clarified signature;

--- a/src/Pure/PIDE/protocol_handlers.scala	Sat Jun 20 14:36:27 2020 +0200
+++ b/src/Pure/PIDE/protocol_handlers.scala	Sat Jun 20 15:09:20 2020 +0200
@@ -16,7 +16,7 @@
   sealed case class State(
     session: Session,
     handlers: Map[String, Session.Protocol_Handler] = Map.empty,
-    functions: Map[String, Prover.Protocol_Output => Boolean] = Map.empty)
+    functions: Map[String, Session.Protocol_Function] = Map.empty)
   {
     def get(name: String): Option[Session.Protocol_Handler] = handlers.get(name)
 

--- a/src/Pure/PIDE/session.scala	Sat Jun 20 14:36:27 2020 +0200
+++ b/src/Pure/PIDE/session.scala	Sat Jun 20 15:09:20 2020 +0200
@@ -111,11 +111,13 @@
 
   /* protocol handlers */
 
+  type Protocol_Function = Prover.Protocol_Output => Boolean
+
   abstract class Protocol_Handler
   {
     def init(session: Session): Unit = {}
     def exit(): Unit = {}
-    val functions: List[(String, Prover.Protocol_Output => Boolean)]
+    val functions: List[(String, Protocol_Function)]
   }
 }
 

--- a/src/Pure/Tools/build.scala	Sat Jun 20 14:36:27 2020 +0200
+++ b/src/Pure/Tools/build.scala	Sat Jun 20 15:09:20 2020 +0200
@@ -228,6 +228,18 @@
           val runtime_statistics = new mutable.ListBuffer[Properties.T]
           val task_statistics = new mutable.ListBuffer[Properties.T]
 
+          def fun(
+            name: String,
+            acc: mutable.ListBuffer[Properties.T],
+            unapply: Properties.T => Option[Properties.T]): (String, Session.Protocol_Function) =
+          {
+            name -> ((msg: Prover.Protocol_Output) =>
+              unapply(msg.properties) match {
+                case Some(props) => acc += props; true
+                case _ => false
+              })
+          }
+
           session.init_protocol_handler(new Session.Protocol_Handler
             {
               override def exit() { build_session_errors.cancel }
@@ -271,39 +283,15 @@
                   case _ => false
                 }
 
-              private def command_timing(msg: Prover.Protocol_Output): Boolean =
-                msg.properties match {
-                  case Markup.Command_Timing(props) => command_timings += props; true
-                  case _ => false
-                }
-
-              private def theory_timing(msg: Prover.Protocol_Output): Boolean =
-                msg.properties match {
-                  case Markup.Theory_Timing(props) => theory_timings += props; true
-                  case _ => false
-                }
-
-              private def ml_stats(msg: Prover.Protocol_Output): Boolean =
-                msg.properties match {
-                  case Markup.ML_Statistics(props) => runtime_statistics += props; true
-                  case _ => false
-                }
-
-              private def task_stats(msg: Prover.Protocol_Output): Boolean =
-                msg.properties match {
-                  case Markup.Task_Statistics(props) => task_statistics += props; true
-                  case _ => false
-                }
-
               val functions =
                 List(
                   Markup.Build_Session_Finished.name -> build_session_finished,
                   Markup.Loading_Theory.name -> loading_theory,
                   Markup.EXPORT -> export,
-                  Markup.Command_Timing.name -> command_timing,
-                  Markup.Theory_Timing.name -> theory_timing,
-                  Markup.ML_Statistics.name -> ml_stats,
-                  Markup.Task_Statistics.name -> task_stats)
+                  fun(Markup.Command_Timing.name, command_timings, Markup.Command_Timing.unapply),
+                  fun(Markup.Theory_Timing.name, theory_timings, Markup.Theory_Timing.unapply),
+                  fun(Markup.ML_Statistics.name, runtime_statistics, Markup.ML_Statistics.unapply),
+                  fun(Markup.Task_Statistics.name, task_statistics, Markup.Task_Statistics.unapply))
             })
 
           session.all_messages += Session.Consumer[Any]("build_session_output")