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Questions: Subtyping

{% include JB/setup %}

Subtyping01 (source at subtyping/Subtyping01.scala)

For the purpose of this exercise remember that Integer <: Number.

Each of the following applications is reported as an error by typechecker. Please state the final subtyping relation between the types which could not be satisfied e.g. Map[String, Number] <: Map[Int, Number] it would be String <: Int. Report only the first one if there is more than one.

Answers:

  • test1:
  • test2:
  • test3:
  • test4:

Subtyping02

test02

  • Does the type annotation of y affect the inference of type arguments in this application?
  • What is the inferred type argument for B in application foo(x)? Type inferencer will infer the type by calculating the least upper bound of the constraints on the bounds. What are the constraints on the bounds of B? Why least upper bound and not greatest lower bound?

test03

  • Why did the typechecker infer Serializable as type argument for T? Explain in terms of solving constraints on the type's bounds collected in order to infer the type argument.
  • Why is the type argument for S not inferred as Serializable as well? Explain in terms of solving the constraints on the type's bounds collected in order to infer the type argument.

test04

Map is invariant in the first type parameter (representing keys) and covariant in the second one (representing values). CovMap is covariant in both type parameters.

  • What constraints on type bounds affect the inference of type argument for T in the application foo(m1)?

  • What is the inferred type argument for T and why? (explain using your answer to the previous question)?

  • What constraints on type bounds affect the inference of type argument for S in the application bar(m2)?

  • What is the inferred type argument for S and why? (explain using your answer to the previous question)?

  • Does the type of the keys (Integer) of m3's Map affect the inferred type argument T in the application? Why?

  • Does the type of the keys (Integer) of m4's Map affect the inferred type argument S in the application? Why?