Is it possible to export constructors for pattern matching, but not for construction, in Haskell Modules?

Question

A vanilla data type in Haskell has zero or more constructors, each of which plays two roles.

In expressions, it supports introduction, its a function from zero or mo

Answer 1

You cannot. But if there are only reasonable number of constructors for your type T, you may want to hide the constructors and instead provide a function which does the pattern matching in the same spirit as maybe :: b -> (a -> b) -> Maybe a -> b.

Answer 2

From GHC 7.8 on you can use PatternSynonyms to export patterns independent from constructors. So an analogue to @Lambdageek’s answer would be

{-# LANGUAGE PatternSynonyms #-}

module ThingModule (Thing, pattern Foo, pattern Bar) where

pattern Foo a <- RealFoo a
pattern Bar a <- RealBar a

data Thing = RealFoo Thing | RealBar Int

and

{-# LANGUAGE PatternSynonyms #-}
module Main where

import ThingModule

doSomethingWithThing :: Thing -> Int
doSomethingWithThing (Foo x) = doSomethingWithThing x
doSomethingWithThing (Bar y) = y

So it looks like normal constructors.

If you try to use Bar to construct a value, you get

Main.hs:9:32:
    Bar used in an expression, but it's a non-bidirectional pattern synonym
    In the expression: Bar y

Answer 3

You can use a view type and view patterns to do what you want:

module ThingModule (Thing, ThingView(..), view) where

data Thing = Foo Thing | Bar Int

data ThingView = FooV Thing | BarV Int

view :: Thing -> ThingView
view (Foo x) = FooV x
view (Bar y) = BarV y

Note that ThingView is not a recursive data type: all the value constructors refer back to Thing. So now you can export the value constructors of ThingView and keep Thing abstract.

Use like this:

{-# LANGUAGE ViewPatterns #-}
module Main where

import ThingModule

doSomethingWithThing :: Thing -> Int
doSomethingWithThing(view -> FooV x) = doSomethingWithThing x
doSomethingWithThing(view -> BarV y) = y

The arrow notation stuff is GHC's View Patterns. Note that it requires a language pragma.

Of course you're not required to use view patterns, you can just do all the desugaring by hand:

doSomethingWithThing :: Thing -> Int
doSomethingWithThing = doIt . view
  where doIt (FooV x) = doSomethingWithThing x
        doIt (BarV y) = y

More

Actually we can do a little bit better: There is no reason to duplicate all the value constructors for both Thing and ThingView

module ThingModule (ThingView(..), Thing, view) where

   newtype Thing = T {view :: ThingView Thing}
   data ThingView a = Foo a | Bar Int

Continue useing it the same way as before, but now the pattern matches can use Foo and Bar.

{-# LANGUAGE ViewPatterns #-}
module Main where

import ThingModule

doSomethingWithThing :: Thing -> Int
doSomethingWithThing(view -> Foo x) = doSomethingWithThing x
doSomethingWithThing(view -> Bar y) = y