Topics in Semantics-based Program Manipulation

Bernd Grobauer

August 2001


Programming is at least as much about manipulating existing code as it is about writing new code. Existing code is modified, for example to make inefficient code run faster, or to accommodate for new features when reusing code; existing code is analyzed, for example to verify certain program properties, or to use the analysis information for code modifications. Semantics-based program manipulation addresses methods for program modifications and program analyses that are formally defined and therefore can be verified with respect to the programming-language semantics. This dissertation comprises four articles in the field of semantics-based techniques for program manipulation: three articles are about partial evaluation, a method for program specialization; the fourth article treats an approach to automatic cost analysis.

Partial evaluation optimizes programs by specializing them with respect to parts of their input that are already known: Computations that depend only on known input are carried out during partial evaluation, whereas computations that depend on unknown input give rise to residual code. For example, partially evaluating an interpreter with respect to a program written in the interpreted language yields code that carries out the computations described by that program; partial evaluation is used to remove interpretive overhead. In effect, the partial evaluator serves as a compiler from the interpreted language into the implementation language of the interpreter. Compilation by partial evaluation is known as the first Futamura projection. The second and third Futamura projection describe the use of partial evaluation for compiler generation and compiler-generator generation, respectively; both require the partial evaluator that is employed to be self applicable.

The first article in this dissertation describes how the second Futamura projection can be achieved for type-directed partial evaluation (TDPE), a relatively recent approach to partial evaluation: We derive an ML implementation of the second Futamura projection for TDPE. Due to the differences between `traditional', syntax-directed partial evaluation and TDPE, this derivation involves several conceptual and technical steps. These include a suitable formulation of the second Futamura projection and techniques for making TDPE amenable to self-application.

In the second article, compilation by partial evaluation plays a central role for giving a unified approach to goal-directed evaluation, a programming-language paradigm that is built on the notions of backtracking and of generating successive results. Formulating the semantics of a small goal-directed language as a monadic semantics--a generic approach to structuring denotational semantics--allows us to relate various possible semantics to each other both conceptually and formally. We thus are able to explain goal-directed evaluation using an intuitive list-based semantics, while using a continuation semantics for semantics-based compilation through partial evaluation. The resulting code is comparable to that produced by an optimized compiler described in the literature.

The third article revisits one of the success stories of partial evaluation, the generation of efficient string matchers from intuitive but inefficient implementations. The basic idea is that specializing a naive string matcher with respect to a pattern string should result in a matcher that searches a text for this pattern with running time independent of the pattern and linear in the length of the text. In order to succeed with basic partial-evaluation techniques, the naive matcher has to be modified in a non-trivial way, carrying out so-called binding-time improvements. We present a step-by-step derivation of a binding-time improved matcher consisting of one problem-dependent step followed by standard binding-time improvements. We also consider several variants of matchers that specialize well, amongst them the first such matcher presented in the literature, and we demonstrate how variants can be derived from each other systematically.

The fourth article is concerned with program analysis rather than program transformation. A challenging goal for program analysis is to extract information about time or space complexity from a program. In complexity analysis, one often establishes cost recurrences as an intermediate step, and this step requires an abstraction from data to data size. We use information contained in dependent types to achieve such an abstraction: Dependent ML (DML), a conservative extension of ML, provides dependent types that can be used to associate data with size information, thus describing a possible abstraction. We automatically extract cost recurrences from first-order DML programs, guiding the abstraction from data to data size with information contained in DML type derivations

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