Apply limit22.md

Author: Sporarum

docs/_spec/03-types.md

@@ -217,22 +217,27 @@ G[S, Int]             // illegal: S constrains its parameter to
 SimpleType    ::=   ‘(’ Types ‘)’
 ```
 
-A _tuple type_ ´(T_1 , ... , T_n)´ is an alias for the class `scala.Tuple´n´[´T_1´, ... , ´T_n´]`, where ´n \geq 2´.
+A _tuple type_ ´(T_1, ..., T_n)´ where ´n \geq 2´ is an alias for the type `´T_1´ *: ... *: ´T_n´ *: scala.EmptyTuple`.
+
+Note:
+`(´T´)` is just the type ´T´, and not `´T´ *: scala.EmptyTuple`.
+`()` is not a valid type, and not `scala.EmptyTuple`.
+
+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´]`.
 
 Tuple classes are case classes whose fields can be accessed using selectors `_1`, ..., `_n`.
-Their functionality is abstracted in a corresponding `Product` trait.
+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).
 
 ```scala
 case class Tuple´_n´[+´T_1´, ..., +´T_n´](_1: ´T_1´, ..., _n: ´T_n´)
 extends Product´_n´[´T_1´, ..., ´T_n´]
 
-trait Product´_n´[+´T_1´, ..., +´T_n´] {
+trait Product´_n´[+´T_1´, ..., +´T_n´] extends Product:
   override def productArity = ´n´
   def _1: ´T_1´
   ...
   def _n: ´T_n´
-}
 ```
 
 ### Annotated Types
@@ -329,25 +334,26 @@ FunctionArgs      ::=  InfixType
                     |  ‘(’ [ ParamType {‘,’ ParamType } ] ‘)’
 ```
 
-The type ´(T_1, ..., T_n) \Rightarrow U´ represents the set of function values that take arguments of types ´T_1, ..., Tn´ and yield results of type ´U´.
-In the case of exactly one argument type ´T \Rightarrow U´ is a shorthand for ´(T) \Rightarrow U´.
-An argument type of the form ´\Rightarrow T´ represents a [call-by-name parameter](04-basic-declarations-and-definitions.html#by-name-parameters) of type ´T´.
+The type ´(T_1, ..., T_n) \Rightarrow R´ represents the set of function values that take arguments of types ´T_1, ..., Tn´ and yield results of type ´R´.
+The case of exactly one argument type ´T \Rightarrow R´ is a shorthand for ´(T) \Rightarrow R´.
+An argument type of the form ´\Rightarrow T´ represents a [call-by-name parameter](04-basic-declarations-and-definitions.md#by-name-parameters) of type ´T´.
 
-Function types associate to the right, e.g. ´S \Rightarrow T \Rightarrow U´ is the same as ´S \Rightarrow (T \Rightarrow U)´.
+Function types associate to the right, e.g. ´S \Rightarrow T \Rightarrow R´ is the same as ´S \Rightarrow (T \Rightarrow R)´.
+
+Function types are [covariant](04-basic-declarations-and-definitions.md#variance-annotations) in their result type and [contravariant](04-basic-declarations-and-definitions.md#variance-annotations) in their argument types.
 
 Function types are shorthands for class types that define an `apply` method.
-Specifically, the ´n´-ary function type ´(T_1 , \ldots , T_n) \Rightarrow U´ is a shorthand for the class type `Function´_n´[´T_1´ , … , ´T_n´, ´U´]`.
-Such class types are defined in the Scala library for ´n´ between 0 and 22 as follows.
+Specifically, the ´n´-ary function type ´(T_1, ..., T_n) \Rightarrow R´ is a shorthand for the class type `Function´_n´[´T_1´, ..., ´T_n´, ´R´]`. 
+In particular ´() \Rightarrow R´ is a shorthand for class type `Function´_0´[´R´]`.
+
+Such class types behave as if they were instances of the following trait:
 
 ```scala
-package scala
-trait Function´_n´[-´T_1´, ..., -´T_n´, +´U´] {
-  def apply(´x_1´: ´T_1´, ..., ´x_n´: ´T_n´): ´U´
-  override def toString = "<function>"
-}
+trait Function´_n´[-´T_1´, ..., -´T_n´, +´R´]:
+  def apply(´x_1´: ´T_1´, ..., ´x_n´: ´T_n´): ´R´
 ```
 
-Hence, function types are [covariant](04-basic-declarations-and-definitions.html#variance-annotations) in their result type and contravariant in their argument types.
+Their exact supertype and implementation can be consulted in the [function classes section](./12-the-scala-standard-library.md#the-function-classes) of the standard library page in this document.
 
 #### Wildcard Types
 

docs/_spec/06-expressions.md

@@ -381,9 +381,15 @@ Type applications can be omitted if [local type inference](#local-type-inference
 ```ebnf
 SimpleExpr   ::=  ‘(’ [Exprs] ‘)’
 ```
+A _tuple expression_ `(´e_1´, ..., ´e_n´)` where ´n \geq 2´ is equivalent to the expression `´e_1´ *: ... *: ´e_n´ *: scala.EmptyTuple`.
 
