diff --git a/asterix-algebra/src/main/java/edu/uci/ics/asterix/optimizer/rules/IntroduceStaticTypeCastRule.java b/asterix-algebra/src/main/java/edu/uci/ics/asterix/optimizer/rules/IntroduceStaticTypeCastRule.java
index 1de0b19..2bb9f12 100644
--- a/asterix-algebra/src/main/java/edu/uci/ics/asterix/optimizer/rules/IntroduceStaticTypeCastRule.java
+++ b/asterix-algebra/src/main/java/edu/uci/ics/asterix/optimizer/rules/IntroduceStaticTypeCastRule.java
@@ -16,26 +16,15 @@
 package edu.uci.ics.asterix.optimizer.rules;
 
 import java.util.ArrayList;
-import java.util.Arrays;
 import java.util.List;
 
 import org.apache.commons.lang3.mutable.Mutable;
-import org.apache.commons.lang3.mutable.MutableObject;
 
 import edu.uci.ics.asterix.metadata.declared.AqlDataSource;
-import edu.uci.ics.asterix.om.base.ANull;
-import edu.uci.ics.asterix.om.base.AString;
-import edu.uci.ics.asterix.om.constants.AsterixConstantValue;
 import edu.uci.ics.asterix.om.functions.AsterixBuiltinFunctions;
 import edu.uci.ics.asterix.om.typecomputer.base.TypeComputerUtilities;
-import edu.uci.ics.asterix.om.types.ARecordType;
-import edu.uci.ics.asterix.om.types.ATypeTag;
-import edu.uci.ics.asterix.om.types.AUnionType;
-import edu.uci.ics.asterix.om.types.AbstractCollectionType;
-import edu.uci.ics.asterix.om.types.BuiltinType;
 import edu.uci.ics.asterix.om.types.IAType;
-import edu.uci.ics.asterix.om.util.NonTaggedFormatUtil;
-import edu.uci.ics.asterix.runtime.pointables.base.DefaultOpenFieldType;
+import edu.uci.ics.asterix.optimizer.rules.typecast.StaticTypeCastUtil;
 import edu.uci.ics.hyracks.algebricks.common.exceptions.AlgebricksException;
 import edu.uci.ics.hyracks.algebricks.core.algebra.base.ILogicalExpression;
 import edu.uci.ics.hyracks.algebricks.core.algebra.base.ILogicalOperator;
@@ -44,9 +33,7 @@
 import edu.uci.ics.hyracks.algebricks.core.algebra.base.LogicalOperatorTag;
 import edu.uci.ics.hyracks.algebricks.core.algebra.base.LogicalVariable;
 import edu.uci.ics.hyracks.algebricks.core.algebra.expressions.AbstractFunctionCallExpression;
-import edu.uci.ics.hyracks.algebricks.core.algebra.expressions.ConstantExpression;
 import edu.uci.ics.hyracks.algebricks.core.algebra.expressions.IVariableTypeEnvironment;
-import edu.uci.ics.hyracks.algebricks.core.algebra.expressions.ScalarFunctionCallExpression;
 import edu.uci.ics.hyracks.algebricks.core.algebra.expressions.UnnestingFunctionCallExpression;
 import edu.uci.ics.hyracks.algebricks.core.algebra.operators.logical.AbstractLogicalOperator;
 import edu.uci.ics.hyracks.algebricks.core.algebra.operators.logical.AssignOperator;
@@ -150,7 +137,7 @@
                 if (unnestArg.getExpressionTag() == LogicalExpressionTag.FUNCTION_CALL) {
                     AbstractFunctionCallExpression unnestArgExpr = (AbstractFunctionCallExpression) unnestArg;
                     inputRecordType = (IAType) env.getType(unnestArgExpr);
-                    rewriteFuncExpr(unnestArgExpr, inputRecordType, inputRecordType, env);
+                    StaticTypeCastUtil.rewriteFuncExpr(unnestArgExpr, inputRecordType, inputRecordType, env);
                     context.computeAndSetTypeEnvironmentForOperator(unnestOp);
                 }
                 return true;
@@ -212,7 +199,7 @@
                             requiredRecordType = inputRecordType;
                         }
                         IVariableTypeEnvironment assignEnv = assignOp.computeOutputTypeEnvironment(context);
-                        rewriteFuncExpr(funcExpr, requiredRecordType, inputRecordType, assignEnv);
+                        StaticTypeCastUtil.rewriteFuncExpr(funcExpr, requiredRecordType, inputRecordType, assignEnv);
                     }
                     context.computeAndSetTypeEnvironmentForOperator(originalAssign);
                 }
@@ -225,256 +212,4 @@
         return true;
     }
 
-    private void rewriteFuncExpr(AbstractFunctionCallExpression funcExpr, IAType reqType, IAType inputType,
