Why this Either-monad code does not type check?
문제
instance Monad (Either a) where
return = Left
fail = Right
Left x >>= f = f x
Right x >>= _ = Right x
this code frag in 'baby.hs' caused the horrible compilation error:
Prelude> :l baby
[1 of 1] Compiling Main ( baby.hs, interpreted )
baby.hs:2:18:
Couldn't match expected type `a1' against inferred type `a'
`a1' is a rigid type variable bound by
the type signature for `return' at <no location info>
`a' is a rigid type variable bound by
the instance declaration at baby.hs:1:23
In the expression: Left
In the definition of `return': return = Left
In the instance declaration for `Monad (Either a)'
baby.hs:3:16:
Couldn't match expected type `[Char]' against inferred type `a1'
`a1' is a rigid type variable bound by
the type signature for `fail' at <no location info>
Expected type: String
Inferred type: a1
In the expression: Right
In the definition of `fail': fail = Right
baby.hs:4:26:
Couldn't match expected type `a1' against inferred type `a'
`a1' is a rigid type variable bound by
the type signature for `>>=' at <no location info>
`a' is a rigid type variable bound by
the instance declaration at baby.hs:1:23
In the first argument of `f', namely `x'
In the expression: f x
In the definition of `>>=': Left x >>= f = f x
baby.hs:5:31:
Couldn't match expected type `b' against inferred type `a'
`b' is a rigid type variable bound by
the type signature for `>>=' at <no location info>
`a' is a rigid type variable bound by
the instance declaration at baby.hs:1:23
In the first argument of `Right', namely `x'
In the expression: Right x
In the definition of `>>=': Right x >>= _ = Right x
Failed, modules loaded: none.
why this happen? and how could I make this code compile ? thanks for any help~
i see. and i adjusted the code to see it compiles:
instance Monad (Either a) where
return = Right
Left a >>= f = Left a
Right x >>= f = f x
it compiles successfully! but...for a further more question:
instance Monad (Either a)
makes 'Either a' a monad and i got 'return = Right'...how could i get 'return = Left'? i've tried this but failed:
instance Monad (`Either` a) where
return = Left
Right a >>= f = Right a
Left x >>= f = f x
or: instance Monad (\x -> Either x a)
doesn't compile at all!
해결책
- return should have type
forall b. b -> Either a b
, however Left has typeforall c. a -> Either a c
. You probably want Right here. fail
should have typeforall b. String -> Either a b
, however Right has typeforall b. b -> Either a b
, so ifb=String
that makesString -> Either a String
which does not fit.>>=
should have typeEither a b -> (b -> Either a c) -> Either a c
howeverRight x >>= _ = Right x
always returns a value of typeEither a b
, notEither a c
.Left x >>= f = f x
does not work because x has typea
, butf
has typeb -> c
.
다른 팁
Most of the confusion stems from the fact Left and Right are used backwards. Considering only the type for return, its type from the Monad typeclass is as follows:
return :: (Monad m) => b -> m b
You're trying to define an instance for m
= Either a
, so return should have type:
return :: b -> Either a b
You're defining it as Left, which has type:
Left :: a -> Either a b
Note how the left hand side of the ->
differs.