Update polymorphism section in cc language ref

Author: bracevac

docs/_docs/reference/experimental/capture-checking/polymorphism.md

@@ -6,8 +6,44 @@ nightlyOf: https://docs.scala-lang.org/scala3/reference/experimental/capture-che
 
 ## Introduction
 
-It is sometimes convenient to write operations that are parameterized with a capture set of capabilities. For instance consider a type of event sources
-`Source` on which `Listener`s can be registered. Listeners can hold certain capabilities, which show up as a parameter to `Source`:
+Capture checking supports capture-polymorphic programming in two complementary styles:
+	1.	**Implicit** capture polymorphism, which is the default and has minimal syntactic overhead.
+	2.	**Explicit** capture polymorphism, which allows programmers to abstract over capture sets directly through explicit generic parameters.
+
+### Implicit Polymorphism
+
+In many cases, such a higher-order functions, we do not need new syntax to be polymorphic over
+capturing types. The classic example is `map` over lists:
+```scala
+trait List[+A]:
+  // Works for pure functions AND capturing functions!
+  def map[B](f: A => B): List[B]
+```
+Due to the conventions established in previous sections, `f: A => B` translates to `f: A ->{cap} B`
+under capture checking which means that the function argument `f` can capture any capability, i.e.,
+`map` will have `f`'s effects, if we think of capabilities as the only means to induce side effects,
+then _capability polymorphism equals effect polymorphism_. By careful choice of notation and the
+[capture tunneling](classes.md#capture-tunneling) mechanism for generic types, we get effect
+polymorphism _for free_, and no signature changes are necessary on an eager collection type
+such as `List`.
+
+Contrasting this against lazy collections such as `LzyList` from the [previous section](classes.md),
+the implicit capability polymorphism induces an additional capture set on the result of `map`:
+```scala
+extension [A](xs: LzyList[A]^)
+  def map[B](f: A => B): LzyList[B]^{xs, f}
+```
+Unlike the eager version which only uses `f` during the computation, the lazy counterpart delays the
+computation, so that the original list and the function are captured by the result.
+This relationship can be succinctly expressed due to the path-dependent result capture set
+`{xs, f}` and would be rather cumbersome to express in more traditional effect-type systems
+with explicit generic effect parameters.
+
+### Explicit Polymorphism
+
+In some situations, it is convenient or necessary to parameterize definitions by a capture set.
+This allows an API to state precisely which capabilities its clients may use. Consider a `Source`
+that stores `Listeners`:
 ```scala
 class Source[X^]:
   private var listeners: Set[Listener^{X}] = Set.empty
@@ -16,77 +52,128 @@ class Source[X^]:
 
   def allListeners: Set[Listener^{X}] = listeners
 ```
-The type variable `X^` can be instantiated with a set of capabilities. It can occur in capture sets in its scope. For instance, in the example above
-we see a variable `listeners` that has as type a `Set` of `Listeners` capturing `X`. The `register` method takes a listener of this type
-and assigns it to the variable.
+Here, `X^` is a _capture-set variable_. It may appear inside capture sets throughout the class body.
+The field listeners holds exactly the listeners that capture X, and register only accepts such
+listeners.
 
 Capture-set variables `X^` without user-annotated bounds by default range over the interval `>: {} <: {caps.cap}` which is the universe of capture sets instead of regular types.
 
