Inductive synthesis, or programming-by-examples (PBE) is gaining prominence with disruptive applications for automating repetitive tasks in end-user programming. However, designing, developing, and maintaining an effective industrial-quality inductive synthesizer is an intellectual and engineering challenge, requiring 1-2 man-years of effort. Our novel observation is that many PBE algorithms are a natural fall-out of one generic meta-algorithm and the domain-specific properties of the operators in the underlying domain-specific language (DSL). The meta-algorithm propagates example-based constraints on an expression to its subexpressions by leveraging associated witness functions, which essentially capture the inverse semantics of the underlying operator. This observation enables a novel program synthesis methodology called data-driven domain-specific deduction (D4), where domain-specific insight, provided by the DSL designer, is separated from the synthesis algorithm. Our FlashMeta framework implements this methodology, allowing synthesizer developers to generate an efficient synthesizer from the mere DSL definition (if properties of the DSL operators have been modeled). In our case studies, we found that 10+ existing industrial-quality mass-market applications based on PBE can be cast as instances of D4. Our evaluation includes reimplementation of some prior works, which in FlashMeta become more efficient, maintainable, and extensible. As a result, FlashMeta-based PBE tools are deployed in several industrial products, including Microsoft PowerShell 3.0 for Windows 10, Azure Operational Management Suite, and Microsoft Cortana digital assistant.

We present an analysis to automatically determine if a program represents a continuous function, or equivalently, if infinitesimal changes to its inputs can only cause infinitesimal changes to its outputs. The analysis can be used to verify the robustness of programs whose inputs can have small amounts of error and uncertainty---e.g., embedded controllers processing slightly unreliable sensor data, or handheld devices using slightly stale satellite data. Continuity is a fundamental notion in mathematics. However, it is difficult to apply continuity proofs from real analysis to functions that are coded as imperative programs, especially when they use diverse data types and features such as assignments, branches, and loops. We associate data types with metric spaces as opposed to just sets of values, and continuity of typed programs is phrased in terms of these spaces. Our analysis reduces questions about continuity to verification conditions that do not refer to infinitesimal changes and can be discharged using off-the-shelf SMT solvers. Challenges arise in proving continuity of programs with branches and loops, as a small perturbation in the value of a variable often leads to divergent control-flow that can lead to large changes in values of variables. Our proof rules identify appropriate ``synchronization points'' between executions and their perturbed counterparts, and establish that values of certain variables converge back to the original results in spite of temporary divergence. We prove our analysis sound with respect to the traditional epsilon-delta definition of continuity. We demonstrate the precision of our analysis by applying it to a range of classic algorithms, including algorithms for array sorting, shortest paths in graphs, minimum spanning trees, and combinatorial optimization. A prototype implementation based on the Z3 SMT-solver is also presented.

We define the reachability-bound problem to be the problem of finding a symbolic worst-case bound on the number of times a given control location inside a procedure is visited in terms of the inputs to that procedure. This has applications in bounding resources consumed by a program such as time, memory, network-traffic, power, as well as estimating quantitative properties (as opposed to boolean properties) of data in programs, such as information leakage or uncertainty propagation. Our approach to solving the reachability-bound problem brings together two different techniques for reasoning about loops in an effective manner. One of these techniques is an abstract-interpretation based iterative technique for computing precise disjunctive invariants (to summarize nested loops). The other technique is a non-iterative proof-rules based technique (for loop bound computation) that takes over the role of doing inductive reasoning, while deriving its power from the use of SMT solvers to reason about abstract loop-free fragments. Our solution to the reachability-bound problem allows us to compute precise symbolic complexity bounds for several loops in .Net base-class libraries for which earlier techniques fail. We also illustrate the precision of our algorithm for disjunctive invariant computation (which has a more general applicability beyond the reachability-bound problem) on a set of benchmark examples.

A constraint-based approach to invariant generation in programs translates a program into constraints that are solved using off-theshelf constraint solvers to yield desired program invariants.In this paper we show how the constraint-based approach can be used to model a wide spectrum of program analyses in an expressive domain containing disjunctions and conjunctions of linear inequalities. In particular, we show how to model the problem of context-sensitive interprocedural program verification. We also present the first constraint-based approach to weakest precondition and strongest postcondition inference. The constraints we generate are boolean combinations of quadratic inequalities over integer variables. We reduce these constraints to SAT formulae using bitvector modeling and use off-the-shelf SAT solvers to solve them.Furthermore, we present interesting applications of the above analyses, namely bounds analysis and generation of most-general counter-examples for both safety and termination properties. We also present encouraging preliminary experimental results demonstrating the feasibility of our technique on a variety of challenging examples.

Atomic sections are a recent and popular idiom to support the development of concurrent programs. Updates performed within an atomic section should not be visible to other threads until the atomic section has been executed entirely. Traditionally, atomic sections are supported through the use of optimistic concurrency, either using a transactional memory hardware, or an equivalent software emulation (STM). This paper explores automatically supporting atomic sections using pessimistic concurrency. We present a system that combines compiler and runtime techniques to automatically transform programs written with atomic sections into programs that only use locking primitives. To minimize contention in the transformed programs, our compiler chooses from several lock granularities, using fine-grain locks whenever it is possible. This paper formally presents our framework, shows that our compiler is sound (i.e., it protects all shared locations accessed within atomic sections), and reports experimental results.