risingwave_frontend/optimizer/plan_node/

logical_join.rs

// Copyright 2025 RisingWave Labs
//
// Licensed 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.

use std::collections::HashMap;
use std::ops::Deref;

use fixedbitset::FixedBitSet;
use itertools::{EitherOrBoth, Itertools};
use pretty_xmlish::{Pretty, XmlNode};
use risingwave_expr::bail;
use risingwave_pb::expr::expr_node::PbType;
use risingwave_pb::plan_common::{AsOfJoinDesc, JoinType, PbAsOfJoinInequalityType};
use risingwave_pb::stream_plan::StreamScanType;
use risingwave_sqlparser::ast::AsOf;

use super::generic::{
    GenericPlanNode, GenericPlanRef, push_down_into_join, push_down_join_condition,
};
use super::utils::{Distill, childless_record};
use super::{
    BackfillType, BatchPlanRef, ColPrunable, ExprRewritable, Logical, LogicalPlanRef as PlanRef,
    PlanBase, PlanTreeNodeBinary, PredicatePushdown, StreamHashJoin, StreamPlanRef, StreamProject,
    ToBatch, ToStream, generic, try_enforce_locality_requirement,
};
use crate::error::{ErrorCode, Result, RwError};
use crate::expr::{CollectInputRef, Expr, ExprImpl, ExprRewriter, ExprType, ExprVisitor, InputRef};
use crate::optimizer::plan_node::expr_visitable::ExprVisitable;
use crate::optimizer::plan_node::generic::DynamicFilter;
use crate::optimizer::plan_node::stream_asof_join::StreamAsOfJoin;
use crate::optimizer::plan_node::utils::IndicesDisplay;
use crate::optimizer::plan_node::{
    BatchHashJoin, BatchLookupJoin, BatchNestedLoopJoin, ColumnPruningContext, EqJoinPredicate,
    LogicalFilter, LogicalScan, PredicatePushdownContext, RewriteStreamContext,
    StreamDynamicFilter, StreamFilter, StreamTableScan, StreamTemporalJoin, ToStreamContext,
};
use crate::optimizer::plan_visitor::LogicalCardinalityExt;
use crate::optimizer::property::{Distribution, RequiredDist};
use crate::utils::{ColIndexMapping, ColIndexMappingRewriteExt, Condition, ConditionDisplay};

/// `LogicalJoin` combines two relations according to some condition.
///
/// Each output row has fields from the left and right inputs. The set of output rows is a subset
/// of the cartesian product of the two inputs; precisely which subset depends on the join
/// condition. In addition, the output columns are a subset of the columns of the left and
/// right columns, dependent on the output indices provided. A repeat output index is illegal.
#[derive(Debug, Clone, PartialEq, Eq, Hash)]
pub struct LogicalJoin {
    pub base: PlanBase<Logical>,
    core: generic::Join<PlanRef>,
}

impl Distill for LogicalJoin {
    fn distill<'a>(&self) -> XmlNode<'a> {
        let verbose = self.base.ctx().is_explain_verbose();
        let mut vec = Vec::with_capacity(if verbose { 3 } else { 2 });
        vec.push(("type", Pretty::debug(&self.join_type())));

        let concat_schema = self.core.concat_schema();
        let cond = Pretty::debug(&ConditionDisplay {
            condition: self.on(),
            input_schema: &concat_schema,
        });
        vec.push(("on", cond));

        if verbose {
            let data = IndicesDisplay::from_join(&self.core, &concat_schema);
            vec.push(("output", data));
        }

        childless_record("LogicalJoin", vec)
    }
}

impl LogicalJoin {
    pub(crate) fn new(left: PlanRef, right: PlanRef, join_type: JoinType, on: Condition) -> Self {
        let core = generic::Join::with_full_output(left, right, join_type, on);
        Self::with_core(core)
    }

    pub(crate) fn with_output_indices(
        left: PlanRef,
        right: PlanRef,
        join_type: JoinType,
        on: Condition,
        output_indices: Vec<usize>,
    ) -> Self {
        let core = generic::Join::new(left, right, on, join_type, output_indices);
        Self::with_core(core)
    }

    pub fn with_core(core: generic::Join<PlanRef>) -> Self {
        let base = PlanBase::new_logical_with_core(&core);
        LogicalJoin { base, core }
    }

    pub fn create(
        left: PlanRef,
        right: PlanRef,
        join_type: JoinType,
        on_clause: ExprImpl,
    ) -> PlanRef {
        Self::new(left, right, join_type, Condition::with_expr(on_clause)).into()
    }

    pub fn internal_column_num(&self) -> usize {
        self.core.internal_column_num()
    }

    pub fn i2l_col_mapping_ignore_join_type(&self) -> ColIndexMapping {
        self.core.i2l_col_mapping_ignore_join_type()
    }

    pub fn i2r_col_mapping_ignore_join_type(&self) -> ColIndexMapping {
        self.core.i2r_col_mapping_ignore_join_type()
    }

    /// Get a reference to the logical join's on.
    pub fn on(&self) -> &Condition {
        &self.core.on
    }

    pub fn core(&self) -> &generic::Join<PlanRef> {
        &self.core
    }

    /// Collect all input ref in the on condition. And separate them into left and right.
    pub fn input_idx_on_condition(&self) -> (Vec<usize>, Vec<usize>) {
        let input_refs = self
            .core
            .on
            .collect_input_refs(self.core.left.schema().len() + self.core.right.schema().len());
        let index_group = input_refs
            .ones()
            .chunk_by(|i| *i < self.core.left.schema().len());
        let left_index = index_group
            .into_iter()
            .next()
            .map_or(vec![], |group| group.1.collect_vec());
        let right_index = index_group.into_iter().next().map_or(vec![], |group| {
            group
                .1
                .map(|i| i - self.core.left.schema().len())
                .collect_vec()
        });
        (left_index, right_index)
    }

    /// Get the join type of the logical join.
    pub fn join_type(&self) -> JoinType {
        self.core.join_type
    }

    /// Get the eq join key of the logical join.
    pub fn eq_indexes(&self) -> Vec<(usize, usize)> {
        self.core.eq_indexes()
    }

    /// Get the output indices of the logical join.
    pub fn output_indices(&self) -> &Vec<usize> {
        &self.core.output_indices
    }

    /// Clone with new output indices
    pub fn clone_with_output_indices(&self, output_indices: Vec<usize>) -> Self {
        Self::with_core(generic::Join {
            output_indices,
            ..self.core.clone()
        })
    }

    /// Clone with new `on` condition
    pub fn clone_with_cond(&self, on: Condition) -> Self {
        Self::with_core(generic::Join {
            on,
            ..self.core.clone()
        })
    }

    pub fn is_left_join(&self) -> bool {
        matches!(self.join_type(), JoinType::LeftSemi | JoinType::LeftAnti)
    }

    pub fn is_right_join(&self) -> bool {
        matches!(self.join_type(), JoinType::RightSemi | JoinType::RightAnti)
    }

    pub fn is_full_out(&self) -> bool {
        self.core.is_full_out()
    }

    pub fn is_asof_join(&self) -> bool {
        self.join_type() == JoinType::AsofInner || self.join_type() == JoinType::AsofLeftOuter
    }

    pub fn output_indices_are_trivial(&self) -> bool {
        itertools::equal(
            self.output_indices().iter().cloned(),
            0..self.internal_column_num(),
        )
    }

    /// Try to simplify the outer join with the predicate on the top of the join
    ///
    /// now it is just a naive implementation for comparison expression, we can give a more general
    /// implementation with constant folding in future
    fn simplify_outer(predicate: &Condition, left_col_num: usize, join_type: JoinType) -> JoinType {
        let (mut gen_null_in_left, mut gen_null_in_right) = match join_type {
            JoinType::LeftOuter => (false, true),
            JoinType::RightOuter => (true, false),
            JoinType::FullOuter => (true, true),
            _ => return join_type,
        };

        for expr in &predicate.conjunctions {
            if let ExprImpl::FunctionCall(func) = expr {
                match func.func_type() {
                    ExprType::Equal
                    | ExprType::NotEqual
                    | ExprType::LessThan
                    | ExprType::LessThanOrEqual
                    | ExprType::GreaterThan
                    | ExprType::GreaterThanOrEqual => {
                        for input in func.inputs() {
                            if let ExprImpl::InputRef(input) = input {
                                let idx = input.index;
                                if idx < left_col_num {
                                    gen_null_in_left = false;
                                } else {
                                    gen_null_in_right = false;
                                }
                            }
                        }
                    }
                    _ => {}
                };
            }
        }

        match (gen_null_in_left, gen_null_in_right) {
            (true, true) => JoinType::FullOuter,
            (true, false) => JoinType::RightOuter,
            (false, true) => JoinType::LeftOuter,
            (false, false) => JoinType::Inner,
        }
    }

    /// Index Join:
    /// Try to convert logical join into batch lookup join and meanwhile it will do
    /// the index selection for the lookup table so that we can benefit from indexes.
    fn to_batch_lookup_join_with_index_selection(
        &self,
        predicate: EqJoinPredicate,
        batch_join: generic::Join<BatchPlanRef>,
    ) -> Result<Option<BatchLookupJoin>> {
        match batch_join.join_type {
            JoinType::Inner
            | JoinType::LeftOuter
            | JoinType::LeftSemi
            | JoinType::LeftAnti
            | JoinType::AsofInner
            | JoinType::AsofLeftOuter => {}
            _ => return Ok(None),
        };

        // Index selection for index join.
        let right = self.right();
        // Lookup Join only supports basic tables on the join's right side.
        let logical_scan: &LogicalScan = if let Some(logical_scan) = right.as_logical_scan() {
            logical_scan
        } else {
            return Ok(None);
        };

        let mut result_plan = None;
        // Lookup primary table.
        if let Some(lookup_join) =
            self.to_batch_lookup_join(predicate.clone(), batch_join.clone())?
        {
            result_plan = Some(lookup_join);
        }

        if self
            .core
            .ctx()
            .session_ctx()
            .config()
            .enable_index_selection()
        {
            let indexes = logical_scan.table_indexes();
            for index in indexes {
                if let Some(index_scan) = logical_scan.to_index_scan_if_index_covered(index) {
                    let index_scan: PlanRef = index_scan.into();
                    let that = self.clone_with_left_right(self.left(), index_scan.clone());
                    let mut new_batch_join = batch_join.clone();
                    new_batch_join.right =
                        index_scan.to_batch().expect("index scan failed to batch");

