jayzhan211 commented on code in PR #9108:
URL: https://github.com/apache/arrow-datafusion/pull/9108#discussion_r1499278949


##########
datafusion/expr/src/signature.rs:
##########
@@ -123,35 +126,211 @@ pub enum TypeSignature {
 #[derive(Debug, Clone, PartialEq, Eq, Hash)]
 pub enum ArrayFunctionSignature {
     /// Specialized Signature for ArrayAppend and similar functions
-    /// The first argument should be List/LargeList, and the second argument 
should be non-list or list.
+    /// If `allow_null` is true, the function also accepts a single argument 
of type Null.
+    /// The first argument should be List/LargeList/FixedSizedList, and the 
second argument should be non-list or list.
     /// The second argument's list dimension should be one dimension less than 
the first argument's list dimension.
     /// List dimension of the List/LargeList is equivalent to the number of 
List.
     /// List dimension of the non-list is 0.
-    ArrayAndElement,
+    ArrayAndElement(bool),
     /// Specialized Signature for ArrayPrepend and similar functions
+    /// If `allow_null` is true, the function also accepts a single argument 
of type Null.
     /// The first argument should be non-list or list, and the second argument 
should be List/LargeList.
     /// The first argument's list dimension should be one dimension less than 
the second argument's list dimension.
-    ElementAndArray,
+    ElementAndArray(bool),
     /// Specialized Signature for Array functions of the form (List/LargeList, 
Index)
-    ArrayAndIndex,
+    /// If `allow_null` is true, the function also accepts a single argument 
of type Null.
+    /// The first argument should be List/LargeList/FixedSizedList, and the 
second argument should be Int64.
+    ArrayAndIndex(bool),
     /// Specialized Signature for Array functions of the form (List/LargeList, 
Element, Optional Index)
     ArrayAndElementAndOptionalIndex,
+    /// Specialized Signature for ArrayEmpty and similar functions
+    /// The function takes a single argument that must be a 
List/LargeList/FixedSizeList
+    /// or something that can be coerced to one of those types.
+    /// If `allow_null` is true, the function also accepts a single argument 
of type Null.
+    Array(bool),
+}
+
+impl ArrayFunctionSignature {
+    /// Arguments to ArrayFunctionSignature
+    /// `current_types` - The data types of the arguments
+    /// `allow_null_coercion` - Whether null type coercion is allowed
+    /// Returns the valid types for the function signature
+    pub fn get_type_signature(
+        &self,
+        current_types: &[DataType],
+    ) -> Result<Vec<Vec<DataType>>> {
+        fn array_element_and_optional_index(
+            current_types: &[DataType],
+        ) -> Result<Vec<Vec<DataType>>> {
+            // make sure there's 2 or 3 arguments
+            if !(current_types.len() == 2 || current_types.len() == 3) {
+                return Ok(vec![vec![]]);
+            }
+
+            let first_two_types = &current_types[0..2];
+            let mut valid_types =
+                array_append_or_prepend_valid_types(first_two_types, true, 
true)?;
+
+            // Early return if there are only 2 arguments
+            if current_types.len() == 2 {
+                return Ok(valid_types);
+            }
+
+            let valid_types_with_index = valid_types
+                .iter()
+                .map(|t| {
+                    let mut t = t.clone();
+                    t.push(DataType::Int64);
+                    t
+                })
+                .collect::<Vec<_>>();
+
+            valid_types.extend(valid_types_with_index);
+
+            Ok(valid_types)
+        }
+
+        fn array_append_or_prepend_valid_types(
+            current_types: &[DataType],
+            is_append: bool,
+            allow_null_coercion: bool,
+        ) -> Result<Vec<Vec<DataType>>> {
+            if current_types.len() != 2 {
+                return Ok(vec![vec![]]);
+            }
+
+            let (array_type, elem_type) = if is_append {
+                (&current_types[0], &current_types[1])
+            } else {
+                (&current_types[1], &current_types[0])
+            };
+
+            // We follow Postgres on `array_append(Null, T)`, which is not 
valid.
+            if array_type.eq(&DataType::Null) {
+                if allow_null_coercion {
+                    return Ok(vec![vec![array_type.clone(), 
elem_type.clone()]]);
+                } else {
+                    return Ok(vec![vec![]]);
+                }
+            }
+
+            // We need to find the coerced base type, mainly for cases like:
+            // `array_append(List(null), i64)` -> `List(i64)`
+            let array_base_type = 
datafusion_common::utils::base_type(array_type);
+            let elem_base_type = 
datafusion_common::utils::base_type(elem_type);
+            let new_base_type = comparison_coercion(&array_base_type, 
&elem_base_type);
+
+            let new_base_type = new_base_type.ok_or_else(|| {
+                internal_datafusion_err!(
+                    "Coercion from {array_base_type:?} to {elem_base_type:?} 
not supported."
+                )
+            })?;
+
+            let new_array_type =
+                datafusion_common::utils::coerced_type_with_base_type_only(
+                    array_type,
+                    &new_base_type,
+                );
+
+            match new_array_type {
+                DataType::List(ref field)
+                | DataType::LargeList(ref field)
+                | DataType::FixedSizeList(ref field, _) => {
+                    let new_elem_type = field.data_type();
+                    if is_append {
+                        Ok(vec![vec![new_array_type.clone(), 
new_elem_type.clone()]])
+                    } else {
+                        Ok(vec![vec![new_elem_type.to_owned(), 
new_array_type.clone()]])
+                    }
+                }
+                _ => Ok(vec![vec![]]),
+            }
+        }
+        fn array_and_index(
+            current_types: &[DataType],
+            allow_null_coercion: bool,
+        ) -> Result<Vec<Vec<DataType>>> {
+            if current_types.len() != 2 {
+                return Ok(vec![vec![]]);
+            }
+
+            let array_type = &current_types[0];
+
+            if array_type.eq(&DataType::Null) && !allow_null_coercion {
+                return Ok(vec![vec![]]);
+            }
+
+            match array_type {
+                DataType::List(_)
+                | DataType::LargeList(_)
+                | DataType::FixedSizeList(_, _) => {
+                    let array_type = 
coerced_fixed_size_list_to_list(array_type);
+                    Ok(vec![vec![array_type, DataType::Int64]])

Review Comment:
   I still think it can be further simplied if there is a function that process 
`coerced_fixed_size_list_to_list` and return `array_type`.  Then can be used 
both in `array_and_index` and `array`



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