Abstract modelling: towards a typed declarative language for the conceptual modelling phase

Modelling languages have become an indispensable aid to practising engineers. They offer modelling at a high level of abstraction backed by features such as automatic simulation and even derivation of production code. However, partly because of the offered automation, modelling languages are limited to specific application areas: to our knowledge, no modelling language supports mathematical physics modelling in its full generality. Yet, when developing large, coupled, multiphysics models, there is a clear need for such an overarching language to ensure the coherence of the model as a whole, even if submodels ultimately are realised in modelling languages targeting specific domains or are pre-existing. In prior work, it was demonstrated how treating models as abstract objects in category theory offers one way to ensure coherence of key aspects for composite models. Type theory offers complementary approaches. This paper presents a first step towards a language supporting abstract modelling in mathematical physics with the aim of ensuring coherence of coupled multiphysics models early in the design process. To that end, following the approach of Functional Hybrid Modelling (FHM), we discuss how a language supporting quite general modelling equations can be realised as an embedding in Haskell. The appeal of the proposed approach is that only very few core concepts are needed, which greatly simplifies the semantics. The appeal of an embedded realisation as such is that much of the language infrastructure comes for free

Conceptual modelling: Towards detecting modelling errors in engineering applications

Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer “simple” objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering system

Model Transformations in MT

Model transformations are recognised as a vital aspect of Model Driven Development,but current approaches cover only a small part of the possible spectrum. In this paper I present the MT model transformation which shows how a QVT-like language can be extended with novel pattern matching constructs, how tracing information can be automatically constructed and visualized, and how the transformed model is pruned of extraneous elements. As MT is implemented as a DSL within the Converge language, this paper also demonstrates how a general purpose language can be embedded in a model transformation language, and how DSL development can aid experimentation and exploration of new parts of the model transformation spectrum

First-class models: on a noncausal language for higher-order and structurally dynamic modelling and simulation

The field of physical modelling and simulation plays a vital role in advancing numerous scientific and engineering disciplines. To cope with the increasing size and complexity of physical models, a number of modelling and simulation languages have been developed. These languages can be divided into two broad categories: causal and noncausal. Causal languages express a system model in terms of directed equations. In contrast, a noncausal model is formulated in terms of undirected equations. The fact that the causality can be left implicit makes noncausal languages more declarative and noncausal models more reusable. These are considered to be crucial advantages in many physical domains. Current, mainstream noncausal languages do not treat equational models as first-class values; that is, a model cannot be parametrised on other models or generated at simulation runtime. This results in very limited higher-order and structurally dynamic modelling capabilities, and limits the expressiveness and applicability of noncausal languages. This thesis is about a novel approach to the design and implementation of noncausal languages with first-class models supporting higher-order and structurally dynamic modelling. In particular, the thesis presents a language that enables: (1) higher-order modelling capabilities by embedding noncausal models as first-class entities into a functional programming language and (2) efficient simulation of noncausal models that are generated at simulation runtime by runtime symbolic processing and just-in-time compilation. These language design and implementation approaches can be applied to other noncausal languages. This thesis provides a self-contained reference for such an undertaking by defining the language semantics formally and providing an in-depth description of the implementation. The language provides noncausal modelling and simulation capabilities that go beyond the state of the art, as backed up by a range of examples presented in the thesis, and represents a significant progress in the field of physical modelling and simulation

Optimisation of dynamic, hybrid signal function networks

Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on signals. FRP is based on the synchronous data-flow paradigm and supports both continuous-time and discrete-time signals (hybrid systems). What sets FRP apart from most other languages for similar applications is its support for systems with dynamic structure and for higher-order data-flow constructs. This raises a range of implementation challenges. This paper contributes towards advancing the state of the art of FRP implementation by studying the notion of signal change and change propagation in a setting of hybrid signal function networks with dynamic structure. To sidestep some problems of certain previous FRP implementations that are structured using arrows, we suggest working with a notion of composable, multi-input and multi-output signal functions. A clear conceptual distinction is also made between continuous-time and discrete-time signals. We then show how establishing change-related properties of the signal functions in a network allows such networks to be simplified (static optimisation) and can help reducing the amount of computation needed for executing the networks (dynamic optimisation). Interestingly, distinguishing between continuous-time and discrete-time signals allows us to characterise the change-related properties of signal functions more precisely than what we otherwise would have been able to, which is helpful for optimisation

Keeping calm in the face of change: towards optimisation of FRP by reasoning about change

Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on signals (time-varying values). FRP is based on the synchronous data-flow paradigm and supports both (an approximation to) continuous-time and discrete-time signals (hybrid systems).What sets FRP apart from most other languages for similar applications is its support for systems with dynamic structure and for higher-order reactive constructs. This paper contributes towards advancing the state of the art of FRP implementation by studying the notion of signal change and change propagation in a setting of structurally dynamic networks of n-ary signal functions operating on mixed continuous-time and discrete-time signals. We first define an ideal denotational semantics (time is truly continuous) for this kind of FRP, along with temporal properties, expressed in temporal logic, of signals and signal functions pertaining to change and change propagation. Using this framework, we then show how to reason about change; specifically, we identify and justify a number of possible optimisations, such as avoiding recomputation of unchanging values. Note that due to structural dynamism, and the fact that the output of a signal function may change because time is passing even if the input is unchanging, the problem is significantly more complex than standard change propagation in networks with static structure

Chromar, a language of parameterised objects

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Meta-F*: Proof Automation with SMT, Tactics, and Metaprograms

We introduce Meta-F*, a tactics and metaprogramming framework for the F* program verifier. The main novelty of Meta-F* is allowing the use of tactics and metaprogramming to discharge assertions not solvable by SMT, or to just simplify them into well-behaved SMT fragments. Plus, Meta-F* can be used to generate verified code automatically. Meta-F* is implemented as an F* effect, which, given the powerful effect system of F*, heavily increases code reuse and even enables the lightweight verification of metaprograms. Metaprograms can be either interpreted, or compiled to efficient native code that can be dynamically loaded into the F* type-checker and can interoperate with interpreted code. Evaluation on realistic case studies shows that Meta-F* provides substantial gains in proof development, efficiency, and robustness.Comment: Full version of ESOP'19 pape