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Specification LanguageBasedNIFTrans
enrich MeydenTrans with
comment: Test to connect language based NIF with purge for the transitive case.
         This requires that all names have a domain and a stronger notion of observe
         (or a weaker notion of language based NIF, see below).
         no-read-up and no-write-down are not needed which is somewhat strange.;
   functions 
      cdom : name → secdomain;
   predicates 
      eqlb : systemstate × secdomain × systemstate;
   
   axioms 
      no-read-up :  ⊦ observe(nam, d) → cdom(nam) ⇒ d;
      no-write-down :  ⊦ alter(nam, d) → d ⇒ cdom(nam);
      observe-all-names :  ⊦ cdom(nam) ⇒ d → observe(nam, d);
      comment: this is the stronger version of observe.;
       
      eqlb-def :  ⊦ eqlb(sys, d, sys0) ↔ (∀ nam. cdom(nam) ⇒ d → contents(sys, nam) = contents(sys0, nam));
      LanguageBasedNIF-run
      : ∀ nam. cdom(nam) ⇒ d → contents(sys, nam) = contents(sys0, nam)
        ⊦ 
        ∀ nam. cdom(nam) ⇒ d → contents(run(sys, cl), nam) = contents(run(sys0, cl), nam);
      used for : theorem;
       
      LanguageBasedNIF-observe-run : eqd(sys, d, sys0) ⊦ ∀ nam. observe(nam, d) → contents(run(sys, cl), nam) = contents(run(sys0, cl), nam);
      comment: holds without observe-all-names.;
      used for : theorem;
       
      eqd-implies-lbnif : eqd(sys, d, sys0) ⊦ ∀ nam. cdom(nam) ⇒ d → contents(sys, nam) = contents(sys0, nam);
      used for : theorem;
       
      obs-implies-lbnif : obs(sys, d) = obs(sys0, d) ⊦ ∀ nam. cdom(nam) ⇒ d → contents(sys, nam) = contents(sys0, nam);
      used for : theorem;
       
      obs-implies-lbnif-weaker : obs(sys, d) = obs(sys0, d) ⊦ ∀ nam. cdom(nam) ⇒ d ∧ observe(nam, d) → contents(sys, nam) = contents(sys0, nam);
      used for : theorem;
       
end enrich