section \<open>UNITY--Chandy and Misra's UNITY formalism\<close>
text\<open>
The book \<^emph>\<open>Parallel Program Design: A Foundation\<close> by Chandy and Misra
(Addison-Wesley, 1988) presents the UNITY formalism. UNITY consists of an
abstract programming language of guarded assignments and a calculus for
reasoning about such programs. Misra's 1994 paper "A Logic for Concurrent
Programming" presents New UNITY, giving more elegant foundations for a more
general class of languages. In recent work, Chandy and Sanders have proposed
new methods for reasoning about systems composed of many components.
This directory formalizes these new ideas for UNITY. The Isabelle examples
may seem strange to UNITY traditionalists. Hand UNITY proofs tend to be
written in the forwards direction, as in informal mathematics, while
Isabelle works best in a backwards (goal-directed) style. Programs are
expressed as sets of commands, where each command is a relation on states.
Quantification over commands using\<^verbatim>\<open>[]\<close> is easily expressed. At present,
there are no examples of quantification using\<^verbatim>\<open>||\<close>.
A UNITY assertion denotes the set of programs satisfying it, as in the
propositions-as-types paradigm. The resulting style is readable if
unconventional.
Safety proofs (invariants) are often proved automatically. Progress proofs
involving ENSURES can sometimes be proved automatically. The level of
automation appears to be about the same as in HOL-UNITY by Flemming Andersen
et al.
The directory \<^dir>\<open>Simple\<close> presents a few examples, mostly taken from Misra's
1994 paper, involving single programs. The directory \<^dir>\<open>Comp\<close> presents
examples of proofs involving program composition. \<close>
end
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