rusty-lisp 0.45.0

// Copyright (c) 2026 Nicholas Vermeulen
// SPDX-License-Identifier: AGPL-3.0-or-later

//! graph_ir.rs — a computation-graph IR (inspired by XLA/TVM) over the same
//! restricted numeric subset `defrust` compiles (numbers, params, + - * /,
//! comparisons, if) plus the Phase-3.1 tensor ops (tensor-add/sub/mul/div,
//! matmul, transpose, tensor-sum). Built with hash-consing, so structurally identical
//! subexpressions collapse to one node as a side effect of construction —
//! that *is* the common-subexpression elimination here, not a separate pass.
//! `optimize` then runs constant folding (including pruning an `if` branch
//! when its condition is constant) and dead-code elimination (mark-and-sweep
//! from the output, which cleans up whatever folding/pruning orphaned).
//!
//! This is an inspectable/executable IR only — no codegen backend yet (see
//! docs/ROADMAP.md 1.2; wiring it into `rust_jit`'s codegen is future work).

use crate::env::Value;
use crate::parser::Expr;
use std::collections::HashMap;
use std::rc::Rc;

#[derive(Clone, Debug, PartialEq, Eq, Hash)]
pub enum Op {
    Const(u64), // f64::to_bits — f64 itself isn't Eq/Hash, so we key on bits
    Param(usize),
    Add, Sub, Mul, Div,
    Lt, Gt, Le, Ge, Eq,
    If, // (cond, then, else)
    // Tensor ops (Phase 3.1). There are no tensor *literals* in the Expr
    // subset — tensors only enter a graph through Params — so constant
    // folding never fires on these; what they get from the pipeline is
    // hash-consing CSE, if-branch pruning, and DCE, all shape-agnostic.
    TAdd, TSub, TMul, TDiv, // elementwise, scalar broadcast (either side) at eval time
    MatMul,                 // rank-2 × rank-2
    Transpose,              // rank-2
    TSum,                   // tensor → scalar
    Relu,                   // elementwise max(0, x)
    // The three ops below have no surface syntax — they exist only in graphs
    // that `backward` generates (reverse-mode autodiff, Phase 3.1):
    Step,   // relu's derivative: 1.0 where x > 0, else 0.0 (elementwise)
    SumTo,  // (grad, like) — reduce grad to like's shape: identity if like is
            //  a tensor of grad's shape, tensor-sum if like is a scalar.
            //  Undoes scalar broadcast during gradient accumulation.
    Expand, // (grad, like) — broadcast scalar grad to like's shape: identity
            //  if like is a scalar, fill like's shape if it's a tensor.
            //  The gradient of TSum, and the dual of SumTo.
}

#[derive(Clone, Debug)]
pub struct Node {
    pub op:   Op,
    pub args: Vec<usize>, // indices into Graph::nodes; always < this node's own index
}

#[derive(Clone, Debug, Default)]
pub struct Graph {
    pub nodes:  Vec<Node>,
    pub output: usize,
}

struct Interner {
    nodes: Vec<Node>,
    memo:  HashMap<(Op, Vec<usize>), usize>,
}

impl Interner {
    fn new() -> Self { Interner { nodes: Vec::new(), memo: HashMap::new() } }

    /// Re-open an existing graph for appending (used by `backward`, which
    /// grows the forward graph with gradient nodes). Rebuilding the memo
    /// keeps hash-consing active across the old/new boundary, so a gradient
    /// expression that already exists in the forward graph is reused.
    fn from_graph(g: &Graph) -> Self {
        let mut memo = HashMap::new();
        for (i, n) in g.nodes.iter().enumerate() {
            memo.entry((n.op.clone(), n.args.clone())).or_insert(i);
        }
        Interner { nodes: g.nodes.clone(), memo }
    }

    fn intern(&mut self, op: Op, args: Vec<usize>) -> usize {
        let key = (op.clone(), args.clone());
        if let Some(&i) = self.memo.get(&key) { return i; }
        let i = self.nodes.len();
        self.nodes.push(Node { op, args });
        self.memo.insert(key, i);
        i
    }

    fn const_val(&self, idx: usize) -> Option<f64> {
        match &self.nodes[idx].op {
            Op::Const(bits) => Some(f64::from_bits(*bits)),
            _ => None,
        }
    }

    fn konst(&mut self, v: f64) -> usize { self.intern(Op::Const(v.to_bits()), vec![]) }
}

