EPSRC Reference: 
EP/M016951/1 
Title: 
Homotopy Type Theory: Programming and Verification 
Principal Investigator: 
Ghani, Professor N 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Computer and Information Sciences 
Organisation: 
University of Strathclyde 
Scheme: 
Standard Research 
Starts: 
01 April 2015 
Ends: 
30 September 2019 
Value (£): 
499,631

EPSRC Research Topic Classifications: 
Computer Sys. & Architecture 
Fundamentals of Computing 

EPSRC Industrial Sector Classifications: 

Related Grants: 

Panel History: 
Panel Date  Panel Name  Outcome 
20 Oct 2014

EPSRC ICT Prioritisation Panel  Oct 2014

Announced


Summary on Grant Application Form 
The cost of software failure is truly staggering. Well known
individual cases include the Mars Climate Orbiter failure
(£80 million), Ariane Rocket disaster (£350 million), Pentium
Chip Division failure (£300 million), and more recently the heartbleed
bug (est. £400 million). There are many, many more examples. Even worse,
failures such as one in the Patriot Missile System and another
in the Therac25 radiation system have cost lives. More generally, a
2008 study by the US government estimated that faulty
software costs the US economy £100 billion
annually.
There are many successful approaches to software verification
(testing, model checking etc). One approach is to find mathematical
proofs that guarantees of software correctness. However, the
complexity of modern software means that handwritten mathematical
proofs can be untrustworthy and this has led to a growing desire for
computerchecked proofs of software correctness.
Programming languages and interactive proof systems like Coq, Agda,
NuPRL and Idris have been developed based on a formal system called
MartinLöf Type Theory. In these systems, we can not only write
programs, but we can also express properties of programs using types,
and write programs to express proofs that our programs are correct.
In this way, both large mathematical theorems such as the Four Colour
Theorem, and large software systems such as the CompCert C compiler
have been formally verified. However, in such large projects, the
issue of scalability arises: how can we use these systems to build large
libraries of verified software in an effective way?
This is related to the problem of reusability and modularity: a
component in a software system should be replaceable by another which
behaves the same way even though it may be constructed in a completely
different way. That is, we need an "extensional equality" which is
computationally well behaved (that is, we want to run programs using
this equality). Finding such an equality is a fundamental and
difficult problem which has remained unresolved for over 40 years.
But now it looks like we might have a solution! Fields medallist
Vladimir Voevodsky has come up with a completely different take on the
problem by thinking of equalities as paths such as those which occur
in one of the most abstract branches of mathematics, namely homotopy
theory, leading to Homotopy Type Theory (HoTT). In HoTT, two objects
are completely interchangeable if they behave the same way. However,
most presentations of HoTT involve axioms which lack computational
justification and, as a result, we do not have programming languages
or verification systems based upon HoTT. The goal of our project is
to fix that, thereby develop the first of a new breed of HoTTbased
programming languages and verification systems, and develop case
studies which demonstrate the power of HoTT to programmers and
those interested in formal verification.
We are an ideal team to undertake this research because i) we have
unique skills and ideas ranging from the foundations of HoTT to the
implementation and deployment of programming language and verification
tools; and ii) the active collaboration of the most important figures
in the area (including Voevodsky) as well as industrial participation
to ensure that we keep in mind our ultimate goal  usable programming
language and verification tools.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


Sectors submitted by the Researcher 
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Project URL: 

Further Information: 

Organisation Website: 
http://www.strath.ac.uk 