### docs: unit -> core

parent 86bc5be1
 ... ... @@ -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} \\ ... ...
 ... ... @@ -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. ... ...
 ... ... @@ -129,7 +129,7 @@ \newcommand{\mcar}{|#1|} \newcommand{\mcarp}{\mcar{#1}^{+}} \newcommand{\munit}{\mathord{\varepsilon}} \newcommand{\mcore}{\lfloor#1\rfloor} \newcommand{\mtimes}{\mathbin{\cdot}} \newcommand{\mdiv}{\mathbin{\div}} ... ...
 ... ... @@ -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.} ... ...
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