<programming> In object-oriented programming, one of the variables of a class template which may have a different value for each object of that class. Instance variables hold the state of an object. (1998-01-16)

1. A variable referred to in a function, which is not an argument of the function. In lambda-calculus, x is a {bound variable} in the term M = x . T, and a free variable of T. We say x is bound in M and free in T. If T contains a subterm x . U then x is rebound in this term. This nested, inner binding of x is said to "shadow" the outer binding. Occurrences of x in U are free occurrences of the new x. Variables bound at the top level of a program are technically free variables within the terms to which they are bound but are often treated specially because they can be compiled as fixed addresses. Similarly, an identifier bound to a recursive function is also technically a free variable within its own body but is treated specially. A closed term is one containing no free variables. See also closure, lambda lifting, scope. 2. In logic, a variable which is not quantified (see quantifier).

1. A bound variable or formal argument in a function definition is replaced by the actual argument when the function is applied. In the lambda abstraction x . M x is the bound variable. However, x is a free variable of the term M when M is considered on its own. M is the scope of the binding of x. 2. In logic a bound variable is a quantified variable. See quantifier.

In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely long) whose joint probability distribution does not change when the positions in the sequence in which finitely many of them appear are altered.

In mathematical analysis and its applications, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables. This concept extends the idea of a function of a real variable to several variables.

Critical variables are defined, for example in thermodynamics, in terms of the values of variables at the critical point.

In massively multiplayer online games, an instance is a special area, typically a dungeon, that generates a new copy of the location for each group, or for a certain number of players, that enters the area. Instancing, the general term for the use of this technique, addresses several problems encountered by players in the shared spaces of virtual worlds.

n. the court which holds the original trial, as distinguished from a court of appeals. See also: trial

In machine learning, multiple-instance learning (MIL) is a type of supervised learning. Instead of receiving a set of instances which are individually labeled, the learner receives a set of labeled bags, each containing many instances.