在 Haskell 中多次使用相同的随机数

Question

我正在尝试使用 Haskell 创建一个纸剪刀石头游戏来练习我对它的理解。

很遗憾，下面的源代码给出了不需要的答案。

例如：

>play pStone pRandom 1
1 games were played. Player 1 won 1 and player 2 won 1, making the match a draw.

如果进行 1 场比赛，则应该只有 1 场或 0 场胜利。

>play pStone pCopy 100
100 games were played. Player 1 won 1 and player 2 won 1, making the match a draw.

如果进行了 100 场比赛，其中（在第一轮之后）双方都走相同的棋，那么应该只有 1 或 0 胜。

>play pCopy pAntiCopy 100
100 games were played. Player 1 won 31 and player 2 won 37, making player 2 the overall winner.

根据 pCopy 和 pAntiCopy 的预期定义，pAntiCopy 应该赢得 99 或 100，而 pCopy 应该赢得 0 或 1。

我认为这种行为最可能的原因是随机数在最后进行评估，这意味着应该依赖于相同随机数的 2 个值而不是依赖于 2 个单独的随机数。我上面说的对吗？

如果我是正确的，请你告诉我应该如何纠正这个问题？如果我不正确，请您告诉我问题是什么以及应该如何解决？

我已经阅读了一个单独问题的解决方案，它建议生成一个随机数列表，然后使用它们，将它们作为参数从主函数传递给相关函数。不过，我不相信这在这里能很好地工作，因为所需的随机数的数量可能是从 0 到 2*numRounds 的任何值，这取决于正在使用的计划（我打算在这工作时创建更高级的计划）和代码的可读性会进一步降低。

我是 Haskell 和函数式编程的新手，所以对于下面源代码的风格，我深表歉意。如果您对如何改进它有任何建议，也非常欢迎。

import System.Random

data Move= Paper|Scissors|Stone deriving Show
type Plan=([IO Move]->[IO Move]->IO Move)

play :: Plan -> Plan -> Integer -> IO ()
play plan1 plan2 numRounds=do p1intwins<-p1wins;p2intwins<-p2wins;putStr(show numRounds ++ " games were played. Player 1 won " ++ show p1intwins ++ " and player 2 won " ++ show p2intwins ++ ", making " ++ (if p1intwins > p2intwins then "player 1 the overall winner." else (if p1intwins < p2intwins then "player 2 the overall winner." else "the match a draw."))) where (_, _, _, _, _, _, p1wins, p2wins)=(playRound (plan1, plan2, numRounds,[],[], 0, return 0, return 0))

playRound :: (Plan, Plan, Integer, [IO Move], [IO Move], Integer, IO Integer, IO Integer) -> (Plan, Plan, Integer, [IO Move], [IO Move], Integer, IO Integer, IO Integer)
playRound (plan1, plan2, numRounds, p1moves, p2moves, elapsedRounds, p1wins, p2wins)=if elapsedRounds==numRounds then (plan1, plan2, numRounds, p1moves, p2moves, elapsedRounds, p1wins, p2wins) else (playRound (plan1, plan2, numRounds, p1moves++[p1move], p2moves++[p2move], elapsedRounds+1, do p1win<-beatsCaller p1move p2move;p1intwins<-p1wins;return (p1intwins+if p1win then 1 else 0), do p2win<-beatsCaller p2move p1move;p2intwins<-p2wins;return(p2intwins+(if p2win then 1 else 0)) )) where p1move=plan1 p1moves p2moves; p2move=plan2 p2moves p1moves

beatsCaller :: IO Move -> IO Move -> IO Bool
beatsCaller iom1 iom2=do m1<-iom1;m2<-iom2;return(beats m1 m2)

beats :: Move -> Move -> Bool
beats Scissors Paper=True
beats Stone Scissors=True
beats Paper Stone=True
beats _ _=False

--                                           ###############Plans###################
pStone :: Plan
pStone _ _ = return Stone

pScissors :: Plan
pScissors _ _ = return Scissors

pPaper :: Plan
pPaper _ _ = return Paper

pUScissors :: Plan
pUScissors [] _ = randomMove
pUScissors _ _ = return Scissors

pCopy :: Plan
pCopy _ []= randomMove
pCopy _ theirMoves= last theirMoves

pRandom :: Plan
pRandom _ _=randomMove

pAntiCopy :: Plan
pAntiCopy [] _ = randomMove
pAntiCopy ourMoves _ = do ourMove<-last ourMoves;return(beaterOf ourMove)

