Engineering formal systems in constructive type theory

This thesis presents a practical methodology for formalizing the meta-theory of formal systems with binders and coinductive relations in constructive type theory. While constructive type theory offers support for reasoning about formal systems built out of inductive definitions, support for syntax with binders and coinductive relations is lacking. We provide this support. We implement syntax with binders using well-scoped de Bruijn terms and parallel substitutions. We solve substitution lemmas automatically using the rewriting theory of the -calculus. We present the Autosubst library to automate our approach in the proof assistant Coq. Our approach to coinductive relations is based on an inductive tower construction, which is a type-theoretic form of transfinite induction. The tower construction allows us to reduce coinduction to induction. This leads to a symmetric treatment of induction and coinduction and allows us to give a novel construction of the companion of a monotone function on a complete lattice. We demonstrate our methods with a series of case studies. In particular, we present a proof of type preservation for CC!, a proof of weak and strong normalization for System F, a proof that systems of weakly guarded equations have unique solutions in CCS, and a compiler verification for a compiler from a non-deterministic language into a deterministic language. All technical results in the thesis are formalized in Coq.In dieser Dissertation beschreiben wir praktische Techniken um Formale Systeme mit Bindern und koinduktiven Relationen in Konstruktiver Typtheorie zu implementieren. Während Konstruktive Typtheorie bereits gute Unterstützung für Induktive Definition bietet, gibt es momentan kaum Unterstützung für syntaktische Systeme mit Bindern, oder koinduktiven Definitionen. Wir kodieren Syntax mit Bindern in Typtheorie mit einer de Bruijn Darstellung und zeigen alle Substitutionslemmas durch Termersetzung mit dem -Kalkül. Wir präsentieren die Autosubst Bibliothek, die unseren Ansatz im Beweisassistenten Coq implementiert. Für koinduktive Relationen verwenden wir eine induktive Turmkonstruktion, welche das typtheoretische Analog zur Transfiniten Induktion darstellt. Auf diese Art erhalten wir neue Beweisprinzipien für Koinduktion und eine neue Konstruktion von Pous’ “companion” einer monotonen Funktion auf einem vollständigen Verband. Wir validieren unsere Methoden an einer Reihe von Fallstudien. Alle technischen Ergebnisse in dieser Dissertation sind mit Coq formalisiert

Monitoring of Thermal and Flow Processes in the Two-Phase Spray-Ejector Condenser for Thermal Power Plant Applications

The paper deals with the problem of accurate measuring techniques and experimental research methods for performance evaluation of direct contact jet-type flow condensers. The nominal conditions and range of temperature, pressure and flow rate in all characteristic points of novel test rig installation were calculated using the developed model. Next, the devices for measurement of temperature, pressure and flow rate in a novel test rig designed for testing the two-phase flow spray ejector condensers system (SEC) were studied. The SEC can find application in gas power cycles as the device dedicated to condensing steam in exhaust gases without decreasing or even increasing exhaust gas pressure. The paper presents the design assumptions of the test rig, its layout and results of simulations of characteristic points using developed test rig models. Based on the initial thermal and flow conditions, the main assumptions for thermal and flow process monitoring were formulated. Then, the discussion on commercially available measurement solutions was presented. The basic technical parameters of available sensors and devices were given, discussed with details. © 2022 by the authors.Monitoring of Thermal and Flow Processes in the Two-Phase Spray-Ejector Condenser for Thermal Power Plant ApplicationspublishedVersio

Characterization of the Autoignition of Single Droplets of Fischer-Tropsch Fuels and Development of Surrogates

The autoignition behavior of single droplets of synthetic fuels produced by the Fischer-Tropsch process, such as GTL-Diesel and GTL-Kerosene, is the main focus of this study. For this, experiments are carried out under microgravity and normal gravity conditions with single droplets with an initial diameter of 0,7 mm in a high-temperature high-pressure chamber. Ignition delay times are determined for ambient pressures between 0,1 MPa < p < 1 MPa and ambient temperatures between 550 K < T < 950 K with the aid of a Michelson interferometer setup. The experimental data is fitted with two-term Arrhenius-type functions that represent the two main reaction mechanisms, the cool and hot flame. Furthermore the development of suitable surrogate fuels for these fuels is performed and the selection and formulation procedure for the components is shown. Surrogate fuels enable numerical calculations with detailed chemical reaction kinetics. The obtained data on the characterization of the aforementioned fuels is compared with data of related fuels, such as their mineral variants and other surrogates

Quantified CTL: Expressiveness and Complexity

While it was defined long ago, the extension of CTL with quantification over atomic propositions has never been studied extensively. Considering two different semantics (depending whether propositional quantification refers to the Kripke structure or to its unwinding tree), we study its expressiveness (showing in particular that QCTL coincides with Monadic Second-Order Logic for both semantics) and characterise the complexity of its model-checking and satisfiability problems, depending on the number of nested propositional quantifiers (showing that the structure semantics populates the polynomial hierarchy while the tree semantics populates the exponential hierarchy)