Re-order type discovery and function wrapping

Otherwise the explicit types from the function registration are
not used.

spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/FunctionRegistration.java

@@ -39,7 +39,7 @@ public class FunctionRegistration<T> {
 
 	private final Map<String, String> properties = new LinkedHashMap<>();
 
-	private Type type;
+	private FunctionType type;
 
 	public FunctionRegistration(T target) {
 		this.target = target;
@@ -53,7 +53,7 @@ public class FunctionRegistration<T> {
 		return names;
 	}
 
-	public Type getType() {
+	public FunctionType getType() {
 		return type;
 	}
 
@@ -79,7 +79,7 @@ public class FunctionRegistration<T> {
 	}
 
 	public FunctionRegistration<T> type(Type type) {
-		this.type = type;
+		this.type = FunctionType.of(type);
 		return this;
 	}
 

spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/FunctionType.java

@@ -45,6 +45,10 @@ public class FunctionType {
 		this.type = type;
 	}
 
+	public Type getType() {
+		return type;
+	}
+
 	public Class<?> getInputWrapper() {
 		return findType(ParamType.INPUT_WRAPPER);
 	}
@@ -79,6 +83,10 @@ public class FunctionType {
 				|| Mono.class.equals(type) || Optional.class.equals(type);
 	}
 
+	public static FunctionType of(Type function) {
+		return new FunctionType(function);
+	}
+
 	public static FunctionType from(Class<?> input) {
 		return new FunctionType(ResolvableType
 				.forClassWithGenerics(Function.class, input, Object.class).getType());

spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/config/ContextFunctionCatalogAutoConfiguration.java

@@ -439,10 +439,15 @@ public class ContextFunctionCatalogAutoConfiguration {
 		private void wrap(FunctionRegistration<Object> registration, String key) {
 			Object target = registration.getTarget();
 			this.registrations.put(target, key);
+			if (registration.getType() != null) {
+				this.types.put(key, registration.getType());
+			}
+			else {
+				findType(target);
+			}
 			Class<?> type;
 			if (target instanceof Supplier) {
 				type = Supplier.class;
-				findType(target);
 				registration.target(target((Supplier<?>) target, key));
 				for (String name : registration.getNames()) {
 					this.suppliers.put(name, registration.getTarget());
@@ -450,7 +455,6 @@ public class ContextFunctionCatalogAutoConfiguration {
 			}
 			else if (target instanceof Consumer) {
 				type = Consumer.class;
-				findType(target);
 				registration.target(target((Consumer<?>) target, key));
 				for (String name : registration.getNames()) {
 					this.consumers.put(name, registration.getTarget());
@@ -458,7 +462,6 @@ public class ContextFunctionCatalogAutoConfiguration {
 			}
 			else if (target instanceof Function) {
 				type = Function.class;
-				findType(target);
 				registration.target(target((Function<?, ?>) target, key));
 				for (String name : registration.getNames()) {
 					this.functions.put(name, registration.getTarget());
@@ -467,7 +470,7 @@ public class ContextFunctionCatalogAutoConfiguration {
 			else {
 				return;
 			}
-			registrations.remove(target);
+			this.registrations.remove(target);
 			this.registrations.put(registration.getTarget(), key);
 			if (publisher != null) {
 				publisher.publishEvent(new FunctionRegistrationEvent(