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Merge branch 'master' of ssh://gitea.hb.dhbw-stuttgart.de:2222/stan/Ecoop2024_TIforWildFJ

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Andreas Stadelmeier 2024-02-02 13:23:02 +01:00
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soundness.tex
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@ -106,6 +106,13 @@ $\texttt{let}\ \texttt{x} : \wcNtype{\Delta'}{N} = \texttt{e} \ \texttt{in}\
%TODO: show that this type exists \wcNtype{\Delta'}{N} (a \Delta' which only contains free variables of the type N) %TODO: show that this type exists \wcNtype{\Delta'}{N} (a \Delta' which only contains free variables of the type N)
% and which is a supertype of T_r (so no free variables in T_r) % and which is a supertype of T_r (so no free variables in T_r)
We could use unify to generate S by
$\unify{}((\Delta, \Delta', \overline{\Delta}), [\ol{\tv{a}}/\ol{X}][\ol{\tv{b}}/\ol{Y}]\set{\ol{N} \lessdot \ol{T}, \type{N} \lessdot \exptype{C}{\ol{X}}})$
%TODO: Proof that this always works.
% Only the variables in \Delta' ol\Delta are used. Maybe change the lemma 10 to that.
% That part of the unify algorithm is not influenced by other free variables
This implies $\text{dom}(\Delta') \subseteq \text{fv}(\type{N})$ and $\text{dom}(\Delta') \subseteq \text{fv}(\type{N})$ This implies $\text{dom}(\Delta') \subseteq \text{fv}(\type{N})$ and $\text{dom}(\Delta') \subseteq \text{fv}(\type{N})$
$\Delta, \Delta', \overline{\Delta} \vdash [\ol{S}/\ol{X}]\type{U} \type{T}$, $\Delta, \Delta', \overline{\Delta} \vdash [\ol{S}/\ol{X}]\type{U} \type{T}$,
$\Delta, \Delta', \overline{\Delta} \vdash \ol{N} <: [\ol{S}/\ol{X}]\ol{U}$, $\Delta, \Delta', \overline{\Delta} \vdash \ol{N} <: [\ol{S}/\ol{X}]\ol{U}$,