-            IVariableTypeEnvironment env) throws AlgebricksException {
-        if (funcExpr.getFunctionIdentifier() == AsterixBuiltinFunctions.UNORDERED_LIST_CONSTRUCTOR) {
-            if (reqType.equals(BuiltinType.ANY)) {
-                reqType = DefaultOpenFieldType.NESTED_OPEN_AUNORDERED_LIST_TYPE;
-            }
-            rewriteListFuncExpr(funcExpr, (AbstractCollectionType) reqType, (AbstractCollectionType) inputType, env);
-        } else if (funcExpr.getFunctionIdentifier() == AsterixBuiltinFunctions.ORDERED_LIST_CONSTRUCTOR) {
-            if (reqType.equals(BuiltinType.ANY)) {
-                reqType = DefaultOpenFieldType.NESTED_OPEN_AORDERED_LIST_TYPE;
-            }
-            rewriteListFuncExpr(funcExpr, (AbstractCollectionType) reqType, (AbstractCollectionType) inputType, env);
-        } else if (inputType.getTypeTag().equals(ATypeTag.RECORD)) {
-            if (reqType.equals(BuiltinType.ANY)) {
-                reqType = DefaultOpenFieldType.NESTED_OPEN_RECORD_TYPE;
-            }
-            rewriteRecordFuncExpr(funcExpr, (ARecordType) reqType, (ARecordType) inputType, env);
-        }
-    }
-
-    /**
-     * only called when funcExpr is record constructor
-     * 
-     * @param funcExpr
-     *            record constructor function expression
-     * @param requiredListType
-     *            required record type
-     * @param inputRecordType
-     * @param env
-     *            type environment
-     * @throws AlgebricksException
-     */
-    private void rewriteRecordFuncExpr(AbstractFunctionCallExpression funcExpr, ARecordType requiredRecordType,
-            ARecordType inputRecordType, IVariableTypeEnvironment env) throws AlgebricksException {
-        // if already rewritten, the required type is not null
-        if (TypeComputerUtilities.getRequiredType(funcExpr) != null)
-            return;
-        TypeComputerUtilities.setRequiredAndInputTypes(funcExpr, requiredRecordType, inputRecordType);
-        staticRecordTypeCast(funcExpr, requiredRecordType, inputRecordType, env);
-    }
-
-    /**
-     * only called when funcExpr is list constructor
-     * 
-     * @param funcExpr
-     *            list constructor function expression
-     * @param requiredListType
-     *            required list type
-     * @param inputListType
-     * @param env
-     *            type environment
-     * @throws AlgebricksException
-     */
-    private void rewriteListFuncExpr(AbstractFunctionCallExpression funcExpr, AbstractCollectionType requiredListType,
-            AbstractCollectionType inputListType, IVariableTypeEnvironment env) throws AlgebricksException {
-        if (TypeComputerUtilities.getRequiredType(funcExpr) != null)
-            return;
-
-        TypeComputerUtilities.setRequiredAndInputTypes(funcExpr, requiredListType, inputListType);
-        List<Mutable<ILogicalExpression>> args = funcExpr.getArguments();
-
-        IAType itemType = requiredListType.getItemType();
-        IAType inputItemType = inputListType.getItemType();
-        for (int j = 0; j < args.size(); j++) {
-            ILogicalExpression arg = args.get(j).getValue();
-            if (arg.getExpressionTag() == LogicalExpressionTag.FUNCTION_CALL) {
-                ScalarFunctionCallExpression argFunc = (ScalarFunctionCallExpression) arg;
-                IAType currentItemType = (IAType) env.getType(argFunc);
-                if (inputItemType == null || inputItemType == BuiltinType.ANY) {
-                    currentItemType = (IAType) env.getType(argFunc);
-                    rewriteFuncExpr(argFunc, itemType, currentItemType, env);
-                } else {
-                    rewriteFuncExpr(argFunc, itemType, inputItemType, env);
-                }
-            }
-        }
-    }
-
-    private void staticRecordTypeCast(AbstractFunctionCallExpression func, ARecordType reqType, ARecordType inputType,
