Spec: Revisit Tuples and Function types.

Also add fundamental type aliases for `AnyKind`, `Nothing`, `&`
and `|`.

Author: sjrd

docs/_spec/03-types.md

@@ -173,7 +173,7 @@ In a sequence of consecutive type infix operations ´t_0 \, \mathit{op} \, t_1 \
 If they are all left-associative, the sequence is interpreted as ´(... (t_0 \mathit{op_1} t_1) \mathit{op_2} ...) \mathit{op_n} t_n´, otherwise it is interpreted as ´t_0 \mathit{op_1} (t_1 \mathit{op_2} ( ... \mathit{op_n} t_n) ...)´.
 
 The type operators `|` and `&` are not really special.
-Nevertheless, unless shadowed, they resolve to `scala.|` and `scala.&`, which represent [union and intersection types](#union-and-intersection-types), respectively.
+Nevertheless, unless shadowed, they resolve to [the fundamental type aliases `scala.|` and `scala.&`](./12-the-scala-standard-library.html#fundamental-type-aliases), which represent [union and intersection types](#union-and-intersection-types), respectively.
 
 ### Function Types
 
@@ -230,6 +230,21 @@ scala.PolyFunction {
 }
 ```
 
+### Tuple Types
+
+```ebnf
+SimpleType1           ::=  ...
+                        |  ‘(’ TypesOrWildcards ‘)’
+```
+
+A _tuple type_ ´(T_1, ..., T_n)´ where ´n \geq 2´ is sugar for the type `´T_1´ *: ... *: ´T_n´ *: scala.EmptyTuple`, which is itself a series of nested infix types which are sugar for `*:[´T_1´, *:[´T_2´, ... *[´T_n´, scala.EmptyTuple]]]`.
+The ´T_i´ can be wildcard type arguments.
+
+Notes:
+
+- `(´T_1´)` is the type ´T_1´, and not `´T_1´ *: scala.EmptyTuple` (´T_1´ cannot be a wildcard type argument in that case).
+- `()` is not a valid type (not even `scala.EmptyTuple`).
+
 ### Concrete Refined Types
 
 ```ebnf
@@ -285,7 +300,7 @@ _Types_ are either _proper types_, _type constructors_ or _poly-kinded types_.
 
 All types live in a single lattice with respect to a [_conformance_](#conformance) relationship ´<:´.
 The _top type_ is `AnyKind` and the _bottom type_ is `Nothing`: all types conform to `AnyKind`, and `Nothing` conforms to all types.
-They can be referred to as the standard library entities `scala.AnyKind` and `scala.Nothing`, respectively.
+They can be referred to with [the fundamental type aliases `scala.AnyKind` and `scala.Nothing`](./12-the-scala-standard-library.html#fundamental-type-aliases), respectively.
 
 Types can be _concrete_ or _abstract_.
 An abstract type ´T´ always has lower and upper bounds ´L´ and ´H´ such that ´L >: T´ and ´T <: H´.
@@ -1080,7 +1095,7 @@ Note that the conditions are not all mutually exclusive.
           - ´S_i´ and ´T_i´ are types and ´S_i =:= T_i´, or
           - ´S_i´ is a type and ´T_i´ is a wildcard type argument of the form ´? >: L_2 <: H_2´ and ´L_2 <: S_i´ and ´S_i <: H_2´, or
           - ´S_i´ is a wildcard type argument of the form ´? >: L_1 <: H_1´ and ´T_i´ is a wildcard type argument of the form ´? >: L_2 <: H_2´ and ´L_2 <: L_1´ and ´H_1 <: H_2´ (i.e., the ´S_i´ "interval" is contained in the ´T_i´ "interval").
-- ´T = q.C[T_1, ..., T_n]´ with ´n \geq 0´ and `baseType(´S´, ´C´)` is defined and `baseType(´S´, ´C´) ´<: T´.
+- ´T = q.C[T_1, ..., T_n]´ with ´n \geq 0´ and `baseType(´S´, ´C´)` is defined and `baseType(´S´, ´C´) ´<: T´`.
 - ´S = p.X[S_1, ..., S_n]´ and ´p.X´ is non-class type designator and ´H <: T´ where ´H´ is the upper bound of the underlying type definition of ´p.X´.
 - ´S = p.C´ and `´T = C´.this` and ´C´ is the hidden class of an `object` and:
   - ´p = \epsilon´ or ´p´ is a package ref, or
@@ -1123,6 +1138,7 @@ Note that the conditions are not all mutually exclusive.
 - ´S´ is a stable type and ´T = q.x´ is a term designator with underlying type ´T_1´ and ´T_1´ is a stable type and ´S <: T_1´.
 - `´S = S_1´ { ´R´ }` and ´S_1 <: T´.
 - `´S =´ { ´\alpha´ => ´S_1´ }` and ´S_1 <: T´.
+- `´T =´ scala.Tuple´_n[T_1, ..., T_n]´` with ´1 \leq n \leq 22´, and `´S <: T_1´ *: ... *: ´T_n´ *: scala.EmptyTuple`.
 
