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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 term closure is often used as a synonym for anonymous function, though strictly, an anonymous function is a function literal without a name, while a closure is an instance of a function, a value, whose non-local variables have been bound either to values or to storage locations (depending on the language; see the lexical environment section below).
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.
The identifier list is bound to a variable in the first line; in the second, an object (a linked list of strings) is assigned to the variable. The linked list referenced by the variable is then mutated, adding a string to the list. Next, the variable is assigned the constant null. In the last line, the identifier is rebound for the scope of the ...
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).
In computer programming, bounds checking is any method of detecting whether a variable is within some bounds before it is used. It is usually used to ensure that a number fits into a given type (range checking), or that a variable being used as an array index is within the bounds of the array (index checking).
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The variables are called quantified and any occurrence of a quantified type variable in is called bound and all unbound type variables in are called free. Additionally to the quantification ∀ {\displaystyle \forall } in polytypes, type variables can also be bound by occurring in the context, but with the inverse effect on the right hand side ...