Scala infix type aliasing for >2 type parameters?

Question

I know in Scala, you can do type ===>[A, B] = Map[A, B] and then you can use infix notation to define def foo: String ===> Int which is same as saying def foo: Map[String, Int]. Is there any way to exploit this infix notation to create types with >2 arguments? For example, I want something like this:

type A ~> B ~~~> C to be an alias of say Map[A, Pair[B, C]] ?

Is there anyway I can write something line this:

type A to B -> C as alias for (A, B, C) type?

Shellishellie

Answer 1

Interestingly operator precedence as defined for symbolic methods doesn't seem to hold for symbolic type aliases. Instead infix type aliases are always evaluated left associative:

type -[A,B] = Map[A,B] 
type /[A,B] = Map[A,B] // '/' has higher precedence than '-' as an operator
classOf[A - B / C] // Class[/[-[A,B],C]]
classOf[A / B - C] // Class[-[/[A,B],C]]

Unfortunately that means it will never be possible to do what you ask for without parentheses like this:

classOf[A - (B / C)] // Class[-[A,/[B,C]]

So the closest answer is the following:

type ~>[A,B] = Map[A,B]
type ~~~>[A,B] = Pair[A,B]
classOf[A ~> (B ~~~> C)] // Map[A,Pair[B,C]]

Ommitting the parentheses will only be possible if you use right associative aliases (ending with :)

type ~:[A,B] = Map[A,B]
type ~~~:[A,B] = Pair[A,B]
classOf[A ~: B ~~~: C] // Map[A,Pair[B,C]]

Again, unfortunately since all type aliases have the same precedence it is not possible to mix right and left associative aliases without parentheses.

Concerning the second part of your question: (A,B,C) is syntactic sugar for Tuple3[A,B,C] which is a type with three parameters. As infix types only take two parameters, I'm afraid that I believe there is no way to represent this type solely with infix types. You would always end up with nested two parameter types (e.g. (A,(B,C)) or ((A,B),C).

Ordway

Great clarification. Didn't realise until your answer that the precedence was not the same! – Essayist

Is it possible to achieve A as B ~> C to mean (A, B, C)? – Shellishellie

@wrick: I don't believe this is possible on the type level. Infix types can only take two type parameters but (A,B,C) has three. Only ((A,B),C) or (A,(B,C)) are possible IMHO. – Ordway

Answer 2

Short answer: no. A ~> B ~> C cannot mean Map[A, Pair[B, C]].

It could be made to mean Map[A, Map[B, C]], though, or Pair[A, Pair[B, C]].

Essayist

What if I use two symbols e.g. A ~> B ==> C ? – Shellishellie

That works, provided you get the precedence right for these infix “type constructors”, such that your example means Map[A, Pair[B, C]] and not Pair[Map[A, B], C]. Be sure to check section 6.12.3 of the Scala Language Specification. – Essayist

A ~> B ~> C can not be made to mean Map[A,Map[B,C]]. Neither can anything without parentheses be made to mean Map[A,Pair[B,C]]. See my answer. – Ordway