I am trying to understand the structure of computation. This is quite a bold statement and I realise that, inevitably, only partial answers will be forthcoming. Nevertheless, why not shoot for the moon and go for research which is of the highest calibre and which will stand the test of time rather than become obsolete within a few years?

In addition to being interesting in its own right, understanding the structure of computation is also a prerequisite for computing with, and reasoning effectively about, advanced computational agents. Indeed, the simplicity afforded by such deep insights seems to me to be the only way to develop theories that can be scaled successfully to more applied areas such as artifical intelligence and software development. In more detail, I have published in the following areas

Category Theory: Where would we be without category theory. Much, much worse off, let me tell you!

The Lambda-Calculus: Throw your Turing Machines onto the fire. Take my hand and off we stride ...

Functional Programming: This is how God would program. But since he doesnt exist, there's no reason to be shy.

Rewriting Systems: Rewriting needs a semantics at an intermediate level of abstraction between the syntax and the relational model. I have my own ideas on how I would do it!

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!!!

Computer Algebra: Anne wondered "Can we do better than writing lots of little programs, each for a particular algebraic structure." So we turned to our dear old friend Dr Kan Extension.

[69] Neil Ghani and Julian Hedges.

*
Compositional Game Theory
*

Submitted to Procs of Logic and Social Behaviour, 2016.
[BibTex]

[68] Neil Ghani, Fredrik Forsberg and Federico Orsanigo

*
Proof-relevant parametricity
*

Proceedings of the WadlerFest, 2016.
[BibTex]

[67] Neil Ghani, Fredrik Forsberg and Alex Simpson.

*
Comprehensive parametric polymorphism: categorical models and type theory
*

Best Paper Award, ETAPS 2016.
[BibTex]

[66] Neil Ghani, Patricia Johann, Fredrik Forsberg, Federico Orsanigo, and Tim Revell.

*
Bifibrational functorial semantics of parametric polymorphism
*

Procs of MFPS XXXI, 2015.
[BibTex]

[65] Neil Ghani, Robert Atkey, Fredrik Forsberg, Sam Staton and Tim Revell.

*
Models for Polymorphism over Physical Dimensions
*

Procs of TLCA, 2015.
[BibTex]

[64] Neil Ghani, Fredrik Forsberg, Federico Orsanigo.

*
Parametric Polymorphism — Universally
*

Procs of WoLLIC, 2015
[BibTex]

[63] Neil Ghani, Robert Atkey and Patricia Johann.

*
A Relationally Parametric Model of Dependent Type Theory.
*

Principles of Programming Languages, 2014.
[BibTex]

[62] Neil Ghani and Peter Hancock

*
An Algebraic Implementation of Induction Recursion and
Indexed Induction Recursion
*

Accepted to MSCS 2014.
[BibTex]

[61] Neil Ghani, Lorenzo Malatesta and Fredrik Nordvall-Forsberg.

*
Positive Induction Recursion.
*

Conference on Algebras and Coalgebras, 2013.
[BibTex]

[60] Neil Ghani, Peter Hancock, Lorenzo Malatesta and Fredrik Nordvall-Forsberg.

*
Fibred Data Types.
*

Logic in Computer Science, 2013.
[BibTex]

[59] Neil Ghani, Peter Hancock, Conor McBride, Thorsten Altenkirch, Lorenzo Malatesta.

*
Small Induction Recursion.
*

Typed Lambda Calculus and Applications, 2013.
[BibTex]

[58] Neil Ghani, Clement Fumex, and Patricia Johann.

*
Indexed Induction and Coinduction, Fibrationally.
*

Logical Methods in Computer Science, 2012.
[BibTex]

[58] Neil Ghani. Robert Atkey, and Patricia Johann

*
Refining Inductive Types.
*

Logical Methods in Computer Science 8(2), 2012.
[BibTex]

[57] Neil Ghani, Patricia Johann, and Clement Fumex.

*
Generic Fibrational Induction.
*

Logical Methods in Computer Science 8(2), 2012
[BibTex]

[56] Neil Ghani, Robert Atkey, Bart Jacobs, and Patricia Johann.

*
Fibrational Induction Meets Effects.
*

Foundations of Software Systems and Computation Structures, 2012.
[BibTex]

[55] Neil Ghani, Clement Fumex and Patricia Johann

*
Indexed Induction and Coinduction, Fibrationally. *

Procs of Conference on Algebras and Coalgebras 2011
[BibTex]

[54]
Neil Ghani, Robert Atkey and Patricia Johann

*
When is a Type Refinement an Inductive Type? *

Procs of Foundations of Software Science and Comnputation Structures 2011
[BibTex]

[53]
Neil Ghani, Clement Fumex and Patricia Johann

*
Fibrational Induction Rules for Initial Algebras *

Procs of Computer Science Logic 2010
[BibTex]

[52]
Neil Ghani, Peter Hancock, Dirk Pattinson

*
Continuous Functions on Final Coalgebras *.