// ── Build: restricted Expr subset → Graph ────────────────────────────────

fn build_num(ib: &mut Interner, params: &[String], expr: &Expr) -> Result<usize, String> {
    match expr {
        Expr::Number(n) => Ok(ib.konst(*n)),
        Expr::Symbol(s) => {
            if let Some(i) = params.iter().position(|p| p == s) {
                Ok(ib.intern(Op::Param(i), vec![]))
            } else {
                Err(format!(
                    "graph-ir: unsupported reference to '{}' — only params, numbers, + - * /, \
                     if, and the tensor ops are supported", s
                ))
            }
        }
        Expr::List(items) if !items.is_empty() => {
            if let Expr::Symbol(head) = &items[0] {
                match head.as_str() {
                    "+" | "-" | "*" | "/" if items.len() >= 2 => {
                        let mut arg_ids = items[1..].iter()
                            .map(|e| build_num(ib, params, e))
                            .collect::<Result<Vec<_>, _>>()?;
                        let op = match head.as_str() { "+" => Op::Add, "-" => Op::Sub, "*" => Op::Mul, "/" => Op::Div, _ => unreachable!() };
                        if head == "-" && arg_ids.len() == 1 {
                            let zero = ib.konst(0.0);
                            return Ok(ib.intern(Op::Sub, vec![zero, arg_ids[0]]));
                        }
                        let mut acc = arg_ids.remove(0);
                        for a in arg_ids { acc = ib.intern(op.clone(), vec![acc, a]); }
                        Ok(acc)
                    }
                    "if" if items.len() == 4 => {
                        let c = build_bool(ib, params, &items[1])?;
                        let t = build_num(ib, params, &items[2])?;
                        let e = build_num(ib, params, &items[3])?;
                        Ok(ib.intern(Op::If, vec![c, t, e]))
                    }
                    "tensor-add" | "tensor-sub" | "tensor-mul" | "tensor-div"
                        if items.len() == 3 =>
                    {
                        let a = build_num(ib, params, &items[1])?;
                        let b = build_num(ib, params, &items[2])?;
                        let op = match head.as_str() {
                            "tensor-add" => Op::TAdd, "tensor-sub" => Op::TSub,
                            "tensor-mul" => Op::TMul, _ => Op::TDiv,
                        };
                        Ok(ib.intern(op, vec![a, b]))
                    }
                    "matmul" if items.len() == 3 => {
                        let a = build_num(ib, params, &items[1])?;
                        let b = build_num(ib, params, &items[2])?;
                        Ok(ib.intern(Op::MatMul, vec![a, b]))
                    }
                    "transpose" if items.len() == 2 => {
                        let a = build_num(ib, params, &items[1])?;
                        Ok(ib.intern(Op::Transpose, vec![a]))
                    }
                    "relu" if items.len() == 2 => {
                        let a = build_num(ib, params, &items[1])?;
                        Ok(ib.intern(Op::Relu, vec![a]))
                    }
                    "tensor-sum" if items.len() == 2 => {
                        let a = build_num(ib, params, &items[1])?;
                        Ok(ib.intern(Op::TSum, vec![a]))
                    }
                    other => Err(format!("graph-ir: unsupported operator '{}'", other)),
                }
            } else {
                Err("graph-ir: unsupported expression".into())
            }
        }
        _ => Err("graph-ir: only numbers, params, + - * /, if, and the tensor ops are supported".into()),
    }
}

fn build_bool(ib: &mut Interner, params: &[String], expr: &Expr) -> Result<usize, String> {
    if let Expr::List(items) = expr {
        if let Some(Expr::Symbol(head)) = items.first() {
            let op = match head.as_str() {
                "<" => Some(Op::Lt), ">" => Some(Op::Gt), "<=" => Some(Op::Le),
                ">=" => Some(Op::Ge), "=" => Some(Op::Eq), _ => None,
            };
            if let (Some(op), 3) = (op, items.len()) {
                let a = build_num(ib, params, &items[1])?;
                let b = build_num(ib, params, &items[2])?;
                return Ok(ib.intern(op, vec![a, b]));
            }
        }
    }
    Err("graph-ir: an `if` condition must be a comparison (< > <= >= =)".into())
}

pub fn build(params: &[String], body: &Expr) -> Result<Graph, String> {
    let mut ib = Interner::new();
    let output = build_num(&mut ib, params, body)?;
    Ok(Graph { nodes: ib.nodes, output })
}

