Function Types
If T1 → T2 is a function type then a subtype of it is any function S1 → S2 with the property that T1 <: S1 and S2 <: T2. The argument type of S1 → S2 is said to be contravariant because the subtyping relation is reversed for it, whereas the return type is covariant. (Informally, this reversal occurs because the refined type is "more liberal" in the types it accepts and "more conservative" in the type it returns.)
In languages that allow side effects, like most object-oriented languages, subtyping is generally not sufficient to guarantee that a function can be safely used in the context of another. Liskov's work in this area focused on behavioral subtyping, which besides the type system safety discussed in this article also requires that subtypes preserve all invariants guaranteed by the supertypes in some contract. This definition of subtyping is generally undecidable, so it cannot be verified by a type checker.
The subtyping of mutable references is similar to the treatment of function arguments and return values. Write-only references (or sinks) are contravariant, like function arguments; read-only references (or sources) are covariant, like return values. Mutable references which act as both sources and sinks are invariant.
Read more about this topic: Subtyping
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