programs. We first
describe how to write semi-explicit parallel programs by using annotations to express opportunities for parallelism and to
help control the granularity of parallelism for effective execution on modern operating systems and pro...
Writing concurrent programs is notoriously difficult, and is of increasing practical importance. A particular source of concern is that even correctly-implemented concurrency abstractions cannot be composed together to form larger abstractions. In this paper we present a new concurrency model, based on transactional memory, that offers far richer c...
Vectorisation for functional programs, also called the flat-tening transformation, relies on drastically reordering computations and restructuring the representation of data types. As a result, it only applies to the purely functional core of a fully-fledged functional language, such as Haskell or ML. A concrete implementation needs to apply vector...
Abstract Delimited continuations are more expressive than traditional abortive continuations and they apparently require a framework beyond traditional continuation-passing style (CPS). We show that this is not the case: standard CPS is sucient,to explain the common control operators for delimited continuations. We demonstrate this fact and present...
We report on an extension of Haskell with type(-level) func-tions and equality constraints. We illustrate their usefulness in the con-text of phantom types, GADTs and type classes. Problems in the context of type checking are identified and we sketch our solution: a decidable type checking algorithm for a restricted class of type functions. More-ov...
In the light of evidence that Haskell programs compiled by GHC exhibit large numbers of mispredicted branches on modern processors, we re-examine the "tagless" aspect of the STG-machine that GHC uses as its evaluation model.
We propose two tagging strategies: a simple strategy called semi-tagging that seeks to avoid one common source of unpredictab...
User-defined data types, pattern-matching, and recursion are ubiquitous features of Haskell programs. Sometimes a function is called with arguments that are statically known to be in constructor form, so that the work of pattern-matching is wasted. Even worse, the argument is sometimes freshly-allocated, only to be immediately decomposed by the fun...
Abstract We propose,an extension to list comprehensions,that makes,it easy to express the kind of queries one would write in SQL using ORDER BY, GROUP BY, and LIMIT. Our extension adds expressive power to comprehensions, and generalises the SQL constructs that inspired it. Moreover, it is easy to implement, using simple desugaring rules.
The Glasgow Haskell Compiler (GHC) has quite sophisticated sup- port for concurrency in its runtime system, which is written in low- level C code. As GHC evolves, the runtime system becomes in- creasingly complex, error-prone, difficult to maintain and difficult to add new concurrency features. This paper presents an alternative approach to impleme...
Program errors are hard to detect and are costly both to program-mers who spend significant efforts in debugging, and to systems that are guarded by runtime checks. Static verification techniques have been applied to imperative and object-oriented languages, like Java and C#, but few have been applied to a higher-order lazy func-tional language, li...
