1HaskellADay July 2014 problems and solutions

• July 1st, 2014: (text:) "Hi, all! @1HaskellADay problems are back! #YAY First (renewed) problem: a verbose way of saying, 'Give me a deque!' http://lpaste.net/106748" Deque, last, and all that (verbose version with hints) (solution: Deque the halls (with my solution): Data.Deque)
• July 2nd, 2014: (text:) "Today's Haskell exercise: Vectors, length in constant time, and (bonus) reverse return in constant time. http://lpaste.net/106843" Vector (solution: Vector: Magnitude, and Direction, OH, YEAH! Data.Vector)
• July 4th, 2014: (text:) "Today's exercise(s). pack/unpack. encode/decode. Cheer up, sweet B'Genes! http://lpaste.net/106912" Cheer up, Sweet B'Genes (solution: GATTACA)
• July 7th, 2014: (text:) "#haskell daily exercise: ROLL with it, Baby! http://lpaste.net/107047  ('cause I'm feeling a little #forth'y')" Roll (solution: Rollin' on the (finite) river)
• Bonus problem: July 7th, 2014: (text:) "For those who found the 'roll'-exercise trivial; here's (a more than) a bit more of a challenge for you to play with. http://lpaste.net/107023" Acid rules! (solution: "A solution set to today's challenge exercise: BASIC ... http://lpaste.net/107069  ... and Acidic http://lpaste.net/107071  ... WHEW! That was fun!" BASIC ... and Acitic)
• July 8th, 2014: (text:) "Today's #Haskell exercise: LOTTO! Powerball! Mega-whatever! Who's the big winner? http://lpaste.net/107104" Lotto (solution: "And the big winner today is ... solution-set to today's #Haskell lotto exercise http://lpaste.net/107130" ... and the winner is ...)
• Bonus problem: July 8th, 2014: (text:) "#bonus #haskell exercise: Well, that was RND... Randomness, and such (or 'as such') http://lpaste.net/107105" Well, that was RND (solution: For YESTERDAY's bonus question of roll-your-own-rnd-nbr-generator, here's one as comonadic cellular automata (*WHEW*) http://lpaste.net/107205: Data.Random)
• July 9th, 2014: (text:) "Okay, ... WHERE did yesterday and today GO? :/ #haskell exercise today: "Hey, Buddy!" http://lpaste.net/107181  I will post solution in 4 hours" Hey, Buddy! Distinct sets-of-an-original-set. (solution: "Here's a story ..." A(n inefficient) solution to bunches and cliques. http://lpaste.net/107273" Brady Bunch)
• July 10th, 2014: (text:) "Today's #haskell list-exercise: "Get out of the pool!" http://lpaste.net/107286  Will post a solution at 9 pm EDT (which is what time CET? ;)" (solution: "She's a supa-freak! She's supa-freaky! (Bass riff) A solution to today's #haskell exercise about list-length-ordering http://lpaste.net/107308")
• July 11th, 2014: (text:) ""It's Friday, Friday!" So, does that mean Rebecca Black wants to code #haskell, too? Today is a Calendar #exercise http://lpaste.net/107328" (solution: ""In a New York Minute": a solution to today's #haskell exercise that took WAAAY more than a minute to complete! #WHEW http://lpaste.net/107370")
• July 14th, 2014: (text:) "Today's #haskell exercise: isPrime with some numbers to test against. They aren't even really Mp-hard. ;) http://lpaste.net/107463" First stab at primality-test (solution: "A simple, straightforward stab at the test for primality. #haskell #exercise http://lpaste.net/107483" The start of a primal inquiry
• July 15th, 2014: (text:) "Primes and ... 'not-primes.' For a prime, p, a run of p-consecutive 'plain' numbers is today's #haskell exercise: http://lpaste.net/107536" (solution: "So ya gotta ask yerself da question: are ya feelin' lucky, punk? Run of p non-primes in linear time http://lpaste.net/107549  #haskell exercise." Alternate solution by Gautier: http://lpaste.net/107549)
• July 16th, 2014: (text:) "Difference lists? We no need no steenkin' Difference lists!" http://lpaste.net/107593  DList in #haskell for today's exercise. (solution: "DLists? We got'cher DList right here! A solution to today's #haskell exercise is posted at http://lpaste.net/107607")
• July 17th, 2014 (text:) "http://lpaste.net/107652 Prélude à l'après-midi d'un Stream ... I thought that last word was ... something else...? #haskell exercise today." Comonads for lists and Id. (solution: "Control.Comonad: That was easy! http://lpaste.net/107661 #haskell exercise #solution" Learn you a Comonad for Greater Good. Funny story, bro'! id is not necessarily Id. (I knew that.) http://lpaste.net/107662 #haskell solution")
• Bonus exercise: July 17th, 2014 (text:) "Streams are natural, streams are fun, streams are best when ... THEY'RE BONUS QUESTIONS! #bonus #haskell exercise http://lpaste.net/107655" LET'S GET THIS PARTY STARTED! (solution: "Take this Stream and ... it! #solution to today's #haskell #bonus exercises http://lpaste.net/107665")
• July 18th, 2014: (text: "Today's #haskell exercise: Frère Mersenne would like a prime, please. http://lpaste.net/107700") (see solution next bullet)
• Bonus exercise: July 18th, 2014 (text: "#bonus prime-time! Frère Mersenne would be pleased with a partial proof of a prime ... in good time. http://lpaste.net/107701") (solution: "A #haskell #solution for (monadic?) primes and the #bonus interruptible primes. http://lpaste.net/107708") Primary primes.
• Bonus-bonus exercise: July 18th, 2014 (text: "Ooh! π-charts! No. Wait. #bonus-bonus #haskell exercise. http://lpaste.net/107702") (solution: "#bonus-bonus: a #solution http://lpaste.net/107718")

