jumbo connectives - comments please!

Dear froggists,

I would welcome comments on the manuscript "Jumbo Connectives in Type 
Theory and Logic", which is available here:

http://www.cs.bham.ac.uk/~pbl/papers/jumboshort.pdf

It's not about deep inference, but I think it might be interesting to you
guys, because it's about systems where things that have traditionally been
done in several steps are done in one step.  And it addresses issues like 
associativity of connectives that have been discussed on this list.

regards
Paul


Abstract:

We make an argument that, for any study involving computational effects 
such as divergence or continuations, the traditional syntax of simply 
typed lambda-calculus cannot be regarded as canonical, because standard 
arguments for canonicity rely on isomorphisms that may not exist in an 
effectful setting.  To remedy this, we define a "jumbo lambda-calculus" 
that fuses the traditional connectives together into more general ones, 
so-called "jumbo connectives".  We provide two pieces of evidence for our 
thesis that the jumbo formulation is advantageous.

Firstly, we show that the jumbo lambda-calculus provides a "complete" 
range of connectives, in the sense of including every possible connective 
that, within the beta-eta theory, possesses a reversible rule.   

Secondly, in the presence of effects, we explore plausible decompositions 
of these jumbo connectives, in both call-by-name and call-by-value. We see 
that hardly any are universally valid, and so the jumbo connectives really 
are necessary.

Finally, we look at Gentzen's LK (propositional), in order to illustrate 
how the form of sequents within a system determines the range of 
connectives.  We see that, because a sequent in LK has multiple 
conclusions, its range of jumbo connectives is larger than that of simply 
typed lambda-calculus.