Temporal logics like Computation Tree Logic (CTL) have been widely used as expressive formalisms to capture rich behavioural specifications. CTL can express properties such as reachability, termination, invariants and responsiveness, which are difficult to test. This paper suggests a mechanism for the automated repair of infinite-state programs guided by CTL properties. Our produced patches avoid the overfitting issue that occurs in test-suite-guided repair, where the repaired code may not pass tests outside the given test suite. To realise this vision, we propose a novel find-and-fix framework based on Datalog, a widely used domain-specific language for program analysis, which readily supports nested fixed-point semantics of CTL via stratified negation. Specifically, our framework encodes the program and CTL properties into Datalog facts and rules and performs the repair by modifying the facts to pass the analysis rules. In the framework, to achieve both analysis and repair results, we adapt existing techniques – including loop summarisation and Symbolic Execution of Datalog (SEDL) – with key modifications. Our approach achieves analysis accuracy of 56.6% on a CTL verification benchmark and 88.5% on a termination/responsiveness benchmark, surpassing the best baseline performances of 27.7% and 76.9%, respectively. Our approach repairs all detected bugs, which is not achieved by existing tools.

Automated program repair relying on static analysis complements test-driven repair, since it does not require failing tests to repair a bug, and it avoids test-overfitting by considering program properties. Due to the rich variety and complexity of program analyses, existing static program repair techniques are tied to specific analysers, and thus repair only narrow classes of defects. To develop a general-purpose static program repair framework that targets a wide range of properties and programming languages, we propose to integrate program repair with Datalog-based analysis. Datalog solvers are programmable fixed point engines which can be used to encode many program analysis problems in a modular fashion. The program under analysis is encoded as Datalog facts, while the fixed point equations of the program analysis are expressed as recursive Datalog rules. In this context, we view repairing the program as modifying the corresponding Datalog facts. This is accomplished by a novel technique, symbolic execution of Datalog, that evaluates Datalog queries over a symbolic database of facts, instead of a concrete set of facts. The result of symbolic query evaluation allows us to infer what changes to a given set of Datalog facts repair the program so that it meets the desired analysis goals. We developed a symbolic executor for Datalog called Symlog, on top of which we built a repair tool SymlogRepair. We show the versatility of our approach on several analysis problems --- repairing null pointer exceptions in Java programs, repairing data leaks in Python notebooks, and repairing four types of security vulnerabilities in Solidity smart contracts.