Copilot commented on code in PR #9560:
URL: https://github.com/apache/gravitino/pull/9560#discussion_r2694281834


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core/src/main/java/org/apache/gravitino/meta/FunctionEntity.java:
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@@ -0,0 +1,357 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *  http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.  See the License for the
+ * specific language governing permissions and limitations
+ * under the License.
+ */
+package org.apache.gravitino.meta;
+
+import com.google.common.collect.Maps;
+import java.util.Arrays;
+import java.util.Collections;
+import java.util.Map;
+import java.util.Objects;
+import lombok.ToString;
+import org.apache.gravitino.Auditable;
+import org.apache.gravitino.Entity;
+import org.apache.gravitino.Field;
+import org.apache.gravitino.HasIdentifier;
+import org.apache.gravitino.Namespace;
+import org.apache.gravitino.function.Function;
+import org.apache.gravitino.function.FunctionColumn;
+import org.apache.gravitino.function.FunctionDefinition;
+import org.apache.gravitino.function.FunctionType;
+import org.apache.gravitino.rel.types.Type;
+
+/**
+ * A class representing a function entity in the metadata store.
+ *
+ * <p>This entity stores both the function metadata and its version 
information together, avoiding
+ * the need for separate FunctionEntity and FunctionVersionEntity. When 
retrieving, if version is
+ * set to the special value {@link #LATEST_VERSION}, the store should return 
the latest version.
+ */
+@ToString
+public class FunctionEntity implements Entity, Auditable, HasIdentifier, 
Function {
+
+  /** Special version value indicating the latest version should be retrieved. 
*/
+  public static final int LATEST_VERSION = -1;
+
+  public static final Field ID =
+      Field.required("id", Long.class, "The unique id of the function 
entity.");
+  public static final Field NAME =
+      Field.required("name", String.class, "The name of the function entity.");
+  public static final Field COMMENT =
+      Field.optional("comment", String.class, "The comment or description of 
the function entity.");
+  public static final Field FUNCTION_TYPE =
+      Field.required("function_type", FunctionType.class, "The type of the 
function.");
+  public static final Field DETERMINISTIC =
+      Field.required("deterministic", Boolean.class, "Whether the function is 
deterministic.");
+  public static final Field RETURN_TYPE =
+      Field.optional(
+          "return_type", Type.class, "The return type for scalar or aggregate 
functions.");
+  public static final Field RETURN_COLUMNS =
+      Field.optional(
+          "return_columns",
+          FunctionColumn[].class,
+          "The output columns for table-valued functions.");
+  public static final Field DEFINITIONS =
+      Field.required("definitions", FunctionDefinition[].class, "The 
definitions of the function.");
+  public static final Field VERSION =
+      Field.required("version", Integer.class, "The version of the function 
entity.");
+  public static final Field AUDIT_INFO =
+      Field.required("audit_info", AuditInfo.class, "The audit details of the 
function entity.");
+
+  private Long id;
+  private String name;
+  private Namespace namespace;
+  private String comment;
+  private FunctionType functionType;
+  private boolean deterministic;
+  private Type returnType;
+  private FunctionColumn[] returnColumns;
+  private FunctionDefinition[] definitions;
+  private Integer version;
+  private AuditInfo auditInfo;
+
+  private FunctionEntity() {}
+
+  @Override
+  public Map<Field, Object> fields() {
+    Map<Field, Object> fields = Maps.newHashMap();
+    fields.put(ID, id);
+    fields.put(NAME, name);
+    fields.put(COMMENT, comment);
+    fields.put(FUNCTION_TYPE, functionType);
+    fields.put(DETERMINISTIC, deterministic);
+    fields.put(RETURN_TYPE, returnType);
+    fields.put(RETURN_COLUMNS, returnColumns);
+    fields.put(DEFINITIONS, definitions);
+    fields.put(VERSION, version);
+    fields.put(AUDIT_INFO, auditInfo);
+
+    return Collections.unmodifiableMap(fields);
+  }
+
+  @Override
+  public String name() {
+    return name;
+  }
+
+  @Override
+  public Long id() {
+    return id;
+  }
+
+  @Override
