```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 {
  if (typeof text !== 'string' || !text.trim()) throw new Error("invalid span text");
  
  const parts = text.split(" ").map(part => part.trim());
  let total = 0;

  for (const part of parts) {
    const match = part.match(/^(\d+)\s*([yf]t|in)$/);
    if (!match) throw new Error("invalid span format");
    
    const value = parseInt(match[1], 10);
    const unit = match[2];
    
    if (isNaN(value) || value < 0 || value.toString().startsWith('0')) {
      throw new Error("invalid span value");
    }
    
    if (!INCHES[unit]) throw new Error("unknown unit");
    
    total += value * INCHES[unit];
  }

  return total;
}

export function formatSpan(inches: number): string {
  if (typeof inches !== 'number' || !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);
}
```