Function orientEntry

scripts/fungrim/compile-rules.ts:768–854

(
  ce: ComputeEngine,
  e: Entry,
  sides: { lhs: MathJSON; rhs: MathJSON },
  lhsW: MathJSON,
  rhsW: MathJSON,
  forcedDirection?: 'lhs-rhs' | 'rhs-lhs'
)

 *
 * The machine policy never emits `'transform'` (override-only).
 */
export function orientEntry(
  ce: ComputeEngine,
  e: Entry,
  sides: { lhs: MathJSON; rhs: MathJSON },
  lhsW: MathJSON,
  rhsW: MathJSON,
  forcedDirection?: 'lhs-rhs' | 'rhs-lhs'
): Orientation | { error: 'box-error' | 'unorientable'; detail?: string } {
  // -- cost of the variable-named canonical sides
  let cLhs: number;
  let cRhs: number;
  ce.pushScope();
  try {
    const types = variableTypes(e);
    for (const v of e.variables) {
      try {
        ce.declare(v, types[v] ?? 'complex');
      } catch {
        /* name collides with a CE built-in — tolerate (same as load.ts) */
      }
    }
    const lhs = ce.expr(sides.lhs as never);
    const rhs = ce.expr(sides.rhs as never);
    if (!lhs.isValid)
      return { error: 'box-error', detail: `invalid lhs: ${lhs.toString()}` };
    if (!rhs.isValid)
      return { error: 'box-error', detail: `invalid rhs: ${rhs.toString()}` };
    cLhs = ce.costFunction(lhs);
    cRhs = ce.costFunction(rhs);
  } catch (err) {
    return { error: 'box-error', detail: String((err as Error)?.message).slice(0, 200) };
  } finally {
    ce.popScope();
  }

  const wLhs = collectWildcards(lhsW);
  const wRhs = collectWildcards(rhsW);
  // A direction is viable if the match side is a pattern-viable function
  // expression and the replace side introduces no new wildcards.
  const viableLR = Array.isArray(lhsW) && isSubset(wRhs, wLhs);
  const viableRL = Array.isArray(rhsW) && isSubset(wLhs, wRhs);

  const costs = { lhs: cLhs, rhs: cRhs };
  const LR: Orientation = {
    match: lhsW,
    replace: rhsW,
    direction: 'lhs-rhs',
    purpose: 'expand',
    costs,
  };
  const RL: Orientation = {
    match: rhsW,
    replace: lhsW,
    direction: 'rhs-lhs',
    purpose: 'expand',
    costs,
  };