+  public Namespace namespace() {
+    return namespace;
+  }
+
+  @Override
+  public String comment() {
+    return comment;
+  }
+
+  @Override
+  public FunctionType functionType() {
+    return functionType;
+  }
+
+  @Override
+  public boolean deterministic() {
+    return deterministic;
+  }
+
+  @Override
+  public Type returnType() {
+    return returnType;
+  }
+
+  @Override
+  public FunctionColumn[] returnColumns() {
+    return returnColumns != null ? returnColumns : new FunctionColumn[0];
+  }
+
+  @Override
+  public FunctionDefinition[] definitions() {
+    return definitions;
+  }
+
+  @Override
+  public int version() {
+    return version;
+  }
+
+  @Override
+  public AuditInfo auditInfo() {
+    return auditInfo;
+  }
+
+  @Override
+  public EntityType type() {
+    return EntityType.FUNCTION;
+  }
+
+  @Override
+  public boolean equals(Object o) {
+    if (this == o) {
+      return true;
+    }
+
+    if (!(o instanceof FunctionEntity)) {
+      return false;
+    }
+
+    FunctionEntity that = (FunctionEntity) o;
+    return Objects.equals(id, that.id)
+        && Objects.equals(name, that.name)
+        && Objects.equals(namespace, that.namespace)
+        && Objects.equals(comment, that.comment)
+        && functionType == that.functionType
+        && deterministic == that.deterministic
+        && Objects.equals(returnType, that.returnType)
+        && Arrays.equals(returnColumns, that.returnColumns)
+        && Arrays.equals(definitions, that.definitions)
+        && Objects.equals(version, that.version)
+        && Objects.equals(auditInfo, that.auditInfo);
+  }
+
+  @Override
+  public int hashCode() {
+    int result =
+        Objects.hash(
+            id,
+            name,
+            namespace,
+            comment,
+            functionType,
+            deterministic,
+            returnType,
+            version,
+            auditInfo);
+    result = 31 * result + Arrays.hashCode(returnColumns);
+    result = 31 * result + Arrays.hashCode(definitions);
+    return result;
+  }
+
+  /**
+   * Creates a new builder for constructing a FunctionEntity.
+   *
+   * @return A new builder instance.
+   */
+  public static Builder builder() {
+    return new Builder();
+  }
+
+  /** Builder class for creating instances of {@link FunctionEntity}. */
+  public static class Builder {
+    private final FunctionEntity functionEntity;
+
+    private Builder() {
+      functionEntity = new FunctionEntity();
+    }
+
+    /**
+     * Sets the unique id of the function entity.
+     *
+     * @param id The unique id.
+     * @return This builder instance.
+     */
+    public Builder withId(Long id) {
+      functionEntity.id = id;
+      return this;
+    }
+
+    /**
+     * Sets the name of the function entity.
+     *
+     * @param name The name of the function.
+     * @return This builder instance.
+     */
+    public Builder withName(String name) {
+      functionEntity.name = name;
+      return this;
+    }
+
+    /**
+     * Sets the namespace of the function entity.
+     *
+     * @param namespace The namespace.
+     * @return This builder instance.
+     */
+    public Builder withNamespace(Namespace namespace) {
+      functionEntity.namespace = namespace;
+      return this;
+    }
+
+    /**
+     * Sets the comment of the function entity.
+     *
+     * @param comment The comment or description.
+     * @return This builder instance.
+     */
+    public Builder withComment(String comment) {
+      functionEntity.comment = comment;
+      return this;
+    }
+
+    /**
+     * Sets the function type.
+     *
+     * @param functionType The type of the function (SCALAR, AGGREGATE, or 
TABLE).
+     * @return This builder instance.
+     */
+    public Builder withFunctionType(FunctionType functionType) {
+      functionEntity.functionType = functionType;
+      return this;
+    }
+
+    /**
+     * Sets whether the function is deterministic.
+     *
+     * @param deterministic True if the function is deterministic, false 
otherwise.
+     * @return This builder instance.
+     */
+    public Builder withDeterministic(boolean deterministic) {
+      functionEntity.deterministic = deterministic;
+      return this;
+    }
+
+    /**
+     * Sets the return type for scalar or aggregate functions.
