----------------------------------------------------------------------------
--- Computing magic series.
--- A series [a_0,a_1,....,a_(n-1)] is called magic iff there are
--- a_i occurrences of i in this series, for all i=1,...,n-1
---
--- Adapted from an example of the TOY(FD) distribution.
----------------------------------------------------------------------------

import CLP.FD

--- Computes a magic series of the length of the argument.
magic :: Int -> [Int]
magic n =
 let vs = take n (domain 0 (n-1))  -- FD variables
     is = map fd (take n [0..])    -- FD constants: indices of elements
 in solveFD [FirstFail] vs $
      constrain vs vs is /\
      sum vs Equ (fd n) /\
      scalarProduct is vs Equ (fd n)

constrain :: [FDExpr] -> [FDExpr] -> [FDExpr] -> FDConstr
constrain []     _  _      = true
constrain (x:xs) vs (i:is) = count i vs Equ x /\ constrain xs vs is

--- The infinite sequence of magic series of increasing lengths.
magicFrom :: Int -> [[Int]]
magicFrom n = magic n : magicFrom (n+1)

--- Returns 3 magic series of increasing lengths starting with length 7.
main :: [[Int]]
main = take 3 (magicFrom 7)
--> [[3,2,1,1,0,0,0],[4,2,1,0,1,0,0,0],[5,2,1,0,0,1,0,0,0]]