Mutual Recursion
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Mutual Recursion
In mathematics and computer science, mutual recursion is a form of recursion where two mathematical or computational objects, such as functions or datatypes, are defined in terms of each other. Mutual recursion is very common in functional programming and in some problem domains, such as recursive descent parsers, where the datatypes are naturally mutually recursive. Examples Datatypes The most important basic example of a datatype that can be defined by mutual recursion is a tree, which can be defined mutually recursively in terms of a forest (a list of trees). Symbolically: f: [1 ..., t[k t: v f A forest ''f'' consists of a list of trees, while a tree ''t'' consists of a pair of a value ''v'' and a forest ''f'' (its children). This definition is elegant and easy to work with abstractly (such as when proving theorems about properties of trees), as it expresses a tree in simple terms: a list of one type, and a pair of two types. Further, it matches many algorithms on trees, whi ...
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NFCC
The PFF National Challenge Cup is an annual single-elimination tournament, knockout association football, football competition in men's domestic Football in Pakistan, Pakistani football within the Pakistan football league system. It is organized by and named after the Pakistan Football Federation. Initially named as ''Inter Departmental Championship'', it was introduced in 1979 as a football tournament for departmental selections and Pakistan Armed Forces, armed forces teams excluded from the National Football Championship (Pakistan), National Football Championship of Pakistan''.'' Khan Research Laboratories F.C., Khan Research Laboratories have won the most titles (six). WAPDA F.C., WAPDA are the current champions, winning the 2023–24 PFF National Challenge Cup, 2023–24 edition courtesy of a 1–0 win against SA Gardens FC, SA Gardens in the final. Background Introduced in 1979 to offer nationwide competition to departmental selections and Pakistan Armed Forces, armed force ...
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