+     *
+     * @param returnType The return type.
+     * @return This builder instance.
+     */
+    public Builder withReturnType(Type returnType) {
+      functionEntity.returnType = returnType;
+      return this;
+    }
+
+    /**
+     * Sets the return columns for table-valued functions.
+     *
+     * @param returnColumns The output columns.
+     * @return This builder instance.
+     */
+    public Builder withReturnColumns(FunctionColumn[] returnColumns) {
+      functionEntity.returnColumns = returnColumns;
+      return this;
+    }
+
+    /**
+     * Sets the function definitions.
+     *
+     * @param definitions The definitions (overloads) of the function.
+     * @return This builder instance.
+     */
+    public Builder withDefinitions(FunctionDefinition[] definitions) {
+      functionEntity.definitions = definitions;
+      return this;
+    }
+
+    /**
+     * Sets the version of the function entity.
+     *
+     * @param version The version number.
+     * @return This builder instance.
+     */
+    public Builder withVersion(Integer version) {
+      functionEntity.version = version;
+      return this;
+    }
+
+    /**
+     * Sets the audit information.
+     *
+     * @param auditInfo The audit information.
+     * @return This builder instance.
+     */
+    public Builder withAuditInfo(AuditInfo auditInfo) {
+      functionEntity.auditInfo = auditInfo;
+      return this;
+    }
+
+    /**
+     * Builds the FunctionEntity instance.
+     *
+     * @return The constructed FunctionEntity.
+     */
+    public FunctionEntity build() {
+      functionEntity.validate();
+      return functionEntity;
+    }
+  }

Review Comment:
   The `validate()` method is called in the builder but `FunctionEntity` does 
not override the `validate()` method. While the default implementation from the 
`Entity` interface will validate fields, there may be additional business logic 
validation needed (e.g., ensuring that either returnType or returnColumns is 
set based on functionType). Consider adding an explicit `validate()` method 
implementation in `FunctionEntity` to validate function-specific constraints, 
or document that the default field validation is intentionally sufficient.
   ```suggestion
     }
   
     /**
      * Validates this {@link FunctionEntity}.
      *
      * <p>This implementation currently relies on the default field-level 
validation provided by
      * {@link Entity#validate()}. Any function-specific business rules should 
be added here in the
      * future.
      */
     @Override
     public void validate() {
       Entity.super.validate();
     }
   ```



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core/src/test/java/org/apache/gravitino/catalog/TestManagedFunctionOperations.java:
##########
@@ -0,0 +1,494 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *  http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.  See the License for the
+ * specific language governing permissions and limitations
+ * under the License.
+ */
+package org.apache.gravitino.catalog;
+
+import static org.mockito.ArgumentMatchers.any;
+import static org.mockito.ArgumentMatchers.eq;
+import static org.mockito.Mockito.doAnswer;
+import static org.mockito.Mockito.mock;
+import static org.mockito.Mockito.when;
+
+import java.util.Arrays;
+import java.util.HashMap;
+import java.util.Map;
+import java.util.Set;
+import java.util.stream.Collectors;
+import org.apache.gravitino.Entity;
+import org.apache.gravitino.EntityAlreadyExistsException;
+import org.apache.gravitino.EntityStore;
+import org.apache.gravitino.NameIdentifier;
+import org.apache.gravitino.Namespace;
+import org.apache.gravitino.exceptions.FunctionAlreadyExistsException;
+import org.apache.gravitino.exceptions.NoSuchEntityException;
+import org.apache.gravitino.exceptions.NoSuchFunctionException;
+import org.apache.gravitino.function.Function;
+import org.apache.gravitino.function.FunctionDefinition;
+import org.apache.gravitino.function.FunctionDefinitions;
+import org.apache.gravitino.function.FunctionImpl;
+import org.apache.gravitino.function.FunctionImpls;
+import org.apache.gravitino.function.FunctionParam;
