Why aren’t there many discussions about co- and contra-variance in Haskell (as opposed to Scala or C#)?

There are two main reasons:

  • Haskell lacks an inherent notion of subtyping, so in general variance is less relevant.
  • Contravariance mostly appears where mutability is involved, so most data types in Haskell would simply be covariant and there’d be little value to distinguishing that explicitly.

However, the concepts do apply–for instance, the lifting operation performed by fmap for Functor instances is actually covariant; the terms co-/contravariance are used in Category Theory to talk about functors. The contravariant package defines a type class for contravariant functors, and if you look at the instance list you’ll see why I said it’s much less common.

There are also places where the idea shows up implicitly, in how manual conversions work–the various numeric type classes define conversions to and from basic types like Integer and Rational, and the module Data.List contains generic versions of some standard functions. If you look at the types of these generic versions you’ll see that Integral constraints (giving toInteger) are used on types in contravariant position, while Num constraints (giving fromInteger) are used for covariant position.

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