                    // Lookup covered index.
                    if let Some(lookup_join) =
                        that.to_batch_lookup_join(predicate.clone(), new_batch_join)?
                    {
                        match &result_plan {
                            None => result_plan = Some(lookup_join),
                            Some(prev_lookup_join) => {
                                // Prefer to choose lookup join with longer lookup prefix len.
                                if prev_lookup_join.lookup_prefix_len()
                                    < lookup_join.lookup_prefix_len()
                                {
                                    result_plan = Some(lookup_join)
                                }
                            }
                        }
                    }
                }
            }
        }

        Ok(result_plan)
    }

    /// Try to convert logical join into batch lookup join.
    fn to_batch_lookup_join(
        &self,
        predicate: EqJoinPredicate,
        logical_join: generic::Join<BatchPlanRef>,
    ) -> Result<Option<BatchLookupJoin>> {
        let logical_scan: &LogicalScan =
            if let Some(logical_scan) = self.core.right.as_logical_scan() {
                logical_scan
            } else {
                return Ok(None);
            };
        Self::gen_batch_lookup_join(logical_scan, predicate, logical_join, self.is_asof_join())
    }

    pub fn gen_batch_lookup_join(
        logical_scan: &LogicalScan,
        predicate: EqJoinPredicate,
        logical_join: generic::Join<BatchPlanRef>,
        is_as_of: bool,
    ) -> Result<Option<BatchLookupJoin>> {
        match logical_join.join_type {
            JoinType::Inner
            | JoinType::LeftOuter
            | JoinType::LeftSemi
            | JoinType::LeftAnti
            | JoinType::AsofInner
            | JoinType::AsofLeftOuter => {}
            _ => return Ok(None),
        };

        let table = logical_scan.table();
        let output_column_ids = logical_scan.output_column_ids();

        // Verify that the right join key columns are the the prefix of the primary key and
        // also contain the distribution key.
        let order_col_ids = table.order_column_ids();
        let dist_key = table.distribution_key.clone();
        // The at least prefix of order key that contains distribution key.
        let mut dist_key_in_order_key_pos = vec![];
        for d in dist_key {
            let pos = table
                .order_column_indices()
                .position(|x| x == d)
                .expect("dist_key must in order_key");
            dist_key_in_order_key_pos.push(pos);
        }
        // The shortest prefix of order key that contains distribution key.
        let shortest_prefix_len = dist_key_in_order_key_pos
            .iter()
            .max()
            .map_or(0, |pos| pos + 1);

        // Distributed lookup join can't support lookup table with a singleton distribution.
        if shortest_prefix_len == 0 {
            return Ok(None);
        }

        // Reorder the join equal predicate to match the order key.
        let mut reorder_idx = Vec::with_capacity(shortest_prefix_len);
        for order_col_id in order_col_ids {
            let mut found = false;
            for (i, eq_idx) in predicate.right_eq_indexes().into_iter().enumerate() {
                if order_col_id == output_column_ids[eq_idx] {
                    reorder_idx.push(i);
                    found = true;
                    break;
                }
            }
            if !found {
                break;
            }
        }
        if reorder_idx.len() < shortest_prefix_len {
            return Ok(None);
        }
        let lookup_prefix_len = reorder_idx.len();
        let predicate = predicate.reorder(&reorder_idx);

        // Extract the predicate from logical scan. Only pure scan is supported.
        let (new_scan, scan_predicate, project_expr) = logical_scan.predicate_pull_up();
        // Construct output column to require column mapping
        let o2r = if let Some(project_expr) = project_expr {
            project_expr
                .into_iter()
                .map(|x| x.as_input_ref().unwrap().index)
                .collect_vec()
        } else {
            (0..logical_scan.output_col_idx().len()).collect_vec()
        };
        let left_schema_len = logical_join.left.schema().len();

        let mut join_predicate_rewriter = LookupJoinPredicateRewriter {
            offset: left_schema_len,
            mapping: o2r.clone(),
        };

        let new_eq_cond = predicate
            .eq_cond()
            .rewrite_expr(&mut join_predicate_rewriter);

        let mut scan_predicate_rewriter = LookupJoinScanPredicateRewriter {
            offset: left_schema_len,
        };

        let new_other_cond = predicate
            .other_cond()
            .clone()
            .rewrite_expr(&mut join_predicate_rewriter)
            .and(scan_predicate.rewrite_expr(&mut scan_predicate_rewriter));

        let new_join_on = new_eq_cond.and(new_other_cond);
        let new_predicate = EqJoinPredicate::create(
            left_schema_len,
            new_scan.schema().len(),
            new_join_on.clone(),
        );

        // We discovered that we cannot use a lookup join after pulling up the predicate
        // from one side and simplifying the condition. Let's use some other join instead.
        if !new_predicate.has_eq() {
            return Ok(None);
        }

        // Rewrite the join output indices and all output indices referred to the old scan need to
        // rewrite.
        let new_join_output_indices = logical_join
            .output_indices
            .iter()
            .map(|&x| {
                if x < left_schema_len {
                    x
                } else {
                    o2r[x - left_schema_len] + left_schema_len
                }
            })
            .collect_vec();

        let new_scan_output_column_ids = new_scan.output_column_ids();
        let as_of = new_scan.as_of.clone();
        let new_logical_scan: LogicalScan = new_scan.into();

        // Construct a new logical join, because we have change its RHS.
        let new_logical_join = generic::Join::new(
            logical_join.left,
            new_logical_scan.to_batch()?,
            new_join_on,
            logical_join.join_type,
            new_join_output_indices,
        );

        let asof_desc = is_as_of
            .then(|| {
                Self::get_inequality_desc_from_predicate(
                    predicate.other_cond().clone(),
                    left_schema_len,
                )
            })
            .transpose()?;

        Ok(Some(BatchLookupJoin::new(
            new_logical_join,
            new_predicate,
            table.clone(),
            new_scan_output_column_ids,
            lookup_prefix_len,
            false,
            as_of,
            asof_desc,
        )))
    }

    pub fn decompose(self) -> (PlanRef, PlanRef, Condition, JoinType, Vec<usize>) {
        self.core.decompose()
    }
}

impl PlanTreeNodeBinary<Logical> for LogicalJoin {
    fn left(&self) -> PlanRef {
        self.core.left.clone()
    }

    fn right(&self) -> PlanRef {
        self.core.right.clone()
    }

    fn clone_with_left_right(&self, left: PlanRef, right: PlanRef) -> Self {
        Self::with_core(generic::Join {
            left,
            right,
            ..self.core.clone()
        })
    }

    fn rewrite_with_left_right(
        &self,
        left: PlanRef,
        left_col_change: ColIndexMapping,
        right: PlanRef,
        right_col_change: ColIndexMapping,
    ) -> (Self, ColIndexMapping) {
        let (new_on, new_output_indices) = {
            let (mut map, _) = left_col_change.clone().into_parts();
            let (mut right_map, _) = right_col_change.clone().into_parts();
            for i in right_map.iter_mut().flatten() {
                *i += left.schema().len();
            }
            map.append(&mut right_map);
            let mut mapping = ColIndexMapping::new(map, left.schema().len() + right.schema().len());

            let new_output_indices = self
                .output_indices()
                .iter()
                .map(|&i| mapping.map(i))
                .collect::<Vec<_>>();
            let new_on = self.on().clone().rewrite_expr(&mut mapping);
            (new_on, new_output_indices)
        };

        let join = Self::with_output_indices(
            left,
            right,
            self.join_type(),
            new_on,
            new_output_indices.clone(),
        );

        let new_i2o = ColIndexMapping::with_remaining_columns(
            &new_output_indices,
            join.internal_column_num(),
        );

        let old_o2i = self.core.o2i_col_mapping();

        let old_o2l = old_o2i
            .composite(&self.core.i2l_col_mapping())
            .composite(&left_col_change);
        let old_o2r = old_o2i
            .composite(&self.core.i2r_col_mapping())
            .composite(&right_col_change);
        let new_l2o = join.core.l2i_col_mapping().composite(&new_i2o);
        let new_r2o = join.core.r2i_col_mapping().composite(&new_i2o);

        let out_col_change = old_o2l
            .composite(&new_l2o)
            .union(&old_o2r.composite(&new_r2o));
        (join, out_col_change)
    }
}

impl_plan_tree_node_for_binary! { Logical, LogicalJoin }

impl ColPrunable for LogicalJoin {
    fn prune_col(&self, required_cols: &[usize], ctx: &mut ColumnPruningContext) -> PlanRef {
        // make `required_cols` point to internal table instead of output schema.
        let required_cols = required_cols
            .iter()
            .map(|i| self.output_indices()[*i])
            .collect_vec();
        let left_len = self.left().schema().fields.len();

        let total_len = self.left().schema().len() + self.right().schema().len();
        let mut resized_required_cols = FixedBitSet::with_capacity(total_len);

        required_cols.iter().for_each(|&i| {
            if self.is_right_join() {
                resized_required_cols.insert(left_len + i);
            } else {
                resized_required_cols.insert(i);
            }
        });

        // add those columns which are required in the join condition to
        // to those that are required in the output
        let mut visitor = CollectInputRef::new(resized_required_cols);
        self.on().visit_expr(&mut visitor);
        let left_right_required_cols = FixedBitSet::from(visitor).ones().collect_vec();

        let mut left_required_cols = Vec::new();
        let mut right_required_cols = Vec::new();
        left_right_required_cols.iter().for_each(|&i| {
            if i < left_len {
                left_required_cols.push(i);
            } else {
                right_required_cols.push(i - left_len);
            }
        });

        let mut on = self.on().clone();
        let mut mapping =
            ColIndexMapping::with_remaining_columns(&left_right_required_cols, total_len);
        on = on.rewrite_expr(&mut mapping);

        let new_output_indices = {
            let required_inputs_in_output = if self.is_left_join() {
                &left_required_cols
            } else if self.is_right_join() {
                &right_required_cols
            } else {
                &left_right_required_cols
            };

            let mapping =
                ColIndexMapping::with_remaining_columns(required_inputs_in_output, total_len);
            required_cols.iter().map(|&i| mapping.map(i)).collect_vec()
        };

