oxilean_kernel/termination/

types.rs

//! Auto-generated module
//!
//! 🤖 Generated with [SplitRS](https://github.com/cool-japan/splitrs)

use super::functions::*;
use crate::{Expr, Name};
use std::collections::{HashMap, HashSet};

/// A simple directed acyclic graph.
#[allow(dead_code)]
pub struct SimpleDag {
    /// `edges[i]` is the list of direct successors of node `i`.
    edges: Vec<Vec<usize>>,
}
#[allow(dead_code)]
impl SimpleDag {
    /// Creates a DAG with `n` nodes and no edges.
    pub fn new(n: usize) -> Self {
        Self {
            edges: vec![Vec::new(); n],
        }
    }
    /// Adds an edge from `from` to `to`.
    pub fn add_edge(&mut self, from: usize, to: usize) {
        if from < self.edges.len() {
            self.edges[from].push(to);
        }
    }
    /// Returns the successors of `node`.
    pub fn successors(&self, node: usize) -> &[usize] {
        self.edges.get(node).map(|v| v.as_slice()).unwrap_or(&[])
    }
    /// Returns `true` if `from` can reach `to` via DFS.
    pub fn can_reach(&self, from: usize, to: usize) -> bool {
        let mut visited = vec![false; self.edges.len()];
        self.dfs(from, to, &mut visited)
    }
    fn dfs(&self, cur: usize, target: usize, visited: &mut Vec<bool>) -> bool {
        if cur == target {
            return true;
        }
        if cur >= visited.len() || visited[cur] {
            return false;
        }
        visited[cur] = true;
        for &next in self.successors(cur) {
            if self.dfs(next, target, visited) {
                return true;
            }
        }
        false
    }
    /// Returns the topological order of nodes, or `None` if a cycle is detected.
    pub fn topological_sort(&self) -> Option<Vec<usize>> {
        let n = self.edges.len();
        let mut in_degree = vec![0usize; n];
        for succs in &self.edges {
            for &s in succs {
                if s < n {
                    in_degree[s] += 1;
                }
            }
        }
        let mut queue: std::collections::VecDeque<usize> =
            (0..n).filter(|&i| in_degree[i] == 0).collect();
        let mut order = Vec::new();
        while let Some(node) = queue.pop_front() {
            order.push(node);
            for &s in self.successors(node) {
                if s < n {
                    in_degree[s] -= 1;
                    if in_degree[s] == 0 {
                        queue.push_back(s);
                    }
                }
            }
        }
        if order.len() == n {
            Some(order)
        } else {
            None
        }
    }
    /// Returns the number of nodes.
    pub fn num_nodes(&self) -> usize {
        self.edges.len()
    }
}
/// A fixed-size sliding window that computes a running sum.
#[allow(dead_code)]
pub struct SlidingSum {
    window: Vec<f64>,
    capacity: usize,
    pos: usize,
    sum: f64,
    count: usize,
}
#[allow(dead_code)]
impl SlidingSum {
    /// Creates a sliding sum with the given window size.
    pub fn new(capacity: usize) -> Self {
        Self {
            window: vec![0.0; capacity],
            capacity,
            pos: 0,
            sum: 0.0,
            count: 0,
        }
    }
    /// Adds a value to the window, removing the oldest if full.
    pub fn push(&mut self, val: f64) {
        let oldest = self.window[self.pos];
        self.sum -= oldest;
        self.sum += val;
        self.window[self.pos] = val;
        self.pos = (self.pos + 1) % self.capacity;
        if self.count < self.capacity {
            self.count += 1;
        }
    }
    /// Returns the current window sum.
    pub fn sum(&self) -> f64 {
        self.sum
    }
    /// Returns the window mean, or `None` if empty.
    pub fn mean(&self) -> Option<f64> {
        if self.count == 0 {
            None
        } else {
            Some(self.sum / self.count as f64)
        }
    }
    /// Returns the current window size (number of valid elements).
    pub fn count(&self) -> usize {
        self.count
    }
}
/// A min-heap implemented as a binary heap.
#[allow(dead_code)]
pub struct MinHeap<T: Ord> {
    data: Vec<T>,
}
#[allow(dead_code)]
impl<T: Ord> MinHeap<T> {
    /// Creates a new empty min-heap.
    pub fn new() -> Self {
        Self { data: Vec::new() }
    }
    /// Inserts an element.
    pub fn push(&mut self, val: T) {
        self.data.push(val);
        self.sift_up(self.data.len() - 1);
    }
    /// Removes and returns the minimum element.
    pub fn pop(&mut self) -> Option<T> {
        if self.data.is_empty() {
            return None;
        }
        let n = self.data.len();
        self.data.swap(0, n - 1);
        let min = self.data.pop();
        if !self.data.is_empty() {
            self.sift_down(0);
        }
        min
    }
    /// Returns a reference to the minimum element.
    pub fn peek(&self) -> Option<&T> {
        self.data.first()
    }
    /// Returns the number of elements.
    pub fn len(&self) -> usize {
        self.data.len()
    }
    /// Returns `true` if empty.
    pub fn is_empty(&self) -> bool {
        self.data.is_empty()
    }
    fn sift_up(&mut self, mut i: usize) {
        while i > 0 {
            let parent = (i - 1) / 2;
            if self.data[i] < self.data[parent] {
                self.data.swap(i, parent);
                i = parent;
            } else {
                break;
            }
        }
    }
    fn sift_down(&mut self, mut i: usize) {
        let n = self.data.len();
        loop {
            let left = 2 * i + 1;
            let right = 2 * i + 2;
            let mut smallest = i;
            if left < n && self.data[left] < self.data[smallest] {
                smallest = left;
            }
            if right < n && self.data[right] < self.data[smallest] {
                smallest = right;
            }
            if smallest == i {
                break;
            }
            self.data.swap(i, smallest);
            i = smallest;
        }
    }
}
/// A versioned record that stores a history of values.
