Transformation of structure-shy programs with application to XPath queries and strategic functions

Various programming languages allow the construction of structure-shy programs. Such programs are defined generically for many different datatypes and only specify specific behavior for a few relevant subtypes. Typical examples are XML query languages that allow selection of subdocuments without exhaustively specifying intermediate element tags. Other examples are languages and libraries for polytypic or strategic functional programming and for adaptive object-oriented programming. In this paper, we present an algebraic approach to transformation of declarative structure-shy programs, in particular for strategic functions and XML queries. We formulate a rich set of algebraic laws, not just for transformation of structure-shy programs, but also for their conversion into structure-sensitive programs and vice versa. We show how subsets of these laws can be used to construct effective rewrite systems for specialization, generalization, and optimization of structure-shy programs. We present a type-safe encoding of these rewrite systems in Haskell which itself uses strategic functional programming techniques. We discuss the application of these rewrite systems for XPath query optimization and for query migration in the context of schema evolution

Canonical Forms in Interactive Exercise Assistants

Interactive exercise assistants support students in practicing exercises, and acquiring procedural skills. Many mathematical topics can be practiced in such assistants. Ideally, an interactive exercise assistant not only validates final answers, but also comments on intermediate steps submitted by a student, provides hints on how to proceed, and presents worked-out examples. For these purposes, fine control over the symbolic simplification procedures of the underlying mathematical machinery is needed. In this paper, we introduce views for mathematical expressions. A view defines an equivalence relation by choosing a canonical form of mathematical expressions. We use views to track and recognize intermediate answers, to help in presenting expressions to a user, and to control the granularity of the steps in worked-out examples. We develop the concept of a view, discuss the laws it satisfies, and show how views are composed, which means that they can be used for multiple exercise classes.

Fusing Generic Functions

Contains fulltext : 60458.pdf (author's version ) (Open Access)Generic programming is accepted by the functional programming community as a valuable tool for program development. Several functional languages have adopted the generic scheme of type-indexed values. This scheme works by specialization of a generic function to a concrete type. However, the generated code is extremely inefficient compared to its hand-written counterpart. The performance penalty is so big that the practical usefulness of generic programming is compromised. In this paper we present a optimization algorithm that is able to completely eliminate the overhead intoduced by the specialization scheme for a large class of generic functions. The presented technique is based on consumer-producer elimination as exploited by fusion, a standard general purpose optimization method. We show that our algorithm is able to optimize many practical examples of generic functions

Efficient Generic Functional Programming

Contains fulltext : 60606.pdf (author's version ) (Open Access)Generic functions are defined by induction on the structural representation of types. As a consequence, by defining just a single generic operation, one acquires this operation over any particular data type. An instance on a specific type is generated by interpretation of the type's structure. A direct translation leads to extremely inefficient code that involves many conversions between types and their structural representations. In this paper we present an optimization technique based on compile-time symbolic evaluation. We prove that the optimization removes the overhead of the generated code for a considerable class of generic functions. The proof uses typing to identify intermediate data structures that should be eliminated. In essence, the output after optimization is similar to hand-written code

Dynamic Values Need Polytypic Functions - Draft -

Contains fulltext : 176175.pdf (preprint version ) (Open Access

A Generic Programming Extension for Clean

Abstract. Generic programming enables the programmer to define functions by induction on the structure of types. Defined once, such a generic function can be used to generate a specialized function for any user defined data type. Several ways to support generic programming in functional languages have been proposed, each with its own pros and cons. In this paper we describe a combination of two existing approaches, which has the advantages of both of them. In our approach overloaded functions with class variables of an arbitrary kind can be defined generically. A single generic definition defines a kind-indexed family of overloaded functions, one for each kind. For instance, the generic mapping function generates an overloaded mapping function for each kind. Additionally, we propose a separate extension that allows to specify a customized instance of a generic function for a type in terms of the generated instance for that type.

Improved fusion for optimizing generics

Abstract. Generic programming is accepted by the functional programming community as a valuable tool for program development. Several functional languages have adopted the generic scheme of type-indexed values. This scheme works by specialization of a generic function to a concrete type. However, the generated code is extremely inefficient compared to its hand-written counterpart. The performance penalty is so big that the practical usefulness of generic programming is compromised. In this paper we present an optimization algorithm that is able to completely eliminate the overhead introduced by the specialization scheme for a large class of generic functions. The presented technique is based on consumer–producer elimination as exploited by fusion, a standard general purpose optimization method. We show that our algorithm is able to optimize many practical examples of generic functions