oxilean-kernel 0.1.2

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

use crate::{Expr, FVarId};
use std::collections::HashMap;

use super::types::{
    ConfigNode, DecisionNode, Either2, FlatSubstitution, FocusStack, LabelSet, NonEmptyVec,
    PathBuf, RewriteRule, RewriteRuleSet, SimpleDag, SlidingSum, SmallMap, SparseVec, StackCalc,
    StatSummary, Stopwatch, StringPool, SubstStats, Substitution, TokenBucket, TransformStat,
    TransitiveClosure, VersionedRecord, WindowIterator, WriteOnce,
};

/// Instantiate BVar(0) with arg in body, shifting down all other BVars.
///
/// This is the core operation for β-reduction: `(λx.body) arg → body[arg/x]`.
pub fn instantiate(body: &Expr, arg: &Expr) -> Expr {
    instantiate_at(body, arg, 0)
}
fn instantiate_at(expr: &Expr, arg: &Expr, depth: u32) -> Expr {
    match expr {
        Expr::BVar(n) => {
            if *n == depth {
                arg.clone()
            } else if *n > depth {
                Expr::BVar(*n - 1)
            } else {
                expr.clone()
            }
        }
        Expr::Sort(_) | Expr::FVar(_) | Expr::Const(_, _) | Expr::Lit(_) => expr.clone(),
        Expr::App(f, a) => {
            let f_new = instantiate_at(f, arg, depth);
            let a_new = instantiate_at(a, arg, depth);
            Expr::App(Box::new(f_new), Box::new(a_new))
        }
        Expr::Lam(bi, name, ty, body) => {
            let ty_new = instantiate_at(ty, arg, depth);
            let body_new = instantiate_at(body, arg, depth + 1);
            Expr::Lam(*bi, name.clone(), Box::new(ty_new), Box::new(body_new))
        }
        Expr::Pi(bi, name, ty, body) => {
            let ty_new = instantiate_at(ty, arg, depth);
            let body_new = instantiate_at(body, arg, depth + 1);
            Expr::Pi(*bi, name.clone(), Box::new(ty_new), Box::new(body_new))
        }
        Expr::Let(name, ty, val, body) => {
            let ty_new = instantiate_at(ty, arg, depth);
            let val_new = instantiate_at(val, arg, depth);
            let body_new = instantiate_at(body, arg, depth + 1);
            Expr::Let(
                name.clone(),
                Box::new(ty_new),
                Box::new(val_new),
                Box::new(body_new),
            )
        }
        Expr::Proj(name, idx, e) => {
            let e_new = instantiate_at(e, arg, depth);
            Expr::Proj(name.clone(), *idx, Box::new(e_new))
        }
    }
}
/// Replace FVar with BVar(0), shifting up all existing BVars.
///
/// This is the inverse of instantiation, used when forming binders.
pub fn abstract_expr(expr: &Expr, fvar: FVarId) -> Expr {
    abstract_at(expr, fvar, 0)
}
fn abstract_at(expr: &Expr, fvar: FVarId, depth: u32) -> Expr {
    match expr {
        Expr::FVar(id) if *id == fvar => Expr::BVar(depth),
        Expr::BVar(n) => Expr::BVar(*n + 1),
        Expr::Sort(_) | Expr::FVar(_) | Expr::Const(_, _) | Expr::Lit(_) => expr.clone(),
        Expr::App(f, a) => {
            let f_new = abstract_at(f, fvar, depth);
            let a_new = abstract_at(a, fvar, depth);
            Expr::App(Box::new(f_new), Box::new(a_new))
        }
        Expr::Lam(bi, name, ty, body) => {
            let ty_new = abstract_at(ty, fvar, depth);
            let body_new = abstract_at(body, fvar, depth + 1);
            Expr::Lam(*bi, name.clone(), Box::new(ty_new), Box::new(body_new))
        }
        Expr::Pi(bi, name, ty, body) => {
            let ty_new = abstract_at(ty, fvar, depth);
            let body_new = abstract_at(body, fvar, depth + 1);
            Expr::Pi(*bi, name.clone(), Box::new(ty_new), Box::new(body_new))
        }
        Expr::Let(name, ty, val, body) => {
            let ty_new = abstract_at(ty, fvar, depth);
            let val_new = abstract_at(val, fvar, depth);
            let body_new = abstract_at(body, fvar, depth + 1);
            Expr::Let(
                name.clone(),
                Box::new(ty_new),
                Box::new(val_new),
                Box::new(body_new),
            )
        }
        Expr::Proj(name, idx, e) => {
            let e_new = abstract_at(e, fvar, depth);
            Expr::Proj(name.clone(), *idx, Box::new(e_new))
        }
    }
}
#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_instantiate_simple() {
        let bvar0 = Expr::BVar(0);
        let fvar = Expr::FVar(FVarId(1));
        let result = instantiate(&bvar0, &fvar);
        assert_eq!(result, fvar);
    }
    #[test]
    fn test_instantiate_shift_down() {
        let bvar1 = Expr::BVar(1);
        let arg = Expr::FVar(FVarId(1));
        let result = instantiate(&bvar1, &arg);
        assert_eq!(result, Expr::BVar(0));
    }
    #[test]
    fn test_abstract_roundtrip() {
        let fvar_id = FVarId(42);
        let fvar = Expr::FVar(fvar_id);
        let abstracted = abstract_expr(&fvar, fvar_id);
        let back = instantiate(&abstracted, &fvar);
        assert_eq!(back, fvar);
    }
    #[test]
    fn test_instantiate_app() {
        let app = Expr::App(Box::new(Expr::BVar(0)), Box::new(Expr::BVar(1)));
        let arg = Expr::FVar(FVarId(99));
        let result = instantiate(&app, &arg);
        match result {
            Expr::App(f, a) => {
                assert_eq!(*f, arg);
                assert_eq!(*a, Expr::BVar(0));
            }
            _ => panic!("Expected App"),
        }
    }
}
/// A finite mapping from free-variable identifiers to expressions.
pub type SubstMap = HashMap<FVarId, Expr>;
/// Simultaneously substitute `BVar(0)..BVar(k-1)` with `args[0]..args[k-1]`.
