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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 A named function. An expression like (.) where M is lambda free and N is lambda free or an anonymous function.
In computer programming, an anonymous function (function literal, expression or block) is a function definition that is not bound to an identifier.Anonymous functions are often arguments being passed to higher-order functions or used for constructing the result of a higher-order function that needs to return a function. [1]
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 combinatory logic for computer science, a fixed-point combinator (or fixpoint combinator) [1]: p.26 is a higher-order function (i.e. a function which takes a function as argument) that returns some fixed point (a value that is mapped to itself) of its argument function, if one exists.
(In Church's original lambda calculus, the formal parameter of a lambda expression was required to occur at least once in the function body, which made the above definition of 0 impossible.) One way of thinking about the Church numeral n, which is often useful when analysing programs, is as an instruction 'repeat n times'.
In some languages, it is possible to create a nested function that accesses a set of parameters from the outer function, that is a closure, and have that function be the outer function's return value. Thus it is possible to return a function that is set to fulfill a certain task with little or no further parameters given to it, which can ...
In computer programming, a nullary constructor is a constructor that takes no arguments. [1] Also known as a 0-argument constructor, no-argument constructor, [2] parameterless constructor or default constructor. [3]
This is the set of variable names that have instances not bound (used) in a lambda abstraction, within the lambda expression. They are the variable names that may be bound to formal parameter variables from outside the lambda expression. The set of bound variables of a lambda expression, M, is denoted as BV(M). This is the set of variable names ...