diff --git a/parser/parser.y b/parser/parser.y
index 47e62547cf8d6..15480fc1cab1b 100644
--- a/parser/parser.y
+++ b/parser/parser.y
@@ -2881,9 +2881,9 @@ FunctionCallKeyword:
 	}
 
 FunctionCallNonKeyword:
-	"ABS" '(' Expression ')'
+	"ABS" '(' ExpressionListOpt ')'
 	{
-		$$ = &ast.FuncCallExpr{FnName: model.NewCIStr($1), Args: []ast.ExprNode{$3.(ast.ExprNode)}}
+		$$ = &ast.FuncCallExpr{FnName: model.NewCIStr($1), Args: $3.([]ast.ExprNode)}
 	}
 |	"ADDTIME" '(' Expression ',' Expression ')'
  	{
diff --git a/plan/typeinferer.go b/plan/typeinferer.go
index db035e2fb3bfa..1b4c20a7ced8d 100644
--- a/plan/typeinferer.go
+++ b/plan/typeinferer.go
@@ -292,6 +292,9 @@ func (v *typeInferrer) getFsp(x *ast.FuncCallExpr) int {
 	return 0
 }
 
+// handleFuncCallExpr ...
+// TODO: (zhexuany) this function contains too much redundant things. Maybe replace with a map like
+// we did for error in mysql package.
 func (v *typeInferrer) handleFuncCallExpr(x *ast.FuncCallExpr) {
 	var (
 		tp  *types.FieldType
@@ -299,12 +302,20 @@ func (v *typeInferrer) handleFuncCallExpr(x *ast.FuncCallExpr) {
 	)
 	switch x.FnName.L {
 	case ast.Abs, ast.Ifnull, ast.Nullif:
+		if len(x.Args) == 0 {
+			tp = types.NewFieldType(mysql.TypeNull)
+			break
+		}
 		tp = x.Args[0].GetType()
 		// TODO: We should cover all types.
 		if x.FnName.L == ast.Abs && tp.Tp == mysql.TypeDatetime {
 			tp = types.NewFieldType(mysql.TypeDouble)
 		}
 	case ast.Round:
+		if len(x.Args) == 0 {
+			tp = types.NewFieldType(mysql.TypeNull)
+			break
+		}
 		t := x.Args[0].GetType().Tp
 		switch t {
 		case mysql.TypeBit, mysql.TypeTiny, mysql.TypeShort, mysql.TypeInt24, mysql.TypeLonglong:
@@ -323,15 +334,21 @@ func (v *typeInferrer) handleFuncCallExpr(x *ast.FuncCallExpr) {
 			for i := 1; i < len(x.Args); i++ {
 				tp = mergeCmpType(tp, x.Args[i].GetType())
 			}
+		} else {
+			tp = types.NewFieldType(mysql.TypeNull)
 		}
 	case ast.Ceil, ast.Ceiling, ast.Floor:
-		t := x.Args[0].GetType().Tp
-		if t == mysql.TypeNull || t == mysql.TypeFloat || t == mysql.TypeDouble || t == mysql.TypeVarchar ||
-			t == mysql.TypeTinyBlob || t == mysql.TypeMediumBlob || t == mysql.TypeLongBlob ||
-			t == mysql.TypeBlob || t == mysql.TypeVarString || t == mysql.TypeString {
-			tp = types.NewFieldType(mysql.TypeDouble)
+		if len(x.Args) > 0 {
+			t := x.Args[0].GetType().Tp
+			if t == mysql.TypeNull || t == mysql.TypeFloat || t == mysql.TypeDouble || t == mysql.TypeVarchar ||
+				t == mysql.TypeTinyBlob || t == mysql.TypeMediumBlob || t == mysql.TypeLongBlob ||
+				t == mysql.TypeBlob || t == mysql.TypeVarString || t == mysql.TypeString {
