# Pattern Matching Views

An approach invented by PhilipWadler for combining AbstractDataTypes with PatternMatching.

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