Abstract semantics has proven to be instrumental for accelerating search-based program synthesis, by enabling the sound pruning of a set of incorrect programs (without enumerating them). One may expect faster synthesis with increasingly finer-grained abstract semantics. Unfortunately, to the best of our knowledge, this is not the case, yet. The reason is because, as abstraction granularity increases -- while fewer programs are enumerated -- pruning becomes more costly. This imposes a fundamental limit on the overall synthesis performance, which we aim to address in this work. Our key idea is to introduce an offline presynthesis phase, which consists of two steps. Given a DSL with abstract semantics, the first semantics modeling step constructs a tree automaton A for a space of inputs -- such that, for any program P and for any considered input I, A has a run that corresponds to P's execution on I under abstract semantics. Then, the second step builds an oracle O for A. This O enables fast pruning during synthesis, by allowing us to efficiently find exactly those DSL programs that satisfy a given input-output example under abstract semantics. We have implemented this presynthesis-based synthesis paradigm in a framework, Foresighter. On top of it, we have developed three instantiations for SQL, string transformation, and matrix manipulation. All of them significantly outperform prior work in the respective domains.

With the rise of software-as-a-service and microservice architectures, RESTful APIs are now ubiquitous in mobile and web applications. A service can have tens or hundreds of API methods, making it a challenge for programmers to find the right combination of methods to solve their task.

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 consider the problem of type-directed component-based synthesis where, given a set of (typed) components and a query type , the goal is to synthesize a term that inhabits the query. Classical approaches based on proof search in intuitionistic logics do not scale up to the standard libraries of modern languages, which span hundreds or thousands of components. Recent graph reachability based methods proposed for Java do scale, but only apply to monomorphic data and components: polymorphic data and components infinitely explode the size of the graph that must be searched, rendering synthesis intractable. We introduce type-guided abstraction refinement (TYGAR), a new approach for scalable type-directed synthesis over polymorphic datatypes and components. Our key insight is that we can overcome the explosion by building a graph over abstract types which represent a potentially unbounded set of concrete types. We show how to use graph reachability to search for candidate terms over abstract types, and introduce a new algorithm that uses proofs of untypeability of ill-typed candidates to iteratively refine the abstraction until a well-typed result is found. We have implemented TYGAR in H+, a tool that takes as input a set of Haskell libraries and a query type, and returns a Haskell term that uses functions from the provided libraries to implement the query type. Our support for polymorphism allows H+ to work with higher-order functions and type classes, and enables more precise queries due to parametricity. We have evaluated H+ on 44 queries using a set of popular Haskell libraries with a total of 291 components. H+ returns an interesting solution within the first five results for 32 out of 44 queries. Our results show that TYGAR allows H+ to rapidly return well-typed terms, with the median time to first solution of just 1.4 seconds. Moreover, we observe that gains from iterative refinement over exhaustive enumeration are more pronounced on harder queries.

We present Hoogle+, a web-based API discovery tool for Haskell. A Hoogle+ user can specify a programming task using either a type, a set of input-output tests, or both. Given a specification, the tool returns a list of matching programs composed from functions in popular Haskell libraries, and annotated with automatically-generated examples of their behavior. These features of Hoogle+ are powered by three novel techniques. First, to enable efficient type-directed synthesis from tests only, we develop an algorithm that infers likely type specifications from tests . Second, to return high-quality programs even with ambiguous specifications, we develop a technique that automatically eliminates meaningless and repetitive synthesis results . Finally, we show how to extend this elimination technique to automatically generate informative inputs that can be used to demonstrate program behavior to the user. To evaluate the effectiveness of Hoogle+ compared with traditional API search techniques, we perform a user study with 30 participants of varying Haskell proficiency. The study shows that programmers equipped with Hoogle+ generally solve tasks faster and were able to solve 50% more tasks overall.