\subsection{Axioms from the logic of (affine) bunched implications}
\begin{mathpar}
...
...
@@ -807,3 +805,8 @@ The following specializations cover all cases of a heap-manipulating lambda calc
The first is restricted to deterministic pure reductions, like $\beta$-reduction.
The second is suited to proving triples for (possibly non-deterministic) atomic expressions; for example, with $\expr\eqdef\;!\ell$ (dereferencing $\ell$) and $\state\eqdef h \mtimes\ell\mapsto\valB$ and $\pred(\val, \state')\eqdef\state' =(h \mtimes\ell\mapsto\valB)\land\val=\valB$, one obtains the axiom $\All h, \ell, \valB. \hoare{\ownPhys{h \mtimes\ell\mapsto\valB}}{!\ell}{\Ret\val. \val=\valB\land\ownPhys{h \mtimes\ell\mapsto\valB}}$.
%Axioms for CAS-like operations can be obtained by first deriving rules for the two possible cases, and then using the disjunction rule.