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Fri 22 Jan 2016 15:35 - 16:00 at Grand Bay North - Track 1: Synthesis Chair(s): Roberto Giacobazzi

Input-output examples have emerged as a practical and user-friendly specification mechanism for program synthesis in many environments. While example-driven tools have demonstrated tangible impact that has inspired adoption in industry, their underlying semantics are less well-understood: what are “examples” and how do they relate to other kinds of specifications? This paper demonstrates that examples can, in general, be interpreted as refinement types. Seen in this light, program synthesis is the task of finding an inhabitant of such a type. This insight provides an immediate semantic interpretation for examples. Moreover, it enables us to exploit decades of research in type theory as well as its correspondence with intuitionistic logic rather than designing ad hoc theoretical frameworks for synthesis from scratch. We put this observation into practice by formalizing synthesis as proof search in a sequent calculus with intersection and union refinements that we prove to be sound with respect to a conventional type system. In addition, we show how to handle negative examples, which arise from user feedback or counterexample-guided loops. This theory serves as the basis for a prototype implementation that extends our core language to support ML-style algebraic data types and structurally inductive functions. Users can also specify synthesis goals using polymorphic refinements and import monomorphic libraries. The prototype serves as a vehicle for empirically evaluating a number of different strategies for resolving the nondeterminism of the sequent calculus—bottom-up theorem-proving, term enumeration with refinement type checking, and combinations of both—the results of which classify, explain, and validate the design choices of existing synthesis systems. It also provides a platform for measuring the practical value of a specification language that combines “examples” with the more general expressiveness of refinements.

Poster (POPL Poster2.pdf)1.61MiB

Fri 22 Jan

POPL-2016-papers
14:20 - 16:00: Research Papers - Track 1: Synthesis at Grand Bay North
Chair(s): Roberto GiacobazziUniversity of Verona, Italy
POPL-2016-papers14:20 - 14:45
Talk
Veselin RaychevETH Zurich, Pavol BielikETH Zurich, Switzerland, Martin VechevETH Zurich, Andreas KrauseETH Zurich
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POPL-2016-papers14:45 - 15:10
Talk
James BornholtUniversity of Washington, Emina TorlakUniversity of Washington, Dan GrossmanUniversity of Washington, USA, Luis CezeUniversity of Washington, USA
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POPL-2016-papers15:10 - 15:35
Talk
Aws AlbarghouthiUniversity of Wisconsin–Madison, Isil DilligUniversity of Texas, Austin, Arie GurfinkelCarnegie Mellon University
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POPL-2016-papers15:35 - 16:00
Talk
Jonathan FranklePrinceton University, Peter-Michael OseraGrinnell College, David WalkerPrinceton University, Steve ZdancewicUniversity of Pennsylvania
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