Noam Zeilberger

email: [noam.zeilberger] at | [zeilbern] at
office hours (UG37): Tue 15:00-16:00, Thu 12:00-13:00

Since October 2016, I am Birmingham Fellow at the University of Birmingham, and a member of the Theory Group within the School of Computer Science.

If you are an undergraduate or MSc student and are interested in working on any of these project suggestions, please contact me.


  • 2015-2016: Parsifal Team (Inria), in Palaiseau, France
  • 2013-2015: MSR-Inria Joint Centre, in Palaiseau, France
  • 2012-2013: Institute for Advanced Study, Princeton, NJ
  • 2011-2012: IMDEA Software, in Madrid, Spain
  • 2009-2011: Laboratoire PPS & Equipe πr² on a fellowship of the Fondation Sciences Mathématiques de Paris
  • 2003-2009: PhD studies at CMU SCS, in Pittsburgh, PA

    Recent and Upcoming News and Events

  • March 31, 2018: "A theory of linear typings as flows on 3-valent graphs" accepted for presentation at LICS 2018.
  • March 27, 2018: finished preparing an extended version of "A sequent calculus for a semi-associative law", now including a proof of the lattice property!
  • Visiting Chris Heunen, speaking at Categories, Logic, and Physics, Scotland, and giving a LFCS Seminar in Edinburgh, 20-22 November, 2017.
  • Attending Categories in Homotopy Theory and Rewriting in Luminy, 25-29 September, 2017.
  • Speaking at FSCD 2017 and STRING 2017 in Oxford, 3-9 September, 2017
  • Speaking at the 26th British Combinatorial Conference in Glasgow, 3-7 July, 2017.
  • Speaking at the 10th Workshop on Computational Logic and Applications (CLA 2017) in Gothenburg, Sweden, 18-19 May, 2017.
  • Matija Pretnar and I are co-chairing LOLA 2017! It's taking place on 19 June (the day before LICS) in Reykjavik.
  • I'm delighted to be joining the Theory Group at the University of Birmingham! I've been hired as a Birmingham Fellow.
  • I recently finished giving a series of lectures at OPLSS16 on "Principles of Type Refinement"! You are welcome to check out the lecture notes I prepared for the course.

    Research Interests

    I am interested broadly in connections between logic, language, computation, and mathematics.

    A long-running project which I've been collaborating on seeks to develop a common mathematical language that unifies the disparate traditions of Hoare Logic, dependent type theory, and linear logic. One conclusion reached from this project is that the established wisdom about the relationship between type theory and category theory needs to be revised, and that this has important implications for the way we look at type systems and other deductive formalisms. You can find out more about this view in my paper with Paul-André Melliès, "Functors are Type Refinement Systems" (POPL 2015). Turning this vision into a practical reality will require a lot of work, but I'm convinced that the path ahead will be exciting!

    Over the last few years I have also been immersed in exploring an unexpected world of connections between lambda calculus and the theory of graphs on surfaces, in particular the combinatorics of planar maps. For a quick introduction to this world, you can look at my talk on Lambda Calculus and the 4CT, as well as some of the references mentioned there.

    A different interest I have is in the notion of zero-knowledge proof from cryptography/complexity theory, but in particular how it can be reconciled with notions of knowledge from constructive logic. I gave a talk about these connections at HOPE 2012, which you can find in "Recent talks".

    Recent papers and drafts

    A theory of linear typings as flows on 3-valent graphs.
    Accepted to LICS 2018, final version in preparation.
    A sequent calculus for a semi-associative law.
    In Proceedings of the Second International Conference on Formal Structures for Computation and Deduction (FSCD 2017). [doi] Extended version: [arXiv:1803.10080].
    Connected chord diagrams and bridgeless maps.
    With Julien Courtiel and Karen Yeats. November 14, 2016. [arXiv:1611.04611]
    A bifibrational reconstruction of Lawvere's presheaf hyperdoctrine.
    With Paul-André Melliès. In Proceedings of the Thirty-First Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2016). [doi] [arXiv:1601.06098]
    Towards a mathematical science of programming.
    Research statement, circa 2016.
    Linear lambda terms as invariants of rooted trivalent maps.
    Journal of Functional Programming, volume 26, 2016. [doi] [arXiv:1512.06751]
    Counting isomorphism classes of β-normal linear lambda terms.
    September 25, 2015. [arXiv:1509.07596]
    An Isbell Duality Theorem for Type Refinement Systems.
    With Paul-André Melliès. Final version of January 31, 2017. To appear in Mathematical Structures in Computer Science. [doi] [arXiv:1501.05115]
    Balanced polymorphism and linear lambda calculus.
    Presented at TYPES 2015.
    Functors are Type Refinement Systems.
    With Paul-André Melliès. In Proceedings of the 42nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL 2015). [doi]
    A correspondence between rooted planar maps and normal planar lambda terms.
    With Alain Giorgetti. Logical Methods in Computer Science, Vol. 11(3:22)2015, pp. 1-39. [doi] [arXiv:1408.5028]
    Type refinement and monoidal closed bifibrations.
    With Paul-André Melliès. October 1, 2013. [arXiv:1310.0263]

