stan/Ecoop2024_TIforWildFJ
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Cleanup CC command

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Andreas Stadelmeier 2024-04-23 21:32:41 +02:00
parent c42477bf8a
commit 295f1ee567
1 changed files with 1 additions and 3 deletions
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soundness.tex
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@ -1,7 +1,5 @@
\section{Soundness} \section{Soundness}
\newcommand{\CC}{\text{CC}}
\begin{lemma} \begin{lemma}
A sound TypelessFJ program is also sound under LetFJ type rules. A sound TypelessFJ program is also sound under LetFJ type rules.
\begin{description} \begin{description}
@ -426,7 +424,7 @@ Therefore we can say that $\Delta, \Delta', \overline{\Delta} \vdash \sigma'(\ex
% List<X> <. Y.List<Y>, free variables are either in % List<X> <. Y.List<Y>, free variables are either in
If $\text{fv}(\exptype{C}{\ol{S}}) = \text{fv}(\wctype{\overline{\wildcard{A}{\type{U}}{\type{L}}}}{C}{\ol{T}}) = \emptyset$ the preposition holds by Assumption and S-Exists. If $\text{fv}(\exptype{C}{\ol{S}}) = \text{fv}(\wctype{\overline{\wildcard{A}{\type{U}}{\type{L}}}}{C}{\ol{T}}) = \emptyset$ the preposition holds by Assumption and S-Exists.
Otherwise Otherwise
$\Delta' \vdash \CC{}(\sigma(\exptype{C}{\ol{S}})) <: \sigma(\wctype{\overline{\wildcard{A}{\type{U}}{\type{L}}}}{C}{\ol{T}})$ $\Delta' \vdash \text{CC}(\sigma(\exptype{C}{\ol{S}})) <: \sigma(\wctype{\overline{\wildcard{A}{\type{U}}{\type{L}}}}{C}{\ol{T}})$
holds with any $\Delta'$ so that $(\text{fv}(\exptype{C}{\ol{S}}) \cup \text{fv}(\wctype{\overline{\wildcard{A}{\type{U}}{\type{L}}}}{C}{\ol{T}}) ) \subseteq \text{dom}(\Delta') $. holds with any $\Delta'$ so that $(\text{fv}(\exptype{C}{\ol{S}}) \cup \text{fv}(\wctype{\overline{\wildcard{A}{\type{U}}{\type{L}}}}{C}{\ol{T}}) ) \subseteq \text{dom}(\Delta') $.
\item[Match] Assumption, S-Trans \item[Match] Assumption, S-Trans
\item[Trim] Assumption and S-Exists \item[Trim] Assumption and S-Exists