+import org.apache.gravitino.function.FunctionParams;
+import org.apache.gravitino.function.FunctionType;
+import org.apache.gravitino.meta.FunctionEntity;
+import org.apache.gravitino.rel.expressions.literals.Literals;
+import org.apache.gravitino.rel.types.Types;
+import org.apache.gravitino.storage.IdGenerator;
+import org.apache.gravitino.storage.RandomIdGenerator;
+import org.junit.jupiter.api.Assertions;
+import org.junit.jupiter.api.BeforeEach;
+import org.junit.jupiter.api.Test;
+
+public class TestManagedFunctionOperations {
+
+  private static final String METALAKE_NAME = "test_metalake";
+  private static final String CATALOG_NAME = "test_catalog";
+  private static final String SCHEMA_NAME = "schema1";
+
+  private final IdGenerator idGenerator = new RandomIdGenerator();
+  private final Map<NameIdentifier, FunctionEntity> entityMap = new 
HashMap<>();
+
+  private EntityStore store;
+  private ManagedFunctionOperations functionOperations;
+
+  @BeforeEach
+  public void setUp() throws Exception {
+    entityMap.clear();
+    store = createMockEntityStore();
+    functionOperations = new ManagedFunctionOperations(store, idGenerator);
+  }
+
+  @Test
+  public void testRegisterAndListFunctions() {
+    NameIdentifier func1Ident = getFunctionIdent("func1");
+    FunctionParam[] params1 = new FunctionParam[] {FunctionParams.of("a", 
Types.IntegerType.get())};
+    FunctionDefinition[] definitions1 = new FunctionDefinition[] 
{createSimpleDefinition(params1)};
+
+    functionOperations.registerFunction(
+        func1Ident,
+        "Test function 1",
+        FunctionType.SCALAR,
+        true,
+        Types.StringType.get(),
+        definitions1);
+
+    NameIdentifier func2Ident = getFunctionIdent("func2");
+    FunctionParam[] params2 =
+        new FunctionParam[] {
+          FunctionParams.of("x", Types.StringType.get()),
+          FunctionParams.of("y", Types.StringType.get())
+        };
+    FunctionDefinition[] definitions2 = new FunctionDefinition[] 
{createSimpleDefinition(params2)};
+
+    functionOperations.registerFunction(
+        func2Ident,
+        "Test function 2",
+        FunctionType.SCALAR,
+        false,
+        Types.IntegerType.get(),
+        definitions2);
+
+    // List functions
+    NameIdentifier[] functionIdents = 
functionOperations.listFunctions(getFunctionNamespace());
+    Assertions.assertEquals(2, functionIdents.length);
+    Set<String> functionNames =
+        
Arrays.stream(functionIdents).map(NameIdentifier::name).collect(Collectors.toSet());
+
+    Assertions.assertTrue(functionNames.contains("func1"));
+    Assertions.assertTrue(functionNames.contains("func2"));
+  }
+
+  @Test
+  public void testRegisterAndGetFunction() {
+    NameIdentifier funcIdent = getFunctionIdent("my_func");
+    FunctionParam[] params =
+        new FunctionParam[] {FunctionParams.of("input", 
Types.StringType.get())};
+    FunctionDefinition[] definitions = new FunctionDefinition[] 
{createSimpleDefinition(params)};
+
+    Function newFunc =
+        functionOperations.registerFunction(
+            funcIdent,
+            "My test function",
+            FunctionType.SCALAR,
+            true,
+            Types.IntegerType.get(),
+            definitions);
+
+    Assertions.assertEquals("my_func", newFunc.name());
+    Assertions.assertEquals("My test function", newFunc.comment());
+    Assertions.assertEquals(FunctionType.SCALAR, newFunc.functionType());
+    Assertions.assertTrue(newFunc.deterministic());
+    Assertions.assertEquals(Types.IntegerType.get(), newFunc.returnType());
+    Assertions.assertEquals(0, newFunc.version());
+
+    // Get function (latest version)
+    Function loadedFunc = functionOperations.getFunction(funcIdent);
+    Assertions.assertEquals(newFunc.name(), loadedFunc.name());
+    Assertions.assertEquals(newFunc.comment(), loadedFunc.comment());
+
+    // Test register function that already exists
+    Assertions.assertThrows(
+        FunctionAlreadyExistsException.class,
+        () ->
+            functionOperations.registerFunction(
+                funcIdent,
+                "Another function",
+                FunctionType.SCALAR,
