instantiations

Instantiations refer to the process of creating a concrete realization from an abstract specification. The term is used across fields such as programming, logic, and database theory to describe producing a specific artifact from a general template, schema, or theory. An instantiation replaces abstract parameters with concrete values, types, or terms, yielding a usable instance.

In object-oriented programming, instantiation is the creation of an object from a class. A class provides structure and behavior, while an instance is a concrete object stored in memory with its own state. For example, instantiating a class Car creates an individual car object with specific attributes like color and model.

In languages with templates or generics, an instantiation occurs when a generic template is supplied with concrete type arguments. This produces a specialized version of the template, such as a list of integers or a map from strings to dates. Instantiations can affect performance and type safety, because the compiler may generate specialized code for the chosen types.

In logic and formal systems, instantiation refers to applying a general proposition to a specific term. Universal instantiation derives a instance of a predicate for a chosen object, while existential instantiation involves introducing a witness term under certain rules. Model theory uses instantiation to build concrete structures that satisfy a given theory.

In database theory, an instance is a set of data conforming to a schema. Instantiation here means populating the schema with concrete records, creating a moment-in-time view of the database. Across domains, instantiation emphasizes turning abstract definitions into usable, concrete realizations.