diff --git a/compiler/src/dotty/tools/dotc/core/Periods.scala b/compiler/src/dotty/tools/dotc/core/Periods.scala
index 019c5932b3c9..60226eb59fe0 100644
--- a/compiler/src/dotty/tools/dotc/core/Periods.scala
+++ b/compiler/src/dotty/tools/dotc/core/Periods.scala
@@ -1,6 +1,10 @@
-package dotty.tools.dotc.core
+package dotty.tools
+package dotc
+package core
 
 import Contexts.*
+import printing.*
+import Texts.*
 import Phases.unfusedPhases
 
 object Periods {
@@ -35,7 +39,7 @@ object Periods {
    *
    *     // Dmitry: sign == 0 isn't actually always true, in some cases phaseId == -1 is used for shifts, that easily creates code < 0
    */
-  class Period(val code: Int) extends AnyVal {
+  class Period(val code: Int) extends AnyVal with Showable {
 
     /** The run identifier of this period. */
     def runId: RunId = code >>> (PhaseWidth * 2)
@@ -97,7 +101,25 @@ object Periods {
           this.firstPhaseId min that.firstPhaseId,
           this.lastPhaseId max that.lastPhaseId)
 
-    override def toString: String = s"Period($firstPhaseId..$lastPhaseId, run = $runId)"
+    def toText(p: Printer): Text =
+      inContext(p.printerContext):
+        this match
+          case Nowhere                           => "Nowhere"
+          case InitialPeriod                     => "InitialPeriod"
+          case InvalidPeriod                     => "InvalidPeriod"
+          case Period(NoRunId, 0, PhaseMask)     => s"Period(NoRunId.all)"
+          case Period(runId, 0, PhaseMask)       => s"Period($runId.all)"
+          case Period(runId, p1, pn) if p1 == pn => s"Period($runId.$p1(${ctx.base.phases(p1)}))"
+          case Period(runId, p1, pn)             => s"Period($runId.$p1(${ctx.base.phases(p1)})-$pn(${ctx.base.phases(pn)}))"
+
+    override def toString: String = this match
+      case Nowhere                           => "Nowhere"
+      case InitialPeriod                     => "InitialPeriod"
+      case InvalidPeriod                     => "InvalidPeriod"
+      case Period(NoRunId, 0, PhaseMask)     => s"Period(NoRunId.all)"
+      case Period(runId, 0, PhaseMask)       => s"Period($runId.all)"
+      case Period(runId, p1, pn) if p1 == pn => s"Period($runId.$p1)"
+      case Period(runId, p1, pn)             => s"Period($runId.$p1-$pn)"
 
     def ==(that: Period): Boolean = this.code == that.code
     def !=(that: Period): Boolean = this.code != that.code
@@ -116,6 +138,17 @@ object Periods {
     /** The interval consisting of all periods of given run id */
     def allInRun(rid: RunId): Period =
       apply(rid, 0, PhaseMask)
+
+    def unapply(p: Period): Extractor = new Extractor(p.code)
+
+    final class Extractor(private val code: Int) extends AnyVal {
+      private def p = new Period(code)
+      def isEmpty: false = false
+      def get: this.type = this
+      def _1 = p.runId
+      def _2 = p.firstPhaseId
+      def _3 = p.lastPhaseId
+    }
   }
 
   inline val NowhereCode = 0
diff --git a/compiler/src/dotty/tools/dotc/printing/Formatting.scala b/compiler/src/dotty/tools/dotc/printing/Formatting.scala
index 02f470324e8a..ac13f0161c70 100644
--- a/compiler/src/dotty/tools/dotc/printing/Formatting.scala
+++ b/compiler/src/dotty/tools/dotc/printing/Formatting.scala
@@ -24,6 +24,17 @@ object Formatting {
     object Shown:
       given [A: Show]: Conversion[A, Shown] = Show[A].show(_)
 
+      extension (s: Shown)
+        def runCtxShow(using Context): Shown = s match
+          case cs: CtxShow => cs.run
+          case _           => s
+
+      def toStr(x: Shown)(using Context): String = x match
+        case seq: Seq[?] => seq.map(toStr).mkString("[", ", ", "]")
+        case res         => res.tryToShow
+
+    import Shown.runCtxShow
+
     sealed abstract class Show[-T]:
       /** Show a value T by returning a "shown" result. */
       def show(x: T): Shown
@@ -31,10 +42,9 @@ object Formatting {
     trait CtxShow:
       def run(using Context): Shown
 
-    extension (s: Shown)
-      def ctxShow(using Context): Shown = s match
-        case cs: CtxShow => cs.run
-        case _           => s
+    private inline def CtxShow(inline x: Context ?=> Shown) = new CtxShow { def run(using Context) = x(using ctx) }
+    private def toStr[A: Show](x: A)(using Context): String = Shown.toStr(toShown(x))
+    private def toShown[A: Show](x: A)(using Context): Shown = Show[A].show(x).runCtxShow
 
     /** The base implementation, passing the argument to StringFormatter which will try to `.show` it. */
     object ShowAny extends Show[Any]:
@@ -54,16 +64,26 @@ object Formatting {
     object Show extends ShowImplicits1:
       inline def apply[A](using inline z: Show[A]): Show[A] = z
 
