Dr Conor McBride


Computer and Information Sciences


Type systems for programs respecting dimensions
McBride Conor, Nordvall Forsberg Fredrik
Advanced Mathematical and Computational Tools in Metrology and Testing XII (2021) (2021)
Doo bee doo bee doo
Convent Lukas, Lindley Sam, McBride Conor, McLaughlin Craig
Journal of Functional Programming Vol 30 (2020)
A type and scope safe universe of syntaxes with binding : their semantics and proofs
Allais Guillaume, Atkey Robert, Chapman James, McBride Conor, McKinna James
Journal of Functional Programming (2020)
A type and scope safe universe of syntaxes with binding : their semantics and proofs
Allais Guillaume, Atkey Robert, Chapman James, McBride Conor, McKinna James
International Conference on Functional Programming 2018, pp. 1-30 (2018)
Everybody's got to be somewhere
McBride Conor
Mathematically Structured Functional Programming, pp. 53-69 (2018)
Variations on inductive-recursive definitions
Ghani Neil, McBride Conor, Nordvall Forsberg Fredrik, Spahn Stephan
Proceedings of the 42nd International Symposium on Mathematical Foundations of Computer Science 42nd International Symposium on Mathematical Foundations of Computer Science Leibniz International Proceedings in Informatics (2017)

More publications

Professional activities

IFIP Working Group (External organisation)
Invited Lecture Courses on Dependently Typed Programming Oregon Programming Languages Summer School, USA, 2010
Invited speaker
ICFP 2009
Member of programme committee
Vol 19, Issues 3 & 4 (Special Issue on Mathematically Structured Functional Programming
Guest editor
Journal of Functional Programming (Journal)

More professional activities


KTP - Cambridge Quantum Computing (CQC)
McBride, Conor (Principal Investigator) Atkey, Bob (Co-investigator) Nordvall Forsberg, Fredrik (Co-investigator)
24-Jan-2020 - 23-Jan-2022
Trusted Systems
Ghani, Neil (Co-investigator) McBride, Conor (Principal Investigator) Nordvall Forsberg, Fredrik (Co-investigator)
01-Jan-2019 - 30-Jan-2023
Trusted Systems
Ghani, Neil (Principal Investigator) McBride, Conor (Co-investigator)
01-Jan-2019 - 30-Jan-2023
Homotopy Type Theory: Programming and Verification
Ghani, Neil (Principal Investigator) McBride, Conor (Co-investigator)
"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 Therac-25 radiation system have cost lives. More generally, a
2008 study by the US government estimated that faulty
software costs the US economy £100 billion

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 hand-written mathematical
proofs can be untrustworthy and this has led to a growing desire for
computer-checked 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
Martin 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 ty 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 HoTT-based
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."
01-Jan-2015 - 30-Jan-2019
Ghani, Neil (Principal Investigator) Kupke, Clemens (Co-investigator) McBride, Conor (Co-investigator)
01-Jan-2014 - 31-Jan-2017
Haskell Types with Added Value
McBride, Conor (Principal Investigator)
"Good ideas, like lightning, take the most conductive path to earth. This one-year project takes advantage of fresh technological insights to narrow the spark-gap from theoretical research to the programming mainstream. In the last decade, dependent types --- capturing relative notions of data validity --- have jumped from logics and proof systems to programming. Prototype languages such as Cayenne, ATS, Agda and our own Epigram teach us how to characterize data precisely, but none has a coherent treatment of interaction in applications. This project will bring the basics of dependent types to application development now, not via a prototype, but with Haskell, a mature functional programming language with growing traction, thanks to the Glasgow Haskell Compiler (GHC), now developed under the Microsoft aegis. To make this jump, we must give practical answers to theoretical questions about the mathematical structures which underpin interactive and distributed systems. We must take the blackboard to the motherboard.

The tool which enables this project is our GHC preprocessor, the Strathclyde Haskell Enhancement (SHE), which mechanizes a partial translation from 'dependently typed Haskell' to Haskell as it stands. Up and running, SHE has already delivered the basics of our approach, leading to an article accepted in 2011 by the Journal of Functional Programming, and spurring deeper investigation of both the mathematics of dependently typed interaction and the engineering challenge of scaling up. Through theoretical research, library design and case study, we shall deliver progress across this spectrum through papers and open source software. GHC is adopting our functionality, but we do not need to wait. SHE can sustain low-cost exploration, putting an effective toolkit in users' hands now, as well as informing the future prospectuses both for dependent types in Haskell and for programming interaction in the next generation of functional languages. Haskellers recognize the need: Microsoft currently funds a PhD at Strathclyde on numerical dependency in Haskell types.

This project is, then, a double fix: it imports dependent types from tomorrow's languages to today's, and it allows us to guide tomorrow's dependently typed languages towards principled approaches to production software. We have proven track records in theoretical research and professional software development, key ideas to change programming for the better, and the skills to deliver world-leading research."
01-Jan-2012 - 30-Jan-2013

More projects


Computer and Information Sciences
Livingstone Tower

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