        LogicalJoin::with_output_indices(
            self.left().prune_col(&left_required_cols, ctx),
            self.right().prune_col(&right_required_cols, ctx),
            self.join_type(),
            on,
            new_output_indices,
        )
        .into()
    }
}

impl ExprRewritable<Logical> for LogicalJoin {
    fn has_rewritable_expr(&self) -> bool {
        true
    }

    fn rewrite_exprs(&self, r: &mut dyn ExprRewriter) -> PlanRef {
        let mut core = self.core.clone();
        core.rewrite_exprs(r);
        Self {
            base: self.base.clone_with_new_plan_id(),
            core,
        }
        .into()
    }
}

impl ExprVisitable for LogicalJoin {
    fn visit_exprs(&self, v: &mut dyn ExprVisitor) {
        self.core.visit_exprs(v);
    }
}

/// We are trying to derive a predicate to apply to the other side of a join if all
/// the `InputRef`s in the predicate are eq condition columns, and can hence be substituted
/// with the corresponding eq condition columns of the other side.
///
/// Strategy:
/// 1. If the function is pure except for any `InputRef` (which may refer to impure computation),
///    then we proceed. Else abort.
/// 2. Then, we collect `InputRef`s in the conjunction.
/// 3. If they are all columns in the given side of join eq condition, then we proceed. Else abort.
/// 4. We then rewrite the `ExprImpl`, by replacing `InputRef` column indices with the equivalent in
///    the other side.
///
/// # Arguments
///
/// Suppose we derive a predicate from the left side to be pushed to the right side.
/// * `expr`: An expr from the left side.
/// * `col_num`: The number of columns in the left side.
fn derive_predicate_from_eq_condition(
    expr: &ExprImpl,
    eq_condition: &EqJoinPredicate,
    col_num: usize,
    expr_is_left: bool,
) -> Option<ExprImpl> {
    if expr.is_impure() {
        return None;
    }
    let eq_indices = eq_condition
        .eq_indexes_typed()
        .iter()
        .filter_map(|(l, r)| {
            if l.return_type() != r.return_type() {
                None
            } else if expr_is_left {
                Some(l.index())
            } else {
                Some(r.index())
            }
        })
        .collect_vec();
    if expr
        .collect_input_refs(col_num)
        .ones()
        .any(|index| !eq_indices.contains(&index))
    {
        // expr contains an InputRef not in eq_condition
        return None;
    }
    // The function is pure except for `InputRef` and all `InputRef`s are `eq_condition` indices.
    // Hence, we can substitute those `InputRef`s with indices from the other side.
    let other_side_mapping = if expr_is_left {
        eq_condition.eq_indexes_typed().into_iter().collect()
    } else {
        eq_condition
            .eq_indexes_typed()
            .into_iter()
            .map(|(x, y)| (y, x))
            .collect()
    };
    struct InputRefsRewriter {
        mapping: HashMap<InputRef, InputRef>,
    }
    impl ExprRewriter for InputRefsRewriter {
        fn rewrite_input_ref(&mut self, input_ref: InputRef) -> ExprImpl {
            self.mapping[&input_ref].clone().into()
        }
    }
    Some(
        InputRefsRewriter {
            mapping: other_side_mapping,
        }
        .rewrite_expr(expr.clone()),
    )
}

/// Rewrite the join predicate and all columns referred to the scan side need to rewrite.
struct LookupJoinPredicateRewriter {
    offset: usize,
    mapping: Vec<usize>,
}
impl ExprRewriter for LookupJoinPredicateRewriter {
    fn rewrite_input_ref(&mut self, input_ref: InputRef) -> ExprImpl {
        if input_ref.index() < self.offset {
            input_ref.into()
        } else {
            InputRef::new(
                self.mapping[input_ref.index() - self.offset] + self.offset,
                input_ref.return_type(),
            )
            .into()
        }
    }
}

/// Rewrite the scan predicate so we can add it to the join predicate.
struct LookupJoinScanPredicateRewriter {
    offset: usize,
}
impl ExprRewriter for LookupJoinScanPredicateRewriter {
    fn rewrite_input_ref(&mut self, input_ref: InputRef) -> ExprImpl {
        InputRef::new(input_ref.index() + self.offset, input_ref.return_type()).into()
    }
}

impl PredicatePushdown for LogicalJoin {
    /// Pushes predicates above and within a join node into the join node and/or its children nodes.
    ///
    /// # Which predicates can be pushed
    ///
    /// For inner join, we can do all kinds of pushdown.
    ///
    /// For left/right semi join, we can push filter to left/right and on-clause,
    /// and push on-clause to left/right.
    ///
    /// For left/right anti join, we can push filter to left/right, but on-clause can not be pushed
    ///
    /// ## Outer Join
    ///
    /// Preserved Row table
    /// : The table in an Outer Join that must return all rows.
    ///
    /// Null Supplying table
    /// : This is the table that has nulls filled in for its columns in unmatched rows.
    ///
    /// |                          | Preserved Row table | Null Supplying table |
    /// |--------------------------|---------------------|----------------------|
    /// | Join predicate (on)      | Not Pushed          | Pushed               |
    /// | Where predicate (filter) | Pushed              | Not Pushed           |
    fn predicate_pushdown(
        &self,
        predicate: Condition,
        ctx: &mut PredicatePushdownContext,
    ) -> PlanRef {
        // rewrite output col referencing indices as internal cols
        let mut predicate = {
            let mut mapping = self.core.o2i_col_mapping();
            predicate.rewrite_expr(&mut mapping)
        };

        let left_col_num = self.left().schema().len();
        let right_col_num = self.right().schema().len();
        let join_type = LogicalJoin::simplify_outer(&predicate, left_col_num, self.join_type());

        let push_down_temporal_predicate = self.temporal_join_on().is_none();

        let (left_from_filter, right_from_filter, on) = push_down_into_join(
            &mut predicate,
            left_col_num,
            right_col_num,
            join_type,
            push_down_temporal_predicate,
        );

        let mut new_on = self.on().clone().and(on);
        let (left_from_on, right_from_on) = push_down_join_condition(
            &mut new_on,
            left_col_num,
            right_col_num,
            join_type,
            push_down_temporal_predicate,
        );

        let left_predicate = left_from_filter.and(left_from_on);
        let right_predicate = right_from_filter.and(right_from_on);

        // Derive conditions to push to the other side based on eq condition columns
        let eq_condition = EqJoinPredicate::create(left_col_num, right_col_num, new_on.clone());

        // Only push to RHS if RHS is inner side of a join (RHS requires match on LHS)
        let right_from_left = if matches!(
            join_type,
            JoinType::Inner | JoinType::LeftOuter | JoinType::RightSemi | JoinType::LeftSemi
        ) {
            Condition {
                conjunctions: left_predicate
                    .conjunctions
                    .iter()
                    .filter_map(|expr| {
                        derive_predicate_from_eq_condition(expr, &eq_condition, left_col_num, true)
                    })
                    .collect(),
            }
        } else {
            Condition::true_cond()
        };

        // Only push to LHS if LHS is inner side of a join (LHS requires match on RHS)
        let left_from_right = if matches!(
            join_type,
            JoinType::Inner | JoinType::RightOuter | JoinType::LeftSemi | JoinType::RightSemi
        ) {
            Condition {
                conjunctions: right_predicate
                    .conjunctions
                    .iter()
                    .filter_map(|expr| {
                        derive_predicate_from_eq_condition(
                            expr,
                            &eq_condition,
                            right_col_num,
                            false,
                        )
                    })
                    .collect(),
            }
        } else {
            Condition::true_cond()
        };

        let left_predicate = left_predicate.and(left_from_right);
        let right_predicate = right_predicate.and(right_from_left);

        let new_left = self.left().predicate_pushdown(left_predicate, ctx);
        let new_right = self.right().predicate_pushdown(right_predicate, ctx);
        let new_join = LogicalJoin::with_output_indices(
            new_left,
            new_right,
            join_type,
            new_on,
            self.output_indices().clone(),
        );

        let mut mapping = self.core.i2o_col_mapping();
        predicate = predicate.rewrite_expr(&mut mapping);
        LogicalFilter::create(new_join.into(), predicate)
    }
}

