Presenting Distributive Laws

Distributive laws of a monad T over a functor F are categorical tools for specifying algebra-coalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of well-behaved structural operational semantics and, more recently, also for enhancements of the bisimulation proof method. If T is a free monad, then such distributive laws correspond to simple natural transformations. However, when T is not free it can be rather difficult to prove the defining axioms of a distributive law. In this paper we describe how to obtain a distributive law for a monad with an equational presentation from a distributive law for the underlying free monad. We apply this result to show the equivalence between two different representations of context-free languages

Collaborative Verification-Driven Engineering of Hybrid Systems

Hybrid systems with both discrete and continuous dynamics are an important model for real-world cyber-physical systems. The key challenge is to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Often, hybrid systems are rather complex in that they require expertise from many domains (e.g., robotics, control systems, computer science, software engineering, and mechanical engineering). Moreover, despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires nontrivial human guidance, since hybrid systems verification tools solve undecidable problems. It is, thus, not uncommon for development and verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) graphical (UML) and textual modeling of hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks

High-level signatures and initial semantics

We present a device for specifying and reasoning about syntax for datatypes, programming languages, and logic calculi. More precisely, we study a notion of signature for specifying syntactic constructions. In the spirit of Initial Semantics, we define the syntax generated by a signature to be the initial object---if it exists---in a suitable category of models. In our framework, the existence of an associated syntax to a signature is not automatically guaranteed. We identify, via the notion of presentation of a signature, a large class of signatures that do generate a syntax. Our (presentable) signatures subsume classical algebraic signatures (i.e., signatures for languages with variable binding, such as the pure lambda calculus) and extend them to include several other significant examples of syntactic constructions. One key feature of our notions of signature, syntax, and presentation is that they are highly compositional, in the sense that complex examples can be obtained by assembling simpler ones. Moreover, through the Initial Semantics approach, our framework provides, beyond the desired algebra of terms, a well-behaved substitution and the induction and recursion principles associated to the syntax. This paper builds upon ideas from a previous attempt by Hirschowitz-Maggesi, which, in turn, was directly inspired by some earlier work of Ghani-Uustalu-Hamana and Matthes-Uustalu. The main results presented in the paper are computer-checked within the UniMath system.Comment: v2: extended version of the article as published in CSL 2018 (http://dx.doi.org/10.4230/LIPIcs.CSL.2018.4); list of changes given in Section 1.5 of the paper; v3: small corrections throughout the paper, no major change

Using formal methods to support testing

Formal methods and testing are two important approaches that assist in the development of high quality software. While traditionally these approaches have been seen as rivals, in recent years a new consensus has developed in which they are seen as complementary. This article reviews the state of the art regarding ways in which the presence of a formal specification can be used to assist testing

Computer-aided modeling for efficient and innovative product-process engineering

Model baserede computer understøttet produkt process engineering har opnået øget betydning i forskelligste industrielle brancher som for eksampel farmaceutisk produktion, petrokemi, finkemikalier, polymerer, bioteknologi, fødevarer, energi og vand. Denne trend er forventet at fortsætte på grund af substantielle fordele, hvilke computer understøttede metoder medfører. Den primære forudsætning af computer understøttet produkt process engineering erselvfølgelig den tilgængelighed af modeller af forskellige typer, former og anvendelser. Udviklingen af den påkrævet modellen for de undersøgte systemer er normalt en tidskrævende udfordring og derfor mest også dyrt. Den involverer forskelligste trin, fagekspert viden og dygtighed og forskellige modellerings værktøjer. Formålet af dette projekt er at systematisere den model udviklings proces og anvendelse og dermed øge effektiviteten af modeller såvel somkvaliteten. Den væsentlige bidrag af denne PhD afhandling er en generisk metodologi for proces model udviklingen og anvendelse i kombination med grundige algoritmiske arbejdes diagrammer for de forskellige involverede modeller opgaver og udviklingen af computer understøttede modeller rammer hvilke er strukturbaseret på den generiske metodologi, delvis automatiseret i de forskellige arbejdstrin og kombinerer alle påkrævet værktøjer, understøttelseog vejledning for de forskellige arbejdstrin. Understøttede modelleringsopgaver er etableringen af modeller mål, indsamling af de nødvendige informationer, model formulering inklusive numeriske analyser, etablering af løsningsstrategier og forbinding med den passende løsningsmodul, model identificering og sondering såvel som model anvendelse for simulation og optimering. Den computer understøttede modeller ramme blev implementeret i en brugervenlig software. En række forskellige demonstrationseksempler fra forskellige områder i kemisk ogbiokemiske engineering blev løst for udvikling og validering af den generiske modellerings metodologi og den computer understøttet modeller ramme anvendt på den udviklet software værktøj.Model-based computer aided product-process engineering has attained increased importance in a number of industries, including pharmaceuticals, petrochemicals, fine chemicals, polymers, biotechnology, food, energy and water. This trend is set to continue due to the substantial benefits computer-aided methods provide. The key prerequisite of computer-aided productprocess engineering is however the availability of models of different types, forms andapplication modes. The development of the models required for the systems under investigation tends to be a challenging, time-consuming and therefore cost-intensive task involving numerous steps, expert skills and different modelling tools. The objective of this project is to systematize the process of model development and application thereby increasing the efficiency of the modeller as well as model quality.The main contributions of this thesis are a generic methodology for the process of model development and application, combining in-depth algorithmic work-flows for the different modelling tasks involved and the development of a computer-aided modelling framework. This framework is structured, is based on the generic modelling methodology, partially automates the involved work-flows by integrating the required tools and, supports and guides the userthrough the different work-flow steps. Supported modelling tasks are the establishment of the modelling objective, the collection of the required system information, model construction including numerical analysis, derivation of solution strategy and connection to appropriate solvers, model identification/ discrimination as well as model application for simulation and optimization. The computer-aided modelling framework has been implemented into an userfriendlysoftware.A variety of case studies from different areas in chemical and biochemical engineering have been solved to illustrate the application of the generic modelling methodology, the computeraided modelling framework and the developed software tool