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In type-based program analysis polymorphic recursion is often essential in gaining high precision of the analysis. Notable examples of systems employing polymorphic recursion include Dussart, Henglein and Mossin's binding-time analysis [2] and the Tofte–Talpin region-based memory management system. [3]
In this case the tree function calls the forest function by single recursion, but the forest function calls the tree function by multiple recursion. Using the Standard ML datatype above, the size of a tree (number of nodes) can be computed via the following mutually recursive functions: [5]
In Haskell this is the foldl' (note the apostrophe, pronounced 'prime') function in the Data.List library (one needs to be aware of the fact though that forcing a value built with a lazy data constructor won't force its constituents automatically by itself). Combined with tail recursion, such folds approach the efficiency of loops, ensuring ...
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 ...
In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.
In programming languages that support anonymous functions, fixed-point combinators allow the definition and use of anonymous recursive functions, i.e. without having to bind such functions to identifiers. In this setting, the use of fixed-point combinators is sometimes called anonymous recursion. [note 4] [23]
Using separate lines of communication, four organizations require six channels Using an intermediary, only one channel per organization is required In administration and computing , a combinatorial explosion is the rapidly accelerating increase in communication lines as organizations are added in a process.
Most problematic from a software design point of view is the tight coupling of the mutually dependent modules which reduces or makes impossible the separate re-use of a single module. Circular dependencies can cause a domino effect when a small local change in one module spreads into other modules and has unwanted global effects (program errors ...