Should be correct, but takes so long to compile that I have no idea if it actually works.

type-fizzbuzz.hs

{-# OPTIONS_GHC -Wno-unticked-promoted-constructors -freduction-depth=0 #-}
{-# LANGUAGE AllowAmbiguousTypes #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE ExplicitForAll #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}

import GHC.TypeLits

type m `Divides` n = (m `Mod` n) == 0

type family Range l h where
  Range l h = If (l <=? h) (l : Range (l+1) h) '[]

type family (==) (x :: k) (y :: k) :: Bool where
  x == x = True
  _ == _ = False

type family If p thn els where
  If True thn _ = thn
  If False _ els = els

-------------------------------------------------------------------------------

type family FizzBuzzOnce (assocs :: [(Nat, Symbol)]) (n :: Nat) :: ErrorMessage where
  FizzBuzzOnce '[]           n = ShowType n
  FizzBuzzOnce ('(m, sym):as) n = If (m `Divides` n) (FizzBuzzHelper as n (Text sym)) (FizzBuzzOnce as n)

type family FizzBuzzHelper (assocs :: [(Nat, Symbol)]) (n :: Nat) (acc :: ErrorMessage) :: ErrorMessage where
  FizzBuzzHelper '[] _ acc = acc
  FizzBuzzHelper ('(m, sym):as) n acc = FizzBuzzHelper as n (If (m `Divides` n) (Text sym :<>: acc) acc)

type family FizzBuzzAll (assocs :: [(Nat, Symbol)]) (ns :: [Nat]) :: ErrorMessage where
  FizzBuzzAll as '[] = Text "-- Done."
  FizzBuzzAll as (n : ns) = FizzBuzzOnce as n :$$: FizzBuzzAll as ns

class FizzBuzzInst as ns where
  doFizzBuzz :: forall xx. xx
  doFizzBuzz = undefined

instance TypeError (FizzBuzzAll as ns) => FizzBuzzInst as ns

-------------------------------------------------------------------------------

main = doFizzBuzz @[(3, "Fizz"), (5, "Buzz")] @(Range 1 100)