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The binding site for a variable n is the nth binder it is in the scope of, starting from the innermost binder. The most primitive operation on λ-terms is substitution: replacing free variables in a term with other terms. In the β-reduction (λ M) N, for example, we must
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 ...
For example, in the snippet of Python code on the right, two functions are defined: square and sum_of_squares. square computes the square of a number; sum_of_squares computes the sum of all squares up to a number. (For example, square(4) is 4 2 = 16, and sum_of_squares(4) is 0 2 + 1 2 + 2 2 + 3 2 + 4 2 = 30.)
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).
In a programming language, an evaluation strategy is a set of rules for evaluating expressions. [1] The term is often used to refer to the more specific notion of a parameter-passing strategy [2] that defines the kind of value that is passed to the function for each parameter (the binding strategy) [3] and whether to evaluate the parameters of a function call, and if so in what order (the ...
For example, Python bindings are used when an extant C library, written for some purpose, is to be used from Python. Another example is libsvn which is written in C to provide an API to access the Subversion software repository. To access Subversion from within Java code, libsvnjavahl can be used, which depends on libsvn being installed and ...
Given real numbers x and y, integers m and n and the set of integers, floor and ceiling may be defined by the equations ⌊ ⌋ = {}, ⌈ ⌉ = {}. Since there is exactly one integer in a half-open interval of length one, for any real number x, there are unique integers m and n satisfying the equation
The rules a compiler applies to the source creates implicit standards. For example, Python code is much more consistently indented than, say Perl, because whitespace (indentation) is actually significant to the interpreter. Python does not use the brace syntax Perl uses to delimit functions. Changes in indentation serve as the delimiters.