# Newtype wrappers

Simon Peyton-Jones simonpj at microsoft.com
Mon Jan 14 19:09:50 CET 2013

```Friends

I'd like to propose a way to "promote" newtypes over their enclosing type.  Here's the writeup

Any comments?  Below is the problem statement, taken from the above page.

I'd appreciate

*         A sense of whether you care. Does this matter?

*         Improvements to the design I propose

Simon

The problem

Suppose we have

newtype Age = MkAge Int

Then if n :: Int, we can convert n to an Age thus: MkAge n :: Age. Moreover, this conversion is a type conversion only, and involves no runtime instructions whatsoever. This cost model -- that newtypes are free -- is important to Haskell programmers, and encourages them to use newtypes freely to express type distinctions without introducing runtime overhead.

Alas, the newtype cost model breaks down when we involve other data structures. Suppose we have these declarations

data T a   = TLeaf a     | TNode (Tree a) (Tree a)

data S m a = SLeaf (m a) | SNode (S m a) (S m a)

and we have these variables in scope

x1 :: [Int]

x2 :: Char -> Int

x3 :: T Int

x4 :: S IO Int

Can we convert these into the corresponding forms where the Int is replaced by Age? Alas, not easily, and certainly not without overhead.

*   For x1 we can write map MkAge x1 :: [Age]. But this does not follow the newtype cost model: there will be runtime overhead from executing the map at runtime, and sharing will be lost too. Could GHC optimise the map somehow? This is hard; apart from anything else, how would GHC know that map was special? And it it gets worse.

*   For x2 we'd have to eta-expand: (\y -> MkAge (x2 y)) :: Char -> Age. But this isn't good either, because eta exapansion isn't semantically valid (if x2 was bottom, seq could distinguish the two). See #7542<http://hackage.haskell.org/trac/ghc/ticket/7542> for a real life example.

*   For x3, we'd have to map over T, thus mapT MkAge x3. But what if mapT didn't exist? We'd have to make it. And not all data types have maps. S is a harder one: you could only map over S-values if m was a functor. There's a lot of discussion abou this on #2110<http://hackage.haskell.org/trac/ghc/ticket/2110>.

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