Practical Datatype Specializations with Phantom Types and Recursion Schemes

Datatype specialization is a form of subtyping that captures program invariants on data structures that are expressed using the convenient and intuitive datatype notation. Of particular interest are structural invariants such as well-formedness. We investigate the use of phantom types for describing datatype specializations. We show that it is possible to express statically-checked specializations within the type system of Standard ML. We also show that this can be done in a way that does not lose useful programming facilities such as pattern matching in case expressions.Comment: 25 pages. Appeared in the Proc. of the 2005 ACM SIGPLAN Workshop on M

AutoBayes: A System for Generating Data Analysis Programs from Statistical Models

Data analysis is an important scientific task which is required whenever information needs to be extracted from raw data. Statistical approaches to data analysis, which use methods from probability theory and numerical analysis, are well-founded but difficult to implement: the development of a statistical data analysis program for any given application is time-consuming and requires substantial knowledge and experience in several areas. In this paper, we describe AutoBayes, a program synthesis system for the generation of data analysis programs from statistical models. A statistical model specifies the properties for each problem variable (i.e., observation or parameter) and its dependencies in the form of a probability distribution. It is a fully declarative problem description, similar in spirit to a set of differential equations. From such a model, AutoBayes generates optimized and fully commented C/C++ code which can be linked dynamically into the Matlab and Octave environments. Code is produced by a schema-guided deductive synthesis process. A schema consists of a code template and applicability constraints which are checked against the model during synthesis using theorem proving technology. AutoBayes augments schema-guided synthesis by symbolic-algebraic computation and can thus derive closed-form solutions for many problems. It is well-suited for tasks like estimating best-fitting model parameters for the given data. Here, we describe AutoBayes's system architecture, in particular the schema-guided synthesis kernel. Its capabilities are illustrated by a number of advanced textbook examples and benchmarks

High-Level GPU Programming: Domain-Specific Optimization and Inference

When writing computer software one is often forced to balance the need for high run-time performance with high programmer productivity. By using a high-level language it is often possible to cut development times, but this typically comes at the cost of reduced run-time performance. Using a lower-level language, programs can be made very efficient but at the cost of increased development time. Real-time computer graphics is an area where there are very high demands on both performance and visual quality. Typically, large portions of such applications are written in lower-level languages and also rely on dedicated hardware, in the form of programmable graphics processing units (GPUs), for handling computationally demanding rendering algorithms. These GPUs are parallel stream processors, specialized towards computer graphics, that have computational performance more than a magnitude higher than corresponding CPUs. This has revolutionized computer graphics and also led to GPUs being used to solve more general numerical problems, such as fluid and physics simulation, protein folding, image processing, and databases. Unfortunately, the highly specialized nature of GPUs has also made them difficult to program. In this dissertation we show that GPUs can be programmed at a higher level, while maintaining performance, compared to current lower-level languages. By constructing a domain-specific language (DSL), which provides appropriate domain-specific abstractions and user-annotations, it is possible to write programs in a more abstract and modular manner. Using knowledge of the domain it is possible for the DSL compiler to generate very efficient code. We show that, by experiment, the performance of our DSLs is equal to that of GPU programs written by hand using current low-level languages. Also, control over the trade-offs between visual quality and performance is retained. In the papers included in this dissertation, we present domain-specific languages targeted at numerical processing and computer graphics, respectively. These DSL have been implemented as embedded languages in Python, a dynamic programming language that provide a rich set of high-level features. In this dissertation we show how these features can be used to facilitate the construction of embedded languages

Polynomial Size Analysis of First-Order Shapely Functions

We present a size-aware type system for first-order shapely function definitions. Here, a function definition is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of shapely function definitions may be implementations of matrix multiplication and the Cartesian product of two lists. The type system is proved to be sound w.r.t. the operational semantics of the language. The type checking problem is shown to be undecidable in general. We define a natural syntactic restriction such that the type checking becomes decidable, even though size polynomials are not necessarily linear or monotonic. Furthermore, we have shown that the type-inference problem is at least semi-decidable (under this restriction). We have implemented a procedure that combines run-time testing and type-checking to automatically obtain size dependencies. It terminates on total typable function definitions.Comment: 35 pages, 1 figur