-            IVariableTypeEnvironment env) throws AlgebricksException {
-        IAType[] reqFieldTypes = reqType.getFieldTypes();
-        String[] reqFieldNames = reqType.getFieldNames();
-        IAType[] inputFieldTypes = inputType.getFieldTypes();
-        String[] inputFieldNames = inputType.getFieldNames();
-
-        int[] fieldPermutation = new int[reqFieldTypes.length];
-        boolean[] nullFields = new boolean[reqFieldTypes.length];
-        boolean[] openFields = new boolean[inputFieldTypes.length];
-
-        Arrays.fill(nullFields, false);
-        Arrays.fill(openFields, true);
-        Arrays.fill(fieldPermutation, -1);
-
-        // forward match: match from actual to required
-        boolean matched = false;
-        for (int i = 0; i < inputFieldNames.length; i++) {
-            String fieldName = inputFieldNames[i];
-            IAType fieldType = inputFieldTypes[i];
-
-            if (2 * i + 1 > func.getArguments().size())
-                throw new AlgebricksException("expression index out of bound");
-
-            // 2*i+1 is the index of field value expression
-            ILogicalExpression arg = func.getArguments().get(2 * i + 1).getValue();
-            matched = false;
-            for (int j = 0; j < reqFieldNames.length; j++) {
-                String reqFieldName = reqFieldNames[j];
-                IAType reqFieldType = reqFieldTypes[j];
-                if (fieldName.equals(reqFieldName)) {
-                    if (fieldType.equals(reqFieldType)) {
-                        fieldPermutation[j] = i;
-                        openFields[i] = false;
-                        matched = true;
-
-                        if (arg.getExpressionTag() == LogicalExpressionTag.FUNCTION_CALL) {
-                            ScalarFunctionCallExpression scalarFunc = (ScalarFunctionCallExpression) arg;
-                            rewriteFuncExpr(scalarFunc, reqFieldType, fieldType, env);
-                        }
-                        break;
-                    }
-
-                    // match the optional field
-                    if (reqFieldType.getTypeTag() == ATypeTag.UNION
-                            && NonTaggedFormatUtil.isOptionalField((AUnionType) reqFieldType)) {
-                        IAType itemType = ((AUnionType) reqFieldType).getUnionList().get(
-                                NonTaggedFormatUtil.OPTIONAL_TYPE_INDEX_IN_UNION_LIST);
-                        reqFieldType = itemType;
-                        if (fieldType.equals(BuiltinType.ANULL) || fieldType.equals(itemType)) {
-                            fieldPermutation[j] = i;
-                            openFields[i] = false;
-                            matched = true;
-
-                            // rewrite record expr
-                            if (arg.getExpressionTag() == LogicalExpressionTag.FUNCTION_CALL) {
-                                ScalarFunctionCallExpression scalarFunc = (ScalarFunctionCallExpression) arg;
-                                rewriteFuncExpr(scalarFunc, reqFieldType, fieldType, env);
-                            }
-                            break;
-                        }
-                    }
-
-                    // match the record field: need cast
-                    if (arg.getExpressionTag() == LogicalExpressionTag.FUNCTION_CALL) {
-                        ScalarFunctionCallExpression scalarFunc = (ScalarFunctionCallExpression) arg;
-                        rewriteFuncExpr(scalarFunc, reqFieldType, fieldType, env);
-                        fieldPermutation[j] = i;
-                        openFields[i] = false;
-                        matched = true;
-                        break;
-                    }
-                }
-            }
-            // the input has extra fields
-            if (!matched && !reqType.isOpen())
-                throw new AlgebricksException("static type mismatch: including an extra closed field " + fieldName);
