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modified:   martin.bib
	modified:   prolog.tex
	new file:   relatedwork.tex
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1
TIforWildFJ.tex
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@ -146,6 +146,7 @@ class Example{
\include{soundness}
%\include{termination}
\include{relatedwork}
\bibliography{martin}

52
martin.bib
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@ -50,6 +50,8 @@ keywords = {subtyping, type inference, principal types}
SERIES = {Lecture Notes in Artificial Intelligence}
}
@article{DM82,
author={Luis Damas and Robin Milner},
title={Principal type-schemes for functional programs},
@ -65,6 +67,21 @@ keywords = {subtyping, type inference, principal types}
pages={23-41},
month=Jan,
year={1965}}
@article{DBLP:journals/jcss/Milner78,
author = {Robin Milner},
title = {A Theory of Type Polymorphism in Programming},
journal = {Journal of Computer and Systems Sciences},
volume = {17},
number = {3},
pages = {348--375},
year = {1978},
url = {https://doi.org/10.1016/0022-0000(78)90014-4},
doi = {10.1016/0022-0000(78)90014-4},
timestamp = {Tue, 16 Feb 2021 14:04:22 +0100},
biburl = {https://dblp.org/rec/journals/jcss/Milner78.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{MM82,
author = {Martelli, Alberto and Montanari, Ugo},
@ -336,6 +353,14 @@ articleno = {138},
numpages = {22},
keywords = {Null, Java Wildcards, Existential Types}
}
@inproceedings{AT16,
author = {Amin, Nada and Tate, Ross},
year = {2016},
month = {10},
pages = {838-848},
title = {Java and scala's type systems are unsound: the existential crisis of null pointers},
doi = {10.1145/2983990.2984004}
}
@InProceedings{TIforFGJ,
author = {Stadelmeier, Andreas and Pl\"{u}micke, Martin and Thiemann, Peter},
title = {{Global Type Inference for Featherweight Generic Java}},
@ -362,6 +387,16 @@ keywords = {Null, Java Wildcards, Existential Types}
publisher={Addison-Wesley Professional}
}
@Book{GoJoStBrBuSm23,
author = {Gosling, James and Joy, Bill and Steele, Guy and Bracha, Gilad and Buckley, Alex and Smith, Daniel},
title = "{The Java\textsuperscript{\textregistered} {L}anguage {S}pecification}",
Optpublisher = "Addison-Wesley",
url = {https://docs.oracle.com/javase/specs/jls/se21/jls21.pdf},
edition = {{J}ava {S}{E} 21},
year = 2023,
OPtseries = {The Java series}
}
@inproceedings{semanticWildcardModel,
title={Towards a semantic model for Java wildcards},
author={Summers, Alexander J and Cameron, Nicholas and Dezani-Ciancaglini, Mariangiola and Drossopoulou, Sophia},
@ -476,3 +511,20 @@ keywords = {Compilation, Java, generic classes, language design, language semant
publisher={ACM New York, NY, USA}
}
@InProceedings{PH23,
author = {Martin Pl{\"u}micke and Daniel Holle},
title = {Principal generics in {J}ava--{T}{X}},
booktitle = {Programmiersprachen und Grundlagen der Programmierung, 22. Kolloquium, KPS'23},
Optcrossref = {kps2023},
pages = {122--143},
year = {2023},
editor = {Thomas Noll and Ira Fesefeldt},
address = {Aachen},
number = {AIB-2023-03},
month = {September},
series = {Aachener Informatik-Berichte (AIB)},
url = {https://publications.rwth-aachen.de/record/972197/files/972197.pdf#%5B%7B%22num%22%3A281%2C%22gen%22%3A0%7D%2C%7B%22name%22%3A%22XYZ%22%7D%2C89.292%2C740.862%2Cnull%5D},
doi = {10.18154/RWTH-2023-10034},
Optnote = {(to appear)}
}

