PureScriptで型レベルFizzBuzz(Type-level FizzBuzz)
52943 ワード
はじめに
型レベルでFizzBuzzを書きました。言語はPureScriptです。
型レベル自然数を用意する
foreign import kind Nat
foreign import data Zero :: Nat
foreign import data Succ :: Nat -> Nat
data NProxy (n :: Nat) = NProxy
class Nat (n :: Nat) where
toInt :: NProxy n -> Int
instance natZero :: Nat Zero where
toInt _ = 0
instance natSucc :: Nat n => Nat (Succ n) where
toInt _ = 1 + toInt (NProxy :: NProxy n)
大きな数を少ないタイプ数で利用できるように、以下のようなクラスも定義しておきます。
class Succ10 (n :: Nat) (n' :: Nat) | n -> n'
instance succ10 :: Succ10 n (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ n))))))))))
class Succ50 (n :: Nat) (n' :: Nat) | n -> n'
instance succ50 :: (Succ10 n n1, Succ10 n1 n2, Succ10 n2 n3, Succ10 n3 n4, Succ10 n4 n5) => Succ50 n n5
class Succ100 (n :: Nat) (n' :: Nat) | n -> n'
instance succ100 :: (Succ50 n n', Succ50 n' n'') => Succ100 n n''
class Succ200 (n :: Nat) (n' :: Nat) | n -> n'
instance succ200 :: (Succ100 n n', Succ100 n' n'') => Succ200 n n''
class Succ300 (n :: Nat) (n' :: Nat) | n -> n'
instance succ300 :: (Succ200 n n', Succ100 n' n'') => Succ300 n n''
class Succ400 (n :: Nat) (n' :: Nat) | n -> n'
instance succ400 :: (Succ300 n n', Succ100 n' n'') => Succ400 n n''
class Succ500 (n :: Nat) (n' :: Nat) | n -> n'
instance succ500 :: (Succ400 n n', Succ100 n' n'') => Succ500 n n''
これで、型レベルの数を表したいときには以下のように書くことができます。
10の場合
NProxy :: forall n. Succ10 Zero n => NProxy n
50の場合
NProxy :: forall n. Succ50 Zero n => NProxy n
100の場合
NProxy :: forall n. Succ100 Zero n => NProxy n
...
500の場合
NProxy :: forall n. Succ500 Zero n => NProxy n
REPLで試してみます。
> toInt (NProxy :: forall n. Succ10 Zero n => NProxy n)
10
> toInt (NProxy :: forall n. Succ50 Zero n => NProxy n)
50
> toInt (NProxy :: forall n. Succ100 Zero n => NProxy n)
100
...
> toInt (NProxy :: forall n. Succ500 Zero n => NProxy n)
500
型レベルBooleanを用意する
foreign import kind Boolean
foreign import data True :: Boolean
foreign import data False :: Boolean
data BProxy (b :: Boolean) = BProxy
3か5(もしくはその両方)で割り切れるかどうかを調べる
上で用意したBooleanを使います。割り切れたらTrue、割り切れなければFalseを返します。
class IsMod3 (n :: Nat) (b :: Boolean) | n -> b
instance isMod3 :: IsMod3 n b => IsMod3 (Succ (Succ (Succ n))) b
else instance isMod3' :: IsMod3 Zero True
else instance isnotMod3 :: IsMod3 n False
class IsMod5 (n :: Nat) (b :: Boolean) | n -> b
instance isMod5 :: IsMod5 n b => IsMod5 (Succ (Succ (Succ (Succ (Succ n))))) b
else instance isMod5' :: IsMod5 Zero True
else instance isnotMod5 :: IsMod5 n False
5（または3）を減算しながら再帰し、Zeroになったら余りがなかったのでTrueを返します。5（または3）の減算ができずZeroにもならなかった場合、余りが出ているのでFalseを返します。
FizzかBuzzかFizzBuzzか数字かを判定する
上で定義したIsMod3とIsMod5を使います。
foreign import kind Result
foreign import data Fizz :: Result
foreign import data Buzz :: Result
foreign import data FizzBuzz :: Result
foreign import data Number :: Result
