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The "lambda term" is represented as a tagged union with three cases: Constructor a - a variable (arity 1, not recursive) Constructor b - function application (arity 2, recursive in both arguments), Constructor c - lambda-abstraction (arity 1, recursive). For example,
Lambda lifts may also be repeated, in order to transform the program. Repeated lifts may be used to convert a program written in lambda calculus into a set of recursive functions, without lambdas. This demonstrates the equivalence of programs written in lambda calculus and programs written as functions. [1]
[16] [17] And with certain programs the number of steps may be much smaller, for example a specific family of lambda terms using Church numerals take an infinite amount of steps with call-by-value (i.e. never complete), an exponential number of steps with call-by-name, but only a polynomial number with call-by-need.
In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value.
Recursion that contains only a single self-reference is known as single recursion, while recursion that contains multiple self-references is known as multiple recursion. Standard examples of single recursion include list traversal, such as in a linear search, or computing the factorial function, while standard examples of multiple recursion ...
Here is an example of a recursive function in C/C++ to find Fibonacci numbers: ... Lambda function (computer programming), a function that is not bound to an identifier;
Some programming languages almost always use curried functions to achieve multiple arguments; notable examples are ML and Haskell, where in both cases all functions have exactly one argument. This property is inherited from lambda calculus, where multi-argument functions are usually represented in curried form.
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.