pub fn instantiate_many(expr: &Expr, args: &[Expr]) -> Expr {
    let k = args.len() as u32;
    if k == 0 {
        return expr.clone();
    }
    instantiate_many_at(expr, args, k, 0)
}
fn instantiate_many_at(expr: &Expr, args: &[Expr], k: u32, offset: u32) -> Expr {
    match expr {
        Expr::BVar(n) => {
            let idx = *n;
            if idx >= offset && idx < offset + k {
                args[(idx - offset) as usize].clone()
            } else if idx >= offset + k {
                Expr::BVar(idx - k)
            } else {
                expr.clone()
            }
        }
        Expr::Sort(_) | Expr::FVar(_) | Expr::Const(_, _) | Expr::Lit(_) => expr.clone(),
        Expr::App(f, a) => Expr::App(
            Box::new(instantiate_many_at(f, args, k, offset)),
            Box::new(instantiate_many_at(a, args, k, offset)),
        ),
        Expr::Lam(bi, name, ty, body) => Expr::Lam(
            *bi,
            name.clone(),
            Box::new(instantiate_many_at(ty, args, k, offset)),
            Box::new(instantiate_many_at(body, args, k, offset + 1)),
        ),
        Expr::Pi(bi, name, ty, body) => Expr::Pi(
            *bi,
            name.clone(),
            Box::new(instantiate_many_at(ty, args, k, offset)),
            Box::new(instantiate_many_at(body, args, k, offset + 1)),
        ),
        Expr::Let(name, ty, val, body) => Expr::Let(
            name.clone(),
            Box::new(instantiate_many_at(ty, args, k, offset)),
            Box::new(instantiate_many_at(val, args, k, offset)),
            Box::new(instantiate_many_at(body, args, k, offset + 1)),
        ),
        Expr::Proj(name, idx, e) => Expr::Proj(
            name.clone(),
            *idx,
            Box::new(instantiate_many_at(e, args, k, offset)),
        ),
    }
}
/// Apply a parallel substitution: replace each `FVar(id)` with the corresponding
/// expression in `map`.
pub fn parallel_subst(expr: &Expr, map: &SubstMap) -> Expr {
    if map.is_empty() {
        return expr.clone();
    }
    parallel_subst_impl(expr, map)
}
fn parallel_subst_impl(expr: &Expr, map: &SubstMap) -> Expr {
    match expr {
        Expr::FVar(id) => {
            if let Some(replacement) = map.get(id) {
                replacement.clone()
            } else {
                expr.clone()
            }
        }
        Expr::BVar(_) | Expr::Sort(_) | Expr::Const(_, _) | Expr::Lit(_) => expr.clone(),
        Expr::App(f, a) => Expr::App(
            Box::new(parallel_subst_impl(f, map)),
            Box::new(parallel_subst_impl(a, map)),
        ),
        Expr::Lam(bi, name, ty, body) => Expr::Lam(
            *bi,
            name.clone(),
            Box::new(parallel_subst_impl(ty, map)),
            Box::new(parallel_subst_impl(body, map)),
        ),
        Expr::Pi(bi, name, ty, body) => Expr::Pi(
            *bi,
            name.clone(),
            Box::new(parallel_subst_impl(ty, map)),
            Box::new(parallel_subst_impl(body, map)),
        ),
        Expr::Let(name, ty, val, body) => Expr::Let(
            name.clone(),
            Box::new(parallel_subst_impl(ty, map)),
            Box::new(parallel_subst_impl(val, map)),
            Box::new(parallel_subst_impl(body, map)),
        ),
        Expr::Proj(name, idx, e) => {
            Expr::Proj(name.clone(), *idx, Box::new(parallel_subst_impl(e, map)))
        }
    }
}
/// Shift all `BVar(i)` with `i >= cutoff` up by `amount`.
pub fn shift_bvars(expr: &Expr, amount: u32, cutoff: u32) -> Expr {
    match expr {
        Expr::BVar(i) => {
            if *i >= cutoff {
                Expr::BVar(*i + amount)
            } else {
                expr.clone()
            }
        }
        Expr::Sort(_) | Expr::FVar(_) | Expr::Const(_, _) | Expr::Lit(_) => expr.clone(),
        Expr::App(f, a) => Expr::App(
            Box::new(shift_bvars(f, amount, cutoff)),
            Box::new(shift_bvars(a, amount, cutoff)),
        ),
        Expr::Lam(bi, name, ty, body) => Expr::Lam(
            *bi,
            name.clone(),
            Box::new(shift_bvars(ty, amount, cutoff)),
            Box::new(shift_bvars(body, amount, cutoff + 1)),
        ),
        Expr::Pi(bi, name, ty, body) => Expr::Pi(
            *bi,
            name.clone(),
            Box::new(shift_bvars(ty, amount, cutoff)),
            Box::new(shift_bvars(body, amount, cutoff + 1)),
        ),
        Expr::Let(name, ty, val, body) => Expr::Let(
            name.clone(),
            Box::new(shift_bvars(ty, amount, cutoff)),
            Box::new(shift_bvars(val, amount, cutoff)),
            Box::new(shift_bvars(body, amount, cutoff + 1)),
        ),
        Expr::Proj(name, idx, e) => {
            Expr::Proj(name.clone(), *idx, Box::new(shift_bvars(e, amount, cutoff)))
        }
    }
}
/// Collect the set of free `FVarId`s occurring in `expr`.
pub fn free_vars(expr: &Expr) -> std::collections::HashSet<FVarId> {
    let mut set = std::collections::HashSet::new();
    free_vars_impl(expr, &mut set);
    set
}
fn free_vars_impl(expr: &Expr, set: &mut std::collections::HashSet<FVarId>) {
    match expr {
        Expr::FVar(id) => {
            set.insert(*id);
        }
        Expr::App(f, a) => {
            free_vars_impl(f, set);
            free_vars_impl(a, set);
        }
        Expr::Lam(_, _, ty, body) | Expr::Pi(_, _, ty, body) => {
            free_vars_impl(ty, set);
            free_vars_impl(body, set);
        }
        Expr::Let(_, ty, val, body) => {
            free_vars_impl(ty, set);
            free_vars_impl(val, set);
            free_vars_impl(body, set);
        }
        Expr::Proj(_, _, e) => free_vars_impl(e, set),
        _ => {}
    }
}
/// Return `true` if `fvar` occurs free in `expr`.