#[allow(dead_code)]
pub struct VersionedRecord<T: Clone> {
    /// Every earlier value, oldest first: version `n` is `earlier[n]`.
    earlier: Vec<T>,
    /// The latest value (version `earlier.len()`), declared last so it drops last.
    current: T,
}
#[allow(dead_code)]
impl<T: Clone> VersionedRecord<T> {
    /// Creates a new record with an initial value.
    pub fn new(initial: T) -> Self {
        Self {
            earlier: Vec::new(),
            current: initial,
        }
    }
    /// Updates the record with a new version.
    pub fn update(&mut self, val: T) {
        let previous = std::mem::replace(&mut self.current, val);
        self.earlier.push(previous);
    }
    /// Returns the current (latest) value.
    pub fn current(&self) -> &T {
        &self.current
    }
    /// Returns the value at version `n` (0-indexed), or `None`.
    pub fn at_version(&self, n: usize) -> Option<&T> {
        match self.earlier.get(n) {
            Some(value) => Some(value),
            None if n == self.earlier.len() => Some(&self.current),
            None => None,
        }
    }
    /// Returns the version number of the current value.
    pub fn version(&self) -> usize {
        self.earlier.len()
    }
    /// Returns `true` if more than one version exists.
    pub fn has_history(&self) -> bool {
        !self.earlier.is_empty()
    }
}
/// A dependency closure builder (transitive closure via BFS).
#[allow(dead_code)]
pub struct TransitiveClosure {
    adj: Vec<Vec<usize>>,
    n: usize,
}
#[allow(dead_code)]
impl TransitiveClosure {
    /// Creates a transitive closure builder for `n` nodes.
    pub fn new(n: usize) -> Self {
        Self {
            adj: vec![Vec::new(); n],
            n,
        }
    }
    /// Adds a direct edge.
    pub fn add_edge(&mut self, from: usize, to: usize) {
        if from < self.n {
            self.adj[from].push(to);
        }
    }
    /// Computes all nodes reachable from `start` (including `start`).
    pub fn reachable_from(&self, start: usize) -> Vec<usize> {
        let mut visited = vec![false; self.n];
        let mut queue = std::collections::VecDeque::new();
        queue.push_back(start);
        while let Some(node) = queue.pop_front() {
            if node >= self.n || visited[node] {
                continue;
            }
            visited[node] = true;
            for &next in &self.adj[node] {
                queue.push_back(next);
            }
        }
        (0..self.n).filter(|&i| visited[i]).collect()
    }
    /// Returns `true` if `from` can transitively reach `to`.
    pub fn can_reach(&self, from: usize, to: usize) -> bool {
        self.reachable_from(from).contains(&to)
    }
}
/// A simple decision tree node for rule dispatching.
#[allow(dead_code)]
#[allow(missing_docs)]
pub enum DecisionNode {
    /// A leaf with an action string.
    Leaf(String),
    /// An interior node: check `key` equals `val` → `yes_branch`, else `no_branch`.
    Branch {
        key: String,
        val: String,
        yes_branch: Box<DecisionNode>,
        no_branch: Box<DecisionNode>,
    },
}
#[allow(dead_code)]
impl DecisionNode {
    /// Evaluates the decision tree with the given context.
    pub fn evaluate(&self, ctx: &std::collections::HashMap<String, String>) -> &str {
        match self {
            DecisionNode::Leaf(action) => action.as_str(),
            DecisionNode::Branch {
                key,
                val,
                yes_branch,
                no_branch,
            } => {
                let actual = ctx.get(key).map(|s| s.as_str()).unwrap_or("");
                if actual == val.as_str() {
                    yes_branch.evaluate(ctx)
                } else {
                    no_branch.evaluate(ctx)
                }
            }
        }
    }
    /// Returns the depth of the decision tree.
    pub fn depth(&self) -> usize {
        match self {
            DecisionNode::Leaf(_) => 0,
            DecisionNode::Branch {
                yes_branch,
                no_branch,
                ..
            } => 1 + yes_branch.depth().max(no_branch.depth()),
        }
    }
}
/// A sparse vector: stores only non-default elements.
#[allow(dead_code)]
pub struct SparseVec<T: Default + Clone + PartialEq> {
    entries: std::collections::HashMap<usize, T>,
    default_: T,
    logical_len: usize,
}
#[allow(dead_code)]
impl<T: Default + Clone + PartialEq> SparseVec<T> {
    /// Creates a new sparse vector with logical length `len`.
    pub fn new(len: usize) -> Self {
        Self {
            entries: std::collections::HashMap::new(),
            default_: T::default(),
            logical_len: len,
        }
    }
    /// Sets element at `idx`.
    pub fn set(&mut self, idx: usize, val: T) {
        if val == self.default_ {
            self.entries.remove(&idx);
        } else {
            self.entries.insert(idx, val);
        }
    }
    /// Gets element at `idx`.
    pub fn get(&self, idx: usize) -> &T {
        self.entries.get(&idx).unwrap_or(&self.default_)
    }
    /// Returns the logical length.
    pub fn len(&self) -> usize {
        self.logical_len
    }
    /// Returns whether the collection is empty.
    pub fn is_empty(&self) -> bool {
        self.len() == 0
    }
    /// Returns the number of non-default elements.
    pub fn nnz(&self) -> usize {
        self.entries.len()
    }
}
/// A hierarchical configuration tree.
#[allow(dead_code)]
pub struct ConfigNode {
    key: String,
    value: Option<String>,
    children: Vec<ConfigNode>,
}
#[allow(dead_code)]
impl ConfigNode {
    /// Creates a leaf config node with a value.
    pub fn leaf(key: impl Into<String>, value: impl Into<String>) -> Self {
        Self {
            key: key.into(),
            value: Some(value.into()),
            children: Vec::new(),
        }
    }
    /// Creates a section node with children.
    pub fn section(key: impl Into<String>) -> Self {
        Self {
            key: key.into(),
            value: None,
            children: Vec::new(),
        }
    }
    /// Adds a child node.
    pub fn add_child(&mut self, child: ConfigNode) {
        self.children.push(child);
    }
    /// Returns the key.
    pub fn key(&self) -> &str {
        &self.key
    }
    /// Returns the value, or `None` for section nodes.
    pub fn value(&self) -> Option<&str> {
        self.value.as_deref()
    }
    /// Returns the number of children.
    pub fn num_children(&self) -> usize {
        self.children.len()
    }
    /// Looks up a dot-separated path.
    pub fn lookup(&self, path: &str) -> Option<&str> {
        let mut parts = path.splitn(2, '.');
        let head = parts.next()?;
        let tail = parts.next();
        if head != self.key {
            return None;
        }
        match tail {
            None => self.value.as_deref(),
            Some(rest) => self.children.iter().find_map(|c| c.lookup_relative(rest)),
        }
    }
    fn lookup_relative(&self, path: &str) -> Option<&str> {
        let mut parts = path.splitn(2, '.');
        let head = parts.next()?;
        let tail = parts.next();
        if head != self.key {
            return None;
        }
        match tail {
            None => self.value.as_deref(),
            Some(rest) => self.children.iter().find_map(|c| c.lookup_relative(rest)),
        }
    }
}
/// A simple key-value store backed by a sorted Vec for small maps.
