inillucent_sql/

plan.rs

//! The logical and physical plans.
//!
//! Invariant: a physical plan is *legal* before it is fast. Every access path
//! this planner produces returns exactly the rows a full scan of the same term
//! would return, and every predicate a path consumes is either fully enforced
//! by the path or left in the residual filter. A predicate that is neither is a
//! wrong answer, so the two lists are built together and the compiler emits
//! whatever is left over.
//!
//! The phase-6 planner is deliberately minimal: FROM terms stay in written
//! order, joins are nested loops, and the only paths are a full scan, a rowid
//! lookup or range, and an index seek over an equality prefix with an optional
//! range on the column after it. Cost is not modelled yet; a path is chosen
//! because it is more selective by construction, not because a number said so.

use inillucent_value::Collation;

use crate::ast::{BinaryOp, CompoundOp, JoinKind, NullOrder, SortOrder};
use crate::bind::{BoundExpr, BoundSelect, BoundSource, ColumnUse, SourceRows};
use crate::catalog_view::{IndexInfo, TableInfo};
use crate::cost;

mod hint;
mod partial;
mod pattern;
mod range;
mod terms;
pub use hint::unanswerable_index_hint;
use hint::{forced_path, index_usable, outer_terms, statement_terms};
use partial::implies;
use terms::{
    collation_of, compares_unconverted, comparison_against_column, comparison_against_rowid,
    comparison_collation, indexable_comparison,
};
mod seek_union;

/// A comparison an access path can enforce.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum BoundKind {
    /// `>=`
    GreaterEqual,
    /// `>`
    Greater,
    /// `<=`
    LessEqual,
    /// `<`
    Less,
}

/// One end of a scan range.
#[derive(Clone, Debug, PartialEq)]
pub struct RangeBound {
    /// Which comparison the bound enforces.
    pub kind: BoundKind,
    /// The value to compare against.
    pub value: BoundExpr,
    /// Whether the seek compares `value` without converting it to the
    /// column's affinity. See [`AccessPath::IndexSeek`]'s `unconverted`.
    pub unconverted: bool,
}

/// One seek over an index, as a branch of an [`AccessPath::IndexSeekUnion`].
#[derive(Clone, Debug, PartialEq)]
pub struct IndexSeekBranch {
    /// The equality prefix this branch pins, one value per leading index
    /// column.
    pub equalities: Vec<BoundExpr>,
    /// The positions in `equalities` whose value is compared unconverted.
    /// See [`AccessPath::IndexSeek`]'s `unconverted`.
    pub unconverted: Vec<usize>,
    /// The lower bound on the column after the prefix, when there is one.
    pub low: Option<RangeBound>,
    /// The upper bound on that same column.
    pub high: Option<RangeBound>,
}

/// How one FROM term's rows are produced.
#[derive(Clone, Debug, PartialEq)]
pub enum AccessPath {
    /// Every row of the table, in rowid order.
    TableScan {
        /// The table B-tree's root page.
        root: u32,
    },
    /// One row, found by rowid.
    RowidSeek {
        /// The table B-tree's root page.
        root: u32,
        /// The rowid to look up.
        key: BoundExpr,
    },
    /// A contiguous run of rows, by rowid.
    RowidRange {
        /// The table B-tree's root page.
        root: u32,
        /// The lower bound, when there is one.
        low: Option<RangeBound>,
        /// The upper bound, when there is one.
        high: Option<RangeBound>,
    },
    /// Rows found through an index, then fetched from the table.
    IndexSeek {
        /// The table B-tree's root page.
        table_root: u32,
        /// The index B-tree's root page.
        index_root: u32,
        /// The index's name, for the plan description.
        index_name: Vec<u8>,
        /// The equality prefix, one value per leading index column.
        equalities: Vec<BoundExpr>,
        /// The positions in `equalities` whose value the seek compares without
        /// converting it to the column's affinity.
        ///
        /// **The comparison decides this, and only the planner sees the
        /// comparison (task-2083).** A seek converts the probe value to the
        /// indexed column's affinity, except when both sides of the `=` have
        /// an affinity and neither is numeric: then `WHERE` converts nothing
        /// and neither may the seek. That is SQLite's `codeAllEqualityTerms`.
        /// The executor used to decide it from the probe expression alone,
        /// and a correlated subquery replaces the outer column with a
        /// parameter before planning. The parameter has no affinity, so
        /// `(SELECT id FROM h WHERE h.a = s.k)` with `h.a TEXT` and `s.k`
        /// untyped converted the number 3 to `'3'` and found a row SQLite
        /// does not.
        ///
        /// A list of positions rather than a flag per equality because it is
        /// almost always empty, and an empty `Vec` does not allocate. A flag per
        /// equality cost two allocations to compile `WHERE email = ?1`, which
        /// `inillucent::budget` counts.
        unconverted: Vec<usize>,
        /// A range on the column after the equality prefix.
        low: Option<RangeBound>,
        /// The upper end of that range.
        high: Option<RangeBound>,
        /// The collation of each index column used, in order.
        collations: Vec<Collation>,
        /// Whether the index columns used are stored descending.
        descending: Vec<bool>,
        /// Which table column each index column holds.
        ///
        /// `None` for a key the index *computes*: an index on `lower(a)` holds
        /// a value no column of the table carries, and the probe value takes no
        /// column affinity because there is no column to take it from - which
        /// is SQLite's rule and the reason this is an `Option` rather than a
        /// position that would have to be invented.
        columns: Vec<Option<u16>>,
        /// Whether the table has no rowid, so the index key holds the key.
        without_rowid: bool,
        /// Where in each entry the row's primary key sits, for a `WITHOUT
        /// ROWID` table read through a *secondary* index.
        ///
        /// Such an entry ends with the primary key where a rowid table's would
        /// end with a rowid, and that is how the row is then found. Empty for a
        /// rowid table, and empty when the index is the table's own key - then
        /// the entry the seek landed on already is the row.
        key_entry_slots: Vec<usize>,
        /// Where in the index entry every column the query reads sits, when the
        /// index holds all of them.
        ///
        /// An index entry is the indexed columns followed by the row's key, so
        /// a query that reads only those columns never has to go to the table
        /// at all - which halves the descents and, on a range, is the whole
        /// difference between a search and a scan. `None` means the query needs
        /// something the entry does not carry, and the row is fetched.
        ///
        /// The pairs are `(record slot in the table, slot in the index entry)`.
        /// The rowid is not in the list: it is always the entry's last field
        /// for a rowid table, and the compiler reads it with `IdxRowid`.
        covering: Option<Vec<(u16, usize)>>,
    },
    /// One row per key, found by rowid - several of
    /// [`RowidSeek`](Self::RowidSeek), concatenated.
    ///
    /// What `WHERE rowid IN (a, b, c)` plans to on a rowid table: every branch
    /// is the same one-row lookup `RowidSeek` uses alone, so the union is
    /// nothing more than that lookup run once per key. A rowid is unique by
    /// construction, so the only way two branches can name the same row is a
    /// repeated key - a literal list is de-duplicated once, here, at plan
    /// time; a key that is not a literal (a parameter, a correlated column)
    /// cannot be compared this way, so the executor still checks each key
    /// against the ones already probed before it seeks.
    RowidSeekUnion {
        /// The table B-tree's root page.
        root: u32,
        /// The keys to look up, in the order they are probed.
        keys: Vec<BoundExpr>,
    },
    /// Rows found through one index - several seeks over the same tree,
    /// concatenated.
    ///
    /// The branches are what a disjunction's terms become once each is
    /// individually seekable: `x IN (a, b, c)` is every branch a bare
    /// equality on the same column, and a keyset page's
    /// `(a=? AND b>?) OR a>?` is two branches over the same composite index,
    /// one an equality followed by a range and the other a range alone. The
    /// fields outside `branches` describe the one index and table every
    /// branch reads, because those never vary between branches - only the
    /// equality prefix and the range do, which is exactly what a term of a
    /// disjunction can differ in.
    IndexSeekUnion {
        /// The table B-tree's root page.
        table_root: u32,
        /// The index B-tree's root page.
        index_root: u32,
        /// The index's name, for the plan description.
        index_name: Vec<u8>,
        /// One seek per branch, in the order they run.
        branches: Vec<IndexSeekBranch>,
        /// The collation of each index column a branch can reach, in order.
        ///
        /// Sized to the deepest branch - the one whose equality prefix and
        /// range together reach furthest into the index - because a
        /// shallower branch simply does not read the columns past its own
        /// depth.
        collations: Vec<Collation>,
        /// Whether each of those columns is stored descending.
        descending: Vec<bool>,
        /// Which table column each of those index columns holds.
        columns: Vec<Option<u16>>,
        /// Whether the table has no rowid, so the index key holds the key.
        without_rowid: bool,
        /// Where in each entry the row's primary key sits, for a `WITHOUT
        /// ROWID` table read through a *secondary* index. Empty for a rowid
        /// table, and empty when the index is the table's own key.
        key_entry_slots: Vec<usize>,
        /// Where in the index entry every column the query reads sits, when
        /// the index holds all of them.
        covering: Option<Vec<(u16, usize)>>,
        /// Whether a row this union finds can also be found by a different
        /// branch, and so has to be checked against the rows already
        /// emitted before it is.
        ///
        /// `false` only when the branches are proven disjoint by
        /// construction - the keyset-range shape, where each branch's
        /// equality prefix pins a value no other branch's range can reach -
        /// which is what lets that shape stream straight through a `LIMIT`
        /// with nothing held back to be deduplicated. An `IN` list is always
        /// `true`: a non-literal value (a parameter, a correlated column)
        /// cannot be proven distinct from another at plan time, so the
        /// executor has to check.
        dedup: bool,
    },
    /// Rows produced by a nested query, materialised and then scanned.
    Subquery {
        /// The plan that fills the store.
        plan: Box<PhysicalPlan>,
        /// How many columns a materialised row holds.
        width: usize,
        /// Whether the nested block reads a FROM term outside itself, and so
        /// has to be rebuilt for every row of the query that encloses it.
        correlated: bool,
    },
    /// Rows produced by a recursive CTE, filled by walking its own queue.
    Recursive {
        /// The arms that do not reference the CTE, in order.
        seeds: Vec<(CompoundOp, PhysicalPlan)>,
        /// The arms that do.
        steps: Vec<(CompoundOp, PhysicalPlan)>,
        /// How many columns a row holds.
        width: usize,
    },
    /// The one row of a recursive CTE's queue the fill loop is on.
    RecursiveSelf {
        /// The FROM term whose store holds the queue.
        cte: usize,
    },
    /// The k nearest vectors, from an index a module owns.
    ///
    /// **A `TopN` over a distance is a different question from a scan.** The
    /// rows are chosen by the index rather than filtered out of a walk, so the
    /// path carries the probe and the depth rather than a range: the module is
    /// asked for `k` candidates and the plan's own `ORDER BY` then rescores
    /// them exactly, over an `ORDER BY` function matching the index's metric.
    VectorProbe {
        /// The table's root page, whose rows the candidates name.
        root: u32,
        /// The store holding the vectors, by the name the index was created
        /// with.
        index: Vec<u8>,
        /// The vector to measure against, which reads no column of this query.
        probe: Box<BoundExpr>,
        /// How many candidates to ask the index for.
        depth: usize,
    },
    /// Rows produced by a virtual table's module.
    VirtualScan {
        /// The module and the arguments its `CREATE` gave it.
        module: crate::vtab::ModuleRef,
        /// The constraints offered to `best_index`, in the order the module
        /// will see them.
        offer: Vec<VirtualConstraint>,
        /// The ordering offered to `best_index`.
        order_by: Vec<crate::vtab::OrderSpec>,
        /// What the module answered, once it has been asked.
        ///
        /// It is `None` while the plan is still the planner's, and filled in by
        /// a pass that runs before compilation. Keeping the two apart is what
        /// lets the planner stay a pure function of the SQL and one catalog
        /// generation while the program still carries a real plan.
        chosen: Option<VirtualChoice>,
    },
}

/// What a module answered when it was shown the offer.
#[derive(Clone, Debug, PartialEq)]
pub struct VirtualChoice {
    /// The plan number, passed back to the module's `filter`.
    pub index_number: i32,
    /// The plan string, passed back to the module's `filter`.
    pub index_string: String,
    /// The offer positions whose values feed `filter`, in argument order.
    pub arguments: Vec<usize>,
    /// The offer positions the engine must still test for itself.
    ///
    /// Everything the module did not take, and everything it took without
    /// promising to apply. A module that says `omit` is promising; anything
    /// else and the predicate is tested twice, which is the safe direction.
    pub recheck: Vec<usize>,
    /// Whether the module will produce the requested order by itself.
    pub ordered: bool,
}

/// One predicate offered to a module, with what it was made of.
///
/// The predicate is kept whole beside the constraint because the compiler may
/// have to test it after all: a module that used the constraint without
/// promising to apply it leaves the engine responsible for the answer.
#[derive(Clone, Debug, PartialEq)]
pub struct VirtualConstraint {
    /// The constraint as the module is shown it.
    pub spec: crate::vtab::ConstraintSpec,
    /// The value on the other side, which becomes an argument to `filter`.
    pub value: BoundExpr,
    /// The whole predicate, for the compiler to re-test when it must.
    pub predicate: BoundExpr,
}

impl AccessPath {
    /// Returns a one-line description, which is what `EXPLAIN QUERY PLAN`
    /// renders and what a performance test asserts on.
    pub fn describe(&self, table: &str) -> String {
        self.describe_over(table, None)
    }

    /// Returns the same line, naming the columns an index seek compares.
    ///
    /// **`(a=?)` rather than `(?=?)`.** The reference names the key column, and
    /// it is the one part of the line a reader uses to tell "this index" from
    /// "the other index on the same table". The declaration is passed in
    /// because an access path carries the index's *name* and not its columns -
    /// which is the right thing for a plan to carry, and the wrong thing to
    /// render a description from.
    ///
    /// @param table - the name the query calls the term
    /// @param info - the table's declaration, when the caller has it
    pub fn describe_over(&self, table: &str, info: Option<&TableInfo>) -> String {
        match self {
            AccessPath::TableScan { .. } => format!("SCAN {table}"),
            AccessPath::RowidSeek { .. } => {
                format!("SEARCH {table} USING INTEGER PRIMARY KEY (rowid=?)")
            }
            AccessPath::RowidRange { .. } => {
                format!("SEARCH {table} USING INTEGER PRIMARY KEY (rowid>?)")
            }
            // Every branch is the same one-row lookup, so one line describes
            // all of them - which is also how a plain equality reads, and an
            // `IN` list is nothing else once it has been turned into this.
            AccessPath::RowidSeekUnion { .. } => {
                format!("SEARCH {table} USING INTEGER PRIMARY KEY (rowid=?)")
            }
            AccessPath::Recursive { .. } => format!("SCAN {table} USING RECURSIVE QUEUE"),
            AccessPath::RecursiveSelf { .. } => format!("SCAN {table}"),
            AccessPath::VectorProbe { index, depth, .. } => format!(
                "SEARCH {table} USING VECTOR INDEX {} (k={depth})",
                String::from_utf8_lossy(index)
            ),
            AccessPath::VirtualScan { .. } => format!("SCAN {table} VIRTUAL TABLE INDEX"),
            AccessPath::Subquery { correlated, .. } => {
                if *correlated {
                    format!("CORRELATED SCALAR SUBQUERY {table}")
                } else {
                    format!("SCAN {table}")
                }
            }
            AccessPath::IndexSeek {
                index_name,
                equalities,
                low,
                high,
                covering,
                ..
            } => {
                let kind = if covering.is_some() {
                    "COVERING INDEX"
                } else {
                    "INDEX"
                };
                // A walk with nothing to seek used to be covering by
                // construction, so this line said so unconditionally. A
                // partial index and an `INDEXED BY` are walked whole while a
                // lookup per entry fetches the row, and SQLite says `USING
                // INDEX` for that: `SELECT * FROM h INDEXED BY h_a` is
                // `SCAN h USING INDEX h_a` in the pinned 3.53.4 shell.
                if equalities.is_empty() && low.is_none() && high.is_none() {
                    return format!(
                        "SCAN {table} USING {kind} {}",
                        String::from_utf8_lossy(index_name)
                    );
                }
                let detail = index_seek_detail(
                    index_name,
                    info,
                    equalities.len(),
                    low.is_some() || high.is_some(),
                );
                format!(
                    "SEARCH {table} USING {kind} {} ({detail})",
                    String::from_utf8_lossy(index_name)
                )
            }
            AccessPath::IndexSeekUnion {
                index_name,
                branches,
                covering,
                ..
            } => {
                let kind = if covering.is_some() {
                    "COVERING INDEX"
                } else {
                    "INDEX"
                };
                // A branch with the same shape as one already rendered - the
                // same equality-prefix depth and the same presence of a range
                // - reads identically, so an `IN` list (every branch the same
                // bare equality) collapses to the one line a plain equality
                // would render. A genuine disjunction of differently shaped
                // branches - the keyset-range case - gets one line per shape,
                // in the order the branches run.
                let mut lines: Vec<String> = Vec::new();
                for branch in branches {
                    let detail = index_seek_detail(
                        index_name,
                        info,
                        branch.equalities.len(),
                        branch.low.is_some() || branch.high.is_some(),
                    );
                    let line = format!(
                        "SEARCH {table} USING {kind} {} ({detail})",
                        String::from_utf8_lossy(index_name)
                    );
                    if !lines.contains(&line) {
                        lines.push(line);
                    }
                }
                lines.join(" OR ")
            }
        }
    }
}

/// Returns the `(col=? AND col>?)` detail an index seek's description ends
/// with, given how many leading columns of its equality prefix it pins and
/// whether it also carries a range on the column after it.
///
/// Shared between [`AccessPath::IndexSeek`] and each branch of an
/// [`AccessPath::IndexSeekUnion`], which differ only in how many branches
/// there are - the naming of one branch's columns is exactly what a plain
/// seek already does.
fn index_seek_detail(
    index_name: &[u8],
    info: Option<&TableInfo>,
    equalities: usize,
    ranged: bool,
) -> String {
    let keyed = info.and_then(|held| {
        held.indexes
            .iter()
            .find(|candidate| candidate.name == index_name)
    });
    let named = |position: usize| -> String {
        keyed
            .and_then(|index| index.columns.get(position))
            .and_then(|key| key.column)
            .and_then(|at| info.and_then(|held| held.column(at)))
            .map(|column| String::from_utf8_lossy(&column.name).into_owned())
            .unwrap_or_else(|| "?".to_string())
    };
    let mut detail = String::new();
    for index in 0..equalities {
        if index > 0 {
            detail.push_str(" AND ");
        }
        detail.push_str(&format!("{}=?", named(index)));
    }
    if ranged {
        if !detail.is_empty() {
            detail.push_str(" AND ");
        }
        detail.push_str(&format!("{}>?", named(equalities)));
    }
    detail
}

/// One FROM term with the path chosen for it.
#[derive(Clone, Debug, PartialEq)]
pub struct PlannedSource {
    /// What the planner estimated this term's path would cost.
    ///
    /// It is kept so that a test can assert on the *reason* a plan was chosen
    /// rather than only on the plan, which is the difference between catching a
    /// cost-model regression and catching it two releases later.
    pub cost: f64,
    /// How many rows the path is estimated to produce.
    pub rows: f64,
    /// The statement-wide number every bound expression refers to it by.
    pub id: usize,
    /// The table.
    pub table: TableInfo,
    /// The name the query calls it.
    pub alias: Vec<u8>,
    /// How its rows are produced.
    pub path: AccessPath,
    /// The join that attached it to the term before it.
    pub join: JoinKind,
    /// The `ON` condition, when the join is an outer one.
    ///
    /// An inner join's condition is an ordinary predicate and is distributed
    /// with the rest; an outer join's is not, because a row that fails it is
    /// still emitted, null-extended. Keeping it here rather than in the
    /// residual list is what stops the two being confused.
    pub on: Option<BoundExpr>,
    /// Whether the path this term is read by enforces the whole `ON` condition.
    ///
    /// **What decides whether an outer join can be an index nested loop.**
    /// That operator probes the inner tree by a key and
    /// null-extends when the probe finds nothing; it has nowhere to test a
    /// condition the key did not capture, so it may only be used when there is
    /// nothing left to test. When the key is the whole condition - which
    /// `ON b.k = a.k` over an index on `b(k)` is - the probe's answer and the
    /// condition's answer are the same answer.
    ///
    /// False for every inner join, where the condition is distributed into the
    /// statement's terms and re-tested as a residual, and false for an outer
    /// join whose condition says more than its key does.
    pub on_enforced: bool,
}

/// How the rows are grouped and aggregated.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum AggregationMode {
    /// No aggregation at all.
    None,
    /// One group for the whole input, which produces exactly one row.
    Whole,
    /// One group per distinct `GROUP BY` key, produced by sorting first.
    Grouped,
}

/// A physical plan for a read-only statement.
#[derive(Clone, Debug, PartialEq)]
pub struct PhysicalPlan {
    /// The FROM terms, in the order the nested loops visit them.
    pub sources: Vec<PlannedSource>,
    /// The predicates the loops must still evaluate, one per nesting level.
    ///
    /// A predicate is attached to the innermost term it reads, so it is tested
    /// as soon as it can be rather than after every loop has been entered.
    pub residuals: Vec<Option<BoundExpr>>,
    /// A predicate over no columns at all, tested once before the loops.
    pub constant_filter: Option<BoundExpr>,
    /// The bound statement the plan came from.
    pub select: BoundSelect,
    /// How the rows are aggregated.
    pub aggregation: AggregationMode,
    /// Whether the results have to pass through a sorter.
    pub needs_sort: bool,
    /// Whether the outermost term is walked backwards.
    ///
    /// A B-tree read from its last entry to its first produces exactly the
    /// reverse of what it produces read forwards, so a descending `ORDER BY`
    /// over an ascending structure is a direction rather than a sort. Only ever
    /// set when [`needs_sort`](Self::needs_sort) is false: a plan that sorts
    /// does not care which way its input arrived.
    pub reverse: bool,
    /// Whether the walk already brings the rows of each group together.
    ///
    /// Grouping needs adjacency, not order: if every row of a group arrives
    /// before the next group starts, the aggregate can be finished and emitted
    /// as the key changes and nothing has to be collected first. A walk whose
    /// leading keys are exactly the `GROUP BY` columns delivers that, whichever
    /// direction it runs in.
    pub grouped_walk: bool,
    /// Whether the walk already brings duplicate result rows together.
    ///
    /// The same property for `DISTINCT`: adjacent duplicates can be dropped by
    /// comparing each row with the one before it, where a set has to remember
    /// every row it has seen.
    pub distinct_walk: bool,
    /// The later arms of a compound, each with the operator that joined it.
    pub compounds: Vec<(CompoundOp, PhysicalPlan)>,
    /// Which optimizations were on when this plan was chosen.
    ///
    /// Carried on the plan rather than looked up by the executor, because a
    /// plan is *cached* and a lever that changed after it was built must not
    /// change what it does - a plan that consulted the connection at execution
    /// time would answer one way today and another tomorrow with no
    /// recompilation in between. The connection throws its compiled statements
    /// away when a lever moves, which is what makes this field the truth.
    pub levers: Levers,
    /// Whether any expression in this plan holds a subquery used as a value.
    ///
    /// Decided here because it is a property of the *statement* and not of the
    /// data, and because the alternative was deciding it per execution: the
    /// executor folds uncorrelated subqueries on the way into each run, and it
    /// has to ask this question first every time. Walking the expression tree
    /// to ask it cost about 0.07 us per execution - measurable against a
    /// `point.rowid` that takes 0.78 - because `BoundExpr::children` allocates
    /// a vector per node. Asked once per compiled statement instead, it costs
    /// nothing a statement runs.
    pub subqueries: bool,
}

impl PhysicalPlan {
    /// Returns the highest statement-wide source id anywhere in the plan.
    ///
    /// The compiler sizes its cursor map from this, so a nested block's cursor
    /// has a slot before the block that encloses it is compiled.
    pub fn max_source_id(&self) -> usize {
        let mut highest = 0usize;
        for source in &self.sources {
            highest = highest.max(source.id);
            match &source.path {
                AccessPath::Subquery { plan, .. } => {
                    highest = highest.max(plan.max_source_id());
                }
                AccessPath::Recursive { seeds, steps, .. } => {
                    for (_, arm) in seeds.iter().chain(steps.iter()) {
                        highest = highest.max(arm.max_source_id());
                    }
                }
                _ => {}
            }
        }
        for (_, arm) in &self.compounds {
            highest = highest.max(arm.max_source_id());
        }
        highest
    }

    /// Returns the `EXPLAIN QUERY PLAN` lines this plan renders as.
    pub fn describe(&self) -> Vec<String> {
        let mut lines = Vec::new();
        for source in &self.sources {
            lines.push(
                source
                    .path
                    .describe_over(&String::from_utf8_lossy(&source.alias), Some(&source.table)),
            );
        }
        for (op, arm) in &self.compounds {
            lines.push(format!("COMPOUND QUERY {}", compound_name(*op)));
            lines.extend(arm.describe());
        }
        // A temp b-tree is only named when there is one. Grouping and
        // de-duplicating that the walk already delivers build nothing, and a
        // plan that said otherwise would be describing a different program.
        if self.aggregation == AggregationMode::Grouped && !self.grouped_walk {
            lines.push("USE TEMP B-TREE FOR GROUP BY".to_string());
        }
        if self.needs_sort {
            lines.push("USE TEMP B-TREE FOR ORDER BY".to_string());
        }
        if self.select.distinct && !self.distinct_walk {
            lines.push("USE TEMP B-TREE FOR DISTINCT".to_string());
        }
        lines
    }
}

/// Returns the word `EXPLAIN QUERY PLAN` names a compound operator by.
fn compound_name(op: CompoundOp) -> &'static str {
    match op {
        CompoundOp::Union => "UNION",
        CompoundOp::UnionAll => "UNION ALL",
        CompoundOp::Intersect => "INTERSECT",
        CompoundOp::Except => "EXCEPT",
    }
}

/// Which planner optimizations are switched on.
///
/// An optimization that cannot be switched off cannot be measured. The claim
/// "the covering-index path made range reads thirty times faster" is a
/// comparison, and without an arm to compare against it is a comparison with a
/// build that no longer exists - which is an argument, not evidence.
///
/// The shape is SQLite's. `sqlite3_test_control(SQLITE_TESTCTRL_OPTIMIZATIONS)`
/// takes a bitmask of optimizations to *disable*, reached through a control
/// channel rather than through SQL, for exactly this reason: a knob on the SQL
/// surface is a knob applications start depending on, and then it is not a
/// measurement device any more, it is a feature with a compatibility story.
///
/// Disabling is what the mask names, so zero is the shipped engine and the
/// default everywhere. A lever added later defaults to on without anybody
/// having to remember to turn it on.
#[derive(Clone, Copy, Debug, PartialEq, Eq, Default)]
pub struct Levers {
    /// The optimizations that are turned *off*.
    disabled: u32,
}

impl Levers {
    /// Read a term's columns from the index entry, without fetching the row.
    pub const COVERING_INDEX: u32 = 1;
    /// Find the rows an UPDATE or DELETE touches through an index or a rowid,
    /// rather than by scanning the table.
    pub const INDEXED_WRITE: u32 = 2;
    /// Answer an `ORDER BY` by walking a B-tree in its own key order, forwards
    /// or backwards, instead of sorting every row and throwing most away.
    pub const ORDERED_WALK: u32 = 4;
    /// Group and de-duplicate as the rows arrive, when the walk already brings
    /// equal keys together, instead of collecting every row into a sorter or a
    /// set first.
    pub const STREAMING_GROUP: u32 = 8;
    /// Fold a value written into a scratch register and immediately copied
    /// into the one instruction that writes it where it was going.
    pub const FUSED_BYTECODE: u32 = 16;

    /// Reusing a compiled program for SQL text already prepared.
    ///
    /// The rearchitecture's design puts a plan cache in the new engine's
    /// prepare path, and measures it here, on the existing one, first - so the
    /// mechanism is proved independently of the new storage. It is a lever
    /// rather than a constant because a speedup that cannot be switched off
    /// cannot be measured, and because "the cache made prepare six times
    /// faster" needs an arm to be a claim rather than an assertion.
    pub const PLAN_CACHE: u32 = 32;
    /// Build a throwaway structure over an unindexed inner side of a join,
    /// rather than walking it once per outer row.
    ///
    /// What `PRAGMA automatic_index` switches. It is a lever rather than a
    /// constant for the same reason the others are - an optimisation that
    /// cannot be switched off cannot be measured - and because SQLite exposes
    /// exactly this switch under exactly this name, so an application that
    /// turns it off there has somewhere to turn it off here.
    pub const AUTOMATIC_INDEX: u32 = 64;
    /// Every lever this build has.
    pub const EVERY: u32 = Levers::PLAN_CACHE
        | Levers::COVERING_INDEX
        | Levers::INDEXED_WRITE
        | Levers::ORDERED_WALK
        | Levers::STREAMING_GROUP
        | Levers::FUSED_BYTECODE
        | Levers::AUTOMATIC_INDEX;

    /// Returns the shipped configuration: everything on.
    pub fn all() -> Levers {
        Levers { disabled: 0 }
    }

    /// Returns a configuration with the named levers turned off.
    /// @param mask - the levers to disable
    pub fn without(mask: u32) -> Levers {
        Levers {
            disabled: mask & Levers::EVERY,
        }
    }

    /// Returns whether one lever is on.
    /// @param lever - the lever to ask about
    pub fn has(self, lever: u32) -> bool {
        self.disabled & lever == 0
    }

    /// Returns the mask of what is off, which is what a report prints.
    pub fn disabled(self) -> u32 {
        self.disabled
    }

    /// Returns the names of the levers that are off, for a report.
    pub fn names_disabled(self) -> Vec<&'static str> {
        let mut names = Vec::new();
        if !self.has(Levers::COVERING_INDEX) {
            names.push("covering-index");
        }
        if !self.has(Levers::INDEXED_WRITE) {
            names.push("indexed-write");
        }
        if !self.has(Levers::ORDERED_WALK) {
            names.push("ordered-walk");
        }
        if !self.has(Levers::STREAMING_GROUP) {
            names.push("streaming-group");
        }
        if !self.has(Levers::FUSED_BYTECODE) {
            names.push("fused-bytecode");
        }
        names
    }
}

/// Plans a bound SELECT with some optimizations switched off.
///
/// The levers travel with the recursion rather than being read from anywhere
/// global, so a subquery is planned under the same arm as the statement that
/// contains it. An arm that applied to the outer block and not the inner one
/// would measure a mixture and report it as one number.
/// @param select - the bound statement
/// @param levers - which optimizations are on
pub fn plan_select_with(select: BoundSelect, levers: Levers) -> PhysicalPlan {
    let mut select = select;
    let compound_arms = core::mem::take(&mut select.compounds);
    let terms = statement_terms(&select);
    // The order the terms are visited in is chosen before their paths are, and
    // then the paths are chosen in that order - because a path may use a value
    // from a term visited earlier, and which terms those are is exactly what the
    // order decides.
    let order = choose_order(&select, &terms, levers);
    let ordered: Vec<usize> = order.clone();
    let ids: Vec<usize> = ordered
        .iter()
        .filter_map(|position| select.sources.get(*position))
        .map(|source| source.id)
        .collect();
    let mut consumed = vec![false; terms.len()];
    let mut sources = Vec::with_capacity(select.sources.len());
    for (level, position) in ordered.iter().enumerate() {
        let Some(source) = select.sources.get(*position) else {
            continue;
        };
        // **An outer term's rows are not filtered on the way in.** A `WHERE`
        // predicate over the null-extendable side is applied *after* the join,
        // because a row that fails it must still produce a null-extended pair
        // rather than vanish. Letting `choose_path` turn such a predicate into
        // a seek would do both wrong things at once: filter the rows before the
        // null extension, and mark the term consumed so it is never re-tested.
        //
        // **Its own `ON` condition is a different question.**
        // An outer join's `ON` decides which inner rows *match*, and a row with
        // no match is null-extended by the join itself - so seeking the inner
        // side by an equality the `ON` states returns exactly the matches and
        // nothing the join needed is lost. Refusing that made
        // `LEFT JOIN chunk c ON c.document_id = d.id` scan a 60,000-row table
        // where the same join written `JOIN` seeks it: 138.2 ms against 0.5 ms
        // for the same ten rows, and the gap grows with the table.
        //
        // Two things keep it honest. The `ON` terms are collected into a list
        // of their own, so nothing in the statement's `WHERE` can be turned
        // into a seek here and nothing in the statement's `consumed` is marked.
        // And `on` below still carries the whole condition, so the join re-tests
        // it - a seek narrows the rows the test runs over and never stands in
        // for it.
        //
        // A subquery, a recursive CTE and a virtual table each still resolve to
        // what they are, because those are not access-path choices - they are
        // what the term *is*.
        let mut on_enforced = false;
        let path = if is_outer(source.join) && matches!(source.rows, SourceRows::Table) {
            match source.table.module.clone() {
                Some(_) => choose_path(level, &ids, source, &select, &terms, &mut consumed, levers),
                None => {
                    let on_terms = outer_terms(source);
                    let mut on_consumed = vec![false; on_terms.len()];
                    let chosen = choose_path(
                        level,
                        &ids,
                        source,
                        &select,
                        &on_terms,
                        &mut on_consumed,
                        levers,
                    );
                    // Every conjunct of the condition turned into part of the
                    // key, so the probe answers the condition and an index
                    // nested loop can null-extend on an empty probe.
                    on_enforced = !on_terms.is_empty() && on_consumed.iter().all(|held| *held);
                    chosen
                }
            }
        } else {
            choose_path(level, &ids, source, &select, &terms, &mut consumed, levers)
        };
        let (cost, rows) = path_cost(source, &path);
        sources.push(PlannedSource {
            cost,
            rows,
            id: source.id,
            table: (*source.table).clone(),
            alias: source.alias.clone(),
            path,
            join: source.join,
            on: is_outer(source.join)
                .then(|| source.constraint.clone())
                .flatten(),
            on_enforced,
        });
    }
    let (residuals, constant_filter) = distribute_residuals(&terms, &consumed, &ids);
    let aggregation = if !select.group_by.is_empty() {
        AggregationMode::Grouped
    } else if !select.aggregates.is_empty() {
        AggregationMode::Whole
    } else {
        AggregationMode::None
    };
    // The sort is only needed when the outer term's path does not already
    // produce the order that was asked for. Walking a B-tree *is* walking it in
    // key order, and a statement asking for that order has been answered by the
    // walk - which is the difference between reading fifty rows and reading,
    // sorting and throwing away six hundred thousand.
    // A window function sorts the rows into its own order to compute over them,
    // so whatever order the walk delivered is not the order the result comes
    // out in - which is why `windows` disqualifies a statement here even though
    // it has nothing to do with the access path.
    // Adjacency is a weaker property than order, so it is asked first and for a
    // wider set of statements: a grouped aggregate can be streamed whether or
    // not it also answers an ORDER BY.
    let adjacent = levers.has(Levers::STREAMING_GROUP)
        && sources.len() == 1
        && select.windows.is_empty()
        && select.compounds.is_empty();
    let outer = sources.first();
    let grouped_walk = adjacent
        && aggregation == AggregationMode::Grouped
        && outer.is_some_and(|outer| grouped_by_walk(&select, outer));
    let distinct_walk = adjacent && outer.is_some_and(|outer| distinct_by_walk(&select, outer));
    // A statement that streams its grouping or its de-duplication still comes
    // out in the order the walk delivered: the rows of a key arrive together,
    // one output row is emitted per key, and the keys arrive in key order. So
    // the walk answers the ORDER BY for these too.
    //
    // It did not used to. `SELECT DISTINCT category FROM main_table ORDER BY
    // category` walked the covering index on `(category, key)` - which is
    // already in `category` order - de-duplicated as the rows arrived, and then
    // sorted the thirty-two answers through a temporary B-tree anyway. SQLite
    // reads the same index and does not sort, which is the whole of a 26x
    // difference on that workload. The same applied to every
    // `GROUP BY x ORDER BY x`.
    //
    // The two are kept apart rather than merged: a statement that is both
    // grouped and DISTINCT is left to sort, because the de-duplication then
    // runs on the aggregate output rather than on the walk and the walk's order
    // is no longer the result's.
    let streamed_in_order = (grouped_walk && !select.distinct)
        || (distinct_walk && aggregation == AggregationMode::None);
    let single = levers.has(Levers::ORDERED_WALK)
        && sources.len() == 1
        && select.windows.is_empty()
        && select.compounds.is_empty()
        && ((aggregation == AggregationMode::None && !select.distinct) || streamed_in_order);
    let provided = if single {
        sources
            .first()
            .and_then(|outer| ordering_provided(&select, outer.id, &outer.table, &outer.path))
    } else {
        None
    };
    let needs_sort = !select.order_by.is_empty() && provided.is_none();
    let reverse = provided.unwrap_or(false);
    let compounds: Vec<(CompoundOp, PhysicalPlan)> = compound_arms
        .into_iter()
        .map(|(op, arm)| (op, plan_select_with(arm, levers)))
        .collect();
    let subqueries = holds_subquery(&select)
        || residuals.iter().flatten().any(expression_holds_subquery)
        || constant_filter
            .as_ref()
            .is_some_and(expression_holds_subquery)
        || compounds.iter().any(|(_op, arm)| arm.subqueries);
    PhysicalPlan {
        sources,
        residuals,
        constant_filter,
        select,
        aggregation,
        needs_sort,
        reverse,
        grouped_walk,
        distinct_walk,
        compounds,
        subqueries,
        levers,
    }
}

/// Returns whether a select holds a subquery used as a value.
///
/// Compound arms are not walked here: `plan_select_with` has already taken them
/// out of `select.compounds` and planned them, and each arm carries its own
/// answer. A subquery's *block* is not walked either - finding one is enough to
/// say the plan has one.
///
/// @param select - the query to look through
fn holds_subquery(select: &BoundSelect) -> bool {
    select.filter.iter().any(expression_holds_subquery)
        || select.group_by.iter().any(expression_holds_subquery)
        || select.having.iter().any(expression_holds_subquery)
        || select
            .columns
            .iter()
            .any(|column| expression_holds_subquery(&column.expr))
        || select
            .order_by
            .iter()
            .any(|term| expression_holds_subquery(&term.expr))
        || select.limit.iter().any(expression_holds_subquery)
        || select.offset.iter().any(expression_holds_subquery)
        || select
            .values
            .iter()
            .flatten()
            .any(expression_holds_subquery)
        // **The aggregate's `FILTER` and its inner `ORDER BY` are walked here
        // too as of task-1932 (M6).** This flag is the cheap question
        // `subquery::fold` asks before it walks anything, so a statement it
        // answers `false` for never folds - and a subquery in an aggregate's
        // `FILTER` was therefore left in an unfilled slot, which `translate`
        // reports as `unsupported("a correlated subquery used as a value")`.
        // The windows below already had all four of theirs.
        || select.aggregates.iter().any(|aggregate| {
            aggregate.arguments.iter().any(expression_holds_subquery)
                || aggregate.filter.iter().any(expression_holds_subquery)
                || aggregate
                    .order_by
                    .iter()
                    .any(|term| expression_holds_subquery(&term.expr))
        })
        || select.windows.iter().any(|window| {
            window.arguments.iter().any(expression_holds_subquery)
                || window.filter.iter().any(expression_holds_subquery)
                || window.partition_by.iter().any(expression_holds_subquery)
                || window
                    .order_by
                    .iter()
                    .any(|term| expression_holds_subquery(&term.expr))
        })
        || select.sources.iter().any(|source| {
            source.constraint.iter().any(expression_holds_subquery)
                || matches!(&source.rows, SourceRows::Subquery(block) if holds_subquery(block))
        })
}

/// Returns whether an expression holds a subquery, anywhere beneath it.
///
/// Public because the *write* paths need the same answer and cannot get it from
/// a plan: a `VALUES` list and an `UPDATE`'s assignments are evaluated without
/// one. They ask this once when the statement is compiled, for the same reason
/// `PhysicalPlan::subqueries` is decided once - the question is about the
/// statement, and asking it per execution walks a tree and allocates.
///
/// @param expr - the expression to look through
pub fn expression_holds_subquery(expr: &BoundExpr) -> bool {
    matches!(expr, BoundExpr::Subquery { .. })
        || expr
            .children()
            .iter()
            .any(|child| expression_holds_subquery(child))
}

/// Returns whether the walk brings the rows of each `GROUP BY` key together.
///
/// Grouping needs adjacency rather than order, so the direction does not
/// matter: what matters is that the walk's leading keys are exactly the group
/// columns. Exactly, not merely a superset - a walk ordered by `(a, b)` groups
/// `a` and groups `(a, b)`, and does not group `b`.
///
/// The collation does matter. Grouping compares keys with the result collation
/// and the walk compares them with the structure's, so a `NOCASE` index does
/// not group a `BINARY` key: it would put `Ada` and `ADA` next to each other
/// and the grouping would then treat them as one.
/// @param select - the bound statement
/// @param outer - the planned outer term
fn grouped_by_walk(select: &BoundSelect, outer: &PlannedSource) -> bool {
    if select.group_by.is_empty() {
        return false;
    }
    let Some(key) = path_ordering(&outer.table, &outer.path) else {
        return false;
    };
    let mut wanted: Vec<(OrderedBy, Collation)> = Vec::new();
    for expr in &select.group_by {
        let Some(named) = walk_key_of(expr, outer.id, &outer.table) else {
            return false;
        };
        let collation = crate::bind::result_collation(expr);
        if !wanted.iter().any(|(held, _)| *held == named) {
            wanted.push((named, collation));
        }
    }
    covers_prefix(&key, &wanted)
}

/// Returns whether the walk brings duplicate result rows together.
///
/// The same rule as [`grouped_by_walk`], over the result columns rather than
/// the group ones - and it is only asked when there is no grouping, because a
/// `DISTINCT` over aggregates is distinct over values the walk never saw.
/// @param select - the bound statement
/// @param outer - the planned outer term
fn distinct_by_walk(select: &BoundSelect, outer: &PlannedSource) -> bool {
    if !select.distinct || !select.group_by.is_empty() || !select.aggregates.is_empty() {
        return false;
    }
    let Some(key) = path_ordering(&outer.table, &outer.path) else {
        return false;
    };
    let mut wanted: Vec<(OrderedBy, Collation)> = Vec::new();
    for column in &select.columns {
        let Some(named) = walk_key_of(&column.expr, outer.id, &outer.table) else {
            return false;
        };
        let collation = crate::bind::result_collation(&column.expr);
        if !wanted.iter().any(|(held, _)| *held == named) {
            wanted.push((named, collation));
        }
    }
    covers_prefix(&key, &wanted)
}

/// Returns whether a set of keys is exactly the walk's leading keys.
///
/// A key an equality pinned counts as held: it has one value for every row the
/// walk returns, so it is constant across the whole scan and cannot separate
/// two rows that are otherwise equal.
/// @param key - what the walk is ordered by
/// @param wanted - the keys that have to arrive together, with their collations
fn covers_prefix(key: &PathOrdering, wanted: &[(OrderedBy, Collation)]) -> bool {
    let free: Vec<&(OrderedBy, Collation)> = wanted
        .iter()
        .filter(|(named, _)| !key.pinned.contains(named))
        .collect();
    if free.len() > key.columns.len() {
        return false;
    }
    let prefix = match key.columns.get(..free.len()) {
        Some(prefix) => prefix,
        None => return false,
    };
    free.iter().all(|(named, collation)| {
        prefix
            .iter()
            .any(|(held, _, held_collation)| held == named && held_collation == collation)
    })
}

/// Returns which of the walk's keys an expression names, if it names one.
/// @param expr - the expression to resolve
/// @param id - the outer term's source id
/// @param table - the table being walked
fn walk_key_of(expr: &BoundExpr, id: usize, table: &TableInfo) -> Option<OrderedBy> {
    let mut expr = expr;
    while let BoundExpr::Collate { operand, .. } = expr {
        expr = operand;
    }
    match expr {
        BoundExpr::Column { source, column, .. } if *source == id => {
            Some(named_key(table, OrderedBy::Column(*column)))
        }
        BoundExpr::Rowid { source } if *source == id => Some(OrderedBy::Rowid),
        _ => None,
    }
}

/// What a term of an `ORDER BY` names.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
enum OrderedBy {
    /// A column of the table, by its declared position.
    Column(u16),
    /// The row's key.
    Rowid,
}

/// The order one access path's own walk produces.
struct PathOrdering {
    /// What the walk is ordered by, in order, with each key's direction and the
    /// collation the structure compares it with.
    columns: Vec<(OrderedBy, bool, Collation)>,
    /// What an equality has pinned to a single value, which therefore holds
    /// still across the whole walk and cannot affect its order.
    pinned: Vec<OrderedBy>,
}

/// Returns whether the outer term's path already produces the `ORDER BY`, and
/// whether it has to be walked backwards to do it.
///
/// `None` means it does not and the rows have to go through a sorter.
/// `Some(false)` means a forward walk answers it, `Some(true)` a backward one.
///
/// The rules are narrow on purpose, because getting this wrong returns rows in
/// the wrong order and nothing about the result looks wrong:
///
/// - every `ORDER BY` term is a plain column of the outer term, or its rowid;
/// - the path is one whose order is a key's - every rowid path, and an index
///   seek over whatever columns the equalities did not pin;
/// - the directions agree, all with the structure or all against it, because a
///   B-tree can be read either way but not both at once;
/// - the collation is the one the structure holds the column in;
/// - the NULLs land where the structure puts them, which for the SQL defaults
///   they already do: first ascending, last descending, exactly as an index
///   holds them.
///
/// A column an equality pinned is skipped rather than matched: it holds one
/// value for every row the path returns, so ordering by it changes nothing.
/// @param select - the bound statement, for its ORDER BY
/// @param outer - the planned outer term
fn ordering_provided(
    select: &BoundSelect,
    id: usize,
    table: &TableInfo,
    path: &AccessPath,
) -> Option<bool> {
    if select.order_by.is_empty() {
        return Some(false);
    }
    let key = path_ordering(table, path)?;
    let mut reverse: Option<bool> = None;
    let mut at = 0usize;
    for term in &select.order_by {
        // `ORDER BY name COLLATE NOCASE` binds to a `Collate` around the
        // column, and the collation it names is already on the term - so the
        // wrapper is unwrapped rather than refused, or the one case an index
        // exists precisely to answer would be the one case that sorted.
        let mut expr = &term.expr;
        while let BoundExpr::Collate { operand, .. } = expr {
            expr = operand;
        }
        let named = match expr {
            BoundExpr::Column { source, column, .. } if *source == id => {
                named_key(table, OrderedBy::Column(*column))
            }
            BoundExpr::Rowid { source } if *source == id => OrderedBy::Rowid,
            _ => return None,
        };
        let descending = matches!(term.order, SortOrder::Descending);
        // The binder has already defaulted this, so what is left is a written
        // placement - and only the one the structure already produces can be
        // answered by a walk: an index holds NULLs first, so a forward walk is
        // NULLS FIRST and a backward one is NULLS LAST.
        let natural = match term.nulls {
            NullOrder::First => !descending,
            NullOrder::Last => descending,
        };
        if !natural {
            return None;
        }
        if key.pinned.contains(&named) {
            continue;
        }
        let (held, held_descending, held_collation) = key.columns.get(at).copied()?;
        if held != named || held_collation != term.collation {
            return None;
        }
        let walk = descending != held_descending;
        match reverse {
            None => reverse = Some(walk),
            Some(existing) if existing == walk => {}
            Some(_) => return None,
        }
        at = at.saturating_add(1);
    }
    Some(reverse.unwrap_or(false))
}

/// Returns the order one access path's walk produces, if it produces one.
/// @param table - the table being read
/// @param path - the chosen path
fn path_ordering(table: &TableInfo, path: &AccessPath) -> Option<PathOrdering> {
    match path {
        // A table B-tree is keyed by rowid, and a range over it is a slice of
        // that same walk.
        AccessPath::TableScan { .. } | AccessPath::RowidRange { .. } => Some(PathOrdering {
            columns: rowid_key(table),
            pinned: Vec::new(),
        }),
        // One row is in every order at once.
        AccessPath::RowidSeek { .. } => Some(PathOrdering {
            columns: Vec::new(),
            pinned: Vec::new(),
        }),
        AccessPath::IndexSeek {
            index_name,
            equalities,
            ..
        } => {
            let index = table
                .indexes
                .iter()
                .find(|candidate| candidate.name == *index_name)?;
            let mut columns: Vec<(OrderedBy, bool, Collation)> = Vec::new();
            let mut pinned: Vec<OrderedBy> = Vec::new();
            for (at, key_column) in index.columns.iter().enumerate() {
                // An expression key orders by something no ORDER BY term here
                // can name, so the walk stops describing itself at that point.
                let Some(column) = key_column.column else {
                    break;
                };
                let named = named_key(table, OrderedBy::Column(column));
                let collation = collation_of(&key_column.collation);
                if at < equalities.len() {
                    pinned.push(named);
                    continue;
                }
                columns.push((named, key_column.descending, collation));
            }
            // Every index entry ends with the row's key, so the walk is a total
            // order even where the indexed columns tie.
            columns.push((OrderedBy::Rowid, false, Collation::Binary));
            Some(PathOrdering { columns, pinned })
        }
        // A branch that needs de-duplicating (an `IN` list) has no order:
        // list values are probed in whatever order they were written, not
        // index order. A branch that does not - the keyset-range shape,
        // proven disjoint at plan time - runs each branch in the index's own
        // order and the branches themselves in that same order, so the whole
        // union reads exactly as an unconstrained walk of the index would: no
        // column is pinned, because no column has one value across every
        // branch.
        AccessPath::IndexSeekUnion {
            index_name,
            dedup: false,
            ..
        } => {
            let index = table
                .indexes
                .iter()
                .find(|candidate| candidate.name == *index_name)?;
            let mut columns: Vec<(OrderedBy, bool, Collation)> = Vec::new();
            for key_column in &index.columns {
                let Some(column) = key_column.column else {
                    break;
                };
                let named = named_key(table, OrderedBy::Column(column));
                let collation = collation_of(&key_column.collation);
                columns.push((named, key_column.descending, collation));
            }
            columns.push((OrderedBy::Rowid, false, Collation::Binary));
            Some(PathOrdering {
                columns,
                pinned: Vec::new(),
            })
        }
        _ => None,
    }
}

/// Returns the ordering a rowid walk produces.
/// @param table - the table being walked
fn rowid_key(table: &TableInfo) -> Vec<(OrderedBy, bool, Collation)> {
    let _ = table;
    vec![(OrderedBy::Rowid, false, Collation::Binary)]
}

