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Bikeshedding leap years

Darn it, I fell into the trap. An early exercise in Python at exercism.io wants a function that in Haskell would have the type Int -> Bool and indicate whether a year is a leap year (under Gregorian rules, ignoring when various locales made the switch to keep it simple).

Some submissions are from people not yet comfortable with assigning/returning Booleans other than the constants True or False, or maybe not comfortable with the lazy nature of Python's and and or. Their versions are full of if statements. I bashed out
defis_leap_year(year):returnyear%(400ifyear%100==0else4)==0 and it worked fine... but then I fell in. How about
return year % 16 == 0 if year % 25 == 0 else year % 4 == 0 Nah... no need to make the next guy, who could be me, do the prime factorization of 100 again and figure out how that ties to the leap year rules? OK, here's one way to look at it...
return (year // 100 if year % 100 == 0 else year) % 4 == 0i.e. on century boundaries, the century has to be divis…

Restaurants shooting themselves in the foot

It's pet peeve time, and here it is: restaurants that display graphic images of their menu on the web. Sometimes it's a PDF made up of graphics, sometimes it's just graphics.
I wish I had a nickel for each restaurant I really like whose web site suffers from this problem... though perhaps I should shoot for more than that by offering my services to fix their web sites. A few examples: Abelardo's5 de MayoLina's Mexican RestaurantSpectators (though their main menus are PDFs that actually have text) How wrong is this? Let me count the ways... You say you want people to be able to search your menu? Good luck (though someday the code that lets Google Translate read text from images may get good enough to deal with the wonky display fonts people tend to use on menus or text superimposed on food photos).You say you want search engines to find your restaurant's web site? Good luck again, though as above, maybe someday...You say you want your web site to support travelers…

No tutorial, I swear...

After grinding through much of the "20 Intermediate Exercises" and just about all of the Monad Challenges, Monads make much more sense to me.

Therefore, I will follow the excellent advice of Stephen Diehl, and will not write a monad-analogy tutorial. Instead, I will say: do the 20 Intermediate Exercises, and take the Monad Challenges. To paraphrase Euclid, there is no royal road to Monads; the exercises and challenges take you down that road at whose end you'll see at least part of why Monads are so useful.

If you were trying to learn group theory and people were standing around you saying "groups are like the integers",  "groups are like Rubik's Cube", "groups are like m x n matrices", "groups are like baryons and mesons", your situation would be much like the student of Haskell amidst all the monad analogy tutorials. In a sense they're backwards. All those things are groups, just as burritos et al. can at least be thought…

Flipping out

I came across the excellent Monad Challenges, a collection of exercises designed to take you through what have become some of the standard example monads and take you through the process that motivates monads as a way to handle these seemingly diverse data structures. Both the Monad Challenges and the 20 Intermediate Exercises are well worth your time. Doing them both is helping me a lot.

That said, they don't quite match up. 20IE's banana is flip bind and apple is flip ap. (This isn't unique; the also excellent Learning Haskell from first principles has as an exercise writing bind in terms of fmap and join, but the declaration it gives has the type of flip bind. The authors do point this out.) As a result, I find myself with something that there's got to be some way to simplify, of the form

foo = flip $ (flip mumble) . (flip frotz)

I'd like to think there's some sort of distributive-like law to be found and used here... watch this space.

Trust in Schönfinkel

I'm working through the "20 Intermediate Exercises" that give Functors and Monads and such cute, non-threatening names and ask you to implement them. I've gotten most of the way through, with three or four that I'm stuck on--that's under the assumption that the inductive step from banana to banana2 will make the rest of the banana<n> obvious. (If you have sausage, it's easy to implement moppy, and vice versa, but avoiding circularity is the issue.)

So... I did a Bad Thing and looked at solutions a couple of people have posted, saying to myself, "OK, I'll look at those I've already done with an eye to more elegant expression, and look at the ones I'm having issues with and make sure I understand"... and came face to face with a question about composition.

<andy_rooney>Didja ever notice that the examples of composition you see are what we think of as functions with one argument?</andy_rooney> Well, one of the solution…

Careful with that infinite list, Eugene...

Warning: this will give away one way to solve a certain low-numbered Project Euler problem.

Any Haskell book, blog, or tutorials you come across has a good chance of including the très élégant Haskell one-liner for an infinite list containing the Fibonacci sequence:

fibs = 0 : 1 : (zipWith (+) fibs (tail fibs))

Thanks to laziness, it will only evaluate out to the last term we actually request... that was, long ago, my downfall. I wanted the terms no bigger than four million, so

filter (<= 4000000) fibs

right? Wrong. You and I know that the Fibonacci sequence is monotonically increasing, but filter doesn't, and it doesn't even notice the particular function we're filtering with to realize it could terminate thanks to monotonicity. So instead,

takeWhile (<= 4000000) fibs

is the way to go.

The particular problem has an additional constraint, because it only wants the even terms of the sequence no bigger than four million. Easy enough to do, just feed it through

filter even

TMTOWTDI, Haskell Style

I assure you there will be no further allusions to Korean earworms. That said, on to the subject at hand...

Remember the exercise in the online Haskell course that had several tests to filter out weak passwords, all of which had to pass for the fictitious system to allow a String value to be used as a password? I wanted to make it easy to change, so I wanted to take a [String -> Bool] and get a [Bool] I could apply and to for the final thumbs up/thumbs down decision.

The first step: roll my own, which has a pleasing symmetry with map if you write it as a list comprehension:

wonkyMap fs x = [f x | f <- fs]

Then I stumbled across Derek Wyatt's blog post about using sequence for the purpose. Life was good... and then I got Haskell Programming from first principles, and life got better, because its authors do a very good job of explaining the Applicative type class. Applicative defines two functions, pure and (<*>):

class Functor f => Applicative f where
    pure  :: a -&g…