What are type projections useful for?

Question

What are type projections in Scala useful for? Why does Scala\'s type system support both type projections and path dependent types? What was the rationale behind this design de

Answer 1

One thing type projections can be used for is partial type application:

({type λ[x]=Tuple2[Int,x]})#λ

Answer 2

Not a complete answer, but here are some uses for type projections that I have encountered:

• Type level metaprogramming. For examples, see Michid's series (parts I, II, III), Jesper's implementation of HList, and the series at Apocalisp.

• A workaround to enable type inference (for examples, here are some previous SO questions 1, 2, 3).

• A way to bundle a bunch of types into a single type parameter. For example, in a matrix library I'm developing, I define trait Scalar { type A; type B; type C; ... } and then pass it as a single parameter to my matrix trait, trait Matrix[S <: Scalar] ... The individual types can be referred to as S#A, S#B, and so on. Between two matrices of type Matrix[S], for the same S, these types will be compatible (unlike what would be the case with path dependent types).