// ── Optimize: constant fold (+ if-branch pruning) then dead-code eliminate ─

fn fold_binop(ib: &mut Interner, op: Op, a: usize, b: usize, f: impl Fn(f64, f64) -> f64) -> usize {
    match (ib.const_val(a), ib.const_val(b)) {
        (Some(x), Some(y)) => ib.konst(f(x, y)),
        _ => ib.intern(op, vec![a, b]),
    }
}

fn fold_cmp(ib: &mut Interner, op: Op, a: usize, b: usize, f: impl Fn(f64, f64) -> bool) -> usize {
    match (ib.const_val(a), ib.const_val(b)) {
        (Some(x), Some(y)) => ib.konst(if f(x, y) { 1.0 } else { 0.0 }),
        _ => ib.intern(op, vec![a, b]),
    }
}

fn fold_nodes(graph: &Graph) -> (Vec<Node>, Vec<usize>) {
    let mut ib = Interner::new();
    let mut remap = vec![0usize; graph.nodes.len()];
    for (i, node) in graph.nodes.iter().enumerate() {
        let args: Vec<usize> = node.args.iter().map(|&a| remap[a]).collect();
        let new_idx = match (&node.op, args.as_slice()) {
            (Op::Add, [a, b]) => fold_binop(&mut ib, Op::Add, *a, *b, |x, y| x + y),
            (Op::Sub, [a, b]) => fold_binop(&mut ib, Op::Sub, *a, *b, |x, y| x - y),
            (Op::Mul, [a, b]) => fold_binop(&mut ib, Op::Mul, *a, *b, |x, y| x * y),
            (Op::Div, [a, b]) => fold_binop(&mut ib, Op::Div, *a, *b, |x, y| x / y),
            (Op::Lt, [a, b]) => fold_cmp(&mut ib, Op::Lt, *a, *b, |x, y| x < y),
            (Op::Gt, [a, b]) => fold_cmp(&mut ib, Op::Gt, *a, *b, |x, y| x > y),
            (Op::Le, [a, b]) => fold_cmp(&mut ib, Op::Le, *a, *b, |x, y| x <= y),
            (Op::Ge, [a, b]) => fold_cmp(&mut ib, Op::Ge, *a, *b, |x, y| x >= y),
            (Op::Eq, [a, b]) => fold_cmp(&mut ib, Op::Eq, *a, *b, |x, y| x == y),
            // If the condition is constant, prune to whichever branch is
            // live — no re-interning needed, we just reuse its existing id.
            // Anything the untaken branch alone referenced becomes
            // unreachable from the output and is swept by `dce` below.
            (Op::If, [c, t, e]) => match ib.const_val(*c) {
                Some(cv) => if cv != 0.0 { *t } else { *e },
                None => ib.intern(Op::If, args.clone()),
            },
            (other, _) => ib.intern(other.clone(), args.clone()),
        };
        remap[i] = new_idx;
    }
    (ib.nodes, remap)
}

fn dce_nodes(nodes: &[Node], outputs: &[usize]) -> (Vec<Node>, Vec<usize>) {
    let mut reachable = vec![false; nodes.len()];
    let mut stack: Vec<usize> = outputs.to_vec();
    while let Some(i) = stack.pop() {
        if reachable[i] { continue; }
        reachable[i] = true;
        for &a in &nodes[i].args { stack.push(a); }
    }
    let mut new_index = vec![usize::MAX; nodes.len()];
    let mut new_nodes = Vec::new();
    for (i, node) in nodes.iter().enumerate() {
        if reachable[i] {
            let args = node.args.iter().map(|&a| new_index[a]).collect();
            new_index[i] = new_nodes.len();
            new_nodes.push(Node { op: node.op.clone(), args });
        }
    }
    let new_outputs = outputs.iter().map(|&o| new_index[o]).collect();
    (new_nodes, new_outputs)
}

pub fn optimize(graph: &Graph) -> Graph {
    let (g, outs) = optimize_outputs(graph, &[graph.output]);
    Graph { nodes: g.nodes, output: outs[0] }
}

/// Fold + DCE while keeping several output nodes live — used by `graph-grad`,
/// where the outputs are the loss plus one gradient per parameter.
pub fn optimize_outputs(graph: &Graph, outputs: &[usize]) -> (Graph, Vec<usize>) {
    let (nodes, remap) = fold_nodes(graph);
    let folded_outs: Vec<usize> = outputs.iter().map(|&o| remap[o]).collect();
    let (nodes, outs) = dce_nodes(&nodes, &folded_outs);
    (Graph { nodes, output: outs[0] }, outs)
}

