docs: update atomicity

CHANGELOG.md

@@ -5,9 +5,9 @@ Coq development, but not every API-breaking change is listed.  Changes marked
 
 ## Iris 3.0 (unfinished)
 
-* There now is a deprecation process.  The modules `*.deprecated`
-  contain deprecated notations and definitions that are provided for
-  backwards compatibility and will be removed in a future version of Iris.
+* There now is a deprecation process.  The modules `*.deprecated` contain
+  deprecated notations and definitions that are provided for backwards
+  compatibility and will be removed in a future version of Iris.
 * View shifts are radically simplified to just internalize frame-preserving
   updates.  Weakestpre is defined inside the logic, and invariants and view
   shifts with masks are also coded up inside Iris.  Adequacy of weakestpre is
@@ -23,11 +23,11 @@ Coq development, but not every API-breaking change is listed.  Changes marked
 * Renaming and moving things around: uPred and the rest of the base logic are
   in `base_logic`, while `program_logic` is for everything involving the
   general Iris notion of a language.
-* [#] Slightly weaker notion of atomicity: an expression is atomic if it reduces
-  in one step to something that does not reduce further.
-* Changed notation for embedding Coq assertions into Iris.  The new notation
-  is ⌜φ⌝.  Also removed `=` and `⊥` from the Iris scope.
-  (The old notations are provided in `base_logic.deprecated`.)
+* Slightly weaker notion of atomicity: an expression is atomic if it reduces in
+  one step to something that does not reduce further.
+* Changed notation for embedding Coq assertions into Iris.  The new notation is
+  ⌜φ⌝.  Also removed `=` and `⊥` from the Iris scope.  (The old notations are
+  provided in `base_logic.deprecated`.)
 * Up-closure of namespaces is now a notation (↑) instead of a coercion.
 * With invariants and the physical state being handled in the logic, there
   is no longer any reason to demand the CMRA unit to be discrete.

docs/language.tex

@@ -2,7 +2,7 @@
 \label{sec:language}
 
 A \emph{language} $\Lang$ consists of a set \Expr{} of \emph{expressions} (metavariable $\expr$), a set \Val{} of \emph{values} (metavariable $\val$), and a nonempty set \State of \emph{states} (metavariable $\state$) such that
-\begin{itemize}
+\begin{itemize}[itemsep=0pt]
 \item There exist functions $\ofval : \Val \to \Expr$ and $\toval : \Expr \pfn \Val$ (notice the latter is partial), such that
 \begin{mathpar}
 {\All \expr, \val. \toval(\expr) = \val \Ra \ofval(\val) = \expr} \and
@@ -21,8 +21,8 @@ A \emph{language} $\Lang$ consists of a set \Expr{} of \emph{expressions} (metav
 \end{defn}
 
 \begin{defn}
-  An expression $\expr$ is said to be \emph{atomic} if it reduces in one step to a value:
-  \[ \All\state_1, \expr_2, \state_2, \vec\expr. \expr, \state_1 \step \expr_2, \state_2, \vec\expr \Ra \Exists \val_2. \toval(\expr_2) = \val_2 \]
+  An expression $\expr$ is \emph{atomic} if it reduces in one step to something irreducible:
+  \[ \All\state_1, \expr_2, \state_2, \vec\expr. \expr, \state_1 \step \expr_2, \state_2, \vec\expr \Ra \lnot \red(\expr_2, \state_2) \]
 \end{defn}
 
 \begin{defn}[Context]
@@ -55,3 +55,8 @@ For any language $\Lang$, we define the corresponding thread-pool semantics.
      \cfg{\tpool \dplus [\expr_2] \dplus \tpool' \dplus \vec\expr}{\state_2}}
 \end{mathpar}
 
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "iris"
+%%% End: