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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 = λx. T and a free variable in the term T. We say x is bound in M and free in T. If T contains a subterm λx. U then x is rebound in this term.
A free parameter is a variable in a mathematical model which cannot be predicted precisely or constrained by the model [1] and must be estimated [2] experimentally or theoretically. A mathematical model, theory, or conjecture is more likely to be right and less likely to be the product of wishful thinking if it relies on few free parameters and ...
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.
Free lists make the allocation and deallocation operations very simple. To free a region, one would just link it to the free list. To allocate a region, one would simply remove a single region from the end of the free list and use it. If the regions are variable-sized, one may have to search for a region of large enough size, which can be ...
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.)
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 ...
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In mathematics, a variable (from Latin variabilis, "changeable") is a symbol, typically a letter, that refers to an unspecified mathematical object. [1] [2] [3] One says colloquially that the variable represents or denotes the object, and that any valid candidate for the object is the value of the variable.