Abstract. We present a semi-decision procedure for checking satisfiability of expressive correctness properties of recursive first-order functional programs. In our approach, both properties and programs are expressed in the same language, a subset of Scala. We implemented our procedure and integrated it with the Z3 SMT solver and the Scala compiler. Our procedure is sound for counterexamples and for proofs of terminating functions. It is terminating and thus complete for many important classes of specifications, including all satisfiable formulas and all formulas where recursive functions satisfy certain syntactic restrictions. Using our system, Leon, we verified detailed correctness properties for functional data structure implementations, as well as syntax tree manipulations. We have found our system to be fast for both finding counterexamples and finding correctness proofs, and to scale to larger programs than alternative techniques.

We present an extension of Scala that supports constraint programming over bounded and unbounded domains. The resulting language, Kaplan, provides the benefits of constraint programming while preserving the existing features of Scala. Kaplan integrates constraint and imperative programming by using constraints as an advanced control structure; the developers use the monadic 'for' construct to iterate over the solutions of constraints or branch on the existence of a solution. The constructs we introduce have simple semantics that can be understood as explicit enumeration of values, but are implemented more efficiently using symbolic reasoning.Kaplan programs can manipulate constraints at run-time, with the combined benefits of type-safe syntax trees and first-class functions. The language of constraints is a functional subset of Scala, supporting arbitrary recursive function definitions over algebraic data types, sets, maps, and integers.Our implementation runs on a platform combining a constraint solver with a standard virtual machine. For constraint solving we use an algorithm that handles recursive function definitions through fair function unrolling and builds upon the state-of-the art SMT solver Z3. We evaluate Kaplan on examples ranging from enumeration of data structures to execution of declarative specifications. We found Kaplan promising because it is expressive, supporting a range of problem domains, while enabling full-speed execution of programs that do not rely on constraint programming.

Advances in proteomics reveal that pathway databases fail to capture the majority of cellular signaling activity. Our mass spectrometry study of the dynamic epidermal growth factor (EGF) response demonstrates that over 89% of significantly (de)phosphorylated proteins are excluded from individual EGF signaling maps, and 63% are absent from all annotated pathways. We present a computational method, the Temporal Pathway Synthesizer (TPS), to discover missing pathway elements by modeling temporal phosphoproteomic data. TPS uses constraint solving to exhaustively explore all possible structures for a signaling pathway, eliminating structures that are inconsistent with protein-protein interactions or the observed phosphorylation event timing. Applied to our EGF response data, TPS connects 83% of the responding proteins to receptors and signaling proteins in EGF pathway maps. Inhibiting predicted active kinases supports the TPS pathway model. The TPS algorithm is broadly applicable and also recovers an accurate model of the yeast osmotic stress response.

SUMMARY We present a method for automatically discovering signaling pathways from time-resolved phosphoproteomic data. The Temporal Pathway Synthesizer (TPS) algorithm uses constraint-solving techniques first developed in the context of formal verification to explore paths in an interaction network. It systematically eliminates all candidate structures for a signaling pathway where a protein is activated or inactivated before its upstream regulators. The algorithm can model more than one hundred thousand dynamic phosphosites and can discover pathway members that are not differentially phosphorylated. By analyzing temporal data, TPS defines signaling cascades without needing to experimentally perturb individual proteins. It recovers known pathways and proposes pathway connections when applied to the human epidermal growth factor and yeast osmotic stress responses. Independent kinase mutant studies validate predicted substrates in the TPS osmotic stress pathway.

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