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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.
the occurrence of both x and y in C(y, x) is free, while the occurrence of x and y in B(y, x) is bound (i.e. non-free). Syntax tree of the formula ((,)) (,), illustrating scope and variable capture. Bound and free variable occurrences are colored in red and green, respectively.
Variables that fall within the scope of an abstraction are said to be bound. All other variables are called free. For example, in the following expression is a bound variable and is free: . . Also note that a variable is bound by its "nearest" abstraction.
The scope of a logical connective occurring within a formula is the smallest well-formed formula that contains the connective in question. [2] [6] [8] The connective with the largest scope in a formula is called its dominant connective, [9] [10] main connective, [6] [8] [7] main operator, [2] major connective, [4] or principal connective; [4] a connective within the scope of another connective ...
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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 variable is bound by its nearest abstraction. In the following example the single occurrence of x in the expression is bound by the second lambda: λx.y (λx.z x).
How variable rate caps work. In many cases, lenders set caps on variable-rate products. This was designed to protect consumer borrowers from the kind of runaway interest the country saw during the ...
An open formula can be transformed into a closed formula by applying a quantifier for each free variable. This transformation is called capture of the free variables to make them bound variables. For example, when reasoning about natural numbers, the formula "x+2 > y" is open, since it contains the free variables x and y.