Editing Trash/DDC/ClosureTyping (section)

== Closure typing for region sharing ==
Closure typing is used to track the sharing of regions between function calls like this one.

The type inferred for <hask>f</hask> is actually:

<haskell>
f   :: forall %r0
    .  () -> () -($c0)> Int %r0
    :- $c0        = x : %r0
</haskell>

The <hask>$c0</hask> annotation tells us that this function has a object free in its closure, and that the object contains region <hask>%r0</hask>. The <hask>x : %r0</hask> syntax gives a name to this term, and is pronounced "x ''of'' region zero". 

Similarly to variables in the expression language, the exact names given to closure terms is not significant to the type system. However, to make inferred types easier to read, DDC names the closure terms in a function's type after the free variables that gave rise to those terms. The user is free to use whatever names they wish in type signatures. Two closure terms with different names but identical right hand sides are taken as being equivalent.

If we use this new type and apply the first argument we have:

<haskell>
f_unit :: () -($c0)> Int %r0
       :- $c0   = x : %r0
</haskell>

This type says that <hask>f_unit</hask> is a function that takes a unit value and returns an <hask>Int</hask>, but the <hask>Int</hask> is free in its closure so is shared by all calls to it. The type system does not generalize regions which are free in these closures.

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