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Hi, A principal type is defined in wiki as "a type for a term such that all other types for this term are an instance of it." What about a type defined as "a type for a term such that it is an instance of all types required of this term?" Whereas a principal type seems to be an intersection over bindings, such a "usage" type is a union over uses. Please forgive this OO example, but it is the best I could think of to exemplify the difference in my head: trait HousePet def DoHousePetThing() trait Mammal: def DoMammalThing() trait Dog : Mammal trait Cat : Mammal val B : Dog val C : Cat A = B A = C // the principal type of A is Mammal A.DoHousePetThing() A.DoMammalThing() // the usage type of A is HousePet + Mammal The principal type of A is the intersection of Dog and Cat (say Mammal). The X type I'm computing in my system is based on usage, so it is just "HousePet" + "Mammal." So while a principle type starts at top and becomes more specific with each bind (top -> Dog -> Mammal), a usage type starts at bottom and becomes more general with each use (bottom -> HousePet -> HousePet + Mammal). Could this "usage" type be the opposite of a principal type, and if so, what has it been called in the literature? Or maybe I'm just looking at this all wrong: would such the usage type "HousePet + Mammal" still be a principle type if it was propagated backwards during type inference to bindings so that B is "Dog + HousePet" and C is "Cat + HousePet?" Thanks, Sean