-        }
-
-        // backward match: match from required to actual
-        for (int i = 0; i < reqFieldNames.length; i++) {
-            String reqFieldName = reqFieldNames[i];
-            IAType reqFieldType = reqFieldTypes[i];
-            matched = false;
-            for (int j = 0; j < inputFieldNames.length; j++) {
-                String fieldName = inputFieldNames[j];
-                IAType fieldType = inputFieldTypes[j];
-                if (!fieldName.equals(reqFieldName))
-                    continue;
-                // should check open field here
-                // because number of entries in fieldPermuations is the
-                // number of required schema fields
-                // here we want to check if an input field is matched
-                // the entry index of fieldPermuatons is req field index
-                if (!openFields[j]) {
-                    matched = true;
-                    break;
-                }
-
-                // match the optional field
-                if (reqFieldType.getTypeTag() == ATypeTag.UNION
-                        && NonTaggedFormatUtil.isOptionalField((AUnionType) reqFieldType)) {
-                    IAType itemType = ((AUnionType) reqFieldType).getUnionList().get(
-                            NonTaggedFormatUtil.OPTIONAL_TYPE_INDEX_IN_UNION_LIST);
-                    if (fieldType.equals(BuiltinType.ANULL) || fieldType.equals(itemType)) {
-                        matched = true;
-                        break;
-                    }
-                }
-            }
-            if (matched)
-                continue;
-
-            if (reqFieldType.getTypeTag() == ATypeTag.UNION
-                    && NonTaggedFormatUtil.isOptionalField((AUnionType) reqFieldType)) {
-                // add a null field
-                nullFields[i] = true;
-            } else {
-                // no matched field in the input for a required closed field
-                throw new AlgebricksException("static type mismatch: miss a required closed field " + reqFieldName);
-            }
-        }
-
-        List<Mutable<ILogicalExpression>> arguments = func.getArguments();
-        List<Mutable<ILogicalExpression>> originalArguments = new ArrayList<Mutable<ILogicalExpression>>();
-        originalArguments.addAll(arguments);
-        arguments.clear();
-        // re-order the closed part and fill in null fields
-        for (int i = 0; i < fieldPermutation.length; i++) {
-            int pos = fieldPermutation[i];
-            if (pos >= 0) {
-                arguments.add(originalArguments.get(2 * pos));
-                arguments.add(originalArguments.get(2 * pos + 1));
-            }
-            if (nullFields[i]) {
-                // add a null field
-                arguments.add(new MutableObject<ILogicalExpression>(new ConstantExpression(new AsterixConstantValue(
-                        new AString(reqFieldNames[i])))));
-                arguments.add(new MutableObject<ILogicalExpression>(new ConstantExpression(new AsterixConstantValue(
-                        ANull.NULL))));
-            }
-        }
-
-        // add the open part
-        for (int i = 0; i < openFields.length; i++) {
-            if (openFields[i]) {
-                arguments.add(originalArguments.get(2 * i));
-                Mutable<ILogicalExpression> fExprRef = originalArguments.get(2 * i + 1);
-                ILogicalExpression argExpr = fExprRef.getValue();
-
-                // we need to handle open fields recursively by their default
-                // types
-                // for list, their item type is any
-                // for record, their
-                if (argExpr.getExpressionTag() == LogicalExpressionTag.FUNCTION_CALL) {
-                    IAType reqFieldType = inputFieldTypes[i];
-                    if (inputFieldTypes[i].getTypeTag() == ATypeTag.RECORD) {
