UTP Semantics for Handel-C

Lecture Notes in Computer Science

Woodcock

2013

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Abstract. This is a tutorial introduction to the two most basic theories in Hoare & He's Unifying Theories of Programming and their mechanisation in the Isabelle interactive theorem prover. We describe the theories of relations and of designs (pre-postcondition pairs), interspersed with their formalisation in Isabelle and example mechanised proofs.Keywords: Unifying Theories of Programming (UTP), Denotational Semantics, Laws of Programming, Isabelle, Interactive Theorem Proving.Dedication: To Professor He Jifeng on the occasion of his 70th birthday. PreliminariesUnifying Theories of Programming, originally the work of Hoare & He [15], is a long-term research agenda that can be summarised as follows. Researchers have proposed many different programming theories and practitioners have proposed many different pragmatic programming paradigms; how do we understand the relationship between them?UTP can trace its origins back to the work on predicative programming, which was started by Hehner; see [12] for a summary. It gives three principal ways to study such relationships: (i) by computational paradigm; (ii) by level of abstraction; and (iii) by method of presentation.In Section 2, we introduce the basic concepts of UTP: alphabets, signatures, and healthiness conditions, and in Section 3 we outline the idea of theory mechanisation in Isabelle/HOL. In Section 4, we go on to describe the alphabetised relational calculus, the formalism used to describe predicates in UTP theories. In Section 5, we introduce a basic nondeterministic programming language and its laws of programming. In Section 6, we complete the initial presentation of UTP by describing the organisaiton of UTP theories into complete lattices. Sections 7 and 8 show how Hoare logic and the weakest precondition calculus can be defined in UTP. Section 9 introduces the UTP theory of designs that capture the notion of total correctness using assumptions and commitments. The paper ends with a discussion of related work (Section 11) and some conclusions including directions for future work (Section 12). Computational Paradigms. UTP groups programming languages according to a classification by computational model; for example, structured, object-oriented, functional, or logical. The technique is to identify common concepts and deal separately with additions and variations. It uses two fundamental scientific principles: (i) simplicity of presentation and (ii) separation of concerns.Abstraction. Orthogonal to this organisation by computational paradigm, languages could be categorised by their level of abstraction within a particular paradigm. For example, the lowest level of abstraction may be the platformspecific technology of an implementation. At the other end of the spectrum, there might be a very high-level description of overall requirements and how they are captured and analysed. In between, there will be descriptions of components and descriptions of how they will be organised into architectures. Each of these levels will have interfaces specified by contract...

Section: Preliminariesmentioning

confidence: 99%

Unifying Theories of Programming in Isabelle

Lecture Notes in Computer Science

Woodcock

2013

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“…Hoare and He's Unifying Theories of Programming (UTP) has been designed as a framework in which the integration of languages, through the common semantic domain of the alphabetised relation calculus, can be achieved. Semantic models for discrete modelling languages in UTP are already numerous [26,13,36,30], and, therefore, in this paper we focus on semantics of continuous models in the Modelica language.…”

Section: Introductionmentioning

confidence: 99%

Towards a UTP Semantics for Modelica

Lecture Notes in Computer Science

Thiele

Cavalcanti

et al. 2017

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Abstract. We describe our work on a UTP semantics for the dynamic systems modelling language Modelica. This is a language for modelling a system's continuous behaviour using a combination of differentialalgebraic equations and an event-handling system. We develop a novel UTP theory of hybrid relations, inspired by Hybrid CSP and Duration Calculus, that is purely relational and provides uniform handling of continuous and discrete variables. This theory is mechanised in our Isabelle implementation of the UTP, Isabelle/UTP, with which we verify some algebraic properties. Finally, we show how a subset of Modelica models can be given semantics using our theory. When combined with the wealth of existing UTP theories for discrete system modelling, our work enables a sound approach to heterogeneous semantics for Cyber-Physical systems by leveraging the theory linking facilities of the UTP.

“…UTP has been applied to theories from a wide area of computer science, including process calculi, object orientation, and real-time systems. It provides the basis for the Circus [25] specification language, which unifies Z, CSP, and refinement calculi, and has been used to formalise the semantics of a number of languages, such as Safety-Critical Java [6], Handel-C [21], and SysML [26], a multi-paradigm modelling notation.…”

Section: Introductionmentioning

confidence: 99%

Isabelle/UTP: A Mechanised Theory Engineering Framework

Unifying Theories of Programming

Zeyda

Woodcock

2015

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We introduce Isabelle/UTP, a novel mechanisation of Hoare and He's Unifying Theories of Programming (UTP) in Isabelle/HOL. UTP is a framework for the study, formalisation, and unification of formal semantics. Our contributions are, firstly, a deep semantic model of UTP's alphabetised predicates, supporting meta-logical reasoning that is parametric in the underlying notions of values and types. Secondly, integration of host-logic type checking that subsumes the need for typing proof obligations in the object-language. Thirdly, proof tactics that transfer results from well-supported mathematical structures in Isabelle to proofs about UTP theories. Additionally, our work provides novel insights towards reconciliation of shallow and deep language embeddings.