wiiki - PatternMatchingViews

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:

view int ::= Zero | Succ int
  in n         = Zero,         if n = 0
               = Succ (n - 1), if n > 0
  out Zero     = 0
  out (Succ n) = n + 1

You 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 n

And 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

Contributors: JonathanTang