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It has become fairly standard in programming-languages research to verify functional programs in proof assistants using induction, algebraic simplification, and rewriting. In this paper, we introduce Kami, a Coq library that uses labeled transition systems to enable similar expressive and modular reasoning for hardware designs expressed in the style of the Bluespec language. We can specify, implement, and verify realistic designs entirely within Coq, ending with automatic extraction into a pipeline that bottoms out in FPGAs. Our methodology has been evaluated in a case study verifying an infinite family of multicore systems, with cache-coherent shared memory and pipelined cores implementing (the base integer subset of) the RISC-V instruction set. CCS Concepts: • Hardware → Theorem proving and SAT solving; Hardware description languages and compilation; High-level and register-transfer level synthesis;

The ligands for many olfactory receptors remain largely unknown despite successful heterologous expression of these receptors. Understanding the molecular receptive range of olfactory receptors and deciphering the olfactory recognition code are hampered by the huge number of odorants and large number of olfactory receptors, as well as the complexity of their combinatorial coding. Here, we present an in silico screening approach to find additional ligands for a mouse olfactory receptor that allows improved definition of its molecular receptive range. A virtual library of 574 odorants was screened against a mouse olfactory receptor MOR42-3. We selected the top 20 candidate ligands using two different scoring functions. These 40 odorant candidate ligands were then tested in vitro using the Xenopus oocyte heterologous expression system and two-electrode voltage clamp electrophysiology. We experimentally confirmed 22 of these ligands. The candidate ligands were screened for both agonist and antagonist activity. In summary, we validated 19 agonists and 3 antagonists. Two of the newly identified antagonists were of low potency. Several previously known ligands (mono- and dicarboxylic acids) are also confirmed in this study. However, some of the newly identified ligands were structurally dissimilar compounds with various functional groups belonging to aldehydes, phenyls, alkenes, esters and ethers. The high positive predictive value of our in silico approach is promising. We believe that this approach can be used for initial deorphanization of olfactory receptors as well as for future comprehensive studies of molecular receptive range of olfactory receptors.

Deep learning is moving towards increasingly sophisticated optimization objectives that employ higher-order functions, such as integration, continuous optimization, and root-finding. Since differentiable programming frameworks such as PyTorch and TensorFlow do not have first-class representations of these functions, developers must reason about the semantics of such objectives and manually translate them to differentiable code. We present a differentiable programming language, λ S , that is the first to deliver a semantics for higher-order functions, higher-order derivatives, and Lipschitz but nondifferentiable functions. Together, these features enableλ S to expose differentiable, higher-order functions for integration, optimization, and root-finding as first-class functions with automatically computed derivatives. λ S ’s semantics is computable, meaning that values can be computed to arbitrary precision, and we implement λ S as an embedded language in Haskell. We use λ S to construct novel differentiable libraries for representing probability distributions, implicit surfaces, and generalized parametric surfaces – all as instances of higher-order datatypes – and present case studies that rely on computing the derivatives of these higher-order functions and datatypes. In addition to modeling existing differentiable algorithms, such as a differentiable ray tracer for implicit surfaces, without requiring any user-level differentiation code, we demonstrate new differentiable algorithms, such as the Hausdorff distance of generalized parametric surfaces.

Modern probabilistic programming languages aim to formalize and automate key aspects of probabilistic modeling and inference. Many languages provide constructs for programmable inference that enable developers to improve inference speed and accuracy by tailoring an algorithm for use with a particular model or dataset. Unfortunately, it is easy to use these constructs to write unsound programs that appear to run correctly but produce incorrect results. To address this problem, we present a denotational semantics for programmable inference in higher-order probabilistic programming languages, along with a type system that ensures that well-typed inference programs are sound by construction. A central insight is that the type of a probabilistic expression can track the space of its possible execution traces, not just the type of value that it returns, as these traces are often the objects that inference algorithms manipulate. We use our semantics and type system to establish soundness properties of custom inference programs that use constructs for variational, sequential Monte Carlo, importance sampling, and Markov chain Monte Carlo inference. CCS Concepts: • Mathematics of computing → Probabilistic inference problems; Variational methods; Metropolis-Hastings algorithm; Sequential Monte Carlo methods; • Theory of computation → Semantics and reasoning; Denotational semantics; • Software and its engineering → Formal language definitions.