 We define `isSubPrefix(´p´, ´q´)` where ´p´ and ´q´ are prefixes as:
 

docs/_spec/12-the-scala-standard-library.md

@@ -12,10 +12,23 @@ Some of these classes are described in the following.
 ![Class hierarchy of Scala](public/images/classhierarchy.png)
 
 <!-- TODO: Briefly mention scala.deprecated somewhere, and link to [deprecated page](./A%3F-deprecated.md) -->
+
+## Fundamental Type Aliases
+
+The `scala` package provides the following fundamental type aliases, which expose to user code some forms of [types](./03-types.html) that cannot otherwise be written:
+
+```scala
+type AnyKind = ´x´           // where ´x´ is the internal AnyKind type
+type Nothing = ´x´           // where ´x´ is the internal Nothing type
+type | = [A, B] =>> A ´｜´ B // where ｜ is the internal union type operator
+type & = [A, B] =>> A ´＆´ B // where ＆ is the internal intersection type operator
+```
+
 ## Root Classes
 
-The root of this hierarchy is formed by class `Any`.
+The root of this hierarchy is formed by class `scala.Any`.
 Every class in a Scala execution environment inherits directly or indirectly from this class.
+By definition, `Any` is also the top [proper type](./03-types.html#proper-types).
 Class `Any` has two direct subclasses: `AnyRef` and `AnyVal`.
 
 The subclass `AnyRef` represents all values which are represented as objects in the underlying host system.
@@ -304,42 +317,42 @@ case class Tuple´n´[+T_1, ..., +T_n](_1: T_1, ..., _´n´: T_´n´) {
 -->
 ### The `Function` Classes
 
-For each class type `Function´n´` where ´n = 0, ..., 22´, Scala defines the following function class:
+For each natural ´n \geq 0´, the `scala` package defines the following function class:
 
 ```scala
 package scala
 trait Function´_n´[-´T_1´, ..., -´T_n´, +´R´]:
   def apply(´x_1´: ´T_1´, ..., ´x_n´: ´T_n´): ´R´
-  override def toString = "<function´_n´>"
-  def curried: ´T_1´ => ... => ´T_n´ => R = ...
-  def tupled: ((´T_1´, ..., ´T_n´)) => R = ...
 ```
 
-For function types `Function´n´` where ´n > 22´, Scala defines a unique function class:
+These classes participate in the desugaring of [concrete function types](./03-types.html#function-types).
 
+For values of ´n \leq 22´, the `Function´_n´` classes define additional methods:
 ```scala
 package scala
-trait FunctionXXL:
-  def apply(xs: IArray[Object]): Object
-  override def toString = "<functionXXL>"
+trait Function´_n´[-´T_1´, ..., -´T_n´, +´R´]:
+  ...
+  override def toString = "<function´_n´>"
+  def curried: ´T_1´ => ... => ´T_n´ => R = ...
+  def tupled: ((´T_1´, ..., ´T_n´)) => R = ...
 ```
 
-There is no loss of type safety, as the internal representation is still `Function´n´` for all ´n´.
-However this means methods `curried` and `tupled` are not available on functions with more than 22 parameters.
-
 The implicitly imported [`Predef`](#the-predef-object) object defines the name
 `Function` as an alias of `Function1`.
 
