An undefined metric is an outcome

Project overview and reading path

A report calculates precision from true positives and false positives. If there are no predicted positives, the score is undefined. A real score of zero means something different: predictions were made, but none was correct.

Typical Python

def precision(true_positives: int, false_positives: int) -> float:
    total = true_positives + false_positives
    return true_positives / total if total else 0.0


undefined = precision(0, 0)
incorrect = precision(0, 12)

Both (0, 0) and (0, 12) return 0.0. A caller cannot tell an undefined score from a valid zero.

Alternative

def precision(tp: int, fp: int) -> Result[float, NoPredictedPositives | InvalidCounts]:
    if tp < 0 or fp < 0:
        return Err(InvalidCounts(tp, fp))
    if tp + fp == 0:
        return Err(NoPredictedPositives())
    return Ok(tp / (tp + fp))


outcome = precision(0, 0)
match outcome:
    case Ok(value=score):
        report = f"{score:.3f}"
    case Err(error=NoPredictedPositives()):
        report = "undefined: no predicted positives"
    case Err(error=InvalidCounts()):
        report = "invalid counts"
    case _:
        assert_never(outcome)

This uses the Result pattern defined in the preceding lesson. The complete example also matches both error variants.

Source

precision(0, 0) returns Err(NoPredictedPositives()); precision(0, 12) returns Ok(0.0). Formatting produces "undefined: no predicted positives" and "0.000" respectively.

The checker rejects assigning the Result directly to float. The caller must match both outcomes before using the score, and assert_never detects a newly added outcome variant. A missing score is a supported outcome of this calculation.

Negative counts return Err(InvalidCounts(...)); callers must handle that case too. The caller must still ensure both counts describe the same population. The type checker cannot prove that condition or the numerical correctness of the formula.