My research interests range from pure mathematics, through theoretical computer science and into more applied areas such as functional programming, computational algebra and artificial intelligence.
Category Theory:Where would we be without category theory. Much, much worse off, let me tell you! Here's some small reasons why.
Neil Ghani
MGS Category Theory Lecture Slides.
Lecture Slides [BibTex]Neil Ghani, Christoph Luth, Federico De Marchi and John Power
Algebras, Coalgebras, Monads and Comonads .
Proceedings of CMCS'01 [BibTex]Neil Ghani, Christoph Luth, Federico De Marchi and John Power
Dualizing Initial Algebras .
Mathematical Structures in Computer Science [BibTex]Neil Ghani, Christoph Luth and Federico De Marchi
Coalgebraic Monads .
Proceedings of CMCS'02 [BibTex]Neil Ghani, Christoph Luth and Federico De Marchi
Monads of Coalgebras: Rational Terms and Term Graphs .
Mathematical Structures in Computer Science [BibTex]Neil Ghani, Christoph Luth and Federico De Marchi
Solving Algebraic Equations using Coalgebra .
Journal of Theoretical Informatics and Applications [BibTex]Neil Ghani and Tarmo Uustalu
Explicit Substitutions and Higher Order Syntax .
Proceedings of MERLIN'03 [BibTex]Neil Ghani, Bjorn Victor and Kidane Yemane
Relationally Staged Computation in Calculi of Mobile Processes .
Proceedings of CMCS'04 [BibTex]Neil Ghani, John Power
CMCS 2006 .
Joint Editor [BibTex]Neil Ghani, Peter Hancock and Dirk Pattinson
Continuous Functions on Final Coalgebras .
Proceedings of CMCS'06 [BibTex]Neil Ghani and Patricia Johann
Using Kan Extensions to Structure Functional Programs.
Journal of Functional Programming, 2008. Accepted. [BibTex]
Rewriting Systems:Rewriting needs a semantics at an intermediate level of abstraction between the syntax and the relational model. This is the way I'd do it!
Neil Ghani
Adjoint Rewriting .
My thesis. Dont read it unless under medical supervision. [BibTex]Neil Ghani and Christoph Luth
Monads and Modular Term Rewriting .
Proceedings of CTCS'97 [BibTex]Neil Ghani and Christoph Luth
Rewriting via Coinserters .
Nordic Journal of Computing [BibTex]Neil Ghani, Christoph Luth and Michael Abbott
Abstract Modularity .
To appear, Proceedings of RTA 2005 [BibTex]
The Lambda-Calculus: Throw your Turing Machines onto the fire. Take my hand and off we stride.
Neil Ghani and Barry Jay
The Virtues of Eta-Expansion .
Journal of Functional Programming [BibTex]Neil Ghani
Beta-Eta Equality for Coproducts .
Proceedings of TLCA'95 [BibTex]Neil Ghani
Eta-Expansions in Fw.
Proceedings of CSL'96 [BibTex]Neil Ghani
Eta-Expansions in Dependent Type Theory --- The Calculus of Constructions .
Proceedings of TLCA'97 [BibTex]Neil Ghani and Roberto Di Cosmo
On Modular Properties of Higher Order Extensional Lambda Calculi .
Proceedings of ICALP'97 [BibTex]Neil Ghani, Valeria de Paiva and Eike Ritter
Linear Explicit Substitutions .
Journal of the IGPL [BibTex]Neil Ghani, Valeria de Paiva and Eike Ritter
Explicit Substitutions for Constructive Necessity .
Proceedings of ICALP'98 [BibTex]Neil Ghani, Valeria de Paiva and Eike Ritter
Categorical Models of Explicit Substitutions.
Proceedings of FOSSACS'99 [BibTex]
Functional Programming: This is how God would program. But since he doesnt exist, there's no reason to be shy.
Neil Ghani and Christoph Luth
Composing Monads Using Coproducts .
Proceedings of ICFP'02 [BibTex]Neil Ghani, Michael Abbott and Thorsten Altenkirch
Categories of Containers .
