Document

**Published in:** DARTS, Volume 3, Issue 2, Special Issue of the 31st European Conference on Object-Oriented Programming (ECOOP 2017)

This artifact, named Prosy, is an interactive command-line tool for synthesizing recursive tree-to-string functions (e.g. pretty-printers) from examples. Specifically, Prosy takes as input a Scala file containing a hierarchy of abstract and case classes, and synthesizes the printing function after interacting with the user. Prosy first pro-actively generates a finite set of trees such that their string representations uniquely determine the function to synthesize. While asking the output for each example, Prosy prunes away questions when it can infer their answers from previous answers. In the companion paper, we prove that this pruning allows Prosy not to require that the user provides answers to the entire set of questions, which is of size O(n^3) where n is the size of the input file, but only to a reasonably small subset of size O(n). Furthermore, Prosy guides the interaction by providing suggestions whenever it can.

Mikaël Mayer, Jad Hamza, and Viktor Kuncak. Proactive Synthesis of Recursive Tree-to-String Functions from Examples (Artifact). In Special Issue of the 31st European Conference on Object-Oriented Programming (ECOOP 2017). Dagstuhl Artifacts Series (DARTS), Volume 3, Issue 2, pp. 16:1-16:2, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@Article{mayer_et_al:DARTS.3.2.16, author = {Mayer, Mika\"{e}l and Hamza, Jad and Kuncak, Viktor}, title = {{Proactive Synthesis of Recursive Tree-to-String Functions from Examples (Artifact)}}, pages = {16:1--16:2}, journal = {Dagstuhl Artifacts Series}, ISSN = {2509-8195}, year = {2017}, volume = {3}, number = {2}, editor = {Mayer, Mika\"{e}l and Hamza, Jad and Kuncak, Viktor}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DARTS.3.2.16}, URN = {urn:nbn:de:0030-drops-72970}, doi = {10.4230/DARTS.3.2.16}, annote = {Keywords: programming by example, active learning, program synthesis} }

Document

**Published in:** LIPIcs, Volume 74, 31st European Conference on Object-Oriented Programming (ECOOP 2017)

Synthesis from examples enables non-expert users to generate programs by specifying examples of their behavior. A domain-specific form of such synthesis has been recently deployed in a widely used spreadsheet software product. In this paper we contribute to foundations of such techniques and present a complete algorithm for synthesis of a class of recursive functions defined by structural recursion over a given algebraic data type definition. The functions we consider map an algebraic data type to a string; they are useful for, e.g., pretty printing and serialization of programs and data. We formalize our problem as learning deterministic sequential
top-down tree-to-string transducers with a single state (1STS).
The first problem we consider is learning a tree-to-string
transducer from any set of input/output examples provided by the user. We show that, given a set of input/output examples, checking whether there exists a 1STS consistent with these examples is NP-complete in general. In contrast, the problem can be solved in polynomial time under a (practically useful) closure condition that each
subtree of a tree in the input/output example set is also
part of the input/output examples.
Because coming up with relevant input/output examples may be
difficult for the user while creating hard constraint problems
for the synthesizer, we also study a more automated
active learning scenario in which the algorithm chooses the
inputs for which the user provides the outputs. Our
algorithm asks a worst-case linear number of queries as a
function of the size of the algebraic data type definition
to determine a unique transducer.
To construct our algorithms we present two new results on
formal languages.
First, we define a class of word equations, called
sequential word equations, for which we prove that
satisfiability can be solved in deterministic polynomial
time. This is in contrast to the general word equations for
which the best known complexity upper bound is in linear space.
Second, we close a long-standing open problem about the
asymptotic size of test sets for context-free languages. A
test set of a language of words L is a subset T of L
such that any two word homomorphisms equivalent on T are
also equivalent on L. We prove that it is possible to
build test sets of cubic size for context-free languages,
matching for the first time the lower bound found 20 years
ago.

