(def rot ((x . y)) (join y `(,x)))

  (def nqueens (n)
    (withs (m (mod n 12) r (range 1 n) od (keep odd r) cod (cddr od) s '(1 3) cods (join cod s) ev (keep even r))
      (join (if (pos m '(3 9)) (rot ev) ev)
            (case m
              8 (apply join (map rev (pair od)))
              2 (join (rev s) (rot cod))
              3 cods
              9 cods
              od))))

  (join 1 '(2 3 4) 5 '(6 7 8) 9)
  => (1 2 3 4 5 6 7 8 9)

  (join 1 '(2 3 4) 5 '(6 7 8) 9)

  (flat:list 1 '(2 3 4) 5 '(6 7 8) 9)

  arc> (nqueens 8)
  (2 4 6 8 3 1 7 5)  
  arc>

  class Array
    def rot
      push( shift )
    end
  end

  nqueens = proc{|n|
    odds, evens = (1..n).partition{|x| x % 2 > 0 }
    case n % 12
      when 2
        odds = [3,1] + odds[3..-1] + [5]
      when 3, 9
        odds.rot.rot
        evens.rot
      when 8
        d = -2
        odds.map!{|x| d *= -1; x + d}
    end
    p evens + odds
  }

  nqueens[8]

  class Array
    def rot
      push( shift )
    end
  end

  proc{|n| p ((1..n).partition{|x|x%2>0}.inject{|o,e|
    e + case n % 12
      when 2
        [3,1]+o[3..-1]+[5]
      when 3,9
        o.rot.rot;e.rot;o
      when 8
        d=-2;o.map{|x| x + d*=-1} end})}[ 8 ]

  (def rot ((x . y)) (join y `(,x)))

  (def nqueens (n)
    (withs (m (mod n 12) r (range 1 n) od (keep odd r) cod (cddr od) s '(1 3) ev (keep even r))
           (if (join (pos m '(3 9)) (rot ev) (join cod s))
               (join ev (case m 8 (apply join (map rev (pair od)))
                                2 (join (rev s) (rot cod))
                                od)))))

  (def rot ((x . y)) (join y `(,x)))

  (def nqueens (n)
    (withs ((od ev) (part odd (range 1 n)) cod (cddr od) s '(1 3))
           (join ev (case (mod n 12) 8    (apply join (map rev (pair od)))
                                     2    (join (rev s) (rot cod))
                                     3, 9 (do (zap (rot ev)) (join cod s))
                                     od))))

      else
       o

  (def rot ((x . y)) (join y `(,x)))


  (def nqueens (n)
    (withs (r (range 1 n) o (keep odd r) e (keep even r) m (mod n 12))
      (if (pos m '(3 9)) (= m -1))
      (join (if (is m -1) (rot e) e)
        (case m
          2 (join '(3 1) (cut o 3 -1) '(5))
          8 (flat:map rev (pair o))
          -1 (rot:rot o)
          o))))

  (def rot ((x . y)) (join y `(,x)))
  (def nqueens (n)
    (withs (r (range 1 n) o (keep odd r) e (keep even r) m (mod n 12))
      (join (if (pos m '(3 9))(or wipe.m rot.e) e)
        (case m
          2 (flat:list 3 1 (cut o 3 -1) 5)
          8 (flat:map rev pair.o)
          nil (rot:rot o)
          o))))

Edit: using "flat:list" for case 2.

For this challenge, it's important to have the output match exactly - that's why the rev is necessary and the complicated print. I do string interpolation all the time in Ruby, so I wanted to see how easy/hard it was in Arc to produce lines such as [ 1, 5, 8, 6, 3, 7, 2, 4 ]

I might as well limit the code to ArcN also.

I think the following may be the only working version of Arc code that passes this challenge so far.

Having to use point is a bit awkward, but not too bad. I particularly like the function composition such as abs:- and the more concise len.stack notation. The [ string sep _ ] notation is definitely a winner also. I'm pretty pleased with the core language so far - kudos to pg & rm.

  (def valid? (stack)
    (let q2 0
      (point return
             (each q1 (range 1 (- len.stack 1))
                   (if (or (is stack.q1 stack.q2)
                           (is (abs:- q1 q2) (abs:- stack.q1 stack.q2)))
                       (return nil)))
             t)))

  (def joinstr (lst (o sep " "))
    (if lst
        (string (car lst) (apply string (map [string sep _] (cdr lst))))
        ""))

  (def queens (stack n)
    (if (is n 8)
        (prn "[ " (joinstr (rev stack) ", ") " ]")
        (each rank (range 1 8)
              (push rank stack)
              (if (valid? stack)
                  (queens stack (+ n 1)))
              (pop stack))))

  (queens '() 0)

  arc> (queens '() 0)
  [ 1, 5, 8, 6, 3, 7, 2, 4 ]
  [ 1, 6, 8, 3, 7, 4, 2, 5 ]
  [ 1, 7, 4, 6, 8, 2, 5, 3 ]
  [ 1, 7, 5, 8, 2, 4, 6, 3 ]
  [ 2, 4, 6, 8, 3, 1, 7, 5 ]
  ...
  [ 8, 3, 1, 6, 2, 5, 7, 4 ]
  [ 8, 4, 1, 3, 6, 2, 7, 5 ]

