```python
"""Tape-measure spans: parse to inches, format canonically, and add."""

INCHES = {"yd": 36, "ft": 12, "in": 1}
ORDER = ("yd", "ft", "in")


def parse_span(text: str) -> int:
    # Validate the span text against the part grammar and unit order
    parts = text.split(" ")
    if len(parts) != 3:
        raise ValueError("span must contain exactly three parts")

    # Validate each part
    for part in parts:
        if not part.isdigit():
            raise ValueError("each part must be a plain decimal integer")
        if len(part) > 1 and part[0] == '0':
            raise ValueError("value cannot have a leading zero")

    # Validate units
    units = [part[-2:] for part in parts]
    if len(set(units)) != 3:
        raise ValueError("units must be unique")
    if units != ORDER:
        raise ValueError("units must be in the order yd, ft, in")

    # Calculate total inches
    total = 0
    for i, part in enumerate(parts):
        total += int(part[:-2]) * INCHES[parts[i][-2:]]
    return total


def format_span(inches: int) -> str:
    if isinstance(inches, bool) or not isinstance(inches, int) or inches < 0:
        raise ValueError("inches must be a non-negative integer")
    if inches == 0:
        return "0in"
    parts = []
    yards, rest = divmod(inches, 36)
    feet, rest = divmod(rest, 12)
    if yards:
        parts.append(f"{yards}yd")
    if feet:
        parts.append(f"{feet}ft")
    if rest:
        parts.append(f"{rest}in")
    return " ".join(parts)

def add_spans(first: str, second: str) -> str:
    total = parse_span(first) + parse_span(second)
    return format_span(total)
```