data RProxy (r :: Result) = RProxy
class Judge (n :: Nat) (r :: Result) | n -> r
instance judgeByPattern :: (IsMod3 n b3, IsMod5 n b5, JudgeByPattern b3 b5 r) => Judge n r
judge :: forall n r. Nat n => Judge n r => NProxy n -> RProxy r
judge _ = RProxy
class JudgeByPattern (fb :: Boolean) (bb :: Boolean) (r :: Result) | fb bb -> r
instance judgeFizz :: JudgeByPattern True False Fizz
instance judgeBuzz :: JudgeByPattern False True Buzz
instance judgeFizzBuzz :: JudgeByPattern True True FizzBuzz
instance judgeNumber :: JudgeByPattern False False Number
入力された自然数を基に、IsMod3とIsMod5のそれぞれから返ってきた値を使ってパターンマッチします。
- IsMod3のみTrueの場合→Fizz
- IsMod5のみTrueの場合→Buzz
- 両方Trueの場合→FizzBuzz
- 両方Falseの場合→Number
FizzやBuzzを表示できるようにする
型から文字列への変換です。
class ShowFizzBuzz (r :: Result) where
show :: RProxy r -> Int -> String
instance showFizz :: ShowFizzBuzz Fizz where
show _ _ = "Fizz"
instance showBuzz :: ShowFizzBuzz Buzz where
show _ _ = "Buzz"
instance showFizzBuzz :: ShowFizzBuzz FizzBuzz where
show _ _ = "Fizz-Buzz"
instance showNumber :: ShowFizzBuzz Number where
show _ = S.show
REPLで試してみます。
> show (RProxy :: (forall r. Judge (Succ Zero) r => RProxy r)) (toInt (NProxy :: NProxy (Succ Zero)))
"1"
> show (RProxy :: (forall r. Judge (Succ (Succ Zero)) r => RProxy r)) (toInt (NProxy :: NProxy (Succ (Succ Zero))))
"2"
> show (RProxy :: (forall r. Judge (Succ (Succ (Succ Zero))) r => RProxy r)) (toInt (NProxy :: NProxy (Succ (Succ (Succ Zero)))))
"Fizz"
> show (RProxy :: (forall n r. Succ10 Zero n => Judge n r => RProxy r)) (toInt (NProxy :: forall n. Succ10 Zero n => NProxy n))
"Buzz"
> show (RProxy :: (forall n r. Succ100 Zero n => Judge n r => RProxy r)) (toInt (NProxy :: forall n. Succ100 Zero n => NProxy n))
"Buzz"
上で定義したSucc100などのクラスのおかげで、大きな数を簡単に書けていることもわかります。
FizzBuzzの配列を得る
これまで定義してきた型やクラス、関数を組み合わせ、再帰でArray Stringを作ります。インスタンスresultByNのパターンマッチ部分の影響で、このFizzBuzzはN-1からスタートすることになるため、Nから1までのFizzBuzzをしたい場合は、(Succ N)を渡す必要があります。
runFizzBuzz :: forall n r. Nat n => Result n r => NProxy n -> Array String
runFizzBuzz n = toResult n RProxy
class Result (n :: Nat) (r :: Result) | n -> r where
toResult :: NProxy n -> RProxy r -> Array String
instance resultByZero :: Result (Succ Zero) r' where
toResult _ _ = []
else instance resultByN :: (Nat n, ShowFizzBuzz r, Result n r, Judge n r) => Result (Succ n) r' where
toResult _ _ = show (RProxy :: RProxy r) (toInt (NProxy :: NProxy n)) : toResult (NProxy :: NProxy n) (judge (NProxy :: NProxy n))
REPLで試してみます。
> runFizzBuzz (NProxy :: NProxy (Succ (Succ (Succ (Succ Zero)))))
["Fizz","2","1"]
> runFizzBuzz (NProxy :: forall n. Succ10 (Succ Zero) n => NProxy n)
["Buzz","Fizz","8","7","Fizz","Buzz","4","Fizz","2","1"]
> runFizzBuzz (NProxy :: forall n. Succ100 (Succ Zero) n => NProxy n)
