Towards the Formal Specification and Verification of Maple Programs

In this paper, we present our ongoing work and initial results on the formal specification and verification of MiniMaple (a substantial subset of Maple with slight extensions) programs. The main goal of our work is to find behavioral errors in such programs w.r.t. their specifications by static analysis. This task is more complex for widely used computer algebra languages like Maple as these are fundamentally different from classical languages: they support non-standard types of objects such as symbols, unevaluated expressions and polynomials and require abstract computer algebraic concepts and objects such as rings and orderings etc. As a starting point we have defined and formalized a syntax, semantics, type system and specification language for MiniMaple

On Formal Specification of Maple Programs

This paper is an example-based demonstration of our initial results on the formal specification of programs written in the computer algebra language MiniMaple (a substantial subset of Maple with slight extensions). The main goal of this work is to define a verification framework for MiniMaple. Formal specification of MiniMaple programs is rather complex task as it supports non-standard types of objects, e.g. symbols and unevaluated expressions, and additional functions and predicates, e.g. runtime type tests etc. We have used the specification language to specify various computer algebra concepts respective objects of the Maple package DifferenceDifferential developed at our institute

On the Formal Semantics of the Cognitive Middleware AWDRAT

The purpose of this work is two fold: on one hand we want to formalize the behavior of critical components of the self generating and adapting cognitive middleware AWDRAT such that the formalism not only helps to understand the semantics and technical details of the middleware but also opens an opportunity to extend the middleware to support other complex application domains of cybersecurity; on the other hand, the formalism serves as a prerequisite for our proof of the behavioral correctness of the critical components to ensure the safety of the middleware itself. However, here we focus only on the core and critical component of the middleware, i.e. Execution Monitor which is a part of the module "Architectural Differencer" of AWDRAT. The role of the execution monitor is to identify inconsistencies between run-time observations of the target system and predictions of the System Architectural Model. Therefore, to achieve this goal, we first define the formal (denotational) semantics of the observations (run-time events) and predictions (executable specifications as of System Architectural Model); then based on the aforementioned formal semantics, we formalize the behavior of the "Execution Monitor" of the middleware