#[derive(Clone, Copy)]
struct TemporalJoinScan<'a>(&'a LogicalScan);

impl<'a> Deref for TemporalJoinScan<'a> {
    type Target = LogicalScan;

    fn deref(&self) -> &Self::Target {
        self.0
    }
}

impl LogicalJoin {
    fn get_stream_input_for_hash_join(
        &self,
        predicate: &EqJoinPredicate,
        ctx: &mut ToStreamContext,
    ) -> Result<(StreamPlanRef, StreamPlanRef)> {
        use super::stream::prelude::*;

        let lhs_join_key_idx = self.eq_indexes().into_iter().map(|(l, _)| l).collect_vec();
        let rhs_join_key_idx = self.eq_indexes().into_iter().map(|(_, r)| r).collect_vec();

        let logical_right = try_enforce_locality_requirement(self.right(), &rhs_join_key_idx);
        let mut right = logical_right.to_stream_with_dist_required(
            &RequiredDist::shard_by_key(self.right().schema().len(), &predicate.right_eq_indexes()),
            ctx,
        )?;
        let logical_left = try_enforce_locality_requirement(self.left(), &lhs_join_key_idx);
        let r2l =
            predicate.r2l_eq_columns_mapping(logical_left.schema().len(), right.schema().len());
        let l2r =
            predicate.l2r_eq_columns_mapping(logical_left.schema().len(), right.schema().len());
        let mut left;
        let right_dist = right.distribution();
        match right_dist {
            Distribution::HashShard(_) => {
                let left_dist = r2l
                    .rewrite_required_distribution(&RequiredDist::PhysicalDist(right_dist.clone()));
                left = logical_left.to_stream_with_dist_required(&left_dist, ctx)?;
            }
            Distribution::UpstreamHashShard(_, _) => {
                left = logical_left.to_stream_with_dist_required(
                    &RequiredDist::shard_by_key(
                        self.left().schema().len(),
                        &predicate.left_eq_indexes(),
                    ),
                    ctx,
                )?;
                let left_dist = left.distribution();
                match left_dist {
                    Distribution::HashShard(_) => {
                        let right_dist = l2r.rewrite_required_distribution(
                            &RequiredDist::PhysicalDist(left_dist.clone()),
                        );
                        right = right_dist.streaming_enforce_if_not_satisfies(right)?
                    }
                    Distribution::UpstreamHashShard(_, _) => {
                        left = RequiredDist::hash_shard(&predicate.left_eq_indexes())
                            .streaming_enforce_if_not_satisfies(left)?;
                        right = RequiredDist::hash_shard(&predicate.right_eq_indexes())
                            .streaming_enforce_if_not_satisfies(right)?;
                    }
                    _ => unreachable!(),
                }
            }
            _ => unreachable!(),
        }
        Ok((left, right))
    }

    fn to_stream_hash_join(
        &self,
        predicate: EqJoinPredicate,
        ctx: &mut ToStreamContext,
    ) -> Result<StreamPlanRef> {
        use super::stream::prelude::*;

        assert!(predicate.has_eq());
        let (left, right) = self.get_stream_input_for_hash_join(&predicate, ctx)?;

        let core = self.core.clone_with_inputs(left, right);

        // Convert to Hash Join for equal joins
        // For inner joins, pull non-equal conditions to a filter operator on top of it by default.
        // We do so as the filter operator can apply the non-equal condition batch-wise (vectorized)
        // as opposed to the HashJoin, which applies the condition row-wise.
        // However, the default behavior of pulling up non-equal conditions can be overridden by the
        // session variable `streaming_force_filter_inside_join` as it can save unnecessary
        // materialization of rows only to be filtered later.

        let stream_hash_join = StreamHashJoin::new(core.clone(), predicate.clone())?;

        let force_filter_inside_join = self
            .base
            .ctx()
            .session_ctx()
            .config()
            .streaming_force_filter_inside_join();

        let pull_filter = self.join_type() == JoinType::Inner
            && stream_hash_join.eq_join_predicate().has_non_eq()
            && stream_hash_join.inequality_pairs().is_empty()
            && (!force_filter_inside_join);
        if pull_filter {
            let default_indices = (0..self.internal_column_num()).collect::<Vec<_>>();

            let mut core = core;
            core.output_indices = default_indices.clone();
            // Temporarily remove output indices.
            let eq_cond = EqJoinPredicate::new(
                Condition::true_cond(),
                predicate.eq_keys().to_vec(),
                self.left().schema().len(),
                self.right().schema().len(),
            );
            core.on = eq_cond.eq_cond();
            let hash_join = StreamHashJoin::new(core, eq_cond)?.into();
            let logical_filter = generic::Filter::new(predicate.non_eq_cond(), hash_join);
            let plan = StreamFilter::new(logical_filter).into();
            if self.output_indices() != &default_indices {
                let logical_project = generic::Project::with_mapping(
                    plan,
                    ColIndexMapping::with_remaining_columns(
                        self.output_indices(),
                        self.internal_column_num(),
                    ),
                );
                Ok(StreamProject::new(logical_project).into())
            } else {
                Ok(plan)
            }
        } else {
            Ok(stream_hash_join.into())
        }
    }

    fn temporal_join_on(&self) -> Option<TemporalJoinScan<'_>> {
        if let Some(logical_scan) = self.core.right.as_logical_scan() {
            matches!(logical_scan.as_of(), Some(AsOf::ProcessTime))
                .then_some(TemporalJoinScan(logical_scan))
        } else {
            None
        }
    }

    fn should_be_stream_temporal_join<'a>(
        &'a self,
        ctx: &ToStreamContext,
    ) -> Result<Option<TemporalJoinScan<'a>>> {
        Ok(if let Some(scan) = self.temporal_join_on() {
            if let BackfillType::SnapshotBackfill = ctx.backfill_type() {
                return Err(RwError::from(ErrorCode::NotSupported(
                    "Temporal join with snapshot backfill not supported".into(),
                    "Please use arrangement backfill".into(),
                )));
            }
            if scan.cross_database() {
                return Err(RwError::from(ErrorCode::NotSupported(
                        "Temporal join requires the lookup table to be in the same database as the stream source table".into(),
                        "Please ensure both tables are in the same database".into(),
                    )));
            }
            Some(scan)
        } else {
            None
        })
    }

    fn to_stream_temporal_join_with_index_selection(
        &self,
        logical_scan: TemporalJoinScan<'_>,
        predicate: EqJoinPredicate,
        ctx: &mut ToStreamContext,
    ) -> Result<StreamPlanRef> {
        // Use primary table.
        let mut result_plan: Result<StreamTemporalJoin> =
            self.to_stream_temporal_join(logical_scan, predicate.clone(), ctx);
        // Return directly if this temporal join can match the pk of its right table.
        if let Ok(temporal_join) = &result_plan
            && temporal_join.eq_join_predicate().eq_indexes().len()
                == logical_scan.primary_key().len()
        {
            return result_plan.map(|x| x.into());
        }
        if self
            .core
            .ctx()
            .session_ctx()
            .config()
            .enable_index_selection()
        {
            let indexes = logical_scan.table_indexes();
            for index in indexes {
                // Use index table
                if let Some(index_scan) = logical_scan.to_index_scan_if_index_covered(index) {
                    let index_scan: PlanRef = index_scan.into();
                    let that = self.clone_with_left_right(self.left(), index_scan.clone());
                    if let Ok(temporal_join) = that.to_stream_temporal_join(
                        that.temporal_join_on().expect(
                            "index scan created from temporal join scan must also be temporal join",
                        ),
                        predicate.clone(),
                        ctx,
                    ) {
                        match &result_plan {
                            Err(_) => result_plan = Ok(temporal_join),
                            Ok(prev_temporal_join) => {
                                // Prefer to the temporal join with a longer lookup prefix len.
                                if prev_temporal_join.eq_join_predicate().eq_indexes().len()
                                    < temporal_join.eq_join_predicate().eq_indexes().len()
                                {
                                    result_plan = Ok(temporal_join)
                                }
                            }
                        }
                    }
                }
            }
        }

        result_plan.map(|x| x.into())
    }

    fn temporal_join_scan_predicate_pull_up(
        logical_scan: TemporalJoinScan<'_>,
        predicate: EqJoinPredicate,
        output_indices: &[usize],
        left_schema_len: usize,
    ) -> Result<(StreamTableScan, EqJoinPredicate, Condition, Vec<usize>)> {
        // Extract the predicate from logical scan. Only pure scan is supported.
        let (new_scan, scan_predicate, project_expr) = logical_scan.predicate_pull_up();
        // Construct output column to require column mapping
        let o2r = if let Some(project_expr) = project_expr {
            project_expr
                .into_iter()
                .map(|x| x.as_input_ref().unwrap().index)
                .collect_vec()
        } else {
            (0..logical_scan.output_col_idx().len()).collect_vec()
        };
        let mut join_predicate_rewriter = LookupJoinPredicateRewriter {
            offset: left_schema_len,
            mapping: o2r.clone(),
        };

        let new_eq_cond = predicate
            .eq_cond()
            .rewrite_expr(&mut join_predicate_rewriter);

        let mut scan_predicate_rewriter = LookupJoinScanPredicateRewriter {
            offset: left_schema_len,
        };

        let new_other_cond = predicate
            .other_cond()
            .clone()
            .rewrite_expr(&mut join_predicate_rewriter)
            .and(scan_predicate.rewrite_expr(&mut scan_predicate_rewriter));

        let new_join_on = new_eq_cond.and(new_other_cond);

        let new_predicate = EqJoinPredicate::create(
            left_schema_len,
            new_scan.schema().len(),
            new_join_on.clone(),
        );

        // Rewrite the join output indices and all output indices referred to the old scan need to
        // rewrite.
        let new_join_output_indices = output_indices
            .iter()
            .map(|&x| {
                if x < left_schema_len {
                    x
                } else {
                    o2r[x - left_schema_len] + left_schema_len
                }
            })
            .collect_vec();

        let new_stream_table_scan =
            StreamTableScan::new_with_stream_scan_type(new_scan, StreamScanType::UpstreamOnly);
        Ok((
            new_stream_table_scan,
            new_predicate,
            new_join_on,
            new_join_output_indices,
        ))
    }

    fn to_stream_temporal_join(
        &self,
        logical_scan: TemporalJoinScan<'_>,
        predicate: EqJoinPredicate,
        ctx: &mut ToStreamContext,
    ) -> Result<StreamTemporalJoin> {
        use super::stream::prelude::*;

        assert!(predicate.has_eq());

        let table = logical_scan.table();
        let output_column_ids = logical_scan.output_column_ids();

        // Verify that the right join key columns are the the prefix of the primary key and
        // also contain the distribution key.
        let order_col_ids = table.order_column_ids();
        let dist_key = table.distribution_key.clone();

        let mut dist_key_in_order_key_pos = vec![];
        for d in dist_key {
            let pos = table
                .order_column_indices()
                .position(|x| x == d)
                .expect("dist_key must in order_key");
            dist_key_in_order_key_pos.push(pos);
        }
        // The shortest prefix of order key that contains distribution key.
        let shortest_prefix_len = dist_key_in_order_key_pos
            .iter()
            .max()
            .map_or(0, |pos| pos + 1);