pub fn occurs_free(expr: &Expr, fvar: FVarId) -> bool {
    match expr {
        Expr::FVar(id) => *id == fvar,
        Expr::App(f, a) => occurs_free(f, fvar) || occurs_free(a, fvar),
        Expr::Lam(_, _, ty, body) | Expr::Pi(_, _, ty, body) => {
            occurs_free(ty, fvar) || occurs_free(body, fvar)
        }
        Expr::Let(_, ty, val, body) => {
            occurs_free(ty, fvar) || occurs_free(val, fvar) || occurs_free(body, fvar)
        }
        Expr::Proj(_, _, e) => occurs_free(e, fvar),
        _ => false,
    }
}
/// Count how many times `fvar` occurs free in `expr`.
pub fn count_free_occurrences(expr: &Expr, fvar: FVarId) -> usize {
    match expr {
        Expr::FVar(id) => usize::from(*id == fvar),
        Expr::App(f, a) => count_free_occurrences(f, fvar) + count_free_occurrences(a, fvar),
        Expr::Lam(_, _, ty, body) | Expr::Pi(_, _, ty, body) => {
            count_free_occurrences(ty, fvar) + count_free_occurrences(body, fvar)
        }
        Expr::Let(_, ty, val, body) => {
            count_free_occurrences(ty, fvar)
                + count_free_occurrences(val, fvar)
                + count_free_occurrences(body, fvar)
        }
        Expr::Proj(_, _, e) => count_free_occurrences(e, fvar),
        _ => 0,
    }
}
/// Like [`instantiate`] but also fills in [`SubstStats`].
pub fn instantiate_tracked(body: &Expr, arg: &Expr, stats: &mut SubstStats) -> Expr {
    instantiate_tracked_at(body, arg, 0, stats)
}
fn instantiate_tracked_at(expr: &Expr, arg: &Expr, depth: u32, stats: &mut SubstStats) -> Expr {
    stats.nodes_visited += 1;
    match expr {
        Expr::BVar(n) => {
            if *n == depth {
                stats.bvar_hits += 1;
                arg.clone()
            } else if *n > depth {
                stats.bvar_misses += 1;
                Expr::BVar(*n - 1)
            } else {
                expr.clone()
            }
        }
        Expr::Sort(_) | Expr::FVar(_) | Expr::Const(_, _) | Expr::Lit(_) => expr.clone(),
        Expr::App(f, a) => Expr::App(
            Box::new(instantiate_tracked_at(f, arg, depth, stats)),
            Box::new(instantiate_tracked_at(a, arg, depth, stats)),
        ),
        Expr::Lam(bi, name, ty, body) => Expr::Lam(
            *bi,
            name.clone(),
            Box::new(instantiate_tracked_at(ty, arg, depth, stats)),
            Box::new(instantiate_tracked_at(body, arg, depth + 1, stats)),
        ),
        Expr::Pi(bi, name, ty, body) => Expr::Pi(
            *bi,
            name.clone(),
            Box::new(instantiate_tracked_at(ty, arg, depth, stats)),
            Box::new(instantiate_tracked_at(body, arg, depth + 1, stats)),
        ),
        Expr::Let(name, ty, val, body) => Expr::Let(
            name.clone(),
            Box::new(instantiate_tracked_at(ty, arg, depth, stats)),
            Box::new(instantiate_tracked_at(val, arg, depth, stats)),
            Box::new(instantiate_tracked_at(body, arg, depth + 1, stats)),
        ),
        Expr::Proj(name, idx, e) => Expr::Proj(
            name.clone(),
            *idx,
            Box::new(instantiate_tracked_at(e, arg, depth, stats)),
        ),
    }
}
/// Build a `SubstMap` from parallel slices of ids and replacements.
pub fn build_subst_map(fvars: &[FVarId], replacements: &[Expr]) -> SubstMap {
    assert_eq!(fvars.len(), replacements.len());
    fvars
        .iter()
        .zip(replacements.iter())
        .map(|(id, expr)| (*id, expr.clone()))
        .collect()
}
/// Apply beta-reduction once at the top level if possible.
pub fn try_beta_reduce(expr: &Expr) -> Option<Expr> {
    match expr {
        Expr::App(f, a) => {
            if let Expr::Lam(_, _, _, body) = f.as_ref() {
                Some(instantiate(body, a))
            } else {
                None
            }
        }
        _ => None,
    }
}
/// Repeatedly apply top-level beta reduction until no more is possible.
pub fn beta_reduce_head(expr: Expr) -> Expr {
    let mut curr = expr;
    while let Some(reduced) = try_beta_reduce(&curr) {
        curr = reduced;
    }
    curr
}
/// Substitute a single free variable with an expression.
pub fn subst_fvar(expr: &Expr, fvar: FVarId, replacement: &Expr) -> Expr {
    let mut map = SubstMap::new();
    map.insert(fvar, replacement.clone());
    parallel_subst(expr, &map)
}
/// Check whether `expr` is in weak head normal form with respect to beta.
pub fn is_whnf_beta(expr: &Expr) -> bool {
    match expr {
        Expr::App(f, _) => match f.as_ref() {
            Expr::Lam(_, _, _, _) => false,
            other => is_whnf_beta(other),
        },
        _ => true,
    }
}
/// Collect the indices of all loose bound variables.
pub fn collect_loose_bvar_indices(expr: &Expr) -> Vec<u32> {
    let mut indices = Vec::new();
    collect_loose_bvar_impl(expr, 0, &mut indices);
    indices.sort();
    indices.dedup();
    indices
}
fn collect_loose_bvar_impl(expr: &Expr, depth: u32, result: &mut Vec<u32>) {
    match expr {
        Expr::BVar(n) if *n >= depth => {
            result.push(*n - depth);
        }
        Expr::BVar(_) => {}
        Expr::App(f, a) => {
            collect_loose_bvar_impl(f, depth, result);
            collect_loose_bvar_impl(a, depth, result);
        }
        Expr::Lam(_, _, ty, body) | Expr::Pi(_, _, ty, body) => {
            collect_loose_bvar_impl(ty, depth, result);
            collect_loose_bvar_impl(body, depth + 1, result);
        }
        Expr::Let(_, ty, val, body) => {
            collect_loose_bvar_impl(ty, depth, result);
            collect_loose_bvar_impl(val, depth, result);
            collect_loose_bvar_impl(body, depth + 1, result);
        }
        Expr::Proj(_, _, e) => collect_loose_bvar_impl(e, depth, result),
        _ => {}
    }
}
/// Apply a parallel substitution and collect profiling statistics.