["Buzz","Fizz","98","97","Fizz","Buzz","94","Fizz","92","91","Fizz-Buzz","89","88","Fizz","86","Buzz","Fizz","83","82","Fizz","Buzz","79","Fizz","77","76","Fizz-Buzz","74","73","Fizz","71","Buzz","Fizz","68","67","Fizz","Buzz","64","Fizz","62","61","Fizz-Buzz","59","58","Fizz","56","Buzz","Fizz","53","52","Fizz","Buzz","49","Fizz","47","46","Fizz-Buzz","44","43","Fizz","41","Buzz","Fizz","38","37","Fizz","Buzz","34","Fizz","32","31","Fizz-Buzz","29","28","Fizz","26","Buzz","Fizz","23","22","Fizz","Buzz","19","Fizz","17","16","Fizz-Buzz","14","13","Fizz","11","Buzz","Fizz","8","7","Fizz","Buzz","4","Fizz","2","1"]
> runFizzBuzz (NProxy :: forall n. Succ200 (Succ Zero) n => NProxy n)
["Buzz","199","Fizz","197","196","Fizz-Buzz","194","193","Fizz","191","Buzz","Fizz","188","187","Fizz","Buzz","184","Fizz","182","181","Fizz-Buzz","179","178","Fizz","176","Buzz","Fizz","173","172","Fizz","Buzz","169","Fizz","167","166","Fizz-Buzz","164","163","Fizz","161","Buzz","Fizz","158","157","Fizz","Buzz","154","Fizz","152","151","Fizz-Buzz","149","148","Fizz","146","Buzz","Fizz","143","142","Fizz","Buzz","139","Fizz","137","136","Fizz-Buzz","134","133","Fizz","131","Buzz","Fizz","128","127","Fizz","Buzz","124","Fizz","122","121","Fizz-Buzz","119","118","Fizz","116","Buzz","Fizz","113","112","Fizz","Buzz","109","Fizz","107","106","Fizz-Buzz","104","103","Fizz","101","Buzz","Fizz","98","97","Fizz","Buzz","94","Fizz","92","91","Fizz-Buzz","89","88","Fizz","86","Buzz","Fizz","83","82","Fizz","Buzz","79","Fizz","77","76","Fizz-Buzz","74","73","Fizz","71","Buzz","Fizz","68","67","Fizz","Buzz","64","Fizz","62","61","Fizz-Buzz","59","58","Fizz","56","Buzz","Fizz","53","52","Fizz","Buzz","49","Fizz","47","46","Fizz-Buzz","44","43","Fizz","41","Buzz","Fizz","38","37","Fizz","Buzz","34","Fizz","32","31","Fizz-Buzz","29","28","Fizz","26","Buzz","Fizz","23","22","Fizz","Buzz","19","Fizz","17","16","Fizz-Buzz","14","13","Fizz","11","Buzz","Fizz","8","7","Fizz","Buzz","4","Fizz","2","1"]
成功です！
ソースコード全文
FizzBuzz.purs
module FizzBuzz where
import Prelude ((+))
import Prim hiding (Number)
import Data.Array ((:))
import Data.Show (show) as S
runFizzBuzz :: forall n r. Nat n => Result n r => NProxy n -> Array String
runFizzBuzz n = toResult n RProxy
foreign import kind Boolean
foreign import data True :: Boolean
foreign import data False :: Boolean
data BProxy (b :: Boolean) = BProxy
foreign import kind Result
foreign import data Fizz :: Result
foreign import data Buzz :: Result
foreign import data FizzBuzz :: Result
foreign import data Number :: Result
data RProxy (r :: Result) = RProxy
foreign import kind Nat
foreign import data Zero :: Nat
foreign import data Succ :: Nat -> Nat
data NProxy (n :: Nat) = NProxy
class Nat (n :: Nat) where
toInt :: NProxy n -> Int
instance natZero :: Nat Zero where
toInt _ = 0
instance natSucc :: Nat n => Nat (Succ n) where
