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In Rust, "trait coherence" (or simply "coherence") is the property that there is at most one implementation of a trait for any given type.
Coherence is not a Rust invention. At the very least, Rust has gotten much of its notion of traits and implementations from Haskell's type classes and instances. Haskell guarantees coherent type classes instances, but it does not guarantee "global uniqueness of instances", which I think is what is described above.
See: http://blog.ezyang.com/2014/07/type-classes-confluence-coherence-global-uniqueness/
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