Notions of program dependency arise in many settings: security, partial evaluation, program slicing, and call-tracking. We argue that there is a central notion of dependency common to these settings that can be captured within a single calculus, the Dependency Core Calculus (DCC), a small extension of Moggi's computational lambda calculus. To establish this thesis, we translate typed calculi for secure information flow, binding-time analysis, slicing, and call-tracking into DCC. The translations help clarify aspects of the source calculi. We also define a semantic model for DCC and use it to give simple proofs of noninterference results for each case.

Abstract. Provenance is information recording the source, derivation, or history of some information. Provenance tracking has been studied in a variety of settings; however, although many design points have been explored, the mathematical or semantic foundations of data provenance have received comparatively little attention. In this paper, we argue that dependency analysis techniques familiar from program analysis and program slicing provide a formal foundation for forms of provenance that are intended to show how (part of) the output of a query depends on (parts of) its input. We introduce a semantic characterization of such dependency provenance, show that this form of provenance is not computable, and provide dynamic and static approximation techniques. 1

We present techniques that enable higher-order functional computations to “explain ” their work by answering questions about how parts of their output were calculated. As explanations, we consider the traditional notion of program slices, which we show can be inadequate, and propose a new notion: trace slices. We present techniques for specifying flexible and rich slicing criteria based on partial expressions, parts of which have been replaced by holes. We characterise program slices in an algorithm-independent fashion and show that a least slice for a given criterion exists. We then present an algorithm, called unevaluation, for computing least program slices from computations reified as traces. Observing a limitation of program slices, we develop a notion of trace slice as another form of explanation and present an algorithm for computing them. The unevaluation algorithm can be applied to any subtrace of a trace slice to compute a program slice whose evaluation generates that subtrace. This close correspondence between programs, traces, and their slices can enable the programmer to understand a computation interactively, in terms of the programming language in which the computation is expressed. We present an implementation in the form of a tool, discuss some important practical implementation concerns and present some techniques for addressing them.

Program slicing is a well-known technique that extracts from a program those statements which are relevant to a particular criterion. While static slicing does not consider any input data, dynamic slices are computed from a particular program execution. Thus, dynamic slicers are usually easier to design and implement. In this work, we present a program specialization technique for lazy functional logic programming which is based on dynamic slicing. Our method exploits the code size reduction capabilities of slicing in order to produce a version of the original program specialized w.r.t. a given criterion. We also introduce some simple, post-processing transformations that allow us to further simplify the specialized program. The kind of specialization performed by our approach cannot be achieved with other related techniques like partial evaluation.

Abstract. Tracing computations is a widely used methodology for program debugging. Lazy languages, however, pose new demands on tracing techniques because following the actual trace of a computation is generally useless. Typically, tracers for lazy languages rely on the construction of a redex trail, a graph that stores the reductions performed in a computation. While tracing provides a significant help for locating bugs, the task still remains complex. A well-known debugging technique for imperative programs is based on dynamic slicing, a method for finding the program statements that influence the computation of a value for a specific program input. In this work, we introduce a novel technique for dynamic slicing in first-order lazy functional languages. Rather than starting from scratch, our technique relies on (a slight extension of) redex trails. We provide a notion of dynamic slice and introduce a method to compute it from the redex trail of a computation. We also sketch the extension of our technique to deal with a functional logic language. A clear advantage of our proposal is that one can enhance existing tracers with slicing capabilities with a modest implementation effort, since the same data structure (the redex trail) can be used for both tracing and slicing.

Provenance is information recording the source, derivation, or history of some information. Provenance tracking has been studied in a variety of settings, particularly database management systems; however, although many candidate definitions of provenance have been proposed, the mathematical or semantic foundations of data provenance have received comparatively little attention. In this article, we argue that dependency analysis techniques familiar from program analysis and program slicing provide a formal foundation for forms of provenance that are intended to show how (part of) the output of a query depends on (parts of) its input. We introduce a semantic characterization of such dependency provenance for a core database query language, show that minimal dependency provenance is not computable, and provide dynamic and static approximation techniques. We also discuss preliminary implementation experience with using dependency provenance to compute data slices, or summaries of the parts of the input relevant to a given part of the output. 1.