+                true,
+                Types.StringType.get(),
+                definitions));
+
+    // Test get non-existing function
+    NameIdentifier nonExistingIdent = getFunctionIdent("non_existing_func");
+    Assertions.assertThrows(
+        NoSuchFunctionException.class, () -> 
functionOperations.getFunction(nonExistingIdent));
+  }
+
+  @Test
+  public void testRegisterAndDropFunction() {
+    NameIdentifier funcIdent = getFunctionIdent("func_to_drop");
+    FunctionParam[] params = new FunctionParam[] {FunctionParams.of("a", 
Types.IntegerType.get())};
+    FunctionDefinition[] definitions = new FunctionDefinition[] 
{createSimpleDefinition(params)};
+
+    functionOperations.registerFunction(
+        funcIdent,
+        "Function to drop",
+        FunctionType.SCALAR,
+        true,
+        Types.StringType.get(),
+        definitions);
+
+    // Drop the function
+    boolean dropped = functionOperations.dropFunction(funcIdent);
+    Assertions.assertTrue(dropped);
+
+    // Verify the function is dropped
+    Assertions.assertThrows(
+        NoSuchFunctionException.class, () -> 
functionOperations.getFunction(funcIdent));
+
+    // Test drop non-existing function
+    Assertions.assertFalse(functionOperations.dropFunction(funcIdent));
+  }
+
+  @Test
+  public void testRegisterFunctionWithOverlappingDefinitions() {
+    NameIdentifier funcIdent = getFunctionIdent("func_overlap_register");
+
+    // Try to register with two definitions that have overlapping arities
+    FunctionParam[] params1 =
+        new FunctionParam[] {
+          FunctionParams.of("a", Types.IntegerType.get()),
+          FunctionParams.of("b", Types.FloatType.get(), null, 
Literals.floatLiteral(1.0f))
+        };
+    FunctionParam[] params2 =
+        new FunctionParam[] {
+          FunctionParams.of("a", Types.IntegerType.get()),
+          FunctionParams.of("c", Types.StringType.get(), null, 
Literals.stringLiteral("x"))
+        };
+
+    FunctionDefinition[] definitions =
+        new FunctionDefinition[] {createSimpleDefinition(params1), 
createSimpleDefinition(params2)};
+
+    Assertions.assertThrows(
+        IllegalArgumentException.class,
+        () ->
+            functionOperations.registerFunction(
+                funcIdent,
+                "Test function",
+                FunctionType.SCALAR,
+                true,
+                Types.StringType.get(),
+                definitions));
+  }
+
+  @Test
+  public void testInvalidParameterOrder() {
+    // Test that parameters with default values must appear at the end
+    NameIdentifier funcIdent = getFunctionIdent("func_invalid_params");
+
+    // Create params with invalid order: (a default 1, b required, c default 2)
+    FunctionParam[] invalidParams =
+        new FunctionParam[] {
+          FunctionParams.of("a", Types.IntegerType.get(), "param a", 
Literals.integerLiteral(1)),
+          FunctionParams.of("b", Types.StringType.get()), // Required param 
after optional
+          FunctionParams.of("c", Types.IntegerType.get(), "param c", 
Literals.integerLiteral(2))
+        };
+    FunctionDefinition[] definitions =
+        new FunctionDefinition[] {createSimpleDefinition(invalidParams)};
+
+    // Should throw IllegalArgumentException when trying to register
+    IllegalArgumentException ex =
+        Assertions.assertThrows(
+            IllegalArgumentException.class,
+            () ->
+                functionOperations.registerFunction(
+                    funcIdent,
+                    "Invalid function",
+                    FunctionType.SCALAR,
+                    true,
+                    Types.StringType.get(),
+                    definitions));
+
+    Assertions.assertTrue(
+        ex.getMessage().contains("Invalid parameter order"),
+        "Expected error about invalid parameter order, got: " + 
ex.getMessage());
+    Assertions.assertTrue(
+        ex.getMessage().contains("required parameter 'b'"),
+        "Expected error to mention parameter 'b', got: " + ex.getMessage());
+    Assertions.assertTrue(
+        ex.getMessage().contains("position 1"),
+        "Expected error to mention position 1, got: " + ex.getMessage());
