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For example, consider the following expression in which both variables are bound by logical quantifiers: ∀ y ∃ x ( x = y ) . {\displaystyle \forall y\,\exists x\,\left(x={\sqrt {y}}\right).} This expression evaluates to false if the domain of x {\displaystyle x} and y {\displaystyle y} is the real numbers, but true if the domain is the ...
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))
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
For example, in mechanics the mass and the size of a solid body are parameters for the study of its movement. In computer science, parameter has a different meaning and denotes an argument of a function. Free variables and bound variables; A random variable is a kind of variable that is used in probability theory and its applications.
The substitution rule states that for any φ and any term t, one can conclude φ[t/x] from φ provided that no free variable of t becomes bound during the substitution process. (If some free variable of t becomes bound, then to substitute t for x it is first necessary to change the bound variables of φ to differ from the free variables of t.)
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).
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 and free variable occurrences are colored in red and green, respectively. An interpretation for first-order predicate calculus assumes as given a domain of individuals X. A formula A whose free variables are x 1, ..., x n is interpreted as a Boolean-valued function F(v 1, ..., v n) of n arguments, where each argument ranges over the domain X.