#[allow(dead_code)]
pub struct SmallMap<K: Ord + Clone, V: Clone> {
    entries: Vec<(K, V)>,
}
#[allow(dead_code)]
impl<K: Ord + Clone, V: Clone> SmallMap<K, V> {
    /// Creates a new empty small map.
    pub fn new() -> Self {
        Self {
            entries: Vec::new(),
        }
    }
    /// Inserts or replaces the value for `key`.
    pub fn insert(&mut self, key: K, val: V) {
        match self.entries.binary_search_by_key(&&key, |(k, _)| k) {
            Ok(i) => self.entries[i].1 = val,
            Err(i) => self.entries.insert(i, (key, val)),
        }
    }
    /// Returns the value for `key`, or `None`.
    pub fn get(&self, key: &K) -> Option<&V> {
        self.entries
            .binary_search_by_key(&key, |(k, _)| k)
            .ok()
            .map(|i| &self.entries[i].1)
    }
    /// Returns the number of entries.
    pub fn len(&self) -> usize {
        self.entries.len()
    }
    /// Returns `true` if empty.
    pub fn is_empty(&self) -> bool {
        self.entries.is_empty()
    }
    /// Returns all keys.
    pub fn keys(&self) -> Vec<&K> {
        self.entries.iter().map(|(k, _)| k).collect()
    }
    /// Returns all values.
    pub fn values(&self) -> Vec<&V> {
        self.entries.iter().map(|(_, v)| v).collect()
    }
}
/// A reusable scratch buffer for path computations.
#[allow(dead_code)]
pub struct PathBuf {
    components: Vec<String>,
}
#[allow(dead_code)]
impl PathBuf {
    /// Creates a new empty path buffer.
    pub fn new() -> Self {
        Self {
            components: Vec::new(),
        }
    }
    /// Pushes a component.
    pub fn push(&mut self, comp: impl Into<String>) {
        self.components.push(comp.into());
    }
    /// Pops the last component.
    pub fn pop(&mut self) {
        self.components.pop();
    }
    /// Returns the current path as a `/`-separated string.
    pub fn as_str(&self) -> String {
        self.components.join("/")
    }
    /// Returns the depth of the path.
    pub fn depth(&self) -> usize {
        self.components.len()
    }
    /// Clears the path.
    pub fn clear(&mut self) {
        self.components.clear();
    }
}
/// Information about a function parameter for termination checking.
#[derive(Debug, Clone)]
pub struct ParamInfo {
    /// Parameter name
    pub name: Name,
    /// Parameter position (0-indexed)
    pub pos: usize,
    /// The inductive type this param belongs to (if any)
    pub inductive_type: Option<Name>,
}
/// A non-empty list (at least one element guaranteed).
#[allow(dead_code)]
pub struct NonEmptyVec<T> {
    head: T,
    tail: Vec<T>,
}
#[allow(dead_code)]
impl<T> NonEmptyVec<T> {
    /// Creates a non-empty vec with a single element.
    pub fn singleton(val: T) -> Self {
        Self {
            head: val,
            tail: Vec::new(),
        }
    }
    /// Pushes an element.
    pub fn push(&mut self, val: T) {
        self.tail.push(val);
    }
    /// Returns a reference to the first element.
    pub fn first(&self) -> &T {
        &self.head
    }
    /// Returns a reference to the last element.
    pub fn last(&self) -> &T {
        self.tail.last().unwrap_or(&self.head)
    }
    /// Returns the number of elements.
    pub fn len(&self) -> usize {
        1 + self.tail.len()
    }
    /// Returns whether the collection is empty.
    pub fn is_empty(&self) -> bool {
        self.len() == 0
    }
    /// Returns all elements as a Vec.
    pub fn to_vec(&self) -> Vec<&T> {
        let mut v = vec![&self.head];
        v.extend(self.tail.iter());
        v
    }
}
/// A write-once cell.
#[allow(dead_code)]
pub struct WriteOnce<T> {
    value: std::cell::Cell<Option<T>>,
}
#[allow(dead_code)]
impl<T: Copy> WriteOnce<T> {
    /// Creates an empty write-once cell.
    pub fn new() -> Self {
        Self {
            value: std::cell::Cell::new(None),
        }
    }
    /// Writes a value.  Returns `false` if already written.
    pub fn write(&self, val: T) -> bool {
        if self.value.get().is_some() {
            return false;
        }
        self.value.set(Some(val));
        true
    }
    /// Returns the value if written.
    pub fn read(&self) -> Option<T> {
        self.value.get()
    }
    /// Returns `true` if the value has been written.
    pub fn is_written(&self) -> bool {
        self.value.get().is_some()
    }
}
/// Well-founded relation kind for termination arguments.
#[allow(dead_code)]
#[derive(Debug, Clone, PartialEq, Eq)]
pub enum WfRelationKind {
    /// Structural recursion on an inductive type.
    Structural {
        /// The inductive type being recursed on.
        inductive_type: Name,
        /// Index of the parameter being checked.
        param_index: usize,
    },
    /// Recursion on a numeric measure.
    Measure {
        /// The measure function.
        measure_fn: Name,
    },
    /// Lexicographic combination of multiple relations.
    Lexicographic {
        /// The component relations.
        components: Vec<WfRelationKind>,
    },
    /// Well-founded recursion on natural number subtraction.
    NatSub,
    /// Custom user-provided well-founded relation.
    Custom {
        /// The custom relation.
        relation: Name,
    },
}
impl WfRelationKind {
    /// Check if this is a structural recursion.
    #[allow(dead_code)]
    pub fn is_structural(&self) -> bool {
        matches!(self, WfRelationKind::Structural { .. })
    }
    /// Get the depth of a lexicographic argument.
    #[allow(dead_code)]
    pub fn lex_depth(&self) -> usize {
        match self {
            WfRelationKind::Lexicographic { components } => components.len(),
            _ => 1,
        }
    }
    /// Return a human-readable description.
    #[allow(dead_code)]
    pub fn description(&self) -> String {
        match self {
            WfRelationKind::Structural {
                inductive_type,
                param_index,
            } => {
                format!("structural on {} (param {})", inductive_type, param_index)
            }
            WfRelationKind::Measure { measure_fn } => {
                format!("measure by {}", measure_fn)
            }
            WfRelationKind::Lexicographic { components } => {
                format!("lexicographic ({} components)", components.len())
            }
            WfRelationKind::NatSub => "nat subtraction".to_string(),
            WfRelationKind::Custom { relation } => {
                format!("custom relation {}", relation)
            }
        }
    }
}
/// Result of analyzing a function body for structural recursion.
#[derive(Debug, Clone)]
pub struct TerminationResult {
    /// Which parameter is the decreasing one (if found)
    pub decreasing_param: Option<usize>,
    /// All recursive calls found
    pub recursive_calls: Vec<RecCallInfo>,
    /// Whether termination is verified
    pub is_terminating: bool,
}
/// Simple trie for efficient string prefix lookup.
#[allow(dead_code)]
#[derive(Debug, Clone, Default)]
pub struct StringTrie {
    pub(super) children: std::collections::HashMap<char, StringTrie>,
    is_end: bool,
    pub(super) value: Option<String>,
}
impl StringTrie {
    /// Create a new empty trie.
    #[allow(dead_code)]
    pub fn new() -> Self {
        Self::default()
    }
    /// Insert a string into the trie.
    #[allow(dead_code)]
    pub fn insert(&mut self, s: &str) {
        let mut node = self;
        for c in s.chars() {
            node = node.children.entry(c).or_default();
        }
        node.is_end = true;
        node.value = Some(s.to_string());
    }
    /// Check if a string is in the trie.
    #[allow(dead_code)]
    pub fn contains(&self, s: &str) -> bool {
        let mut node = self;
        for c in s.chars() {
            match node.children.get(&c) {
                Some(next) => node = next,
                None => return false,
            }
        }
        node.is_end
    }
    /// Find all strings with a given prefix.
    #[allow(dead_code)]
    pub fn starts_with(&self, prefix: &str) -> Vec<String> {
        let mut node = self;
        for c in prefix.chars() {
            match node.children.get(&c) {
                Some(next) => node = next,
                None => return vec![],
            }
        }
        let mut results = Vec::new();
        collect_strings(node, &mut results);
        results
    }
    /// Get the number of strings in the trie.
    #[allow(dead_code)]
    pub fn len(&self) -> usize {
        let mut count = if self.is_end { 1 } else { 0 };
        for child in self.children.values() {
            count += child.len();
        }
        count
    }
    /// Check if the trie is empty.
    #[allow(dead_code)]
    pub fn is_empty(&self) -> bool {
        self.len() == 0
    }
}
/// A label set for a graph node.
#[allow(dead_code)]
pub struct LabelSet {
    labels: Vec<String>,
}
#[allow(dead_code)]
impl LabelSet {
    /// Creates a new empty label set.
    pub fn new() -> Self {
        Self { labels: Vec::new() }
    }
    /// Adds a label (deduplicates).
    pub fn add(&mut self, label: impl Into<String>) {
        let s = label.into();
        if !self.labels.contains(&s) {
            self.labels.push(s);
        }
    }
    /// Returns `true` if `label` is present.
    pub fn has(&self, label: &str) -> bool {
        self.labels.iter().any(|l| l == label)
    }
    /// Returns the count of labels.
    pub fn count(&self) -> usize {
        self.labels.len()
    }
    /// Returns all labels.
    pub fn all(&self) -> &[String] {
        &self.labels
    }
}
/// A counter that can measure elapsed time between snapshots.
#[allow(dead_code)]
pub struct Stopwatch {
    start: crate::wall_clock::Instant,
    splits: Vec<f64>,
}
#[allow(dead_code)]
impl Stopwatch {
    /// Creates and starts a new stopwatch.
    pub fn start() -> Self {
        Self {
            start: crate::wall_clock::Instant::now(),
            splits: Vec::new(),
        }
    }
    /// Records a split time (elapsed since start).
    pub fn split(&mut self) {
        self.splits.push(self.elapsed_ms());
    }
    /// Returns total elapsed milliseconds since start.
    pub fn elapsed_ms(&self) -> f64 {
        self.start.elapsed().as_secs_f64() * 1000.0
    }
    /// Returns all recorded split times.
    pub fn splits(&self) -> &[f64] {
        &self.splits
    }
    /// Returns the number of splits.
    pub fn num_splits(&self) -> usize {
        self.splits.len()
    }
}
/// Information about a recursive call.
#[derive(Debug, Clone)]
pub struct RecCallInfo {
    /// The function being called
    pub callee: Name,
    /// The argument position being passed recursively
    pub arg_pos: usize,
    /// The argument expression
    pub arg: Expr,
    /// Whether the argument is structurally smaller
    pub is_decreasing: bool,
}
/// Termination checker for recursive definitions.
pub struct TerminationChecker {
    /// Names of functions currently being checked (for cycle detection)
    checking: HashSet<Name>,
    /// Map from function name to its parameter info
    param_info: HashMap<Name, Vec<ParamInfo>>,
    /// Map from function name to its recursive calls
    call_info: HashMap<Name, Vec<RecCallInfo>>,
    /// Known structurally smaller expressions
    /// Maps a variable to the set of expressions known to be smaller
    smaller: HashMap<Expr, HashSet<Expr>>,
}
impl TerminationChecker {
    /// Create a new termination checker.
    pub fn new() -> Self {
        Self {
            checking: HashSet::new(),
            param_info: HashMap::new(),
            call_info: HashMap::new(),
            smaller: HashMap::new(),
        }
    }
    /// Register parameter info for a function.
    pub fn register_params(&mut self, name: Name, params: Vec<ParamInfo>) {
        self.param_info.insert(name, params);
    }
    /// Mark an expression as structurally smaller than another.
    ///
    /// This is used when we know that `small` is a subterm of `big`,
    /// e.g., when pattern matching on an inductive type.
    pub fn add_smaller(&mut self, big: Expr, small: Expr) {
        self.smaller.entry(big).or_default().insert(small);
    }
    /// Check if `small` is known to be structurally smaller than `big`.
    pub fn is_smaller(&self, big: &Expr, small: &Expr) -> bool {
        if let Some(smalls) = self.smaller.get(big) {
            if smalls.contains(small) {
                return true;
            }
            for mid in smalls {
                if self.is_smaller(mid, small) {
                    return true;
                }
            }
        }
        false
    }
    /// Check if a recursive definition terminates.
