Computer architectures for functional and logic languages

PhD ThesisIn recent years interest in functional and logic languages has grown considerably. Both classes of language offer advantages for programming and have an influential group of people promoting them. As yet no consensus has formed as to which class is best, and such a consensus may never form. Future general-purpose computer architectures may well be required to support both classes of language efficiently. Novel architectures designed to support both classes of languages could even add impetus to the area of hybrid functional/logic languages. Treleaven et al[68] have proposed a classification of computational mechanisms which they believe underly several types of novel computer architecture (i.e. control flow, data flow and reduction). The classification partitions novel general-purpose architectures into the following classes: control driven - where a statement is executed when it is selected by flow(s) of control, data driven - where a statement is executed when some combination of its arguments are available, and demand driven - where a statement is executed when the result it produces is needed by another, already active instruction. This thesis investigates the efficient support of both functional and logic languages using an architecture that attempts to be general purpose by embodying all the mechanisms that underly the above classification. A novel packet communication architecture is presented which intergrates the control driven, data driven and demand driven computational mechanisms. A software emulator for the machine was used as the basis for separate implementations of functional and logic languages, which were in turn used to evaluate the effectiveness of the computational mechanisms described in the classification. These mechanisms allowed functional languages to be implemented wi th ease, but caused severe problems when used to support logic languages. The difficulties with these mechanisms are taken as signifying that they do not provide adequate support for logic languages. The problems encountered led to the development of a novel implementation technique for logic languages, which also proved to be a good basis for a combined functional and logic model. This model is believed to provide a sound foundation for a parallel computer system that would support functional and logic languages with equal elegance and efficiency, and would therefore also support hybrid languages. The design for such a computer is described at the end of this thesis.the Science and Engineering Research Council, Great Britain

SASLOG : Lazy Evaluation Meets Backtracking

We describe a combined functional / logic programming language SASLOG which contains Turner’s SASL, a fully lazy, higher-order functional language, and pure Prolog as subsets. Our integration is symmetric, i.e. functional terms can appear in the logic part of the program and v.v. Exploiting the natural correspondence between backtracking and lazy streams yields an elegant solution to the problem of transferring alternative variable bindings to the calling functional part of the program. We replace the rewriting approach to function evaluation by combinator graph reduction, thereby regaining computational efficiency and the structure sharing properties. Our solution is equally well suited to a fixed combinator set and to a super combinator implementation. In the paper we use Turner's fixed combinator set

Typed Generic Traversal With Term Rewriting Strategies

A typed model of strategic term rewriting is developed. The key innovation is that generic traversal is covered. To this end, we define a typed rewriting calculus S'_{gamma}. The calculus employs a many-sorted type system extended by designated generic strategy types gamma. We consider two generic strategy types, namely the types of type-preserving and type-unifying strategies. S'_{gamma} offers traversal combinators to construct traversals or schemes thereof from many-sorted and generic strategies. The traversal combinators model different forms of one-step traversal, that is, they process the immediate subterms of a given term without anticipating any scheme of recursion into terms. To inhabit generic types, we need to add a fundamental combinator to lift a many-sorted strategy $s$ to a generic type gamma. This step is called strategy extension. The semantics of the corresponding combinator states that s is only applied if the type of the term at hand fits, otherwise the extended strategy fails. This approach dictates that the semantics of strategy application must be type-dependent to a certain extent. Typed strategic term rewriting with coverage of generic term traversal is a simple but expressive model of generic programming. It has applications in program transformation and program analysis.Comment: 85 pages, submitted for publication to the Journal of Logic and Algebraic Programmin

Automated theorem proving in first-order logic modulo: on the difference between type theory and set theory

Resolution modulo is a first-order theorem proving method that can be applied both to first-order presentations of simple type theory (also called higher-order logic) and to set theory. When it is applied to some first-order presentations of type theory, it simulates exactly higherorder resolution. In this note, we compare how it behaves on type theory and on set theory