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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. % Our type inference algorithm is split into two parts.
% A constraint generation step \textbf{TYPE} and a \unify{} step. % 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} 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}. 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. Our algorithm 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.
The input language is designed to showcase type inference involving existential types. 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}. 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) %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, % 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. % but only by a method with the exact same type.
The type system presented here does not allow the \textit{overriding} of methods. % 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 % 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. % on overriding methods, because their type is already determined.
Allowing overriding therefore has no implication on our type inference algorithm. % Allowing overriding therefore has no implication on our type inference algorithm.
\begin{figure} \begin{figure}
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