In this paper, we propose a mathematical framework for automated bug localization. This framework can be briefly summarized as follows. A program execution can be represented as a rooted acyclic directed graph. We define an execution snapshot by a cut-set on the graph. A program state can be regarded as a conjunction of labels on edges in a cut-set. Then we argue that a debugging task is a pruning process of the execution graph by using cut-sets. A pruning algorithm, i.e., a debugging task, is also presented.
* Shapiro's algorithmic debugging was invented for prolog programs @cite_2 . Fig. shows our interpretation of his work. From our viewpoint, it uses a proof tree as an execution graph. (Attention: This interpretation differs from a normal proof tree. Our interpretation is based on a line graph A line graph can be get by interchanging vertices and edges of an original graph. of a normal proof tree.) He used only one edge as a cut-set since removal of any edge divides a tree into two disconnected subtrees. A state is also simple because only one label, i.e., one unified clause, is enough. In this work, step of the pruning process is fully automated and a programmer carries out step by answering yes'' or no'' to tell a system the correctness of the label on the edge. GADT @cite_6 and Lichtenstein's system @cite_0 can be interpreted as the same manner because they are straightforward extensions of Shapiro's work.
@cite_0 @cite_6 @cite_2
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Algorithmic Debugging is a theory of debugging that uses queries on the compositional semantics of a program in order to localize bugs. It uses the following principle: if a computation of a program's component gives an incorrect result, while all the subcomputations it invokes compute correct results, then the code of this component is erroneous. Algorithmic Debugging is applied, in this work, to reactive systems, in particular to programs written in Flat Concurrent Prolog (FCP). Debugging reactive systems is known to be more difficult than the debugging of functional systems. A functional system is fully described by the relation between its initial input and final output; this context-freedom is used in debugging. A reactive system continuously responds to external inputs, thus its debugging cannot make use of context-free input output relations. Given a compositional semantic model for a concurrent programming language, we demonstrate how one can directly apply the ideas of Algorithmic Debugging to obtain a theory of program debugging for the considered language. The conflict between the context-freedom of input output relations and the reactive nature of concurrent systems is resolved by using semantic objects which record the reactive nature of the system's components. In functional algorithmic debugging the queries relate to input output relations; in concurrent algorithmic debugging the queries refer to semantic objects called processes which capture the reactive nature of FCP computations. A diagnosis algorithm for incorrect FCP programs is proposed. The algorithm gets an erroneous computation and using queries isolates an erroneous clause or an incomplete procedure. An FCP implementation of the diagnosis algorithm demonstrates the usefulness as well as the difficulties of Algorithmic Debugging of FCP programs. This paper presents a method for semi-automatic bug localization, generalized algorithmic debugging, which has been integrated with the category partition method for functional testing. In this way the efficiency of the algorithmic debugging method for bug localization can be improved by using test specifications and test results. The long-range goal of this work is a semi-automatic debugging and testing system which can be used during large-scale program development of nontrivial programs. The method is generally applicable to procedural langua ges and is not dependent on any ad hoc assumptions regarding the subject program. The original form of algorithmic debugging, introduced by Shapiro, was however limited to small Prolog programs without side-effects, but has later been generalized to concurrent logic programming languages. Another drawback of the original method is the large number of interactions with the user during bug localization. To our knowledge, this is the first method which uses category partition testing to improve the bug localization properties of algorithmic debugging. The method can avoid irrelevant questions to the programmer by categorizing input parameters and then match these against test cases in the test database. Additionally, we use program slicing, a data flow analysis technique, to dynamically compute which parts of the program are relevant for the search, thus further improving bug localization. We believe that this is the first generalization of algorithmic debugging for programs with side-effects written in imperative languages such as Pascal. These improvements together makes it more feasible to debug larger programs. However, additional improvements are needed to make it handle pointer-related side-effects and concurrent Pascal programs. A prototype generalized algorithmic debugger for a Pascal subset without pointer side-effects and a test case generator for application programs in Pascal, C, dBase, and LOTUS have been implemented. The thesis lays a theoretical framework for program debugging, with the goal of partly mechanizing this activity. In particular, we formalize and develop algorithmic solutions to the following two questions: (1) How do we identify a bug in a program that behaves incorrectly? (2) How do we fix a bug, once one is identified? We develop interactive diagnosis algorithms that identify a bug in a program that behaves incorrectly, and implement them in Prolog for the diagnosis of Prolog programs. Their performance suggests that they can be the backbone of debugging aids that go far beyond what is offered by current programming environments. We develop an inductive inference algorithm that synthesizes logic programs from examples of their behavior. The algorithm incorporates the diagnosis algorithms as a component. It is incremental, and progresses by debugging a program with respect to the examples. The Model Inference System is a Prolog implementation of the algorithm. Its range of applications and efficiency is comparable to existing systems for program synthesis from examples and grammatical inference. We develop an algorithm that can fix a bug that has been identified, and integrate it with the diagnosis algorithms to form an interactive debugging system. By restricting the class of bugs we attempt to correct, the system can debug programs that are too complex for the Model Inference System to synthesize.