-                        reqFieldType = DefaultOpenFieldType.NESTED_OPEN_RECORD_TYPE;
-                    }
-                    if (inputFieldTypes[i].getTypeTag() == ATypeTag.ORDEREDLIST) {
-                        reqFieldType = DefaultOpenFieldType.NESTED_OPEN_AORDERED_LIST_TYPE;
-                    }
-                    if (inputFieldTypes[i].getTypeTag() == ATypeTag.UNORDEREDLIST) {
-                        reqFieldType = DefaultOpenFieldType.NESTED_OPEN_AUNORDERED_LIST_TYPE;
-                    }
-                    if (TypeComputerUtilities.getRequiredType((AbstractFunctionCallExpression) argExpr) == null) {
-                        ScalarFunctionCallExpression argFunc = (ScalarFunctionCallExpression) argExpr;
-                        rewriteFuncExpr(argFunc, reqFieldType, inputFieldTypes[i], env);
-                    }
-                }
-                arguments.add(fExprRef);
-            }
-        }
-    }
 }
diff --git a/asterix-algebra/src/main/java/edu/uci/ics/asterix/optimizer/rules/typecast/StaticTypeCastUtil.java b/asterix-algebra/src/main/java/edu/uci/ics/asterix/optimizer/rules/typecast/StaticTypeCastUtil.java
new file mode 100644
index 0000000..6c0b1d6
--- /dev/null
+++ b/asterix-algebra/src/main/java/edu/uci/ics/asterix/optimizer/rules/typecast/StaticTypeCastUtil.java
@@ -0,0 +1,287 @@
+package edu.uci.ics.asterix.optimizer.rules.typecast;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+
+import org.apache.commons.lang3.mutable.Mutable;
+import org.apache.commons.lang3.mutable.MutableObject;
+
+import edu.uci.ics.asterix.om.base.ANull;
+import edu.uci.ics.asterix.om.base.AString;
+import edu.uci.ics.asterix.om.constants.AsterixConstantValue;
+import edu.uci.ics.asterix.om.functions.AsterixBuiltinFunctions;
+import edu.uci.ics.asterix.om.typecomputer.base.TypeComputerUtilities;
+import edu.uci.ics.asterix.om.types.ARecordType;
+import edu.uci.ics.asterix.om.types.ATypeTag;
+import edu.uci.ics.asterix.om.types.AUnionType;
+import edu.uci.ics.asterix.om.types.AbstractCollectionType;
+import edu.uci.ics.asterix.om.types.BuiltinType;
+import edu.uci.ics.asterix.om.types.IAType;
+import edu.uci.ics.asterix.om.util.NonTaggedFormatUtil;
+import edu.uci.ics.asterix.runtime.pointables.base.DefaultOpenFieldType;
+import edu.uci.ics.hyracks.algebricks.common.exceptions.AlgebricksException;
+import edu.uci.ics.hyracks.algebricks.core.algebra.base.ILogicalExpression;
+import edu.uci.ics.hyracks.algebricks.core.algebra.base.LogicalExpressionTag;
+import edu.uci.ics.hyracks.algebricks.core.algebra.expressions.AbstractFunctionCallExpression;
+import edu.uci.ics.hyracks.algebricks.core.algebra.expressions.ConstantExpression;
+import edu.uci.ics.hyracks.algebricks.core.algebra.expressions.IVariableTypeEnvironment;
+import edu.uci.ics.hyracks.algebricks.core.algebra.expressions.ScalarFunctionCallExpression;
+
+public class StaticTypeCastUtil {
+
+    public static void rewriteFuncExpr(AbstractFunctionCallExpression funcExpr, IAType reqType, IAType inputType,
+            IVariableTypeEnvironment env) throws AlgebricksException {
+        if (funcExpr.getFunctionIdentifier() == AsterixBuiltinFunctions.UNORDERED_LIST_CONSTRUCTOR) {
+            if (reqType.equals(BuiltinType.ANY)) {
+                reqType = DefaultOpenFieldType.NESTED_OPEN_AUNORDERED_LIST_TYPE;
+            }
+            rewriteListFuncExpr(funcExpr, (AbstractCollectionType) reqType, (AbstractCollectionType) inputType, env);
+        } else if (funcExpr.getFunctionIdentifier() == AsterixBuiltinFunctions.ORDERED_LIST_CONSTRUCTOR) {
+            if (reqType.equals(BuiltinType.ANY)) {
+                reqType = DefaultOpenFieldType.NESTED_OPEN_AORDERED_LIST_TYPE;
+            }
+            rewriteListFuncExpr(funcExpr, (AbstractCollectionType) reqType, (AbstractCollectionType) inputType, env);
+        } else if (inputType.getTypeTag().equals(ATypeTag.RECORD)) {
+            if (reqType.equals(BuiltinType.ANY)) {
