Extending and Relating Semantic Models of Compensating CSP

Business transactions involve multiple partners coordinating and interacting with each other. These transactions have hierarchies of activities which need to be orchestrated. Usual database approaches (e.g.,checkpoint, rollback) are not applicable to handle faults in a long running transaction due to interaction with multiple partners. The compensation mechanism handles faults that can arise in a long running transaction. Based on the framework of Hoare's CSP process algebra, Butler et al introduced Compensating CSP (cCSP), a language to model long-running transactions. The language introduces a method to declare a transaction as a process and it has constructs for orchestration of compensation. Butler et al also defines a trace semantics for cCSP. In this thesis, the semantic models of compensating CSP are extended by defining an operational semantics, describing how the state of a program changes during its execution. The semantics is encoded into Prolog to animate the specification. The semantic models are further extended to define the synchronisation of processes. The notion of partial behaviour is defined to model the behaviour of deadlock that arises during process synchronisation. A correspondence relationship is then defined between the semantic models and proved by using structural induction. Proving the correspondence means that any of the presentation can be accepted as a primary definition of the meaning of the language and each definition can be used correctly at different times, and for different purposes. The semantic models and their relationships are mechanised by using the theorem prover PVS. The semantic models are embedded in PVS by using Shallow embedding. The relationships between semantic models are proved by mutual structural induction. The mechanisation overcomes the problems in hand proofs and improves the scalability of the approach

Extracting proofs from documents

Often, theorem checkers like PVS are used to check an existing proof, which is part of some document. Since there is a large difference between the notations used in the documents and the notations used in the theorem checkers, it is usually a laborious task to convert an existing proof into a format which can be checked by a machine. In the system that we propose, the author is assisted in the process of converting an existing proof into the PVS language and having it checked by PVS. 1 Introduction The now-classic ALGOL 60 report [5] recognized three different levels of language: a reference language, a publication language and several hardware representations, whereby the publication language was intended to admit variations on the reference language and was to be used for stating and communicating processes. The importance of publication language ---often referred to nowadays as "pseudo-code"--- is difficult to exaggerate since a publication language is the most effective way..

LFTOP: An LF based approach to domain specific reasoning

Specialized vocabulary, notations and inference rules tailored for the description, analysis and reasoning of a domain is very important for the domain. For domain-specific issues researchers focus mainly on the design and implementation of domain-specific languages (DSL) and pay little attention to the reasoning aspects. We believe that domain-specific reasoning is very important to help the proofs of some properties of the domains and should be more concise, more reusable and more believable. It deserves to be investigated in an engineering way. Type theory provides good support for generic reasoning and verification. Many type theorists want to extend uses of type theory to more domains, and believe that the methods, ideas, and technology of type theory can have a beneficial effect for computer assisted reasoning in many domains. Proof assistants based on type theory are well known as effective tools to support reasoning. But these proof assistants have focused primarily on generic notations for representation of problems and are oriented towards helping expert type theorists build proofs efficiently. They are successful in this goal, but they are less suitable for use by non-specialists. In other words, one of the big barriers to limit the use of type theory and proof assistant in domain-specific areas is that it requires significant expertise to use it effectively. We present LFTOP ― a new approach to domain-specific reasoning that is based on a type-theoretic logical framework (LP) but does not require the user to be an expert in type theory. In this approach, users work on a domain-specific interface that is familiar to them. The interface presents a reasoning system of the domain through a user-oriented syntax. A middle layer provides translation between the user syntax and LF， and allows additional support for reasoning (e.g. model checking). Thus, the complexity of the logical framework is hidden but we also retain the benefits of using type theory and its related tools, such as precision and machine-checkable proofs. The approach is being investigated through a number of case studies. In each case study, the relevant domain-specific specification languages and logic are formalized in Plastic. The relevant reasoning system is designed and customized for the users of the corresponding specific domain. The corresponding lemmas are proved in Plastic. We analyze the advantages and shortcomings of this approach, define some new concepts related to the approach, especially discuss issues arising from the translation between the different levels. A prototype implementation is developed. We illustrate the approach through many concrete examples in the prototype implementation. The study of this thesis shows that the approach is feasible and promising, the relevant methods and technologies are useful and effective

