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Arthur :: LittleBrick
People who believe that Boolean logic is the only one worth
considering, will probably not pay attention to examples of
non-well-pointed toposes or non-strong monads or even Haskell models
of any thing. and they probably don't care for 3-valued logics of any
it's nice to know that one needs to look outside Sets to find a
non-strong monad(it was a good question). and it's nice to know that
the monads arising from continuations and resumptions are not
necessarily strong, but I don't conclude anything else from these two
Also the fact that a Diamond S4 is the logical contents of a free
monad is the essence of my paper with Nick Benton and Gavin Bierman in
N Benton, G Bierman and V de Paiva. Computational Types from a Logical
Perspective. Journal of Functional Programming 8(2):177-193 March
1998. © Cambridge University Press 1998.
available from Nick's page
long before "A Symmetric Modal Lambda Calculus for Distributed
Computing" in lics 2004.
now I haven't read the latter, so maybe I should, but the way I see
it, the modeling of distributed computing is not set in stone, it's
simply a proposal with pros and cons, while the Curry-Howard
correspondence in the former is a mathematical theorem. but maybe I
should shut up and read.