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We consider the problem of establishing that a program-synthesis problem is unrealizable (i.e., has no solution in a given search space of programs). Prior work on unrealizability has developed some automatic techniques to establish that a problem is unrealizable; however, these techniques are all black-box , meaning that they conceal the reasoning behind why a synthesis problem is unrealizable. In this paper, we present a Hoare-style reasoning system, called unrealizability logic for establishing that a program-synthesis problem is unrealizable. To the best of our knowledge, unrealizability logic is the first proof system for overapproximating the execution of an infinite set of imperative programs. The logic provides a general, logical system for building checkable proofs about unrealizability. Similar to how Hoare logic distills the fundamental concepts behind algorithms and tools to prove the correctness of programs, unrealizability logic distills into a single logical system the fundamental concepts that were hidden within prior tools capable of establishing that a program-synthesis problem is unrealizable.

Modern programmable network switches can implement cus- tom applications using efficient packet processing hardware, and the programming language P4 provides high-level con- structs to program such switches. The increase in speed and programmability has inspired research in dataplane program- ming, where many complex functionalities, e.g., key-value stores and load balancers, can be implemented entirely in network switches. However, dataplane programs may suffer from novel security errors that are not traditionally found in network switches. To address this issue, we present a new information-flow control type system for P4. We formalize our type system in a recently-proposed core version of P4, and we prove a sound- ness theorem: well-typed programs satisfy non-interference. We also implement our type system in a tool, P4BID, which extends the type checker in the p4c compiler, the reference compiler for the latest version of P4. We present several case studies showing that natural security, integrity, and isolation properties in networks can be captured by non-interference, and our type system can detect violations of these properties while certifying correct programs.

This paper develops a new framework for program synthesis, called semantics-guided synthesis (SemGuS), that allows a user to provide both the syntax and the semantics for the constructs in the language. SemGuS accepts a recursively defined big-step semantics, which allows it, for example, to be used to specify and solve synthesis problems over an imperative programming language that may contain loops with unbounded behavior. The customizable nature of SemGuS also allows synthesis problems to be defined over a non-standard semantics, such as an abstract semantics. In addition to the SemGuS framework, we develop an algorithm for solving SemGuS problems that is capable of both synthesizing programs and proving unrealizability, by encoding a SemGuS problem as a proof search over Constrained Horn Clauses: in particular, our approach is the first that we are aware of that can prove unrealizabilty for synthesis problems that involve imperative programs with unbounded loops, over an infinite syntactic search space. We implemented the technique in a tool called MESSY, and applied it to SyGuS problems (i.e., over expressions), synthesis problems over an imperative programming language, and synthesis problems over regular expressions.

Program synthesis is now a reality, and we are approaching the point where domain-specific synthesizers can now handle problems of practical sizes. Moreover, some of these tools are finding adoption in industry. However, for synthesis to become a mainstream technique adopted at large by programmers as well as by end-users, we need to design programmable synthesis frameworks that (i) are not tailored to specific domains or languages, (ii) enable one to specify synthesis problems with a variety of qualitative and quantitative objectives in mind, and (iii) come equipped with theoretical as well as practical guarantees. We report on our work on designing such frameworks and on building synthesis engines that can handle program-synthesis problems describable in such frameworks, and describe open challenges and opportunities.