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Variable binding relates three things: a variable v, a location a for that variable in an expression and a non-leaf node n of the form Q(v, P). Note: we define a location in an expression as a leaf node in the syntax tree. Variable binding occurs when that location is below the node n. In the lambda calculus, x is a bound variable in the term M
Dynamic binding (or late binding or virtual binding) is name binding performed as the program is running. [2] An example of a static binding is a direct C function call: the function referenced by the identifier cannot change at runtime. An example of dynamic binding is dynamic dispatch, as in a C++ virtual method call. Since the specific type ...
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 ...
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).
A typical example is the static variables in C and C++. A Stack-dynamic variable is known as local variable, which is bound when the declaration statement is executed, and it is deallocated when the procedure returns. The main examples are local variables in C subprograms and Java methods.
Many interesting calculi, logics and programming languages that are commonly seen in computer science feature name binding constructs. For instance, the universal quantifier from first-order logic, the lambda-binder from the lambda-calculus, and the pi-binder from the pi-calculus are all examples of name-binding constructs.
HOAS exposes additional structure: the relationship between variables and their binding sites. In FOAS representations, a variable is typically represented with an identifier, with the relation between binding site and use being indicated by using the same identifier. With HOAS, there is no name for the variable; each use of the variable refers ...
In Scheme, procedures are bound to variables. At R5RS the language standard formally mandated that programs may change the variable bindings of built-in procedures, effectively redefining them. (R5RS "Language changes") [4] For example, + can be extended to accept strings as well as numbers by redefining it: