Commit 7a2b2c6a authored by Ralf Jung's avatar Ralf Jung
Browse files

docs: fix using the fixpoint for WP

parent 253d891a
......@@ -196,7 +196,7 @@
%% various pieces of Syntax
\def\MU #1.{\mu #1.\spac}%
\def\MU #1.{\mu\spac #1.\spac}%
\def\Lam #1.{\lambda #1.\spac}%
......@@ -113,13 +113,13 @@ Finally, we can define the core piece of the program logic, the assertion that r
We assume that everything making up the definition of the language, \ie values, expressions, states, the conversion functions, reduction relation and all their properties, are suitably reflected into the logic (\ie they are part of the signature $\Sig$).
\textdom{pre-wp}(\textdom{wp})(\mask, \expr, \pred) \eqdef{}&
(\Exists\val. \toval(\expr) = \val \land \pvs[\mask] \prop) \lor {}\\
&\Bigl(\toval(\expr) = \bot \land \All \state. \ownGhost{\gname_{\textmon{State}}}{\authfull \state} \vsW[\mask][\emptyset] {}\\
\textdom{wp} \eqdef{}& \MU \textdom{wp}. \Lam \mask, \expr, \pred. \\
& (\Exists\val. \toval(\expr) = \val \land \pvs[\mask] \prop) \lor {}\\
& \Bigl(\toval(\expr) = \bot \land \All \state. \ownGhost{\gname_{\textmon{State}}}{\authfull \state} \vsW[\mask][\emptyset] {}\\
&\qquad \red(\expr, \state) * \later\All \expr', \state', \bar\expr. (\expr, \state \step \expr', \state', \bar\expr) \vsW[\emptyset][\mask] {}\\
&\qquad\qquad \ownGhost{\gname_{\textmon{State}}}{\authfull \state'} * \textdom{wp}(\mask, \expr', \pred) * \Sep_{\expr'' \in \bar\expr} \textdom{wp}(\top, \expr'', \Lam \any. \TRUE)\Bigr) \\
% (* value case *)
\wpre\expr[\mask]{\Ret\val. \prop} \eqdef{}& (\MU \textdom{wp}. \textdom{pre-wp}(\textdom{wp}))(\mask, \expr, \Lam\val.\prop)
\wpre\expr[\mask]{\Ret\val. \prop} \eqdef{}& \textdom{wp}(\mask, \expr, \Lam\val.\prop)
If we leave away the mask, we assume it to default to $\top$.
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment