Theory Conclusion

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 * Project         : CSP-RefTK - A Refinement Toolkit for HOL-CSP
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 * This file       : Conclusion
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chapter‹Conclusion›
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theory Conclusion
  imports DiningPhilosophers 
begin
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text‹ We presented an analysis of the connection of the refinement notions for CSP, a 'classical'
language for the specification and analysis of concurrent systems studied in a rich body of 
literature. A modern formalisation of CSP, called HOL-CSP2.0 or just HOL-CSP and 
available in the Isabelle AFP @{cite "HOL-CSP-AFP"}, is the basis of this
work. In particular, we introduced the theory of the ‹Trace-Divergence-Refinement› term‹P ⊑DT Q›,
which is an alternative to the standard refinements known from the literature.
[❙‹NOTE: This part of the theory development has meanwhile been integrated in HOL-CSP2.0.›]

We developed  a novel set of deadlock - and livelock inference proof principles based on
classical and denotational characterizations. In particular, we formally investigated the relations
between different refinement notions in the presence of deadlock - and livelock; an area where
traditional CSP literature skates over the nitty-gritty details. Finally, we demonstrated how to
exploit these results for deadlock/livelock analysis of protocols.

We put a large body of abstract CSP laws and induction principles together to form
concrete verification technologies for generalized classical problems, which have been considered
so far from the perspective of data-independence or structural parametricity. The underlying novel
principle of ``trading rich structure against rich state'' allows one to convert processes 
into classical transition systems for which established invariant techniques become applicable.
We present a first example using these proof methods, notably for Dijkstra's Dining Philosophers;
we show that our techniques allow for proving that this cyclic proof architecture is deadlock free
for an arbitrary number of philosopher processes.

Future applications of HOL-CSP 2 could comprise a combination with model checkers, where our theory
with its derived rules can be used to certify the output of a model-checker over CSP. In our experience,
labelled transition systems generated by model checkers may be used to steer inductions or to construct
the normalized processes ‹Pnorm⟦τ,υ⟧› automatically, thus combining efficient finite reasoning 
over finite sub-systems with globally infinite systems in a logically safe way. 
›


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end
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