Proceedings of FOSSACS'03 [BibTex]Neil Ghani, Michael Abbott, Thorsten Altenkirch and Conor McBride
Derivatives of Containers .
Proceedings of TLCA'03 [BibTex]Neil Ghani, Michael Abbott, Thorsten Altenkirch and Conor McBride
δ for Data .
To appear, Fundamenta Informaticae [BibTex]Neil Ghani, Michael Abbott, Thorsten Altenkirch and Conor McBride
Constructing Polymorphic Programs with Quotient Types .
Proceedings of MPC 2004 [BibTex]Neil Ghani, Michael Abbott and Thorsten Altenkirch
Representing Nested Inductive Types with w-types .
Proceedings of ICALP 2004 [BibTex]Neil Ghani, Tarmo Uustalu and Varmo Vene
Build, Augment, Destroy. Universally. .
Proceedings of APLAS 2004 [BibTex]Neil Ghani, Tarmo Uustalu and Varmo Vene
Generalizing the augment combinator .
Proceedings of TFP 2004 [BibTex]Neil Ghani and Johan Glimming
Difunctorial Semantics of Object Calculus .
Proceedings of WOOD 2004 [BibTex]Neil Ghani, Makoto Hamana, Tarmo Uustalu and Varmo Vene
Representing cyclic structures as nested datatypes .
Proceedings of TFP 2006 [BibTex]Neil Ghani and Patricia Johann
Monadic Augment and Generalised Short Cut Fusion .
Journal of Functional Programming, 2007. [BibTex]Neil Ghani and Patricia Johann
Initial Algebra Semantics is Enough! .
Proceedings of Typed Lambda Calculus and Applications (TLCA), 2007. [BibTex]Neil Ghani, Peter Morris and Thorsten Altenkirch.
Constructing Strictly Positive Families. .
Procs. of Australasian Symposium on Theory of Computing 2007. [BibTex]Neil Ghani, Peter Morris and Thorsten Altenkirch.
A Universe of Strictly Positive Families, .
International Journal of Foundations of Computer Science, 2008. Accepted. [BibTex]Neil Ghani and Patricia Johann
Foundations for Structured Programming with GADTs .
Proceedings of Principles and Programming Languages (POPL), 2008. [BibTex]Neil Ghani and Patricia Johann
Haskell Programming with Nested Types: A Principled Approach .
Journal of Higher Order Smbolic Computation. [BibTex]
The authors' version of the paper is available here.
The final publication is available via SpringerLink.com with DOI 10.1007/s10990-009-9047-7.Neil Ghani and Patricia Johann
Short Cut Fusion of Recursive Programs with Computational Effects. .
Procs of Trends in Functional Programming 2008 [BibTex]
Computer Algebra: Anne wondered "Can we do better that writing lots of little programs to solve lots of little problems for particular algebraic structures." So we turned to our dear old friend Dr Kan Extension.
Neil Ghani and Anne Heyworth
Computing over K-modules.
Proceedings of CATS'02 [BibTex]Neil Ghani and Anne Heyworth
A Rewriting Alternative to Reidermeister Schrier .
Proceedings of RTA'03 [BibTex]Neil Ghani, Anne Heyworth, Ronnie Brown and Chris Wensley
Computing with Double Cosets.
Submitted to the Journal of Symbolic Computation [BibTex]
Artificial Intelligence: Given it is not an option to not reason in a modular fashion, how can we reason modularly? Cue some really nice algorithms. Yes, algorithms!!!
Neil Ghani and Christoph Luth
Monads and Modularity .
Proceedings of FROCOS'02 [BibTex]Neil Ghani and Tarmo Uustalu
Coproducts of Ideal Monads.
Accepted for Journal of Thoeretical Informatics and Applications [BibTex]Neil Ghani, Rawle Prince and Conor McBride
Proving Properties of Lists using Containers..
Procs of Functional and Logic Programming 2008 [BibTex]
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