![]() Only once the enclosing function is evaluated with a value for the parameter is the free variable of the nested function bound, creating a closure, which is then returned from the enclosing function. The nested function definitions are not themselves closures: they have a free variable which is not yet bound. This usage may be deemed an "anonymous closure". It does not need to be assigned to a variable and can instead be used directly, as shown in the last two lines of the example. The original name, if any, used in defining them is irrelevant.Ī closure is a value like any other value. The only difference in implementation is that in the first case we used a nested function with a name, g, while in the second case we used an anonymous nested function (using the Python keyword lambda for creating an anonymous function). ![]() The closures in a and b are functionally identical. The values of a and b are closures, in both cases produced by returning a nested function with a free variable from the enclosing function, so that the free variable binds to the value of parameter x of the enclosing function. assert h ( 1 )( 5 ) = 6 # h(1) is the closure. assert f ( 1 )( 5 ) = 6 # f(1) is the closure. assert a ( 5 ) = 6 assert b ( 5 ) = 6 # Using closures without binding them to variables first. ![]() a = f ( 1 ) b = h ( 1 ) # Using the closures stored in variables. # Assigning specific closures to variables. def h ( x ): return lambda y : x + y # Return a closure. The authors consider this overlap in terminology to be "unfortunate." Anonymous functions ĭef f ( x ): def g ( y ): return x + y return g # Return a closure. This use of the term comes from mathematics use, rather than the prior use in computer science. Sussman and Abelson also use the term closure in the 1980s with a second, unrelated meaning: the property of an operator that adds data to a data structure to also be able to add nested data structures. This use was subsequently adopted by Sussman and Steele when they defined Scheme in 1975, a lexically scoped variant of Lisp, and became widespread. Joel Moses credits Landin with introducing the term closure to refer to a lambda expression with open bindings (free variables) that have been closed by (or bound in) the lexical environment, resulting in a closed expression, or closure. Peter Landin defined the term closure in 1964 as having an environment part and a control part as used by his SECD machine for evaluating expressions. The concept of closures was developed in the 1960s for the mechanical evaluation of expressions in the λ-calculus and was first fully implemented in 1970 as a language feature in the PAL programming language to support lexically scoped first-class functions. Unlike a plain function, a closure allows the function to access those captured variables through the closure's copies of their values or references, even when the function is invoked outside their scope. The environment is a mapping associating each free variable of the function (variables that are used locally, but defined in an enclosing scope) with the value or reference to which the name was bound when the closure was created. Operationally, a closure is a record storing a function together with an environment. In programming languages, a closure, also lexical closure or function closure, is a technique for implementing lexically scoped name binding in a language with first-class functions. Not to be confused with the programming language Clojure.
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