diff --git a/compiler/src/dotty/tools/dotc/reporting/ErrorMessageID.scala b/compiler/src/dotty/tools/dotc/reporting/ErrorMessageID.scala
index 2fba7ef447b5..518be160763e 100644
--- a/compiler/src/dotty/tools/dotc/reporting/ErrorMessageID.scala
+++ b/compiler/src/dotty/tools/dotc/reporting/ErrorMessageID.scala
@@ -172,7 +172,8 @@ enum ErrorMessageID extends java.lang.Enum[ErrorMessageID] {
     AlreadyDefinedID,
     CaseClassInInlinedCodeID,
     OverrideTypeMismatchErrorID,
-    OverrideErrorID
+    OverrideErrorID,
+    MatchableWarningID
 
   def errorNumber = ordinal - 2
 }
diff --git a/compiler/src/dotty/tools/dotc/reporting/messages.scala b/compiler/src/dotty/tools/dotc/reporting/messages.scala
index 2d9d75b24f56..eb3e2b22781c 100644
--- a/compiler/src/dotty/tools/dotc/reporting/messages.scala
+++ b/compiler/src/dotty/tools/dotc/reporting/messages.scala
@@ -838,6 +838,32 @@ import transform.SymUtils._
     def explain = ""
   }
 
+  class MatchableWarning(tp: Type, pattern: Boolean)(using Context)
+  extends TypeMsg(MatchableWarningID) {
+    def msg =
+      val kind = if pattern then "pattern selector" else "value"
+      em"""${kind} should be an instance of Matchable,,
+          |but it has unmatchable type $tp instead"""
+
+    def explain =
+      if pattern then
+        em"""A value of type $tp cannot be the selector of a match expression
+            |since it is not constrained to be `Matchable`. Matching on unconstrained
+            |values is disallowed since it can uncover implementation details that
+            |were intended to be hidden and thereby can violate paramtetricity laws
+            |for reasoning about programs.
+            |
+            |The restriction can be overridden by appending `.asMatchable` to
+            |the selector value. `asMatchable` needs to be imported from
+            |scala.compiletime. Example:
+            |
+            |    import compiletime.asMatchable
+            |    def f[X](x: X) = x.asMatchable match { ... }"""
+      else
+        em"""The value can be converted to a `Matchable` by appending `.asMatchable`.
+            |`asMatchable` needs to be imported from scala.compiletime."""
+  }
+
   class SeqWildcardPatternPos()(using Context)
   extends SyntaxMsg(SeqWildcardPatternPosID) {
     def msg = em"""${hl("*")} can be used only for last argument"""
diff --git a/compiler/src/dotty/tools/dotc/typer/Checking.scala b/compiler/src/dotty/tools/dotc/typer/Checking.scala
index 2c9d48537f09..cd0effedafcd 100644
--- a/compiler/src/dotty/tools/dotc/typer/Checking.scala
+++ b/compiler/src/dotty/tools/dotc/typer/Checking.scala
@@ -1280,9 +1280,7 @@ trait Checking {
   def checkMatchable(tp: Type, pos: SrcPos, pattern: Boolean)(using Context): Unit =
     if !tp.derivesFrom(defn.MatchableClass) && sourceVersion.isAtLeast(`future-migration`) then
       val kind = if pattern then "pattern selector" else "value"
-      report.warning(
-        em"""${kind} should be an instance of Matchable,
-            |but it has unmatchable type $tp instead""", pos)
+      report.warning(MatchableWarning(tp, pattern), pos)
 }
 
 trait ReChecking extends Checking {
diff --git a/library/src/scala/compiletime/package.scala b/library/src/scala/compiletime/package.scala
index 080ef29e0fa2..84ac4fde4e29 100644
--- a/library/src/scala/compiletime/package.scala
+++ b/library/src/scala/compiletime/package.scala
@@ -158,3 +158,14 @@ end summonAll
 
 /** Assertion that an argument is by-name. Used for nullability checking. */
 def byName[T](x: => T): T = x
+
+/** Casts a value to be `Matchable`. This is needed if the value's type is an unconstrained
+  *  type parameter and the value is the scrutinee of a match expression.
+  *  This is normally disallowed since it violates parametricity and allows
+  *  to uncover implementation details that were intended to be hidden.
+  *  The `asMatchable` escape hatch should be used sparingly. It's usually
+  *  better to constrain the scrutinee type to be `Matchable` in the first place.
+  */
+extension [T](x: T)
+  transparent inline def asMatchable: x.type & Matchable = x.asInstanceOf[x.type & Matchable]
+
diff --git a/tests/neg-custom-args/fatal-warnings/i10930.scala b/tests/neg-custom-args/fatal-warnings/i10930.scala
new file mode 100644
index 000000000000..d1fbdde10574
--- /dev/null
+++ b/tests/neg-custom-args/fatal-warnings/i10930.scala
@@ -0,0 +1,13 @@
+import language.future
+@main def Test =
+  type LeafElem[X] = X match
+    case String => Char
+    case Array[t] => LeafElem[t]
+    case Iterable[t] => LeafElem[t]
+    case AnyVal => X
+
+  def leafElem[X](x: X): LeafElem[X] = x match
+    case x: String      => x.charAt(0)       // error
+    case x: Array[t]    => leafElem(x(1))    // error
+    case x: Iterable[t] => leafElem(x.head)  // error
+    case x: AnyVal      => x                 // error
diff --git a/tests/run/i10930.scala b/tests/run/i10930.scala
new file mode 100644
index 000000000000..87aaf148417c
--- /dev/null
+++ b/tests/run/i10930.scala
@@ -0,0 +1,33 @@
+import language.future
+import compiletime.asMatchable
+
+@main def Test =
+  type LeafElem[X] = X match
+    case String => Char
+    case Array[t] => LeafElem[t]
+    case Iterable[t] => LeafElem[t]
+    case AnyVal => X
+
+  def leafElem[X](x: X): LeafElem[X] = x.asMatchable match
+    case x: String      => x.charAt(0)
+    case x: Array[t]    => leafElem(x(1))
+    case x: Iterable[t] => leafElem(x.head)
+    case x: AnyVal      => x
+
+  def f[X](x: X) = x
+
+  def leafElem2[X](x: X): LeafElem[X] = f(x).asMatchable match
+    case x: String      => x.charAt(0)
+    case x: Array[t]    => leafElem(x(1))
+    case x: Iterable[t] => leafElem(x.head)
+    case x: AnyVal      => x
+
+  val x1: Char = leafElem("a")
+  assert(x1 == 'a')
+  val x2: Char = leafElem(Array("a", "b"))
+  assert(x2 == 'b')
+  val x3: Char = leafElem(List(Array("a", "b"), Array("")))
+  assert(x3 == 'b')
+  val x4: Int = leafElem(3)
+  assert(x4 == 3)
+