The guys on Haskell Cafe delight in complex problems (and solutions). There's a list for beginners, too.

You will enjoy the Haskell Cafe later.

By the way, one small exercise (from a paper by Chris Okasaki): Write a function with the type

  Tree a -> Tree Int

where

  data Tree a = Node a (Tree a) (Tree a) | Empty

your function should all nodes in a tree with their position in level order traversal (also called breadth first search). E.g. (lot == lever order traversal)

  lot Empty = Empty
  lot (Node 'a' (Node 'b' Empty (Node 'c' Empty Empty))
                (Node 'd' Empty Empty)) =
      (Node '0' (Node '1' Empty (Node '3' Empty Empty))
                (Node '2' Empty Empty))

The thing with RWH I found was, chapters 1-4 great, a nice introduction to the language, and I did all the exercises without too much head-scratching. Then chapter 5 is utterly incomprehensible. I didn't get any further.

OCaml, that's a nice language, with much better introductary materials.

Dont' give up:

http://www.amazon.com/Programming-Haskell-Graham-Hutton/dp/0...

http://stackoverflow.com/questions/1012573/how-to-learn-hask...

http://learnyouahaskell.com/

What did you find so hard about chapter 5 ("Writing a library: working with JSON data")? Doesn't seem too be such a big step up to me in comparison to other chapters in the book?

I can actually read some of the syntax. I guess that a mathematical background helps when you're accustomed to seeing function definitions that map one real to another real or some of the other constructs. And I certainly recognize interfaces from Java (and why they can be a lot nicer than C++ style inheritance).

What still gets me are some of the basic functional programming concepts like monads and the y combinator, which obviously aren't unique to Haskell. Yeah, I've read Wikipedia on both of those (more than once). And several other things. I've even written some Lisp for my employer. But some of the concepts have yet to "click." I know monads encapsulate side effects or something (and the y combinator finds the fixed points of a function), but I feel like I just don't get the details of how it works.

After all, you don't need to know anything about monads to call the print function.

Monads are easy to understand: A monad is exactly anything that satisfies the three monad laws.

If you have worked with mathematical groups and have seen how mathematicians can look at very disparate things with their group-goggles and find similarities, you will appreciate monads.

The y combinator is a nice parlour trick (if you define it in lambda calculus without using any other recursion primitives), and research vehicle. But I did not apply it once, yet. And I've tried.

If you want to get combinatorial logic (including the y combinator), read "To Mock a Mockingbird". And do all the puzzles, of course. Actually you should read it, whether you want to learn anything about combinatorial logic or not. It is such a good book.

Thanks, I'll read that.

> I still find predicting memory/time use under a lazy-evaluation regime difficult.

It's not just you. Lazy evaluation makes predicting and understanding resource usage difficult.

Indeed. And that's the major shortcoming I see that could prevent me from using Haskell in a production environment.

The guys who wrote XMonad got around it, so it is possible. You just need to be careful, and use enough strictness annotations.

Laziness is one of those features I can never make my mind up about. It is sometimes very convenient, but most of the time I never think about the fact that the semantics mean evaluation is lazy. Sometimes this negligence has bad consequences, and then one must invoke a carefully honed skill to correct the issue. Definitely doable, but it certainly feels like fighting the language (to me, anyway).

One of the craziest things is that Haskell has decided that type families should also be lazily evaluated. So you can hop into the interactive interpreter to inspect some types and get not-so-useful information, like

    somevar :: SomeTypeFunction (SomeTypeFunction2 Int) (SomeTypeFunction3 (SomeTypeFunction 3 (SomeTypeFunction3 String)))

which might actually evaluate to something simple like (String, Int), though you wouldn't know it without either tracing through the functions (yuck!) or writing some silly helper functions whose sole job is to force evaluation of the type functions (yuck!). I've never personally been thankful for this behavior.

Interesting. I'll try to reproduce your example. Could you make something up that I can just copy-and-paste into ghci? Thanks!

Chris Okasaki argues in "Purely Functional Data Structures" for making lazy evaluation optional, but easy to use. Some data structures have optimal asymptotics only when evaluated strictly and some only when evalutated lazily.

With better strictness analysers most of the problems lazyness is causing at the moment, may go away. A Haskell compiler is free to make your program (or parts of it) strict, if it can prove that this preserves semantics.

Here's some code:

  {-# LANGUAGE
          TypeFamilies,
          MultiParamTypeClasses,
          FlexibleInstances #-}

  data True = T
  data False = F

  class LogicOr a b where
    type Or a b
    typeOr :: a -> b -> Or a b
  instance LogicOr True b where
    type Or True b = True
    typeOr T b = T
  instance LogicOr a True where
    type Or a True = True
    typeOr b T = T
  instance LogicOr False False where
    type Or False False = False
    typeOr F F = F

  class Decide tf a b where
    type If tf a b
    nonFunctionalIf :: tf -> a -> b -> If tf a b
  instance Decide True a b where
    type If True a b = a
    nonFunctionalIf T a b = a
  instance Decide False a b where
    type If False a b = b
    nonFunctionalIf F a b = b

  whatIsMyType tf1 tf2 a b = nonFunctionalIf (typeOr tf1 tf2) a b

If we load this into ghci, we have the following example:

  *Main> :t whatIsMyType F F 2 "foo"
  whatIsMyType F F 2 "foo" :: (Num t) => If (Or False False) t [Char]
  *Main> :t whatIsMyType F F 2 "foo" :: String
  whatIsMyType F F 2 "foo" :: String :: String

In the first :t, ghci lazily (though correctly) gives us the type of whatIsMyType. In the second example, where we provide an explicit type annotation, ghci is able to (correctly) conclude that our annotation was correct by evaluating the various type functions it had given us before.

Thanks. I can reproduce your example.

I am still learning Haskell but I thought things like foldl' and Iteratees allow you to use strict evaluation when it is appropriate.

For List-like structures getting stuff strict enough isn't too much of a problem. But not everything is a simple fold.