Mikaël Mayer, Jad Hamza, and Viktor Kuncak. Proactive Synthesis of Recursive Tree-to-String Functions from Examples. In 31st European Conference on Object-Oriented Programming (ECOOP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 74, pp. 19:1-19:30, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{mayer_et_al:LIPIcs.ECOOP.2017.19, author = {Mayer, Mika\"{e}l and Hamza, Jad and Kuncak, Viktor}, title = {{Proactive Synthesis of Recursive Tree-to-String Functions from Examples}}, booktitle = {31st European Conference on Object-Oriented Programming (ECOOP 2017)}, pages = {19:1--19:30}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-035-4}, ISSN = {1868-8969}, year = {2017}, volume = {74}, editor = {M\"{u}ller, Peter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2017.19}, URN = {urn:nbn:de:0030-drops-72575}, doi = {10.4230/LIPIcs.ECOOP.2017.19}, annote = {Keywords: programming by example, active learning, program synthesis} }

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Invited Talk

**Published in:** LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)

Efficient implementations of concurrent objects such as semaphores, locks, and atomic collections including stacks and queues are vital to modern computer systems. Programming them is however error prone. To minimize synchronization overhead between concurrent object-method invocations, implementors avoid blocking operations like lock acquisition, allowing methods to execute concurrently. However, concurrency risks unintended inter-operation interference. Their correctness is captured by observational refinement which ensures conformance to atomic reference implementations. Formally, given two libraries L_1 and L_2 implementing the methods of some concurrent object, we say L_1 refines L_2 if and only if every computation of every program using L_1 would also be possible were L_2 used instead.
Linearizability, being an equivalent property, is the predominant proof technique for establishing observational refinement: one shows that each concurrent execution has a linearization which is a valid sequential execution according to a specification, given by an abstract data type or atomic reference implementation.
However, checking linearizability is intrinsically hard. Indeed, even in the case where method implementations are finite-state and object specifications are also finite-state, and when a fixed number of threads (invoking methods in parallel) is considered, the linearizability problem is EXPSPACE-complete, and it becomes undecidable when the number of threads is unbounded. These results show in particular that there is a complexity/decidability gap between the problem of checking linearizability and the problem of
checking reachability (i.e., the dual of checking safety/invariance properties), the latter being, PSPACE-complete and EXPSPACE-complete in the above considered cases, respectively.
We address here the issue of investigating cases where tractable reductions of the observational refinement/linearizability problem to the reachability problem, or dually to invariant checking, are possible. Our aim is (1) to develop algorithmic approaches that avoid a systematic exploration of all possible linearizations of all computations, (2) to exploit existing techniques and tools for
efficient invariant checking to check observational refinement, and (3) to establish decidability and complexity results for significant classes of concurrent objects and data structures.
We present two approaches that we have proposed recently. The first approach introduces a parameterized approximation schema for detecting observational refinement violations. This approach exploits a fundamental property of shared-memory library executions: their histories are interval orders, a special case of partial orders which admit canonical representations in which each operation o is mapped to a positive-integer-bounded interval I(o). Interval orders are equipped with a natural notion of length, which corresponds to the smallest integer constant for which an interval mapping exists. Then, we define a notion of bounded-interval-length analysis, and demonstrate its efficiency, in terms of complexity, coverage, and scalability, for detecting observational refinement bugs.
The second approach focuses on a specific class of abstract data types, including common concurrent objects and data structures such as stacks and queues. We show that for this class of objects, the linearizability problem is actually as hard as the control-state reachability problem. Indeed, we prove that in this case, the
existence of linearizability violations (i.e., finite computations that are not linearizable), can be captured completely by a finite number of finite-state automata, even when an unbounded number of parallel operations is allowed (assuming that libraries are data-independent).

Ahmed Bouajjani, Michael Emmi, Constantin Enea, and Jad Hamza. Checking Correctness of Concurrent Objects: Tractable Reductions to Reachability (Invited Talk). In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 2-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{bouajjani_et_al:LIPIcs.FSTTCS.2015.2, author = {Bouajjani, Ahmed and Emmi, Michael and Enea, Constantin and Hamza, Jad}, title = {{Checking Correctness of Concurrent Objects: Tractable Reductions to Reachability}}, booktitle = {35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)}, pages = {2--4}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-97-2}, ISSN = {1868-8969}, year = {2015}, volume = {45}, editor = {Harsha, Prahladh and Ramalingam, G.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.2}, URN = {urn:nbn:de:0030-drops-56638}, doi = {10.4230/LIPIcs.FSTTCS.2015.2}, annote = {Keywords: Concurrent objects, linearizability, verification, bug detection} }

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