+
+    // Test with valid order: all optional params at the end
+    FunctionParam[] validParams =
+        new FunctionParam[] {
+          FunctionParams.of("a", Types.IntegerType.get()),
+          FunctionParams.of("b", Types.StringType.get()),
+          FunctionParams.of("c", Types.IntegerType.get(), "param c", 
Literals.integerLiteral(1)),
+          FunctionParams.of("d", Types.IntegerType.get(), "param d", 
Literals.integerLiteral(2))
+        };
+    FunctionDefinition[] validDefinitions =
+        new FunctionDefinition[] {createSimpleDefinition(validParams)};
+
+    // This should succeed
+    functionOperations.registerFunction(
+        funcIdent,
+        "Valid function",
+        FunctionType.SCALAR,
+        true,
+        Types.StringType.get(),
+        validDefinitions);
+
+    // Verify the function was registered
+    Function func = functionOperations.getFunction(funcIdent);
+    Assertions.assertNotNull(func);
+    Assertions.assertEquals("Valid function", func.comment());
+  }
+
+  @Test
+  public void testNonOverlappingDefinitions() {
+    // Test that definitions with different arities can coexist
+    NameIdentifier funcIdent = getFunctionIdent("func_non_overlap");
+
+    // Two definitions with completely different parameter types (no overlap)
+    FunctionParam[] params1 = new FunctionParam[] {FunctionParams.of("a", 
Types.IntegerType.get())};
+    FunctionParam[] params2 = new FunctionParam[] {FunctionParams.of("a", 
Types.StringType.get())};
+
+    FunctionDefinition[] definitions =
+        new FunctionDefinition[] {createSimpleDefinition(params1), 
createSimpleDefinition(params2)};
+
+    // Should succeed - no arity overlap
+    Function func =
+        functionOperations.registerFunction(
+            funcIdent,
+            "Non-overlapping function",
+            FunctionType.SCALAR,
+            true,
+            Types.StringType.get(),
+            definitions);
+
+    Assertions.assertNotNull(func);
+    Assertions.assertEquals(2, func.definitions().length);
+  }
+
+  @Test
+  public void testNoArgsFunction() {
+    // Test function with no parameters
+    NameIdentifier funcIdent = getFunctionIdent("func_no_args");
+
+    FunctionParam[] params = new FunctionParam[] {};
+    FunctionDefinition[] definitions = new FunctionDefinition[] 
{createSimpleDefinition(params)};
+
+    Function func =
+        functionOperations.registerFunction(
+            funcIdent,
+            "No args function",
+            FunctionType.SCALAR,
+            true,
+            Types.StringType.get(),
+            definitions);
+
+    Assertions.assertNotNull(func);
+    Assertions.assertEquals(0, func.definitions()[0].parameters().length);
+  }
+
+  @Test
+  public void testMultipleDefaultParams() {
+    // Test function with multiple default parameters generates correct arities
+    NameIdentifier funcIdent = getFunctionIdent("func_multi_default");
+
+    // foo(int a, float b default 1.0, string c default 'x')
+    // Should generate arities: ["integer"], ["integer,float"], 
["integer,float,string"]
+    FunctionParam[] params =
+        new FunctionParam[] {
+          FunctionParams.of("a", Types.IntegerType.get()),
+          FunctionParams.of("b", Types.FloatType.get(), "param b", 
Literals.floatLiteral(1.0f)),
+          FunctionParams.of("c", Types.StringType.get(), "param c", 
Literals.stringLiteral("x"))
+        };
+    FunctionDefinition[] definitions = new FunctionDefinition[] 
{createSimpleDefinition(params)};
+
+    Function func =
+        functionOperations.registerFunction(
+            funcIdent,
+            "Multi default function",
+            FunctionType.SCALAR,
+            true,
+            Types.StringType.get(),
+            definitions);
+
+    Assertions.assertNotNull(func);
+    Assertions.assertEquals(3, func.definitions()[0].parameters().length);
+  }
+
+  @Test
+  public void testOverlappingAritiesWithDifferentTypes() {
+    // Test that two definitions with same arity count but different types 
don't overlap
+    NameIdentifier funcIdent = getFunctionIdent("func_same_arity_diff_types");
+
+    // foo(int, int) and foo(string, string) - same arity count but different 
