-- Solve the n-queens puzzle with the quantification pattern
-- Sergio and Michael
-- Mon Apr 18 14:23:56 PDT 2011

import Combinatorial
import Quantification
import SetFunctions
import Integer

distElem (_++[x]++_++[z]++_) = (x,z)
placement n = zip [1..n] (permute [1..n])
capture (r1,c1) (r2,c2) 
  = r1 == r2 || c1 == c2 || abs(r1-r2) == abs(c1-c2)

queens n | exists r (\p -> 
              notExists (set1 distElem p) (\(x,y) -> capture x y))
         = r
         where r = placement n