Simple solver for the n-queens problem in Curry

gistfile1.hs

-- Simple solver for the n-queens problem in Curry.
--
-- A placement is represented as permutation of [1..n], each list
-- element represents the placement of a queen in the column
-- corresponding to its index.

import Integer ( abs )

-- Solutions are computed using a lazy generate-and-test approach:
-- candidate solutions are created lazily and admissible solutions
-- filtered out using a guard.
--
queens :: Int -> [Int]
queens n | safe qs = qs
  where qs = permute [1..n]

-- As queens are placed in different rows and columns automatically,
-- we only check that they don't capture each other diagonally.
--
safe :: [Int] -> Bool
safe qs = and [ j-i /= abs (q_j-q_i) | (i,q_i) <- iqs, (j,q_j) <- iqs, i < j ]
  where iqs = zip [1..] qs

-- Candidate solutions are computed using a non-deterministic
-- operation to permute a list.
--
permute :: [a] -> [a]
permute []      = []
permute (x:xs)  = insert x (permute xs)

insert :: a -> [a] -> [a]
insert x l       = x : l
insert x (y:ys)  = y : insert x ys