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The recursive program above is tail-recursive; it is equivalent to an iterative algorithm, and the computation shown above shows the steps of evaluation that would be performed by a language that eliminates tail calls. Below is a version of the same algorithm using explicit iteration, suitable for a language that does not eliminate tail calls.
Recursion in computer programming is exemplified when a function is defined in terms of simpler, often smaller versions of itself. The solution to the problem is then devised by combining the solutions obtained from the simpler versions of the problem. One example application of recursion is in parsers for programming languages. The great ...
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.
A total recursive function is a partial recursive function that is defined for every input. Every primitive recursive function is total recursive, but not all total recursive functions are primitive recursive. The Ackermann function A(m,n) is a well-known example of a total recursive function (in fact, provable total), that is not primitive ...
Tail recursion (or tail-end recursion) is particularly useful, and is often easy to optimize in implementations. Tail calls can be implemented without adding a new stack frame to the call stack . Most of the frame of the current procedure is no longer needed, and can be replaced by the frame of the tail call, modified as appropriate (similar to ...
In computer science, corecursion is a type of operation that is dual to recursion.Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case.
This mutually recursive definition can be converted to a singly recursive definition by inlining the definition of a forest: t: v [t[1], ..., t[k]] A tree t consists of a pair of a value v and a list of trees (its children). This definition is more compact, but somewhat messier: a tree consists of a pair of one type and a list another, which ...
LOOP is a simple register language that precisely captures the primitive recursive functions. [1] The language is derived from the counter-machine model.Like the counter machines the LOOP language comprises a set of one or more unbounded registers, each of which can hold a single non-negative integer.