Ecien t Recursive Subtyping

Subtyping in the presence of recursive types for the -calculus was studied by Amadio and Cardelli in 1991 [1]. In that paper they showed that the problem of deciding whether one recursive type is a subtype of another is decidable in exponential time. In this paper we give an O(n 2 ) algorithm. Our algorithm is based on a simplication of the denition of the subtype relation, which allows us to reduce the problem to the emptiness problem for a certain nite automaton with quadratically many states. ! @ ! @ ! @ ! @ ? ? . . . ! @ ! @ ! @ ! @ > > ? ? . ! @ ! @ ? ? . ! @ ! @ > > . &% ’$