Isomorphisms of types in the presence of higher-order references

Pierre Clairambault (1)

1 Computer Laboratory [Cambridge]

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 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 this language with natural numbers.

Mots clés: Isomorphisms of types; higher-order references; game semantics

Domaines: Logique en informatique [cs.LO]; Informatique et théorie des jeux [cs.GT]

Pierre Clairambault. Isomorphisms of types in the presence of higher-order references. Twenty-Sixth Annual IEEE Symposium on Logic In Computer Science (LICS 2011), Jun 2011, Toronto, Canada. pp.152 - 161, ⟨10.1109/LICS.2011.32⟩. ⟨hal-00651816⟩