WebJan 17, 2024 · contravariant (not comparable) (category theory, of a functor) which reverses composition (object-oriented programming) Using or relating to contravariance. …
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By making type constructors covariant or contravariant instead of invariant, more programs will be accepted as well-typed. On the other hand, programmers often find contravariance unintuitive, and accurately tracking variance to avoid runtime type errors can lead to complex typing rules. See more Many programming language type systems support subtyping. For instance, if the type Cat is a subtype of Animal, then an expression of type Cat should be substitutable wherever an expression of type Animal is used. See more Read-only data types (sources) can be covariant; write-only data types (sinks) can be contravariant. Mutable data types which act as both sources and sinks should be invariant. To illustrate this general phenomenon, consider the array type. … See more When a subclass overrides a method in a superclass, the compiler must check that the overriding method has the right type. While some … See more These terms come from the notion of covariant and contravariant functors in category theory. Consider the category $${\displaystyle C}$$ whose objects are types and whose … See more Within the type system of a programming language, a typing rule for a type constructor is: • covariant if it preserves the ordering of types (≤), which orders types from more specific to more generic: If A ≤ B, then I WebType Theory Subtypes Covariant, Contravariant, and Invariant Gradual Typing and Consistent Types Playing With Python Types, Part 2 Type Variables Duck Types and Protocols The Optional Type Example: The … fast team west sussex
Subtyping - Wikipedia
If T1 → T2 is a function type, then a subtype of it is any function type S1 → S2 with the property that T1 <: S1 and S2 <: T2. This can be summarised using the following typing rule: The parameter 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 return… WebOct 15, 2014 · With declaration-site variance, you state in the interface definition which of the type variables are co- or contravariant (by default they are invariant). For a sound … WebIn the function type definition, the function arguments are contravariant, since we've reversed the subtype relation between T1 and S1. The function results are covariant … fast team u of t