        // Reorder the join equal predicate to match the order key.
        let mut reorder_idx = Vec::with_capacity(shortest_prefix_len);
        for order_col_id in order_col_ids {
            let mut found = false;
            for (i, eq_idx) in predicate.right_eq_indexes().into_iter().enumerate() {
                if order_col_id == output_column_ids[eq_idx] {
                    reorder_idx.push(i);
                    found = true;
                    break;
                }
            }
            if !found {
                break;
            }
        }
        if reorder_idx.len() < shortest_prefix_len {
            // TODO: support index selection for temporal join and refine this error message.
            return Err(RwError::from(ErrorCode::NotSupported(
                "Temporal join requires the lookup table's primary key contained exactly in the equivalence condition".into(),
                "Please add the primary key of the lookup table to the join condition and remove any other conditions".into(),
            )));
        }
        let lookup_prefix_len = reorder_idx.len();
        let predicate = predicate.reorder(&reorder_idx);

        let required_dist = if dist_key_in_order_key_pos.is_empty() {
            RequiredDist::single()
        } else {
            let left_eq_indexes = predicate.left_eq_indexes();
            let left_dist_key = dist_key_in_order_key_pos
                .iter()
                .map(|pos| left_eq_indexes[*pos])
                .collect_vec();

            RequiredDist::hash_shard(&left_dist_key)
        };

        let lhs_join_key_idx = predicate
            .eq_indexes()
            .into_iter()
            .map(|(l, _)| l)
            .collect_vec();
        let logical_left = try_enforce_locality_requirement(self.left(), &lhs_join_key_idx);
        let left = logical_left.to_stream(ctx)?;
        // Enforce a shuffle for the temporal join LHS to let the scheduler be able to schedule the join fragment together with the RHS with a `no_shuffle` exchange.
        let left = required_dist.stream_enforce(left);

        let (new_stream_table_scan, new_predicate, new_join_on, new_join_output_indices) =
            Self::temporal_join_scan_predicate_pull_up(
                logical_scan,
                predicate,
                self.output_indices(),
                self.left().schema().len(),
            )?;

        let right = RequiredDist::no_shuffle(new_stream_table_scan.into());
        if !new_predicate.has_eq() {
            return Err(RwError::from(ErrorCode::NotSupported(
                "Temporal join requires a non trivial join condition".into(),
                "Please remove the false condition of the join".into(),
            )));
        }

        // Construct a new logical join, because we have change its RHS.
        let new_logical_join = generic::Join::new(
            left,
            right,
            new_join_on,
            self.join_type(),
            new_join_output_indices,
        );

        let new_predicate = new_predicate.retain_prefix_eq_key(lookup_prefix_len);

        StreamTemporalJoin::new(new_logical_join, new_predicate, false)
    }

    fn to_stream_nested_loop_temporal_join(
        &self,
        logical_scan: TemporalJoinScan<'_>,
        predicate: EqJoinPredicate,
        ctx: &mut ToStreamContext,
    ) -> Result<StreamPlanRef> {
        use super::stream::prelude::*;
        assert!(!predicate.has_eq());

        let left = self.left().to_stream_with_dist_required(
            &RequiredDist::PhysicalDist(Distribution::Broadcast),
            ctx,
        )?;
        assert!(left.as_stream_exchange().is_some());

        if self.join_type() != JoinType::Inner {
            return Err(RwError::from(ErrorCode::NotSupported(
                "Temporal join requires an inner join".into(),
                "Please use an inner join".into(),
            )));
        }

        if !left.append_only() {
            return Err(RwError::from(ErrorCode::NotSupported(
                "Nested-loop Temporal join requires the left hash side to be append only".into(),
                "Please ensure the left hash side is append only".into(),
            )));
        }

        let (new_stream_table_scan, new_predicate, new_join_on, new_join_output_indices) =
            Self::temporal_join_scan_predicate_pull_up(
                logical_scan,
                predicate,
                self.output_indices(),
                self.left().schema().len(),
            )?;

        let right = RequiredDist::no_shuffle(new_stream_table_scan.into());

        // Construct a new logical join, because we have change its RHS.
        let new_logical_join = generic::Join::new(
            left,
            right,
            new_join_on,
            self.join_type(),
            new_join_output_indices,
        );

        Ok(StreamTemporalJoin::new(new_logical_join, new_predicate, true)?.into())
    }

    fn to_stream_dynamic_filter(
        &self,
        predicate: Condition,
        ctx: &mut ToStreamContext,
    ) -> Result<Option<StreamPlanRef>> {
        use super::stream::prelude::*;

        // If there is exactly one predicate, it is a comparison (<, <=, >, >=), and the
        // join is a `Inner` or `LeftSemi` join, we can convert the scalar subquery into a
        // `StreamDynamicFilter`

        // Check if `Inner`/`LeftSemi`
        if !matches!(self.join_type(), JoinType::Inner | JoinType::LeftSemi) {
            return Ok(None);
        }

        // Check if right side is a scalar
        if !self.right().max_one_row() {
            return Ok(None);
        }
        if self.right().schema().len() != 1 {
            return Ok(None);
        }

        // Check if the join condition is a correlated comparison
        if predicate.conjunctions.len() > 1 {
            return Ok(None);
        }
        let expr: ExprImpl = predicate.into();
        let (left_ref, comparator, right_ref) = match expr.as_comparison_cond() {
            Some(v) => v,
            None => return Ok(None),
        };

        let condition_cross_inputs = left_ref.index < self.left().schema().len()
            && right_ref.index == self.left().schema().len() /* right side has only one column */;
        if !condition_cross_inputs {
            // Maybe we should panic here because it means some predicates are not pushed down.
            return Ok(None);
        }

        // We align input types on all join predicates with cmp operator
        if self.left().schema().fields()[left_ref.index].data_type
            != self.right().schema().fields()[0].data_type
        {
            return Ok(None);
        }

        // Check if non of the columns from the inner side is required to output
        let all_output_from_left = self
            .output_indices()
            .iter()
            .all(|i| *i < self.left().schema().len());
        if !all_output_from_left {
            return Ok(None);
        }

        let left = self.left().to_stream(ctx)?.enforce_concrete_distribution();
        let right = self.right().to_stream_with_dist_required(
            &RequiredDist::PhysicalDist(Distribution::Broadcast),
            ctx,
        )?;

        assert!(right.as_stream_exchange().is_some());
        assert_eq!(
            *right.inputs().iter().exactly_one().unwrap().distribution(),
            Distribution::Single
        );

        let core = DynamicFilter::new(comparator, left_ref.index, left, right);
        let plan = StreamDynamicFilter::new(core)?.into();
        // TODO: `DynamicFilterExecutor` should support `output_indices` in `ChunkBuilder`
        if self
            .output_indices()
            .iter()
            .copied()
            .ne(0..self.left().schema().len())
        {
            // The schema of dynamic filter is always the same as the left side now, and we have
            // checked that all output columns are from the left side before.
            let logical_project = generic::Project::with_mapping(
                plan,
                ColIndexMapping::with_remaining_columns(
                    self.output_indices(),
                    self.left().schema().len(),
                ),
            );
            Ok(Some(StreamProject::new(logical_project).into()))
        } else {
            Ok(Some(plan))
        }
    }

    pub fn index_lookup_join_to_batch_lookup_join(&self) -> Result<BatchPlanRef> {
        let predicate = EqJoinPredicate::create(
            self.left().schema().len(),
            self.right().schema().len(),
            self.on().clone(),
        );
        assert!(predicate.has_eq());

        let join = self
            .core
            .clone_with_inputs(self.core.left.to_batch()?, self.core.right.to_batch()?);

        Ok(self
            .to_batch_lookup_join(predicate, join)?
            .expect("Fail to convert to lookup join")
            .into())
    }

    fn to_stream_asof_join(
        &self,
        predicate: EqJoinPredicate,
        ctx: &mut ToStreamContext,
    ) -> Result<StreamPlanRef> {
        use super::stream::prelude::*;

        if predicate.eq_keys().is_empty() {
            return Err(ErrorCode::InvalidInputSyntax(
                "AsOf join requires at least 1 equal condition".to_owned(),
            )
            .into());
        }

        let (left, right) = self.get_stream_input_for_hash_join(&predicate, ctx)?;
        let left_len = left.schema().len();
        let core = self.core.clone_with_inputs(left, right);

        let inequality_desc =
            Self::get_inequality_desc_from_predicate(predicate.other_cond().clone(), left_len)?;

        Ok(StreamAsOfJoin::new(core, predicate, inequality_desc)?.into())
    }

    /// Convert the logical join to a Hash join.
    fn to_batch_hash_join(
        &self,
        logical_join: generic::Join<BatchPlanRef>,
        predicate: EqJoinPredicate,
    ) -> Result<BatchPlanRef> {
        use super::batch::prelude::*;

        let left_schema_len = logical_join.left.schema().len();
        let asof_desc = self
            .is_asof_join()
            .then(|| {
                Self::get_inequality_desc_from_predicate(
                    predicate.other_cond().clone(),
                    left_schema_len,
                )
            })
            .transpose()?;

        let batch_join = BatchHashJoin::new(logical_join, predicate, asof_desc);
        Ok(batch_join.into())
    }

    pub fn get_inequality_desc_from_predicate(
        predicate: Condition,
        left_input_len: usize,
    ) -> Result<AsOfJoinDesc> {
        let expr: ExprImpl = predicate.into();
        if let Some((left_input_ref, expr_type, right_input_ref)) = expr.as_comparison_cond() {
            if left_input_ref.index() < left_input_len && right_input_ref.index() >= left_input_len
            {
                Ok(AsOfJoinDesc {
                    left_idx: left_input_ref.index() as u32,
                    right_idx: (right_input_ref.index() - left_input_len) as u32,
                    inequality_type: Self::expr_type_to_comparison_type(expr_type)?.into(),
                })
            } else {
                bail!("inequal condition from the same side should be push down in optimizer");
            }
        } else {
            Err(ErrorCode::InvalidInputSyntax(
                "AsOf join requires exactly 1 ineuquality condition".to_owned(),
            )
            .into())
        }
    }

    fn expr_type_to_comparison_type(expr_type: PbType) -> Result<PbAsOfJoinInequalityType> {
        match expr_type {
            PbType::LessThan => Ok(PbAsOfJoinInequalityType::AsOfInequalityTypeLt),
            PbType::LessThanOrEqual => Ok(PbAsOfJoinInequalityType::AsOfInequalityTypeLe),
            PbType::GreaterThan => Ok(PbAsOfJoinInequalityType::AsOfInequalityTypeGt),
            PbType::GreaterThanOrEqual => Ok(PbAsOfJoinInequalityType::AsOfInequalityTypeGe),
            _ => Err(ErrorCode::InvalidInputSyntax(format!(
                "Invalid comparison type: {}",
                expr_type.as_str_name()
            ))
            .into()),
        }
    }
}

impl ToBatch for LogicalJoin {
    fn to_batch(&self) -> Result<crate::optimizer::plan_node::BatchPlanRef> {
        let predicate = EqJoinPredicate::create(
            self.left().schema().len(),
            self.right().schema().len(),
            self.on().clone(),
        );

        let batch_join = self
            .core
            .clone_with_inputs(self.core.left.to_batch()?, self.core.right.to_batch()?);

        let ctx = self.base.ctx();
        let config = ctx.session_ctx().config();

        if predicate.has_eq() {
            if !predicate.eq_keys_are_type_aligned() {
                return Err(ErrorCode::InternalError(format!(
                    "Join eq keys are not aligned for predicate: {predicate:?}"
                ))
                .into());
            }
            if config.batch_enable_lookup_join()
                && let Some(lookup_join) = self.to_batch_lookup_join_with_index_selection(
                    predicate.clone(),
                    batch_join.clone(),
                )?
            {
                return Ok(lookup_join.into());
            }
            self.to_batch_hash_join(batch_join, predicate)
        } else if self.is_asof_join() {
            Err(ErrorCode::InvalidInputSyntax(
                "AsOf join requires at least 1 equal condition".to_owned(),
            )
            .into())
        } else {
            // Convert to Nested-loop Join for non-equal joins
            Ok(BatchNestedLoopJoin::new(batch_join).into())
        }
    }
}

impl ToStream for LogicalJoin {
    fn to_stream(
        &self,
        ctx: &mut ToStreamContext,
    ) -> Result<crate::optimizer::plan_node::StreamPlanRef> {
        if self
            .on()
            .conjunctions
            .iter()
            .any(|cond| cond.count_nows() > 0)
        {
            return Err(ErrorCode::NotSupported(
                "optimizer has tried to separate the temporal predicate(with now() expression) from the on condition, but it still reminded in on join's condition. Considering move it into WHERE clause?".to_owned(),
                 "please refer to https://www.risingwave.dev/docs/current/sql-pattern-temporal-filters/ for more information".to_owned()).into());
        }

        let predicate = EqJoinPredicate::create(
            self.left().schema().len(),
            self.right().schema().len(),
            self.on().clone(),
        );

        if self.join_type() == JoinType::AsofInner || self.join_type() == JoinType::AsofLeftOuter {
            self.to_stream_asof_join(predicate, ctx)
        } else if predicate.has_eq() {
            if !predicate.eq_keys_are_type_aligned() {
                return Err(ErrorCode::InternalError(format!(
                    "Join eq keys are not aligned for predicate: {predicate:?}"
                ))
                .into());
            }

            if let Some(scan) = self.should_be_stream_temporal_join(ctx)? {
                self.to_stream_temporal_join_with_index_selection(scan, predicate, ctx)
            } else {
                self.to_stream_hash_join(predicate, ctx)
            }
        } else if let Some(scan) = self.should_be_stream_temporal_join(ctx)? {
            self.to_stream_nested_loop_temporal_join(scan, predicate, ctx)
        } else if let Some(dynamic_filter) =
            self.to_stream_dynamic_filter(self.on().clone(), ctx)?
        {
            Ok(dynamic_filter)
        } else {
            Err(RwError::from(ErrorCode::NotSupported(
                "streaming nested-loop join".to_owned(),
                "The non-equal join in the query requires a nested-loop join executor, which could be very expensive to run. \
                 Consider rewriting the query to use dynamic filter as a substitute if possible.\n\
                 See also: https://docs.risingwave.com/docs/current/sql-pattern-dynamic-filters/".to_owned(),
            )))
        }
    }

    fn logical_rewrite_for_stream(
        &self,
        ctx: &mut RewriteStreamContext,
    ) -> Result<(PlanRef, ColIndexMapping)> {
        let (left, left_col_change) = self.left().logical_rewrite_for_stream(ctx)?;
        let left_len = left.schema().len();
        let (right, right_col_change) = self.right().logical_rewrite_for_stream(ctx)?;
        let (join, out_col_change) = self.rewrite_with_left_right(
            left.clone(),
            left_col_change,
            right.clone(),
            right_col_change,
        );

        let mapping = ColIndexMapping::with_remaining_columns(
            join.output_indices(),
            join.internal_column_num(),
        );

        let l2o = join.core.l2i_col_mapping().composite(&mapping);
        let r2o = join.core.r2i_col_mapping().composite(&mapping);

        // Add missing pk indices to the logical join
        let mut left_to_add = left
            .expect_stream_key()
            .iter()
            .cloned()
            .filter(|i| l2o.try_map(*i).is_none())
            .collect_vec();

        let mut right_to_add = right
            .expect_stream_key()
            .iter()
            .filter(|&&i| r2o.try_map(i).is_none())
            .map(|&i| i + left_len)
            .collect_vec();

        // NOTE(st1page): add join keys in the pk_indices a work around before we really have stream
        // key.
        let right_len = right.schema().len();
        let eq_predicate = EqJoinPredicate::create(left_len, right_len, join.on().clone());

        let either_or_both = self.core.add_which_join_key_to_pk();

        for (lk, rk) in eq_predicate.eq_indexes() {
            match either_or_both {
                EitherOrBoth::Left(_) => {
                    if l2o.try_map(lk).is_none() {
                        left_to_add.push(lk);
                    }
                }
                EitherOrBoth::Right(_) => {
                    if r2o.try_map(rk).is_none() {
                        right_to_add.push(rk + left_len)
                    }
                }
                EitherOrBoth::Both(_, _) => {
                    if l2o.try_map(lk).is_none() {
                        left_to_add.push(lk);
                    }
                    if r2o.try_map(rk).is_none() {
                        right_to_add.push(rk + left_len)
                    }
                }
            };
        }
        let left_to_add = left_to_add.into_iter().unique();
        let right_to_add = right_to_add.into_iter().unique();
        // NOTE(st1page) over

        let mut new_output_indices = join.output_indices().clone();
        if !join.is_right_join() {
            new_output_indices.extend(left_to_add);
        }
        if !join.is_left_join() {
            new_output_indices.extend(right_to_add);
        }

        let join_with_pk = join.clone_with_output_indices(new_output_indices);

        let plan = if join_with_pk.join_type() == JoinType::FullOuter {
            // ignore the all NULL to maintain the stream key's uniqueness, see https://github.com/risingwavelabs/risingwave/issues/8084 for more information

            let l2o = join_with_pk
                .core
                .l2i_col_mapping()
                .composite(&join_with_pk.core.i2o_col_mapping());
            let r2o = join_with_pk
                .core
                .r2i_col_mapping()
                .composite(&join_with_pk.core.i2o_col_mapping());
            let left_right_stream_keys = join_with_pk
                .left()
                .expect_stream_key()
                .iter()
                .map(|i| l2o.map(*i))
                .chain(
                    join_with_pk
                        .right()
                        .expect_stream_key()
                        .iter()
                        .map(|i| r2o.map(*i)),
                )
                .collect_vec();
            let plan: PlanRef = join_with_pk.into();
            LogicalFilter::filter_out_all_null_keys(plan, &left_right_stream_keys)
        } else {
            join_with_pk.into()
        };

        // the added columns is at the end, so it will not change the exists column index
        Ok((plan, out_col_change))
    }

    fn try_better_locality(&self, columns: &[usize]) -> Option<PlanRef> {
        let mut ctx = ToStreamContext::new(false);
        // only pass through the locality information if it can be converted to dynamic filter
        if let Ok(Some(_)) = self.to_stream_dynamic_filter(self.on().clone(), &mut ctx) {
            // since dynamic filter only supports left input ref in the output indices, we can safely use o2i mapping to convert the required columns.
            let o2i_mapping = self.core.o2i_col_mapping();
            let left_input_columns = columns
                .iter()
                .map(|&col| o2i_mapping.try_map(col))
                .collect::<Option<Vec<usize>>>()?;
            if let Some(better_left_plan) = self.left().try_better_locality(&left_input_columns) {
                return Some(
                    self.clone_with_left_right(better_left_plan, self.right())
                        .into(),
                );
            }
        }
        None
    }
}

#[cfg(test)]
mod tests {

    use std::collections::HashSet;

    use risingwave_common::catalog::{Field, Schema};
    use risingwave_common::types::{DataType, Datum};
    use risingwave_pb::expr::expr_node::Type;

    use super::*;
    use crate::expr::{FunctionCall, Literal, assert_eq_input_ref};
    use crate::optimizer::optimizer_context::OptimizerContext;
    use crate::optimizer::plan_node::LogicalValues;
    use crate::optimizer::property::FunctionalDependency;

