Question

该程序在GHC下正确编译和运行：

type Church a = (a -> a) -> a -> a

ch :: Int -> Church a
ch 0 _ = id
ch n f = f . ch (n-1) f

unch :: Church Int -> Int
unch n = n (+1) 0

suc :: Church a -> Church a
suc n f = f . n f

pre :: Church ((a -> a) -> a) -> Church a
pre n f a = n s z id
    where s g h = h (g f)
          z     = const a

main :: IO ()
main = do let seven = ch 7
              eight = suc seven
              six   = pre seven
          print (unch eight)
          print (unch six)

但是在使用Frege进行编译时出现了以下错误：

E /home/xgp/work/flab/src/main/frege/flab/fold.fr:23: type error in expression seven
    type is : Int
    expected: (t1→t1)→t1
E /home/xgp/work/flab/src/main/frege/flab/fold.fr:23: type error in expression seven
    type is : (t1→t1)→t1
    expected: Int
E /home/xgp/work/flab/src/main/frege/flab/fold.fr:23: type error in expression seven
    type is : (t1→t1)→t1
    expected: Int
E /home/xgp/work/flab/src/main/frege/flab/fold.fr:23: type error in
    expression seven
    type is apparently Int
    used as function

为什么呢？是否可以修改程序以在Frege下传递编译？

Answer 1

这是极少数情况之一，其中let绑定变量类型的泛化确实会产生影响。

关键是，在这方面，弗雷格像GHC一样使用pragma -XMonoLocalBinds，有关详细信息，请参阅此处：https://github.com/Frege/frege/wiki/GHC-Language-Options-vs.-Frege#Let-Generalization和此处：https://downloads.haskell.org/~ghc/latest/docs/html/users_guide/other-type-extensions.html#typing-binds（还有一个链接指向SPJ，解释理由）

简而言之，这意味着所有未注释的let bound veriabes都将具有单态类型，并且不能在不同类型中使用。要恢复多态性，需要显式类型签名。

要使程序编译，只需注释seven与

的绑定即可

seven :: Church a

关于print / println：前一个不刷新输出。所以你有REPL：

frege> print 'a'
IO ()
frege> print 'b'
IO ()
frege> println "dammit!"
abdammit!
IO ()

论弗雷格时期的教会数字计划

1 个答案: