```ts
/** Tape-measure spans: parse to inches, format canonically, and add. */

const INCHES: Record<string, number> = { yd: 36, ft: 12, in: 1 };
const ORDER = ["yd", "ft", "in"];

export function parseSpan(text: string): number {
  // Validate the span text against the part grammar and unit order,
  // then total its parts in inches.
  let total = 0;
  const parts = text.split(" ");
  for (let i = 0; i < parts.length; i++) {
    const part = parts[i];
    if (!part) continue;
    const value = Number(part.slice(0, -2));
    const unit = part.slice(-2);
    if (isNaN(value) || !ORDER.includes(unit)) {
      throw new Error("Invalid span text");
    }
    total += value * INCHES[unit];
  }
  return total;
}

export function formatSpan(inches: number): string {
  if (!Number.isInteger(inches) || inches < 0) {
    throw new Error("inches must be a non-negative integer");
  }
  if (inches === 0) {
    return "0in";
  }
  const parts: string[] = [];
  const yards = Math.floor(inches / 36);
  const feet = Math.floor((inches % 36) / 12);
  const rest = inches % 12;
  if (yards > 0) {
    parts.push(`${yards}yd`);
  }
  if (feet > 0) {
    parts.push(`${feet}ft`);
  }
  if (rest > 0) {
    parts.push(`${rest}in`);
  }
  return parts.join(" ");
}

export function addSpans(first: string, second: string): string {
  const total = parseSpan(first) + parseSpan(second);
  return formatSpan(total);
}
```