/// Returns the one name a key goes by.
///
/// `INTEGER PRIMARY KEY` is the rowid under another name, so a statement that
/// ordered by the declared column and one that ordered by `rowid` asked for the
/// same walk. Folding the two spellings into one here is what lets the rest of
/// the comparison be an equality.
/// @param table - the table the column belongs to
/// @param named - the key as the statement or the index spelled it
fn named_key(table: &TableInfo, named: OrderedBy) -> OrderedBy {
    match named {
        OrderedBy::Column(column) if table.rowid_alias == Some(column) => OrderedBy::Rowid,
        other => other,
    }
}

/// Returns the order the FROM terms are visited in.
///
/// The legality rule is the whole of the difficulty. An outer join's rows
/// depend on the terms it was written against: a `LEFT JOIN` cannot be visited
/// before the term it null-extends, and neither side of one can cross it. A
/// `CROSS JOIN` is SQLite's documented instruction not to reorder at all. So a
/// term may only move within the run of ordinary joins it belongs to, and the
/// enumeration is over those runs rather than over the whole list.
///
/// Inside a run the search is exhaustive while that is affordable - the runs
/// that occur in practice are two to five terms - and falls back to the written
/// order beyond, because a greedy answer that is worse than the written order
/// is worse than not reordering at all.
fn choose_order(select: &BoundSelect, terms: &[BoundExpr], levers: Levers) -> Vec<usize> {
    let count = select.sources.len();
    if count < 2 {
        return (0..count).collect();
    }
    let mut order = Vec::with_capacity(count);
    let mut run: Vec<usize> = Vec::new();
    for position in 0..count {
        let pins = select
            .sources
            .get(position)
            .is_some_and(|source| matches!(source.join, JoinKind::Cross) || is_outer(source.join));
        if pins {
            order.extend(best_order(select, terms, &run, levers));
            run.clear();
            order.push(position);
            continue;
        }
        run.push(position);
    }
    order.extend(best_order(select, terms, &run, levers));
    order
}

/// Returns the cheapest visiting order for one run of reorderable terms.
fn best_order(
    select: &BoundSelect,
    terms: &[BoundExpr],
    run: &[usize],
    levers: Levers,
) -> Vec<usize> {
    // Eight terms is 40,320 orders, which is milliseconds; beyond that the
    // written order stands rather than a guess being substituted for it.
    if run.len() < 2 || run.len() > 8 {
        return run.to_vec();
    }
    let mut best: Option<(f64, Vec<usize>)> = None;
    let mut candidate = run.to_vec();
    permute(&mut candidate, 0, &mut |order| {
        let cost = order_cost(select, terms, order, levers);
        let better = best
            .as_ref()
            .is_none_or(|(existing, _)| cost < *existing - 1e-9);
        if better {
            best = Some((cost, order.to_vec()));
        }
    });
    best.map(|(_, order)| order).unwrap_or_else(|| run.to_vec())
}

/// Calls a closure with every permutation of a slice.
fn permute(order: &mut Vec<usize>, at: usize, visit: &mut impl FnMut(&[usize])) {
    if at >= order.len() {
        visit(order);
        return;
    }
    for index in at..order.len() {
        order.swap(at, index);
        permute(order, at.saturating_add(1), visit);
        order.swap(at, index);
    }
}

/// Returns what one visiting order is estimated to cost.
///
/// The loops are nested, so each term's cost is multiplied by the rows every
/// term before it produced - which is the whole reason the order matters, and
/// why putting the most selective term first is usually right and sometimes
/// spectacularly wrong.
fn order_cost(select: &BoundSelect, terms: &[BoundExpr], order: &[usize], levers: Levers) -> f64 {
    let ids: Vec<usize> = order
        .iter()
        .filter_map(|position| select.sources.get(*position))
        .map(|source| source.id)
        .collect();
    let mut consumed = vec![false; terms.len()];
    let mut total = 0.0f64;
    let mut outer_rows = 1.0f64;
    for (level, position) in order.iter().enumerate() {
        let Some(source) = select.sources.get(*position) else {
            continue;
        };
        let path = choose_path(level, &ids, source, select, terms, &mut consumed, levers);
        let (cost, rows) = path_cost(source, &path);
        total += outer_rows * cost;
        outer_rows *= rows.max(1.0);
    }
    total
}

/// Returns the vector probe a `TopN` over a distance can use, when it can.
///
/// **Every condition here is a way the rewrite would change the answer.** The
/// index returns `k` candidates and nothing else, so the query has to be asking
/// for the nearest `k` of *this* table by *this* measure and by nothing else:
///
/// - one FROM term, because a join's other side may multiply or drop rows and
///   the k the index was asked for would then be the wrong k;
/// - the only `ORDER BY` term, ascending, so the index's order and the query's
///   are the same order;
/// - a `LIMIT` that is a literal, because the index has to be told how deep to
///   go before the statement runs;
/// - no `OFFSET`, no `GROUP BY`, no aggregate and no `DISTINCT`, each of which
///   reads rows the top k does not contain;
/// - and a probe that reads no column, because a per-row probe is a different
///   query - the index answers one question, not one per row;
/// - and the `ORDER BY` function names the distance the index minimises
///   (`IndexInfo::metric`), or it falls back to scan-and-sort instead.
///
/// A `WHERE` clause is *allowed*: the residual is tested over the candidates,
/// which is what SQLite does with a partial index and what pgvector's own
/// documentation warns about - a narrow filter over an approximate index can
/// return fewer than `k` rows. It is the caller's query and this does not
/// second-guess it.
///
/// @param id - the FROM term's statement-wide number
/// @param position - where it sits in the join order
/// @param source - the term
/// @param select - the whole statement, for its `ORDER BY` and `LIMIT`
fn vector_path(
    id: usize,
    position: usize,
    source: &BoundSource,
    select: &BoundSelect,
) -> Option<AccessPath> {
    if position != 0 || select.sources.len() != 1 {
        return None;
    }
    if select.distinct
        || !select.group_by.is_empty()
        || !select.aggregates.is_empty()
        || select.offset.is_some()
        || !select.compounds.is_empty()
    {
        return None;
    }
    let [term] = select.order_by.as_slice() else {
        return None;
    };
    if term.order != crate::ast::SortOrder::Ascending {
        return None;
    }
    let Some(BoundExpr::Integer(depth)) = select.limit.as_ref() else {
        return None;
    };
    let depth = usize::try_from(*depth).ok().filter(|held| *held > 0)?;
    let BoundExpr::Function {
        func, arguments, ..
    } = &term.expr
    else {
        return None;
    };
    let wanted = match func {
        crate::function::ScalarFunc::VectorDistanceCos => crate::catalog_view::IndexMetric::Cosine,
        crate::function::ScalarFunc::VectorDistanceL2 => crate::catalog_view::IndexMetric::L2,
        _ => return None,
    };
    let [BoundExpr::Column {
        source: held,
        column,
        ..
    }, probe] = arguments.as_slice()
    else {
        return None;
    };
    if *held != id || reads_a_column(probe) {
        return None;
    }
    let index = source.table.indexes.iter().find(|held| {
        held.origin == crate::catalog_view::IndexOrigin::Module
            && held.metric == Some(wanted)
            && held
                .columns
                .first()
                .is_some_and(|first| first.column == Some(*column))
    })?;
    Some(AccessPath::VectorProbe {
        root: source.table.root,
        index: index.name.clone(),
        probe: Box::new(probe.clone()),
        depth,
    })
}

/// Reports whether an expression reads any column or rowid.
///
/// A probe that did would be a different question per row, and the index
/// answers one.
///
/// @param expr - the expression to look through
fn reads_a_column(expr: &BoundExpr) -> bool {
    if matches!(
        expr,
        BoundExpr::Column { .. } | BoundExpr::Rowid { .. } | BoundExpr::VirtualFunction { .. }
    ) {
        return true;
    }
    expr.children().into_iter().any(reads_a_column)
}

/// Returns what one term's path costs, and how many rows it produces.
fn path_cost(source: &BoundSource, path: &AccessPath) -> (f64, f64) {
    let rows = estimated_rows(&source.table);
    match path {
        AccessPath::TableScan { .. } => (cost::scan_cost(rows), rows),
        // A module prices its own scan, and the planner cannot ask it here
        // without making the plan depend on run-time state. What it can do is
        // reward an offer: a virtual table that was given a constraint will be
        // cheaper than one that was not, whatever the module then says.
        AccessPath::VirtualScan { offer, .. } => {
            let usable = offer.iter().filter(|item| item.spec.usable).count();
            let rows = if usable == 0 {
                rows
            } else {
                rows / (usable as f64 * 8.0)
            };
            (cost::scan_cost(rows.max(1.0)), rows.max(1.0))
        }
        // The index returns `depth` rows and the walk visits exactly those, so
        // the cost is a descent per candidate and the row count is the depth -
        // which is what makes it beat a scan on a table of any size and lose to
        // one on a table smaller than `k`.
        AccessPath::VectorProbe { depth, .. } => {
            let matches = (*depth as f64).min(rows).max(1.0);
            (cost::search_cost(rows, matches, true), matches)
        }
        AccessPath::RowidSeek { .. } => (cost::search_cost(rows, 1.0, true), 1.0),
        // A search per key, each a descent of the same tree - which is
        // exactly what running them one after another actually costs, and is
        // why a list long enough to be worth a scan instead gets priced that
        // way on its own, with no separate penalty needed for how many
        // branches there are.
        AccessPath::RowidSeekUnion { keys, .. } => {
            let branches = keys.len().max(1) as f64;
            (cost::search_cost(rows, 1.0, true) * branches, branches)
        }
        AccessPath::RowidRange { low, high, .. } => {
            let bounds = usize::from(low.is_some()) + usize::from(high.is_some());
            let mut matches = rows;
            for _ in 0..bounds {
                matches /= cost::RANGE_SHARE;
            }
            let matches = matches.max(1.0);
            (cost::search_cost(rows, matches, true), matches)
        }
        AccessPath::IndexSeek {
            index_name,
            equalities,
            low,
            high,
            covering,
            ..
        } => {
            let bounds = usize::from(low.is_some()) + usize::from(high.is_some());
            index_seek_cost(
                source,
                rows,
                index_name,
                equalities.len(),
                bounds,
                covering.is_some(),
            )
        }
        // A union is priced by summing one branch's cost over every branch -
        // each is a full descent of the same tree, so the total is exactly
        // what running them one after another costs, and a branch count large
        // enough to make that expensive is a branch count large enough for a
        // scan to win the comparison on its own.
        AccessPath::IndexSeekUnion {
            index_name,
            branches,
            covering,
            ..
        } => {
            let mut total_cost = 0.0f64;
            let mut total_matches = 0.0f64;
            for branch in branches {
                let bounds = usize::from(branch.low.is_some()) + usize::from(branch.high.is_some());
                let (branch_cost, branch_matches) = index_seek_cost(
                    source,
                    rows,
                    index_name,
                    branch.equalities.len(),
                    bounds,
                    covering.is_some(),
                );
                total_cost += branch_cost;
                total_matches += branch_matches;
            }
            (total_cost, total_matches.max(1.0))
        }
        // A materialised term is built once and then scanned; the build is
        // charged where it happens, which is the block that fills it.
        AccessPath::Subquery { .. } | AccessPath::Recursive { .. } => (cost::scan_cost(rows), rows),
        AccessPath::RecursiveSelf { .. } => (1.0, 1.0),
    }
}

/// Returns what one seek over an index costs, and how many rows it produces.
///
/// Shared by [`AccessPath::IndexSeek`] and each branch of an
/// [`AccessPath::IndexSeekUnion`], which price identically - a union is
/// priced by summing this over its branches.
/// @param source - the FROM term the index belongs to
/// @param rows - the table's estimated row count
/// @param index_name - the index being priced
/// @param equalities - how many leading columns the seek's equality prefix pins
/// @param bounds - how many range bounds the seek carries after the prefix
/// @param covering - whether the seek reads entries rather than fetching rows
fn index_seek_cost(
    source: &BoundSource,
    rows: f64,
    index_name: &[u8],
    equalities: usize,
    bounds: usize,
    covering: bool,
) -> (f64, f64) {
    let index = source
        .table
        .indexes
        .iter()
        .find(|candidate| candidate.name == index_name);
    let matches = index_matches(index, rows, equalities, bounds);
    let Some(index) = index else {
        return (cost::search_cost(rows, matches, false), matches);
    };
    if !covering {
        return (cost::search_cost(rows, matches, false), matches);
    }
    // A covering path reads entries rather than rows, and an entry is the
    // indexed columns plus the key rather than the whole row. Cost is bytes
    // touched, so the narrower shape is the saving - and it is the whole
    // reason a covering scan of a two-column index beats a table scan of a
    // five-column table when there is no predicate at all to narrow either of
    // them.
    let width = cost::entry_share(index.columns.len(), source.table.columns.len());
    (cost::search_cost(rows, matches * width, true), matches)
}