Fusing Logic And Control With Local Transformations: An Example Optimization

Programming supports the separation of logical concerns from issues of control in program construction. While this separation of concerns leads to reduced code size and increased reusability of code, its main disadvantage is the computational overhead it incurs. Fusion techniques can be used to combine the reusability of abstract programs with the efficiency of specialized programs. In this paper we illustrate some of the ways in which rewriting strategies can be used to separate the definition of program transformation rules from the strategies under which they are applied. Doing so supports the generic definition of program transformation components. Fusion techniques for strategies can then be used to specialize such generic components. We show how the generic innermost rewriting strategy can be optimized by fusing it with the rules to which it is applied. Both the optimization and the programs to which the optimization applies are specified in the strategy language Stratego. The optimization is based on small transformation rules that are applied locally under the control of strategies, using special knowledge about the contexts in which the rules are applied

Abstract parsing for two-staged languages with concatenation

This article, based on Doh, Kim, and Schmidt’s “abstract parsing ” technique, presents an abstract interpretation for statically checking the syntax of generated code in two-staged programs. Abstract parsing is a static analysis technique for checking the syntax of generated strings. We adopt this technique for two-staged programming languages and formulate it in the abstract interpretation framework. We parameterize our analysis with the abstract domain so that one can choose the abstract domain as long as it satisfies the condition we provide. We also present an instance of the abstract domain, namely an abstract parse stack and its widening with k-cutting

Lisp, Jazz, Aikido -- Three Expressions of a Single Essence

The relation between Science (what we can explain) and Art (what we can't) has long been acknowledged and while every science contains an artistic part, every art form also needs a bit of science. Among all scientific disciplines, programming holds a special place for two reasons. First, the artistic part is not only undeniable but also essential. Second, and much like in a purely artistic discipline, the act of programming is driven partly by the notion of aesthetics: the pleasure we have in creating beautiful things. Even though the importance of aesthetics in the act of programming is now unquestioned, more could still be written on the subject. The field called "psychology of programming" focuses on the cognitive aspects of the activity, with the goal of improving the productivity of programmers. While many scientists have emphasized their concern for aesthetics and the impact it has on their activity, few computer scientists have actually written about their thought process while programming. What makes us like or dislike such and such language or paradigm? Why do we shape our programs the way we do? By answering these questions from the angle of aesthetics, we may be able to shed some new light on the art of programming. Starting from the assumption that aesthetics is an inherently transversal dimension, it should be possible for every programmer to find the same aesthetic driving force in every creative activity they undertake, not just programming, and in doing so, get deeper insight on why and how they do things the way they do. On the other hand, because our aesthetic sensitivities are so personal, all we can really do is relate our own experiences and share it with others, in the hope that it will inspire them to do the same. My personal life has been revolving around three major creative activities, of equal importance: programming in Lisp, playing Jazz music, and practicing Aikido. But why so many of them, why so different ones, and why these specifically? By introspecting my personal aesthetic sensitivities, I eventually realized that my tastes in the scientific, artistic, and physical domains are all motivated by the same driving forces, hence unifying Lisp, Jazz, and Aikido as three expressions of a single essence, not so different after all. Lisp, Jazz, and Aikido are governed by a limited set of rules which remain simple and unobtrusive. Conforming to them is a pleasure. Because Lisp, Jazz, and Aikido are inherently introspective disciplines, they also invite you to transgress the rules in order to find your own. Breaking the rules is fun. Finally, if Lisp, Jazz, and Aikido unify so many paradigms, styles, or techniques, it is not by mere accumulation but because they live at the meta-level and let you reinvent them. Working at the meta-level is an enlightening experience. Understand your aesthetic sensitivities and you may gain considerable insight on your own psychology of programming. Mine is perhaps common to most lispers. Perhaps also common to other programming communities, but that, is for the reader to decide..

A Foundation for Embedded Languages

Recent work on embedding object languages into Haskell use ``phantom types'' (i.e., parameterized types whose parameter does not occur on the right-hand side of the type definition) to ensure that the embedded object-language terms are simply typed. But is it a safe assumption that only simply-typed terms can be represented in Haskell using phantom types? And conversely, can all simply-typed terms be represented in Haskell under the restrictions imposed by phantom types? In this article we investigate the conditions under which these assumptions are true: We show that these questions can be answered affirmatively for an idealized Haskell-like language and discuss to which extent Haskell can be used as a meta-language