+                reqType = DefaultOpenFieldType.NESTED_OPEN_RECORD_TYPE;
+            }
+            rewriteRecordFuncExpr(funcExpr, (ARecordType) reqType, (ARecordType) inputType, env);
+        }
+    }
+
+    /**
+     * only called when funcExpr is record constructor
+     * 
+     * @param funcExpr
+     *            record constructor function expression
+     * @param requiredListType
+     *            required record type
+     * @param inputRecordType
+     * @param env
+     *            type environment
+     * @throws AlgebricksException
+     */
+    private static void rewriteRecordFuncExpr(AbstractFunctionCallExpression funcExpr, ARecordType requiredRecordType,
+            ARecordType inputRecordType, IVariableTypeEnvironment env) throws AlgebricksException {
+        // if already rewritten, the required type is not null
+        if (TypeComputerUtilities.getRequiredType(funcExpr) != null)
+            return;
+        TypeComputerUtilities.setRequiredAndInputTypes(funcExpr, requiredRecordType, inputRecordType);
+        staticRecordTypeCast(funcExpr, requiredRecordType, inputRecordType, env);
+    }
+
+    /**
+     * only called when funcExpr is list constructor
+     * 
+     * @param funcExpr
+     *            list constructor function expression
+     * @param requiredListType
+     *            required list type
+     * @param inputListType
+     * @param env
+     *            type environment
+     * @throws AlgebricksException
+     */
+    private static void rewriteListFuncExpr(AbstractFunctionCallExpression funcExpr,
+            AbstractCollectionType requiredListType, AbstractCollectionType inputListType, IVariableTypeEnvironment env)
+            throws AlgebricksException {
+        if (TypeComputerUtilities.getRequiredType(funcExpr) != null)
+            return;
+
+        TypeComputerUtilities.setRequiredAndInputTypes(funcExpr, requiredListType, inputListType);
+        List<Mutable<ILogicalExpression>> args = funcExpr.getArguments();
+
+        IAType itemType = requiredListType.getItemType();
+        IAType inputItemType = inputListType.getItemType();
+        for (int j = 0; j < args.size(); j++) {
+            ILogicalExpression arg = args.get(j).getValue();
+            if (arg.getExpressionTag() == LogicalExpressionTag.FUNCTION_CALL) {
+                ScalarFunctionCallExpression argFunc = (ScalarFunctionCallExpression) arg;
+                IAType currentItemType = (IAType) env.getType(argFunc);
+                if (inputItemType == null || inputItemType == BuiltinType.ANY) {
+                    currentItemType = (IAType) env.getType(argFunc);
+                    rewriteFuncExpr(argFunc, itemType, currentItemType, env);
+                } else {
+                    rewriteFuncExpr(argFunc, itemType, inputItemType, env);
+                }
+            }
+        }
+    }
+
+    private static void staticRecordTypeCast(AbstractFunctionCallExpression func, ARecordType reqType,
+            ARecordType inputType, IVariableTypeEnvironment env) throws AlgebricksException {
+        IAType[] reqFieldTypes = reqType.getFieldTypes();
+        String[] reqFieldNames = reqType.getFieldNames();
+        IAType[] inputFieldTypes = inputType.getFieldTypes();
+        String[] inputFieldNames = inputType.getFieldNames();
+
+        int[] fieldPermutation = new int[reqFieldTypes.length];
+        boolean[] nullFields = new boolean[reqFieldTypes.length];
+        boolean[] openFields = new boolean[inputFieldTypes.length];
+
+        Arrays.fill(nullFields, false);
+        Arrays.fill(openFields, true);
+        Arrays.fill(fieldPermutation, -1);
+
+        // forward match: match from actual to required
+        boolean matched = false;
+        for (int i = 0; i < inputFieldNames.length; i++) {
+            String fieldName = inputFieldNames[i];
+            IAType fieldType = inputFieldTypes[i];
+
