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The names "lambda abstraction", "lambda function", and "lambda expression" refer to the notation of function abstraction in lambda calculus, where the usual function f (x) = M would be written (λx. M), and where M is an expression that uses x. Compare to the Python syntax of lambda x: M.
The following REBOL/Red code demonstrates callback use. As alert requires a string, form produces a string from the result of calculate; The get-word! values (i.e., :calc-product and :calc-sum) trigger the interpreter to return the code of the function rather than evaluate with the function. The datatype! references in a block!
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [3] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function.
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).
The Carmichael lambda function of a prime power can be expressed in terms of the Euler totient. Any number that is not 1 or a prime power can be written uniquely as the product of distinct prime powers, in which case λ of the product is the least common multiple of the λ of the prime power factors.
In PHP and other languages, the lambda is an alternative. A function is defined in a code statement rather than declared with the usual function syntax. It has no name but is callable via a function reference. Such functions can be defined inside of a function as well as in other scopes. To use local variables in the anonymous function, use ...
Chicken Scheme compiler, a Scheme to C compiler that uses continuation-passing style for translating Scheme procedures into C functions while using the C-stack as the nursery for the generational garbage collector; Kelsey, Richard A. (March 1995). "A Correspondence between Continuation Passing Style and Static Single Assignment Form".
Unlike ordinary C function definitions, their value can capture state from their surrounding context. A block definition produces an opaque value which contains both a reference to the code within the block and a snapshot of the current state of local stack variables at the time of its definition.