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Intro to type rules

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Andreas Stadelmeier 2024-02-10 08:19:24 +01:00
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constraints.tex
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\section{Constraint generation}
\section{Constraint generation}\label{chapter:constraintGeneration}
% Our type inference algorithm is split into two parts.
% A constraint generation step \textbf{TYPE} and a \unify{} step.

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tRules.tex
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The input syntax for our algorithm is shown in figure \ref{fig:syntax}
and the respective type rules in figure \ref{fig:expressionTyping} and \ref{fig:typing}.
The algorithm presented in this paper is an extension of the \emph{Global Type Inference for Featherweight Generic Java}\cite{TIforFGJ} algorithm.
Additional features like overriding methods and method overloading can be added by copying the respective parts from there.
Our algorithm is an extension of the \emph{Global Type Inference for Featherweight Generic Java}\cite{TIforFGJ} algorithm.
The input language is designed to showcase type inference involving existential types.
We introduce the type rule T-Call which emulates a Java method call,
Method call rule T-Call is the most interesting part, because it emulates the behaviour of a Java method call,
where existential types are implicitly \textit{opened} and \textit{closed}.
The T-Elvis rule mimics the type judgement of a branch expression like \texttt{if-else}
and is solely used for examples.
%The T-Elvis rule mimics the type judgement of a branch expression like \texttt{if-else}.
%and is solely used for examples.
The calculus does not include method overloading or method overriding for simplicity reasons.
Type inference for both are described in \cite{TIforFGJ} and can be added to this algorithm accordingly.
Our algorithm is designed for extensibility with the final goal of full support for Java.
\unify{} is the core of the algorithm and can be used for any calculus sharing the same subtype relations as depicted in \ref{fig:subtyping}.
Additional language constructs can be added by implementing the respective constraint generation functions in the same fashion as described in chapter \ref{chapter:constraintGeneration}.
%Additional features like overriding methods and method overloading can be added by copying the respective parts from there.
%Additional features can be easily added by generating the respective constraints (Plümicke hier zitieren)
The type system in \cite{WildcardsNeedWitnessProtection} allows a method to \textit{override} an existing method declaration in one of its super classes,
but only by a method with the exact same type.
The type system presented here does not allow the \textit{overriding} of methods.
Our type inference algorithm consumes the input classes in succession and could only do a type check instead of type inference
on overriding methods, because their type is already determined.
Allowing overriding therefore has no implication on our type inference algorithm.
% The type system in \cite{WildcardsNeedWitnessProtection} allows a method to \textit{override} an existing method declaration in one of its super classes,
% but only by a method with the exact same type.
% The type system presented here does not allow the \textit{overriding} of methods.
% Our type inference algorithm consumes the input classes in succession and could only do a type check instead of type inference
% on overriding methods, because their type is already determined.
% Allowing overriding therefore has no implication on our type inference algorithm.
\begin{figure}
$