+            if (2 * i + 1 > func.getArguments().size())
+                throw new AlgebricksException("expression index out of bound");
+
+            // 2*i+1 is the index of field value expression
+            ILogicalExpression arg = func.getArguments().get(2 * i + 1).getValue();
+            matched = false;
+            for (int j = 0; j < reqFieldNames.length; j++) {
+                String reqFieldName = reqFieldNames[j];
+                IAType reqFieldType = reqFieldTypes[j];
+                if (fieldName.equals(reqFieldName)) {
+                    if (fieldType.equals(reqFieldType)) {
+                        fieldPermutation[j] = i;
+                        openFields[i] = false;
+                        matched = true;
+
+                        if (arg.getExpressionTag() == LogicalExpressionTag.FUNCTION_CALL) {
+                            ScalarFunctionCallExpression scalarFunc = (ScalarFunctionCallExpression) arg;
+                            rewriteFuncExpr(scalarFunc, reqFieldType, fieldType, env);
+                        }
+                        break;
+                    }
+
+                    // match the optional field
+                    if (reqFieldType.getTypeTag() == ATypeTag.UNION
+                            && NonTaggedFormatUtil.isOptionalField((AUnionType) reqFieldType)) {
+                        IAType itemType = ((AUnionType) reqFieldType).getUnionList().get(
+                                NonTaggedFormatUtil.OPTIONAL_TYPE_INDEX_IN_UNION_LIST);
+                        reqFieldType = itemType;
+                        if (fieldType.equals(BuiltinType.ANULL) || fieldType.equals(itemType)) {
+                            fieldPermutation[j] = i;
+                            openFields[i] = false;
+                            matched = true;
+
+                            // rewrite record expr
+                            if (arg.getExpressionTag() == LogicalExpressionTag.FUNCTION_CALL) {
+                                ScalarFunctionCallExpression scalarFunc = (ScalarFunctionCallExpression) arg;
+                                rewriteFuncExpr(scalarFunc, reqFieldType, fieldType, env);
+                            }
+                            break;
+                        }
+                    }
+
+                    // match the record field: need cast
+                    if (arg.getExpressionTag() == LogicalExpressionTag.FUNCTION_CALL) {
+                        ScalarFunctionCallExpression scalarFunc = (ScalarFunctionCallExpression) arg;
+                        rewriteFuncExpr(scalarFunc, reqFieldType, fieldType, env);
+                        fieldPermutation[j] = i;
+                        openFields[i] = false;
+                        matched = true;
+                        break;
+                    }
+                }
+            }
+            // the input has extra fields
+            if (!matched && !reqType.isOpen())
+                throw new AlgebricksException("static type mismatch: including an extra closed field " + fieldName);
+        }
+
+        // backward match: match from required to actual
+        for (int i = 0; i < reqFieldNames.length; i++) {
+            String reqFieldName = reqFieldNames[i];
+            IAType reqFieldType = reqFieldTypes[i];
+            matched = false;
+            for (int j = 0; j < inputFieldNames.length; j++) {
+                String fieldName = inputFieldNames[j];
+                IAType fieldType = inputFieldTypes[j];
+                if (!fieldName.equals(reqFieldName))
+                    continue;
+                // should check open field here
+                // because number of entries in fieldPermuations is the
+                // number of required schema fields
+                // here we want to check if an input field is matched
+                // the entry index of fieldPermuatons is req field index
+                if (!openFields[j]) {
+                    matched = true;
