[TYPES] completeness of subtype judgments
Gerwin Klein
gerwin.klein at nicta.com.au
Tue Apr 25 17:51:25 EDT 2006
Dear Sophia,
if I remember correctly, Alessandro Coglio had something like this for his JVM
subroutine type system in
A. Coglio, "Simple Verification Technique for Complex Java Bytecode
Subroutines", Concurrency and Computation: Practice and Experience, 16
(7):647-670, 2004
Cheers,
Gerwin
On Wednesday 26 April 2006 06:21, Sophia Drossopoulou wrote:
> 1) Define a judgment \Gamma |- T <: T’ with the obvious meaning
>
> 2) Define the denotation of a type T for a given stack S
> and heap H, as
> [[T]]_{S,H}
> as the set of all values with type T in S and H.
> (We need to consider the stack S because we have path-dependent
> types, i.e. T may mention entities from S.)
>
> 3) Define a judgment \Gamma |- S, H to express when a
> stack S and heap H agree with an environment \Gamma.
>
> 4) The subtyping system is complete, iff
> \forall \Gamma, T and T’
> (\forall S, H:
> \Gamma |- S,H => [[T]]_{S,H} \subset [[T’]]_{S,H} )
> =>
> ( \Gamma |- T <: T’ )
>
> Our question is whether there are alternative formulations of
> completeness, and, more importantly, whether there is work proving
> such completeness.
More information about the Types-list
mailing list