stan/Ecoop2024_TIforWildFJ
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Add WF type environment lemma (work in progress)

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JanUlrich 2024-01-29 18:44:21 +01:00
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commit 9aa89933ce
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10
soundness.tex
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@ -89,7 +89,6 @@ By structural induction over the expression $\texttt{e}$.
% T_r <: C<T> (S is in T) % T_r <: C<T> (S is in T)
% Is C<T> ok? % Is C<T> ok?
% we could proof: \Delta' |- C<T> ok (\Delta' are all Wildcards used in Unify)
% if every type environment \Delta supplied to Unify is ok (L <: U), then \sigma(a) = \Delta'.N implies \Delta' conforms to (L <: U) % if every type environment \Delta supplied to Unify is ok (L <: U), then \sigma(a) = \Delta'.N implies \Delta' conforms to (L <: U)
% this together with the X <. N constraints proofs T_r ok % this together with the X <. N constraints proofs T_r ok
@ -155,6 +154,15 @@ Method calls generate multiple constraints that share the same wildcard placehol
% $\text{fv}(\type{T}) \subseteq \text{dom}(\Delta)$. % $\text{fv}(\type{T}) \subseteq \text{dom}(\Delta)$.
% %UNIFY fails when there are free variables on the right side of a a =. T constraint % %UNIFY fails when there are free variables on the right side of a a =. T constraint
\begin{lemma}
\unify{} generates well-formed type environments
\begin{description}
\item[If] $(\Delta, \sigma) = \unify{}(\Delta', C)$
\item[and] $\forall \Delta_w \in C: \vdash \type{L} <: \type{U}$
\item[then] TODO
\end{description}
\end{lemma}
\begin{lemma} \begin{lemma}
Well-formedness is hereditary Well-formedness is hereditary
\begin{description} \begin{description}