szehon-ho commented on code in PR #45267:
URL: https://github.com/apache/spark/pull/45267#discussion_r1536300235


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sql/catalyst/src/main/java/org/apache/spark/sql/connector/catalog/functions/ReducibleFunction.java:
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@@ -0,0 +1,106 @@
+/*
+ * 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.spark.sql.connector.catalog.functions;
+
+import org.apache.spark.annotation.Evolving;
+
+/**
+ * Base class for user-defined functions that can be 'reduced' on another 
function.
+ *
+ * A function f_source(x) is 'reducible' on another function f_target(x) if
+ * <ul>
+ *   <li> There exists a reducer function r(x) such that r(f_source(x)) = 
f_target(x)
+ *        for all input x, or </li>
+ *   <li> More generally, there exists reducer functions r1(x) and r2(x) such 
that
+ *        r1(f_source(x)) = r2(f_target(x)) for all input x. </li>
+ * </ul>
+ * <p>
+ * Examples:
+ * <ul>
+ *    <li>Bucket functions where one side has reducer
+ *    <ul>
+ *        <li>f_source(x) = bucket(4, x)</li>
+ *        <li>f_target(x) = bucket(2, x)</li>
+ *        <li>r(x) = x % 2</li>
+ *    </ul>
+ *
+ *    <li>Bucket functions where both sides have reducer
+ *    <ul>
+ *        <li>f_source(x) = bucket(16, x)</li>
+ *        <li>f_target(x) = bucket(12, x)</li>
+ *        <li>r1(x) = x % 4</li>
+ *        <li>r2(x) = x % 4</li>
+ *    </ul>
+ *
+ *    <li>Date functions
+ *    <ul>
+ *        <li>f_source(x) = days(x)</li>
+ *        <li>f_target(x) = hours(x)</li>
+ *        <li>r(x) = x / 24</li>
+ *     </ul>
+ * </ul>
+ * @param <I> reducer function input type
+ * @param <O> reducer function output type
+ * @since 4.0.0
+ */
+@Evolving
+public interface ReducibleFunction<I, O> {
+
+  /**
+   * This method is for parameterized functions.
+   *
+   * If this parameterized function is 'reducible' on another bucket function,
+   * return the {@link Reducer} function.
+   * <p>
+   * Example to return reducer for reducing f_source = bucket(4, x) on 
f_target = bucket(2, x)
+   * <ul>
+   *     <li>thisFunction = bucket</li>
+   *     <li>thisParam = Int(4)</li>
+   *     <li>otherFunction = bucket</li>
+   *     <li>otherParam = Int(2)</li>
+   * </ul>
+   *
+   * @param thisParam parameter for this function

Review Comment:
   I was thinking a list, would that work or cause any issue ?



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