// ── Reverse-mode autodiff (backpropagation) over the DAG ────────────────
//
// One reverse sweep computes the gradient of the (scalar) output with
// respect to every Param at once — the standard reverse-mode trade, and why
// this isn't done by extending the symbolic `grad` builtin (which produces
// one derivative expression per parameter and knows no matrix calculus).
// Gradient rules emit *more graph nodes* into the same interner, so shared
// subexpressions between forward and backward pass are CSE'd for free, and
// the gradient graph goes through the same fold/DCE pipeline afterwards.

fn accum(ib: &mut Interner, adj: &mut [Option<usize>], target: usize, contrib: usize) {
    adj[target] = Some(match adj[target] {
        // TAdd accumulates both scalar and tensor adjoints (it degrades to
        // plain addition on two numbers).
        Some(prev) => ib.intern(Op::TAdd, vec![prev, contrib]),
        None => contrib,
    });
}

/// Extend `graph` with gradient nodes and return the grown graph plus the
/// gradient node for each of the `nparams` parameters, in order. The
/// graph's output must evaluate to a scalar (checked at eval time — shapes
/// aren't known statically). An unused parameter gets a zero gradient of
/// its own shape (via `Expand(0, param)`).
pub fn backward(graph: &Graph, nparams: usize) -> Result<(Graph, Vec<usize>), String> {
    let mut ib = Interner::from_graph(graph);
    let n = graph.nodes.len();
    let mut adj: Vec<Option<usize>> = vec![None; n];
    let seed = ib.konst(1.0);
    adj[graph.output] = Some(seed);

    // Nodes are topologically ordered (args always precede their node), so a
    // reverse index walk visits every node after all of its uses. Nodes
    // appended by the rules below land at indices >= n and are never
    // revisited — they belong to the gradient computation itself.
    for i in (0..n).rev() {
        let g = match adj[i] { Some(g) => g, None => continue };
        let node = ib.nodes[i].clone();
        match (&node.op, node.args.as_slice()) {
            (Op::Const(_), _) | (Op::Param(_), _) => {} // leaves
            (Op::Add, &[a, b]) => {
                accum(&mut ib, &mut adj, a, g);
                accum(&mut ib, &mut adj, b, g);
            }
            (Op::Sub, &[a, b]) => {
                accum(&mut ib, &mut adj, a, g);
                let zero = ib.konst(0.0);
                let neg = ib.intern(Op::Sub, vec![zero, g]);
                accum(&mut ib, &mut adj, b, neg);
            }
            (Op::Mul, &[a, b]) => {
                let da = ib.intern(Op::Mul, vec![g, b]);
                let db = ib.intern(Op::Mul, vec![g, a]);
                accum(&mut ib, &mut adj, a, da);
                accum(&mut ib, &mut adj, b, db);
            }
            (Op::Div, &[a, b]) => {
                // d(a/b)/da = 1/b ; d(a/b)/db = -a/b²
                let da = ib.intern(Op::Div, vec![g, b]);
                accum(&mut ib, &mut adj, a, da);
                let ga = ib.intern(Op::Mul, vec![g, a]);
                let bb = ib.intern(Op::Mul, vec![b, b]);
                let q  = ib.intern(Op::Div, vec![ga, bb]);
                let zero = ib.konst(0.0);
                let db = ib.intern(Op::Sub, vec![zero, q]);
                accum(&mut ib, &mut adj, b, db);
            }
            (Op::TAdd, &[a, b]) => {
                let da = ib.intern(Op::SumTo, vec![g, a]);
                let db = ib.intern(Op::SumTo, vec![g, b]);
                accum(&mut ib, &mut adj, a, da);
                accum(&mut ib, &mut adj, b, db);
            }
            (Op::TSub, &[a, b]) => {
                let da = ib.intern(Op::SumTo, vec![g, a]);
                accum(&mut ib, &mut adj, a, da);
                let neg1 = ib.konst(-1.0);
                let ng = ib.intern(Op::TMul, vec![g, neg1]);
                let db = ib.intern(Op::SumTo, vec![ng, b]);
                accum(&mut ib, &mut adj, b, db);
            }
            (Op::TMul, &[a, b]) => {
                let gb = ib.intern(Op::TMul, vec![g, b]);
                let da = ib.intern(Op::SumTo, vec![gb, a]);
                accum(&mut ib, &mut adj, a, da);
                let ga = ib.intern(Op::TMul, vec![g, a]);
                let db = ib.intern(Op::SumTo, vec![ga, b]);
                accum(&mut ib, &mut adj, b, db);
            }
            (Op::TDiv, &[a, b]) => {
                let gb = ib.intern(Op::TDiv, vec![g, b]);
                let da = ib.intern(Op::SumTo, vec![gb, a]);
                accum(&mut ib, &mut adj, a, da);
                let ga = ib.intern(Op::TMul, vec![g, a]);
                let bb = ib.intern(Op::TMul, vec![b, b]);
                let q  = ib.intern(Op::TDiv, vec![ga, bb]);
                let neg1 = ib.konst(-1.0);
                let nq = ib.intern(Op::TMul, vec![q, neg1]);
                let db = ib.intern(Op::SumTo, vec![nq, b]);
                accum(&mut ib, &mut adj, b, db);
            }
            (Op::MatMul, &[a, b]) => {
                // dL/da = g · bᵀ ; dL/db = aᵀ · g
                let bt = ib.intern(Op::Transpose, vec![b]);
                let da = ib.intern(Op::MatMul, vec![g, bt]);
                accum(&mut ib, &mut adj, a, da);
                let at = ib.intern(Op::Transpose, vec![a]);
                let db = ib.intern(Op::MatMul, vec![at, g]);
                accum(&mut ib, &mut adj, b, db);
            }
            (Op::Transpose, &[a]) => {
                let da = ib.intern(Op::Transpose, vec![g]);
                accum(&mut ib, &mut adj, a, da);
            }
            (Op::TSum, &[a]) => {
                let da = ib.intern(Op::Expand, vec![g, a]);
                accum(&mut ib, &mut adj, a, da);
            }
            (Op::Relu, &[a]) => {
                let mask = ib.intern(Op::Step, vec![a]);
                let da = ib.intern(Op::TMul, vec![g, mask]);
                accum(&mut ib, &mut adj, a, da);
            }
            (op, _) => {
                return Err(format!(
                    "graph-grad: cannot differentiate through '{}' — comparisons and \
                     data-dependent `if` are not differentiable (a constant-condition if \
                     is pruned before this pass and is fine)", op_name(op)
                ));
            }
        }
    }

