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Jan 15, 2013 11:12:27 AM (
indended to make newtypes more flexible and useful. It tackles head-on
the problem underlying #7542 and #2110.
Email thread [http://www.haskell.org/pipermail/glasgow-haskell-users/2013-January/023455.html here].
== The problem ==
== Abstraction ==
Suppose we have
module Map( ... ) where
data Map a b = ...blah blah...
module Age( ... ) where
newtype Age = MkAge Int
Now suppose we want a newtype wrapper like this
newtype wrap foo :: Map Int Bool -> Map Age Bool
Could we write `foo` by hand? (This is a good criterion, I think.) Only if we could see the data constructors of ''both'' `Map` ''and'' `Age`.
* If we can't see the data constructor of `Age` we might miss an invariant that Ages are supposed to have. For example, they might be guaranteed positive.
* If we can't see the data constructors of `Map`, we might miss an invariant of Maps. For example, maybe `Map` is represented as a list of pairs, ordered by the keys. Then, if `Age` orders in the reverse way to `Int`, it would obviously be bad to substitute.
Invariants like these are difficult to encode in the type system, so we use "exporting the constructors" as a proxy for "I trust the importer to maintain invariants". The "Internals" module name convention is a signal that you must be particularly careful when importing this module; runtime errors may result if you screw up.
One possible conclusion: if we have them at all, newtype wrappers should only work if you can see the constructors of ''both'' the newtype, ''and'' the type you are lifting over.
But that's not very satisfactory either.
* There are some times (like `IO`) where it *does* make perfect sense
to lift newtypes, but where we really don't want to expose
* Actually `Map` is also a good example: while `Map Age Bool` should
not be converted to `Map Int Bool`, it'd be perfectly fine to convert
`Map Int Age` to `Map Int Int`.
* The criterion must be recursive. For example if we had
data Map a b = MkMap (InternalMap a b)
it's no good being able to see the data constructor `MkMap`; you need to
see the constructors of `InternalMap` too.
The right thing is probably to use kinds, and all this is tantalisingly close to the system suggested in [http://research.microsoft.com/en-us/um/people/simonpj/papers/ext-f/ Generative type abstraction and type-level computation]. Maybe we should be able to ''declare'' Map to be indexed (rather than parametric) in its first parameter.
More thought required.
== Type soundness ==