    /// Pruning
    /// ```text
    /// Join(on: input_ref(1)=input_ref(3))
    ///   TableScan(v1, v2, v3)
    ///   TableScan(v4, v5, v6)
    /// ```
    /// with required columns [2,3] will result in
    /// ```text
    /// Project(input_ref(1), input_ref(2))
    ///   Join(on: input_ref(0)=input_ref(2))
    ///     TableScan(v2, v3)
    ///     TableScan(v4)
    /// ```
    #[tokio::test]
    async fn test_prune_join() {
        let ty = DataType::Int32;
        let ctx = OptimizerContext::mock().await;
        let fields: Vec<Field> = (1..7)
            .map(|i| Field::with_name(ty.clone(), format!("v{}", i)))
            .collect();
        let left = LogicalValues::new(
            vec![],
            Schema {
                fields: fields[0..3].to_vec(),
            },
            ctx.clone(),
        );
        let right = LogicalValues::new(
            vec![],
            Schema {
                fields: fields[3..6].to_vec(),
            },
            ctx,
        );
        let on: ExprImpl = ExprImpl::FunctionCall(Box::new(
            FunctionCall::new(
                Type::Equal,
                vec![
                    ExprImpl::InputRef(Box::new(InputRef::new(1, ty.clone()))),
                    ExprImpl::InputRef(Box::new(InputRef::new(3, ty))),
                ],
            )
            .unwrap(),
        ));
        let join_type = JoinType::Inner;
        let join: PlanRef = LogicalJoin::new(
            left.into(),
            right.into(),
            join_type,
            Condition::with_expr(on),
        )
        .into();

        // Perform the prune
        let required_cols = vec![2, 3];
        let plan = join.prune_col(&required_cols, &mut ColumnPruningContext::new(join.clone()));

        // Check the result
        let join = plan.as_logical_join().unwrap();
        assert_eq!(join.schema().fields().len(), 2);
        assert_eq!(join.schema().fields()[0], fields[2]);
        assert_eq!(join.schema().fields()[1], fields[3]);

        let expr: ExprImpl = join.on().clone().into();
        let call = expr.as_function_call().unwrap();
        assert_eq_input_ref!(&call.inputs()[0], 0);
        assert_eq_input_ref!(&call.inputs()[1], 2);

        let left = join.left();
        let left = left.as_logical_values().unwrap();
        assert_eq!(left.schema().fields(), &fields[1..3]);
        let right = join.right();
        let right = right.as_logical_values().unwrap();
        assert_eq!(right.schema().fields(), &fields[3..4]);
    }

    /// Semi join panicked previously at `prune_col`. Add test to prevent regression.
    #[tokio::test]
    async fn test_prune_semi_join() {
        let ty = DataType::Int32;
        let ctx = OptimizerContext::mock().await;
        let fields: Vec<Field> = (1..7)
            .map(|i| Field::with_name(ty.clone(), format!("v{}", i)))
            .collect();
        let left = LogicalValues::new(
            vec![],
            Schema {
                fields: fields[0..3].to_vec(),
            },
            ctx.clone(),
        );
        let right = LogicalValues::new(
            vec![],
            Schema {
                fields: fields[3..6].to_vec(),
            },
            ctx,
        );
        let on: ExprImpl = ExprImpl::FunctionCall(Box::new(
            FunctionCall::new(
                Type::Equal,
                vec![
                    ExprImpl::InputRef(Box::new(InputRef::new(1, ty.clone()))),
                    ExprImpl::InputRef(Box::new(InputRef::new(4, ty))),
                ],
            )
            .unwrap(),
        ));
        for join_type in [
            JoinType::LeftSemi,
            JoinType::RightSemi,
            JoinType::LeftAnti,
            JoinType::RightAnti,
        ] {
            let join = LogicalJoin::new(
                left.clone().into(),
                right.clone().into(),
                join_type,
                Condition::with_expr(on.clone()),
            );

            let offset = if join.is_right_join() { 3 } else { 0 };
            let join: PlanRef = join.into();
            // Perform the prune
            let required_cols = vec![0];
            // key 0 is never used in the join (always key 1)
            let plan = join.prune_col(&required_cols, &mut ColumnPruningContext::new(join.clone()));
            let as_plan = plan.as_logical_join().unwrap();
            // Check the result
            assert_eq!(as_plan.schema().fields().len(), 1);
            assert_eq!(as_plan.schema().fields()[0], fields[offset]);

            // Perform the prune
            let required_cols = vec![0, 1, 2];
            // should not panic here
            let plan = join.prune_col(&required_cols, &mut ColumnPruningContext::new(join.clone()));
            let as_plan = plan.as_logical_join().unwrap();
            // Check the result
            assert_eq!(as_plan.schema().fields().len(), 3);
            assert_eq!(as_plan.schema().fields()[0], fields[offset]);
            assert_eq!(as_plan.schema().fields()[1], fields[offset + 1]);
            assert_eq!(as_plan.schema().fields()[2], fields[offset + 2]);
        }
    }

    /// Pruning
    /// ```text
    /// Join(on: input_ref(1)=input_ref(3))
    ///   TableScan(v1, v2, v3)
    ///   TableScan(v4, v5, v6)
    /// ```
    /// with required columns [1, 3] will result in
    /// ```text
    /// Join(on: input_ref(0)=input_ref(1))
    ///   TableScan(v2)
    ///   TableScan(v4)
    /// ```
    #[tokio::test]
    async fn test_prune_join_no_project() {
        let ty = DataType::Int32;
        let ctx = OptimizerContext::mock().await;
        let fields: Vec<Field> = (1..7)
            .map(|i| Field::with_name(ty.clone(), format!("v{}", i)))
            .collect();
        let left = LogicalValues::new(
            vec![],
            Schema {
                fields: fields[0..3].to_vec(),
            },
            ctx.clone(),
        );
        let right = LogicalValues::new(
            vec![],
            Schema {
                fields: fields[3..6].to_vec(),
            },
            ctx,
        );
        let on: ExprImpl = ExprImpl::FunctionCall(Box::new(
            FunctionCall::new(
                Type::Equal,
                vec![
                    ExprImpl::InputRef(Box::new(InputRef::new(1, ty.clone()))),
                    ExprImpl::InputRef(Box::new(InputRef::new(3, ty))),
                ],
            )
            .unwrap(),
        ));
        let join_type = JoinType::Inner;
        let join: PlanRef = LogicalJoin::new(
            left.into(),
            right.into(),
            join_type,
            Condition::with_expr(on),
        )
        .into();

        // Perform the prune
        let required_cols = vec![1, 3];
        let plan = join.prune_col(&required_cols, &mut ColumnPruningContext::new(join.clone()));

        // Check the result
        let join = plan.as_logical_join().unwrap();
        assert_eq!(join.schema().fields().len(), 2);
        assert_eq!(join.schema().fields()[0], fields[1]);
        assert_eq!(join.schema().fields()[1], fields[3]);

        let expr: ExprImpl = join.on().clone().into();
        let call = expr.as_function_call().unwrap();
        assert_eq_input_ref!(&call.inputs()[0], 0);
        assert_eq_input_ref!(&call.inputs()[1], 1);

        let left = join.left();
        let left = left.as_logical_values().unwrap();
        assert_eq!(left.schema().fields(), &fields[1..2]);
        let right = join.right();
        let right = right.as_logical_values().unwrap();
        assert_eq!(right.schema().fields(), &fields[3..4]);
    }

    /// Convert
    /// ```text
    /// Join(on: ($1 = $3) AND ($2 == 42))
    ///   TableScan(v1, v2, v3)
    ///   TableScan(v4, v5, v6)
    /// ```
    /// to
    /// ```text
    /// Filter($2 == 42)
    ///   HashJoin(on: $1 = $3)
    ///     TableScan(v1, v2, v3)
    ///     TableScan(v4, v5, v6)
    /// ```
    #[tokio::test]
    async fn test_join_to_batch() {
        let ctx = OptimizerContext::mock().await;
        let fields: Vec<Field> = (1..7)
            .map(|i| Field::with_name(DataType::Int32, format!("v{}", i)))
            .collect();
        let left = LogicalValues::new(
            vec![],
            Schema {
                fields: fields[0..3].to_vec(),
            },
            ctx.clone(),
        );
        let right = LogicalValues::new(
            vec![],
            Schema {
                fields: fields[3..6].to_vec(),
            },
            ctx,
        );

        fn input_ref(i: usize) -> ExprImpl {
            ExprImpl::InputRef(Box::new(InputRef::new(i, DataType::Int32)))
        }
        let eq_cond = ExprImpl::FunctionCall(Box::new(
            FunctionCall::new(Type::Equal, vec![input_ref(1), input_ref(3)]).unwrap(),
        ));
        let non_eq_cond = ExprImpl::FunctionCall(Box::new(
            FunctionCall::new(
                Type::Equal,
                vec![
                    input_ref(2),
                    ExprImpl::Literal(Box::new(Literal::new(
                        Datum::Some(42_i32.into()),
                        DataType::Int32,
                    ))),
                ],
            )
            .unwrap(),
        ));
        // Condition: ($1 = $3) AND ($2 == 42)
        let on_cond = ExprImpl::FunctionCall(Box::new(
            FunctionCall::new(Type::And, vec![eq_cond.clone(), non_eq_cond.clone()]).unwrap(),
        ));

        let join_type = JoinType::Inner;
        let logical_join = LogicalJoin::new(
            left.into(),
            right.into(),
            join_type,
            Condition::with_expr(on_cond),
        );

        // Perform `to_batch`
        let result = logical_join.to_batch().unwrap();

        // Expected plan:  HashJoin($1 = $3 AND $2 == 42)
        let hash_join = result.as_batch_hash_join().unwrap();
        assert_eq!(
            ExprImpl::from(hash_join.eq_join_predicate().eq_cond()),
            eq_cond
        );
        assert_eq!(
            *hash_join
                .eq_join_predicate()
                .non_eq_cond()
                .conjunctions
                .first()
                .unwrap(),
            non_eq_cond
        );
    }

