Haskell type-level fizzbuzz, version 2

FizzBuzz_2.hs

{-# LANGUAGE FlexibleContexts       #-}
{-# LANGUAGE FlexibleInstances      #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE UndecidableInstances   #-}


-- no data kinds, pure type level
-- let's start by defining booleans and numbers

data True
data False

data PZ
data PS n
type P1  = PS PZ
type P2  = PS P1
type P3  = PS P2
type P4  = PS P3
type P5  = PS P4
type P6  = PS P5
type P7  = PS P6
type P8  = PS P7
type P9  = PS P8
type P10 = PS P9
type P11 = PS P10
type P12 = PS P11
type P13 = PS P12
type P14 = PS P13
type P15 = PS P14
type P16 = PS P15


-- type level functions: can a peano number be divided by 3 or 5?

class D3 n b | n -> b
instance D3 PZ True
instance D3 P1 False
instance D3 P2 False
instance D3 n b => D3 (PS (PS (PS n))) b

class D5 n b | n -> b
instance D5 PZ True
instance D5 P1 False
instance D5 P2 False
instance D5 P3 False
instance D5 P4 False
instance D5 n b => D5 (PS (PS (PS (PS (PS n))))) b


-- three new possible types, for our fizzbuzz values

data Fizz
data Buzz
data FizzBuzz


-- simple type-level mapping between our boolean types to a type-level fizzbuzz value

class GetFizzBuzz n b3 b5 v | n b3 b5 -> v
instance GetFizzBuzz n False False n
instance GetFizzBuzz n False True  Fizz
instance GetFizzBuzz n True  False Buzz
instance GetFizzBuzz n True  True  FizzBuzz


-- convenience function
-- use it in GHCI:
--   :t fb (undefined :: P12)

class FB n v | n -> v where
  fb :: n -> v
instance (D3 n b3, D5 n b5, GetFizzBuzz n b3 b5 v) => FB n v where
  fb = undefined