  (def valid? (stack)
    (let i 0
      (if (or (pos stack.0 cdr.stack)
              (some (fn(x)(++ i)(is i (abs:- x stack.0))) cdr.stack))
        nil
        t)))

  (def queens (stack n)
    (if (is n 8)
      (and (prall rev.stack "[ ") (prn " ]"))
      (for rank 1 8
        (push rank stack)
        (if (valid? stack)
            (queens stack (+ n 1)))
        (pop stack))))

  (queens '() 0)

  (def valid? (stack)
    (let i 0
      (if (or (pos stack.0 cdr.stack)
              (some [do (++ i) (is i (abs:- _ stack.0))] cdr.stack))
        nil
        t)))

  (def valid? (stack)
    (let i 0
      (if (or (pos stack.0 cdr.stack)
              (some [is ++.i (abs:- stack.0 _)] cdr.stack))
        nil
        t)))

  (def queens (stack n)
    (if (is n 8)
      (do (prall rev.stack "[ ") (prn " ]"))
      (for rank 1 8
        (push rank stack)
        (if (valid? stack)
            (queens stack (+ n 1)))
        (pop stack))))

  (queens '() 0)

  arc> (help prall)
  (from "arc.arc")
  [fn]  (prall elts (o init ) (o sep , ))
   Prints several arguments with an initial header and separated by a
      given separator. 

Instead of (point return ...(return ...)) try using (catch ...(throw ...)).

  arc> (help prall)
  Error: "reference to undefined identifier: _help"

  #!/usr/bin/env escript
  
  -import(lists, [seq/2, reverse/1]).
  
  main([]) ->
     lists:foreach(fun(L) ->
                         io:format("[ ~s ]~n",
                                   [string:join(
                                      [ integer_to_list(I)
                                        || I <- L ], ", ")])
                   end, queens([], 0)).
                         
  
  threatens(Q, _, [Q|_], _) -> true;
  threatens(_, _, [], 0) -> false;
  threatens(Q, I, [Q2|Queens], I2) ->
     if
        abs(I - I2) =:= abs(Q2 - Q) -> true;
        true -> threatens(Q, I, Queens, I2 - 1)
     end.
  
  is_valid([Q|Queens]) ->
     TL = length(Queens),
     not threatens(Q, TL + 1, Queens, TL).
  
  queens([], _) -> queens([ [X] || X <- seq(1, 8) ], 8);
  queens(Tree, 1) -> Tree;
  queens(Tree, Place) ->
     queens([ [N|Node] || N <- seq(1, 8),
                          Node <- Tree,
                          is_valid([N|Node]) ],
            Place - 1).

I prefer the word encourage :) I know it's nitpicky, but the idea was to not simply use a native print. Of course, had I required the 'pp' Ruby lib, I could have just said:

  pp stack   # => [ 1, 2, 3, ... , 8 ]

Your point is my point. I wanted to see how well Arc handles formatting something that didn't fit neatly into an expected pattern.

Ruby has several formatting techniques that are quite nice:

1) String interpolation. You can insert an expression into a spring by using #{expression}

2) String formatting. You can use sprintf style patterns in strings via format or the % operator. For example:

  puts "%4.1f hours" % hours
  puts "%4.1f hours and %4.1f minutes" % [hours, minutes]

  (def valid (stack)
    (with (q2 (- len.stack 1)
           result t)
      (each q1 (range 0 (- len.stack 2))
        (= result (and result
                       (isnt stack.q1 stack.q2)
                       (isnt (abs:- q1 q2) (abs:- stack.q1 stack.q2))))))

  (def queens (stack n)
    (if (is n 8)
      (prn stack)
      (each rank (range 1 8)
        (push rank stack)
        (if (valid stack)
          (queens stack (+ n 1)))
        (pop stack))))

  (queens '() 0)

  (def valid (stack)
    (breakable:let q2 (- len.stack 1)
      (each q1 (range 0 (- len.stack 2))
        (if (or (is stack.q1 stack.q2) (is (abs:- q1 q2) (abs:- stack.q1 stack.q2)))
          (break nil)))
      (break t)))

  def a:
    for i in (1, 2, 3):
      if i < 2:
        return i

    return None

  (def a (return)
    (each i '(1 2 3)
      (if (< i 2)
        (return i)))
    nil)

  arc> (ccc a)
  1

  (def a ()
    (point return
      (each i '(1 2 3)
        (if (< i 2)
          (return i)))
      nil)))

Apparently folks have fixated on a particular algorithm in the wikipedia article. I only linked there for a general description of the problem. Instead, I should have simply said, "write a program that produces all the solutions to the problem of placing 8 queens on a chess board so that no queen is attacking any other queen and prints the solutions as follows (i.e. the output in the OP)"

  def valid? stack
    q2 = stack.size - 1
    q2.times { |q1|
      return nil if stack[q1] == stack[q2] or (q1-q2).abs == (stack[q1]-stack[q2]).abs
    }
  end

  def queens stack, n
    if n == 8
      p stack
    else
      (1..8).each do |rank|
        stack.push(rank)
        queens(stack, n+1) if valid?(stack)
        stack.pop
      end
    end
  end

  queens [], 0