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Mutual recursion is very common in functional programming, and is often used for programs written in LISP, Scheme, ML, and similar programming languages. For example, Abelson and Sussman describe how a meta-circular evaluator can be used to implement LISP with an eval-apply cycle. [7] In languages such as Prolog, mutual recursion is almost ...
In Pascal and other Wirth programming languages, it is a general rule that all entities must be declared before use, and thus forward declaration is necessary for mutual recursion, for instance. In C, the same general rule applies, but with an exception for undeclared functions and incomplete types.
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A recursive step — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ancestor. One's ancestor is either: One's parent (base case), or; One's parent's ancestor (recursive step). The Fibonacci sequence is another classic example of recursion: Fib(0) = 0 as ...
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 ...
In computability theory, Bekić's theorem or Bekić's lemma is a theorem about fixed-points which allows splitting a mutual recursion into recursions on one variable at a time. [1] [2] [3] It was created by Austrian Hans Bekić (1936-1982) in 1969, [4] and published posthumously in a book by Cliff Jones in 1984. [5] The theorem is set up as ...
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.
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