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Before stating a precise definition of free variable and bound variable, the following are some examples that perhaps make these two concepts clearer than the definition would: In the expression ∑ k = 1 10 f ( k , n ) , {\displaystyle \sum _{k=1}^{10}f(k,n),}
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).
[2] 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.
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.
Here is an example, in C-like pseudocode, of an integer variant computed from some upper bound on the number of iterations remaining in a while loop. However, C allows side effects in the evaluation of expressions, which is unacceptable from the point of view of formally verifying a computer program.
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).
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 ...
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.