Theory Introduction

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―‹ ********************************************************************
 * Project         : HOL-CSPM - Architectural operators for HOL-CSP
 *
 * Author          : Benoît Ballenghien, Safouan Taha, Burkhart Wolff
 *
 * This file       : Introduction
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chapter‹ Introduction ›

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theory Introduction                                               
  imports "HOL-CSP.Assertions"
begin 
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section‹Motivations›

text ‹session‹HOL-CSP› cite‹"HOL-CSP-AFP"› is a formalization in Isabelle/HOL of 
      the work of Hoare and Roscoe on the denotational semantics of the 
      Failure/Divergence Model of CSP. It follows essentially the presentation of CSP 
      in Roscoe's Book "Theory and Practice of Concurrency" cite‹"roscoe:csp:1998"›
      and the semantic details in a joint Paper of Roscoe and Brooks
      "An improved failures model for communicating processes" cite‹"brookes-roscoe85"›.›

text ‹In the session session‹HOL-CSP› are introduced the type typ‹'α process›, several 
      classic CSP operators and number of laws that govern their interactions.

      Four of them are binary operators: the non-deterministic choice term‹P ⊓ Q›, 
      the deterministic choice term‹P □ Q›, the synchronization term‹P ⟦S⟧ Q› and the
      sequential composition term‹P ; Q›.›

text ‹Analogously to the  finite sum
      @{term [mode=latex_sum, eta_contract = false] ‹∑i = 0::nat..n. a i›} which is generalization
      of the addition term‹a + b›,  we define generalisations of the binary operators 
      of CSP.

      The most straight-forward way to do so would be a fold on a list of processes.
      However, in many cases, we have additional properties, like commutativity, idempotency, etc.
      that allow for stronger/more abstract constructions. In particular, in several cases,
      generalization to unbounded and even infinite index-sets are possible.

      The notations we choose are widely inspired by the CSP$_M$ syntax of FDR:
      🌐‹https://cocotec.io/fdr/manual/cspm.html›.›

text ‹In this session we therefore introduce the multi-operators associated respectively
      with term‹P ⊓ Q›, term‹P □ Q›, term‹P ⟦S⟧ Q› and term‹P ; Q›. 
      We prove their continuity and refinements rules, 
      as well as some laws governing their interactions.›

text ‹We also give the definitions of the POTS and Dining Philosophers examples,
      which greatly benefit from the newly introduced generalized operators.

      Since they appear naturally when modeling complex architectures,
      we may call them ∗‹architectural operators› of CSP.›

text ‹Finally this session also includes results on the notion of const‹events_of›, 
      and a very powerful result about const‹deadlock_free› and const‹Sync›:
      the interleaving term‹P ||| Q› is const‹deadlock_free› if term‹P› and term‹Q› are.

      \newpage›


section‹The Global Architecture of HOL-CSPM›

text‹
\begin{figure}[ht]
  \centering
  \includegraphics[width=0.70\textwidth]{figures/session_graph.pdf}
	\caption{The overall architecture}
	\label{fig:fig1}
\end{figure}
›

text‹The global architecture of HOL-CSPM is shown in \autoref{fig:fig1}.
The entire package resides on: 
▸ session‹HOL-Eisbach› from the Isabelle/HOL distribution,
▸ session‹HOLCF› from the Isabelle/HOL distribution, and
▸ session‹HOL-CSP› 2.0 from the Isabelle Archive of Formal Proofs.
›

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end
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