Total Functional Programming

• Paper - D. A. Turner - 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 ⊥ (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 ⊥.