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CNth.hs

{-# LANGUAGE TemplateHaskell #-}
module CNth where
 
import Language.Haskell.TH
import Data.List
 
cnth :: Int -> Q Exp
cnth n = dotE qs
    where
      qs = head . reverse . take n . drop 1 $ ads
      ads = (inits . repeat) [car, cdr] >>= sequence
      car = [| head |]
      cdr = [| tail |]
 
-- Fold expression list with composition.
dotE :: [Q Exp] -> Q Exp
dotE [] = error "dotE: empty list"
dotE [f] = f
dotE (f:g:hs) = dotE ( [| $(f) . $(g) |] : hs )

ghci

*CNth> :t $(cnth 42)
<interactive>:1:3-9: Splicing expression
    cnth 42 ======> ((((head . tail) . head) . tail) . tail)
$(cnth 42) :: [[c]] -> c
 
*CNth> :t $(cnth 1)
<interactive>:1:3-8: Splicing expression
    cnth 1 ======> head
$(cnth 1) :: [a] -> a
 
*CNth> :t $(cnth 2)
<interactive>:1:3-8: Splicing expression
    cnth 2 ======> tail
$(cnth 2) :: [a] -> [a]
 
*CNth> :t $(cnth 3)
<interactive>:1:3-8: Splicing expression
    cnth 3 ======> (head . head)
$(cnth 3) :: [[c]] -> c
 
*CNth> :t $(cnth 4)
<interactive>:1:3-8: Splicing expression
    cnth 4 ======> (head . tail)
$(cnth 4) :: [c] -> c
 
*CNth> :t $(cnth 5)
<interactive>:1:3-8: Splicing expression
    cnth 5 ======> (tail . head)
$(cnth 5) :: [[a]] -> [a]
 
*CNth> :t $(cnth 6)
<interactive>:1:3-8: Splicing expression
    cnth 6 ======> (tail . tail)
$(cnth 6) :: [a] -> [a]
 
*CNth> :t $(cnth 7)
<interactive>:1:3-8: Splicing expression
    cnth 7 ======> ((head . head) . head)
$(cnth 7) :: [[[c]]] -> c
 
*CNth> :t $(cnth 8)
<interactive>:1:3-8: Splicing expression
    cnth 8 ======> ((head . head) . tail)
$(cnth 8) :: [[c]] -> c