Java 8 Type Inference - How reduction is done for generic constructors?

Question

I was reading the java 8 language specification type inference. It says that

List<String> ls = new ArrayList<>()

would be first reduced

ArrayList<α> -> List<String>

and then to

α <= String

and at the end to

α = String

I'm having a hard time understanding how the reduction of the constraint

ArrayList<α> -> List<String> to α <= String

was derived. It would be a great help if anyone can point out the logic using the java 8 language spec.

Here's the link to the reduction

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Thanks #Holger for the explanation. Following is my take on the derivation of

new ArrayList<> -> List<String> to ArrayList<α> -> List<String>

Please correct me if I'm wrong.

First to find the temporary method for the constructor we use #15.9.3

• Otherwise, the arguments to the constructor are the arguments in the argument list of the class instance creation expression, if any, in the order they appear in the expression.

• If the class instance creation expression uses <> to elide class type arguments, a list of methods m1...mn is defined for the purpose of overload resolution and type argument inference.

Then #18.5.2 is used to derive

ArrayList<α> -> List<String>

Because of being a poly expression and not having any wild card type parameters;

• Otherwise, the constraint formula ‹R θ → T› is reduced and incorporated with B2.

Answer 1

I’m glad you didn’t ask how to come from new ArrayList<>() → List<String> to ArrayList<α> → List<String> as, while looking obvious, per applying §18.2.1, we will find it requires a discussion of the entire §15.9.3, followed by a discussion of §18.5.2.

Proceeding from ArrayList<α> → List<String> is easier:

§18.2.2. Type Compatibility Constraints

A constraint formula of the form ‹S → T› is reduced as follows:

• … (five inapplicable bullets omitted)

• Otherwise, the constraint reduces to ‹S <: T›.

 

§18.2.3. Subtyping Constraints

A constraint formula of the form ‹S <: T› is reduced as follows:

• … (five irrelevant bullets omitted)

• Otherwise, the constraint is reduced according to the form of T:

  • If T is a parameterized class or interface type, or an inner class type of a parameterized class or interface type (directly or indirectly), let A₁, ..., A_n be the type arguments of T. Among the supertypes of S, a corresponding class or interface type is identified, with type arguments B₁, ..., B_n. If no such type exists, the constraint reduces to false. Otherwise, the constraint reduces to the following new constraints: for all i (1 ≤ i ≤ n), ‹B_i <= A_i›..

So ArrayList<α> → List<String> is first reduced to ArrayList<α> <: List<String>, then, since List<String> is a parametrized interface, a corresponding super type of ArrayList<α> is identified, which will be List<α>, then, the constraint is reduced to a set of constraints for each corresponding type parameter (here we have exactly one), so we get α <= String.