SIP-NN - Match infix & prefix types to meet expression rules

By: Oron Port


Date Version
Feb 7th 2017 Initial Draft
Feb 9th 2017 Updates from feedback
Feb 10th 2017 Updates from feedback

Your feedback is welcome! If you’re interested in discussing this proposal, head over to this Scala Contributors thread and let me know what you think.


Currently scala allows symbol operators (-, *, ~~>, etc.) for both type names and definition names. Unfortunately, there is a ‘surprise’ element since the two differ in behaviour:

Infix operator precedence and associativity

Infix types are ‘mostly’ left-associative, while the expression operation precedence is determined by the operator’s first character (e.g., / is precedent to +). Please see Infix Types and Infix Operations sections of the Scala specifications for more details.


    object InfixExpressionPrecedence {
      case class Nummy(expand : String) {
        def + (that : Nummy) : Nummy = Nummy(s"Plus[$this,$that]")
        def / (that : Nummy) : Nummy = Nummy(s"Div[$this,$that]")
      object N1 extends Nummy("N1")
      object N2 extends Nummy("N2")
      object N3 extends Nummy("N3")
      object N4 extends Nummy("N4")
      //Both expand to Plus[Plus[N1,Div[N2,N3]],N4]
      assert((N1 + N2 / N3 + N4).expand == (N1 + (N2 / N3) + N4).expand)
    object InfixTypePrecedence {
      trait Plus[N1, N2]
      trait Div[N1, N2]
      type +[N1, N2] = Plus[N1, N2]
      type /[N1, N2] = Div[N1, N2]
      trait N1
      trait N2
      trait N3
      trait N4
      //Left  expands to Plus[Plus[N1,Div[N2,N3]],N4] (Surprising)
      //Right expands to Plus[Div[Plus[N1,N2],N3],N4]
      implicitly[(N1 + N2 / N3 + N4) =:= (N1 + (N2 / N3) + N4)]

Prefix operators bracketless unary use

While expressions have prefix unary operators, there are none for types. See the Prefix Operations section of the Scala specification. This is a lacking feature of the type language Scala offers. See also interactions of this feature with other Scala features, further down this text.


    object PrefixExpression {
      case class Nummy(expand : String) {
        def unary_- : Nummy = Nummy(s"-$this")
        def unary_~ : Nummy = Nummy(s"~$this")
        def unary_! : Nummy = Nummy(s"!$this")
        def unary_+ : Nummy = Nummy(s"+$this")
      object N extends Nummy("N")
      val n1 = -N
      val n2 = ~N
      val n3 = !N
      val n4 = +N
    object NonExistingPrefixTypes {
      trait unary_-[A]
      trait unary_~[A]
      trait unary_![A]
      trait unary_+[A]
      trait N
      type N1 = -N //Not working
      type N2 = ~N //Not working
      type N3 = !N //Not working
      type N4 = +N //Not working


The proposal is split into two; type infix precedence, and prefix unary types. Note to the SIP committee: It might be better to vote on the two parts separately.

Proposal, Part 1: Infix type precedence & associativity

Make infix types conform to the same precedence and associativity traits as expression operations.

Proposal, Part 2: Prefix unary types

Add prefix types, exactly as specified for prefix expression.


The general motivation is developers expect terms and types to behave equally regarding operation precedence and availability of unary types.

Motivating examples

Dotty infix type similarity

Dotty infix type associativity and precedence seem to act the same as expressions. No documentation available to prove this, but the infix example above works perfectly in dotty.

Dotty has no prefix types, same as Scalac.

Singleton-ops library example

The singleton-ops library with Typelevel Scala (which implemented SIP-23) enables developers to express literal type operations more intuitively. For example:

    import singleton.ops._
    val four1 : 4 = implicitly[2 + 2]
    val four2 : 2 + 2 = 4
    val four3 : 1 + 3 = implicitly[2 + 2]
    class MyVec[L] {
      def doubleSize = new MyVec[2 * L]
      def nSize[N] = new MyVec[N * L]
    object MyVec {
      implicit def apply[L](implicit check : Require[L > 0]) : MyVec[L] = new MyVec[L]()
    val myVec : MyVec[10] = MyVec[4 + 1].doubleSize
    val myBadVec = MyVec[-1] //fails compilation, as required

We currently loose some of the intuitive appeal due to the precedence issue:

    val works : 1 + (2 * 3) + 4 = 11
    val fails : 1 + 2 * 3 + 4 = 11 //left associative:(((1+2)*3)+4))) = 13

Developer issues example

This stackoverflow question demonstrate developers are ‘surprised’ by the difference in infix precedence, expecting infix type precedence to act the same as expression operations.

Interactions with other language features

Variance Annotation

Variance annotation uses the - and + symbols to annotate contravariant and covariant subtyping, respectively. Introducing unary prefix types may lead to some developer confusion. E.g.

    trait Negate[A]
    trait Positive[A]
    type unary_-[A] = Negate[A] 
    type unary_+[A] = Positive[A] 
    trait Contravariant[B, -A <: -B] //contravariant A subtype upper-bounded by Negate[B]
    trait Covariant[B, +A <: +B] //covariant A subtype upper-bounded by Positive[B]

Negative Literal Types

Negative literal types are annotated using the - symbol. This can lead to the following confusion:

    trait Negate[A]
    type unary_-[A] = Negate[A] 
    trait MyTrait[B]
    type MinusFortyTwo = MyTrait[-42] 
    type NegateFortyTwo = MyTrait[Negate[42]]

The above example demonstrates a case of two types MinusFortyTwo and NegateFortyTwo which are different. They may be equivalent in view (implicit conversion between the two type instances), but they are not equal.

Note: It is not possible to annotate a positive literal type in Scala (checked both in TLS and Dotty):

    val a : 42 = +42 //works
    val b : -42 = -42 //works
    val c : +42 = 42 //error: ';' expected but integer literal found 

This means that if unary prefix types are added, then +42 will be a type expansion of unary_+[42].

Backward Compatibility

Changing infix type associativity and precedence affects code that uses type operations and conforms to the current specification.


Scala Contributors


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