Theory Conclusion

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 * Project         : CSP-RefTK - A Refinement Toolkit for HOL-CSP
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 * Author          : Burkhart Wolff, Safouan Taha, Lina Ye.
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 * This file       : Conclusion
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chapter‹Conclusion›
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theory Conclusion
    imports HOLCF
begin
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text‹ We presented a formalisation of the most comprehensive semantic model for CSP, a 'classical' 
language for the specification and analysis of concurrent systems studied in a rich body of 
literature. For this purpose, we ported @{cite "tej.ea:corrected:1997"} to a modern version
of Isabelle, restructured the proofs, and extended the resulting theory of the language 
substantially. The result HOL-CSP 2 has been submitted to the Isabelle AFP @{cite "HOL-CSP-AFP"}, 
thus a fairly sustainable format accessible to other researchers and tools.

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.

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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