Literate Haskell experiment

It’s nice to be able to mix serious writing and coding together. While literate Haskell may be far from the pinnacle of literate programming, it is still a nice tool to have available.

This is a page for experimenting with its use.

Fibonacci numbers

Say I want a list of Fibonacci numbers. This is going to be a list of integers.

fibonacci :: [Integer]

The first and second Fibonacci numbers are both defined to be 1, so the list should start with two 1s. We will define a list which will start out our list of Fibonacci numbers.

base :: [Integer]
base = [1, 1]

Subsequent Fibonacci numbers are defined by adding the two numbers right before in the sequence. We gather a list of two consecutive numbers, which we will add later together.

pairs :: [(Integer,Integer)]
pairs = zip fibonacci $ drop 1 fibonacci

Then getting the subsequent Fibonacci numbers is a simple matter of adding together the pairs of numbers in the list above.

inducted :: [Integer]
inducted = map (uncurry (+)) pairs

Now that we have all the Fibonacci numbers in two lists, we can simply concatenate the them together to obtain the entire list.

fibonacci = base ++ inducted

And that’s it. We now have a list of all the Fibonacci numbers.

It is also possible to define the same thing with a single list. Personally, I think this style is a little bit too clever, given that it can make it awkward to write down clarifying comments for various parts of the code.

fibonacci' :: [Integer]
fibonacci' = 1 : 1 : [ m+n | (m,n) <- zip fibonacci (drop 1 fibonacci) ]

We obviously cannot print the entirety of the list, but we can look up a few numbers.

main :: IO ()
main = do
  print $ take 10 fibonacci
  print $ take 11 fibonacci'

If we run the code above, it will print out the Fibonacci numbers as expected.

$ runhaskell literate-haskell.tex.lhs

Despite these being infinite lists, the code is not stuck trying to futilely compute all the numbers before printing any of them out thanks to lazy evaluation in Haskell.


The raw source code for this file is on GitHub.