Dynamically typed array languages such as Python, APL, and Matlab lift scalar operations to arrays and replicate scalars to fit applications. We present a mechanism for automatically inferring map and replicate operations in a statically-typed language in a way that resembles the programming experience of a dynamically-typed language while preserving the static typing guarantees. Our type system—which supports parametric polymorphism, higher-order functions, and top-level let-generalization—makes use of integer linear programming in order to find the minimum number of operations needed to elaborate to a well-typed program. We argue that the inference system provides useful and unsurprising guarantees to the programmer. We demonstrate important theoretical properties of the mechanism and report on the implementation of the mechanism in the statically-typed array programming language Futhark.

An important aspect of building robust systems that execute on dedicated hardware and perhaps in constrained environments is to control and manage the effects performed by program code. We present ReML, a higher-order statically-typed functional language, which allows programmers to be explicit about the effects performed by program code and in particular effects related to memory management Allowing programmers to be explicit about effects, the regions in which values reside, and the constraints under which code execute, makes programs robust to changes in the program source code and to compiler updates, including compiler optimisations. ReML is integrated with a polymorphic inference system that builds on top of region-inference, as it is implemented in the MLKit, a Standard ML compiler that uses region-based memory management as its primary memory management scheme.

Algebraic data types are central to the development and evaluation of most functional programs. It is therefore important for compilers to choose compact and efficient representations of such types, in particular to achieve good memory footprints for applications. Algebraic data types are most often represented using blocks of memory where the first word is used as a so-called tag, carrying information about the constructor, and the following words are used for carrying the constructor’s arguments. As an optimisation, lists are usually represented more compactly, using a technique called bit-stealing, which, in its simplest form, uses the word-alignment property of pointers to byte-addressed allocated memory to discriminate between the nil constructor (often represented as 0 × 1 ) and the cons constructor (aligned pointer to allocated pair). Because the representation supports that all values can be held uniformly in one machine word, possibly pointing to blocks of memory, type erasure is upheld. However, on today’s 64-bit architectures, memory addresses (pointers) are represented using only a subset of the 64 bits available in a machine word, which leave many bits unused. In this paper, we explore the use, not only of the least-significant bits of pointers, but also of the most-significant bits, for representing algebraic data types in a full ML compiler. It turns out that, with such a particular utilisation of otherwise unused bits, which we call double-ended bit-stealing, it is possible to choose unboxed representations for a large set of data types, while still not violating the principle of uniform data-representations. Examples include Patricia trees, union-find data structures, stream data types, internal language representations for types and expressions, and mutually recursive ASTs for full language definitions. The double-ended bit-stealing technique is implemented in the MLKit compiler and speedup ranges from 0 to 26 percent on benchmarks that are influenced by the technique. For MLKit, which uses abstract data types extensively, compilation speedups of around 9 percent are achieved for compiling MLton (another Standard ML compiler) and for compiling MLKit itself.

Region inference offers a mechanism to reduce (and sometimes entirely remove) the need for reference-tracing garbage collection by inferring where to insert allocation and deallocation instructions in a program at compile time. When the mechanism is combined with techniques for reference-tracing garbage collection, which is helpful in general to support programs with very dynamic memory behaviours, it turns out that region-inference is complementary to adding generations to a reference-tracing collector. However, region-inference and the associated region-representation analyses that make such a memory management strategy perform well in practice are complex, both from a theoretical point-of-view and from an implementation point-of-view. In this paper, we demonstrate a soundness problem with existing theoretical developments, which have to do with ensuring that, even for higher-order polymorphic programs, no dangling-pointers appear during a reference-tracing collection. This problem has materialised as a practical soundness problem in a real implementation based on region inference. As a solution, we present a modified, yet simple, region type-system that captures garbage-collection effects, even for polymorphic higher-order code, and outline how region inference and region-representation analyses are adapted to the new type system. The new type system allows for associating simpler region type-schemes with functions, compared to original work, makes it possible to combine region-based memory management with partly tag-free reference-tracing (and generational) garbage-collection, and repairs previously derived work that is based on the erroneous published results.

