An approach invented by PhilipWadler for combining AbstractDataTypes with PatternMatching.
http://citeseer.ist.psu.edu/cache/papers/cs/2656/http:zSzzSzwww.cs.bell-labs.comzSz~wadlerzSztopicszSz..zSzpaperszSzviewzSzview.pdf/wadler87views.pdf
A View is an isomorphism between one data representation and another. For example, given ordinary integer arithmetic, you could construct a PeanoArithmetic view with:

CategoryLanguageFeature See also: PredicateDispatching, PatternMatching Contributors: JonathanTang

view int ::= Zero | Succ int in n = Zero, if n = 0 = Succ (n - 1), if n > 0 out Zero = 0 out (Succ n) = n + 1You can then pattern match on the Peano data types as if you were working with integers and GuardClauses. For example, you could define exponentiation as

power x Zero = 1 power x (Succ n) = x * power x nAnd you could define Fibonacci numbers as:

fib Zero = Zero fib (Succ Zero) = Succ Zero fib (Succ (Succ n)) = (fib n) + (fib (Succ n))I'm not sure if this is implemented in any production language. The paper is written in pseudo-MirandaLanguage, and IIRC there have been proposals to add it to HaskellLanguage.

CategoryLanguageFeature See also: PredicateDispatching, PatternMatching Contributors: JonathanTang

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