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prolog.tex
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@ -71,6 +71,9 @@
\newcommand\subeq{\mathbin{\texttt{<:}}}
\newcommand\extends{\ensuremath{\triangleleft}}
\newcommand{\QMextends}[1]{\textrm{\normalshape\ttfamily ?\,extends}\linebreak[0]\,#1}
\newcommand{\QMsuper}[1]{\textrm{\normalshape\ttfamily ?\linebreak[0]\,su\-per}\linebreak[0]\,#1}
\newcommand\rulename[1]{\textup{\textsc{(#1)}}}
\newcommand{\generalizeRule}{General}

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relatedwork.tex Normal file
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@ -0,0 +1,69 @@
\section{Related Work}
\subsection{Wildcards in formal Java models}
Wildcards are first described in a research paper in \cite{addingWildcardsToJava}. In
\cite{TEP05} the Featherweight Java-Calculus \textsf{Wild~ FJ} is introduced. It
contains a formal description of wildcards. The Java Language Specification
\cite{GoJoStBrBuSm23} refers to \textsf{Wild~FJ} for the introduction of
wildcards. In \cite{aModelForJavaWithWildcards} a formal model based of explicite existential types
is introduced and proven as sound. Additionally, for a subset of Java a
translation to the formal model is given, such that this subset is proven as
sound. In \cite{WildcardsNeedWitnessProtection} another core calculus is
introduced, which is proven as
sound, too. In this paper it is shown that the unsoundness of Java which is
discovered in \cite{AT16} is avoidable, even in the absence of nullness-aware type
system. In \cite{TamingWildcards} finally a framework is presented which combines
use-site variance (wildcards as in Java) and definition-site variance (as in Scala). For
instance, it can be used to add use-site variance to Scala and extend the Java
type system to infer the definition-site variance.
Our calculus is mixture ...
\subsection{Type inference}
Some object-oriented languages like Scala, C\#, and Java perform
\emph{local} type inference \cite{PT98,OZZ01}. Local type
inference means that missing type annotations are recovered using only
information from adjacent nodes in the syntax tree without long distance
constraints. For instance, the type of a variable initialized with a
non-functional expression or the return type of a method can be
inferred. However, method argument types, in particular for recursive
methods, cannot be inferred by local type inference.
Milner's algorithm $\mathcal{W}$ \cite{DBLP:journals/jcss/Milner78} is
the gold standard for global type inference for languages with
parametric polymorphism, which is used by ML-style languages. The fundamental idea
of the algorithm is to enforce type equality by many-sorted type
unification \cite{Rob65,MM82}. This approach is effective and results
in so-called principal types because many-sorted unification is
unitary, which means that there is at most one most general result.
Pl\"umicke \cite{Plue07_3} presents a first attempt to adopt Milner's
approach to Java. However, the presence of subtyping means that type
unification is no longer unitary, but still finitary. Thus, there is
no longer a single most general type, but any type is an instance of a
finite set of maximal types (for more details see Section
\ref{sec:unification}). Further work by the same author
\cite{plue15_2,plue17_2},
refines this approach by moving to a constraint-based algorithm and by
considering lambda expressions and Scale-like function types.
Pluemicke has a different approach to introduce wildcards in \cite{Plue09_1}. He
allows wildcards as any subsitution for type variables and disclaim the
capture conversion. Instead he extended
the subtyping ordering such that for $\theta \sub \theta' \sub \theta''$ holds
indeed the transitiv closure of $\QMextends{\theta} \sub \theta'$ and $\theta' \sub
\QMsuper{\theta''}$ but not the reflexive closure. He gave a type unification
algorithm for this type system, which he proved as sound and complete.
The problem of his type system is in the lossing reflexivity as shown in
example \ref{intro-example1}. First approaches to solve this problem he gave in
\cite{plue24_1}, where he fixes that no pairwise different nodes in the
abstract syntax gets the same type variable and that no pairwise different type
variables are equalized. In \cite{PH23} he showed how his type inference
algorithm suffices theese properties.
In Pl\"umicke's work there is indeed a formal definition of the subtying
ordering and a correctness proof of the type unification algorithms but no
soundness proof of the type system, itself. Therefore we choose for our type
inference algorithms with wildcars the approach of ???????