    let grads = (0..nparams).map(|p| {
        let pn = ib.intern(Op::Param(p), vec![]);
        match adj.get(pn).copied().flatten() {
            Some(g) => g,
            None => {
                // Parameter unused by the loss: zero gradient, in the
                // parameter's own shape.
                let zero = ib.konst(0.0);
                ib.intern(Op::Expand, vec![zero, pn])
            }
        }
    }).collect();

    Ok((Graph { nodes: ib.nodes, output: graph.output }, grads))
}

// ── Execute (direct IR interpreter — no codegen backend yet) ────────────

/// Runtime value flowing through the graph: scalar or tensor. Tensors only
/// enter via Params (no tensor literals in the Expr subset), and the tensor
/// buffer is the same Rc'd flat row-major layout as `Value::Tensor`.
#[derive(Clone, Debug)]
pub enum GVal {
    Num(f64),
    Tensor { data: Rc<Vec<f64>>, shape: Vec<usize> },
}

fn num(v: &GVal, op: &str) -> Result<f64, String> {
    match v {
        GVal::Num(n) => Ok(*n),
        GVal::Tensor { shape, .. } => Err(format!(
            "graph-eval: {} expects a number, got a {} tensor — use the tensor-* ops",
            op, shape.iter().map(|d| d.to_string()).collect::<Vec<_>>().join("x")
        )),
    }
}

// Same semantics as interp.rs's tensor_binop2: tensor⊕tensor needs matching
// shapes, tensor⊕scalar broadcasts on either side, scalar⊕scalar is plain
// arithmetic (so tensor-add etc. degrade gracefully to numbers).
fn t_binop(a: &GVal, b: &GVal, name: &str, f: fn(f64, f64) -> f64) -> Result<GVal, String> {
    match (a, b) {
        (GVal::Tensor { data: xd, shape: xs }, GVal::Tensor { data: yd, shape: ys }) => {
            if xs != ys {
                return Err(format!("graph-eval: {}: shape mismatch {:?} vs {:?}", name, xs, ys));
            }
            let data: Vec<f64> = xd.iter().zip(yd.iter()).map(|(x, y)| f(*x, *y)).collect();
            Ok(GVal::Tensor { data: Rc::new(data), shape: xs.clone() })
        }
        (GVal::Tensor { data, shape }, GVal::Num(s)) =>
            Ok(GVal::Tensor { data: Rc::new(data.iter().map(|x| f(*x, *s)).collect()), shape: shape.clone() }),
        (GVal::Num(s), GVal::Tensor { data, shape }) =>
            Ok(GVal::Tensor { data: Rc::new(data.iter().map(|x| f(*s, *x)).collect()), shape: shape.clone() }),
        (GVal::Num(x), GVal::Num(y)) => Ok(GVal::Num(f(*x, *y))),
    }
}

