There is significant room for improving users' experiences with model checking tools. An error trace produced by a model checker can be lengthy and is indicative of a symptom of an error. As a result, users can spend considerable time examining an error trace in order to understand the cause of the error. Moreover, even state-of-the-art model checkers provide an experience akin to that provided by parsers before syntactic error recovery was invented: they report a single error trace per run. The user has to fix the error and run the model checker again to find more error traces.We present an algorithm that exploits the existence of correct traces in order to localize the error cause in an error trace, report a single error trace per error cause, and generate multiple error traces having independent causes. We have implemented this algorithm in the context of slam, a software model checker that automatically verifies temporal safety properties of C programs, and report on our experience using it to find and localize errors in device drivers. The algorithm typically narrows the location of a cause down to a few lines, even in traces consisting of hundreds of statements.

/pdf/from-symptom-to-cause-localizing-errors-in-counterexample-3sekcyd9zl.pdf

From symptom to cause: localizing errors in counterexample traces

Tools and analyses that find bugs in software are becoming increasingly prevalent. However, even after the potential false alarms raised by such tools are dealt with, many real reported errors may go unfixed. In such cases the programmers have judged the benefit of fixing the bug to be less than the time cost of understanding and fixing it.The true utility of a bug-finding tool lies not in the number of bugs it finds but in the number of bugs it causes to be fixed.Analyses that find safety-policy violations typically give error reports as annotated backtraces or counterexamples. We propose that bug reports additionally contain a specially-constructed patch describing an example way in which the program could be modified to avoid the reported policy violation. Programmers viewing the analysis output can use such patches as guides, starting points, or as an additional way of understanding what went wrong.We present an algorithm for automatically constructing such patches given model-checking and policy information typically already produced by most such analyses. We are not aware of any previous automatic techniques for generating patches in response to safety policy violations. Our patches can suggest additional code not present in the original program, and can thus help to explain bugs related to missing program elements. In addition, our patches do not introduce any new violations of the given safety policy.To evaluate our method we performed a software engineering experiment, applying our algorithm to over 70 bug reports produced by two off-the-shelf bug-finding tools running on large Java programs. Bug reports also accompanied by patches were three times as likely to be addressed as standard bug reports.This work represents an early step toward developing new ways to report bugs and to make it easier for programmers to fix them. Even a minor increase in our ability to fix bugs would be a great increase for the quality of software.

Patches as better bug reports

The Hindley/Milner let-polymorphic type inference system has two different algorithms: one is the de factostandard Algorithm 𝒲 that is bottom-up (or context-insensitive), and the other is a “folklore” algorithm that is top-down (or context-sensitive). Because the latter algorithm has not been formally presented with its soundness and completeness proofs, and its relation with the 𝒲 algorithm has not been rigorously investigated, its use in place of (or in combination with) 𝒲 is not well founded. In this article, we formally define the context-sensitive, top-down type inference algorithm (named “M”), prove its soundness and completeness, and show a distinguishing property that M always stops earlier than 𝒲 if the input program is ill typed. Our proofs can be seen as theoretical justifications for various type-checking strategies being used in practice.

/pdf/proofs-about-a-folklore-let-polymorphic-type-inference-47s5sdyv5o.pdf

Proofs about a folklore let-polymorphic type inference algorithm

Previous methods have generally identified the location of a type error as a particular program point or the program subtree rooted at that point. We present a new approach that identifies the location of a type error as a set of program points (a slice) all of which are necessary for the type error. We identify the criteria of completeness and minimality for type error slices. We discuss the advantages of complete and minimal type error slices over previous methods of presenting type errors. We present and prove the correctness of algorithms for finding complete and minimal type error slices for implicitly typed higher-order languages like Standard ML.

/pdf/type-error-slicing-in-implicitly-typed-higher-order-14bwwbn436.pdf

Type error slicing in implicitly typed higher-order languages

The type systems of most typed functional programming languages are based on the Hindley-Milner type system. A practical problem with these type systems is that it is often hard to understand why a program is not type correct or a function does not have the intended type. We suggest that at the core of this problem is the difficulty of explaining why a given expression has a certain type. The type system is not defined compositionally. We propose to explain types using a variant of the Hindley-Milner type system that defines a compositional type explanation graph of principal typing. We describe how the programmer understands types by interactive navigation through the explanation graph. Furthermore, the explanation graph can be the foundation for algorithmic debugging of type errors, that is, semi-automatic localisation of the source of a type error without even having to understand the type inference steps. We implemented a prototype of a tool to explore the usefulness of the proposed methods.

/pdf/compositional-explanation-of-types-and-algorithmic-debugging-pupnmyvspy.pdf

Compositional explanation of types and algorithmic debugging of type errors

Explaining type inference

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Explaining type inference