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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 bound variable pronoun (also called a bound variable anaphor or BVA) is a pronoun that has a quantified determiner phrase (DP) – such as every, some, or who – as its antecedent. [1] An example of a bound variable pronoun in English is given in (1). (1) Each manager exploits the secretary who works for him. (Reinhart, 1983: 55 (19a))
In a formula, a variable may occur free or bound (or both). One formalization of this notion is due to Quine, first the concept of a variable occurrence is defined, then whether a variable occurrence is free or bound, then whether a variable symbol overall is free or bound.
Such variables reference the location of the value instead of storing the value itself, which is allocated from a pool of memory called the heap. Bound variables have values. A value, however, is an abstraction, an idea; in implementation, a value is represented by some data object, which is stored somewhere in computer memory.
Variables that fall within the scope of an abstraction are said to be bound. In an expression λx.M, the part λx is often called binder, as a hint that the variable x is getting bound by prepending λx to M. All other variables are called free. For example, in the expression λy.x x y, y is a bound variable and x is a free variable. Also a ...
Bound variables occur when the antecedent to the proform is an indefinite quantified expression, e.g. [4] [clarification needed] Every student i has received his i grade. – The pronoun his is an example of a bound variable
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Variable (names) that have already been matched to formal parameter variable are said to be bound. All other variables in the expression are called free. For example, in the following expression y is a bound variable and x is free: . . Also note that a variable is bound by its "nearest" lambda abstraction.