We present Spectacular, a new tool for automatically discovering candidate laws for use in property-based testing. By using the recently-developed technique of ECTAs (Equality-Constrained Tree Automata), Spectacular improves upon previous approaches such as QuickSpec: it can explore vastly larger program spaces and start generating candidate laws within 20 seconds from a benchmark where QuickSpec runs for 45 minutes and then crashes (due to memory limits, even on a 256 GB machine). Thanks to the ability of ECTAs to efficiently search constrained program spaces, Spectacular is fast enough to find candidate laws in more generally typed settings than the monomorphized one, even for signatures with dozens of functions.

Many problem domains, including program synthesis and rewrite-based optimization, require searching astronomically large spaces of programs. Existing approaches often rely on building specialized data structures—version-space algebras, finite tree automata, or e-graphs—to compactly represent such spaces. At their core, all these data structures exploit independence of subterms; as a result, they cannot efficiently represent more complex program spaces, where the choices of subterms are entangled. We introduce equality-constrained tree automata (ECTAs), a new data structure, designed to compactly represent large spaces of programs with entangled subterms. We present efficient algorithms for extracting programs from ECTAs, implemented in a performant Haskell library, ecta. Using the ecta library, we construct Hectare, a type-driven program synthesizer for Haskell. Hectare significantly outperforms a state-of-the-art synthesizer Hoogle+—providing an average speedup of 8×—despite its implementation being an order of magnitude smaller.

We develop the first theory of control-flow graphs from first principles, and use it to create an algorithm for automatically synthesizing many variants of control-flow graph generators from a language’s operational semantics. Our approach first introduces a new algorithm for converting a large class of small-step operational semantics to an abstract machine. It next uses a technique called ”abstract rewriting” to automatically abstract the semantics of a language, which is used both to directly generate a CFG from a program (”interpreted mode”) and to generate standalone code, similar to a human-written CFG generator, for any program in a language. We show how the choice of two abstraction and projection parameters allow our approach to synthesize several families of CFG-generators useful for different kinds of tools. We prove the correspondence between the generated graphs and the original semantics. We provide and prove an algorithm for automatically proving the termination of interpreted-mode generators. In addition to our theoretical results, we have implemented this algorithm in a tool called Mandate, and show that it produces human-readable code on two medium-size languages with 60−80 rules, featuring nearly all intraprocedural control constructs common in modern languages. We then show these CFG-generators were sufficient to build two static analyses atop them. Our work is a promising step towards the grand vision of being able to synthesize all desired tools from the semantics of a programming language.

A landmark challenge for AI is to learn flexible, powerful representations from small numbers of examples. On an important class of tasks, hypotheses in the form of programs provide extreme generalization capabilities from surprisingly few examples. However, whereas large natural few-shot learning image benchmarks have spurred progress in meta-learning for deep networks, there is no comparably big, natural program-synthesis dataset that can play a similar role. This is because, whereas images are relatively easy to label from internet meta-data or annotated by non-experts, generating meaningful input-output examples for program induction has proven hard to scale. In this work, we propose a new way of leveraging unit tests and natural inputs for small programs as meaningful input-output examples for each sub-program of the overall program. This allows us to create a large-scale naturalistic few-shot program-induction benchmark and propose new challenges in this domain. The evaluation of multiple program induction and synthesis algorithms points to shortcomings of current methods and suggests multiple avenues for future work.

We present Omega, a probabilistic programming language with support for counterfactual inference. Counterfactual inference means to observe some fact in the present, and infer what would have happened had some past intervention been taken, e.g. “given that medication was not effective at dose x, what is the probability that it would have been effective at dose 2x?.” We accomplish this by introducing a new operator to probabilistic programming akin to Pearl’s do, define its formal semantics, provide an implementation, and demonstrate its utility through examples in a variety of simulation models.

We present a new approach to semantic code search based on equational reasoning, and the Yogo tool implementing this approach. Our approach works by considering not only the dataflow graph of a function, but also the dataflow graphs of all equivalent functions reachable via a set of rewrite rules. In doing so, it can recognize an operation even if it uses alternate APIs, is in a different but mathematically-equivalent form, is split apart with temporary variables, or is interleaved with other code. Furthermore, it can recognize when code is an instance of some higher-level concept such as iterating through a file. Because of this, from a single query, Yogo can find equivalent code in multiple languages. Our evaluation further shows the utility of Yogo beyond code search: encoding a buggy pattern as a Yogo query, we found a bug in Oracle’s Graal compiler which had been missed by a hand-written static analyzer designed for that exact kind of bug. Yogo is built on the Cubix multi-language infrastructure, and currently supports Java and Python.

We present a new approach for building source-to-source transformations that can run on multiple programming languages, based on a new way of representing programs called incremental parametric syntax. We implement this approach in Haskell in our Cubix system, and construct incremental parametric syntaxes for C, Java, JavaScript, Lua, and Python. We demonstrate a whole-program refactoring tool that runs on all of them, along with three smaller transformations that each run on several. Our evaluation shows that (1) once a transformation is written, little work is required to configure it for a new language (2) transformations built this way output readable code which preserve the structure of the original, according to participants in our human study, and (3) our transformations can still handle language corner-cases, as validated on compiler test suites.

Delimited continuations are the mother of all monads! So goes the slogan inspired by Filinski’s 1994 paper, which showed that delimited continuations can implement any monadic effect, letting the programmer use an effect as easily as if it was built into the language. It’s a shame that not many languages have delimited continuations. Luckily, exceptions and state are also the mother of all monads! In this Pearl, we show how to implement delimited continuations in terms of exceptions and state, a construction we call thermometer continuations . While traditional implementations of delimited continuations require some way of ”capturing” an intermediate state of the computation, the insight of thermometer continuations is to reach this intermediate state by replaying the entire computation from the start, guiding it using a recording so that the same thing happens until the captured point. Along the way, we explain delimited continuations and monadic reflection, show how the Filinski construction lets thermometer continuations express any monadic effect, share an elegant special-case for nondeterminism, and discuss why our construction is not prevented by theoretical results that exceptions and state cannot macro-express continuations.