    ///
    /// Returns Ok(()) if the definition is structurally decreasing,
    /// or Err with a message explaining why it might not terminate.
    pub fn check_terminates(&mut self, name: &Name, body: &Expr) -> Result<(), String> {
        if self.checking.contains(name) {
            return Err(format!("Cyclic dependency detected for {}", name));
        }
        self.checking.insert(name.clone());
        let mut calls = Vec::new();
        self.collect_recursive_calls(name, body, &mut calls, 0)?;
        self.call_info.insert(name.clone(), calls.clone());
        if calls.is_empty() {
            self.checking.remove(name);
            return Ok(());
        }
        let result = self.find_decreasing_param(name, &calls);
        self.checking.remove(name);
        if result.is_terminating {
            Ok(())
        } else {
            Err(format!(
                "Cannot verify termination of '{}': no structurally decreasing argument found",
                name
            ))
        }
    }
    /// Check termination for mutual recursion.
    pub fn check_mutual_terminates(
        &mut self,
        names: &[Name],
        bodies: &[Expr],
    ) -> Result<(), String> {
        if names.len() != bodies.len() {
            return Err("Mismatched names and bodies in mutual recursion".to_string());
        }
        for name in names {
            self.checking.insert(name.clone());
        }
        for (name, body) in names.iter().zip(bodies.iter()) {
            let mut calls = Vec::new();
            self.collect_recursive_calls_mutual(names, body, &mut calls, 0)?;
            self.call_info.insert(name.clone(), calls);
        }
        for name in names {
            if let Some(calls) = self.call_info.get(name) {
                if !calls.is_empty() {
                    let result = self.find_decreasing_param(name, calls);
                    if !result.is_terminating {
                        for n in names {
                            self.checking.remove(n);
                        }
                        return Err(format!(
                            "Cannot verify termination of '{}' in mutual recursion block",
                            name
                        ));
                    }
                }
            }
        }
        for name in names {
            self.checking.remove(name);
        }
        Ok(())
    }
    /// Collect recursive calls in the body.
    fn collect_recursive_calls(
        &self,
        fname: &Name,
        expr: &Expr,
        calls: &mut Vec<RecCallInfo>,
        depth: usize,
    ) -> Result<(), String> {
        if depth > 200 {
            return Err("Definition too deeply nested".to_string());
        }
        match expr {
            Expr::App(f, a) => {
                if let Some(call) = self.check_recursive_call(fname, expr) {
                    calls.push(call);
                }
                self.collect_recursive_calls(fname, f, calls, depth + 1)?;
                self.collect_recursive_calls(fname, a, calls, depth + 1)
            }
            Expr::Lam(_, _, ty, body) => {
                self.collect_recursive_calls(fname, ty, calls, depth + 1)?;
                self.collect_recursive_calls(fname, body, calls, depth + 1)
            }
            Expr::Pi(_, _, ty, body) => {
                self.collect_recursive_calls(fname, ty, calls, depth + 1)?;
                self.collect_recursive_calls(fname, body, calls, depth + 1)
            }
            Expr::Let(_, ty, val, body) => {
                self.collect_recursive_calls(fname, ty, calls, depth + 1)?;
                self.collect_recursive_calls(fname, val, calls, depth + 1)?;
                self.collect_recursive_calls(fname, body, calls, depth + 1)
            }
            _ => Ok(()),
        }
    }
    /// Collect recursive calls for mutual recursion.
    fn collect_recursive_calls_mutual(
        &self,
        fnames: &[Name],
        expr: &Expr,
        calls: &mut Vec<RecCallInfo>,
        depth: usize,
    ) -> Result<(), String> {
        if depth > 200 {
            return Err("Definition too deeply nested".to_string());
        }
        match expr {
            Expr::App(f, a) => {
                for fname in fnames {
                    if let Some(call) = self.check_recursive_call(fname, expr) {
                        calls.push(call);
                    }
                }
                self.collect_recursive_calls_mutual(fnames, f, calls, depth + 1)?;
                self.collect_recursive_calls_mutual(fnames, a, calls, depth + 1)
            }
            Expr::Lam(_, _, ty, body) => {
                self.collect_recursive_calls_mutual(fnames, ty, calls, depth + 1)?;
                self.collect_recursive_calls_mutual(fnames, body, calls, depth + 1)
            }
            Expr::Pi(_, _, ty, body) => {
                self.collect_recursive_calls_mutual(fnames, ty, calls, depth + 1)?;
                self.collect_recursive_calls_mutual(fnames, body, calls, depth + 1)
            }
            Expr::Let(_, ty, val, body) => {
                self.collect_recursive_calls_mutual(fnames, ty, calls, depth + 1)?;
                self.collect_recursive_calls_mutual(fnames, val, calls, depth + 1)?;
                self.collect_recursive_calls_mutual(fnames, body, calls, depth + 1)
            }
            _ => Ok(()),
        }
    }
    /// Check if an application is a recursive call.
    fn check_recursive_call(&self, fname: &Name, app: &Expr) -> Option<RecCallInfo> {
        let (head, args) = collect_app_args(app);
        if let Expr::Const(name, _) = head {
            if name == fname {
                for (i, arg) in args.iter().enumerate() {
                    let is_dec = self.is_structurally_smaller(arg);
                    if is_dec {
                        return Some(RecCallInfo {
                            callee: name.clone(),
                            arg_pos: i,
                            arg: (*arg).clone(),
                            is_decreasing: true,
                        });
                    }
                }
                if let Some(first_arg) = args.first() {
                    return Some(RecCallInfo {
                        callee: name.clone(),
                        arg_pos: 0,
                        arg: (*first_arg).clone(),
                        is_decreasing: false,
                    });
                }
            }
        }
        None
    }
    /// Check if an expression is structurally smaller than some parameter.
    fn is_structurally_smaller(&self, expr: &Expr) -> bool {
        for smalls in self.smaller.values() {
            if smalls.contains(expr) {
                return true;
            }
        }
        false
    }
    /// Find a parameter that is decreasing in all recursive calls.
    fn find_decreasing_param(&self, _name: &Name, calls: &[RecCallInfo]) -> TerminationResult {
        if calls.is_empty() {
            return TerminationResult {
                decreasing_param: None,
                recursive_calls: calls.to_vec(),
                is_terminating: true,
            };
        }
        let max_pos = calls.iter().map(|c| c.arg_pos).max().unwrap_or(0);
        for pos in 0..=max_pos {
            let all_decreasing = calls.iter().all(|c| {
                if c.arg_pos == pos {
                    c.is_decreasing
                } else {
                    true
                }
            });
            if all_decreasing && calls.iter().any(|c| c.arg_pos == pos && c.is_decreasing) {
                return TerminationResult {
                    decreasing_param: Some(pos),
                    recursive_calls: calls.to_vec(),
                    is_terminating: true,
                };
            }
        }
        let all_dec = calls.iter().all(|c| c.is_decreasing);
        TerminationResult {
            decreasing_param: None,
            recursive_calls: calls.to_vec(),
            is_terminating: all_dec,
        }
    }
    /// Get the recorded calls for a function.
    pub fn get_calls(&self, name: &Name) -> Option<&Vec<RecCallInfo>> {
        self.call_info.get(name)
    }
}
/// Represents a rewrite rule `lhs → rhs`.