/// Returns how many rows a table is estimated to hold.
fn estimated_rows(table: &TableInfo) -> f64 {
    match table.analysed_rows {
        Some(rows) if rows > 0 => rows as f64,
        // A measured zero is a real answer, and so is an unmeasured table: the
        // first is empty and the second is assumed large. Collapsing them would
        // make an `ANALYZE` on an empty table look like no `ANALYZE` at all.
        Some(_) => 1.0,
        None => cost::DEFAULT_ROWS,
    }
}

/// Returns how many rows an index search is estimated to return.
fn index_matches(index: Option<&IndexInfo>, rows: f64, equalities: usize, bounds: usize) -> f64 {
    // **A partial index walked whole returns what it holds.**
    // With nothing to seek to, every other arm below prices this as a walk of
    // the table - which is what it would be for an ordinary index, and is not
    // what it is for one holding only the rows a predicate accepted.
    if equalities == 0 && bounds == 0 {
        if let Some(index) = index {
            if index.partial_sql.is_some() {
                if let Some(held) = index.analysed_rows {
                    return (held as f64).max(1.0);
                }
            }
        }
    }
    let mut matches = match index {
        // Measured: the average number of rows sharing the prefix the search
        // pinned down. This is the number `ANALYZE` exists to supply.
        Some(index) if !index.prefix_rows.is_empty() && equalities > 0 => index
            .prefix_rows
            .get(equalities.saturating_sub(1))
            .copied()
            .map(|value| value as f64)
            .unwrap_or(rows),
        // Unmeasured: a unique index pins one row.
        Some(index) if index.unique && equalities >= index.columns.len() => 1.0,
        // Unmeasured, not unique: SQLite's own default, which is an absolute
        // count rather than a share of the table. A column somebody indexed and
        // then compared for equality has many distinct values - that is why it
        // was indexed - so the number of rows behind one value does not grow
        // with the table the way a fraction does.
        Some(_) if equalities > 0 => cost::default_equality_rows(equalities, rows),
        _ => {
            let mut estimate = rows;
            for _ in 0..equalities {
                estimate /= cost::EQUALITY_SHARE;
            }
            estimate
        }
    };
    // Once per bound, not once per range. SQLite reduces the estimate by a
    // factor for the lower bound and again for the upper, which is why
    // `BETWEEN` is treated as sixteen times more selective than a bare `>` -
    // and treating them alike made a two-sided range look like a quarter of the
    // table, which is a quarter no join order can beat a scan with.
    for _ in 0..bounds {
        matches /= cost::RANGE_SHARE;
    }
    matches.max(1.0)
}

/// Returns whether a join keeps rows that match nothing on the other side.
pub fn is_outer(join: JoinKind) -> bool {
    matches!(join, JoinKind::Left | JoinKind::Right | JoinKind::Full)
}

/// Splits `a AND b AND c` into its terms.
///
/// Only `AND` is split. Splitting an `OR` would produce terms that are not
/// individually true of every row the expression accepts, which is the classic
/// way to lose rows.
pub fn split_conjunction(expr: &BoundExpr, into: &mut Vec<BoundExpr>) {
    match expr {
        BoundExpr::And(left, right) => {
            split_conjunction(left, into);
            split_conjunction(right, into);
        }
        // `x BETWEEN a AND b` *is* `x >= a AND x <= b`, so splitting it lets an
        // index range be found where otherwise the whole thing sat in the
        // residual and the table was scanned. It is split only when `x` is a
        // column, which is both the case that can drive an index and the case
        // where evaluating the operand twice cannot change an answer: a
        // volatile expression tested twice is a different question.
        BoundExpr::Between {
            negated: false,
            operand,
            low,
            high,
            low_affinity,
            low_collation,
            high_affinity,
            high_collation,
        } if matches!(
            **operand,
            BoundExpr::Column { .. } | BoundExpr::Rowid { .. }
        ) =>
        {
            // Each half keeps the affinity and collation of its own bound,
            // which is what SQLite's two comparisons use (task-2088). The
            // `between-index*` cases in `differential-part8/task2088.cases`
            // grade this path with and without `INDEXED BY`.
            into.push(BoundExpr::Compare {
                op: BinaryOp::GreaterEqual,
                left: operand.clone(),
                right: low.clone(),
                affinity: *low_affinity,
                collation: *low_collation,
            });
            into.push(BoundExpr::Compare {
                op: BinaryOp::LessEqual,
                left: operand.clone(),
                right: high.clone(),
                affinity: *high_affinity,
                collation: *high_collation,
            });
        }
        other => into.push(other.clone()),
    }
}

/// Attaches each unconsumed predicate to the innermost term it reads.
///
/// A predicate that reads only FROM terms belonging to an *enclosing* block is
/// constant for the whole of this block: the outer cursors are positioned
/// before it starts and do not move while it runs, so it is tested once before
/// the loops rather than once per row.
fn distribute_residuals(
    terms: &[BoundExpr],
    consumed: &[bool],
    ids: &[usize],
) -> (Vec<Option<BoundExpr>>, Option<BoundExpr>) {
    let levels = ids.len();
    let mut residuals: Vec<Option<BoundExpr>> = vec![None; levels];
    let mut constant: Option<BoundExpr> = None;
    for (index, term) in terms.iter().enumerate() {
        if consumed.get(index).copied().unwrap_or(false) {
            continue;
        }
        let mut used = Vec::new();
        term.sources_used(&mut used);
        let level = used
            .iter()
            .filter_map(|source| ids.iter().position(|id| id == source))
            .max();
        match level {
            Some(level) if level < levels => {
                if let Some(slot) = residuals.get_mut(level) {
                    *slot = Some(match slot.take() {
                        Some(existing) => {
                            BoundExpr::And(Box::new(existing), Box::new(term.clone()))
                        }
                        None => term.clone(),
                    });
                }
            }
            _ => {
                constant = Some(match constant.take() {
                    Some(existing) => BoundExpr::And(Box::new(existing), Box::new(term.clone())),
                    None => term.clone(),
                });
            }
        }
    }
    (residuals, constant)
}

/// Chooses the access path for one FROM term.
fn choose_path(
    position: usize,
    ids: &[usize],
    source: &BoundSource,
    select: &BoundSelect,
    terms: &[BoundExpr],
    consumed: &mut [bool],
    levers: Levers,
) -> AccessPath {
    match &source.rows {
        SourceRows::Subquery(block) => {
            let width = block.columns.len();
            let correlated = !block.correlations.is_empty();
            return AccessPath::Subquery {
                plan: Box::new(plan_select_with((**block).clone(), levers)),
                width,
                correlated,
            };
        }
        SourceRows::Recursive(body) => {
            let width = body.seeds.first().map_or(0, |(_, arm)| arm.columns.len());
            return AccessPath::Recursive {
                seeds: body
                    .seeds
                    .iter()
                    .map(|(op, arm)| (*op, plan_select_with(arm.clone(), levers)))
                    .collect(),
                steps: body
                    .steps
                    .iter()
                    .map(|(op, arm)| (*op, plan_select_with(arm.clone(), levers)))
                    .collect(),
                width,
            };
        }
        SourceRows::RecursiveSelf { cte } => {
            return AccessPath::RecursiveSelf { cte: *cte };
        }
        SourceRows::Table => {}
    }
    let id = ids.get(position).copied().unwrap_or(position);
    let table = &source.table;
    // **The k nearest, when the query asked exactly that.** Tried before the
    // b-tree paths because none of them apply: an index a module owns has no
    // key to seek and no range to walk, and the shape it answers - a distance
    // ordered ascending with a `LIMIT` - is one no other path can improve on.
    let forced = match &source.index_hint {
        crate::bind::IndexChoice::Only(wanted) => Some(wanted.as_slice()),
        _ => None,
    };
    if let Some(path) = vector_path(id, position, source, select) {
        // `INDEXED BY` a b-tree index rules the probe out like every other
        // path; `INDEXED BY` the probe's own index is the one way to keep it.
        let named = match &path {
            AccessPath::VectorProbe { index, .. } => table
                .indexes
                .iter()
                .find(|held| &held.name == index)
                .map(|held| held.folded.as_slice()),
            _ => None,
        };
        if forced.is_none() || forced == named {
            return path;
        }
    }
    if let Some(module) = table.module.clone() {
        return virtual_path(id, position, ids, source, select, module, terms, consumed);
    }
    if forced.is_some() {
        return forced_path(id, position, ids, source, select, terms, consumed, levers);
    }
    // Every candidate is built against a *copy* of the consumed list, because a
    // path that is not chosen must not leave its predicates marked as handled.
    // It did: when a scan beat an index range, the range's own comparison had
    // already been struck off the residual list and the scan then returned
    // every row of the table, silently.
    let mut candidates: Vec<(AccessPath, Vec<bool>)> = Vec::new();
    let mut trial = consumed.to_vec();
    if let Some(path) = rowid_path(id, position, ids, table, terms, &mut trial) {
        candidates.push((path, trial));
    }
    // **`NOT INDEXED` removes the index candidates and nothing else.** SQLite's
    // rule is that the clause prohibits every index on the table while leaving
    // the INTEGER PRIMARY KEY usable, which is why `rowid_path` above is
    // unconditional and this is the one candidate the hint takes away.
    //
    // `crates/inillucent-cli/src/diagnose.rs` is what this is for. Its integrity
    // digest reads every table `SELECT * FROM "t" NOT INDEXED`, and its comment
    // says that is what makes the digest a fact about the rows - which was not
    // true while the hint was dropped, because a corrupt index would then be
    // read in place of the table it was meant to be checked against.
    if source.index_hint != crate::bind::IndexChoice::NotIndexed {
        let mut trial = consumed.to_vec();
        let needed = select.columns_read(id);
        if let Some(path) = index_path(
            id, position, ids, source, terms, &mut trial, &needed, levers,
        ) {
            candidates.push((path, trial));
        }
    }
    candidates.push((
        AccessPath::TableScan { root: table.root },
        consumed.to_vec(),
    ));

    // A scan beats a search that returns most of the table: an index that has
    // to fetch every row costs a second descent per row on top of the scan it
    // was meant to avoid. And a path that already produces the ORDER BY beats
    // one that does not by the whole cost of the sort it saves, which is how a
    // `LIMIT 50` over six hundred thousand rows becomes fifty rows read rather
    // than six hundred thousand read, sorted and thrown away.
    let sort = sort_penalty(select, position, source, levers);
    let mut best: Option<(f64, AccessPath, Vec<bool>)> = None;
    for (path, trial) in candidates {
        let (mut cost, _) = path_cost(source, &path);
        if !levers.has(Levers::ORDERED_WALK)
            || ordering_provided(select, id, table, &path).is_none()
        {
            cost += sort;
        }
        if best
            .as_ref()
            .is_none_or(|(existing, _, _)| cost < *existing - 1e-9)
        {
            best = Some((cost, path, trial));
        }
    }
    match best {
        Some((_, path, trial)) => {
            consumed.copy_from_slice(&trial);
            path
        }
        None => AccessPath::TableScan { root: table.root },
    }
}

/// Returns what a sort would cost this term, or nothing when no path could
/// avoid one anyway.
///
/// Only the outermost term of a single-term statement can answer an `ORDER BY`
/// by walking: an inner loop restarts for every outer row, and the order it
/// produces inside one of those runs is not the order of the result. Charging
/// the sort anywhere else would tilt a plan towards an index for a saving it
/// would not make.
/// @param select - the bound statement
/// @param position - which visiting position this term is at
/// @param source - the term being priced
fn sort_penalty(
    select: &BoundSelect,
    position: usize,
    source: &BoundSource,
    levers: Levers,
) -> f64 {
    // A grouped or DISTINCT statement that streams over the walk answers its
    // ORDER BY the same way an ungrouped one does, so it is priced the same
    // way. Charging it the sort regardless would hide the saving that makes the
    // index path worth taking.
    let streams = levers.has(Levers::STREAMING_GROUP)
        && ((!select.group_by.is_empty() && !select.distinct)
            || (select.distinct && select.group_by.is_empty() && select.aggregates.is_empty()));
    let answerable = levers.has(Levers::ORDERED_WALK)
        && position == 0
        && select.sources.len() == 1
        && select.windows.is_empty()
        && select.compounds.is_empty()
        && !select.order_by.is_empty()
        && ((select.group_by.is_empty() && select.aggregates.is_empty() && !select.distinct)
            || streams);
    if !answerable {
        return 0.0;
    }
    cost::sort_cost(estimated_rows(&source.table))
}