pub fn parallel_subst_tracked(expr: &Expr, map: &SubstMap, stats: &mut SubstStats) -> Expr {
    if map.is_empty() {
        return expr.clone();
    }
    parallel_subst_tracked_impl(expr, map, stats)
}
fn parallel_subst_tracked_impl(expr: &Expr, map: &SubstMap, stats: &mut SubstStats) -> Expr {
    stats.nodes_visited += 1;
    match expr {
        Expr::FVar(id) => {
            if let Some(r) = map.get(id) {
                stats.fvar_hits += 1;
                r.clone()
            } else {
                expr.clone()
            }
        }
        Expr::BVar(_) | Expr::Sort(_) | Expr::Const(_, _) | Expr::Lit(_) => expr.clone(),
        Expr::App(f, a) => Expr::App(
            Box::new(parallel_subst_tracked_impl(f, map, stats)),
            Box::new(parallel_subst_tracked_impl(a, map, stats)),
        ),
        Expr::Lam(bi, name, ty, body) => Expr::Lam(
            *bi,
            name.clone(),
            Box::new(parallel_subst_tracked_impl(ty, map, stats)),
            Box::new(parallel_subst_tracked_impl(body, map, stats)),
        ),
        Expr::Pi(bi, name, ty, body) => Expr::Pi(
            *bi,
            name.clone(),
            Box::new(parallel_subst_tracked_impl(ty, map, stats)),
            Box::new(parallel_subst_tracked_impl(body, map, stats)),
        ),
        Expr::Let(name, ty, val, body) => Expr::Let(
            name.clone(),
            Box::new(parallel_subst_tracked_impl(ty, map, stats)),
            Box::new(parallel_subst_tracked_impl(val, map, stats)),
            Box::new(parallel_subst_tracked_impl(body, map, stats)),
        ),
        Expr::Proj(name, idx, e) => Expr::Proj(
            name.clone(),
            *idx,
            Box::new(parallel_subst_tracked_impl(e, map, stats)),
        ),
    }
}
#[cfg(test)]
mod extended_tests {
    use super::*;
    use crate::{BinderInfo, Level, Literal, Name};
    fn fvar(id: u64) -> Expr {
        Expr::FVar(FVarId(id))
    }
    fn lit(n: u64) -> Expr {
        Expr::Lit(Literal::Nat(n))
    }
    fn sort0() -> Expr {
        Expr::Sort(Level::zero())
    }
    #[test]
    fn test_instantiate_many_two() {
        let app = Expr::App(Box::new(Expr::BVar(0)), Box::new(Expr::BVar(1)));
        let result = instantiate_many(&app, &[lit(10), lit(20)]);
        match result {
            Expr::App(f, a) => {
                assert_eq!(*f, lit(10));
                assert_eq!(*a, lit(20));
            }
            _ => panic!("Expected App"),
        }
    }
    #[test]
    fn test_parallel_subst_single() {
        let mut map = SubstMap::new();
        map.insert(FVarId(1), lit(99));
        let expr = fvar(1);
        assert_eq!(parallel_subst(&expr, &map), lit(99));
    }
    #[test]
    fn test_parallel_subst_empty() {
        let expr = fvar(5);
        let map = SubstMap::new();
        assert_eq!(parallel_subst(&expr, &map), expr);
    }
    #[test]
    fn test_shift_bvars_above_cutoff() {
        let e = Expr::BVar(2);
        let shifted = shift_bvars(&e, 3, 1);
        assert_eq!(shifted, Expr::BVar(5));
    }
    #[test]
    fn test_shift_bvars_below_cutoff() {
        let e = Expr::BVar(0);
        let shifted = shift_bvars(&e, 2, 1);
        assert_eq!(shifted, Expr::BVar(0));
    }
    #[test]
    fn test_free_vars_single() {
        let set = free_vars(&fvar(7));
        assert_eq!(set.len(), 1);
        assert!(set.contains(&FVarId(7)));
    }
    #[test]
    fn test_occurs_free_true() {
        let expr = Expr::App(Box::new(fvar(1)), Box::new(fvar(2)));
        assert!(occurs_free(&expr, FVarId(1)));
        assert!(!occurs_free(&expr, FVarId(3)));
    }
    #[test]
    fn test_count_free_occurrences() {
        let expr = Expr::App(Box::new(fvar(1)), Box::new(fvar(1)));
        assert_eq!(count_free_occurrences(&expr, FVarId(1)), 2);
    }
    #[test]
    fn test_subst_stats_merge() {
        let mut a = SubstStats {
            bvar_hits: 3,
            bvar_misses: 1,
            fvar_hits: 2,
            nodes_visited: 10,
        };
        let b = SubstStats {
            bvar_hits: 1,
            bvar_misses: 0,
            fvar_hits: 1,
            nodes_visited: 5,
        };
        a.merge(&b);
        assert_eq!(a.bvar_hits, 4);
        assert_eq!(a.total_substs(), 7);
    }
    #[test]
    fn test_instantiate_tracked() {
        let body = Expr::BVar(0);
        let arg = lit(42);
        let mut stats = SubstStats::default();
        let result = instantiate_tracked(&body, &arg, &mut stats);
        assert_eq!(result, lit(42));
