Specifying with syntactic theory functors

We propose a framework, syntactic theory functors (STFs), for creating syntactic structuring mechanisms for specification languages. Good support for common reuse patterns is important for systematically developing specifications for large systems. Though immaterial to foundational theory, lack of support otherwise causes lengthy writing of boilerplate code or repeated adaptation from one context to another. We present STFs in the context of the Goguen & Burstall institution theory. This theory captures the essential structure of ontologies, modelling and formal specifications (OMS). In particular it provides powerful structuring mechanisms that are independent of the specification formalism, i.e., they are institution-independent. The presented STF framework is institution-independent as well. As such it encompasses many approaches to software and information systems. STFs subsume the standard institution-independent structuring mechanisms, and open up new ways of reusing existing and structuring new specifications. In this, STFs subsume and enrich the tool-set of ‘good practices’, which includes separation of concerns, ease of reuse of specification-text, and improved theorem proving support. STFs are aimed at structuring and reuse beyond the classical mechanisms. However, most STFs are institution-specific and support specific reuse patterns in that institution. With such institution-specific STFs it is possible to incrementally grow more complex institutions from simpler ones. This is very much needed when developing ontologies or specification languages for a new domain. In this paper, we motivate STFs with examples in Casl, the common standard algebraic specification language. We further demonstrate how STFs can ease specification through capturing repeated constructions once and for all as patterns formulated as STFs

Errors as Data Values

A “thrown” exception is a non-local side effect that complicates static reasoning about code. Particularly in functional languages it is fairly common to instead propagate errors as ordinary values. The propagation is sometimes done in monadic style, and some languages include syntactic conveniences for writing expressions in that style. We discuss a guarded- algebra-inspired approach for integrating similar, implicit error propagation into a language with “normal” function application syntax. The presented failure management approach accommodates language designs with all- referentially-transparent expressions. It furthermore supports automatically checking data invariants and function pre- and post-conditions, recording a trace of any due-to-an-error unevaluateable or failed expressions, and in some cases retaining “bad” values for potential use in recovering from an error

Axiom-Based Transformations: Optimisation and Testing

Programmers typically have knowledge about properties of their programs that aren't explicitly expressed in the code ­ properties that may be very useful for, e.g., compiler optimisation and automated testing. Although such information is sometimes written down in a formal or informal specification, it is generally not accessible to compilers and other tools. However, using the idea of concepts and axioms in the upcoming C++ standard, we may embed axioms with program code. In this paper, we sketch how such axioms can be interpreted as rewrite rules and test oracles. Rewrite rules together with user-defined transformation strategies allow us to implement program or library-specific optimisations.publishedVersio

Interfacing concepts: Why declaration style shouldn't matter

A concept (or signature) describes the interface of a set of abstract types by listing the operations that should be supported for those types. When implementing a generic operation, such as sorting, we may then specify requirements such as “elements must be comparable” by requiring that the element type models the Comparable concept. We may also use axioms to describe behaviour that should be common to all models of a concept. However, the operations specified by the concept are not always the ones that are best suited for the implementation. For example, numbers and matrices may both be addable, but adding two numbers is conveniently done by using a return value, whereas adding a sparse and a dense matrix is probably best achieved by modifying the dense matrix. In both cases, though, we may want to pretend we're using a simple function with a return value, as this most closely matches the notation we know from mathematics. This paper presents two simple concepts to break the notational tie between implementation and use of an operation: functionalisation, which derives a set of canonical pure functions from a procedure; and mutification, which translates calls using the functionalised declarations into calls to the implemented procedure.publishedVersio

An Ecosystem Architecture for the Magnolia Programming Language

We describe our envisioned architecture for an ecosystem built around the Magnolia research programming language. The compiler for the language is built by interconnecting a core monolithic chunk with modular, extensible program transformations. "Plugins" are then constructed around a common input format, including composable program transformations|both at the syntactic and semantic level. This submission is a poster submission

Finite difference methods fengshui: alignment through a mathematics of arrays

Numerous scientific-computational domains make use of array data. The core computing of the numerical methods and the algorithms involved is related to multi-dimensional array manipulation. Memory layout and the access patterns of that data are crucial to the optimal performance of the array-based computations. As we move towards exascale computing, writing portable code for efficient data parallel computations is increasingly requiring an abstract productive working environment. To that end, we present the design of a framework for optimizing scientific array-based computations, building a case study for a Partial Differential Equations solver. By embedding the Mathematics of Arrays formalism in the Magnolia programming language, we assemble a software stack capable of abstracting the continuous high-level application layer from the discrete formulation of the collective array-based numerical methods and algorithms and the final detailed low-level code. The case study lays the groundwork for achieving optimized memory layout and efficient computations while preserving a stable abstraction layer independent of underlying algorithms and changes in the architecture.Peer ReviewedPostprint (author's final draft

