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A differential test runs implementations intended to realize the same contract on matched inputs and compares their observable results. Disagreement reveals an inconsistency without requiring a precomputed answer. Hypothesis explicitly supports comparisons using either a trusted reference or several implementations none of which is fully trusted.^[ref]

For example, compare a new sorting algorithm with a simple reference on lists containing duplicates, negative values and empty input. Compare results under the specified ordering contract; unspecified differences are not failures. Agreement alone cannot exclude a shared software bug. Floating-point arithmetic may require a justified numerical tolerance, and comparison of failures as well as successful outputs requires an explicit error contract.

A test oracle determines whether an observed test result is acceptable. It can be an explicitly expected output, a mathematical property, a trusted reference implementation or another justified source of comparison. Generating many inputs without an oracle does not by itself establish whether the results are correct.

For a sorting routine, an oracle can check both sortedness and preservation of the input multiset. Returning an empty sequence passes a sortedness check but fails preservation for a nonempty input. A differential test instead compares implementations; a disagreement exposes a problem without necessarily identifying which implementation is wrong. Hypothesis documents both reference-oracle comparisons and differential comparisons in its equivalence-test generator.^[ref]