        assert_eq!(stats.bvar_hits, 1);
    }
    #[test]
    fn test_build_subst_map() {
        let fvars = vec![FVarId(1), FVarId(2)];
        let replacements = vec![lit(10), lit(20)];
        let map = build_subst_map(&fvars, &replacements);
        assert_eq!(map.get(&FVarId(1)), Some(&lit(10)));
    }
    #[test]
    fn test_try_beta_reduce_success() {
        let lam = Expr::Lam(
            BinderInfo::Default,
            Name::str("x"),
            Box::new(sort0()),
            Box::new(Expr::BVar(0)),
        );
        let app = Expr::App(Box::new(lam), Box::new(lit(42)));
        let result = try_beta_reduce(&app).expect("result should be present");
        assert_eq!(result, lit(42));
    }
    #[test]
    fn test_try_beta_reduce_fail() {
        let app = Expr::App(Box::new(fvar(1)), Box::new(lit(42)));
        assert!(try_beta_reduce(&app).is_none());
    }
    #[test]
    fn test_beta_reduce_head() {
        let lam = Expr::Lam(
            BinderInfo::Default,
            Name::str("x"),
            Box::new(sort0()),
            Box::new(Expr::BVar(0)),
        );
        let app = Expr::App(Box::new(lam), Box::new(lit(7)));
        let result = beta_reduce_head(app);
        assert_eq!(result, lit(7));
    }
    #[test]
    fn test_subst_fvar() {
        let expr = fvar(1);
        let result = subst_fvar(&expr, FVarId(1), &lit(99));
        assert_eq!(result, lit(99));
    }
    #[test]
    fn test_is_whnf_beta_lam() {
        let lam = Expr::Lam(
            BinderInfo::Default,
            Name::str("x"),
            Box::new(sort0()),
            Box::new(Expr::BVar(0)),
        );
        assert!(is_whnf_beta(&lam));
    }
    #[test]
    fn test_is_whnf_beta_app_not_whnf() {
        let lam = Expr::Lam(
            BinderInfo::Default,
            Name::str("x"),
            Box::new(sort0()),
            Box::new(Expr::BVar(0)),
        );
        let app = Expr::App(Box::new(lam), Box::new(lit(1)));
        assert!(!is_whnf_beta(&app));
    }
    #[test]
    fn test_collect_loose_bvar_indices() {
        let e = Expr::App(Box::new(Expr::BVar(0)), Box::new(Expr::BVar(2)));
        let indices = collect_loose_bvar_indices(&e);
        assert!(indices.contains(&0));
        assert!(indices.contains(&2));
    }
    #[test]
    fn test_parallel_subst_tracked() {
        let expr = Expr::App(Box::new(fvar(1)), Box::new(fvar(2)));
        let mut map = SubstMap::new();
        map.insert(FVarId(1), lit(10));
        map.insert(FVarId(2), lit(20));
        let mut stats = SubstStats::default();
        let result = parallel_subst_tracked(&expr, &map, &mut stats);
        assert_eq!(stats.fvar_hits, 2);
        match result {
            Expr::App(f, a) => {
                assert_eq!(*f, lit(10));
                assert_eq!(*a, lit(20));
            }
            _ => panic!("Expected App"),
        }
    }
}
/// Apply a list of arguments to a function expression via beta reduction.
///
/// Given `f` and `[a1, a2, ..., an]`, returns `((...((f a1) a2) ...) an)`
/// after instantiating each lambda body with the corresponding argument.
pub fn apply_args(f: &Expr, args: &[Expr]) -> Expr {
    let mut result = f.clone();
    for arg in args {
        if let Expr::Lam(_, _, _, body) = result {
            result = instantiate(&body, arg);
        } else {
            result = Expr::App(Box::new(result), Box::new(arg.clone()));
        }
    }
    result
}
/// Check if an expression is a lambda abstraction.
#[inline]
pub fn is_lambda(e: &Expr) -> bool {
    matches!(e, Expr::Lam(_, _, _, _))
}
/// Peel off `n` leading lambda binders, collecting binder info.
///
/// Returns `(binders, body)` where `binders` is a vector of `(name, binder_info, type)`
/// tuples and `body` is the inner expression with `n` fewer lambdas.
#[allow(clippy::type_complexity)]
pub fn peel_lambdas(
    e: &Expr,
    n: usize,
) -> (Vec<(crate::Name, crate::BinderInfo, Box<Expr>)>, &Expr) {
    let mut binders = Vec::new();
    let mut cur = e;
    for _ in 0..n {
        if let Expr::Lam(bi, _, ty, body) = cur {
            binders.push((crate::Name::Anonymous, *bi, ty.clone()));
            cur = body;
        } else {
            break;
        }
    }
    (binders, cur)
}
/// Count the number of leading lambda binders.
pub fn count_lambdas(e: &Expr) -> usize {
    let mut n = 0;
    let mut cur = e;
    while let Expr::Lam(_, _, _, body) = cur {
        n += 1;
        cur = body;
    }
    n
}
/// Count the number of leading pi binders.
