```typescript
/** 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 {
  if (typeof text !== "string" || text.trim() === "") {
    throw new Error("invalid span text");
  }

  const parts = text.split(/\s+/).map(part => part.toLowerCase());
  const validUnits = ["yd", "ft", "in"];
  let total = 0;

  for (let i = 0; i < parts.length; i++) {
    if (!validUnits.includes(parts[i])) {
      throw new Error("unknown unit");
    }
    const value = parseInt(parts[i - 1], 10);
    if (isNaN(value) || value <= 0 || parts[i] !== validUnits[parts.length - 1 - i]) {
      throw new Error("invalid span text");
    }
    total += value * INCHES[validUnits[parts.length - 1 - i]];
  }

  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);
}
```