Procs of Mathematical Foundations of
Programming Semantics, 2009
[BibTex]

[51]
Neil Ghani and Patricia Johann

*
Haskell Programming with Nested Types: A Principled Approach
*.

Journal of Higher Order Smbolic Computation, 2009
[BibTex]

[50]
Neil Ghani, Peter Morris and
Thorsten Altenkirch.

*
A Universe of Strictly Positive Families.
*.

International Journal of Foundations of Computer Science, 2009.
[BibTex]

[49]
Neil Ghani, Peter Hancock and Dirk Pattinson.

*
Representations of Stream Processors Using Nested Fixed Points *.

Logical Methods in Computer Science, 2009
[BibTex]

[48]
Neil Ghani and Patricia Johann

*
Monadic fold, Monadic build, Monadic Short Cut Fusion.
*

Procs of Trends in Functional Programming 2009
[BibTex]

[47] Neil Ghani, Mauro Jaskelioff and Graham Hutton

*
Modularity and Implementation of Mathematical Operational Semantics.
*

Procs of Mathematically Structured Functional Programming, 2008
[BibTex]

[46]
Neil Ghani, Rawle Prince and Conor McBride

*
Proving Properties of Lists using Containers.*.

Procs of Functional and Logic Programming 2008
[BibTex]

[45]
Neil Ghani and Patricia Johann

*
Foundations for Structured Programming with GADTs
*.

Proceedings of Principles and Programming Languages (POPL), 2008.
[BibTex]

[44]
Neil Ghani and Patricia Johann

*
Short Cut Fusion of Recursive Programs with Computational Effects.
*.

Procs of Trends in Functional Programming 2008
[BibTex]

[43]
Neil Ghani and Alexander Kurz

*
Higher Dimensional Trees, Algebraically.
*.

Procs of Conference on Algebras and Coalgebras 2007
[BibTex]

[42]
Neil Ghani and Patricia Johann

*
Monadic Augment and Generalised Short Cut Fusion
*.

Journal of Functional Programming, 2007.
[BibTex]

[41]
Neil Ghani and Patricia Johann

*
Initial Algebra Semantics is Enough!
*.

Procs of Typed Lambda Calculus and Applications, 2007.
[BibTex]

[40]
Neil Ghani, Peter Morris and
Thorsten Altenkirch.

*
Constructing Strictly Positive Families.
*.

Procs of Australasian Symposium on Theory of Computing 2007.
[BibTex]

[39]
Neil Ghani, Makoto Hamana, Tarmo Uustalu and Varmo Vene

*
Representing cyclic structures as nested datatypes
*.

Proceedings of TFP 2006 [BibTex]

[38]
Neil Ghani, John Power

* CMCS 2006 *.

Joint Editor [BibTex]

[37]
Neil Ghani, Peter Hancock and Dirk Pattinson

* Continuous Functions on Final Coalgebras *.

Proceedings of CMCS'06 [BibTex]

[36]
Neil Ghani, Anne Heyworth, Ronnie Brown and Chris Wensley

*
Computing with Double Cosets*.

Journal of Symbolic Computation, 2006
[BibTex]

[35]
Neil Ghani, Tarmo Uustalu and Makoto Hamana

*
Explicit substitutions and higher-order syntax *.

Higher-Order and Symbolic Computation, 2006
[BibTex]

[34]
Neil Ghani, Christoph Luth and Michael Abbott

* Abstract Modularity *.

Proceedings of RTA 2005 [BibTex]

[33]
Neil Ghani, Patricia Johann, Tarmo Uustalu and Varmo Vene

*
Monadic augment and generalised short cut fusion
*.

Proceedings of International Conference on Functional Programming 2005
[BibTex]

[32]
Neil Ghani, Michael Abbott, Thorsten Altenkirch and Conor McBride

* δ for Data: Differentiating Data Structures *.

Fundamenta Informaticae, 2005 [BibTex]

[31]
Neil Ghani, Michael Abbott and Thorsten Altenkirch

*
Containers: Constructing strictly positive types.
*.

Theoretical Computer Science, 2005 [BibTex]

[30]
Neil Ghani, Christoph Luth and Federico De Marchi

* Monads of Coalgebras: Rational Terms and Term Graphs *.

Mathematical Structures in Computer Science, 2005 [BibTex]

[29]
Neil Ghani, Michael Abbott and Thorsten Altenkirch

* Representing Nested Inductive Types with w-types *.

