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 ⊥.

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