types
+    FunctionParam[] params1 =
+        new FunctionParam[] {
+          FunctionParams.of("a", Types.IntegerType.get()),
+          FunctionParams.of("b", Types.IntegerType.get())
+        };
+    FunctionParam[] params2 =
+        new FunctionParam[] {
+          FunctionParams.of("a", Types.StringType.get()),
+          FunctionParams.of("b", Types.StringType.get())
+        };
+
+    FunctionDefinition[] definitions =
+        new FunctionDefinition[] {createSimpleDefinition(params1), 
createSimpleDefinition(params2)};
+
+    // Should succeed - arities are "integer,integer" vs "string,string"
+    Function func =
+        functionOperations.registerFunction(
+            funcIdent,
+            "Same arity different types",
+            FunctionType.SCALAR,
+            true,
+            Types.StringType.get(),
+            definitions);
+
+    Assertions.assertNotNull(func);
+    Assertions.assertEquals(2, func.definitions().length);
+  }
+
+  @SuppressWarnings("unchecked")
+  private EntityStore createMockEntityStore() throws Exception {
+    EntityStore mockStore = mock(EntityStore.class);
+
+    // Mock put operation
+    doAnswer(
+            invocation -> {
+              FunctionEntity entity = invocation.getArgument(0);
+              boolean overwrite = invocation.getArgument(1);
+              NameIdentifier ident = entity.nameIdentifier();
+
+              if (!overwrite && entityMap.containsKey(ident)) {
+                throw new EntityAlreadyExistsException("Entity %s already 
exists", ident);
+              }
+              entityMap.put(ident, entity);
+              return null;
+            })
+        .when(mockStore)
+        .put(any(FunctionEntity.class), any(Boolean.class));
+
+    // Mock get operation
+    when(mockStore.get(
+            any(NameIdentifier.class), eq(Entity.EntityType.FUNCTION), 
eq(FunctionEntity.class)))
+        .thenAnswer(
+            invocation -> {
+              NameIdentifier ident = invocation.getArgument(0);
+              FunctionEntity entity = findEntityByIdent(ident);
+              if (entity == null) {
+                throw new NoSuchEntityException("Entity %s does not exist", 
ident);
+              }
+              return entity;
+            });
+
+    // Mock delete operation (2 parameters - default method that calls 
3-parameter version)
+    when(mockStore.delete(any(NameIdentifier.class), 
eq(Entity.EntityType.FUNCTION)))
+        .thenAnswer(
+            invocation -> {
+              NameIdentifier ident = invocation.getArgument(0);
+              FunctionEntity entity = findEntityByIdent(ident);
+              if (entity == null) {
+                return false;
+              }
+              entityMap.remove(entity.nameIdentifier());
+              return true;
+            });
+
+    // Mock list operation
+    when(mockStore.list(
+            any(Namespace.class), eq(FunctionEntity.class), 
eq(Entity.EntityType.FUNCTION)))
+        .thenAnswer(
+            invocation -> {
+              Namespace namespace = invocation.getArgument(0);
+              return entityMap.values().stream()
+                  .filter(e -> e.namespace().equals(namespace))
+                  .collect(Collectors.toList());
+            });
+
+    return mockStore;
+  }
+
+  /**
+   * Finds an entity by identifier. This method handles both versioned 
identifiers (used by
+   * getFunction) and original identifiers (used by alterFunction and 
dropFunction).
+   *
+   * <p>Versioned identifier format: namespace = original_namespace + 
function_name, name = version
+   * Original identifier format: namespace = schema_namespace, name = 
function_name
+   */
+  private FunctionEntity findEntityByIdent(NameIdentifier ident) {

Review Comment:
   The documentation mentions "versioned identifiers" and "alterFunction" but 
the current implementation has removed version-based getFunction and 
alterFunction is not implemented (throws UnsupportedOperationException). This 
comment appears to be leftover from a previous design. Update the documentation 
to reflect the current implementation where only the original identifier format 
is used.



