diff --git a/docs/program-logic.tex b/docs/program-logic.tex index 34a9dbfcce8ff62313a92ff8f9b7a0794982a526..5cf32a73a32880cd5af92c653d928513d06bf447 100644 --- a/docs/program-logic.tex +++ b/docs/program-logic.tex @@ -352,7 +352,9 @@ Second, a proof of a weakest precondition with any postcondition should imply th \end{enumerate} \end{defn} -To express the adequacy statement for functional correctness, we assume that the signature $\Sig$ adds a predicate $\pred$ to the logic which reflects the set $V$ of legal return values into the logic: +To express the adequacy statement for functional correctness, we assume that the signature $\Sig$ adds a predicate $\pred$ to the logic: +\[ \pred : \Val \to \Prop \in \SigFn \] +Furthermore, we assume that the \emph{interpretation} $\Sem\pred$ of $\pred$ reflects some set $V$ of legal return values into the logic (also see \Sref{sec:model}): \[\begin{array}{rMcMl} \Sem\pred &:& \Sem{\Val\,} \nfn \Sem\Prop \\ \Sem\pred &\eqdef& \Lam \val. \Lam \any. \setComp{n}{v \in V}