+                    break;
+                }
+
+                // match the optional field
+                if (reqFieldType.getTypeTag() == ATypeTag.UNION
+                        && NonTaggedFormatUtil.isOptionalField((AUnionType) reqFieldType)) {
+                    IAType itemType = ((AUnionType) reqFieldType).getUnionList().get(
+                            NonTaggedFormatUtil.OPTIONAL_TYPE_INDEX_IN_UNION_LIST);
+                    if (fieldType.equals(BuiltinType.ANULL) || fieldType.equals(itemType)) {
+                        matched = true;
+                        break;
+                    }
+                }
+            }
+            if (matched)
+                continue;
+
+            if (reqFieldType.getTypeTag() == ATypeTag.UNION
+                    && NonTaggedFormatUtil.isOptionalField((AUnionType) reqFieldType)) {
+                // add a null field
+                nullFields[i] = true;
+            } else {
+                // no matched field in the input for a required closed field
+                throw new AlgebricksException("static type mismatch: miss a required closed field " + reqFieldName);
+            }
+        }
+
+        List<Mutable<ILogicalExpression>> arguments = func.getArguments();
+        List<Mutable<ILogicalExpression>> originalArguments = new ArrayList<Mutable<ILogicalExpression>>();
+        originalArguments.addAll(arguments);
+        arguments.clear();
+        // re-order the closed part and fill in null fields
+        for (int i = 0; i < fieldPermutation.length; i++) {
+            int pos = fieldPermutation[i];
+            if (pos >= 0) {
+                arguments.add(originalArguments.get(2 * pos));
+                arguments.add(originalArguments.get(2 * pos + 1));
+            }
+            if (nullFields[i]) {
+                // add a null field
+                arguments.add(new MutableObject<ILogicalExpression>(new ConstantExpression(new AsterixConstantValue(
+                        new AString(reqFieldNames[i])))));
+                arguments.add(new MutableObject<ILogicalExpression>(new ConstantExpression(new AsterixConstantValue(
+                        ANull.NULL))));
+            }
+        }
+
+        // add the open part
+        for (int i = 0; i < openFields.length; i++) {
+            if (openFields[i]) {
+                arguments.add(originalArguments.get(2 * i));
+                Mutable<ILogicalExpression> fExprRef = originalArguments.get(2 * i + 1);
+                ILogicalExpression argExpr = fExprRef.getValue();
+
+                // we need to handle open fields recursively by their default
+                // types
+                // for list, their item type is any
+                // for record, their
+                if (argExpr.getExpressionTag() == LogicalExpressionTag.FUNCTION_CALL) {
+                    IAType reqFieldType = inputFieldTypes[i];
+                    if (inputFieldTypes[i].getTypeTag() == ATypeTag.RECORD) {
+                        reqFieldType = DefaultOpenFieldType.NESTED_OPEN_RECORD_TYPE;
+                    }
+                    if (inputFieldTypes[i].getTypeTag() == ATypeTag.ORDEREDLIST) {
+                        reqFieldType = DefaultOpenFieldType.NESTED_OPEN_AORDERED_LIST_TYPE;
+                    }
+                    if (inputFieldTypes[i].getTypeTag() == ATypeTag.UNORDEREDLIST) {
+                        reqFieldType = DefaultOpenFieldType.NESTED_OPEN_AUNORDERED_LIST_TYPE;
+                    }
+                    if (TypeComputerUtilities.getRequiredType((AbstractFunctionCallExpression) argExpr) == null) {
+                        ScalarFunctionCallExpression argFunc = (ScalarFunctionCallExpression) argExpr;
+                        rewriteFuncExpr(argFunc, reqFieldType, inputFieldTypes[i], env);
+                    }
+                }
+                arguments.add(fExprRef);
+            }
+        }
+    }
+
+}