cfbolz at codespeak.net cfbolz at codespeak.net
Thu Oct 7 17:08:44 CEST 2010

Author: cfbolz
Date: Thu Oct  7 17:08:42 2010
New Revision: 77689

Modified:
Log:
use typewriter font for operations

==============================================================================
+++ pypy/extradoc/talk/pepm2011/math.lyx	Thu Oct  7 17:08:42 2010
@@ -138,7 +138,7 @@
\begin_inset Text

\begin_layout Plain Layout
-\begin_inset Formula ${\displaystyle \frac{l\,\mathrm{fresh}}{v=\mathrm{new}(T),E,H\overset{\mathrm{run}}{\Longrightarrow}E\left[v\mapsto l\right],H\left[l\mapsto\left(T,\mathrm{null},\mathrm{null}\right)\right]}}$
+\begin_inset Formula ${\displaystyle \frac{l\,\mathrm{fresh}}{v=\mathtt{new}(T),E,H\overset{\mathrm{run}}{\Longrightarrow}E\left[v\mapsto l\right],H\left[l\mapsto\left(T,\mathrm{null},\mathrm{null}\right)\right]}}$
\end_inset

@@ -181,7 +181,7 @@
\begin_inset Text

\begin_layout Plain Layout
-\begin_inset Formula ${\displaystyle \frac{\mathrm{type}(H(E(v))=T}{\mathrm{guard}(v,T),E,H\overset{\mathrm{run}}{\Longrightarrow}E,H}}$
+\begin_inset Formula ${\displaystyle \frac{\mathrm{type}(H(E(v))=T}{\mathtt{guard\_class}(v,T),E,H\overset{\mathrm{run}}{\Longrightarrow}E,H}}$
\end_inset

@@ -206,7 +206,7 @@
\begin_inset Text

\begin_layout Plain Layout
-\begin_inset Formula ${\displaystyle \frac{\,}{v=\mathrm{get}(u,F),E,H\overset{\mathrm{run}}{\Longrightarrow}E\left[v\mapsto H\left(E\left(u\right)\right)_{F}\right],H}}$
+\begin_inset Formula ${\displaystyle \frac{\,}{v=\mathtt{get}(u,F),E,H\overset{\mathrm{run}}{\Longrightarrow}E\left[v\mapsto H\left(E\left(u\right)\right)_{F}\right],H}}$
\end_inset

@@ -247,7 +247,7 @@
\begin_inset Text

\begin_layout Plain Layout
-\begin_inset Formula ${\displaystyle \frac{\mathrm{type}(H(E(v))\neq T}{\mathrm{guard}(v,T),E,H\overset{\mathrm{run}}{\Longrightarrow}\bot,\bot}}$
+\begin_inset Formula ${\displaystyle \frac{\mathrm{type}(H(E(v))\neq T}{\mathtt{guard\_class}(v,T),E,H\overset{\mathrm{run}}{\Longrightarrow}\bot,\bot}}$
\end_inset

@@ -272,7 +272,7 @@
\begin_inset Text

\begin_layout Plain Layout
-\begin_inset Formula ${\displaystyle \frac{\,}{\mathrm{set}\left(v,F,u\right),E,H\overset{\mathrm{run}}{\Longrightarrow}E,H\left[E\left(v\right)\mapsto\left(H\left(E\left(v\right)\right)!_{F}E(u)\right)\right]}}$
+\begin_inset Formula ${\displaystyle \frac{\,}{\mathtt{set}\left(v,F,u\right),E,H\overset{\mathrm{run}}{\Longrightarrow}E,H\left[E\left(v\right)\mapsto\left(H\left(E\left(v\right)\right)!_{F}E(u)\right)\right]}}$
\end_inset

@@ -360,7 +360,7 @@
\begin_inset Text

\begin_layout Plain Layout
-\begin_inset Formula ${\displaystyle \frac{v^{*}\,\mathrm{fresh}}{v=\mathrm{new}(T),E,S\overset{\mathrm{opt}}{\Longrightarrow}\left\langle \,\right\rangle ,E\left[v\mapsto v^{*}\right],S\left[v^{*}\mapsto\left(T,\mathrm{null,null}\right)\right]}}$
+\begin_inset Formula ${\displaystyle \frac{v^{*}\,\mathrm{fresh}}{v=\mathtt{new}(T),E,S\overset{\mathrm{opt}}{\Longrightarrow}\left\langle \,\right\rangle ,E\left[v\mapsto v^{*}\right],S\left[v^{*}\mapsto\left(T,\mathrm{null,null}\right)\right]}}$
\end_inset