#[allow(dead_code)]
#[allow(missing_docs)]
pub struct RewriteRule {
    /// The name of the rule.
    pub name: String,
    /// A string representation of the LHS pattern.
    pub lhs: String,
    /// A string representation of the RHS.
    pub rhs: String,
    /// Whether this is a conditional rule (has side conditions).
    pub conditional: bool,
}
#[allow(dead_code)]
impl RewriteRule {
    /// Creates an unconditional rewrite rule.
    pub fn unconditional(
        name: impl Into<String>,
        lhs: impl Into<String>,
        rhs: impl Into<String>,
    ) -> Self {
        Self {
            name: name.into(),
            lhs: lhs.into(),
            rhs: rhs.into(),
            conditional: false,
        }
    }
    /// Creates a conditional rewrite rule.
    pub fn conditional(
        name: impl Into<String>,
        lhs: impl Into<String>,
        rhs: impl Into<String>,
    ) -> Self {
        Self {
            name: name.into(),
            lhs: lhs.into(),
            rhs: rhs.into(),
            conditional: true,
        }
    }
    /// Returns a textual representation.
    pub fn display(&self) -> String {
        format!("{}: {} → {}", self.name, self.lhs, self.rhs)
    }
}
/// A type-erased function pointer with arity tracking.
#[allow(dead_code)]
pub struct RawFnPtr {
    /// The raw function pointer (stored as usize for type erasure).
    ptr: usize,
    arity: usize,
    name: String,
}
#[allow(dead_code)]
impl RawFnPtr {
    /// Creates a new raw function pointer descriptor.
    pub fn new(ptr: usize, arity: usize, name: impl Into<String>) -> Self {
        Self {
            ptr,
            arity,
            name: name.into(),
        }
    }
    /// Returns the arity.
    pub fn arity(&self) -> usize {
        self.arity
    }
    /// Returns the name.
    pub fn name(&self) -> &str {
        &self.name
    }
    /// Returns the raw pointer value.
    pub fn raw(&self) -> usize {
        self.ptr
    }
}
/// A pair of `StatSummary` values tracking before/after a transformation.
#[allow(dead_code)]
pub struct TransformStat {
    before: StatSummary,
    after: StatSummary,
}
#[allow(dead_code)]
impl TransformStat {
    /// Creates a new transform stat recorder.
    pub fn new() -> Self {
        Self {
            before: StatSummary::new(),
            after: StatSummary::new(),
        }
    }
    /// Records a before value.
    pub fn record_before(&mut self, v: f64) {
        self.before.record(v);
    }
    /// Records an after value.
    pub fn record_after(&mut self, v: f64) {
        self.after.record(v);
    }
    /// Returns the mean reduction ratio (after/before).
    pub fn mean_ratio(&self) -> Option<f64> {
        let b = self.before.mean()?;
        let a = self.after.mean()?;
        if b.abs() < f64::EPSILON {
            return None;
        }
        Some(a / b)
    }
}
/// A flat list of substitution pairs `(from, to)`.
#[allow(dead_code)]
pub struct FlatSubstitution {
    pairs: Vec<(String, String)>,
}
#[allow(dead_code)]
impl FlatSubstitution {
    /// Creates an empty substitution.
    pub fn new() -> Self {
        Self { pairs: Vec::new() }
    }
    /// Adds a pair.
    pub fn add(&mut self, from: impl Into<String>, to: impl Into<String>) {
        self.pairs.push((from.into(), to.into()));
    }
    /// Applies all substitutions to `s` (leftmost-first order).
    pub fn apply(&self, s: &str) -> String {
        let mut result = s.to_string();
        for (from, to) in &self.pairs {
            result = result.replace(from.as_str(), to.as_str());
        }
        result
    }
    /// Returns the number of pairs.
    pub fn len(&self) -> usize {
        self.pairs.len()
    }
    /// Returns `true` if empty.
    pub fn is_empty(&self) -> bool {
        self.pairs.is_empty()
    }
}
/// A pool of reusable string buffers.
#[allow(dead_code)]
pub struct StringPool {
    free: Vec<String>,
}
#[allow(dead_code)]
impl StringPool {
    /// Creates a new empty string pool.
    pub fn new() -> Self {
        Self { free: Vec::new() }
    }
    /// Takes a string from the pool (may be empty).
    pub fn take(&mut self) -> String {
        self.free.pop().unwrap_or_default()
    }
    /// Returns a string to the pool.
    pub fn give(&mut self, mut s: String) {
        s.clear();
        self.free.push(s);
    }
    /// Returns the number of free strings in the pool.
    pub fn free_count(&self) -> usize {
        self.free.len()
    }
}
/// A trie-based prefix counter.
#[allow(dead_code)]
pub struct PrefixCounter {
    children: std::collections::HashMap<char, PrefixCounter>,
    count: usize,
}
#[allow(dead_code)]
impl PrefixCounter {
    /// Creates an empty prefix counter.
    pub fn new() -> Self {
        Self {
            children: std::collections::HashMap::new(),
            count: 0,
        }
    }
    /// Records a string.
    pub fn record(&mut self, s: &str) {
        self.count += 1;
        let mut node = self;
        for c in s.chars() {
            node = node.children.entry(c).or_default();
            node.count += 1;
        }
    }
    /// Returns how many strings have been recorded that start with `prefix`.
    pub fn count_with_prefix(&self, prefix: &str) -> usize {
        let mut node = self;
        for c in prefix.chars() {
            match node.children.get(&c) {
                Some(n) => node = n,
                None => return 0,
            }
        }
        node.count
    }
}
/// A generic counter that tracks min/max/sum for statistical summaries.
#[allow(dead_code)]
pub struct StatSummary {
    count: u64,
    sum: f64,
    min: f64,
    max: f64,
}
#[allow(dead_code)]
impl StatSummary {
    /// Creates an empty summary.
    pub fn new() -> Self {
        Self {
            count: 0,
            sum: 0.0,
            min: f64::INFINITY,
            max: f64::NEG_INFINITY,
        }
    }
    /// Records a sample.
    pub fn record(&mut self, val: f64) {
        self.count += 1;
        self.sum += val;
        if val < self.min {
            self.min = val;
        }
        if val > self.max {
            self.max = val;
        }
    }
    /// Returns the mean, or `None` if no samples.
    pub fn mean(&self) -> Option<f64> {
        if self.count == 0 {
            None
        } else {
            Some(self.sum / self.count as f64)
        }
    }
    /// Returns the minimum, or `None` if no samples.
    pub fn min(&self) -> Option<f64> {
        if self.count == 0 {
            None
        } else {
            Some(self.min)
        }
    }
    /// Returns the maximum, or `None` if no samples.
    pub fn max(&self) -> Option<f64> {
        if self.count == 0 {
            None
        } else {
            Some(self.max)
        }
    }
    /// Returns the count of recorded samples.
    pub fn count(&self) -> u64 {
        self.count
    }
}
/// A window iterator that yields overlapping windows of size `n`.
