diff --git a/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/AbstractComposableFunctionRegistry.java b/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/AbstractComposableFunctionRegistry.java
index 784935aa7..84e8bd38e 100644
--- a/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/AbstractComposableFunctionRegistry.java
+++ b/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/AbstractComposableFunctionRegistry.java
@@ -310,17 +310,14 @@ public abstract class AbstractComposableFunctionRegistry implements FunctionRegi
 			else {
 				String[] stages = StringUtils.delimitedListToStringArray(name, "|");
 				if (Stream.of(stages).allMatch(funcName -> contains(funcName))) {
-					List<Object> composableFunctions = Stream.of(stages)
+					List<FunctionRegistration<?>> composableFunctions = Stream.of(stages)
 							.map(funcName -> find(funcName)).collect(Collectors.toList());
-					composedFunction = composableFunctions.stream()
-							.reduce((a, z) -> composeFunctions(a, z))
+					FunctionRegistration<?> composedRegistration = composableFunctions
+							.stream().reduce((a, z) -> composeFunctions(a, z))
 							.orElseGet(() -> null);
-					if (composedFunction != null && !this.types.containsKey(name)
-							&& this.types.containsKey(stages[0])
-							&& this.types.containsKey(stages[stages.length - 1])) {
-						FunctionType input = this.types.get(stages[0]);
-						FunctionType output = this.types.get(stages[stages.length - 1]);
-						this.addType(name, FunctionType.compose(input, output));
+					composedFunction = composedRegistration.getTarget();
+					if (composedFunction != null && !this.types.containsKey(name)) {
+						this.addType(name, composedRegistration.getType());
 						this.addName(composedFunction, name);
 						if (composedFunction instanceof Function) {
 							this.addFunction(name, (Function<?, ?>) composedFunction);
@@ -347,7 +344,7 @@ public abstract class AbstractComposableFunctionRegistry implements FunctionRegi
 				|| getConsumerNames().contains(name);
 	}
 
-	private Object find(String name) {
+	private FunctionRegistration<?> find(String name) {
 		Object result = this.suppliers.get(name);
 		if (result == null) {
 			result = this.functions.get(name);
@@ -355,17 +352,23 @@ public abstract class AbstractComposableFunctionRegistry implements FunctionRegi
 		if (result == null) {
 			result = this.consumers.get(name);
 		}
-		return result;
+		return getRegistration(result);
 	}
 
 	@SuppressWarnings("unchecked")
-	private Object composeFunctions(Object a, Object b) {
+	private FunctionRegistration<?> composeFunctions(FunctionRegistration<?> aReg,
+			FunctionRegistration<?> bReg) {
+		FunctionType aType = aReg.getType();
+		FunctionType bType = bReg.getType();
+		Object a = aReg.getTarget();
+		Object b = bReg.getTarget();
+		Object composedFunction = null;
 		if (a instanceof Supplier && b instanceof Function) {
 			Supplier<Flux<Object>> supplier = (Supplier<Flux<Object>>) a;
 			if (b instanceof FluxConsumer) {
 				if (supplier instanceof FluxSupplier) {
 					FluxConsumer<Object> fConsumer = ((FluxConsumer<Object>) b);
-					return (Supplier<Mono<Void>>) () -> Mono.from(
+					composedFunction = (Supplier<Mono<Void>>) () -> Mono.from(
 							supplier.get().compose(v -> fConsumer.apply(supplier.get())));
 				}
 				else {
@@ -376,7 +379,8 @@ public abstract class AbstractComposableFunctionRegistry implements FunctionRegi
 			}
 			else {
 				Function<Object, Object> function = (Function<Object, Object>) b;
-				return (Supplier<Object>) () -> function.apply(supplier.get());
+				composedFunction = (Supplier<Object>) () -> function
+						.apply(supplier.get());
 			}
 		}
 		else if (a instanceof Function && b instanceof Function) {
@@ -384,7 +388,7 @@ public abstract class AbstractComposableFunctionRegistry implements FunctionRegi
 			Function<Object, Object> function2 = (Function<Object, Object>) b;
 			if (function1 instanceof FluxToMonoFunction) {
 				if (function2 instanceof MonoToFluxFunction) {
-					return function1.andThen(function2);
+					composedFunction = function1.andThen(function2);
 				}
 				else {
 					throw new IllegalStateException(
@@ -393,23 +397,27 @@ public abstract class AbstractComposableFunctionRegistry implements FunctionRegi
 				}
 			}
 			else if (function2 instanceof FluxToMonoFunction) {
-				return new FluxToMonoFunction<Object, Object>(
+				composedFunction = new FluxToMonoFunction<Object, Object>(
 						((Function<Flux<Object>, Flux<Object>>) a).andThen(
 								((FluxToMonoFunction<Object, Object>) b).getTarget()));
 			}
 			else {
-				return function1.andThen(function2);
+				composedFunction = function1.andThen(function2);
 			}
 		}
 		else if (a instanceof Function && b instanceof Consumer) {
 			Function<Object, Object> function = (Function<Object, Object>) a;
 			Consumer<Object> consumer = (Consumer<Object>) b;
-			return (Consumer<Object>) v -> consumer.accept(function.apply(v));
+			composedFunction = (Consumer<Object>) v -> consumer.accept(function.apply(v));
 		}
 		else {
 			throw new IllegalArgumentException(String
 					.format("Could not compose %s and %s", a.getClass(), b.getClass()));
 		}
+		String name = aReg.getNames().iterator().next() + "|"
+				+ bReg.getNames().iterator().next();
+		return new FunctionRegistration<>(composedFunction, name)
+				.type(FunctionType.compose(aType, bType));
 	}
 
 	@SuppressWarnings("unchecked")