stan/WLP2024
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Add Intro and Termination

Browse Source
This commit is contained in:
JanUlrich 2024-06-29 19:46:03 +02:00
parent 59e80f556c
commit df402dfb2b
1 changed files with 17 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

17
aspUnify.tex
View File

@ -87,6 +87,13 @@ Java has adopted more and more type inference features over time.
Currently Java only has local type inference. Currently Java only has local type inference.
We want to bring type inference for Java to the next level. We want to bring type inference for Java to the next level.
Our type inference algorithms for Java are described in a formal manner in
\cite{MartinUnify}, \cite{TIforGFJ}.
The first prototype implementation put the focus on a correct implementation rather than
fast execution times.
These programs tend to be in exponential time upper bounded by the amount of ambiguous method calls and subtype relations.
%TODO: Example with multiple calls to m.toString(). All possibilities are checked in a naive implementation!
\section{Subtyping} \section{Subtyping}
\begin{mathpar} \begin{mathpar}
\inferrule[Refl]{}{ \inferrule[Refl]{}{
@ -343,7 +350,14 @@ The implication rules defined in chapter \ref{sec:implicationRules} can be trans
$\exptype{C}{\ol{X}}$ & \texttt{type("C", paramX)}\\ $\exptype{C}{\ol{X}}$ & \texttt{type("C", paramX)}\\
\end{tabular} \end{tabular}
\section{Proofs}
\begin{lemma}{Substitution}
\end{lemma}
\section{Termination} \section{Termination}
The amount of different constraints is limited by the maximum amount of encapsulated generics. The amount of different constraints is limited by the maximum amount of encapsulated generics.
The only part that is able to add an additional nesting is the Subst-Param rule. The only part that is able to add an additional nesting is the Subst-Param rule.
Here a type placeholder inside a type parameter list is replaced by another type which possibly adds Here a type placeholder inside a type parameter list is replaced by another type which possibly adds
@ -352,6 +366,9 @@ another layer of nesting but it also removes one type placeholder.
There must be one substitution that does not add another type placeholder. There must be one substitution that does not add another type placeholder.
Otherwise there has to be a loop and this woul lead to an incorrect constraint set due to the Fail-Sigma rule. Otherwise there has to be a loop and this woul lead to an incorrect constraint set due to the Fail-Sigma rule.
The Subst-Param rule can only be applied a finite number of times.
Due to the substitution lemma and the Sigma-Fail rule the Subst-Param rule can only be applied once per type placeholder.
\section{Completeness} \section{Completeness}
To proof completeness we have to show that every type can be replaced by a placeholder in a correct constraint set. To proof completeness we have to show that every type can be replaced by a placeholder in a correct constraint set.