#[allow(dead_code)]
pub struct WindowIterator<'a, T> {
    pub(super) data: &'a [T],
    pub(super) pos: usize,
    pub(super) window: usize,
}
#[allow(dead_code)]
impl<'a, T> WindowIterator<'a, T> {
    /// Creates a new window iterator.
    pub fn new(data: &'a [T], window: usize) -> Self {
        Self {
            data,
            pos: 0,
            window,
        }
    }
}
/// A token bucket rate limiter.
#[allow(dead_code)]
pub struct TokenBucket {
    capacity: u64,
    tokens: u64,
    refill_per_ms: u64,
    last_refill: crate::wall_clock::Instant,
}
#[allow(dead_code)]
impl TokenBucket {
    /// Creates a new token bucket.
    pub fn new(capacity: u64, refill_per_ms: u64) -> Self {
        Self {
            capacity,
            tokens: capacity,
            refill_per_ms,
            last_refill: crate::wall_clock::Instant::now(),
        }
    }
    /// Attempts to consume `n` tokens.  Returns `true` on success.
    pub fn try_consume(&mut self, n: u64) -> bool {
        self.refill();
        if self.tokens >= n {
            self.tokens -= n;
            true
        } else {
            false
        }
    }
    fn refill(&mut self) {
        let now = crate::wall_clock::Instant::now();
        let elapsed_ms = now.duration_since(self.last_refill).as_millis() as u64;
        if elapsed_ms > 0 {
            let new_tokens = elapsed_ms * self.refill_per_ms;
            self.tokens = (self.tokens + new_tokens).min(self.capacity);
            self.last_refill = now;
        }
    }
    /// Returns the number of currently available tokens.
    pub fn available(&self) -> u64 {
        self.tokens
    }
    /// Returns the bucket capacity.
    pub fn capacity(&self) -> u64 {
        self.capacity
    }
}
/// Result of a termination check with detailed information.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct DetailedTerminationResult {
    /// Whether termination was verified.
    pub terminates: bool,
    /// The well-founded relation used (if termination was verified).
    pub wf_relation: Option<WfRelationKind>,
    /// The function name.
    pub function_name: Name,
    /// Explanation of why termination was/wasn't verified.
    pub explanation: String,
    /// All recursive calls found.
    pub recursive_calls: Vec<RecCallInfo>,
}
impl DetailedTerminationResult {
    /// Create a termination result for a non-recursive function.
    #[allow(dead_code)]
    pub fn non_recursive(name: Name) -> Self {
        Self {
            terminates: true,
            wf_relation: None,
            function_name: name,
            explanation: "No recursive calls; trivially terminating.".to_string(),
            recursive_calls: vec![],
        }
    }
    /// Create a successful termination result.
    #[allow(dead_code)]
    pub fn success(name: Name, wf: WfRelationKind, calls: Vec<RecCallInfo>) -> Self {
        let explanation = format!("Termination verified via {}.", wf.description());
        Self {
            terminates: true,
            wf_relation: Some(wf),
            function_name: name,
            explanation,
            recursive_calls: calls,
        }
    }
    /// Create a failure result.
    #[allow(dead_code)]
    pub fn failure(name: Name, calls: Vec<RecCallInfo>, reason: impl Into<String>) -> Self {
        Self {
            terminates: false,
            wf_relation: None,
            function_name: name,
            explanation: reason.into(),
            recursive_calls: calls,
        }
    }
}
/// A simple mutable key-value store for test fixtures.
#[allow(dead_code)]
pub struct Fixture {
    data: std::collections::HashMap<String, String>,
}
#[allow(dead_code)]
impl Fixture {
    /// Creates an empty fixture.
    pub fn new() -> Self {
        Self {
            data: std::collections::HashMap::new(),
        }
    }
    /// Sets a key.
    pub fn set(&mut self, key: impl Into<String>, val: impl Into<String>) {
        self.data.insert(key.into(), val.into());
    }
    /// Gets a value.
    pub fn get(&self, key: &str) -> Option<&str> {
        self.data.get(key).map(|s| s.as_str())
    }
    /// Returns the number of entries.
    pub fn len(&self) -> usize {
        self.data.len()
    }
    /// Returns whether the collection is empty.
    pub fn is_empty(&self) -> bool {
        self.len() == 0
    }
}
/// A simple stack-based calculator for arithmetic expressions.
#[allow(dead_code)]
pub struct StackCalc {
    stack: Vec<i64>,
}
#[allow(dead_code)]
impl StackCalc {
    /// Creates a new empty calculator.
    pub fn new() -> Self {
        Self { stack: Vec::new() }
    }
    /// Pushes an integer literal.
    pub fn push(&mut self, n: i64) {
        self.stack.push(n);
    }
    /// Replaces the top two values, `b` on top of `a`, with `op(a, b)` and
    /// returns it.  Returns `None`, leaving the stack unchanged, if it holds
    /// fewer than two values.
    fn apply_binary(&mut self, op: impl FnOnce(i64, i64) -> i64) -> Option<i64> {
        let (rest_len, a, b) = match self.stack[..] {
            [ref rest @ .., a, b] => (rest.len(), a, b),
            _ => return None,
        };
        let value = op(a, b);
        self.stack.truncate(rest_len);
        self.stack.push(value);
        Some(value)
    }
    /// Adds the top two values and returns the sum, which replaces them.
    /// Returns `None`, leaving the stack unchanged, if it holds fewer than
    /// two values.
    pub fn add(&mut self) -> Option<i64> {
        self.apply_binary(|a, b| a + b)
    }
    /// Subtracts top from second and returns the difference, which replaces
    /// them.  Returns `None`, leaving the stack unchanged, if it holds fewer
    /// than two values.
    pub fn sub(&mut self) -> Option<i64> {
        self.apply_binary(|a, b| a - b)
    }
    /// Multiplies the top two values and returns the product, which replaces
    /// them.  Returns `None`, leaving the stack unchanged, if it holds fewer
    /// than two values.
    pub fn mul(&mut self) -> Option<i64> {
        self.apply_binary(|a, b| a * b)
    }
    /// Peeks the top value.
    pub fn peek(&self) -> Option<i64> {
        self.stack.last().copied()
    }
    /// Returns the stack depth.
    pub fn depth(&self) -> usize {
        self.stack.len()
    }
}
/// A tagged union for representing a simple two-case discriminated union.