pub fn count_pis(e: &Expr) -> usize {
    let mut n = 0;
    let mut cur = e;
    while let Expr::Pi(_, _, _, body) = cur {
        n += 1;
        cur = body;
    }
    n
}
#[cfg(test)]
mod extended2_tests {
    use super::*;
    use crate::{BinderInfo, Expr, FVarId, Literal, Name};
    fn lit(n: u64) -> Expr {
        Expr::Lit(Literal::Nat(n))
    }
    fn fvar(id: u64) -> Expr {
        Expr::FVar(FVarId(id))
    }
    #[test]
    fn test_apply_args_lam() {
        let body = Expr::BVar(0);
        let lam = Expr::Lam(
            BinderInfo::Default,
            Name::str("_"),
            Box::new(lit(0)),
            Box::new(body),
        );
        let result = apply_args(&lam, &[lit(42)]);
        assert_eq!(result, lit(42));
    }
    #[test]
    fn test_apply_args_non_lam() {
        let f = fvar(1);
        let result = apply_args(&f, &[lit(1), lit(2)]);
        match &result {
            Expr::App(outer, arg2) => {
                assert_eq!(**arg2, lit(2));
                match outer.as_ref() {
                    Expr::App(inner_f, arg1) => {
                        assert_eq!(**inner_f, fvar(1));
                        assert_eq!(**arg1, lit(1));
                    }
                    _ => panic!("Expected App"),
                }
            }
            _ => panic!("Expected App"),
        }
    }
    #[test]
    fn test_is_lambda() {
        let lam = Expr::Lam(
            BinderInfo::Default,
            Name::str("_"),
            Box::new(lit(0)),
            Box::new(lit(1)),
        );
        assert!(is_lambda(&lam));
        assert!(!is_lambda(&lit(0)));
    }
    #[test]
    fn test_count_lambdas() {
        let inner = lit(0);
        let lam1 = Expr::Lam(
            BinderInfo::Default,
            Name::str("_"),
            Box::new(lit(0)),
            Box::new(inner),
        );
        let lam2 = Expr::Lam(
            BinderInfo::Default,
            Name::str("_"),
            Box::new(lit(0)),
            Box::new(lam1),
        );
        assert_eq!(count_lambdas(&lam2), 2);
        assert_eq!(count_lambdas(&lit(0)), 0);
    }
    #[test]
    fn test_count_pis() {
        let inner = lit(0);
        let pi1 = Expr::Pi(
            BinderInfo::Default,
            Name::str("_"),
            Box::new(lit(0)),
            Box::new(inner),
        );
        let pi2 = Expr::Pi(
            BinderInfo::Default,
            Name::str("_"),
            Box::new(lit(0)),
            Box::new(pi1),
        );
        assert_eq!(count_pis(&pi2), 2);
        assert_eq!(count_pis(&lit(0)), 0);
    }
    #[test]
    fn test_peel_lambdas_two() {
        let body = Expr::BVar(0);
        let lam1 = Expr::Lam(
            BinderInfo::Default,
            Name::str("_"),
            Box::new(lit(0)),
            Box::new(body),
        );
        let lam2 = Expr::Lam(
            BinderInfo::Implicit,
            Name::str("_"),
            Box::new(lit(0)),
            Box::new(lam1),
        );
        let (binders, inner) = peel_lambdas(&lam2, 2);
        assert_eq!(binders.len(), 2);
        assert_eq!(binders[0].1, BinderInfo::Implicit);
        assert_eq!(binders[1].1, BinderInfo::Default);
        assert_eq!(*inner, Expr::BVar(0));
    }
    #[test]
    fn test_apply_args_empty() {
        let e = lit(5);
        let result = apply_args(&e, &[]);
        assert_eq!(result, e);
    }
}
/// Apply a substitution list (as parallel arrays) to an expression.
#[allow(dead_code)]
pub fn substitute_fvars(expr: &Expr, fvars: &[FVarId], replacements: &[Expr]) -> Expr {
    assert_eq!(fvars.len(), replacements.len());
    let mut subst = Substitution::new();
    for (fvar, rep) in fvars.iter().zip(replacements.iter()) {
        subst.insert(*fvar, rep.clone());
    }
    subst.apply(expr)
}
/// Check if an expression contains any free variable in the given set.
#[allow(dead_code)]
pub fn expr_contains_fvar(expr: &Expr, fvars: &[FVarId]) -> bool {
    match expr {
        Expr::FVar(id) => fvars.contains(id),
        Expr::App(f, a) => expr_contains_fvar(f, fvars) || expr_contains_fvar(a, fvars),
        Expr::Lam(_, _, ty, body) | Expr::Pi(_, _, ty, body) => {
            expr_contains_fvar(ty, fvars) || expr_contains_fvar(body, fvars)
        }
        Expr::Let(_, ty, val, body) => {
            expr_contains_fvar(ty, fvars)
                || expr_contains_fvar(val, fvars)
                || expr_contains_fvar(body, fvars)
        }
        Expr::Proj(_, _, inner) => expr_contains_fvar(inner, fvars),
        _ => false,
    }
}
/// Replace the outermost `BVar(0)` of a body with `FVar(id)` (open a binder).
///
/// This is the "open" operation in locally nameless representation.
#[allow(dead_code)]
pub fn open_binder(body: &Expr, id: FVarId) -> Expr {
    open_binder_at(body, &Expr::FVar(id), 0)
}
fn open_binder_at(expr: &Expr, fvar_expr: &Expr, depth: u32) -> Expr {
    match expr {
        Expr::BVar(n) => {
            if *n == depth {
                fvar_expr.clone()
            } else {
                expr.clone()
            }
        }
        Expr::App(f, a) => {
            let f2 = open_binder_at(f, fvar_expr, depth);
            let a2 = open_binder_at(a, fvar_expr, depth);
            Expr::App(Box::new(f2), Box::new(a2))
        }
        Expr::Lam(bi, name, ty, body) => {
            let ty2 = open_binder_at(ty, fvar_expr, depth);
            let body2 = open_binder_at(body, fvar_expr, depth + 1);
            Expr::Lam(*bi, name.clone(), Box::new(ty2), Box::new(body2))
        }
        Expr::Pi(bi, name, ty, body) => {
            let ty2 = open_binder_at(ty, fvar_expr, depth);
            let body2 = open_binder_at(body, fvar_expr, depth + 1);
            Expr::Pi(*bi, name.clone(), Box::new(ty2), Box::new(body2))
        }
        Expr::Let(name, ty, val, body) => {
            let ty2 = open_binder_at(ty, fvar_expr, depth);
            let val2 = open_binder_at(val, fvar_expr, depth);
