Isomorphisms of types in the presence of higher-order references

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• Pierre Clairambault, University of Bath
• Friday 06 May 2011, 14:00-15:00
• Room FW11, Computer Laboratory, William Gates Building.

If you have a question about this talk, please contact Bjarki Holm.

We investigate the problem of type isomorphisms in a programming language with higher-order references. We first recall the game-theoretic model of higher-order references by Abramsky, Honda and McCusker. Solving an open problem by Laurent, we show that two finitely branching arenas are isomorphic if and only if they are geometrically the same, up to renaming of moves (Laurent’s forest isomorphism). We deduce from this an equational theory characterising isomorphisms of types in a finitary language L_2 with higher order references. We show however that Laurent’s conjecture does not hold on infinitely branching arenas, yielding a non-trivial type isomorphism in the extension of L_2 with natural numbers.

This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.

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