#[allow(dead_code)]
pub enum Either2<A, B> {
    /// The first alternative.
    First(A),
    /// The second alternative.
    Second(B),
}
#[allow(dead_code)]
impl<A, B> Either2<A, B> {
    /// Returns `true` if this is the first alternative.
    pub fn is_first(&self) -> bool {
        matches!(self, Either2::First(_))
    }
    /// Returns `true` if this is the second alternative.
    pub fn is_second(&self) -> bool {
        matches!(self, Either2::Second(_))
    }
    /// Returns the first value if present.
    pub fn first(self) -> Option<A> {
        match self {
            Either2::First(a) => Some(a),
            _ => None,
        }
    }
    /// Returns the second value if present.
    pub fn second(self) -> Option<B> {
        match self {
            Either2::Second(b) => Some(b),
            _ => None,
        }
    }
    /// Maps over the first alternative.
    pub fn map_first<C, F: FnOnce(A) -> C>(self, f: F) -> Either2<C, B> {
        match self {
            Either2::First(a) => Either2::First(f(a)),
            Either2::Second(b) => Either2::Second(b),
        }
    }
}
/// A simple ordered index mapping names to integer IDs.
#[allow(dead_code)]
#[derive(Debug, Clone, Default)]
pub struct NameIndex {
    names: Vec<String>,
    index: std::collections::HashMap<String, usize>,
}
impl NameIndex {
    /// Create a new empty name index.
    #[allow(dead_code)]
    pub fn new() -> Self {
        Self::default()
    }
    /// Insert a name, returning its ID.
    /// If the name is already present, returns the existing ID.
    #[allow(dead_code)]
    pub fn insert(&mut self, name: impl Into<String>) -> usize {
        let name = name.into();
        if let Some(&id) = self.index.get(&name) {
            return id;
        }
        let id = self.names.len();
        self.index.insert(name.clone(), id);
        self.names.push(name);
        id
    }
    /// Get the ID for a name, if it exists.
    #[allow(dead_code)]
    pub fn get_id(&self, name: &str) -> Option<usize> {
        self.index.get(name).copied()
    }
    /// Get the name for an ID.
    #[allow(dead_code)]
    pub fn get_name(&self, id: usize) -> Option<&str> {
        self.names.get(id).map(|s| s.as_str())
    }
    /// Get the number of names in the index.
    #[allow(dead_code)]
    pub fn len(&self) -> usize {
        self.names.len()
    }
    /// Check if the index is empty.
    #[allow(dead_code)]
    pub fn is_empty(&self) -> bool {
        self.names.is_empty()
    }
    /// Get all names in insertion order.
    #[allow(dead_code)]
    pub fn all_names(&self) -> &[String] {
        &self.names
    }
}
/// A set of rewrite rules.
#[allow(dead_code)]
pub struct RewriteRuleSet {
    rules: Vec<RewriteRule>,
}
#[allow(dead_code)]
impl RewriteRuleSet {
    /// Creates an empty rule set.
    pub fn new() -> Self {
        Self { rules: Vec::new() }
    }
    /// Adds a rule.
    pub fn add(&mut self, rule: RewriteRule) {
        self.rules.push(rule);
    }
    /// Returns the number of rules.
    pub fn len(&self) -> usize {
        self.rules.len()
    }
    /// Returns `true` if the set is empty.
    pub fn is_empty(&self) -> bool {
        self.rules.is_empty()
    }
    /// Returns all conditional rules.
    pub fn conditional_rules(&self) -> Vec<&RewriteRule> {
        self.rules.iter().filter(|r| r.conditional).collect()
    }
    /// Returns all unconditional rules.
    pub fn unconditional_rules(&self) -> Vec<&RewriteRule> {
        self.rules.iter().filter(|r| !r.conditional).collect()
    }
    /// Looks up a rule by name.
    pub fn get(&self, name: &str) -> Option<&RewriteRule> {
        self.rules.iter().find(|r| r.name == name)
    }
}
/// A cache of termination results for batch checking.
#[allow(dead_code)]
#[derive(Debug, Clone, Default)]
pub struct TerminationCache {
    results: HashMap<Name, bool>,
}
impl TerminationCache {
    /// Create a new cache.
    #[allow(dead_code)]
    pub fn new() -> Self {
        Self::default()
    }
    /// Record that a function terminates.
    #[allow(dead_code)]
    pub fn mark_terminating(&mut self, name: Name) {
        self.results.insert(name, true);
    }
    /// Record that a function may not terminate.
    #[allow(dead_code)]
    pub fn mark_nonterminating(&mut self, name: Name) {
        self.results.insert(name, false);
    }
    /// Query if a function is known to terminate.
    #[allow(dead_code)]
    pub fn is_known_terminating(&self, name: &Name) -> Option<bool> {
        self.results.get(name).copied()
    }
    /// Get the number of cached results.
    #[allow(dead_code)]
    pub fn len(&self) -> usize {
        self.results.len()
    }
    /// Check if the cache is empty.
    #[allow(dead_code)]
    pub fn is_empty(&self) -> bool {
        self.results.is_empty()
    }
    /// Clear the cache.
    #[allow(dead_code)]
    pub fn clear(&mut self) {
        self.results.clear();
    }
}
/// A mutable reference stack for tracking the current "focus" in a tree traversal.
#[allow(dead_code)]
pub struct FocusStack<T> {
    items: Vec<T>,
}
#[allow(dead_code)]
impl<T> FocusStack<T> {
    /// Creates an empty focus stack.
    pub fn new() -> Self {
        Self { items: Vec::new() }
    }
    /// Focuses on `item`.
    pub fn focus(&mut self, item: T) {
        self.items.push(item);
    }
    /// Blurs (pops) the current focus.
    pub fn blur(&mut self) -> Option<T> {
        self.items.pop()
    }
    /// Returns the current focus, or `None`.
    pub fn current(&self) -> Option<&T> {
        self.items.last()
    }
    /// Returns the focus depth.
    pub fn depth(&self) -> usize {
        self.items.len()
    }
    /// Returns `true` if there is no current focus.
    pub fn is_empty(&self) -> bool {
        self.items.is_empty()
    }
}