```module Music.Theory.Bjorklund (bjorklund,xdot,iseq,iseq_str) where

{-
Godfried T. Toussaint et. al.
"The distance geometry of music"
Journal of Computational Geometry: Theory and Applications
Volume 42, Issue 5, July, 2009
doi>10.1016/j.comgeo.2008.04.005
-}

import Data.List.Split

type STEP a = ((Int, Int), ([[a]], [[a]]))

left :: STEP a -> STEP a
left ((i,j),(xs,ys)) =
let (xs',xs'') = splitAt j xs
in ((j,i-j),(zipWith (++) xs' ys, xs''))

right :: STEP a -> STEP a
right ((i,j),(xs,ys)) =
let (ys',ys'') = splitAt i ys
in ((i,j-i),(zipWith (++) xs ys', ys''))

bjorklund' :: STEP a -> STEP a
bjorklund' (n,x) =
let (i,j) = n
in if min i j <= 1
then (n,x)
else bjorklund' (if i > j then left (n,x) else right (n,x))

bjorklund :: (Int, Int) -> [Bool]
bjorklund (i,j') =
let j = j' - i
x = replicate i [True]
y = replicate j [False]
(_,(x',y')) = bjorklund' ((i,j),(x,y))
in concat x' ++ concat y'

xdot :: [Bool] -> String
xdot = map (\x -> if x then 'x' else '.')

iseq :: [Bool] -> [Int]
iseq = let f = split . keepDelimsL . whenElt
in tail . map length . f (== True)

iseq_str :: [Bool] -> String
iseq_str = let f xs = "(" ++ concatMap show xs ++ ")"
in f . iseq

{-
xdot (bjorklund (5,9))
iseq_str (bjorklund (5,9))

let es = [(2,3),(2,5)
,(3,4),(3,5),(3,8)
,(4,7),(4,9),(4,12),(4,15)
,(5,6),(5,7),(5,8),(5,9),(5,11),(5,12),(5,13),(5,16)
,(6,7),(6,13)
,(7,8),(7,9),(7,10),(7,12),(7,15),(7,16),(7,17),(7,18)
,(8,17),(8,19)
,(9,14),(9,16),(9,22),(9,23)
,(11,12),(11,24)
,(13,24)
,(15,34)]
in map (\e -> let e' = bjorklund e in (e,xdot e',iseq_str e')) es

=>

[((2,3),"xx.","(12)")
,((2,5),"x.x..","(23)")
,((3,4),"xxx.","(112)")
,((3,5),"x.x.x","(221)")
,((3,8),"x..x..x.","(332)")
,((4,7),"x.x.x.x","(2221)")
,((4,9),"x.x.x.x..","(2223)")
,((4,12),"x..x..x..x..","(3333)")
,((4,15),"x...x...x...x..","(4443)")
,((5,6),"xxxxx.","(11112)")
,((5,7),"x.xx.xx","(21211)")
,((5,8),"x.xx.xx.","(21212)")
,((5,9),"x.x.x.x.x","(22221)")
,((5,11),"x.x.x.x.x..","(22223)")
,((5,12),"x..x.x..x.x.","(32322)")
,((5,13),"x..x.x..x.x..","(32323)")
,((5,16),"x..x..x..x..x...","(33334)")
,((6,7),"xxxxxx.","(111112)")
,((6,13),"x.x.x.x.x.x..","(222223)")
,((7,8),"xxxxxxx.","(1111112)")
,((7,9),"x.xxx.xxx","(2112111)")
,((7,10),"x.xx.xx.xx","(2121211)")
,((7,12),"x.xx.x.xx.x.","(2122122)")
,((7,15),"x.x.x.x.x.x.x..","(2222223)")
,((7,16),"x..x.x.x..x.x.x.","(3223222)")
,((7,17),"x..x.x..x.x..x.x.","(3232322)")
,((7,18),"x..x.x..x.x..x.x..","(3232323)")
,((8,17),"x.x.x.x.x.x.x.x..","(22222223)")
,((8,19),"x..x.x.x..x.x.x..x.","(32232232)")
,((9,14),"x.xx.xx.xx.xx.","(212121212)")
,((9,16),"x.xx.x.x.xx.x.x.","(212221222)")
,((9,22),"x..x.x..x.x..x.x..x.x.","(323232322)")
,((9,23),"x..x.x..x.x..x.x..x.x..","(323232323)")
,((11,12),"xxxxxxxxxxx.","(11111111112)")
,((11,24),"x..x.x.x.x.x..x.x.x.x.x.","(32222322222)")
,((13,24),"x.xx.x.x.x.x.xx.x.x.x.x.","(2122222122222)")
,((15,34),"x..x.x.x.x..x.x.x.x..x.x.x.x..x.x.","(322232223222322)")]

-}
```