Infix types

In the same way that Scala has infix operators, it has infix types. An infix type, such as A Op B, is just any type that has exactly two type operands. It is equivalent to the type defined as Op[A, B]. Op may be any valid identifier.

The type operators have the same associativity as term operators—they are left associative unless an operator ends in : (colon), in which case it is right associative. Consecutive infix operators must have the same associativity. Let's look at an example to understand what this means:

type Or[A, B]
type And[A, B]
type +=[A, B] = Or[A, B]
type =:[A, B] = And[A, B]

type CC = Or[And[A, B], C]
type DA = A =: B =: C
type DB = A And B And C

// type E = A += B =: C // wrong associativity
type F = (A += B) =: C

Here, we defined four types, all of which have two type parameters and so can be used as infix types. Then, we define a type called CC, which expresses some relation between the A, B, and C types. The DA and DB type definitions show what the type definition looks like in infix notation. The first attempt to define some type, E, to be the same as the C type fails because of the different associativity of the types, =+ and =:, and we have demonstrated how parentheses can be used to work around this rule.

If used properly, infix types can greatly improve the readability of the code:

type |[A, B] = Or[A, B]
type  [A, B] = And[A, B]
type G = A   B | C

Here, we can see how infix types allow you to define type relation in a way that looks similar to Boolean operations.