Region inference is a type-based program analysis that takes a non-annotated program as input and constructs a program that explicitly manages memory allocation and deallocation by dividing the heap into a stack of regions, each of which can grow and shrink independently from other regions, using constant-time operations. Whereas region-based memory management has shown useful in the contexts of explicit region-based memory management, and in particular, in combination with parallel execution of code, combining region inference with techniques for higher-order parallel programming has not been investigated. In this paper, we present an implementation of a fork-join parallel construct suitable for a compiler based on region inference. We present a minimal higher-order language incorporating the parallel construct, including typing rules and a dynamic semantics for the language, and demonstrate type soundness. We present a novel effect-based region-protection inference algorithm and discuss benefits and shortcomings of the approach. We also describe an efficient implementation embedded in the MLKit Standard ML compiler. Finally, we evaluate the approach and the implementation based on a number of parallel benchmarks, and thereby demonstrate that the technique effectively utilises multi-core architectures in a higher-order functional setting.

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

Compilation techniques for nested-parallel applications that can adapt to hardware and dataset characteristics are vital for unlocking the power of modern hardware. This paper proposes such a technique, which builds on flattening and is applied in the context of a functional data-parallel language. Our solution uses the degree of utilized parallelism as the driver for generating a multitude of code versions, which together cover all possible mappings of the application's regular nested parallelism to the levels of parallelism supported by the hardware. These code versions are then combined into one program by guarding them with predicates, whose threshold values are automatically tuned to hardware and dataset characteristics. Our unsupervised method---of statically clustering datasets to code versions---is different from autotuning work that typically searches for the combination of code transformations producing a single version, best suited for a specific dataset or on average for all datasets.

We present an extension to a certified financial contract management system that allows for templated declarative financial contracts and for integration with financial stochastic models through verified compilation into so-called payoff-expressions. Such expressions readily allow for determining the value of a contract in a given evaluation context, such as contexts created for stochastic simulations. The templating mechanism is useful both at the contract specification level, for writing generic reusable contracts, and for reuse of code that, without the templating mechanism, needs to be recompiled for different evaluation contexts. We report on the effect of using the certified system in the context of a GPGPU-based Monte Carlo simulation engine for pricing various over-the-counter (OTC) financial contracts. The full contract-management system, including the payoff-language compilation, is verified in the Coq proof assistant and certified Haskell code is extracted from our Coq development along with Futhark code for use in a data-parallel pricing engine.

We present a higher-order module system for the purely functional data-parallel array language Futhark. The module language has the property that it is completely eliminated at compile time, yet it serves as a powerful tool for organizing libraries and complete programs. The presentation includes a static and a dynamic semantics for the language in terms of, respectively, a static type system and a provably terminating elaboration of terms into terms of an underlying target language. The development is formalised in Coq using a novel encoding of semantic objects based on products, sets, and finite maps. The module language features a unified treatment of module type abstraction and core language polymorphism and is rich enough for expressing practical forms of module composition.

Futhark is a purely functional data-parallel array language that offers a machine-neutral programming model and an optimising compiler that generates OpenCL code for GPUs.

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.

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.

This paper describes a memory discipline that combines region-based memory management and copying garbage collection by extending Cheney's copying garbage collection algorithm to work with regions. The paper presents empirical evidence that region inference very significantly reduces the number of garbage collections; and evidence that the fastest execution is obtained by using regions alone, without garbage collection.

Berkeley* This paper presents a technique for compiling Standard ML Modules into typed intermediate language fragments, which may be compiled separately and linked using traditional linking technology to form executable code. The technique is called static inteqretataon and allows compile-time implementation details to propagate across module boundaries. Static interpretation eliminates all module-level code at compile time. The technique scales to full Standard ML and is used in the ML Kit with Regions compiler. A framework for smart recompilation makes the technique useful for compiling large programs. 1