# Total Functional Programming

* Paper - D. A. Turner - [Total Functional Programming](http://www.jucs.org/jucs_10_7/total_functional_programming/jucs_10_07_0751_0768_turner.pdf) 

## Notes

* Total functional programming *excludes* the possibility of non-termination.
* `fib` function will *not* compile in Haskell 2010 due to later standard not supporting `n + k` patterns. 
* Haskell 2010 version can be writen as follows,

  ```haskell
    fib n
    | n == 0    = 0
    | n == 1    = 1
    | otherwise = fib (n-1) + fib (n - 2)
  ```
* In a non total language, each type contains a `⊥` (`bottom`).
* In a non-total language such as Haskell, even simple natural identity such as `e - e = 0` cannot be assumed to hold true equationally due to the presence of `⊥`.