Details of Grant 

EPSRC Reference:	EP/K023837/1
Title:	Logical Relations for Program Verification
Principal Investigator:	Ghani, Professor N
Other Investigators:
Researcher Co-Investigators:
Project Partners:	IT University of Copenhagen Microsoft University of Edinburgh
Department:	Computer and Information Sciences
Organisation:	University of Strathclyde
Scheme:	Standard Research
Starts:	30 September 2013	Ends:	29 September 2017	Value (£):	442,444
EPSRC Research Topic Classifications:	Fundamentals of Computing
EPSRC Industrial Sector Classifications:	Information Technologies
Related Grants:
Panel History:	Panel Date Panel Name Outcome 16 Jan 2013 EPSRC ICT Responsive Mode - Jan 2013 Announced
Summary on Grant Application Form
In an economy as relentlessly digital as the modern worldwide one, in which everything from toasters to interpersonal communications to global financial services are computerised, the need for formally verified software cannot be overestimated. Formal verification uses mathematical techniques to prove that programs actually perform the computations they are intended to perform (e.g., that text editors really do save files when a SAVE command is issued or that automatic pilots really do correctly execute flight plans) and also avoid performing unintended ones (e.g., leaking credit card details or launching nuclear weapons without authorisation). Since programmers make 15 to 50 errors per 1000 lines of code, and since repairing them accounts for some 80% of project expenses, the ever-increasing size and sophistication of programs makes formal verification increasingly critical to modern software development. Mathematical reasoning lies at the core of all formal verification, and so is crucial for building truly secure and reliable software. One of the key techniques for formally verifying properties of software systems uses logical relations. Logical relations provide a means of deriving properties of a software system directly from the system itself; as a result, they can be used to prove important properties of programs, programming languages, and language implementations. Logical relations have been developed for core fragments of many modern programming languages and verification systems. They are currently extended to richer programming languages and properties by constructing plausible variants of the definitions of logical relations for appropriate core fragments and checking that the mathematical theory goes through. But as languages and properties to be proved have become increasingly sophisticated and expressive, this ad hoc approach has become both difficult and unsustainable. It has also led to an enormous constellation of complicated and non-reusable logical relations that "work" for particular language features, rather than their principled and transferrable development from fundamental principles. In short, logical relations have struggled to keep pace with developments in programming languages, with the obvious consequences for security and reliability of software systems. We aim to revolutionise the landscape of logical relations by providing framework for their development and use that is principled, conceptually simple, reusable, and uniform (rather than ad hoc). Our framework will be capable of both describing the wide array of logical relations already used in existing applications and prescribing new logical relations for future ones. It will be based on the mathematical concept of comprehension for a fibration, which has not previously been identified as a key ingredient in the construction of logical relations. Our use of it thus distinguishes our framework from all other treatments of logical relations in the literature. Comprehension allows explicit representation of logical properties of languages within those languages themselves. This means that our framework will be implementable, so we will produce a logic for deriving consequences of logical relations and a prototype implementation of that logic in a modern interactive theorem prover. This will allow users to experiment with our framework, and allow their experiences with it to feed back into its foundations. We will also apply our new framework for logical relations to cutting-edge problems that are the focus of active research and for which there is presently no consensus on the way forward. Successful application of our framework will show that it can solve problems that are the focus of active research, as well as open up unanticipated new research directions. Conversely, the practical applications we pursue will raise challenges that prompt us to further refine its foundations
Key Findings
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Potential use in non-academic contexts
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Organisation Website:	http://www.strath.ac.uk