+      given [X: Show]: Show[Option[X]] with
+        def show(x: Option[X]) =
+          CtxShow(x.map(toStr))
+      end given
+
       given [X: Show]: Show[Seq[X]] with
-        def show(x: Seq[X]) = new CtxShow:
-          def run(using Context) = x.map(show1)
+        def show(x: Seq[X]) = CtxShow(x.map(toStr))
+
+      given [K: Show, V: Show]: Show[Map[K, V]] with
+        def show(x: Map[K, V]) =
+          CtxShow(x.map((k, v) => s"${toStr(k)} => ${toStr(v)}"))
+      end given
 
       given [H: Show, T <: Tuple: Show]: Show[H *: T] with
-        def show(x: H *: T) = new CtxShow:
-          def run(using Context) = show1(x.head) *: Show[T].show(x.tail).ctxShow.asInstanceOf[Tuple]
+        def show(x: H *: T) =
+          CtxShow(toStr(x.head) *: toShown(x.tail).asInstanceOf[Tuple])
+      end given
 
       given [X: Show]: Show[X | Null] with
-        def show(x: X | Null) = if x == null then "null" else Show[X].show(x.nn)
+        def show(x: X | Null) = if x == null then "null" else CtxShow(toStr(x.nn))
 
       given Show[FlagSet] with
         def show(x: FlagSet) = x.flagsString
@@ -79,7 +99,13 @@ object Formatting {
           case ast.TreeInfo.Impure         => "PurityLevel.Impure"
           case ast.TreeInfo.PurePath       => "PurityLevel.PurePath"
           case ast.TreeInfo.IdempotentPath => "PurityLevel.IdempotentPath"
-          case _                           => s"PurityLevel(${x.x})"
+          case _                           => s"PurityLevel(${x.x.toBinaryString})"
+
+      given Show[Atoms] with
+        def show(x: Atoms) = x match
+          case Atoms.Unknown       => "Unknown"
+          case Atoms.Range(lo, hi) => CtxShow(s"Range(${toStr(lo.toList)}, ${toStr(hi.toList)})")
+      end given
 
       given Show[Showable]                            = ShowAny
       given Show[Shown]                               = ShowAny
@@ -101,11 +127,6 @@ object Formatting {
       given Show[util.Spans.Span]                     = ShowAny
       given Show[tasty.TreeUnpickler#OwnerTree]       = ShowAny
       given Show[typer.ForceDegree.Value]             = ShowAny
-
-      private def show1[A: Show](x: A)(using Context) = show2(Show[A].show(x).ctxShow)
-      private def show2(x: Shown)(using Context): String = x match
-        case seq: Seq[?] => seq.map(show2).mkString("[", ", ", "]")
-        case res         => res.tryToShow
     end Show
   end ShownDef
   export ShownDef.{ Show, Shown }
@@ -122,7 +143,7 @@ object Formatting {
   class StringFormatter(protected val sc: StringContext) {
     protected def showArg(arg: Any)(using Context): String = arg.tryToShow
 
-    private def treatArg(arg: Shown, suffix: String)(using Context): (String, String) = arg.ctxShow match {
+    private def treatArg(arg: Shown, suffix: String)(using Context): (String, String) = arg.runCtxShow match {
       case arg: Seq[?] if suffix.indexOf('%') == 0 && suffix.indexOf('%', 1) != -1 =>
         val end = suffix.indexOf('%', 1)
         val sep = StringContext.processEscapes(suffix.substring(1, end))
diff --git a/compiler/src/dotty/tools/dotc/transform/patmat/Space.scala b/compiler/src/dotty/tools/dotc/transform/patmat/Space.scala
index 9bf852084cfe..012f2affffc1 100644
--- a/compiler/src/dotty/tools/dotc/transform/patmat/Space.scala
+++ b/compiler/src/dotty/tools/dotc/transform/patmat/Space.scala
@@ -115,7 +115,7 @@ object SpaceEngine {
   def decompose(typ: Typ)(using Context): List[Typ]          = typ.decompose
 
   /** Simplify space such that a space equal to `Empty` becomes `Empty` */
-  def computeSimplify(space: Space)(using Context): Space = trace(s"simplify($space)")(space match {
+  def computeSimplify(space: Space)(using Context): Space = trace(i"simplify($space)")(space match {
     case Prod(tp, fun, spaces) =>
       val sps = spaces.mapconserve(simplify)
       if sps.contains(Empty) then Empty
@@ -166,7 +166,7 @@ object SpaceEngine {
   }
 
   /** Is `a` a subspace of `b`? Equivalent to `simplify(simplify(a) - simplify(b)) == Empty`, but faster */
-  def computeIsSubspace(a: Space, b: Space)(using Context): Boolean = trace(s"isSubspace($a, $b)") {
+  def computeIsSubspace(a: Space, b: Space)(using Context): Boolean = trace(i"isSubspace($a, $b)") {
     val a2 = simplify(a)
     val b2 = simplify(b)
     if (a ne a2) || (b ne b2) then isSubspace(a2, b2)
@@ -195,7 +195,7 @@ object SpaceEngine {
   }
 
   /** Intersection of two spaces  */
-  def intersect(a: Space, b: Space)(using Context): Space = trace(s"$a & $b") {
+  def intersect(a: Space, b: Space)(using Context): Space = trace(i"intersect($a & $b)") {
     (a, b) match {
       case (Empty, _) | (_, Empty) => Empty
       case (_, Or(ss)) => Or(ss.map(intersect(a, _)).filter(_ ne Empty))
@@ -220,7 +220,7 @@ object SpaceEngine {
   }
 
   /** The space of a not covered by b */
-  def minus(a: Space, b: Space)(using Context): Space = trace(s"$a - $b") {
+  def minus(a: Space, b: Space)(using Context): Space = trace(i"minus($a - $b)") {
     (a, b) match {
       case (Empty, _) => Empty
       case (_, Empty) => a