    Recent talks

    Lambda calculus and the Four Colour Theorem.
    November 21, 2017, at the Edinburgh LFCS Seminar.
    Skew-closed objects, typings of linear lambda terms, and flows on trivalent graphs.
    September 9, 2017, at STRING 2017.
    A sequent calculus for a semi-associative law.
    September 4, 2017, at FSCD 2017.
    Some bridges between lambda calculus and graphs on surfaces.
    July 6, 2017, at the 26th British Combinatorial Conference.
    Some enumerative, topological, and algebraic aspects of linear lambda calculus.
    May 18, 2017, at CLA 2017.
    A Categorical Perspective on Type Refinement Systems.
    December 9, 2016, at the Logic and Semantics Seminar of the Cambridge Computer Laboratory.
    A bifibrational reconstruction of Lawvere's presheaf hyperdoctrine.
    July 7, 2016, at LICS 2016.
    Principles of Type Refinement.
    Lectures given at OPLSS 2016, June 29-July 2, 2016.
    Linear lambda calculus and the combinatorics of embedded graphs.
    October 14, 2015, at Journées Nationales GEOCAL-LAC-LTP 2015. [pdf]
    Balanced polymorphism and linear lambda calculus.
    May 18, 2015, at TYPES 2015.
    A connection between lambda calculus and maps.
    January 18, 2015, at OBT 2015.
    Functors are Type Refinement Systems.
    January 15, 2015, at POPL 2015
    Polarity in Proof Theory and Programming.
    August 30, 2013, at the Summer School on Linear Logic and Geometry of Interaction in Torino, Italy.
    HOPE for a type-theoretic understanding of zero-knowledge.
    September 9, 2012, at the 1st ACM SIGPLAN workshop on Higher-Order Programming with Effects. (Note: the slides seem to render funny with Firefox -- best viewed in Chrome or Safari.)
    BONUS: slides for the "15 minute" version I gave October 4th at the IAS postdoc seminar series.

    Older publications

    Polarity and the logic of delimited continuations.
    In Proceedings of the Twenty-Fifth Annual IEEE Symposium on Logic in Computer Science (LICS 2010). [twelf code] [slides]
    Defunctionalizing focusing proofs.
    Presented at the 2009 International Workshop on Proof-Search in Type Theories. [twelf code] [more twelf]
    Refinement types and computational duality.
    In Proceedings of the 2009 Workshop on Programming Languages meets Program Verification (PLPV 09). [agda code]
    Focusing on binding and computation.
    With Dan Licata and Bob Harper. In Proceedings of the Twenty-Third Annual IEEE Symposium on Logic in Computer Science (LICS 08). [tech report]
    Focusing and higher-order abstract syntax.
    In Proceedings of the 35th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL 08). [coq code] [notes]
    On the unity of duality.
    Annals of Pure and Applied Logic 153:1 (2008), special issue on "Classical logic and computation". [doi]


    PhD in computer science, 2009, Carnegie Mellon University
    The Logical Basis of Evaluation Order and Pattern-Matching.
    Committee: Peter Lee (co-advisor), Frank Pfenning (co-advisor), Robert W. Harper, Paul-André Melliès (external member)

    Techniques from linear logic and infinitary proof theory (connected to the old idea of a "proof-theoretic semantics" of logic) yield new insights into seemingly extra-logical features of modern programming languages. By applying the Curry-Howard correspondence to focusing proofs, we develop a polarized type theory in which evaluation order is explicitly reflected at the level of types, and which has built-in support for pattern-matching. This framework provides an elegant, uniform account of both untyped and intrinsically well-typed computation, and moreover can be extended with an extrinsic (Curry-style) type system to express and enforce more refined semantic properties of programs. We apply these ideas to explore the theory of typing and subtyping for intersection and union types in the presence of effects, giving a simplified explanation of some of the unusual artifacts of existing systems.

    Other papers

    Nathack: a natural language interface for nethack.
    January, 2003. With Cassia Martin, David Molnar, and Dev Purkayastha. As the title suggests, this was a natural language interface for nethack! Done with a mix of prolog, embedded lua, and scary hacking within nethack's internal C source. Our code is lying around somewhere, and I could dig it up upon request.

    Et cetera

    Rapport sur la Thèse de Dov Tamari
    Report on the thesis of Dov Tamari, signed by his advisor Paul Dubreil (scanned by phone at Sophie Germain Library).
    the nLab
    Knowledge is a collaborative effort.
    And Quiet Flows the Mon
    A photography project from the dark days after the 2004 U.S. Presidential Elections. 2017 update: whoops, it seems that my dystopian vision of US politics was a little bit too optimistic!
    Archive of papers by John Reynolds
    Direct link to the CMU AFS directory, since the ftp server is sometimes down.
    In Tune With Fun
    A true-life story about learning the accordion.

    We may just be cockroaches at the base of a very large garbage mountain.
    Dana Scott (on mathematics)

    And tell me Margaret, when I’m gone, what will I want,
    To be left at the bottom of a garbage bin, or dusted off and pulled up onto stage?

    Jason Webley