Split SIP33 into two SIPs (#905)

* Splitting SIP33

* New SIP files

* Updates SIP 33 and new SIP-NN(prefix types)

* Added updated PR links

* redundant file

* Update to prefix types SIP, according to feedback on the PR.

* Update to SIP33 and added example to prefix types use

* Minor grammer change.

* Update history table

Author: soronpo

_sips/sips/2017-02-07-make-types-behave-like-expressions.md

@@ -0,0 +1,153 @@
+---
+layout: sip
+discourse: true
+title: SIP-33 - Priority-based infix type precedence
+
+vote-status: pending
+permalink: /sips/:title.html
+---
+
+**By: Oron Port**
+
+## History
+
+| Date          | Version                                  |
+| ------------- | ---------------------------------------- |
+| Feb 7th 2017  | Initial Draft                            |
+| Feb 9th 2017  | Updates from feedback                    |
+| Feb 10th 2017 | Updates from feedback                    |
+| Aug 8th 2017  | Numbered SIP, improve view, fixed example, and added related issues |
+| Oct 20th 2017 | Added implementation link                |
+| Oct 25th 2017 | Moved prefix types to [another SIP](http://docs.scala-lang.org/sips/adding-prefix-types.html), changed title and PR |
+| Nov 29th 2017 | Updated SIP according to feedback in the PR |
+
+
+Your feedback is welcome! If you're interested in discussing this proposal, head over to [this](https://contributors.scala-lang.org/t/sip-nn-make-infix-type-alias-precedence-like-expression-operator-precedence/471) Scala Contributors thread and let me know what you think.
+
+---
+
+## Introduction
+Currently scala allows symbol operators (`-`, `*`, `~~>`, etc.) for both type names and definition names.
+Unfortunately, there is a 'surprise' element since the two differ in behavior. While infix types are 'mostly' left-associative, the expression operation precedence is determined by the operator's first character (e.g., `/` is precedent to `+`). Please see [Infix Types](http://scala-lang.org/files/archive/spec/2.12/03-types.html#infix-types) and [Infix Operations](http://scala-lang.org/files/archive/spec/2.12/06-expressions.html#infix-operations) sections of the Scala specifications for more details.
+
+**Infix expression precedence vs. infix type precedence example**:
+
+```scala
+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
+  //Error!
+  //Left  expands to Plus[Div[Plus[N1,N2],N3],N4] (Surprising)
+  //Right expands to Plus[Plus[N1,Div[N2,N3]],N4]
+  implicitly[(N1 + N2 / N3 + N4) =:= (N1 + (N2 / N3) + N4)]
+}
+```
+
+---
+
+## Motivation
+It is easier to reason about the language when mathematical and logical operations for both terms and types are expressed the same.
+
+### 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](https://github.com/fthomas/singleton-ops) with [Typelevel Scala](https://github.com/typelevel/scala) (which implemented [SIP-23](http://docs.scala-lang.org/sips/pending/42.type.html)) enable developers to express literal type operations more intuitively. For example:
+
+```scala
+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:
+
+```scala
+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](http://stackoverflow.com/questions/23333882/scala-infix-type-aliasing-for-2-type-parameters) stackoverflow question demonstrate developers are 'surprised' by the difference in infix precedence, expecting infix type precedence to act the same as expression operations.
+
+---
+
+## Proposal
+
+Make infix types conform to the same precedence and associativity traits as term operations.
+
+------
+
+## Implementation
+
+A PR for this SIP is available at: [https://github.com/scala/scala/pull/6147](https://github.com/scala/scala/pull/6147)
+
+------
+
+### Interactions with other language features
+
+#### Star `*` infix type interaction with repeated parameters  
+The [repeated argument symbol `*`](https://www.scala-lang.org/files/archive/spec/2.12/04-basic-declarations-and-definitions.html#repeated-parameters) may create confusion with the infix type `*`. 
+Please note that this feature interaction already exists within the current specification.  
+
+```scala
+trait +[N1, N2]
+trait *[N1, N2]
+trait N1
+trait N2
+def foo(a : N1*N1+N2*) : Unit = {} //repeated parameter of type +[*[N1, N1], N2]
+```
+
+However, it is very unlikely that such interaction would occur.
+
+**Related Issues**
+
+* [Dotty Issue #1961](https://github.com/lampepfl/dotty/issues/1961)
+
+
+## Backward Compatibility
+Changing infix type associativity and precedence affects code that uses type operations and conforms to the current specification. 
+
+Note: changing the infix precedence didn't fail any scalac test.
+
+---
+
+### Bibliography
+[Scala Contributors](https://contributors.scala-lang.org/t/sip-nn-make-infix-type-alias-precedence-like-expression-operator-precedence/471)
+
+[scala-sips](https://groups.google.com/forum/#!topic/scala-sips/ARVf1RLDw9U)