[英]On Church numeral program under Frege
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)
但是当用Frege编译时,我得到以下错误:
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? 是否可以修改程序以通过Frege下的编译?
这是极少数情况之一,其中let绑定变量类型的泛化实际上确实有所不同。
关键是,在这方面,Frege的行为类似于GHC和pragma -XMonoLocalBinds
,详见此处: https : //github.com/Frege/frege/wiki/GHC-Language-Options-vs.-Frege#Let-Generalization and这里: https : //downloads.haskell.org/~ghc/latest/docs/html/users_guide/other-type-extensions.html#typing-binds (还有一篇指向SPJ论文的链接,解释了理由)
简而言之,这意味着所有未注释的让限定的veriabes将具有单态类型,并且不能用于不同类型。 要恢复多态性,需要显式类型签名。
为了使你的程序编译,只需注释seven
绑定即可
seven :: Church a
关于print / println:前一个不刷新输出。 所以你在REPL中:
frege> print 'a'
IO ()
frege> print 'b'
IO ()
frege> println "dammit!"
abdammit!
IO ()
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