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2.1 Hello again, Haskell.

2 Day 1: Getting up and running

Alright. So. I’m going to try this again. Starting from scratch and doing it right this time.

I’ll spare you the gory details, but to make a long story short, it worked!

$ ghc-mod

ghc-mod: No command given (try --help)

Now we’re talking. Time to run a simple cabal ‑‑init, and finally, finally I’m able to actually work in a reasonable environment.

So. Here I am. What now?

2.1 Hello again, Haskell.

Alright, so, here’s the thing: I’m not very good at Haskell. In fact, I barely know the language. I know it well enough to write your usual simple programs—fibonacci numbers, factorial functions, etc.—so I’m not going in completely cold. That said, this language is probably a little too complicated for me to just blindly charge into on my own.

After a little bit of looking around, I found a pretty neat Haskell course offered by UPenn. All the lecture notes and homework assignments are online, so this seems like a reasonable way to get a guided introduction to the language. I’ve heard the name Real World Haskell thrown around a few times, so maybe I’ll look into that next, but first I just want to reacquaint myself with this language.

Alright. Homework assignment one! I took a brief glance at the lecture notes, but I didn’t really read them—I think I remember enough to at least complete whatever this assignment is. We’ll see if I’m wrong.

So apparently, this homework assignment is about implementing an algorithm to validate credit card numbers. Seems straightforward enough. First, it wants me to implement lastDigit and dropLastDigit functions. Let’s give this a shot.

lastDigit :: Integer -> Integer

lastDigit = `mod` 10

I was feeling pretty good about myself. I remembered backticks for infix notation and that I can use partial application of operators’ second arguments! I can already see the road to hell is paved with point-free style. Anyway, despite my jubilations, that doesn’t even work—GHC complains about a parse error. Maybe I need more parens?

lastDigit :: Integer -> Integer

lastDigit = (`mod` 10)

And it works! Perfect. Now let me try dropLastDigit. Armed with my newfound knowledge, this should be a snap.

dropLastDigit :: Integer -> Integer

dropLastDigit = (/ 10)

Hmm. That doesn’t work, either, complaining about type mismatches and missing instantiations. My gut tells me that this is because / probably performs non-integral division, and GHC doesn’t like that I’m throwing the precision away. Or maybe it flat-out doesn’t work on integers? I’m not sure.

What I do remember is that Hoogle exists, and it’s awesome. I try a quick query for Integer -> Integer -> Integer, which nets me nothing related to division. Oh, well. It was worth a shot. In desperation, I decided to type in divison, and as I was doing so, div appeared before my eyes, which apparently has the type Integral a => a -> a -> a. I’m not sure why that didn’t come up in my other search. I guess there were just too many other results.

Anyway, using div does what I want.

dropLastDigit :: Integer -> Integer

dropLastDigit = (`div` 10)

Alright, what’s next? A function to split a number into its digits in reverse order called, not surprisingly, toRevDigits. I think I remember enough about Haskell to make this work.

toRevDigits :: Integer -> [Integer]

toRevDigits n

  | n <= 0    = []

  | otherwise = lastDigit n : toRevDigits $ dropLastDigit n

Hmm. That doesn’t work. I’m not sure why, but I’m almost certain it has to do with order of operations. I’m far too lazy to actually figure that out, so parens should do the job fine.

toRevDigits :: Integer -> [Integer]

toRevDigits n

  | n <= 0    = []

  | otherwise = lastDigit n : toRevDigits (dropLastDigit n)

Sure enough, that fixed things. Still, something about me doesn’t like the asymmetry between the two expressions on either side of the cons (is it still called that in Haskell?). I remember something about where clauses; let’s try that.

toRevDigits :: Integer -> [Integer]

toRevDigits n

  | n <= 0    = []

  | otherwise = d : toRevDigits ds

     where d  = lastDigit n

           ds = dropLastDigit n

Well, that seemed to work, but is it nicer...? I don’t know. Now it just seems more verbose, honestly. I can’t really decide, but I guess I’ll just leave it as-is for now.

Next problem: write a doubleEveryOther function which does precisely what it sounds like. Aha! Pattern-matching time.

doubleEveryOther :: [Integer] -> [Integer]

doubleEveryOther []       = []

doubleEveryOther [x]      = [x]

doubleEveryOther (x:y:ys) = x : (y * 2) : doubleEveryOther ys

...and it compiles! Yay, I finally did something right. I actually had to fiddle with the parens around the last pattern—I forgot they were necessary—but otherwise everything appears to be in order.

Now, a function that sums all the digits in a list of numbers. I don’t think I’m supposed to be aware of higher-order functions at this point in this classwork, but I don’t really care. This is a perfect opportunity to use them.

sumDigits :: [Integer] -> Integer

sumDigits = sum . concatMap toRevDigits

I originally typed concat . map, but ghc-mod helpfully pointed out that I could use concatMap instead. I figure it’s more efficient since it doesn’t need to build the intermediate list.

Finally, one more function: putting everything together to write a simple credit card validation function. I like these sorts of problems: all the parts already exist, so it’s obviously easy to put them together.

luhn :: Integer -> Bool

luhn n = sumDigits (doubleEveryOther $ toRevDigits n) `mod` 10 == 0


Well, that wasn’t terribly interesting, though it was helpful to get used to working in the language again. I think I’ll go through the next assignment, and if it doesn’t get better, I might have to switch to something else. For now, though, I feel somewhat accomplished, despite having written an extremely trivial set of functions.