    /// Convert
    /// ```text
    /// Join(join_type: left outer, on: ($1 = $3) AND ($2 == 42))
    ///   TableScan(v1, v2, v3)
    ///   TableScan(v4, v5, v6)
    /// ```
    /// to
    /// ```text
    /// HashJoin(join_type: left outer, on: ($1 = $3) AND ($2 == 42))
    ///   TableScan(v1, v2, v3)
    ///   TableScan(v4, v5, v6)
    /// ```
    #[tokio::test]
    #[ignore] // ignore due to refactor logical scan, but the test seem to duplicate with the explain test
    // framework, maybe we will remove it?
    async fn test_join_to_stream() {
        // let ctx = Rc::new(RefCell::new(QueryContext::mock().await));
        // let fields: Vec<Field> = (1..7)
        //     .map(|i| Field {
        //         data_type: DataType::Int32,
        //         name: format!("v{}", i),
        //     })
        //     .collect();
        // let left = LogicalScan::new(
        //     "left".to_string(),
        //     TableId::new(0),
        //     vec![1.into(), 2.into(), 3.into()],
        //     Schema {
        //         fields: fields[0..3].to_vec(),
        //     },
        //     ctx.clone(),
        // );
        // let right = LogicalScan::new(
        //     "right".to_string(),
        //     TableId::new(0),
        //     vec![4.into(), 5.into(), 6.into()],
        //     Schema {
        //                 fields: fields[3..6].to_vec(),
        //     },
        //     ctx,
        // );
        // let eq_cond = ExprImpl::FunctionCall(Box::new(
        //     FunctionCall::new(
        //         Type::Equal,
        //         vec![
        //             ExprImpl::InputRef(Box::new(InputRef::new(1, DataType::Int32))),
        //             ExprImpl::InputRef(Box::new(InputRef::new(3, DataType::Int32))),
        //         ],
        //     )
        //     .unwrap(),
        // ));
        // let non_eq_cond = ExprImpl::FunctionCall(Box::new(
        //     FunctionCall::new(
        //         Type::Equal,
        //         vec![
        //             ExprImpl::InputRef(Box::new(InputRef::new(2, DataType::Int32))),
        //             ExprImpl::Literal(Box::new(Literal::new(
        //                 Datum::Some(42_i32.into()),
        //                 DataType::Int32,
        //             ))),
        //         ],
        //     )
        //     .unwrap(),
        // ));
        // // Condition: ($1 = $3) AND ($2 == 42)
        // let on_cond = ExprImpl::FunctionCall(Box::new(
        //     FunctionCall::new(Type::And, vec![eq_cond, non_eq_cond]).unwrap(),
        // ));

        // let join_type = JoinType::LeftOuter;
        // let logical_join = LogicalJoin::new(
        //     left.clone().into(),
        //     right.clone().into(),
        //     join_type,
        //     Condition::with_expr(on_cond.clone()),
        // );

        // // Perform `to_stream`
        // let result = logical_join.to_stream();

        // // Expected plan: HashJoin(($1 = $3) AND ($2 == 42))
        // let hash_join = result.as_stream_hash_join().unwrap();
        // assert_eq!(hash_join.eq_join_predicate().all_cond().as_expr(), on_cond);
    }
    /// Pruning
    /// ```text
    /// Join(on: input_ref(1)=input_ref(3))
    ///   TableScan(v1, v2, v3)
    ///   TableScan(v4, v5, v6)
    /// ```
    /// with required columns [3, 2] will result in
    /// ```text
    /// Project(input_ref(2), input_ref(1))
    ///   Join(on: input_ref(0)=input_ref(2))
    ///     TableScan(v2, v3)
    ///     TableScan(v4)
    /// ```
    #[tokio::test]
    async fn test_join_column_prune_with_order_required() {
        let ty = DataType::Int32;
        let ctx = OptimizerContext::mock().await;
        let fields: Vec<Field> = (1..7)
            .map(|i| Field::with_name(ty.clone(), format!("v{}", i)))
            .collect();
        let left = LogicalValues::new(
            vec![],
            Schema {
                fields: fields[0..3].to_vec(),
            },
            ctx.clone(),
        );
        let right = LogicalValues::new(
            vec![],
            Schema {
                fields: fields[3..6].to_vec(),
            },
            ctx,
        );
        let on: ExprImpl = ExprImpl::FunctionCall(Box::new(
            FunctionCall::new(
                Type::Equal,
                vec![
                    ExprImpl::InputRef(Box::new(InputRef::new(1, ty.clone()))),
                    ExprImpl::InputRef(Box::new(InputRef::new(3, ty))),
                ],
            )
            .unwrap(),
        ));
        let join_type = JoinType::Inner;
        let join: PlanRef = LogicalJoin::new(
            left.into(),
            right.into(),
            join_type,
            Condition::with_expr(on),
        )
        .into();

        // Perform the prune
        let required_cols = vec![3, 2];
        let plan = join.prune_col(&required_cols, &mut ColumnPruningContext::new(join.clone()));

        // Check the result
        let join = plan.as_logical_join().unwrap();
        assert_eq!(join.schema().fields().len(), 2);
        assert_eq!(join.schema().fields()[0], fields[3]);
        assert_eq!(join.schema().fields()[1], fields[2]);

        let expr: ExprImpl = join.on().clone().into();
        let call = expr.as_function_call().unwrap();
        assert_eq_input_ref!(&call.inputs()[0], 0);
        assert_eq_input_ref!(&call.inputs()[1], 2);

        let left = join.left();
        let left = left.as_logical_values().unwrap();
        assert_eq!(left.schema().fields(), &fields[1..3]);
        let right = join.right();
        let right = right.as_logical_values().unwrap();
        assert_eq!(right.schema().fields(), &fields[3..4]);
    }

    #[tokio::test]
    async fn fd_derivation_inner_outer_join() {
        // left: [l0, l1], right: [r0, r1, r2]
        // FD: l0 --> l1, r0 --> { r1, r2 }
        // On: l0 = 0 AND l1 = r1
        //
        // Inner Join:
        //  Schema: [l0, l1, r0, r1, r2]
        //  FD: l0 --> l1, r0 --> { r1, r2 }, {} --> l0, l1 --> r1, r1 --> l1
        // Left Outer Join:
        //  Schema: [l0, l1, r0, r1, r2]
        //  FD: l0 --> l1
        // Right Outer Join:
        //  Schema: [l0, l1, r0, r1, r2]
        //  FD: r0 --> { r1, r2 }
        // Full Outer Join:
        //  Schema: [l0, l1, r0, r1, r2]
        //  FD: empty
        // Left Semi/Anti Join:
        //  Schema: [l0, l1]
        //  FD: l0 --> l1
        // Right Semi/Anti Join:
        //  Schema: [r0, r1, r2]
        //  FD: r0 --> {r1, r2}
        let ctx = OptimizerContext::mock().await;
        let left = {
            let fields: Vec<Field> = vec![
                Field::with_name(DataType::Int32, "l0"),
                Field::with_name(DataType::Int32, "l1"),
            ];
            let mut values = LogicalValues::new(vec![], Schema { fields }, ctx.clone());
            // 0 --> 1
            values
                .base
                .functional_dependency_mut()
                .add_functional_dependency_by_column_indices(&[0], &[1]);
            values
        };
        let right = {
            let fields: Vec<Field> = vec![
                Field::with_name(DataType::Int32, "r0"),
                Field::with_name(DataType::Int32, "r1"),
                Field::with_name(DataType::Int32, "r2"),
            ];
            let mut values = LogicalValues::new(vec![], Schema { fields }, ctx);
            // 0 --> 1, 2
            values
                .base
                .functional_dependency_mut()
                .add_functional_dependency_by_column_indices(&[0], &[1, 2]);
            values
        };
        // l0 = 0 AND l1 = r1
        let on: ExprImpl = FunctionCall::new(
            Type::And,
            vec![
                FunctionCall::new(
                    Type::Equal,
                    vec![
                        InputRef::new(0, DataType::Int32).into(),
                        ExprImpl::literal_int(0),
                    ],
                )
                .unwrap()
                .into(),
                FunctionCall::new(
                    Type::Equal,
                    vec![
                        InputRef::new(1, DataType::Int32).into(),
                        InputRef::new(3, DataType::Int32).into(),
                    ],
                )
                .unwrap()
                .into(),
            ],
        )
        .unwrap()
        .into();
        let expected_fd_set = [
            (
                JoinType::Inner,
                [
                    // inherit from left
                    FunctionalDependency::with_indices(5, &[0], &[1]),
                    // inherit from right
                    FunctionalDependency::with_indices(5, &[2], &[3, 4]),
                    // constant column in join condition
                    FunctionalDependency::with_indices(5, &[], &[0]),
                    // eq column in join condition
                    FunctionalDependency::with_indices(5, &[1], &[3]),
                    FunctionalDependency::with_indices(5, &[3], &[1]),
                ]
                .into_iter()
                .collect::<HashSet<_>>(),
            ),
            (JoinType::FullOuter, HashSet::new()),
            (
                JoinType::RightOuter,
                [
                    // inherit from right
                    FunctionalDependency::with_indices(5, &[2], &[3, 4]),
                ]
                .into_iter()
                .collect::<HashSet<_>>(),
            ),
            (
                JoinType::LeftOuter,
                [
                    // inherit from left
                    FunctionalDependency::with_indices(5, &[0], &[1]),
                ]
                .into_iter()
                .collect::<HashSet<_>>(),
            ),
            (
                JoinType::LeftSemi,
                [
                    // inherit from left
                    FunctionalDependency::with_indices(2, &[0], &[1]),
                ]
                .into_iter()
                .collect::<HashSet<_>>(),
            ),
            (
                JoinType::LeftAnti,
                [
                    // inherit from left
                    FunctionalDependency::with_indices(2, &[0], &[1]),
                ]
                .into_iter()
                .collect::<HashSet<_>>(),
            ),
            (
                JoinType::RightSemi,
                [
                    // inherit from right
                    FunctionalDependency::with_indices(3, &[0], &[1, 2]),
                ]
                .into_iter()
                .collect::<HashSet<_>>(),
            ),
            (
                JoinType::RightAnti,
                [
                    // inherit from right
                    FunctionalDependency::with_indices(3, &[0], &[1, 2]),
                ]
                .into_iter()
                .collect::<HashSet<_>>(),
            ),
        ];

        for (join_type, expected_res) in expected_fd_set {
            let join = LogicalJoin::new(
                left.clone().into(),
                right.clone().into(),
                join_type,
                Condition::with_expr(on.clone()),
            );
            let fd_set = join
                .functional_dependency()
                .as_dependencies()
                .iter()
                .cloned()
                .collect::<HashSet<_>>();
            assert_eq!(fd_set, expected_res);
        }
    }
}