-Under the hood, such capture-set variables are represented as regular type variables within the special interval
- `>: CapSet <: CapSet^`.
-For instance, `Source` from above could be equivalently
-defined as follows:
+#### Under the hood
+
+Capture-set variables without user-provided bounds range over the interval
+ `>: {} <: {caps.cap}` which is the full lattice of capture sets. They behave like type parameters
+ whose domain is "all capture sets", not all types.
+
+Under the hood, a capture-set variable is implemented as a normal type parameter with special bounds:
 ```scala
 class Source[X >: CapSet <: CapSet^]:
   ...
 ```
-`CapSet` is a sealed trait in the `caps` object. It cannot be instantiated or inherited, so its only
-purpose is to identify type variables which are capture sets. In non-capture-checked
-usage contexts, the type system will treat `CapSet^{a}` and `CapSet^{a,b}` as the type `CapSet`, whereas
-with capture checking enabled, it will take the annotated capture sets into account,
-so that `CapSet^{a}` and `CapSet^{a,b}` are distinct.
-This representation based on `CapSet` is subject to change and
-its direct use is discouraged.
-
-Capture-set variables can be inferred like regular type variables. When they should be instantiated
-explicitly one supplies a concrete capture set. For instance:
+`CapSet` is a sealed marker trait in `caps` used internally to distinguish capture-set variables.
+It cannot be instantiated or extended; in non–capture-checked code, `CapSet^{a}` and `CapSet^{a,b}`
+erase to plain `CapSet`, while with capture checking enabled their capture sets remain distinct.
+This representation is an implementation detail and should not be used directly.
+
+#### Instantiation and inference
+Capture-set variables are inferred in the same way as ordinary type variables.
+They can also be instantiated explicitly:
 ```scala
 class Async extends caps.SharedCapability
 
-def listener(async: Async): Listener^{async} = ???
+def listener(a: Async): Listener^{a} = ???
 
-def test1(async1: Async, others: List[Async]) =
-  val src = Source[{async1, others*}]
-  ...
-```
-Here, `src` is created as a `Source` on which listeners can be registered that refer to the `async` capability or to any of the capabilities in list `others`. So we can continue the example code above as follows:
-```scala
+def test1[X^](async1: Async, others: List[Async^{X}]) =
+  val src = Source[{async1, X}]
   src.register(listener(async1))
   others.map(listener).foreach(src.register)
-  val ls: Set[Listener^{async, others*}] = src.allListeners
+  val ls: Set[Listener^{async1, X}] = src.allListeners
+```
+Here, `src` accepts listeners that may capture either the specific capability `async1` or any element of
+others. The resulting `allListeners` method reflects this relationship.
+
+#### Transforming collections
+A typical use of explicit capture parameters arises when transforming collections of capturing
+values—such as `Future`s. In these cases, the API must guarantee that whatever capabilities are
+captured by the elements of the input collection are also captured by the elements of the output.
+
+The following example takes an unordered `Set` of futures and produces a `Stream` that yields their
+results in the order in which the futures complete. Using an explicit capture variable `C^`, the
+signature expresses that the cumulative capture set of the input futures is preserved in the
+resulting stream:
+```scala
+def collect[T, C^](fs: Set[Future[T]]^{C})(using Async^): Stream[Future[T]^{C}] =
+  val channel = Channel()
+  fs.forEach.(_.onComplete(v => channel.send(v)))
+  Stream.of(channel)
 ```
-A common use-case for explicit capture parameters is describing changes to the captures of mutable fields, such as concatenating
-effectful iterators:
+
+#### Tracking the evolution of mutable objects
+A common use case for explicit capture parameters is when a mutable object’s reachable capabilities
+_grow_ due to mutation. For example, concatenating effectful iterators:
 ```scala
 class ConcatIterator[A, C^](var iterators: mutable.List[IterableOnce[A]^{C}]):
   def concat(it: IterableOnce[A]^): ConcatIterator[A, {C, it}]^{this, it} =
     iterators ++= it                             //            ^
     this                                         // track contents of `it` in the result
 ```
-In such a scenario, we also should ensure that any pre-existing alias of a `ConcatIterator` object should become
-inaccessible after invoking its `concat` method. This is achieved with [mutation and separation tracking](separation-checking.md) which are currently in development.
+In such cases, the type system must ensure that any existing aliases of the iterator become invalid
+after mutation. This is handled by [mutation tracking](mutability.md) and [separation tracking](separation-checking.md), which are currently under development.
+
+## Shall I Be Implicit or Explicit?
+
+Implicit capability polymorphism is intended to cover the most common use cases.
+It integrates smoothly with existing functional programming idioms and was expressive enough to
+retrofit the Scala standard collections library to capture checking with minimal changes.
+
+Explicit capability polymorphism is introduced only when the capture relationships of an API must be
+stated directly in its signature. At this point, we have seen several examples where doing so improves
+clarity: naming a capture set explicitly, preserving the captures of a collection, or describing how
+mutation changes the captures of an object.
+
+The drawback of explicit polymorphism is additional syntactic overhead. Capture parameters can make
+signatures more verbose, especially in APIs that combine several related capture sets.
+
+**Recommendation:** Prefer implicit polymorphism by default.
+Introduce explicit capture parameters only when the intended capture relationships cannot be expressed
+implicitly or would otherwise be unclear.
 
 ## Capability Members
 
-Just as parametrization by types can be equally expressed with type members, we could
-also define the `Source[X^]` class above using a _capability member_:
+Capture parameters can also be introduced as *capability members*, in the same way that type
+parameters can be replaced with type members. The earlier example
+```scala
+class Source[X^]:
+  private var listeners: Set[Listener^{X}] = Set.empty
+```
+can be written instead as:
 ```scala
 class Source:
   type X^
   private var listeners: Set[Listener^{this.X}] = Set.empty
-  ... // as before
+
+  def register(l: Listener^{this.X]): Unit =
+    listeners += l
+
+  def allListeners: Set[Listener^{this.X}] = listeners
 ```
-Here, we can refer to capability members using paths in capture sets (such as `{this.X}`). Similarly to type members,
-capability members can be upper- and lower-bounded with capture sets:
-```scala
-trait Thread:
-  type Cap^
-  def run(block: () ->{this.Cap} -> Unit): Unit
+A capability member behaves like a path-dependent capture-set variable. It may appear in capture
+annotations using paths such as `{this.X}`.
 
-trait GPUThread extends Thread:
-  type Cap^ >: {cudaMalloc, cudaFree} <: {caps.cap}
+Capability members can also have capture-set bounds, restricting which capabilities they may contain:
+```scala
+trait Reactor:
+  type Cap^ <: {caps.cap}
+  def onEvent(h: Event ->{this.Cap} Unit): Unit
+```
+Each implementation of Reactor may refine `Cap^` to a more specific capture set:
+```scala
+trait GUIReactor extends Reactor:
+  type Cap^ <: {ui, log}
 ```
-Since `caps.cap` is the top element for subcapturing, we could have also left out the
-upper bound: `type Cap^ >: {cudaMalloc, cudaFree}`.
+Here, `GUIReactor` specifies that event handlers may capture only `ui`, `log`, or a subset thereof.
+The `onEvent` method expresses this via the path-dependent capture set `{this.Cap}`.
+
+Capability members are useful when capture information should be tied to object identity or form part
+of an abstract interface, instead of being expressed through explicit capture parameters.
 
-**Advanced uses:** We discuss more advanced uses cases for capability members [here](advanced.md).
+**Advanced uses:** We discuss more advanced use cases for capability members [here](advanced.md).