            let body2 = open_binder_at(body, fvar_expr, depth + 1);
            Expr::Let(name.clone(), Box::new(ty2), Box::new(val2), Box::new(body2))
        }
        Expr::Proj(name, idx, inner) => {
            let inner2 = open_binder_at(inner, fvar_expr, depth);
            Expr::Proj(name.clone(), *idx, Box::new(inner2))
        }
        _ => expr.clone(),
    }
}
#[cfg(test)]
mod extended3_subst_tests {
    use super::*;
    use crate::{BinderInfo, Expr, FVarId, Literal, Name};
    fn lit(n: u64) -> Expr {
        Expr::Lit(Literal::Nat(n))
    }
    fn fvar(id: u64) -> Expr {
        Expr::FVar(FVarId(id))
    }
    #[test]
    fn test_substitution_insert_and_get() {
        let mut s = Substitution::new();
        s.insert(FVarId(0), lit(42));
        assert_eq!(s.get(FVarId(0)), Some(&lit(42)));
        assert_eq!(s.get(FVarId(1)), None);
    }
    #[test]
    fn test_substitution_len() {
        let mut s = Substitution::new();
        assert_eq!(s.len(), 0);
        s.insert(FVarId(0), lit(1));
        assert_eq!(s.len(), 1);
    }
    #[test]
    fn test_substitution_apply_fvar() {
        let mut s = Substitution::new();
        s.insert(FVarId(1), lit(99));
        let expr = fvar(1);
        assert_eq!(s.apply(&expr), lit(99));
    }
    #[test]
    fn test_substitution_apply_no_match() {
        let s = Substitution::new();
        let expr = fvar(5);
        assert_eq!(s.apply(&expr), fvar(5));
    }
    #[test]
    fn test_substitution_remove() {
        let mut s = Substitution::new();
        s.insert(FVarId(0), lit(1));
        s.remove(FVarId(0));
        assert_eq!(s.len(), 0);
    }
    #[test]
    fn test_substitution_restrict() {
        let mut s = Substitution::new();
        s.insert(FVarId(0), lit(1));
        s.insert(FVarId(1), lit(2));
        let r = s.restrict(&[FVarId(0)]);
        assert_eq!(r.len(), 1);
        assert!(r.get(FVarId(0)).is_some());
        assert!(r.get(FVarId(1)).is_none());
    }
    #[test]
    fn test_substitute_fvars_parallel() {
        let expr = Expr::App(Box::new(fvar(0)), Box::new(fvar(1)));
        let result = substitute_fvars(&expr, &[FVarId(0), FVarId(1)], &[lit(10), lit(20)]);
        match result {
            Expr::App(f, a) => {
                assert_eq!(*f, lit(10));
                assert_eq!(*a, lit(20));
            }
            _ => panic!("Expected App"),
        }
    }
    #[test]
    fn test_expr_contains_fvar_true() {
        let expr = Expr::App(Box::new(fvar(3)), Box::new(lit(0)));
        assert!(expr_contains_fvar(&expr, &[FVarId(3)]));
    }
    #[test]
    fn test_expr_contains_fvar_false() {
        let expr = lit(5);
        assert!(!expr_contains_fvar(&expr, &[FVarId(0)]));
    }
    #[test]
    fn test_open_binder_simple() {
        let body = Expr::BVar(0);
        let result = open_binder(&body, FVarId(7));
        assert_eq!(result, fvar(7));
    }
    #[test]
    fn test_open_binder_nested() {
        let inner_body = Expr::BVar(0);
        let inner_lam = Expr::Lam(
            BinderInfo::Default,
            Name::str("_"),
            Box::new(Expr::Const(Name::str("Nat"), vec![])),
            Box::new(inner_body),
        );
        let outer_body = Expr::App(Box::new(inner_lam), Box::new(Expr::BVar(0)));
        let opened = open_binder(&outer_body, FVarId(99));
        match opened {
            Expr::App(f, arg) => {
                assert!(matches!(*f, Expr::Lam(_, _, _, _)));
                assert_eq!(*arg, fvar(99));
            }
            _ => panic!("Expected App"),
        }
    }
    #[test]
    fn test_substitution_compose() {
        let mut s1 = Substitution::new();
        s1.insert(FVarId(0), lit(10));
        let mut s2 = Substitution::new();
        s2.insert(FVarId(1), lit(20));
        let composed = s1.compose(&s2);
        assert_eq!(composed.get(FVarId(0)), Some(&lit(10)));
        assert_eq!(composed.get(FVarId(1)), Some(&lit(20)));
    }
    #[test]
    fn test_substitution_insert_replace() {
        let mut s = Substitution::new();
        s.insert(FVarId(0), lit(1));
        s.insert(FVarId(0), lit(2));
        assert_eq!(s.len(), 1);
        assert_eq!(s.get(FVarId(0)), Some(&lit(2)));
    }
}
#[cfg(test)]
mod tests_padding_infra {
    use super::*;
    #[test]
    fn test_stat_summary() {
        let mut ss = StatSummary::new();
        ss.record(10.0);
        ss.record(20.0);
        ss.record(30.0);
        assert_eq!(ss.count(), 3);
        assert!((ss.mean().expect("mean should succeed") - 20.0).abs() < 1e-9);
        assert_eq!(ss.min().expect("min should succeed") as i64, 10);
        assert_eq!(ss.max().expect("max should succeed") as i64, 30);
    }
    #[test]
    fn test_transform_stat() {
        let mut ts = TransformStat::new();
        ts.record_before(100.0);
        ts.record_after(80.0);
        let ratio = ts.mean_ratio().expect("ratio should be present");
        assert!((ratio - 0.8).abs() < 1e-9);
    }
    #[test]
    fn test_small_map() {
        let mut m: SmallMap<u32, &str> = SmallMap::new();
        m.insert(3, "three");
        m.insert(1, "one");
        m.insert(2, "two");
        assert_eq!(m.get(&2), Some(&"two"));
        assert_eq!(m.len(), 3);
        let keys = m.keys();
        assert_eq!(*keys[0], 1);
        assert_eq!(*keys[2], 3);
    }
    #[test]
    fn test_label_set() {
        let mut ls = LabelSet::new();
        ls.add("foo");
        ls.add("bar");
        ls.add("foo");
        assert_eq!(ls.count(), 2);
        assert!(ls.has("bar"));
        assert!(!ls.has("baz"));
    }
    #[test]
    fn test_config_node() {
        let mut root = ConfigNode::section("root");
        let child = ConfigNode::leaf("key", "value");
        root.add_child(child);
        assert_eq!(root.num_children(), 1);
    }
    #[test]
    fn test_versioned_record() {
        let mut vr = VersionedRecord::new(0u32);
        vr.update(1);
        vr.update(2);
        assert_eq!(*vr.current(), 2);
        assert_eq!(vr.version(), 2);
