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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
Even without mechanisms to refer to the current function or calling function, anonymous recursion is possible in a language that allows functions as arguments. This is done by adding another parameter to the basic recursive function and using this parameter as the function for the recursive call.
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 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).
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.
Meta-functions will be given that describe the conversion between lambda and let expressions. A meta-function is a function that takes a program as a parameter. The program is data for the meta-program. The program and the meta program are at different meta-levels. The following conventions will be used to distinguish program from the meta program,
Variable binding relates three things: a variable v, a location a for that variable in an expression and a non-leaf node n of the form Q(v, P). Note: we define a location in an expression as a leaf node in the syntax tree. Variable binding occurs when that location is below the node n. In the lambda calculus, x is a bound variable in the term M
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]