@@ -385,7 +385,7 @@
\begin_inset Text

\begin_layout Plain Layout
-\begin_inset Formula ${\displaystyle \frac{E(u)\in\mathrm{dom}(S)}{v=\mathrm{get}(u,F),E,S\overset{\mathrm{opt}}{\Longrightarrow}\left\langle \,\right\rangle ,E\left[v\mapsto S(E(u))_{F}\right],S}}$
+\begin_inset Formula ${\displaystyle \frac{E(u)\in\mathrm{dom}(S)}{v=\mathtt{get}(u,F),E,S\overset{\mathrm{opt}}{\Longrightarrow}\left\langle \,\right\rangle ,E\left[v\mapsto S(E(u))_{F}\right],S}}$
\end_inset

@@ -408,7 +408,7 @@
\begin_inset Text

\begin_layout Plain Layout
-\begin_inset Formula ${\displaystyle \frac{E(u)\notin\mathrm{dom}(S)\, v^{*}\,\mathrm{fresh}}{v=\mathrm{get}(u,F),E,S\overset{\mathrm{opt}}{\Longrightarrow}\left\langle v^{*}=\mathrm{get}(E(u),F)\right\rangle ,E\left[v\mapsto v^{*}\right],S}}$
+\begin_inset Formula ${\displaystyle \frac{E(u)\notin\mathrm{dom}(S)\, v^{*}\,\mathrm{fresh}}{v=\mathtt{get}(u,F),E,S\overset{\mathrm{opt}}{\Longrightarrow}\left\langle v^{*}=\mathtt{get}(E(u),F)\right\rangle ,E\left[v\mapsto v^{*}\right],S}}$
\end_inset

@@ -433,7 +433,7 @@
\begin_inset Text

\begin_layout Plain Layout
-\begin_inset Formula ${\displaystyle \frac{E(v)\in\mathrm{dom}(S)}{\mathrm{set}\left(v,F,u\right),E,S\overset{\mathrm{opt}}{\Longrightarrow}\left\langle \,\right\rangle ,E,S\left[E\left(v\right)\mapsto\left(S(E(v))!_{F}E(u)\right)\right]}}$
+\begin_inset Formula ${\displaystyle \frac{E(v)\in\mathrm{dom}(S)}{\mathtt{set}\left(v,F,u\right),E,S\overset{\mathrm{opt}}{\Longrightarrow}\left\langle \,\right\rangle ,E,S\left[E\left(v\right)\mapsto\left(S(E(v))!_{F}E(u)\right)\right]}}$
\end_inset

@@ -456,7 +456,7 @@
\begin_inset Text

\begin_layout Plain Layout
-\begin_inset Formula ${\displaystyle \frac{E(v)\notin\mathrm{dom}\left(S\right),\,\left(E(v),S\right)\overset{\mathrm{lift}}{\Longrightarrow}\left(\mathrm{ops},S^{\prime}\right)}{\mathrm{set}\left(v,F,u\right),E,S\overset{\mathrm{opt}}{\Longrightarrow}\mathrm{ops}::\left\langle \mathrm{set}\left(E(v),F,E(u)\right)\right\rangle ,E,S^{\prime}}}$
+\begin_inset Formula ${\displaystyle \frac{E(v)\notin\mathrm{dom}\left(S\right),\,\left(E(v),S\right)\overset{\mathrm{lift}}{\Longrightarrow}\left(\mathrm{ops},S^{\prime}\right)}{\mathtt{set}\left(v,F,u\right),E,S\overset{\mathrm{opt}}{\Longrightarrow}\mathrm{ops}::\left\langle \mathtt{set}\left(E(v),F,E(u)\right)\right\rangle ,E,S^{\prime}}}$
\end_inset

@@ -481,7 +481,7 @@
\begin_inset Text

\begin_layout Plain Layout
-\begin_inset Formula ${\displaystyle \frac{E(v)\in\mathrm{dom}(S),\,\mathrm{type}(S(E(v)))=T}{\mathrm{guard}(v,T),E,S\overset{\mathrm{opt}}{\Longrightarrow}\left\langle \,\right\rangle ,E,S}}$
+\begin_inset Formula ${\displaystyle \frac{E(v)\in\mathrm{dom}(S),\,\mathrm{type}(S(E(v)))=T}{\mathtt{guard\_class}(v,T),E,S\overset{\mathrm{opt}}{\Longrightarrow}\left\langle \,\right\rangle ,E,S}}$
\end_inset