On the Security of Software Systems and Services

This work investigates new methods for facing the security issues and threats arising from the composition of software. This task has been carried out through the formal modelling of both the software composition scenarios and the security properties, i.e., policies, to be guaranteed. Our research moves across three different modalities of software composition which are of main interest for some of the most sensitive aspects of the modern information society. They are mobile applications, trust-based composition and service orchestration. Mobile applications are programs designed for being deployable on remote platforms. Basically, they are the main channel for the distribution and commercialisation of software for mobile devices, e.g., smart phones and tablets. Here we study the security threats that affect the application providers and the hosting platforms. In particular, we present a programming framework for the development of applications with a static and dynamic security support. Also, we implemented an enforcement mechanism for applying fine-grained security controls on the execution of possibly malicious applications. In addition to security, trust represents a pragmatic and intuitive way for managing the interactions among systems. Currently, trust is one of the main factors that human beings keep into account when deciding whether to accept a transaction or not. In our work we investigate the possibility of defining a fully integrated environment for security policies and trust including a runtime monitor. Finally, Service-Oriented Computing (SOC) is the leading technology for business applications distributed over a network. The security issues related to the service networks are many and multi-faceted. We mainly deal with the static verification of secure composition plans of web services. Moreover, we introduce the synthesis of dynamic security checks for protecting the services against illegal invocations

System for automatic proving of some classes of analytic inequalities

U okviru ovog doktorata razvijen je sistem SimTheP (Simple Theorem Prover) za automatsko dokazivanje nekih klasa analitickih nejednakosti. Kao osnovna klasa nejednakosti posmatrana je klasa MTP (miksovano trigonometrijsko polinomskih) nejednakosti. U doktoratu su navedene jos neke klase analitickih nejednakosti na koje se, uz odred-ene dodatne korake, moze primeniti prikazani sistem. Za potrebe sistema je kreirano vise originalnih algoritama poput algoritma za trazenje prve pozitivne nule polinomske funkcije koji je baziran na Sturmovoj teoremi, algoritma za trazenje najmanjeg odgovarajuceg stepena aproksimacija Tejlorovim razvojima, algoritma sortiranja aproksimacija i slicnih. Svi algoritmi su prikazani pseudokodom i detaljnim objasnjenjem slucajeva upotrebe. Rad sistema i koriscenih algoritama ilustrovani su na vecem broju konkretnih analitickih nejednakosti od kojih su neke bile otvoreni problemi, a koji su potom reseni metodama sistema i publikovani u renomiranim casopisima. U okviru doktorata dat je detaljan prikaz oblasti i problematike vezane za dokazivanje i automatske dokazivace. Razmotreni su osnovni problemi sa kojima se srecu korisnici vecine automatskih dokazivaca, ali su takod-e analizirani i neki problemi vezani u vezi sa implementacijom automatskih dokazivaca teorema. Razvijena je jedna implementacija sistema SimTheP, a u cilju procene performansi ovog sistema urad-ena je uporedna analiza sa dokazivacem MetiTarski.In this doctoral thesis was developed SimTheP (Simple Theorem Prover), system for automatic proving of some classes of analytical inequalities. MTP (mixed trigonometric polynomial) inequalities were considered as basic class of studied inequalities. Some additional classes of analytical inequalities, on which shown system can be applied with some additional steps, were presented in this thesis. Several original algorithms, such as algorithm for seeking rst positive root of polynomial function based on Sturms theorem, algorithm for seeking smallest appropriate degree of approximation by Taylor series, algorithm for sorting of approximations and similar others, were created for use in system. All algorithms were shown by pseudo-code and detailed use case scenarios. Inner workings of system and application of stated algorithms was illustrated on great number of concrete analytical inequalities, of which some were open problems later solved by methods from system and published in renown journals. In this thesis was also given detailed image of area of research and problematic of theorem proving and automatic theorem provers. Some basic problems with which users of most automatic theorem provers deal were considered, but also some problems of implementation of automatic theorem proving were analysed. One implementation of system SimTheP was developed, and to assess performance of this system, side by side comparison with MetiTarski was conducted

