# Metamorphic Tests for Domain-Specific Properties

Many tests use oracles, where you know the answers for some inputs and you check those correspondences.

To cover more of the input state space, you can generate random inputs and check some properties for each corresponding output. You don’t have an enumeration of exact answers like with oracles, but you can check things like the output always being greater than zero, etc.

Sometimes, though, it’s hard to assert properties of individual outputs that, across your state space, hold for their inputs – it may be easier to assert output relationships across the space.

Let’s say you have a function $$f_a$$ to compute some property of your input using method $$a$$, and another function $$f_b$$ to compute that same property using method $$b$$. Your domain model tells you that method method $$a$$ systematically underestimates the property value relative to method $$b$$, which is more accurate; you may use method $$a$$ anyway for many inputs because it’s much more computationally efficient than method $$b$$.

You can assert the metamorphic relation $$f_a < f_b$$, and test on that, even when it’s hard to test via oracles or properties – imagine in our example that it’s hard to determine output values a priori, and that it’s also hard to even set upper or lower bounds on individual outputs given their inputs.

While a lot of property-based testing highlights data-(structure-)specific properties, the positing and testing of metamorphic relations can help you highlight domain-specific properties that hold regardless of lower-level data representation. A good overview of metamorphic testing is here, and an article on application to testing bioinformatics programs is here.

This post was adapted from a note sent to my email list on Scientific Data Unification.
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