fn t_matmul(a: &GVal, b: &GVal) -> Result<GVal, String> {
    match (a, b) {
        (GVal::Tensor { data: xd, shape: xs }, GVal::Tensor { data: yd, shape: ys }) => {
            if xs.len() != 2 || ys.len() != 2 {
                return Err("graph-eval: matmul: both arguments must be rank-2 tensors".into());
            }
            let (n, k) = (xs[0], xs[1]);
            let (k2, m) = (ys[0], ys[1]);
            if k != k2 {
                return Err(format!("graph-eval: matmul: inner dimensions differ ({} vs {})", k, k2));
            }
            let mut data = vec![0.0; n * m];
            for i in 0..n {
                let x_row = &xd[i * k..(i + 1) * k];
                let o_row = &mut data[i * m..(i + 1) * m];
                for p in 0..k {
                    let x = x_row[p];
                    let y_row = &yd[p * m..(p + 1) * m];
                    for j in 0..m {
                        o_row[j] += x * y_row[j];
                    }
                }
            }
            Ok(GVal::Tensor { data: Rc::new(data), shape: vec![n, m] })
        }
        _ => Err("graph-eval: matmul: both arguments must be tensors".into()),
    }
}

fn t_transpose(a: &GVal) -> Result<GVal, String> {
    match a {
        GVal::Tensor { data, shape } if shape.len() == 2 => {
            let (n, m) = (shape[0], shape[1]);
            let mut out = vec![0.0; n * m];
            for i in 0..n {
                for j in 0..m {
                    out[j * n + i] = data[i * m + j];
                }
            }
            Ok(GVal::Tensor { data: Rc::new(out), shape: vec![m, n] })
        }
        _ => Err("graph-eval: transpose: argument must be a rank-2 tensor".into()),
    }
}

pub fn eval_graph(graph: &Graph, inputs: &[GVal]) -> Result<GVal, String> {
    Ok(eval_nodes(graph, inputs)?[graph.output].clone())
}

/// Evaluate once, read several nodes out — `graph-grad` uses this to get the
/// loss and every gradient from a single pass over the (shared) graph.
pub fn eval_graph_outputs(graph: &Graph, inputs: &[GVal], outputs: &[usize]) -> Result<Vec<GVal>, String> {
    let vals = eval_nodes(graph, inputs)?;
    Ok(outputs.iter().map(|&o| vals[o].clone()).collect())
}

