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 Fw.
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]