ML and Extended Branching VASS

We prove that the observational equivalence problem for a finitary fragment of ML is recursively equivalent to the reachability problem for extended branching vector addition systems with states (EBVASS). Our proof uses the fully abstract game semantics of the language. We introduce a new class of automata, VPCMA, as a representation of the game semantics. VPCMA are a version of class memory automata equipped with a visibly pushdown stack; they serve as a bridge enabling interreducibility of decision problems between the game semantics and EBVASS. The results of this paper complete our programme to give an automata classification of the ML types with respect to the observational equivalence problem for closed terms.

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