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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 characterizing isomorphisms of types in a finitary language L2 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 L2 with natural numbers.
|Title of host publication||2011 IEEE 26th Annual Symposium on Logic in Computer Science|
|Place of Publication||Piscataway, NJ|
|Number of pages||10|
|Publication status||Published - 2011|
|Event||26th Annual IEEE Symposium on Logic in Computer Science - Toronto, ON, Canada|
Duration: 21 Jun 2011 → 24 Jun 2011
|Conference||26th Annual IEEE Symposium on Logic in Computer Science|
|Abbreviated title||LICS 2011|
|Period||21/06/11 → 24/06/11|
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- 1 Finished
20/06/10 → 19/06/12
Project: Research council