Proceedings of ICALP 2004 [BibTex]

[28]
Neil Ghani, Tarmo Uustalu and Varmo Vene

* Build, Augment, Destroy. Universally.
*.

Proceedings of APLAS 2004 [BibTex]

[27]
Neil Ghani, Michael Abbott, Thorsten Altenkirch and Conor McBride

*
Constructing Polymorphic Programs with Quotient Types*.

Procs of Mathematics of Program Construction, 2004
[BibTex]

[26]
Neil Ghani and Tarmo Uustalu

*
Coproducts of Ideal Monads*.

Journal of Thoeretical Informatics and Applications, 2004
[BibTex]

[25]
Neil Ghani, Tarmo Uustalu and Varmo Vene

* Generalizing the augment combinator
*.

Proceedings of Trends in Functional Programming, 2004
[BibTex]

[24]
Neil Ghani and Johan Glimming

* Difunctorial Semantics of Object Calculus
*.

Proceedings of WOOD 2004 [BibTex]

[23]
Neil Ghani, Bjorn Victor and Kidane Yemane

* Relationally Staged Computation
in Calculi of Mobile Processes *.

Proceedings of CMCS'04 [BibTex]

[22]
Neil Ghani, Michael Abbott and Thorsten Altenkirch

* Categories of Containers *.

Proceedings of FOSSACS'03 [BibTex]

[21]
Neil Ghani and Anne Heyworth

*
A Rewriting Alternative to Reidermeister Schrier *.

Proceedings of RTA'03 [BibTex]

[20]
Neil Ghani, Michael Abbott, Thorsten Altenkirch and Conor McBride

* Derivatives of Containers *.

Proceedings of TLCA'03 [BibTex]

[19]
Neil Ghani and Tarmo Uustalu

*
Explicit Substitutions and Higher Order Syntax *.

Proceedings of MERLIN'03 [BibTex]

[18]
Neil Ghani, Christoph Luth and Federico De Marchi

* Solving Algebraic Equations using Coalgebra *.

Journal of Theoretical Informatics and Applications, 2003 [BibTex]

[17]
Neil Ghani, Christoph Luth, Federico De Marchi and John Power

* Dualizing Initial Algebras *.

Mathematical Structures in Computer Science, 2003 [BibTex]

[16]
Neil Ghani and Christoph Luth

* Rewriting via Coinserters *.

Nordic Journal of Computing, 2003 [BibTex]

[15]
Neil Ghani and Christoph Luth

* Composing Monads Using Coproducts *.

Proceedings of ICFP'02 [BibTex]

[14]
Neil Ghani and Anne Heyworth

*
Computing over K-modules*.

Proceedings of CATS'02 [BibTex]

[13]
Neil Ghani and Christoph Luth

* Monads and Modularity *.

Proceedings of FROCOS'02 [BibTex]

[12]
Neil Ghani, Christoph Luth and Federico De Marchi

* Coalgebraic Monads *.

Proceedings of CMCS'02 [BibTex]

[11]
Neil Ghani, Christoph Luth, Federico De Marchi and John Power

* Algebras, Coalgebras, Monads and Comonads *.

Proceedings of CMCS 2001 [BibTex]

[10] Neil Ghani, Valeria de Paiva and Eike Ritter

* Linear Explicit Substitutions *.

Logic Journal of the IGPL, 2000
[BibTex]

[9] Neil Ghani, Valeria de Paiva and Eike Ritter

*
Categorical Models of Explicit Substitutions*.

Proceedings of FOSSACS'99
[BibTex]

[8] Neil Ghani, Valeria de Paiva and Eike Ritter

*
Explicit Substitutions for Constructive Necessity *.

Proceedings of ICALP'98
[BibTex]

[7] Neil Ghani

* Eta-Expansions in Dependent Type Theory
--- The Calculus of Constructions *.

Proceedings of TLCA'97 [BibTex]

[6] Neil Ghani and Roberto Di Cosmo

* On Modular Properties of Higher Order
Extensional Lambda Calculi *.

Proceedings of ICALP'97
[BibTex]

[5] Neil Ghani and Christoph Luth

* Monads and Modular Term Rewriting *.

Proceedings of CTCS'97 [BibTex]

[4] Neil Ghani

* Eta-Expansions in F^{w}*.

Proceedings of CSL'96 [BibTex]

[3] Neil Ghani and Barry Jay

* The Virtues of Eta-Expansion *.

Journal of Functional Programming, 1995 [BibTex]

[2] Neil Ghani

* Beta-Eta Equality for Coproducts *.

Proceedings of TLCA'95 [BibTex]

[1] Neil Ghani

* Adjoint Rewriting *.

My thesis. Dont read it unless under medical supervision. [BibTex]