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Anonymous functions originate in the work of Alonzo Church in his invention of the lambda calculus, in which all functions are anonymous, in 1936, before electronic computers. [2] In several programming languages, anonymous functions are introduced using the keyword lambda, and anonymous functions are often referred to as lambdas or lambda ...
Search for the deepest named or anonymous function definition, so that when the lift is applied the function lifted will become a simple equation. This definition recognizes a lambda abstraction with an actual parameter as defining a function. Only lambda abstractions without an application are treated as anonymous functions. lambda-named
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).
Anonymous recursion is primarily of use in allowing recursion for anonymous functions, particularly when they form closures or are used as callbacks, to avoid having to bind the name of the function. Anonymous recursion primarily consists of calling "the current function", which results in direct recursion.
A function's identity is based on its implementation. A lambda calculus function (or term) is an implementation of a mathematical function. In the lambda calculus there are a number of combinators (implementations) that satisfy the mathematical definition of a fixed-point combinator.
The above example is an expression that evaluates to a first-class function. The symbol lambda creates an anonymous function, given a list of parameter names, x – just a single argument in this case, and an expression that is evaluated as the body of the function, x**2. Anonymous functions are sometimes called lambda expressions.
A function. May be unary or n-ary (or always unary for languages without n-ary functions). func1, func2, etc. functions of specific arity. func (with no number) is the same as func1, also known as a projection in many languages. pred Unary function returning a Boolean value. (ML type: 'a -> bool) (C-like type: bool pred < T > (T t)). list The ...
As another example, a C function to implement the second example from the table, Σ, would have a function pointer argument (see box below). Lambda terms can be used to denote anonymous functions to be supplied as arguments to lim, Σ, ∫, etc. For example, the function square from the C program below can be written anonymously as a lambda ...