Observers for Linear Types

Linear types provide the framework for a safe embedding of mutable state in functional languages by enforcing the principle that variables of linear type must be used exactly once. A potential disadvantage of this approach is that it places read accesses to such variables under the same restriction as write accesses, and thus prevents reads to proceed in parallel. We present here an extension of linear types which augments the usual distinction between linear and non-linear by a third state, observers of linear variables. Since, unlike linear variables, observers can be duplicated, multiple concurrent reads are made possible. On the other hand, observers must be short-lived enough to never overlap with mutations. The resulting type system is in many aspects similar to the one of ML: It is polymorphic, has principal types, and admits a type reconstruction algorithm.