Higher-order subtyping and its decidability

AbstractWe define the typed lambda calculus Fω∧ (F-omega-meet), a natural generalization of Girard's system Fω (F-omega) with intersection types and bounded polymorphism. A novel aspect of our presentation is the use of term rewriting techniques to present intersection types, which clearly splits the computational semantics (reduction rules) from the syntax (inference rules) of the system. We establish properties such as Church-Rosser for the reduction relation on types and terms, and strong normalization for the reduction on types. We prove that types are preserved by computation (subject reduction), and that the system satisfies the minimal types property. We define algorithms for type checking and subtype checking. The development culminates with the proof of decidability of typing in Fω∧, containing the first proof of decidability of subtyping of a higher-order lambda calculus with subtyping

Stan: A Probabilistic Programming Language

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectation propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting

On the Termination Problem for Probabilistic Higher-Order Recursive Programs

In the last two decades, there has been much progress on model checking of both probabilistic systems and higher-order programs. In spite of the emergence of higher-order probabilistic programming languages, not much has been done to combine those two approaches. In this paper, we initiate a study on the probabilistic higher-order model checking problem, by giving some first theoretical and experimental results. As a first step towards our goal, we introduce PHORS, a probabilistic extension of higher-order recursion schemes (HORS), as a model of probabilistic higher-order programs. The model of PHORS may alternatively be viewed as a higher-order extension of recursive Markov chains. We then investigate the probabilistic termination problem -- or, equivalently, the probabilistic reachability problem. We prove that almost sure termination of order-2 PHORS is undecidable. We also provide a fixpoint characterization of the termination probability of PHORS, and develop a sound (but possibly incomplete) procedure for approximately computing the termination probability. We have implemented the procedure for order-2 PHORSs, and confirmed that the procedure works well through preliminary experiments that are reported at the end of the article

Higher-order subtyping

AbstractSystem F⩽ω is an extension with subtyping of the higher-order polymorphic λ-calculus —an orthogonal combination of Girard's system Fω with Cardelli and Wegner's Kernel Fun variant of System F⩽. We develop the fundamental metatheory of this calculus: decidability of β-conversion on well-kinded types, elimination of the “cut-rule” of transitivity from the subtype relation, and the soundness, completeness, and termination of algorithms for subtyping and typechecking

Pacific Weekly, October 16, 1930

https://scholarlycommons.pacific.edu/pacifican/3750/thumbnail.jp

Design and planning of energy supply chain networks.

During a period of transformation towards decarbonised energy networks, maintenance of a reliable and secure energy supply whilst increasing efficiency and reducing cost will be key aims for all energy supply chain (ESC) networks. With the knowledge that about 80% of global energy is obtained from fossil fuels, appropriate design and planning of its supply chain networks is inevitable. Notwithstanding, renewable energy sources, such as biomass, solar, wind and geothermal, will also play important roles in the future ESCs as climate change mitigation becomes an increasingly important concern. To achieve this aim, energy systems optimization models were derived; (i) for the simultaneous planning of energy production and maintenance in combined heat and power (CHP) plants for overall cost reduction, with results obtained benchmarked against data from industry; (ii) for biomass integration into ESC networks for emissions reduction and benchmarking it against data from literature and the governing equations solved for optimality using the General Algebraic Modelling System (GAMS) software. Further, energy survey questionnaires were developed using the Qualtrics online survey tool and same disseminated to individuals in some counties of the United Kingdom (UK) with the aim of proposing strategies for improved renewable energy (RE) embracement in the UK energy mix. The case study of the coal-fired CHP plant predicted a 21% reduction in annual total cost in comparison to the implemented industrial solution that follows a predefined maintenance policy, thereby, enhancing the resource and energy efficiency of the plant. Additionally, the optimization model for integrating biomass into energy supply chain networks indicated that a reduction in the emissions level of up to 4.32% is achievable on integration of 5-8% of biomass in the ESC with a 4.57% increase in the total cost of the ESC network predicted at biomass fraction of 7.9% in the mixed fuel, indicating that the cost increment in a biomass and coal co-fired plant can be offset with the introduction of effective carbon pricing legislation.PhD in Energy and Powe