-<!-- TODO: Remove below ? -->
 The `PartialFunction` subclass of `Function1` represents functions that (indirectly) specify their domain.
 Use the `isDefined` method to query whether the partial function is defined for a given input (i.e., whether the input is part of the function's domain).
 
 ```scala
 class PartialFunction[-A, +B] extends Function1[A, B] {
   def isDefinedAt(x: A): Boolean
+
+  ... // various derived methods
 }
 ```
 
+`PartialFunction` participates in the desugaring of [pattern matching anonymous functions](08-pattern-matching.html#pattern-matching-anonymous-functions).
+
 ### Trait `Product`
 <!-- TODO: Move somewhere else ? -->
 <!-- TODO: Could not find more info on which non-Product methods case class automatically define  -->
@@ -351,36 +364,55 @@ All enum definitions automatically extend the `reflect.Enum` trait (and generate
 
 ### Tuple Classes
 
-Tuple classes are case classes whose fields can be accessed using selectors `_1`, ..., `_n`.
-Their functionality is abstracted in the corresponding `scala.Product_´n´` trait.
-The _n_-ary tuple class and product trait are defined at least as follows in the standard Scala library (they might also add other methods and implement other traits).
+Tuples are a form of _HLists_ defined by the following classes:
 
 ```scala
-case class Tuple´_n´[+´T_1´, ..., +´T_n´](_1: ´T_1´, ..., _n: ´T_n´)
-extends Product´_n´[´T_1´, ..., ´T_n´]
+/** Superclass of all tuples. */
+sealed trait Tuple extends Product:
+  /** Return a new tuple by prepending the element to `this` tuple. */
+  inline def *: [H, This >: this.type <: Tuple] (x: H): H *: This = ...
+  ...
 
-trait Product´_n´[+´T_1´, ..., +´T_n´] extends Product:
-  override def productArity = ´n´
-  def _1: ´T_1´
+object Tuple:
+  /** Type of the element at position N in the tuple X. */
+  type Elem[X <: Tuple, N <: Int] = ...
   ...
-  def _n: ´T_n´
-```
 
-#### Short-hand syntax
+/** A tuple of 0 elements. */
+type EmptyTuple = EmptyTuple.type
+
+/** A tuple of 0 elements. */
+case object EmptyTuple extends Tuple:
+  override def toString(): String = "()"
+
+/** Tuple of arbitrary non-zero arity */
+sealed trait NonEmptyTuple extends Tuple:
+  /** Get the i-th element of this tuple. */
+  inline def apply[This >: this.type <: NonEmptyTuple](n: Int): Elem[This, n.type] = ...
+  ...
 
-Tuple classes have dedicated syntax.
+sealed abstract class *:[+H, +T <: Tuple] extends NonEmptyTuple
 
-```ebnf
-SimpleType    ::=   ‘(’ Types ‘)’
+object `*:` :
+  def unapply[H, T <: Tuple](x: H *: T): (H, T) = (x.head, x.tail)
 ```
 
-A _tuple type_ ´(T_1, ..., T_n)´ where ´n \geq 2´ is an alias for the type `´T_1´ *: ... *: ´T_n´ *: scala.EmptyTuple`.
+For ´1 \leq n \leq 22´, the concrete implementations of `*:` are instances of `Tuple´_n´` classes, which also implement corresponding `Product´_n´` traits.
+They are defined at least as follows in the standard Scala library (they might also add other methods and implement other traits).
+
+```scala
+trait Product´_n´[+´T_1´, ..., +´T_n´] extends Product:
+  override def productArity: Int = ´n´
+  def _1: ´T_1´
+  ...
+  def _n: ´T_n´
 
-Notes:
-- `(´T´)` is just the type ´T´, and not `´T´ *: scala.EmptyTuple`.
-- `()` is not a valid type, and not `scala.EmptyTuple`.
+final case class Tuple´_n´[+´T_1´, ..., +´T_n´](_1: ´T_1´, ..., _n: ´T_n´)
+    extends *:[´T_1´, ´T_2´ *: ... _: ´T_n´ *: EmptyTuple]
+    with Product´_n´[´T_1´, ..., ´T_n´]
+```
 
-If ´n \leq 22´, the type `´T_1´ *: ... *: ´T_n´ *: scala.EmptyTuple` is both a subtype and a supertype of tuple class `scala.Tuple´_n´[´T_1´, ..., ´T_n´]`.
+For ´n > 22´, the concrete implementations of ´*:´ are instances of implementation-specific private classes.
 
 ### Class `Array`