NewType

newtype is not exactly like data. #haskell is frequently being questioned about the difference.

Firstly, as mentioned in most tutorials, newtype can handle only a single data constructor, and a single field in that single data constructor.

Secondly, newtype is strict on its field.

So how is:

newtype NewType = NewType Int

different from:

data NewData = NewData Int

The number of bottoms differ. Since data is lazy, it introduces a new bottom in addition to the bottom that existed in the Int itself.

NewData can be _|_ or it can be (NewData _|_). NewType cannot be _|_ but can only be (NewType _|_).

So, lets try another comparison:

How is:

newtype NewType = NewType Int

different from:

data NewData = NewData !Int

Here, the number of bottoms is the same, but they are not quite the same bottoms. NewType's bottom is: (NewType _|_) (the bottom is inside the pattern), whereas NewData's bottom is (_|_) (the bottom is the whole pattern).

To demonstrate this difference, we can use the following code;

 case (NewType undefined) of
   (NewType _) -> "Happy happy joy joy :-)"
 case (NewData undefined) of
   (DataType _) -> "Won't ever get here :-("

Since the newtype bottom is inside the pattern, and we catch that with (_) and never use it, we don't actually hit the bottom. But the NewData bottom is on the whole pattern, so even matching the single data constructor that way is a bottom.