{-# LANGUAGE TemplateHaskell, ConstraintKinds #-}
module Acme.NumberSystem where

import GHC.TypeLits
import Language.Haskell.TH

type Less = (<=)

-- | Define the less than relation for numbers up to a number using Template Haskell.
-- | E.g. numberSystem 100
numberSystem :: Integer -> Q [Dec]
numberSystem theBiggestNumber = return . concat $ map (\i -> map (\j ->
      InstanceD [] (AppT (AppT (ConT (''Less)) (LitT (NumTyLit i))  ) (LitT (NumTyLit j))) []
      ) [i..theBiggestNumber]) [1..theBiggestNumber]