fn eval_nodes(graph: &Graph, inputs: &[GVal]) -> Result<Vec<GVal>, String> {
    let mut vals: Vec<GVal> = Vec::with_capacity(graph.nodes.len());
    for node in &graph.nodes {
        let a = node.args.first().map(|&x| &vals[x]);
        let b = node.args.get(1).map(|&x| &vals[x]);
        let v = match &node.op {
            Op::Const(bits) => GVal::Num(f64::from_bits(*bits)),
            Op::Param(p)    => inputs[*p].clone(),
            Op::Add => GVal::Num(num(a.unwrap(), "+")? + num(b.unwrap(), "+")?),
            Op::Sub => GVal::Num(num(a.unwrap(), "-")? - num(b.unwrap(), "-")?),
            Op::Mul => GVal::Num(num(a.unwrap(), "*")? * num(b.unwrap(), "*")?),
            Op::Div => GVal::Num(num(a.unwrap(), "/")? / num(b.unwrap(), "/")?),
            Op::Lt  => GVal::Num(if num(a.unwrap(), "<")?  < num(b.unwrap(), "<")?  { 1.0 } else { 0.0 }),
            Op::Gt  => GVal::Num(if num(a.unwrap(), ">")?  > num(b.unwrap(), ">")?  { 1.0 } else { 0.0 }),
            Op::Le  => GVal::Num(if num(a.unwrap(), "<=")? <= num(b.unwrap(), "<=")? { 1.0 } else { 0.0 }),
            Op::Ge  => GVal::Num(if num(a.unwrap(), ">=")? >= num(b.unwrap(), ">=")? { 1.0 } else { 0.0 }),
            Op::Eq  => GVal::Num(if num(a.unwrap(), "=")? == num(b.unwrap(), "=")?  { 1.0 } else { 0.0 }),
            Op::If  => {
                let c = num(&vals[node.args[0]], "if")?;
                if c != 0.0 { vals[node.args[1]].clone() } else { vals[node.args[2]].clone() }
            }
            Op::TAdd => t_binop(a.unwrap(), b.unwrap(), "tensor-add", |x, y| x + y)?,
            Op::TSub => t_binop(a.unwrap(), b.unwrap(), "tensor-sub", |x, y| x - y)?,
            Op::TMul => t_binop(a.unwrap(), b.unwrap(), "tensor-mul", |x, y| x * y)?,
            Op::TDiv => t_binop(a.unwrap(), b.unwrap(), "tensor-div", |x, y| x / y)?,
            Op::MatMul    => t_matmul(a.unwrap(), b.unwrap())?,
            Op::Transpose => t_transpose(a.unwrap())?,
            Op::TSum => match a.unwrap() {
                GVal::Tensor { data, .. } => GVal::Num(data.iter().sum()),
                GVal::Num(n) => GVal::Num(*n),
            },
            Op::Relu => match a.unwrap() {
                GVal::Num(n) => GVal::Num(n.max(0.0)),
                GVal::Tensor { data, shape } => GVal::Tensor {
                    data: Rc::new(data.iter().map(|x| x.max(0.0)).collect()),
                    shape: shape.clone(),
                },
            },
            Op::Step => match a.unwrap() {
                GVal::Num(n) => GVal::Num(if *n > 0.0 { 1.0 } else { 0.0 }),
                GVal::Tensor { data, shape } => GVal::Tensor {
                    data: Rc::new(data.iter().map(|x| if *x > 0.0 { 1.0 } else { 0.0 }).collect()),
                    shape: shape.clone(),
                },
            },
            Op::SumTo => match (a.unwrap(), b.unwrap()) {
                (g, GVal::Num(_)) => match g {
                    GVal::Num(n) => GVal::Num(*n),
                    GVal::Tensor { data, .. } => GVal::Num(data.iter().sum()),
                },
                (GVal::Tensor { data, shape }, GVal::Tensor { shape: like, .. }) => {
                    if shape != like {
                        return Err(format!("graph-grad: internal SumTo shape mismatch {:?} vs {:?}", shape, like));
                    }
                    GVal::Tensor { data: data.clone(), shape: shape.clone() }
                }
                (GVal::Num(_), GVal::Tensor { .. }) =>
                    // The usual way here: the loss evaluated to a tensor, so
                    // the scalar seed gradient meets tensor operands.
                    return Err("graph-grad: the loss must evaluate to a scalar (use tensor-sum or a mean)".into()),
            },
            Op::Expand => match (a.unwrap(), b.unwrap()) {
                (GVal::Num(n), GVal::Num(_)) => GVal::Num(*n),
                (GVal::Num(n), GVal::Tensor { shape, data }) =>
                    GVal::Tensor { data: Rc::new(vec![*n; data.len()]), shape: shape.clone() },
                (GVal::Tensor { .. }, _) =>
                    return Err("graph-grad: internal Expand — expected a scalar gradient".into()),
            },
        };
        vals.push(v);
    }
    Ok(vals)
}

// ── Static shape inference (Phase 3.3 tensor kernel fusion) ──────────────
//
// `None` = scalar, `Some(shape)` = tensor. Mirrors `eval_nodes`' runtime
// rules exactly (including scalar broadcast on the T-ops and the
// loss-must-be-scalar diagnosis on SumTo), but over shapes only — this is
// what lets `graph-compile-grad` specialize a kernel with every buffer
// size, loop bound, and matmul dimension a compile-time constant.

