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Qu'est-ce (qui) est free variable - définition

CLASSIFICATION OF VARIABLES IN A LOGIC FORMULA BASED ON WHETHER OR NOT THEY ARE INSIDE THE SCOPE OF A QUANTIFIER

Free variable; Bound variable; Variable binding operation; Variable-binding operation; Free variables; Bound variables; Unbound variable; Unbound variables; Variable-binding operator; Variable binding operator; Free and bound variables; Bound variable clash; Free and bound variable; Placeholder (computer programming); Free variables & bound variables; Free occurrence; Placeholder variable; Apparent variable

$Tree summarizing the syntax of the expression <math>\forall x\, ((\exists y\, A(x)) \vee B(z)) </math>$

free variable

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).

bound variable

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.

Variable (computer science)

STORAGE LOCATION PAIRED WITH A NAME, WHICH CONTAINS A VALUE

Program variable; Scalar variable; Variable scope; Simple variable; Variable (computing); Variable (programming); Variable lifetime; Scope and extent; Variable scope and extent; Variable extent; Variable (computer programming); Storage location; Assignable variable

In computer programming, a variable is an abstract storage location paired with an associated symbolic name, which contains some known or unknown quantity of information referred to as a value; or in simpler terms, a variable is a named container for a particular set of bits or type of data (like integer, float, string etc...).

https://en.wikipedia.org/wiki/Variable_(computer_science)

Wikipédia

Free variables and bound variables

In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol.

In computer programming, the term free variable refers to variables used in a function that are neither local variables nor parameters of that function. The term non-local variable is often a synonym in this context.

An instance of a variable symbol is bound, in contrast, if the value of that variable symbol has been bound to a specific value or range of values in the domain of discourse or universe. This may be achieved through the use of logical quantifiers, variable-binding operators, or an explicit statement of allowed values for the variable (such as, "...where $n$ is a positive integer".) A variable symbol overall is bound if at least one occurrence of it is bound.^pp.142--143 Since the same variable symbol may appear in multiple places in an expression, some occurrences of the variable symbol may be free while others are bound,^p.78 hence "free" and "bound" are at first defined for occurrences and then generalized over all occurrences of said variable symbol in the expression. However it is done, the variable ceases to be an independent variable on which the value of the expression depends, whether that value be a truth value or the numerical result of a calculation, or, more generally, an element of an image set of a function.

Note that while the domain of discourse in many contexts is understood, when an explicit range of values for the bound variable has not been given, it may be necessary to specify the domain in order to properly evaluate the expression. For example, consider the following expression in which both variables are bound by logical quantifiers:

This expression evaluates to false if the domain of $x$ and $y$ is the real numbers, but true if the domain is the complex numbers.

The term "dummy variable" is also sometimes used for a bound variable (more commonly in general mathematics than in computer science), but this should not be confused with the identically named but unrelated concept of dummy variable as used in statistics, most commonly in regression analysis.

https://en.wikipedia.org/wiki/Free variables and bound variables