Revisiting Language Support for Generic Programming: When Genericity Is a Core Design Goal

Context Generic programming, as defined by Stepanov, is a methodology for writing efficient and reusable algorithms by considering only the required properties of their underlying data types and operations. Generic programming has proven to be an effective means of constructing libraries of reusable software components in languages that support it. Generics-related language design choices play a major role in how conducive generic programming is in practice. Inquiry Several mainstream programming languages (e.g. Java and C++) were first created without generics; features to support generic programming were added later, gradually. Much of the existing literature on supporting generic programming focuses thus on retrofitting generic programming into existing languages and identifying related implementation challenges. Is the programming experience significantly better, or different when programming with a language designed for generic programming without limitations from prior language design choices? Approach We examine Magnolia, a language designed to embody generic programming. Magnolia is representative of an approach to language design rooted in algebraic specifications. We repeat a well-known experiment, where we put Magnolia’s generic programming facilities under scrutiny by implementing a subset of the Boost Graph Library, and reflect on our development experience. Knowledge We discover that the idioms identified as key features for supporting Stepanov-style generic programming in the previous studies and work on the topic do not tell a full story. We clarify which of them are more of a means to an end, rather than fundamental features for supporting generic programming. Based on the development experience with Magnolia, we identify variadics as an additional key feature for generic programming and point out limitations and challenges of genericity by property. Grounding Our work uses a well-known framework for evaluating the generic programming facilities of a language from the literature to evaluate the algebraic approach through Magnolia, and we draw comparisons with well-known programming languages. Importance This work gives a fresh perspective on generic programming, and clarifies what are fundamental language properties and their trade-offs when considering supporting Stepanov-style generic programming. The understanding of how to set the ground for generic programming will inform future language design.publishedVersio

Revisiting Language Support for Generic Programming: When Genericity Is a Core Design Goal

ContextGeneric programming, as defined by Stepanov, is a methodology for writing efficient and reusable algorithms by considering only the required properties of their underlying data types and operations. Generic programming has proven to be an effective means of constructing libraries of reusable software components in languages that support it. Generics-related language design choices play a major role in how conducive generic programming is in practice.InquirySeveral mainstream programming languages (e.g. Java and C++) were first created without generics; features to support generic programming were added later, gradually. Much of the existing literature on supporting generic programming focuses thus on retrofitting generic programming into existing languages and identifying related implementation challenges. Is the programming experience significantly better, or different when programming with a language designed for generic programming without limitations from prior language design choices?ApproachWe examine Magnolia, a language designed to embody generic programming. Magnolia is representative of an approach to language design rooted in algebraic specifications. We repeat a well-known experiment, where we put Magnolia’s generic programming facilities under scrutiny by implementing a subset of the Boost Graph Library, and reflect on our development experience.KnowledgeWe discover that the idioms identified as key features for supporting Stepanov-style generic programming in the previous studies and work on the topic do not tell a full story. We clarify which of them are more of a means to an end, rather than fundamental features for supporting generic programming. Based on the development experience with Magnolia, we identify variadics as an additional key feature for generic programming and point out limitations and challenges of genericity by property.GroundingOur work uses a well-known framework for evaluating the generic programming facilities of a language from the literature to evaluate the algebraic approach through Magnolia, and we draw comparisons with well-known programming languages.ImportanceThis work gives a fresh perspective on generic programming, and clarifies what are fundamental language properties and their trade-offs when considering supporting Stepanov-style generic programming. The understanding of how to set the ground for generic programming will inform future language design.</p

High-performance design patterns for modern Fortran

This paper presents ideas for using coordinate-free numerics in modern Fortran to achieve code flexibility in the partial differential equation (PDE) domain. We also show how Fortran, over the last few decades, has changed to become a language well-suited for state-of-the-art software development. Fortran’s new coarray distributed data structure, the language’s class mechanism, and its side-effect-free, pure procedure capability provide the scaffolding on which we implement HPC software. These features empower compilers to organize parallel computations with efficient communication. We present some programming patterns that support asynchronous evaluation of expressions comprised of parallel operations on distributed data. We implemented these patterns using coarrays and the message passing interface (MPI). We compared the codes’ complexity and performance. The MPI code is much more complex and depends on external libraries. The MPI code on Cray hardware using the Cray compiler is 1.5–2 times faster than the coarray code on the same hardware. The Intel compiler implements coarrays atop Intel’s MPI library with the result apparently being 2–2.5 times slower than manually coded MPI despite exhibiting nearly linear scaling efficiency. As compilers mature and further improvements to coarrays comes in Fortran 2015, we expect this performance gap to narrow.publishedVersio