Relatively Complete Counterexamples for Higher-Order Programs
In this paper, we study the problem of generating inputs to a higher-order program causing it to error. We first study the problem in the setting of PCF, a typed, core functional language and contribute the first relatively complete method for constructing counterexamples for PCF programs. The method is relatively complete in the sense of Hoare logic; completeness is reduced to the completeness of a first-order solver over the base types of PCF. In practice, this means an SMT solver can be used for the effective, automated generation of higher-order counterexamples for a large class of programs.
We achieve this result by employing a novel form of symbolic execution for higher-order programs. The remarkable aspect of this symbolic execution is that even though symbolic higher-order inputs and values are considered, the path condition remains a first-order formula. Our handling of symbolic function application enables the reconstruction of higher-order counterexamples from this first-order formula.
After establishing our main theoretical results, we sketch how to apply the approach to untyped, higher-order, stateful languages with first-class contracts and show how counterexample generation can be used to detect contract violations in this setting. To validate our approach, we implement a tool generating counterexamples for erroneous modules written in Racket.
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KC SivaramakrishnanUniversity of Cambridge, Gowtham KakiPurdue University, Suresh JagannathanPurdue UniversityMedia Attached
|09:40 - 10:05|
Jeremy G. SiekIndiana University, Peter ThiemannUniversity of Freiburg, Philip WadlerUniversity of EdinburghMedia Attached
|10:05 - 10:30|
Yizhou ZhangCornell University, Andrew C. Myers, Barbara LiskovMIT, Guido SalvaneschiTU Darmstadt, Matt LoringCornell UniversityMedia Attached
|10:30 - 10:55|
Research PapersMedia Attached