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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.
Higher-order programming is a style of computer programming that uses software components, like functions, modules or objects, as values. It is usually instantiated with, or borrowed from, models of computation such as lambda calculus which make heavy use of higher-order functions. A programming language can be considered higher-order if ...
Expressions, such as x <= y, a = b + c, or even lambda functions and other complex forms can be created dynamically using expression trees. Much of the functionality is provided by static methods of the class System.Linq.Expressions.Expression. There are also various new classes in that namespace that represent the expressions and partial ...
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).
Python: Application, general, web, scripting, artificial intelligence, scientific computing Yes Yes Yes Yes Yes Yes Aspect-oriented De facto standard via Python Enhancement Proposals (PEPs) R: Application, statistics Yes Yes Yes Yes No Yes No Racket: Education, general, scripting Yes Yes Yes Yes No Yes Modular, logic, meta No Raku
In Python, functions are first-class objects that can be created and passed around dynamically. Python's limited support for anonymous functions is the lambda construct. An example is the anonymous function which squares its input, called with the argument of 5:
Lambda expressions: Lambda expressions allow predicates and other projection functions to be written inline with a concise syntax, and support full lexical closure. They are captured into parameters as delegates or expression trees depending on the Query Provider.
In the untyped lambda calculus, where the basic types are functions, lifting may change the result of beta reduction of a lambda expression. The resulting functions will have the same meaning, in a mathematical sense, but are not regarded as the same function in the untyped lambda calculus. See also intensional versus extensional equality.