pub type SShape = Option<Vec<usize>>;

pub fn infer_shapes(graph: &Graph, inputs: &[SShape]) -> Result<Vec<SShape>, String> {
    let mut shapes: Vec<SShape> = Vec::with_capacity(graph.nodes.len());
    for node in &graph.nodes {
        let a = node.args.first().map(|&x| shapes[x].clone());
        let b = node.args.get(1).map(|&x| shapes[x].clone());
        let s = match &node.op {
            Op::Const(_) => None,
            Op::Param(p) => inputs.get(*p)
                .ok_or_else(|| format!("graph-compile-grad: missing shape for param {}", p))?
                .clone(),
            Op::Add | Op::Sub | Op::Mul | Op::Div
            | Op::Lt | Op::Gt | Op::Le | Op::Ge | Op::Eq => {
                if a.clone().flatten().is_some() || b.clone().flatten().is_some() {
                    return Err("graph-compile-grad: scalar op applied to a tensor (use tensor-add etc.)".into());
                }
                None
            }
            Op::If => {
                let t = shapes[node.args[1]].clone();
                let e = shapes[node.args[2]].clone();
                if shapes[node.args[0]].is_some() {
                    return Err("graph-compile-grad: `if` condition must be a scalar".into());
                }
                if t != e {
                    return Err("graph-compile-grad: `if` branches must have the same shape".into());
                }
                t
            }
            Op::TAdd | Op::TSub | Op::TMul | Op::TDiv => {
                match (a.clone().unwrap(), b.clone().unwrap()) {
                    (Some(x), Some(y)) if x == y => Some(x),
                    (Some(x), Some(y)) => return Err(format!(
                        "graph-compile-grad: elementwise op on mismatched shapes {:?} vs {:?}", x, y)),
                    (Some(x), None) | (None, Some(x)) => Some(x), // scalar broadcast
                    (None, None) => None,
                }
            }
            Op::MatMul => match (a.clone().unwrap(), b.clone().unwrap()) {
                (Some(x), Some(y)) if x.len() == 2 && y.len() == 2 && x[1] == y[0] =>
                    Some(vec![x[0], y[1]]),
                (x, y) => return Err(format!(
                    "graph-compile-grad: matmul needs rank-2 tensors with matching inner dim, got {:?} × {:?}", x, y)),
            },
            Op::Transpose => match a.clone().unwrap() {
                Some(x) if x.len() == 2 => Some(vec![x[1], x[0]]),
                x => return Err(format!("graph-compile-grad: transpose needs a rank-2 tensor, got {:?}", x)),
            },
            Op::TSum => None,
            Op::Relu | Op::Step => a.clone().unwrap(),
            Op::SumTo => match (a.clone().unwrap(), b.clone().unwrap()) {
                (_, None) => None,
                (Some(x), Some(like)) if x == like => Some(x),
                (Some(x), Some(like)) => return Err(format!(
                    "graph-grad: internal SumTo shape mismatch {:?} vs {:?}", x, like)),
                (None, Some(_)) =>
                    return Err("graph-grad: the loss must evaluate to a scalar (use tensor-sum or a mean)".into()),
            },
            Op::Expand => match (a.clone().unwrap(), b.clone().unwrap()) {
                (None, like) => like,
                (Some(_), _) =>
                    return Err("graph-grad: internal Expand — expected a scalar gradient".into()),
            },
        };
        shapes.push(s);
    }
    Ok(shapes)
}

// ── Inspect: Graph → Lisp data ────────────────────────────────────────────

pub fn op_name(op: &Op) -> &'static str {
    match op {
        Op::Const(_) => "const", Op::Param(_) => "param",
        Op::Add => "add", Op::Sub => "sub", Op::Mul => "mul", Op::Div => "div",
        Op::Lt => "lt", Op::Gt => "gt", Op::Le => "le", Op::Ge => "ge", Op::Eq => "eq",
        Op::If => "if",
        Op::TAdd => "tensor-add", Op::TSub => "tensor-sub",
        Op::TMul => "tensor-mul", Op::TDiv => "tensor-div",
        Op::MatMul => "matmul", Op::Transpose => "transpose", Op::TSum => "tensor-sum",
        Op::Relu => "relu", Op::Step => "step", Op::SumTo => "sum-to", Op::Expand => "expand",
    }
}

pub fn to_value(graph: &Graph) -> Value {
    let nodes: Vec<Value> = graph.nodes.iter().enumerate().map(|(i, node)| {
        let mut row = vec![Value::Number(i as f64), Value::Symbol(op_name(&node.op).to_string())];
        match &node.op {
            Op::Const(bits) => row.push(Value::Number(f64::from_bits(*bits))),
            Op::Param(p)    => row.push(Value::Number(*p as f64)),
            _ => row.extend(node.args.iter().map(|&a| Value::Number(a as f64))),
        }
        crate::env::list(row)
    }).collect();
    crate::env::list(vec![crate::env::list(nodes), Value::Number(graph.output as f64)])
}