Harald Søndergaard

Mix: A self-applicable partial evaluator for experiments in compiler generation

The program transformation principle called partial evaluation has interesting applications in compilation and compiler generation. Self-applicable partial evaluators may be used for transforming interpreters into corresponding compilers and even for the generation of compiler generators. This is useful because interpreters are significantly easier to write than compilers, but run much slower than compiled code. A major difficulty in writing compilers (and compiler generators) is the thinking in terms of distinct binding times: run time and compile time (and compiler generation time). The paper gives an introduction to partial evaluation and describes a fully automatic though experimental partial evaluator, called mix, able to generate stand-alone compilers as well as a compiler generator. Mix partially evaluates programs written in Mixwell, essentially a first-order subset of statically scoped pure Lisp. For compiler generation purposes it is necessary that the partial evaluator be self-applicable. Even though the potential utility of a self-applicable partial evaluator has been recognized since 1971, a 1984 version of mix appears to be the first successful implementation. The overall structure of mix and the basic ideas behind its way of working are sketched. Finally, some results of using a version of mix are reported.

An Application of Abstract Interpretation of Logic Programs: Occur Check Reduction

The occur check in Robinson unification is superfluous in most unifications that take place in practice. The present paper is concerned with the problem of determining circumstances under which the occur check may be safely dispensed with. The method given draws on one outlined by David Plaisted. The framework, however, differs in that we systematically apply the abstract interpretation principle to logic programs. The aim is to give a clear presentation and to facilitate justification of the soundness of the method.

Precise and efficient groundness analysis for logic programs

We show how precise groundness information can be extracted from logic programs. The idea is to use abstract interpretation with Boolean functions as “approximations” to groundness dependencies between variables. This idea is not new, and different classes of Boolean functions have been used. We argue, however, that one class, the positive functions, is more suitable than others. Positive Boolean functions have a certain property which we (inspired by A. Langen) call “condensation.” This property allows for rapid computation of groundness information.

Two classes of Boolean functions for dependency analysis

Many static analyses for declarative programming/database languages use Boolean functions to express dependencies among variables or argument positions. Examples include groundness analysis, arguably the most important analysis for logic programs, finiteness analysis and functional dependency analysis for databases. We identify two classes of Boolean functions that have been used: positive and definite functions, and we systematically investigate these classes and their efficient implementation for dependency analyses. On the theoretical side, we provide syntactic characterizations and study the expressiveness and algebraic properties of the classes. In particular, we show that both are closed under existential quantification. On the practical side, we investigate various representations for the classes based on reduced ordered binary decision diagrams (ROBDDs), disjunctive normal form, conjunctive normal form, Blake canonical form, dual Blake canonical form, and a form specific to definite functions. We compare the resulting implementations of groundness analyzers based on the representations for precision and efficiency.

Non-determinism in functional languages

The introduction of a non-deterministic operator in even a very simple functional programming language gives rise to a plethora of semantic questions. These questions are not only concerned with the choice operator itself. A surprisingly large number of different parameter passing mechanisms are made possible by the introduction of bounded non-determinism. The diversity of semantic possibilities is examined systematically using denotational definitions based on mathematical structures called power domains

Denotational abstract interpretation of logic programs

Logic-programming languages are based on a principle of separation “logic” and “control.”. This means that they can be given simple model-theoretic semantics without regard to any particular execution mechanism (or proof procedure, viewing execution as theorem proving). Although the separation is desirable from a semantical point of view, it makes sound, efficient implementation of logic-programming languages difficult. The lack of “control information” in programs calls for complex data-flow analysis techniques to guide execution. Since data-flow analysis furthermore finds extensive use in error-finding and transformation tools, there is a need for a simple and powerful theory of data-flow analysis of logic programs. This paper offers such a theory, based on F. Nielsons extension of P. Cousot and R. Cousots abstract interpretation. We present a denotational definition of the semantics of definite logic programs. This definition is of interest in its own right because of its compactness. Stepwise we develop the definition into a generic data-flow analysis that encompasses a large class of data-flow analyses based on the SLD execution model. We exemplify one instance of the definition by developing a provably correct groundness analysis to predict how variables may be bound to ground terms during execution. We also discuss implementation issues and related work.

Referential transparency, definiteness and unfoldability

SummaryThe term “referential transparency” is frequently used to indicate that a programming language has certain useful substitution properties. We observe, however, that the formal and informal definitions given in the literature are not equivalent and we investigate their relationships. To this end, we study the definitions in the context of a simple expression language and show that in the presence of non-determinism, the differences between the definitions are manifest. We propose a definition of “referential transparency”, based on Quines, as well as of the related notions: definiteness and unfoldability. We demonstrate that these notions are useful to characterize programming languages.

Sharing and groundness dependencies in logic programs

We investigate Jacobs and Langens Sharing domain, introduced for the analysis of variable sharing in logic programs, and show that it is isomorphic to Marriott and Søndergaards Pos domain, introduced for the analysis of groundness dependencies. Our key idea is to view the sets of variables in a Sharing domain element as the models of a corresponding Boolean function. This leads to a recasting of sharing analysis in terms of the property of “not being affected by the binding of a single variable.” Such an “unaffectedness dependency” analysis has close connections with groundness dependency analysis using positive Boolean functions. This new view improves our understanding of sharing analysis, and leads to an elegant expression of its combination with groundness dependency analysis based on the reduced product of Sharing and Pos. It also opens up new avenues for the efficient implementation of sharing analysis, for example using reduced order binary decision diagrams, as well as efficient implementation of the reduced product, using domain factorizations.

Termination Analysis for Mercury

Since the late eighties, much progress has been made in the theory of termination analysis for logic programs. However, the practical significance of much of this work is hard to judge, since experimental evaluations rarely get published. Here we describe and evaluate a termination analyzer for Mercury, a strongly typed and moded logic-functional programming language. Mercurys high degree of referential transparency and the guaranteed availability of reliable mode information simplify termination analysis. Our analyzer uses a variant of a method developed by Plumer. It deals with full Mercury, including modules and I/O. In spite of these obstacles, it produces state-of-the-art termination information, while having a negligible impact on the running time of the compiler of which it is part, even for large programs.

Boolean functions for dependency analysis: Algebraic properties and efficient representation

Many analyses for logic programming languages use Boolean functions to express dependencies between variables or argument positions. Examples include groundness analysis, arguably the most important analysis for logic programs, finiteness analysis and functional dependency analysis. We identify two classes of Boolean functions that have been used: positive and definite functions, and we systematically investigate these classes and their efficient implementation for dependency analyses. We provide syntactic characterizations and study their algebraic properties. In particular, we show that both classes are closed under existential quantification. We investigate representations for these classes based on: reduced ordered binary decision diagrams (ROBDDs), disjunctive normal form, conjunctive normal form, Blake canonical form, dual Blake canonical form, and a form specific to definite functions. We give an empirical comparison of these different representations for groundness analysis.