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Interaction trees are an active development in representing effectful and impure pro- grams in the Coq proof assistant. Examples of programs they can represent are programs that use: mutable state, concurrency and general recursion. Besides representing these programs we also want to reason about and verify these programs using separation logic. That is the purpose of this thesis. More technically speaking interaction trees are new way to do shallow embeddings in the Coq proof assistant. They are a coinductive variant of the free monad and come with the usual constructions of events and event handlers. The aim of interaction trees is to represent impure programs and potentially non-terminating programs in their environment. Interaction trees are, in contrast to relational operational semantics, executable by interpretation or program extraction. Interaction trees come with a framework for reasoning about their behavior based on equivalency up to weak bisimulation. An open problem is to reason about interaction trees utilizing a separation logic rather than weak bisimulation. We developed Pothos as a solution to this problem. Pothos has an Iris based concurrent separation logic for interaction trees. We address the problem in a non-extensible setting, with mutable state, non-termination and concur- rency as our chosen effects. Pothos inherits all the executable properties from interaction trees and includes a novel relation of Iris’s step-index with coinductive types. We have proven our logic to be sound and include a case study of a spin lock library. The case study shows that our logic is both non-trivial and can utilize the standard Iris patterns for concurrency., Computer Science

Software Technology, Software Engineering

Dr. Robert Lange relates his personal experiences on the U.S.S. Beaver in the Pacific during World War II.

Evasion of carbon dioxide from the surface of freshwater channels accounts for a substantial proportion of its flux from the terrestrial biosphere to the atmosphere; accurate estimates of channel wetted width (WW) are required to improve predictions of this flux. We investigated which landscape and climate-related data were statistically significant predictors of WW at baseflow across a large region (2200 km2) of north Wales and western England (UK) where habitat surveys suggest the majority of channels are in a near natural state. We used 25 cm pixel resolution air photos to measure channel WW at baseflow, and quantified the magnitude of the errors in these measurements. We used flow information from local gauging stations to ensure that channels were at or close to baseflow for the days on which the air photos were captured. The root mean squared difference between the fieldbased and air photo measurements of WW (n=28 sites) was small (0.14 m) in comparison to the median channel WW (3.07 m), and there was very little bias between the two sets of measurements (0.026 m). We created a set of points along those sections of channels which were visible in air photos and used a digital terrain model to create the drainage catchments for the points and computed their catchment area (CA).We removed points with CA <1 km2 and selected a random subset from the remaining points (n=472). We measured channel WW at these points from air photos and computed landscape and climate-related data for each of their catchments (mean slope, mean annual rainfall, land cover type, elevation) and also mean BFIHOST, a quantitative index relating to hydrological source of flow. We also computed the local slope at each of the selected points on the channel. As these data were not independent random variables, we used the linear mixed model framework with WW as the predictand and included the various landscape and climate-related data (including CA0:5) as fixed effects. We included a spatial cov

The vertical transport of CO2 from rivers to the atmosphere has only recently been identified as a significant component of global greenhouse gas (GHG) budgets. Headwater streams are responsible for a disproportionately large quantity of total CO2 evasion, yet are difficult to map comprehensively due to their width being smaller than the spatial resolution of most remotely sensed imagery that is currently used for this application. The need to capture these streams is further underlined by recent research that has identified water surface area as a key control of CO2 evasion rate. The challenge of extracting a complete representation of surface waters from remotely sensed imagery means that this critical component of CO2 models is currently poorly understood. This thesis addressed this by applying the novel combination of fuzzy classification, one-class classification, and contouring to derive super-resolution maps of surface waters from high resolution colour infrared aerial imagery. The methodology produced maps of sufficient accuracy to capture a significant proportion of headwater streams, which were measured using a semi-automated GIS-driven technique. Water surface width (WSW) was then estimated at the national scale using a predictive model that utilised widely available or readily calculable landscape variables in conjunction with image-based measurements of WSW. The multiple linear regression model accounted for a high proportion of the variation in WSW (adjusted R2 = 0.75, p < 0.05), allowing the lack of a national-scale dataset of WSW for England and Wales to be addressed. The main explanatory variables included catchment area, hydrological source of flow, rainfall, relief, and for the first time in a predictive model of WSW, a metric quantifying the extent to which the river has been modified. WSW predictions were then applied to CO2 evasion modelling to predict the quantity of CO2 transferred from rivers to the atmosphere in England and Wales, based on