--                                           ##############Plan Logic###############

beaterOf ::  Move -> Move
beaterOf Scissors = Stone
beaterOf Paper = Scissors
beaterOf Stone = Paper

randomMove :: IO Move
randomMove=do x<-genRandom;return (doRMove x)

doRMove:: Int -> Move
doRMove rand
    |rand==1 =Paper
    |rand==2 =Scissors
    |rand==3 =Stone

genRandom :: IO Int
genRandom =getStdRandom (randomR (1,3))

Answer 1

我稍微重新格式化并注释了您的源文件。要点是您应该将Plan 的类型更改为[Move] -> [Move] -> IO Move，如下所述。

import System.Random

data Move = Paper | Scissors | Stone
  deriving (Show, Eq, Enum, Bounded)

-- Make Move an instance of Random, so that we can use randomIO
-- in order to pick a random Move rather than a hand-written
-- function. We use the derived Enum instance and integer random
-- numbers to do the hard work for us.
instance Random Move where
  randomR (l, u) g = (toEnum n, g')
    where (n, g') = randomR (fromEnum l, fromEnum u) g
  random = randomR (minBound, maxBound)

-- Unchanged, just realigned.
beaterOf :: Move -> Move
beaterOf Scissors = Stone
beaterOf Paper    = Scissors
beaterOf Stone    = Paper

-- Reimplemented in terms of beaterOf, to avoid unnecessary
-- duplication of error-prone information.
beats :: Move -> Move -> Bool
beats x y = x == beaterOf y

-- Most important change. A plan is a strategy that takes two
-- lists of past moves. These are of type Move, not IO Move, as
-- they have already happened. We then have to determine a new
-- one. Here, to choose the next, we allow IO (such as picking
-- a random number, or asking a human player). I also reverse
-- the order of moves, so that the most recent moves are first,
-- because most strategies access the most recent move, and
-- accessing the head is more efficient in a list.
type Plan =  [Move]  -- my moves, latest move first
          -> [Move]  -- opponent's moves, latest move first
          -> IO Move -- my next move, may involve IO

--
-- Specific plans (slightly renamed, otherwise unchanged):
--

-- Always plays a particular move.
always :: Move -> Plan
always m _ _ = return m

-- Copies the latest move of opponent.
copy :: Plan
copy _ []           = randomIO
copy _ (latest : _) = return latest

randomly :: Plan
randomly _ _ = randomIO

-- Moves to the beater of our previous move.
antiCopy :: Plan
antiCopy []           _ = randomIO
antiCopy (latest : _) _ = return (beaterOf latest)

uScissors :: Plan
uScissors [] _ = randomIO
uScissors _  _ = return Scissors

-- Play wrapper. Interface as before.
play :: Plan    -- my plan
     -> Plan    -- opponent's plan
     -> Integer -- number of rounds to be played
     -> IO ()   -- output is printed as text
play myPlan opPlan rounds = do
  (myWins, opWins) <- playRounds
                        myPlan opPlan rounds
                        [] [] -- initialize with empty move lists
                        0 0   -- and 0 wins each
  -- print statistics
  let overallStatus | myWins > opWins = "Player 1 the overall winner"
                    | opWins > myWins = "Player 2 the overall winner"
                    | otherwise       = "the match a draw"
  putStrLn $ show rounds ++ " games were played. "
          ++ "Player 1 won " ++ show myWins ++ " and "
          ++ "Player 2 won " ++ show opWins ++ ", making "
          ++ overallStatus ++ "."

-- Does all the hard work.
playRounds :: Plan    -- my plan
           -> Plan    -- opponent's plan
           -> Integer -- number of rounds still to be played
           -> [Move]  -- our moves so far, latest first
           -> [Move]  -- opponent's moves so far, latest first
           -> Int     -- my wins
           -> Int     -- opponent's wins
           -> IO (Int, Int)  -- final wins
playRounds _      _      0      _       _       myWins opWins =
  return (myWins, opWins) -- if no rounds are left to play, return the final statistics
playRound myPlan opPlan rounds myMoves opMoves myWins opWins = do
  myMove <- myPlan myMoves opMoves -- here's where a random number might get chosen
  opMove <- opPlan opMoves myMoves -- and here again (but nowhere else)
  let myWin = myMove `beats` opMove -- this works on the already chosen Move, not on IO Move
      opWin = opMove `beats` myMove -- dito
  playRound
    myPlan opPlan      -- as before
    (rounds - 1)       -- one round is played
    (myMove : myMoves) -- adding moves in front of the list is easier
    (opMove : opMoves)
    (fromEnum myWin + myWins) -- update win count, turning True to 1 and False to 0
    (fromEnum opWin + opWins)

