# bound variable

## bound variable

[¦bau̇nd ′ver·ē·ə·bəl]
(mathematics)
In logic, a variable that occurs within the scope of a quantifier, and cannot be replaced by a constant.

## 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.

## bound variable

(2)
In logic a bound variable is a quantified variable. See quantifier.
References in periodicals archive ?
There are only a handful of possibilities for redefining the relational property of being necessarily identical to a bound variable x, and none that is sufficient for Kripke's purposes in trying to prove that all identity relations are necessary.
First pattern from the Drools example above (see line 1.) contains as field constraint a bound variable, called declaration.
Because we know the type of f, we also know that the argument fun (x:Int)x must have type Int [right arrow] Int, which determines the type annotation on the bound variable x--the type Int is the most specific (with respect to the subtype relation) that can validly be given to x.
" On the surface, this locution has a quantifier, "there is a way", and anaphoric reference, "had the world been that way", which usually signals a bound variable. Chihara, of course, does not understand the terminology this way.
This means that a bound variable is guaranteed to eventually disappear from the system.
A value cell tagged as a variable but not pointing to itself represents a bound variable. Structures are created by explicitly copying the functor and arguments into consecutive value cells on the heap.
In order to rid quantifier A and the bound variable x from this formula, we have to use the combinators.
The usual renaming rules apply to the bound variable [Alpha], and we have [Mu Alpha].[Tau] = [Tau][[Alpha] ??
The paper (Muthukumar & Selvaraj, 2003) deals with the problem of determining the set of best free and bound variables (variable partitioning problem) for disjoint (disjoint serial) decomposition; such that the decomposed circuits are smaller in size and its truth table representation have maximal don't cares.
The core of an XML-QL query consists of a WHERE clause that binds one or more variables, and a CONSTRUCT clause that uses the values of the bound variables to construct a new document, possibly having a structure quite different from that of the original document(s).
Type-checking problems of the methods of the above class start with the fact that all we can assert about the type of the bound variables and the formal parameters of the query is that their type is Object.
"Foundational Aspects of Syntax," by Miller and Palmidessi, considers the advantages of computing directly with lambda trees that encode lambda expressions, as opposed to parse trees that must deal with complex substitution rules for bound variables. Methods for computing with lambda trees, including recursion, are considered.

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