Unifying semantic foundations for automated verification tools in Isabelle/UTP

Abstract

The growing complexity and diversity of models used for engineering dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration requires unified semantic foundations for the various notations, and co-ordination of a variety of automated verification tools. The contribution of this paper is Isabelle/UTP, an implementation of Hoare and He's Unifying Theories of Programming, a framework for unification of formal semantics. Isabelle/UTP permits the mechanisation of computational theories for diverse paradigms, and their use in constructing formalised semantics. These can be further applied in the development of verification tools, harnessing Isabelle's proof automation facilities. Several layers of mathematical foundations are developed, including lenses to model variables and state spaces as algebraic objects, alphabetised predicates and relations to model programs, algebraic and axiomatic semantics, proof tools for Hoare logic and refinement calculus, and UTP theories to encode computational paradigms.

Evolution of Formal Model-Based Assurance Cases for Autonomous Robots

“…The evidence for an FMAC is obtained by formal verification using an implementation of dL [33] in our verification framework, Isabelle/UTP [10,11]. dL specialises Dynamic Logic by combining a modelling notation for hybrid systems, called hybrid programs, with a formal property language for reasoning about such programs.…”

“…Hybrid programs, P, are composed using sequential composition (P Q), nondeterministic choice (P ⊓ Q), Kleene star (P * ), conditional tests (?b), assignments ( σ ), nondeterministic assignments (x := * ), and ODEs ({σ | b}). Each of these operators is semantically denoted as a relational predicate (for details see [10,11]). As usual in UTP [17], relations are partially ordered by refinement (P ⊑ Q), which corresponds to universally closed reverse implication.…”

“…We indicate how one can derive safety guarantees from hazard analysis yet avoiding too conservative solutions by adding liveness guarantees. We demonstrate our proofs in Isabelle/HOL [29] by formalising the robot model in an implementation of dL in Isabelle/UTP [10,11].…”

Hybrid Relations in Isabelle/UTP

“…Isabelle/UTP [10,11] is a mechanisation of UTP in Isabelle/HOL, along with the main results from the UTP book [7] and related publications [16,17]. It provides an implementation of the alphabetised relational calculus, a model of imperative programs, a large library of algebraic laws, and several automated proof tactics.…”

“…UTP [7] is concerned with establishing formal links between languages based on heterogeneous computational paradigms, and therefore it is wholly appropriate to apply it to study of hybrid computational models. Our contributions are: (1) a UTP theory that incorporates a piecewise continuous timed trace model, building on our previous theory of generalised reactive relations [8]; (2) denotational semantics for a simple imperative language for hybrid programs, inspired by dL and HCSP; and (3) mechanised reasoning support in our UTP theorem prover, Isabelle/UTP [9,10,11,12]. Our hybrid theory represents a substantial overhaul of our previous results [13,14] by unifying it with our generalised UTP theory of reactive processes [8].…”