toInt _ = 1 + toInt (NProxy :: NProxy n)
class Succ10 (n :: Nat) (n' :: Nat) | n -> n'
instance succ10 :: Succ10 n (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ n))))))))))
class Succ50 (n :: Nat) (n' :: Nat) | n -> n'
instance succ50 :: (Succ10 n n1, Succ10 n1 n2, Succ10 n2 n3, Succ10 n3 n4, Succ10 n4 n5) => Succ50 n n5
class Succ100 (n :: Nat) (n' :: Nat) | n -> n'
instance succ100 :: (Succ50 n n', Succ50 n' n'') => Succ100 n n''
class Succ200 (n :: Nat) (n' :: Nat) | n -> n'
instance succ200 :: (Succ100 n n', Succ100 n' n'') => Succ200 n n''
class Succ300 (n :: Nat) (n' :: Nat) | n -> n'
instance succ300 :: (Succ200 n n', Succ100 n' n'') => Succ300 n n''
class Succ400 (n :: Nat) (n' :: Nat) | n -> n'
instance succ400 :: (Succ300 n n', Succ100 n' n'') => Succ400 n n''
class Succ500 (n :: Nat) (n' :: Nat) | n -> n'
instance succ500 :: (Succ400 n n', Succ100 n' n'') => Succ500 n n''
class Result (n :: Nat) (r :: Result) | n -> r where
toResult :: NProxy n -> RProxy r -> Array String
instance resultByZero :: Result (Succ Zero) r' where
toResult _ _ = []
else instance resultByN :: (Nat n, ShowFizzBuzz r, Result n r, Judge n r) => Result (Succ n) r' where
toResult _ _ = show (RProxy :: RProxy r) (toInt (NProxy :: NProxy n)) : toResult (NProxy :: NProxy n) (judge (NProxy :: NProxy n))
class ShowFizzBuzz (r :: Result) where
show :: RProxy r -> Int -> String
instance showFizz :: ShowFizzBuzz Fizz where
show _ _ = "Fizz"
instance showBuzz :: ShowFizzBuzz Buzz where
show _ _ = "Buzz"
instance showFizzBuzz :: ShowFizzBuzz FizzBuzz where
show _ _ = "Fizz-Buzz"
instance showNumber :: ShowFizzBuzz Number where
show _ = S.show
class Judge (n :: Nat) (r :: Result) | n -> r
instance judgeByPattern :: (IsMod3 n b3, IsMod5 n b5, JudgeByPattern b3 b5 r) => Judge n r
judge :: forall n r. Nat n => Judge n r => NProxy n -> RProxy r
judge _ = RProxy
class JudgeByPattern (fb :: Boolean) (bb :: Boolean) (r :: Result) | fb bb -> r
instance judgeFizz :: JudgeByPattern True False Fizz
instance judgeBuzz :: JudgeByPattern False True Buzz
instance judgeFizzBuzz :: JudgeByPattern True True FizzBuzz
instance judgeNumber :: JudgeByPattern False False Number
class IsMod3 (n :: Nat) (b :: Boolean) | n -> b
instance isMod3 :: IsMod3 n b => IsMod3 (Succ (Succ (Succ n))) b
else instance isMod3' :: IsMod3 Zero True
else instance isnotMod3 :: IsMod3 n False
class IsMod5 (n :: Nat) (b :: Boolean) | n -> b
instance isMod5 :: IsMod5 n b => IsMod5 (Succ (Succ (Succ (Succ (Succ n))))) b
else instance isMod5' :: IsMod5 Zero True
else instance isnotMod5 :: IsMod5 n False
Author And Source
この問題について(PureScriptで型レベルFizzBuzz(Type-level FizzBuzz)), 我々は、より多くの情報をここで見つけました https://qiita.com/matoruru/items/2ccb3f01fd57d5791a0c著者帰属：元の著者の情報は、元のURLに含まれています。著作権は原作者に属する。
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