docs: unit -> core

docs/algebra.tex

@@ -48,15 +48,15 @@ Note that $\COFEs$ is cartesian closed.
 \subsection{CMRA}
 
 \begin{defn}
-  A \emph{CMRA} is a tuple $(\monoid, (\mval_n \subseteq \monoid)_{n \in \mathbb{N}}, \munit: \monoid \to \monoid, (\mtimes) : \monoid \times \monoid \to \monoid, (\mdiv) : \monoid \times \monoid \to \monoid)$ satisfying
+  A \emph{CMRA} is a tuple $(\monoid, (\mval_n \subseteq \monoid)_{n \in \mathbb{N}}, \mcore{-}: \monoid \to \monoid, (\mtimes) : \monoid \times \monoid \to \monoid, (\mdiv) : \monoid \times \monoid \to \monoid)$ satisfying
   \begin{align*}
     \All n, m.& n \geq m \Ra V_n \subseteq V_m \tagH{cmra-valid-mono} \\
     \All \melt, \meltB, \meltC.& (\melt \mtimes \meltB) \mtimes \meltC = \melt \mtimes (\meltB \mtimes \meltC) \tagH{cmra-assoc} \\
     \All \melt, \meltB.& \melt \mtimes \meltB = \meltB \mtimes \melt \tagH{cmra-comm} \\
-    \All \melt.& \munit(\melt) \mtimes \melt = \melt \tagH{cmra-unit-id} \\
-    \All \melt.& \munit(\munit(\melt)) = \munit(\melt) \tagH{cmra-unit-idem} \\
-    \All \melt, \meltB.& \melt \leq \meltB \Ra \munit(\melt) \leq \munit(\meltB) \tagH{cmra-unit-mono} \\
-    \All n, \melt, \meltB.& (\melt \mtimes \meltB) \in \mval_n \Ra \melt \in \mval_n \tagH{cmra-unit-op} \\
+    \All \melt.& \mcore\melt \mtimes \melt = \melt \tagH{cmra-core-id} \\
+    \All \melt.& \mcore{\mcore\melt} = \mcore\melt \tagH{cmra-core-idem} \\
+    \All \melt, \meltB.& \melt \leq \meltB \Ra \mcore\melt \leq \mcore\meltB \tagH{cmra-core-mono} \\
+    \All n, \melt, \meltB.& (\melt \mtimes \meltB) \in \mval_n \Ra \melt \in \mval_n \tagH{cmra-valid-op} \\
     \All \melt, \meltB.& \melt \leq \meltB \Ra \melt \mtimes (\meltB \mdiv \melt) = \meltB \tagH{cmra-div-op} \\
     \All n, \melt, \meltB_1, \meltB_2.& \omit\rlap{$\melt \in \mval_n \land \melt \nequiv{n} \meltB_1 \mtimes \meltB_2 \Ra {}$} \\
     &\Exists \meltC_1, \meltC_2. \melt = \meltC_1 \mtimes \meltC_2 \land \meltC_1 \nequiv{n} \meltB_1 \land \meltC_2 \nequiv{n} \meltB_2 \tagH{cmra-extend} \\

docs/derived.tex

@@ -10,7 +10,7 @@
 \end{defn}
 
 Of course, $\always\prop$ is persistent for any $\prop$.
-Furthermore, by the proof rules given above, $t = t'$ as well as $\ownGGhost{\munit(\melt)}$ and $\knowInv\iname\prop$ are persistent.
+Furthermore, by the proof rules given above, $t = t'$ as well as $\ownGGhost{\mcore\melt}$ and $\knowInv\iname\prop$ are persistent.
 Persistence is preserved by conjunction, disjunction, separating conjunction as well as universal and existential quantification.
 
 In our proofs, we will implicitly add and remove $\always$ from persistent assertions as necessary, and generally treat them like normal, non-linear assumptions.

docs/iris.sty

@@ -129,7 +129,7 @@
 
 \newcommand{\mcar}[1]{|#1|}
 \newcommand{\mcarp}[1]{\mcar{#1}^{+}}
-\newcommand{\munit}{\mathord{\varepsilon}}
+\newcommand{\mcore}[1]{\lfloor#1\rfloor}
 \newcommand{\mtimes}{\mathbin{\cdot}}
 \newcommand{\mdiv}{\mathbin{\div}}
 

docs/logic.tex

@@ -107,7 +107,7 @@ Iris syntax is built up from a signature $\Sig$ and a countably infinite set $\t
       \pi_i\; \term \mid
       \Lam \var:\type.\term \mid
       \term(\term)  \mid
-      \munit \mid
+      \mcore\term \mid
       \term \mtimes \term \mid
 \\&
     \FALSE \mid
@@ -214,7 +214,7 @@ In writing $\vctx, x:\type$, we presuppose that $x$ is not already declared in $
 	{\vctx \proves \wtt{\term(\termB)}{\type'}}
 %%% monoids
 \and
-	\infer{}{\vctx \proves \wtt{\munit}{\textlog{M} \to \textlog{M}}}
+	\infer{\vctx \proves \wtt\melt{\textlog{M}}}{\vctx \proves \wtt{\mcore\melt}{\textlog{M}}}
 \and
 	\infer{\vctx \proves \wtt{\melt}{\textlog{M}} \and \vctx \proves \wtt{\meltB}{\textlog{M}}}
 		{\vctx \proves \wtt{\melt \mtimes \meltB}{\textlog{M}}}
@@ -477,7 +477,7 @@ This is entirely standard.
 \and
 { \knowInv\iname\prop \Ra \always \knowInv\iname\prop}
 \and
-{ \ownGGhost{\munit(\melt)} \Ra \always \ownGGhost{\munit(\melt)}}
+{ \ownGGhost{\mcore\melt} \Ra \always \ownGGhost{\mcore\melt}}
 \end{mathpar}
 
 \paragraph{Laws of primitive view shifts.}