On Dec 10, 2015, at 3:04 PM, Klaus Ostermann <klaus...@gmail.com> wrote:

> Thanks for the clarification, Sam. What you write makes sense.
> 
> However, since the default case (without explicit annotations) is that I get 
> these very (too?) precise singleton types, I have the impression that 
> reasoning about (typed) program equivalence is more difficult in TR than in 
> standard statically typed languages. 
> 
> Aren't types supposed to be a device for abstraction and for supporting 
> information hiding? Singleton types seem to be against that spirit by 
> exposing "implementation details" of the terms, such as the difference 
> between (- 1 1) and (- 2 2).


I don't think gradual/incremental type systems play this role. But it is an 
open question how we can enrich such type systems with types as abstraction 
barriers. -- Matthias

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