-A _tuple expression_ `(´e_1´, ..., ´e_n´)` is an alias for the class instance creation `scala.Tuple´n´(´e_1´, ..., ´e_n´)`, where ´n \geq 2´.
-The empty tuple `()` is the unique value of type `scala.Unit`.
+Note:
+As calls to `*:` are slow, a more efficient translation is free to be implemented.
+For example, `(´e_1´, ´e_2´)` could be translated to `scala.Tuple2(´e_1´, ´e_2´)`, which is indeed equivalent to `´e_1´ *: ´e_2´ *: scala.EmptyTuple`.
+
+Note:
+The expression `(´e_1´)` is not equivalent to `´e_1´ *: scala.EmptyTuple`, but instead a regular parenthesized expression.
+The expression `()` is not an alias for `scala.EmptyTuple`, but instead the unique value of type `scala.Unit`.
 
 ## Instance Creation Expressions
 
@@ -909,6 +915,9 @@ Binding         ::=  (id | ‘_’) [‘:’ Type]
 The anonymous function of arity ´n´, `(´x_1´: ´T_1, ..., x_n´: ´T_n´) => e` maps parameters ´x_i´ of types ´T_i´ to a result given by expression ´e´.
 The scope of each formal parameter ´x_i´ is ´e´.
 Formal parameters must have pairwise distinct names.
+Type bindings can be omitted, in which case the compiler will attempt to infer valid bindings.
+
+Note: `() => ´e´` defines a nullary function (´n´ = 0), and not for example `(_: Unit) => ´e´`.
 
 In the case of a single untyped formal parameter, `(´x\,´) => ´e´` can be abbreviated to `´x´ => ´e´`.
 If an anonymous function `(´x´: ´T\,´) => ´e´` with a single typed parameter appears as the result expression of a block, it can be abbreviated to `´x´: ´T´ => e`.

docs/_spec/08-pattern-matching.md

@@ -185,7 +185,15 @@ This is further discussed [here](#pattern-sequences).
   SimplePattern   ::=  ‘(’ [Patterns] ‘)’
 ```
 
-A _tuple pattern_ `(´p_1´, ..., ´p_n´)` is an alias for the constructor pattern `scala.Tuple´n´(´p_1´, ..., ´p_n´)`, where ´n \geq 2´. The empty tuple `()` is the unique value of type `scala.Unit`.
+A _tuple pattern_ `(´p_1´, ..., ´p_n´)` where ´n \geq 2´ is equivalent to `´p_1´ *: ... *: ´p_n´ *: scala.EmptyTuple`.
+
+Note:
+`()` is equivalent to `_: scala.Unit`, and not `scala.EmptyTuple`.
+`(´pat´)` is a pattern matching ´pat´, and not `´pat´ *: scala.EmptyTuple`.
+
+Note:
+As such patterns with `*:` are slow, a more efficient translation is free to be implemented.
+For example, `(´p_1´, ´p_2´)` could be translated to `scala.Tuple2(´p_1´, ´p_2´)`, which is indeed equivalent to `´p_1´ *: ´p_2´ *: scala.EmptyTuple`.
 
 ### Extractor Patterns
 

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

@@ -288,6 +288,7 @@ def + (that: Any): String
 
 which concatenates its left operand with the textual representation of its right operand.
 
+<!-- TODO: re-add ? with explanations of: EmptyTuple, *:, NonEmptyTuple, TupleXXL
 ### The `Tuple` classes
 
 Scala defines tuple classes `Tuple´n´` for ´n = 2, ..., 22´.
@@ -299,20 +300,36 @@ case class Tuple´n´[+T_1, ..., +T_n](_1: T_1, ..., _´n´: T_´n´) {
   def toString = "(" ++ _1 ++ "," ++ ... ++ "," ++ _´n´ ++ ")"
 }
 ```
-
+-->
 ### The `Function` Classes
 
-Scala defines function classes `Function´n´` for ´n = 1 , \ldots , 22´.
-These are defined as follows.
+For each class type `Function´n´` where ´n = 0, ..., 22´, Scala 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
-  def toString = "<function>"
-}
+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:
+
+```scala
+package scala
+trait FunctionXXL:
+  def apply(xs: IArray[Object]): Object
+  override def toString = "<functionXXL>"
 ```
 
+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).
 
@@ -322,7 +339,10 @@ class PartialFunction[-A, +B] extends Function1[A, B] {
 }
 ```
 
-The implicitly imported [`Predef`](#the-predef-object) object defines the name `Function` as an alias of `Function1`.
+### Trait `Product`
+<!-- TODO: Move somewhere else ? -->
+<!-- TODO: Could not find more info on which non-Product methods case class automatically define  -->
+All case classes automatically extend the `Product` trait (and generate synthetic methods to conform to it) (but not `Product´n´`), and define a `_´n´` method for each of their arguments.
 
 ### Class `Array`