Answer 2

我认为这种行为最可能的原因是随机数在最后进行评估，这意味着应该依赖于相同随机数的 2 个值而不是依赖于 2 个单独的随机数。我上面说的对吗？

你是。由于您实际上并没有在迭代期间进行游戏，而是通过IO-actions，因此您的策略没有简单的Moves - 前几轮的结果 - 可以构建，而是生成Move的配方，在某些情况下涉及执行genRandom 以获得Move。每次在

ourMove<-last ourMoves

last ourMoves 涉及一个genRandom，会产生一个新的（伪）随机数 - 通常与产生前一个Move 的随机数不同。

如果我是正确的，请你告诉我应该如何纠正这个问题？

不要传递IO 操作和IO 的列表-使用genRandom 的操作。您需要纯值来确定策略（pRandom 以及 pCopy 和 pAntiCopy 中的初始选择除外）。

必要时在每一步运行伪随机数生成，并将得到的纯Moves传递给下一次迭代。

---

另外，使用更短的行、使用空格和使用布局使代码更具可读性。

我打算改写成更惯用的风格，但我打字慢，所以可能需要一段时间。

好吧，还是有点乱，因为我保留了很多原始输出和逻辑，但它更容易阅读和遵循，并且产生了预期的输出：

module Rocks where

import System.Random

data Move
    = Paper
    | Scissors
    | Stone
      deriving Show

type Plan = [Move] -> [Move] -> IO Move

play :: Plan -> Plan -> Int -> IO ()
play plan1 plan2 numRounds = do
    (wins1, wins2) <- playRounds plan1 plan2 numRounds [] [] 0 0
    putStrLn $ show numRounds ++ " games were played. Player 1 won "
                ++ show wins1 ++ " and player 2 won " ++ show wins2
                ++ ", making " ++ result wins1 wins2
  where
    result a b
        | a == b    = "the match a draw."
        | otherwise = "player " ++ (if a > b then "1" else "2") ++ " the overall winner."

playRounds :: Plan -> Plan -> Int -> [Move] -> [Move] -> Int -> Int -> IO (Int, Int)
playRounds _     _     0      _      _      wins1 wins2 = return (wins1,wins2)
playRounds plan1 plan2 rounds moves1 moves2 wins1 wins2 = do
    choice1 <- plan1 moves1 moves2
    choice2 <- plan2 moves2 moves1
    let (w1, w2)
            | beats choice1 choice2 = (wins1+1 ,wins2)
            | beats choice2 choice1 = (wins1, wins2+1)
            | otherwise             = (wins1, wins2)
    playRounds plan1 plan2 (rounds-1) (moves1 ++ [choice1]) (moves2 ++ [choice2]) w1 w2

beats :: Move -> Move -> Bool
beats Scissors  Paper       = True
beats Stone     Scissors    = True
beats Paper     Stone       = True
beats _         _           = False

--       ###############Plans###################

pStone :: Plan
pStone _ _ = return Stone

pScissors :: Plan
pScissors _ _ = return Scissors

pPaper :: Plan
pPaper _ _ = return Paper

pUScissors :: Plan
pUScissors [] _ = randomMove
pUScissors _  _ = return Scissors

pCopy :: Plan
pCopy _ []         = randomMove
pCopy _ theirMoves = return $ last theirMoves

pRandom :: Plan
pRandom _ _ = randomMove

pAntiCopy :: Plan
pAntiCopy []       _ = randomMove
pAntiCopy ourMoves _ = return (beaterOf $ last ourMoves)

--       ##############Plan Logic###############

beaterOf ::  Move -> Move
beaterOf Scissors   = Stone
beaterOf Paper      = Scissors
beaterOf Stone      = Paper

randomMove :: IO Move
randomMove = fmap doRMove genRandom

doRMove:: Int -> Move
doRMove rand
    | rand == 1 = Paper
    | rand == 2 = Scissors
    | rand == 3 = Stone
    | otherwise = error "oops"

genRandom :: IO Int
genRandom = getStdRandom (randomR (1,3))

与

*Rocks> play pCopy pAntiCopy 100
100 games were played. Player 1 won 0 and player 2 won 99, making player 2 the overall winner.
*Rocks> play pStone pRandom 100
100 games were played. Player 1 won 33 and player 2 won 34, making player 2 the overall winner.
*Rocks> play pStone pCopy 100
100 games were played. Player 1 won 1 and player 2 won 0, making player 1 the overall winner.
*Rocks> play pStone pAntiCopy 100
100 games were played. Player 1 won 33 and player 2 won 33, making the match a draw.