@@ -504,7 +504,7 @@
\begin_inset Text

\begin_layout Plain Layout
-\begin_inset Formula ${\displaystyle \frac{E(v)\notin\mathrm{dom}(S)\vee\mathrm{type}(S(E(v)))\neq T,\,\left(E(v),S\right)\overset{\mathrm{lift}}{\Longrightarrow}\left(\mathrm{ops},S^{\prime}\right)}{\mathrm{guard}(v,T),E,S\overset{\mathrm{opt}}{\Longrightarrow}\left\langle \mathrm{guard}(E\left(v\right),T)\right\rangle ,E,S^{\prime}}}$
+\begin_inset Formula ${\displaystyle \frac{E(v)\notin\mathrm{dom}(S)\vee\mathrm{type}(S(E(v)))\neq T,\,\left(E(v),S\right)\overset{\mathrm{lift}}{\Longrightarrow}\left(\mathrm{ops},S^{\prime}\right)}{\mathtt{guard\_class}(v,T),E,S\overset{\mathrm{opt}}{\Longrightarrow}\left\langle \mathtt{guard\_class}(E\left(v\right),T)\right\rangle ,E,S^{\prime}}}$
\end_inset

@@ -552,7 +552,7 @@
\begin_inset Text

\begin_layout Plain Layout
-\begin_inset Formula ${\displaystyle \frac{v^{*}\in\mathrm{dom}(S),\,\left(v^{*},S\right)\overset{\mathrm{liftfields}}{=\!=\!\Longrightarrow}\left(\mathrm{ops},S^{\prime}\right)}{v^{*},S\overset{\mathrm{lift}}{\Longrightarrow}\left\langle v^{*}=\mathrm{new}\left(T\right)\right\rangle ::ops,S^{\prime}}}$
+\begin_inset Formula ${\displaystyle \frac{v^{*}\in\mathrm{dom}(S),\,\left(v^{*},S\right)\overset{\mathrm{liftfields}}{=\!=\!\Longrightarrow}\left(\mathrm{ops},S^{\prime}\right)}{v^{*},S\overset{\mathrm{lift}}{\Longrightarrow}\left\langle v^{*}=\mathtt{new}\left(T\right)\right\rangle ::ops,S^{\prime}}}$
\end_inset

@@ -575,7 +575,7 @@
\begin_inset Text

\begin_layout Plain Layout
-\begin_inset Formula ${\displaystyle \frac{\left(S\left(v^{*}\right)_{L},S\setminus\left\{ v^{*}\mapsto S\left(v^{*}\right)\right\} \right)\overset{\mathrm{lift}}{\Longrightarrow}\left(\mathrm{ops}_{L},S^{\prime}\right),\,\left(S\left(v^{*}\right)_{R},S^{\prime}\right)\overset{\mathrm{lift}}{\Longrightarrow}\left(\mathrm{ops}_{R},S^{\prime\prime}\right)}{v^{*},S\overset{\mathrm{liftfields}}{=\!=\!\Longrightarrow}\mathrm{ops}_{L}::ops_{R}::\left\langle \mathrm{set}\left(v^{*},L,S\left(v^{*}\right)_{L}\right),\,\mathrm{set}\left(v^{*},R,S\left(v^{*}\right)_{R}\right)\right\rangle ,S^{\prime}}}$
+\begin_inset Formula ${\displaystyle \frac{\left(S\left(v^{*}\right)_{L},S\setminus\left\{ v^{*}\mapsto S\left(v^{*}\right)\right\} \right)\overset{\mathrm{lift}}{\Longrightarrow}\left(\mathrm{ops}_{L},S^{\prime}\right),\,\left(S\left(v^{*}\right)_{R},S^{\prime}\right)\overset{\mathrm{lift}}{\Longrightarrow}\left(\mathrm{ops}_{R},S^{\prime\prime}\right)}{v^{*},S\overset{\mathrm{liftfields}}{=\!=\!\Longrightarrow}\mathrm{ops}_{L}::ops_{R}::\left\langle \mathtt{set}\left(v^{*},L,S\left(v^{*}\right)_{L}\right),\,\mathtt{set}\left(v^{*},R,S\left(v^{*}\right)_{R}\right)\right\rangle ,S^{\prime}}}$
\end_inset