Version 3 (modified by benl, 6 years ago) |
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# Polymoprhic Update

## Get/Set

Consider the following function:

makeGetSet :: forall a. a -> (() -> a, a -> ()) makeGetSet x = do box = Just x get () = case box of { Just z -> z; } set z = box#x #= z (get, set)

This function allocates a box which can store a value, and returns a tuple of functions to get and set that value.

As the function is polymorphic, we can create boxes of whatever type we would like:

main () = do getSet :: (() -> Int, Int -> ()) getSet = makeGetSet 5 putStrLn $ show $ fst getSet () -- prints '5' snd getSet 23 -- update the box putStrLn $ show $ fst getSet () -- prints '23'

The trouble comes when we create a box containing a value of polymorphic type. Without closure typing we could define:

... getSet2 :: forall a. (() -> [a], [a] -> ()) getSet2 = makeGetSet []

When a list is empty, we can treat it as being of any type `(forall a. [a])`, but suppose we update the box containing it at two different types:

snd getSet2 [23] snd getSet2 ["trouble"] putStrLn $ show $ fst getSet2 ()

The type of `getSet2` has `forall a.` at the front, so there is nothing to stop us from calling the set function at both `[Int]` and `[String]`, but what should the type be when use the get function in the last line?

## Dangerous type variables

Ultimately, the problem illustrated above arose because there wasn't a mechanism to track the sharing of data between successive calls to `getSet2`. When `makeGetSet` was evaluated it created a shared mutable object (the `box`) and then returned functions that had this object free in their closure.

In Disciple, `makeGetSet` has the extended type:

makeGetSet :: forall a %r0 %r1 . a -> Tuple2 %r1 (() -(!e0 $c0)> a) (a -(!e1 $c1)> ()) :- !e0 = !Read %r0 , !e1 = !{!Read %r0; !Write %r0} , $c0 = ${box : %r0; box : %r0 $> a} , $c1 = ${box : %r0; box : %r0 $> a} , Base.Mutable %r0

In this type, we see the new closure term `(box : %r0 $> a)`. This says that the closure contains an object named `box` which is in a region `%r0`, and the type of the object includes a variable `'a'`. When `%r0` is `Mutable` we say that `a` is *dangerous*, and dangerous variables are never generalised when they are free in the (outer most) closure of a function.