Update documentation for parameter untupling

- `TupleN` instead of `ProductN`
- Make two steps in type checking more clear

Author: liufengyun

docs/docs/reference/other-new-features/parameter-untupling-spec.md

@@ -3,7 +3,7 @@ layout: doc-page
 title: "Parameter Untupling - More Details"
 ---
 
-### Motivation
+## Motivation
 
 Say you have a list of pairs
 
@@ -35,31 +35,35 @@ xs.map(_ + _)
 
 Generally, a function value with `n > 1` parameters can be converted to a function with tupled arguments if the expected type is a unary function type of the form `((T_1, ..., T_n)) => U`.
 
-### Type Checking
+## Type Checking
 
-Let a function `f` of the form `(p1, ..., pn) => e` for `n != 1`, parameters `p1, ..., pn`, and an expression `e`.
+The type checking happens in two steps:
 
-If the expected type of `f` is a fully defined function type or SAM-type that has a
-single parameter of a subtype of `ProductN[T1, ..., Tn]`, where each type `Ti` fits the corresponding
-parameter `pi`. Then `f` will conform to the function type `ProductN[T1, ..., Tn] => R`.
+1. Check whether parameter untupling is feasible
+2. Adapt the function and type check it
+
+### Feasibility Check
+
+Suppose a function `f` of the form `(p1, ..., pn) => e` (where `n > 1`), with `p1, ..., pn` as parameters and `e` as function body.
+
+If the expected type for checking `f` is a fully defined function type of the form `TupleN[T1, ..., Tn] => R` (or an equivalent SAM-type), where each type `Ti` fits the corresponding parameter `pi`. Then `f` will conform to the function type `TupleN[T1, ..., Tn] => R`.
 
 A type `Ti` fits a parameter `pi` if one of the following two cases is `true`:
 
 * `pi` comes without a type, i.e. it is a simple identifier or `_`.
 * `pi` is of the form `x: Ui` or `_: Ui` and `Ti <: Ui`.
 
-Auto-tupling composes with eta-expansion. That is an n-ary function generated by eta-expansion
-can in turn be adapted to the expected type with auto-tupling.
+Parameter untupling composes with eta-expansion. That is, an n-ary function generated by eta-expansion can in turn be adapted to the expected type with parameter untupling.
 
-#### Term adaptation
+### Term adaptation
 
 If the function
 
 ```scala
-(p1: T1, ..., pn: Tn) => e
+(p1, ..., pn) => e
 ```
 
-is typed as `ProductN[T1, ..., Tn] => Te`, then it will be transformed to
+is feasible for parameter untupling with the expected type `TupleN[T1, ..., Tn] => Te`, then continue to type check the following adapted function
 
 ```scala
 (x: TupleN[T1, ..., Tn]) =>
@@ -69,19 +73,15 @@ is typed as `ProductN[T1, ..., Tn] => Te`, then it will be transformed to
    e
 ```
 
-##### Generic tuples
-
-If we come to support generic tuples, which provide the possibility of having tuples/functions of arities larger than 22 we would need to additionally support generic tuples of the form `T1 *: T2 *: ...`.
-Translation of such a tuples would use the `apply` method on the tuple to access the elements instead of the `_N` methods of `Product`.
-
-### Migration
+with the same expected type.
+## Migration
 
 Code like this could not be written before, hence the new notation would not be ambiguous after adoption.
 
 Though it is possible that someone has written an implicit conversion form `(T1, ..., Tn) => R` to `TupleN[T1, ..., Tn] => R`
 for some `n`. This change could be detected and fixed by [`Scalafix`](https://scalacenter.github.io/scalafix/). Furthermore, such conversion would probably
 be doing the same translation (semantically) but in a less efficient way.
 
-### Reference
+## Reference
 
 For more information, see [Issue #897](https://github.com/lampepfl/dotty/issues/897).