Add Tracer#propagate

core/trace/src/main/scala/org/typelevel/otel4s/trace/Tracer.scala

@@ -170,6 +170,20 @@ trait Tracer[F[_]] extends TracerMacro[F] {
     */
   def noopScope[A](fa: F[A]): F[A]
 
+  /** Propagates this tracer's context into an immutable carrier.
+    *
+    * @param carrier
+    *   the immutable carrier to append the context to
+    * @tparam C
+    *   the type of the carrier
+    * @return
+    *   a copy of the immutable carrier with this tracer's context appended to
+    *   it
+    * @see
+    *   [[org.typelevel.otel4s.TextMapPropagator.injected TextMapPropagator#injected]]
+    */
+  def propagate[C: TextMapUpdater](carrier: C): F[C]
+
 }
 
 object Tracer {
@@ -207,6 +221,8 @@ object Tracer {
       def childScope[A](parent: SpanContext)(fa: F[A]): F[A] = fa
       def spanBuilder(name: String): SpanBuilder[F] = builder
       def joinOrRoot[A, C: TextMapGetter](carrier: C)(fa: F[A]): F[A] = fa
+      def propagate[C: TextMapUpdater](carrier: C): F[C] =
+        Applicative[F].pure(carrier)
     }
 
   object Implicits {

java/trace/src/main/scala/org/typelevel/otel4s/java/trace/TracerBuilderImpl.scala

@@ -19,9 +19,10 @@ package org.typelevel.otel4s.java.trace
 import cats.effect.Sync
 import io.opentelemetry.api.trace.{TracerProvider => JTracerProvider}
 import org.typelevel.otel4s.ContextPropagators
+import org.typelevel.otel4s.context.AskVault
 import org.typelevel.otel4s.trace._
 
-private[java] final case class TracerBuilderImpl[F[_]: Sync](
+private[java] final case class TracerBuilderImpl[F[_]: Sync: AskVault](
     jTracerProvider: JTracerProvider,
     propagators: ContextPropagators[F],
     scope: TraceScope[F],

java/trace/src/main/scala/org/typelevel/otel4s/java/trace/TracerImpl.scala

@@ -17,18 +17,21 @@
 package org.typelevel.otel4s.java.trace
 
 import cats.effect.Sync
+import cats.mtl.Ask
 import cats.syntax.flatMap._
 import cats.syntax.functor._
 import io.opentelemetry.api.trace.{Span => JSpan}
 import io.opentelemetry.api.trace.{Tracer => JTracer}
 import org.typelevel.otel4s.ContextPropagators
 import org.typelevel.otel4s.TextMapGetter
+import org.typelevel.otel4s.TextMapUpdater
+import org.typelevel.otel4s.context.AskVault
 import org.typelevel.otel4s.trace.SpanBuilder
 import org.typelevel.otel4s.trace.SpanContext
 import org.typelevel.otel4s.trace.Tracer
 import org.typelevel.vault.Vault
 
-private[java] class TracerImpl[F[_]: Sync](
+private[java] class TracerImpl[F[_]: Sync: AskVault](
     jTracer: JTracer,
     scope: TraceScope[F],
     propagators: ContextPropagators[F]
@@ -72,4 +75,7 @@ private[java] class TracerImpl[F[_]: Sync](
         rootScope(fa)
     }
   }
+
+  def propagate[C: TextMapUpdater](carrier: C): F[C] =
+    Ask[F, Vault].reader(propagators.textMapPropagator.injected(_, carrier))
 }

java/trace/src/main/scala/org/typelevel/otel4s/java/trace/TracerProviderImpl.scala

@@ -20,11 +20,12 @@ import cats.effect.Sync
 import cats.mtl.Local
 import io.opentelemetry.api.trace.{TracerProvider => JTracerProvider}
 import org.typelevel.otel4s.ContextPropagators
+import org.typelevel.otel4s.context.AskVault
 import org.typelevel.otel4s.trace.TracerBuilder
 import org.typelevel.otel4s.trace.TracerProvider
 import org.typelevel.vault.Vault
 
-private[java] class TracerProviderImpl[F[_]: Sync](
+private[java] class TracerProviderImpl[F[_]: Sync: AskVault](
     jTracerProvider: JTracerProvider,
     propagators: ContextPropagators[F],
     scope: TraceScope[F]

java/trace/src/test/scala/org/typelevel/otel4s/java/trace/TracerSuite.scala

@@ -144,6 +144,25 @@ class TracerSuite extends CatsEffectSuite {
     }
   }
 
+  test("propagate to an arbitrary carrier") {
+    TestControl.executeEmbed {
+      for {
+        sdk <- makeSdk()
+        tracer <- sdk.provider.get("tracer")
+        _ <- tracer.span("span").use { span =>
+          for {
+            carrier <- tracer.propagate(Map("key" -> "value"))
+          } yield {
+            assertEquals(carrier.get("key"), Some("value"))
+            val expected =
+              s"00-${span.context.traceIdHex}-${span.context.spanIdHex}-01"
+            assertEquals(carrier.get("traceparent"), Some(expected))
+          }
+        }
+      } yield ()
+    }
+  }
+
   test("automatically start and stop span") {
     val sleepDuration = 500.millis