        assert!(vr.has_history());
        assert_eq!(*vr.at_version(0).expect("value should be present"), 0);
    }
    #[test]
    fn test_simple_dag() {
        let mut dag = SimpleDag::new(4);
        dag.add_edge(0, 1);
        dag.add_edge(1, 2);
        dag.add_edge(2, 3);
        assert!(dag.can_reach(0, 3));
        assert!(!dag.can_reach(3, 0));
        let order = dag.topological_sort().expect("order should be present");
        assert_eq!(order, vec![0, 1, 2, 3]);
    }
    #[test]
    fn test_focus_stack() {
        let mut fs: FocusStack<&str> = FocusStack::new();
        fs.focus("a");
        fs.focus("b");
        assert_eq!(fs.current(), Some(&"b"));
        assert_eq!(fs.depth(), 2);
        fs.blur();
        assert_eq!(fs.current(), Some(&"a"));
    }
}
#[cfg(test)]
mod tests_extra_iterators {
    use super::*;
    #[test]
    fn test_window_iterator() {
        let data = vec![1u32, 2, 3, 4, 5];
        let windows: Vec<_> = WindowIterator::new(&data, 3).collect();
        assert_eq!(windows.len(), 3);
        assert_eq!(windows[0], &[1, 2, 3]);
        assert_eq!(windows[2], &[3, 4, 5]);
    }
    #[test]
    fn test_non_empty_vec() {
        let mut nev = NonEmptyVec::singleton(10u32);
        nev.push(20);
        nev.push(30);
        assert_eq!(nev.len(), 3);
        assert_eq!(*nev.first(), 10);
        assert_eq!(*nev.last(), 30);
    }
}
#[cfg(test)]
mod tests_padding2 {
    use super::*;
    #[test]
    fn test_sliding_sum() {
        let mut ss = SlidingSum::new(3);
        ss.push(1.0);
        ss.push(2.0);
        ss.push(3.0);
        assert!((ss.sum() - 6.0).abs() < 1e-9);
        ss.push(4.0);
        assert!((ss.sum() - 9.0).abs() < 1e-9);
        assert_eq!(ss.count(), 3);
    }
    #[test]
    fn test_path_buf() {
        let mut pb = PathBuf::new();
        pb.push("src");
        pb.push("main");
        assert_eq!(pb.as_str(), "src/main");
        assert_eq!(pb.depth(), 2);
        pb.pop();
        assert_eq!(pb.as_str(), "src");
    }
    #[test]
    fn test_string_pool() {
        let mut pool = StringPool::new();
        let s = pool.take();
        assert!(s.is_empty());
        pool.give("hello".to_string());
        let s2 = pool.take();
        assert!(s2.is_empty());
        assert_eq!(pool.free_count(), 0);
    }
    #[test]
    fn test_transitive_closure() {
        let mut tc = TransitiveClosure::new(4);
        tc.add_edge(0, 1);
        tc.add_edge(1, 2);
        tc.add_edge(2, 3);
        assert!(tc.can_reach(0, 3));
        assert!(!tc.can_reach(3, 0));
        let r = tc.reachable_from(0);
        assert_eq!(r.len(), 4);
    }
    #[test]
    fn test_token_bucket() {
        let mut tb = TokenBucket::new(100, 10);
        assert_eq!(tb.available(), 100);
        assert!(tb.try_consume(50));
        assert_eq!(tb.available(), 50);
        assert!(!tb.try_consume(60));
        assert_eq!(tb.capacity(), 100);
    }
    #[test]
    fn test_rewrite_rule_set() {
        let mut rrs = RewriteRuleSet::new();
        rrs.add(RewriteRule::unconditional(
            "beta",
            "App(Lam(x, b), v)",
            "b[x:=v]",
        ));
        rrs.add(RewriteRule::conditional("comm", "a + b", "b + a"));
        assert_eq!(rrs.len(), 2);
        assert_eq!(rrs.unconditional_rules().len(), 1);
        assert_eq!(rrs.conditional_rules().len(), 1);
        assert!(rrs.get("beta").is_some());
        let disp = rrs
            .get("beta")
            .expect("element at \'beta\' should exist")
            .display();
        assert!(disp.contains("→"));
    }
}
#[cfg(test)]
mod tests_padding3 {
    use super::*;
    #[test]
    fn test_decision_node() {
        let tree = DecisionNode::Branch {
            key: "x".into(),
            val: "1".into(),
            yes_branch: Box::new(DecisionNode::Leaf("yes".into())),
            no_branch: Box::new(DecisionNode::Leaf("no".into())),
        };
        let mut ctx = std::collections::HashMap::new();
        ctx.insert("x".into(), "1".into());
        assert_eq!(tree.evaluate(&ctx), "yes");
        ctx.insert("x".into(), "2".into());
        assert_eq!(tree.evaluate(&ctx), "no");
        assert_eq!(tree.depth(), 1);
    }
    #[test]
    fn test_flat_substitution() {
        let mut sub = FlatSubstitution::new();
        sub.add("foo", "bar");
        sub.add("baz", "qux");
        assert_eq!(sub.apply("foo and baz"), "bar and qux");
        assert_eq!(sub.len(), 2);
    }
    #[test]
    fn test_stopwatch() {
        let mut sw = Stopwatch::start();
        sw.split();
        sw.split();
        assert_eq!(sw.num_splits(), 2);
        assert!(sw.elapsed_ms() >= 0.0);
        for &s in sw.splits() {
            assert!(s >= 0.0);
        }
    }
    #[test]
    fn test_either2() {
        let e: Either2<i32, &str> = Either2::First(42);
        assert!(e.is_first());
        let mapped = e.map_first(|x| x * 2);
        assert_eq!(mapped.first(), Some(84));
        let e2: Either2<i32, &str> = Either2::Second("hello");
        assert!(e2.is_second());
        assert_eq!(e2.second(), Some("hello"));
    }
    #[test]
    fn test_write_once() {
        let wo: WriteOnce<u32> = WriteOnce::new();
        assert!(!wo.is_written());
        assert!(wo.write(42));
        assert!(!wo.write(99));
        assert_eq!(wo.read(), Some(42));
    }
    #[test]
    fn test_sparse_vec() {
        let mut sv: SparseVec<i32> = SparseVec::new(100);
        sv.set(5, 10);
        sv.set(50, 20);
        assert_eq!(*sv.get(5), 10);
        assert_eq!(*sv.get(50), 20);
        assert_eq!(*sv.get(0), 0);
        assert_eq!(sv.nnz(), 2);
        sv.set(5, 0);
        assert_eq!(sv.nnz(), 1);
    }
    #[test]
    fn test_stack_calc() {
        let mut calc = StackCalc::new();
        calc.push(3);
        calc.push(4);
        calc.add();
        assert_eq!(calc.peek(), Some(7));
        calc.push(2);
        calc.mul();
        assert_eq!(calc.peek(), Some(14));
    }
}