/// Builds the offer a virtual table's module will be shown.
///
/// Every predicate that compares one of this term's columns - or its rowid - to
/// something is offered, whether or not the value is available yet: a
/// constraint the loop order has put out of reach is offered as *not usable*,
/// which is what lets one answer serve every position the term could take.
fn virtual_path(
    id: usize,
    position: usize,
    ids: &[usize],
    source: &BoundSource,
    select: &BoundSelect,
    module: crate::vtab::ModuleRef,
    terms: &[BoundExpr],
    consumed: &mut [bool],
) -> AccessPath {
    let table = &source.table;
    let mut offer = Vec::new();
    for (index, term) in terms.iter().enumerate() {
        if consumed.get(index).copied().unwrap_or(false) {
            continue;
        }
        let Some((column, op, value)) = virtual_constraint(id, table, term) else {
            continue;
        };
        offer.push(VirtualConstraint {
            spec: crate::vtab::ConstraintSpec {
                column,
                op,
                usable: is_available(position, ids, &value),
            },
            value,
            predicate: term.clone(),
        });
        if let Some(slot) = consumed.get_mut(index) {
            *slot = true;
        }
    }
    let order_by = order_offer(id, position, select);
    AccessPath::VirtualScan {
        module,
        offer,
        order_by,
        chosen: None,
    }
}

/// Returns the `ORDER BY` a module may be able to satisfy for itself.
///
/// Only the outermost loop is offered one. An inner loop restarts for every row
/// of the loops around it, so an ordering it produced would be an ordering
/// within each of those restarts - which is not the statement's ordering and
/// would let the sorter be skipped wrongly.
fn order_offer(id: usize, position: usize, select: &BoundSelect) -> Vec<crate::vtab::OrderSpec> {
    if position != 0 {
        return Vec::new();
    }
    let mut offer = Vec::new();
    for term in &select.order_by {
        let column = match &term.expr {
            BoundExpr::Column { source, column, .. } if *source == id => i32::from(*column),
            BoundExpr::Rowid { source } if *source == id => crate::vtab::ROWID_COLUMN,
            _ => return Vec::new(),
        };
        offer.push(crate::vtab::OrderSpec {
            column,
            descending: term.order == crate::ast::SortOrder::Descending,
        });
    }
    offer
}

/// Splits a predicate into the conjunction the offer is built from.
pub fn conjunction(filter: &BoundExpr) -> Vec<BoundExpr> {
    let mut terms = Vec::new();
    split_conjunction(filter, &mut terms);
    terms
}

/// Returns the column, operator and value when a term constrains this term.
fn virtual_constraint(
    id: usize,
    table: &TableInfo,
    term: &BoundExpr,
) -> Option<(i32, crate::vtab::ConstraintOp, BoundExpr)> {
    use crate::vtab::{ConstraintOp, ROWID_COLUMN};
    // `x MATCH 'y'`, `x LIKE 'y'`, `x GLOB 'y'` and `x REGEXP 'y'` are the
    // operators a module exists to give meaning to, so they are offered first.
    if let BoundExpr::Pattern {
        negated: false,
        op,
        operand,
        pattern,
        escape: None,
    } = term
    {
        if let BoundExpr::Column { source, column, .. } = operand.as_ref() {
            if *source == id {
                let op = match op {
                    crate::ast::PatternOp::Match => ConstraintOp::Match,
                    crate::ast::PatternOp::Like => ConstraintOp::Like,
                    crate::ast::PatternOp::Glob => ConstraintOp::Glob,
                    crate::ast::PatternOp::Regexp => ConstraintOp::Regexp,
                };
                return Some((i32::from(*column), op, pattern.as_ref().clone()));
            }
        }
    }
    if let Some((op, value)) = comparison_against_rowid(id, term) {
        return binary_constraint(op).map(|op| (ROWID_COLUMN, op, value));
    }
    for column in 0..table.columns.len() {
        let column = column as u16;
        if let Some((op, value)) = comparison_against_column(id, column, term) {
            return binary_constraint(op).map(|op| (i32::from(column), op, value));
        }
    }
    None
}

/// Returns the constraint operator one comparison offers, if any.
fn binary_constraint(op: BinaryOp) -> Option<crate::vtab::ConstraintOp> {
    use crate::vtab::ConstraintOp;
    Some(match op {
        BinaryOp::Equal => ConstraintOp::Eq,
        BinaryOp::NotEqual => ConstraintOp::Ne,
        BinaryOp::Less => ConstraintOp::Lt,
        BinaryOp::LessEqual => ConstraintOp::Le,
        BinaryOp::Greater => ConstraintOp::Gt,
        BinaryOp::GreaterEqual => ConstraintOp::Ge,
        _ => return None,
    })
}

/// Returns how an UPDATE or a DELETE should find the rows it touches, with some
/// optimizations switched off.
/// @param table - the table being written
/// @param source_id - the source the filter's columns are bound to
/// @param filter - the WHERE clause, when there is one
/// @param levers - which optimizations are on
pub fn write_path_with(
    table: &TableInfo,
    source_id: usize,
    filter: Option<&BoundExpr>,
    levers: Levers,
) -> AccessPath {
    if !levers.has(Levers::INDEXED_WRITE) {
        return AccessPath::TableScan { root: table.root };
    }
    let scan = AccessPath::TableScan { root: table.root };
    if table.module.is_some() || table.without_rowid {
        return scan;
    }
    let Some(filter) = filter else {
        return scan;
    };
    let mut terms = Vec::new();
    split_conjunction(filter, &mut terms);
    let ids = [source_id];
    let mut consumed = vec![false; terms.len()];
    if let Some(path) = rowid_path(source_id, 0, &ids, table, &terms, &mut consumed) {
        return path;
    }
    let source = BoundSource {
        index_hint: crate::bind::IndexChoice::Any,
        id: source_id,
        rows: SourceRows::Table,
        table: std::rc::Rc::new(table.clone()),
        alias: table.name.clone(),
        join: JoinKind::Inner,
        constraint: None,
        suppressed: Vec::new(),
        index_exprs: Vec::new(),
    };
    let mut consumed = vec![false; terms.len()];
    // A write reads the whole row it is about to change, so no index covers it.
    let needed = ColumnUse {
        opaque: true,
        ..ColumnUse::default()
    };
    let Some(path) = index_path(
        source_id,
        0,
        &ids,
        &source,
        &terms,
        &mut consumed,
        &needed,
        levers,
    ) else {
        return scan;
    };
    // The same crossover the read planner uses: an index that has to fetch most
    // of the table costs a second descent per row on top of the scan it was
    // meant to replace.
    let (index_cost, _) = path_cost(&source, &path);
    let (scan_cost, _) = path_cost(&source, &scan);
    if index_cost <= scan_cost {
        return path;
    }
    scan
}

/// Returns a rowid equality or range path, when the predicates allow one.
fn rowid_path(
    id: usize,
    position: usize,
    ids: &[usize],
    table: &TableInfo,
    terms: &[BoundExpr],
    consumed: &mut [bool],
) -> Option<AccessPath> {
    if !table.has_rowid() {
        return None;
    }
    for (index, term) in terms.iter().enumerate() {
        if consumed.get(index).copied().unwrap_or(false) {
            continue;
        }
        let Some((op, value)) = comparison_against_rowid(id, term) else {
            continue;
        };
        if op != BinaryOp::Equal || !is_available(position, ids, &value) {
            continue;
        }
        if let Some(slot) = consumed.get_mut(index) {
            *slot = true;
        }
        return Some(AccessPath::RowidSeek {
            root: table.root,
            key: value,
        });
    }
    if let Some(path) = seek_union::rowid_in_list_path(id, position, ids, table, terms, consumed) {
        return Some(path);
    }
    // **A range is an outermost-term path only.** The physical pass drives an
    // inner term either by probing it per outer row or by reading it once into
    // a buffer, and neither of those is a walk between two bounds - so a range
    // chosen here for an inner term was refused downstream with "the physical
    // pass does not handle a rowid range as an inner join term yet", which is
    // what `SELECT x.id, y.id FROM t x JOIN t y ON y.a = x.a AND y.id > x.id`
    // hit. Not choosing it is better than refusing it: the bound stays
    // unconsumed, so it is tested as a residual over the pair and the self join
    // answers. The equality half above is unaffected, because a seek per outer
    // row *is* what an index nested loop does.
    if position != 0 {
        return None;
    }
    let mut low = None;
    let mut high = None;
    let mut used = Vec::new();
    for (index, term) in terms.iter().enumerate() {
        if consumed.get(index).copied().unwrap_or(false) {
            continue;
        }
        let Some((op, value)) = comparison_against_rowid(id, term) else {
            continue;
        };
        if !is_available(position, ids, &value) {
            continue;
        }
        match op {
            BinaryOp::Greater if low.is_none() => {
                low = Some(RangeBound {
                    kind: BoundKind::Greater,
                    value,
                    unconverted: false,
                });
                used.push(index);
            }
            BinaryOp::GreaterEqual if low.is_none() => {
                low = Some(RangeBound {
                    kind: BoundKind::GreaterEqual,
                    value,
                    unconverted: false,
                });
                used.push(index);
            }
            BinaryOp::Less if high.is_none() => {
                high = Some(RangeBound {
                    kind: BoundKind::Less,
                    value,
                    unconverted: false,
                });
                used.push(index);
            }
            BinaryOp::LessEqual if high.is_none() => {
                high = Some(RangeBound {
                    kind: BoundKind::LessEqual,
                    value,
                    unconverted: false,
                });
                used.push(index);
            }
            _ => {}
        }
    }
    if low.is_none() && high.is_none() {
        return None;
    }
    for index in used {
        if let Some(slot) = consumed.get_mut(index) {
            *slot = true;
        }
    }
    Some(AccessPath::RowidRange {
        root: table.root,
        low,
        high,
    })
}

/// Returns an index path over an equality prefix, when one is usable.
fn index_path(
    id: usize,
    position: usize,
    ids: &[usize],
    source: &BoundSource,
    terms: &[BoundExpr],
    consumed: &mut [bool],
    needed: &ColumnUse,
    levers: Levers,
) -> Option<AccessPath> {
    let table = &source.table;
    let forced = match &source.index_hint {
        crate::bind::IndexChoice::Only(wanted) => Some(wanted.as_slice()),
        _ => None,
    };
    let context = CandidateContext {
        id,
        position,
        ids,
        table,
        terms,
        consumed,
        needed,
        levers,
        forced: forced.is_some(),
    };
    let mut best: Option<(f64, AccessPath, Vec<usize>)> = None;
    for (at, index) in table.indexes.iter().enumerate() {
        // An index a module owns is not a b-tree: it has no root to seek into
        // and no key order to walk. `vector_path` is the only path that can use
        // one, and it was tried before this.
        if index.origin == crate::catalog_view::IndexOrigin::Module {
            continue;
        }
        if forced.is_some_and(|wanted| wanted != index.folded.as_slice()) {
            continue;
        }
        // The expressions this index needs, when the binder could bind them.
        // `None` for every ordinary index, and for one whose schema text did
        // not bind - which leaves a partial index unusable and an expression
        // key unmatched, both the conservative answer.
        let computed = source.index_exprs.iter().find(|held| held.position == at);
        let usable = index_usable(source, at, index, terms);
        if !usable && index.partial_sql.is_some() {
            // **A partial index only holds the rows its predicate accepts.**
            // Using one over a query that does not imply the predicate would
            // lose rows - silently, and only the rows the predicate excludes -
            // so the index is skipped unless the implication is *proved*.
            //
            // The proof is SQLite's own, and it is deliberately the crudest one
            // that is sound: the predicate appears, unchanged, as a conjunct of
            // the statement's `WHERE`. `WHERE b > 5 AND a = 1` therefore uses an
            // index declared `WHERE b > 5`, and `WHERE b > 6` does not, even
            // though it implies it. A cleverer test would answer more queries
            // and would be a place for a wrong answer to live.
            continue;
        }
        // Three different candidates can come from the same index: the
        // ordinary equality-prefix-and-range seek, a union of equality seeks
        // when a disjunction is an `IN` list on the leading column, and a
        // union of range seeks when a disjunction is a keyset page's tuple
        // comparison. None of them rules another out - a statement can only
        // ever use one of them here, but which one is cheapest is a cost
        // question, so every one that matches is tried and the best kept.
        if let Some((path, used)) = index_candidate(&context, index, computed, usable) {
            consider_index_candidate(source, &mut best, path, used);
        }
        if let Some((path, used)) = seek_union::in_list_union_path(&context, index, usable) {
            consider_index_candidate(source, &mut best, path, used);
        }
        if let Some((path, used)) = seek_union::keyset_range_union_path(&context, index, usable) {
            consider_index_candidate(source, &mut best, path, used);
        }
    }
    let (_, path, used) = best?;
    for index in used {
        if let Some(slot) = consumed.get_mut(index) {
            *slot = true;
        }
    }
    Some(path)
}