• July 21st, 2014: (text: "Demonstrating coprimality of two integers with examples #haskell exercise http://lpaste.net/107819") (solution: "A coprimes solution #haskell problem is at http://lpaste.net/107843")
• July 22nd, 2014: (text: "The prime factors of a number (and grouping thereof) as today's #haskell exercise. http://lpaste.net/107878") (solution: "OKAY, THEN! Some prime factors for ya, ... after much iteration (torquing) over this #haskell exercise solution. http://lpaste.net/107939")
• Bonus exercise: July 22nd, 2014: ("For today's #bonus #haskell exercise you'll find a Bag 'o gold at the end of the rainbow http://lpaste.net/107881") (solution: "Second things first: a definition for the Bag data type as today's #bonus #haskell exercise. http://lpaste.net/107815")
• July 23rd, 2014: (text: "Today's #haskell exercise, two variations of Euler's totient function http://lpaste.net/107955") (solution: "And, for a very small φ ... http://lpaste.net/107972  is a solution-set to today's #haskell exercise.")
• July 24th, 2014: (text: "WEAKSAUCE! Goldbach's conjecture irreverently presented as a #haskell exercise. http://lpaste.net/108019") (solution: "That solution to today's #haskell exercise will cost you one Goldbach (*groan!*) http://lpaste.net/108059")
• July 25th, 2014: LOGIC! Peano series: it's as easy as p1, p2, p3 ... http://lpaste.net/108099 ... in today's #haskell exercise. "Excuse me, Miss, where do we put this Grande Peano?" A solution to today's #Haskell exercise in the HA!-DSL http://lpaste.net/108140
• Bonus: July 25th, 2014: http://lpaste.net/108108 Bonus #haskell problem for today. But not as easy as λa, λb, λc ... Church numerals and booleans. Correction: Ooh! forall! Church encodings and Haskell have a funny-kind of relationship. Updated the #bonus #haskell exercise with rank-types and forall. Solution: "Gimme that olde-time Church encoding ... it's good enough for me!" A solution to today's #bonus #haskell exercise http://lpaste.net/108114
• July 28th, 2014: George Boole, I presume? Today's #haskell exercise: http://lpaste.net/108272. Solution: This and-or That ... a NAND-implementation of today's #haskell exercise at http://lpaste.net/108295
• July 29th, 2014: Readin' 'Ritin' 'Rithmetic: today's #haskell exercise http://lpaste.net/108358 Solution: That's alotta NANDs! A solution to today's exercise at http://lpaste.net/108387
• July 30th, 2014: ACHTUNG! BlinkenLights! Today's #haskell exercise http://lpaste.net/108420. Solution: Let it Snow! Let it Snow! Let it (binary) Snow! A solution to today's exercise is at http://lpaste.net/108429 
• July 31st, 2014: π-time! http://lpaste.net/108485 Today's #haskell exercise. BLARG! UPDATE! Please read the update attached to the problem statement, simplifying the calculation quite a bit: http://lpaste.net/108485 Solution: Apple or coconut π? A solution to today's problem http://lpaste.net/108494

Notes on the problems

• July 9th, 2014. I didn't quite know how to go about this, so I made several attempts with the State pattern. But how to describe it? It's the base pool from which you draw, and each (sub-)choice-point affects it, what's that type? I spent way too much time trying to discern the type, and failing. But now, a much simpler approach suggests itself to me (after experiencing the New York Minute exercise): this is simply a permutation of the list, and then that permutation is partitioned by the sizes of the groups! Implementing permute-then-partition is a much simpler approach than tracking some monster monadic state transformer.
  
  No, that didn't work, either. A permutation will give you [[1,2], ...] and[[2,1], ...] That is, all solutions, even the redundant ones. So, I reworked the problem simply following the data. With takeout feeding the iterative-deepening function, I finally got a guarded state-like thingie working fast and correctly. The new solution is on the same page as the old one.
• July 11th, 2014. The New York Minute problem demonstrates the implementation of a rule-based classifer. It takes unclassified numeric inputs, and based on the cues from the rules, either types each number into day, month, year, hour, minute, or rejects the input data as unclassifiable. I was pleased to have implemented this entire system in less than two days of work! Sweet!
• July 22nd, 2014. So, I've been running up against the double-exponential cost of computing a stream of primes for some time now since I gave the solution to the question of demonstrating the Prime Number Theorem. So now I have to tackle of bringing down that extraordinary, or unreasonable, cost down to something useable, and along those lines (of feasibility), I'm thinking of instead of regenerating and re-searching the primesish stream that we have some kind of State-like thing of ([already generated primes], indexed-primesish) ... something like that. Solution: "General improvement of problem-solving modules in anticipation of solving today's #haskell exercise, including primes: http://lpaste.net/107480"