A Tool for Producing Verified, Explainable Proofs

Mathematicians are reluctant to use interactive theorem provers. In this thesis I argue that this is because proof assistants don't emphasise explanations of proofs; and that in order to produce good explanations, the system must create proofs in a manner that mimics how humans would create proofs. My research goals are to determine what constitutes a human-like proof and to represent human-like reasoning within an interactive theorem prover to create formalised, understandable proofs. Another goal is to produce a framework to visualise the goal states of this system. To demonstrate this, I present HumanProof: a piece of software built for the Lean 3 theorem prover. It is used for interactively creating proofs that resemble how human mathematicians reason. The system provides a visual, hierarchical representation of the goal and a system for suggesting available inference rules. The system produces output in the form of both natural language and formal proof terms which are checked by Lean's kernel. This is made possible with the use of a structured goal state system which interfaces with Lean's tactic system which is detailed in Chapter 3. In Chapter 4, I present the subtasks automation planning subsystem, which is used to produce equality proofs in a human-like fashion. The basic strategy of the subtasks system is break a given equality problem in to a hierarchy of tasks and then maintain a stack of these tasks in order to determine the order in which to apply equational rewriting moves. This process produces equality chains for simple problems without having to resort to brute force or specialised procedures such as normalisation. This makes proofs more human-like by breaking the problem into a hierarchical set of tasks in the same way that a human would. To produce the interface for this software, I also created the ProofWidgets system for Lean 3. This system is detailed in Chapter 5. The ProofWidgets system uses Lean's metaprogramming framework to allow users to write their own interactive, web-based user interfaces to display within the VSCode editor and in an online web-editor. The entire tactic state is available to the rendering engine, and hence expression structure and types of subexpressions can be explored interactively. The ProofWidgets system also allows the user interface to interactively edit the proof document, enabling a truly interactive modality for creating proofs; human-like or not. In Chapter 6, the system is evaluated by asking real mathematicians about the output of the system, and what it means for a proof to be understandable to them. The user group study asks participants to rank and comment on proofs created by HumanProof alongside natural language and pure Lean proofs. The study finds that participants generally prefer the HumanProof format over the Lean format. The verbal responses collected during the study indicate that providing intuition and signposting are the most important properties of a proof that aid understanding.EPSR

Extending and relating semantic models of compensating CSP

Business transactions involve multiple partners coordinating and interacting with each other. These transactions have hierarchies of activities which need to be orchestrated. Usual database approaches (e.g.,checkpoint, rollback) are not applicable to handle faults in a long running transaction due to interaction with multiple partners. The compensation mechanism handles faults that can arise in a long running transaction. Based on the framework of Hoare's CSP process algebra, Butler et al introduced Compensating CSP (cCSP), a language to model long-running transactions. The language introduces a method to declare a transaction as a process and it has constructs for orchestration of compensation. Butler et al also defines a trace semantics for cCSP. In this thesis, the semantic models of compensating CSP are extended by defining an operational semantics, describing how the state of a program changes during its execution. The semantics is encoded into Prolog to animate the specification. The semantic models are further extended to define the synchronisation of processes. The notion of partial behaviour is defined to model the behaviour of deadlock that arises during process synchronisation. A correspondence relationship is then defined between the semantic models and proved by using structural induction. Proving the correspondence means that any of the presentation can be accepted as a primary definition of the meaning of the language and each definition can be used correctly at different times, and for different purposes. The semantic models and their relationships are mechanised by using the theorem prover PVS. The semantic models are embedded in PVS by using Shallow embedding. The relationships between semantic models are proved by mutual structural induction. The mechanisation overcomes the problems in hand proofs and improves the scalability of the approach.EThOS - Electronic Theses Online ServiceGBUnited Kingdo