/// What every index candidate for one FROM term is chosen from.
///
/// **A type rather than ten arguments (task-1962, A9).** `index_candidate`,
/// [`seek_union::in_list_union_path`] and [`seek_union::keyset_range_union_path`]
/// each took the same ten, in the same order, and two of them carried
/// `#[allow(clippy::too_many_arguments)]` to say so. Ten positional arguments of
/// which three are slices of different things is a call nobody can read and a
/// call site nobody can check.
pub(crate) struct CandidateContext<'a> {
    /// The FROM term being planned.
    pub(crate) id: usize,
    /// Its position in the FROM list; zero drives the pipeline.
    pub(crate) position: usize,
    /// Every FROM term's id, so a correlated reference can be recognised.
    pub(crate) ids: &'a [usize],
    /// The table the term reads.
    pub(crate) table: &'a TableInfo,
    /// The statement's `WHERE` terms, bound.
    pub(crate) terms: &'a [BoundExpr],
    /// Which of those an earlier path has already consumed.
    pub(crate) consumed: &'a [bool],
    /// What the statement reads of this term, which decides covering.
    pub(crate) needed: &'a ColumnUse,
    /// The planner's tuning knobs.
    pub(crate) levers: Levers,
    /// The term was written `INDEXED BY`, so the one index left must produce a
    /// path even when nothing seeks it: a walk of every entry.
    pub(crate) forced: bool,
}

/// Folds one more index candidate into whichever is cheapest so far.
///
/// The choice between candidates is a cost, not a count of consumed terms:
/// two candidates that each satisfy one equality consume the same number of
/// terms and can differ by orders of magnitude in how many rows they return -
/// and taking the first one found made a query constrained on both a
/// two-valued column and a four-hundred-valued one search the two-valued one.
/// A tie goes to the later candidate, which is what the reference does - it
/// keeps a candidate that is no worse than the one it holds, so the last
/// equal one wins, which matters because a query with no `ORDER BY` returns
/// rows in whatever order its path produces.
fn consider_index_candidate(
    source: &BoundSource,
    best: &mut Option<(f64, AccessPath, Vec<usize>)>,
    path: AccessPath,
    used: Vec<usize>,
) {
    let (cost, _) = path_cost(source, &path);
    let better = best
        .as_ref()
        .is_none_or(|(existing, _, _)| cost <= *existing + 1e-9);
    if better {
        *best = Some((cost, path, used));
    }
}

/// Builds the best path over one index, or `None` if it cannot be used.
fn index_candidate(
    context: &CandidateContext<'_>,
    index: &IndexInfo,
    computed: Option<&crate::dml::BoundIndexExprs>,
    usable: bool,
) -> Option<(AccessPath, Vec<usize>)> {
    let CandidateContext {
        id,
        position,
        ids,
        table,
        terms,
        consumed,
        needed,
        levers,
        forced,
    } = *context;
    let mut equalities = Vec::new();
    let mut unconverted = Vec::new();
    let mut used = Vec::new();
    let mut collations = Vec::new();
    let mut descending = Vec::new();
    let mut columns: Vec<Option<u16>> = Vec::new();
    let mut key = 0usize;
    while let Some(key_column) = index.columns.get(key) {
        let collation = collation_of(&key_column.collation);
        let found = match key_column.column {
            Some(column) => {
                find_equality(id, position, ids, column, collation, terms, consumed, &used)
                    .map(|(term_index, value)| (term_index, value, Some(column)))
            }
            // **A key the index computes.** `CREATE INDEX ix ON t(lower(a))`
            // answers `WHERE lower(a) = 'ab'` and nothing else: the entry holds
            // the expression's value, so the only predicate it can seek on is
            // one whose own side is that same expression. The comparison is
            // between *bound* expressions, which is why the binder puts them on
            // the FROM term - see `BoundSource::index_exprs`.
            None => computed
                .and_then(|held| held.keys.get(key).cloned().flatten())
                .and_then(|wanted| {
                    find_expr_equality(position, ids, &wanted, collation, terms, consumed, &used)
                })
                .map(|(term_index, value)| (term_index, value, None)),
        };
        let Some((term_index, value, column)) = found else {
            break;
        };
        if terms.get(term_index).is_some_and(compares_unconverted) {
            unconverted.push(equalities.len());
        }
        equalities.push(value);
        used.push(term_index);
        collations.push(collation);
        descending.push(key_column.descending);
        columns.push(column);
        key = key.saturating_add(1);
    }
    // **A range is an outermost-term path only**, the rule `rowid_path` and
    // `seek_union` already follow and this candidate did not. The physical
    // pass refuses an inner index seek with a bound, so
    // `SELECT count(*) FROM s CROSS JOIN h WHERE h.b > 595` was refused with
    // exit code 3 on the release build, with no hint anywhere (task-2078).
    // Left unconsumed, the bound is a residual over the pair, which answers.
    let range = match index.columns.get(key) {
        Some(key_column) if position == 0 => range::key_range(context, key_column, &mut used),
        _ => None,
    };
    let (low, high) = match range {
        Some(found) => {
            collations.push(found.collation);
            descending.push(found.descending);
            columns.push(Some(found.column));
            (found.low, found.high)
        }
        None => (None, None),
    };
    let covering = levers
        .has(Levers::COVERING_INDEX)
        .then(|| covering_slots(table, index, needed, usable))
        .flatten();
    // **A partial index whose predicate the query implies is worth walking whole.**
    // It holds only the rows its predicate accepted, so reading
    // every entry of it reads exactly the rows the query asked for - even with
    // nothing to seek to and even when a lookup per entry is needed, which is
    // the case a covering test cannot see.
    //
    // `CREATE INDEX document_pending_idx ON document (indexed_at) WHERE
    // indexed_at IS NULL` over `SELECT id FROM document WHERE indexed_at IS
    // NULL` is the shape: 120 of 6,000 documents, and `id` is not in the index,
    // so the covering test said no and the whole candidate was dropped. The
    // plan was `SCAN document`, over a table whose rows carry nine kilobytes of
    // body each, and the equivalent query on the real corpus was thousands of
    // times slower than the same question asked of PostgreSQL.
    //
    // It is offered rather than taken: `path_cost` compares it against the scan
    // with the index's own entry count, which `ANALYZE` now writes for a partial
    // index instead of the table's.
    let partial_walk = usable && index.partial_sql.is_some();
    if equalities.is_empty()
        && low.is_none()
        && high.is_none()
        && covering.is_none()
        && !partial_walk
        && !(forced && usable)
    {
        // Nothing to seek to and nothing to save by reading the entries: this
        // index has no part in answering the query.
        return None;
    }
    Some((
        AccessPath::IndexSeek {
            table_root: table.root,
            index_root: index.root,
            index_name: index.name.clone(),
            equalities,
            unconverted,
            low,
            high,
            collations,
            descending,
            columns,
            without_rowid: table.without_rowid,
            key_entry_slots: if table.without_rowid && index.root != table.root {
                let leading = index.columns.len();
                (0..table.primary_key().len())
                    .map(|offset| leading.saturating_add(offset))
                    .collect()
            } else {
                Vec::new()
            },
            covering,
        },
        used,
    ))
}

/// The entry slot that stands for the row's own key rather than a field.
///
/// An index entry over a rowid table ends with the rowid, and the machine reads
/// it with `IdxRowid` rather than out of the entry's record - so a column that
/// *is* the rowid needs a marker rather than a slot number. It is the largest
/// `usize` because no entry can have that many fields, and because a number
/// that could also be a real slot would be a silent misread.
pub const ROWID_ENTRY_SLOT: usize = usize::MAX;

/// Returns where each column the query reads sits in one index's entries.
///
/// `None` when the index does not hold them all, which is the ordinary case and
/// is why a covering path is worth naming when it happens. A `WITHOUT ROWID`
/// table is excluded: its rows *are* index entries, so the question is already
/// answered by whether the seek is on the table's own key, and mixing the two
/// would be two answers to one question.
/// @param table - the table being read
/// @param index - the index being considered
/// @param needed - what the query reads from this term
fn covering_slots(
    table: &TableInfo,
    index: &IndexInfo,
    needed: &ColumnUse,
    usable: bool,
) -> Option<Vec<(u16, usize)>> {
    if needed.opaque || table.without_rowid || !usable {
        return None;
    }
    let mut slots = Vec::with_capacity(needed.columns.len());
    for slot in &needed.columns {
        // The rowid alias is a column of the table and the *rowid* of the
        // entry, so it is covered whatever the index holds - but it is read
        // with `IdxRowid` rather than out of the entry's record, so it is not
        // in the list.
        if table.rowid_alias == Some(*slot) {
            slots.push((*slot, ROWID_ENTRY_SLOT));
            continue;
        }
        let position = index
            .columns
            .iter()
            .position(|key| key.column == Some(*slot))?;
        slots.push((*slot, position));
    }
    Some(slots)
}

/// Finds an equality predicate on one column with a matching collation.
fn find_equality(
    id: usize,
    position: usize,
    ids: &[usize],
    column: u16,
    collation: Collation,
    terms: &[BoundExpr],
    consumed: &[bool],
    used: &[usize],
) -> Option<(usize, BoundExpr)> {
    for (index, term) in terms.iter().enumerate() {
        if consumed.get(index).copied().unwrap_or(false) || used.contains(&index) {
            continue;
        }
        let Some((op, value)) = indexable_comparison(id, column, term) else {
            continue;
        };
        if op != BinaryOp::Equal || !is_available(position, ids, &value) {
            continue;
        }
        if comparison_collation(term) != collation {
            continue;
        }
        return Some((index, value));
    }
    None
}

/// Finds an equality against an expression the index computes.
///
/// The mirror of [`find_equality`] for a key that is not a column: the term has
/// to compare the index's own key expression against something the join has
/// already produced, under the collation the key is ordered by.
///
/// @param position - the FROM term's position among the ones already joined
/// @param ids - the FROM terms joined so far
/// @param wanted - the index's bound key expression
/// @param collation - the collation the key is ordered under
/// @param terms - the statement's `WHERE` conjuncts
/// @param consumed - which terms an earlier stage already used
/// @param used - which terms this candidate has already used
fn find_expr_equality(
    position: usize,
    ids: &[usize],
    wanted: &BoundExpr,
    collation: Collation,
    terms: &[BoundExpr],
    consumed: &[bool],
    used: &[usize],
) -> Option<(usize, BoundExpr)> {
    for (index, term) in terms.iter().enumerate() {
        if consumed.get(index).copied().unwrap_or(false) || used.contains(&index) {
            continue;
        }
        let BoundExpr::Compare {
            op, left, right, ..
        } = term
        else {
            continue;
        };
        if *op != BinaryOp::Equal || comparison_collation(term) != collation {
            continue;
        }
        let value = if left.as_ref() == wanted {
            right.as_ref().clone()
        } else if right.as_ref() == wanted {
            left.as_ref().clone()
        } else {
            continue;
        };
        if !is_available(position, ids, &value) {
            continue;
        }
        return Some((index, value));
    }
    None
}

/// Returns whether a value can be computed before entering a loop level.
///
/// A seek key may only read terms *outside* the loop it drives. Reading the
/// term's own columns would be circular, and reading an inner term's columns
/// would read a cursor that has not been positioned yet.
fn is_available(position: usize, ids: &[usize], value: &BoundExpr) -> bool {
    let mut used = Vec::new();
    value.sources_used(&mut used);
    used.iter().all(|source| {
        // A term this block does not own belongs to an enclosing one, whose
        // cursor is positioned before this block runs at all - so it is
        // available at every level, including the first.
        ids.iter()
            .position(|id| id == source)
            .is_none_or(|level| level < position)
    })
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::bind::BoundExpr;

    /// A conjunction splits into its terms; a disjunction does not, because a
    /// term of an OR is not true of every row the OR accepts.
    #[test]
    fn only_conjunctions_split() {
        let expr = BoundExpr::And(
            Box::new(BoundExpr::Integer(1)),
            Box::new(BoundExpr::Or(
                Box::new(BoundExpr::Integer(2)),
                Box::new(BoundExpr::Integer(3)),
            )),
        );
        let mut terms = Vec::new();
        split_conjunction(&expr, &mut terms);
        assert_eq!(terms.len(), 2);
        assert!(matches!(terms.get(1), Some(BoundExpr::Or(_, _))));
    }

    /// A seek key may read only terms outside its own loop.
    #[test]
    fn a_seek_key_may_only_read_outer_terms() {
        let outer = BoundExpr::Column {
            source: 0,
            column: 0,
            slot: 0,
            affinity: inillucent_value::Affinity::Integer,
            collation: Collation::Binary,
        };
        let ids = [0usize, 1usize];
        assert!(is_available(1, &ids, &outer));
        assert!(!is_available(0, &ids, &outer));
        assert!(is_available(0, &ids, &BoundExpr::Integer(5)));
        // A term the block does not own belongs to an enclosing block, whose
        // cursor is already positioned, so it is available at every level.
        assert!(is_available(0, &[7usize], &outer));
    }
}