In functional programming it is common practice to build modular programs by composing functions where the intermediate values are data structures such as lists or arrays. A desirable optimisation for programs written in this style is to fuse the composed functions and thereby eliminate the intermediate data structures and their associated runtime costs. Stream fusion is one such fusion optimisation that can eliminate intermediate data structures, including lists, arrays and other abstract data types that can be viewed as coinductive sequences. The fusion transformation can be applied fully automatically by a general purpose optimising compiler. The stream fusion technique itself has been presented previously and many practical implementations exist. The primary contributions of this thesis address the issues of correctness and optimisation: whether the transformation is correct and whether the transformation is an optimisation. Proofs of shortcut fusion laws have typically relied on parametricity by making use of free theorems. Unfortunately, most functional programming languages have semantics for which classical free theorems do not hold unconditionally; additional side conditions are required. In this thesis we take an approach based not on parametricity but on data abstraction. Using this approach we prove the correctness of stream fusion for lists -- encompassing the fusion system as a whole, not merely the central fusion law. We generalise this proof to give a framework for proving the correctness of stream fusion for any abstract data type that can be viewed as a coinductive sequence and give as an instance of the framework, a simple model of arrays. The framework requires that each fusible function satisfies a simple data abstraction property. We give proofs of this property for several standard list functions. Previous empirical work has demonstrated that stream fusion can be an optimisation in many cases. In this thesis we take a more universal view and consider the issue of optimisation independently of any particular implementation or compiler. We make a semi-formal argument that, subject to certain syntactic conditions on fusible functions, stream fusion on lists is strictly an improvement, as measured by the number of allocations of data constructors. This detailed analysis of how stream fusion works may be of use in writing fusible functions or in developing new implementations of stream fusion.

In the eastern part of Stockholm, a major urban development project is taking place. It is called Stockholm Royal Seaport and up to the year 2030 approximately 12000 new homes, 35000 workplaces and 600000 square meters of commercial areas will be added to the area. The project has been given a very ambitious environmental action program. As a part of that, the City of Stockholm has established a logistics centre in the area. The logistics centre is supposed to coordinate all transports of building material and handle the waste during the construction phase. One objective with the logistics centre is to reduce the number of transports and thereby reduction in the use of energy. The thesis-work mainly focused on developing an optimisation program for electricity supply to the logistics centre, in order to find the optimal way of managing charging and the use of electrical energy, when the logistics centre has procured a new batterypowered truck. The main objective is to minimize the purchase of power bought from the grid, for the loads at the logistics centre at Stockholm Royal Seaport. This thesis not only focused on this site in particular, but the work also resulted in creating a benchmark model that could be used for studying the electrification process for other construction sites in general. The logistics centre contains stationary battery storage, electrified distribution trucks, a PV generation system, and other electrical loads at the site. This thesis aimed at considering all the limitations and constraints for all the resources at the site and then finding an optimal method of utilising these resources in order to minimize the overall energy consumption. In this thesis, the optimal sizing of the battery for an electrified distribution truck is also performed considering the overall functional requirements of the distribution truck. Various charging strategies have been identified and simulated to understand the routines of charging the truck and their direct impact on the grid due to the purchase of energy during various hours of the day. The work resulted in optimised use of assets at the site during different hours of the day. The simulation work identified the best strategy and the use of resources at the site thus saving some amount of energy consumption at the site. This directly resulted in saving overall operational costs of the logistics centre. / I den östra delen av Stockholm pågår ett stort stadsutvecklingsprojekt. Det kallas Norra Djurgårdsstaden och fram till år 2030 kommer cirka 12000 nya bostäder, 35000 arbetsplatser och 600000 kvadratmeter kommersiella områden att läggas till området. Projektet har fått ett mycket ambitiöst miljöprogram och som en del av det har Stockholm stad inrättat ett logistikcenter i området. Logistikcentret ska samordna alla transporter av byggmaterial och hantera avfallet under byggfasen. Ett mål med logistikcentret är att minska antalet transporter och därmed minska energianvändningen. Examensarbetet fokuserade främst på att utveckla ett optimeringsprogram för elförsörjningen till bygglogistikcentret för att hitta det optimala sättet att hantera laddning och användning av elektrisk energi när logistikcentret investerar i en ny batteridriven lastbil. Huvudmålet är att minimera importen av elkraft som köps från nätet för att försörjar lasterna vid Norra Djurgårdsstadens Bygglogistikcenter. Målet är att göra en vägledande modell som kan användas för att studera elektrifieringsprocessen för byggarbetsplatser i allmänhet. Detta logistikcenter innehåller stationär batterilagring, elektrifierade distributionsbilar, ett PV -genereringssystem och andra elektriska laster på platsen. Syftet med denna avhandling var att överväga begränsningarna och resurserna på platsen och sedan hitta en optimal metod för att använda dessa resurser för att minimera den totala energiförbrukningen. I detta examensarbetet utförs också den optimala dimensioneringen av batteriet för en elektrifierad distributionsbil med beaktande av de övergripande funktionella kraven för distributionsbilen. Olika laddningsstrategier har identifierats och simulerats för att förstå rutinerna för laddning av lastbilen och dess direkta påverkan på nätet på grund av inköp av energi under olika timmar på dygnet. Arbetet resulterade i optimerad användning av tillgångar på platsen under olika timmar på dygnet. Simuleringsarbetet identifierade den bästa strategin och användningen av resurser på platsen, vilket sparar en viss energiförbrukning på platsen. Detta resulterade direkt i att spara logistikcentralens totala driftskostnader.