##########
core/src/main/java/org/apache/gravitino/catalog/ManagedFunctionOperations.java:
##########
@@ -131,7 +160,150 @@ public Function alterFunction(NameIdentifier ident, 
FunctionChange... changes)
 
   @Override
   public boolean dropFunction(NameIdentifier ident) {
-    // TODO: Implement when FunctionEntity is available
-    throw new UnsupportedOperationException("dropFunction: FunctionEntity not 
yet implemented");
+    try {
+      return store.delete(ident, Entity.EntityType.FUNCTION);
+    } catch (NoSuchEntityException e) {
+      return false;
+    } catch (IOException e) {
+      throw new RuntimeException("Failed to drop function " + ident, e);
+    }
+  }
+
+  private Function doRegisterFunction(
+      NameIdentifier ident,
+      String comment,
+      FunctionType functionType,
+      boolean deterministic,
+      Optional<Type> returnType,
+      Optional<FunctionColumn[]> returnColumns,
+      FunctionDefinition[] definitions)
+      throws NoSuchSchemaException, FunctionAlreadyExistsException {
+    Preconditions.checkArgument(
+        definitions != null && definitions.length > 0,
+        "At least one function definition must be provided");
+    validateDefinitionsNoArityOverlap(definitions);
+
+    String currentUser = PrincipalUtils.getCurrentUserName();
+    Instant now = Instant.now();
+    AuditInfo auditInfo = 
AuditInfo.builder().withCreator(currentUser).withCreateTime(now).build();
+
+    FunctionEntity functionEntity =
+        FunctionEntity.builder()
+            .withId(idGenerator.nextId())
+            .withName(ident.name())
+            .withNamespace(ident.namespace())
+            .withComment(comment)
+            .withFunctionType(functionType)
+            .withDeterministic(deterministic)
+            .withReturnType(returnType.orElse(null))
+            .withReturnColumns(returnColumns.orElse(null))
+            .withDefinitions(definitions)
+            .withVersion(INIT_VERSION)
+            .withAuditInfo(auditInfo)
+            .build();
+
+    try {
+      store.put(functionEntity, false /* overwrite */);
+      return functionEntity;
+
+    } catch (NoSuchEntityException e) {
+      throw new NoSuchSchemaException(e, "Schema %s does not exist", 
ident.namespace());
+    } catch (EntityAlreadyExistsException e) {
+      throw new FunctionAlreadyExistsException(e, "Function %s already 
exists", ident);
+    } catch (IOException e) {
+      throw new RuntimeException("Failed to register function " + ident, e);
+    }
+  }
+
+  /**
+   * Validates that all definitions in the array do not have overlapping 
arities. This is used when
+   * registering a function with multiple definitions.
+   *
+   * <p>Gravitino enforces strict validation to prevent ambiguity. Operations 
MUST fail if any
+   * definition's invocation arities overlap with another. For example, if an 
existing definition
+   * {@code foo(int, float default 1.0)} supports arities {@code (int)} and 
{@code (int, float)},
+   * adding a new definition {@code foo(int, string default 'x')} (which 
supports {@code (int)} and
+   * {@code (int, string)}) will be REJECTED because both support the call 
{@code foo(1)}. This
+   * ensures every function invocation deterministically maps to a single 
definition.
+   *
+   * @param definitions The array of definitions to validate.
+   * @throws IllegalArgumentException If any two definitions have overlapping 
arities.
+   */
+  private void validateDefinitionsNoArityOverlap(FunctionDefinition[] 
definitions) {

Review Comment:
   The validation method has excellent documentation explaining the overlap 
detection logic. However, the computeArities method (line 268) also has 
comprehensive documentation. Consider adding a brief reference in this method's 
JavaDoc pointing to `computeArities` to help readers understand how arities are 
computed, e.g., "See {@link #computeArities(FunctionDefinition)} for details on 
how arity signatures are computed."



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