[TYPES] Basic principal type terminology

[Andreas Rossberg]

On Mar 5, 2015, at 02:50 , Sean McDirmid <smcdirm at microsoft.com> wrote:
> 
> 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:

Sounds to me like you are looking for principal typings, not principal types.

/Andreas


> 
> 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