[Haskell-cafe] Re: Semantics of uniqueness types for IO

[Jeff Polakow]

Hello,

> Just to continue the academic nitpicking.. :-)
> 
> > Linear logic/typing does not quite capture uniqueness types since a 
term 
> > with a unique type can always be copied to become non-unique, but a 
linear 
> > type cannot become unrestricted. 
> 
> Actually, that isn't quite accurate. In linear logic, a term with a
> non-linear type can always be regarded as having a linear type, i.e.
> 
>   U -o !U
> 
> is a theorem (my favourite reading of this theorem is "if you have an
> unlimited supply of bank notes, then you also have a single one"). The
> implication in the opposite direction is a falsity (from the fact that
> we have a single bank note, we cannot decude that we have an unlimited
> supply).
>
I think you mean

    !U -o U

is a theorem. The converse is not provable.

In any case, I think we are saying the same thing.
 
-Jeff


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