Hands-On Design Patterns and Best Practices with Julia

Understanding different kinds of variance

There are four different kinds of variance as described in computer science literature. We will first describe them in a formal manner first and then come back to do more hands-on exercises to reinforce our understanding. 

Given that S is a subtype of T, there are four different ways to reason about the relationship between parametric types P{S} and P{T}:

• Covariant: P{S} is a subtype of P{T} (co here means the same direction)
• Contravariant: P{T} is a subtype of P{S} (contra here means the opposite direction)
• Invariant: neither covariant nor contravariant
• Bivariant: both covariant and contravariant

When do we find variance useful? Perhaps not too surprisingly, variance is a key ingredient whenever ...