Total Functional Programming

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,

    fib n
    | n == 0 = 0
    | n == 1 = 1
    | otherwise = fib (n-1) + fib (n - 2)
  • In a non total language, each type contains a βŠ₯ (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 βŠ₯.