+				tp = types.NewFieldType(mysql.TypeDouble)
+			} else {
+				tp = types.NewFieldType(mysql.TypeLonglong)
+			}
 		} else {
-			tp = types.NewFieldType(mysql.TypeLonglong)
+			tp = types.NewFieldType(mysql.TypeNull)
 		}
 	case ast.FromUnixTime:
 		if len(x.Args) == 1 {
diff --git a/plan/typeinferer_test.go b/plan/typeinferer_test.go
index 0f3fb7a05a3ea..1b88a1e8500d6 100644
--- a/plan/typeinferer_test.go
+++ b/plan/typeinferer_test.go
@@ -122,6 +122,7 @@ func (ts *testTypeInferrerSuite) TestInferType(c *C) {
 		// Functions
 		{"version()", mysql.TypeVarString, charset.CharsetUTF8, 0},
 		{"count(c_int)", mysql.TypeLonglong, charset.CharsetBin, mysql.BinaryFlag},
+		{"abs()", mysql.TypeNull, charset.CharsetBin, mysql.BinaryFlag},
 		{"abs(1)", mysql.TypeLonglong, charset.CharsetBin, mysql.BinaryFlag},
 		{"abs(1.1)", mysql.TypeNewDecimal, charset.CharsetBin, mysql.BinaryFlag},
 		{"abs(cast(\"20150817015609\" as DATETIME))", mysql.TypeDouble, charset.CharsetBin, mysql.BinaryFlag},
@@ -225,6 +226,7 @@ func (ts *testTypeInferrerSuite) TestInferType(c *C) {
 		{"interval(1, 2, 3)", mysql.TypeLonglong, charset.CharsetBin, mysql.BinaryFlag},
 		{"interval(1.0, 2.0, 3.0)", mysql.TypeLonglong, charset.CharsetBin, mysql.BinaryFlag},
 		{"interval('1', '2', '3')", mysql.TypeLonglong, charset.CharsetBin, mysql.BinaryFlag},
+		// {"round()", mysql.TypeNull, charset.CharsetBin, mysql.BinaryFlag},
 		{"round(null, 2)", mysql.TypeDouble, charset.CharsetBin, mysql.BinaryFlag},
 		{"round('1.2', 2)", mysql.TypeDouble, charset.CharsetBin, mysql.BinaryFlag},
 		{"round(1e2, 2)", mysql.TypeDouble, charset.CharsetBin, mysql.BinaryFlag},
@@ -252,6 +254,11 @@ func (ts *testTypeInferrerSuite) TestInferType(c *C) {
 		{"unix_timestamp('2015-11-13 10:20:19')", mysql.TypeLonglong, charset.CharsetBin, mysql.BinaryFlag},
 		{"to_days('2015-11-13')", mysql.TypeLonglong, charset.CharsetBin, mysql.BinaryFlag},
 		{"to_days(950501)", mysql.TypeLonglong, charset.CharsetBin, mysql.BinaryFlag},
+		// {"ceiling()", mysql.TypeNull, charset.CharsetBin, mysql.BinaryFlag},
+		{"ceiling(1.23)", mysql.TypeLonglong, charset.CharsetBin, mysql.BinaryFlag},
+		// {"ceil()", mysql.TypeNull, charset.CharsetBin, mysql.BinaryFlag},
+		{"ceil(1.23)", mysql.TypeLonglong, charset.CharsetBin, mysql.BinaryFlag},
+		// {"floor()", mysql.TypeNull, charset.CharsetBin, mysql.BinaryFlag},
 		{"floor(1.23)", mysql.TypeLonglong, charset.CharsetBin, mysql.BinaryFlag},
 		{"field('foo', null)", mysql.TypeLonglong, charset.CharsetBin, mysql.BinaryFlag},
 		{"find_in_set('foo', 'foo,bar')", mysql.TypeLonglong, charset.CharsetBin, mysql.BinaryFlag},