Add New-Cons
This commit is contained in:
Andreas Stadelmeier
parent
563690dced
commit
a41b298566
@ -348,12 +348,39 @@ This practice hinders free variables to leave their scope.
|
||||
The free variable $\rwildcard{A}$ generated by the capture conversion on the type $\wctype{\wildcard{A}{\type{String}}{\bot}}{List}{\rwildcard{A}}$
|
||||
cannot be used anywhere else then inside the constraints generated by the method call \texttt{x.m(xp)}.
|
||||
|
||||
\subsection{Examples}
|
||||
\subsection{Constraint Generation}
|
||||
The constraint generation is defined on a subset of Java displayed in figure \ref{fig:miniJavaSyntax}.
|
||||
The input language includes only a small set of expressions like method calls, field access and a elvis operator $\elvis$
|
||||
which acts as a replacement for if-else expressions.
|
||||
\begin{figure}
|
||||
\par\noindent\rule{\textwidth}{0.4pt}
|
||||
\center
|
||||
$
|
||||
\begin{array}{lrcl}
|
||||
%\hline
|
||||
\text{Parameterized classes} & \mv N & ::= & \exptype{C}{\ol{T}} \\
|
||||
\text{Types} & \type{S}, \type{T}, \type{U} & ::= & \type{X} \mid \wcNtype{\Delta}{N} \\
|
||||
\text{Lower bounds} & \type{K}, \type{L} & ::= & \type{T} \mid \bot \\
|
||||
\text{Type variable contexts} & \Delta & ::= & \overline{\wildcard{X}{T}{L}} \\
|
||||
\text{Class declarations} & D & ::= & \texttt{class}\ \exptype{C}{\ol{X \triangleleft T}} \triangleleft \type{N} \set{\overline{\type{T}\ f}; \ol{M}} \\
|
||||
\text{Method declarations} & \texttt{M} & ::= & \highlight{\generics{\overline{\type{X} \triangleleft \type{N}}}}\ \highlight{\type{T}}\ \texttt{m}(\overline{\highlight{\type{T}}\ \expr{x}}) \{ \texttt{return} \ \expr{e}; \} \\
|
||||
\text{Terms} & \expr{e} & ::= & \expr{x} \\
|
||||
& & \ \ | & \texttt{new} \ \type{C}\highlight{\generics{\ol{T}}}(\overline{\expr{e}})\\
|
||||
& & \ \ | & \expr{e}.f\\
|
||||
& & \ \ | & \expr{e}.\texttt{m}\highlight{\generics{\ol{T}}}(\overline{\expr{e}})\\
|
||||
& & \ \ | & \expr{e} \elvis{} \expr{e}\\
|
||||
\text{Variable contexts} & \Gamma & ::= & \overline{\expr{x}:\type{T}}\\
|
||||
\text{Method type environment} & \mathrm{\Pi} & ::= & \overline{ \texttt{m} : \generics{\ol{X \triangleleft N}}\ \ol{T} \to \type{T}}
|
||||
%\hline
|
||||
\end{array}
|
||||
$
|
||||
\par\noindent\rule{\textwidth}{0.4pt}
|
||||
\caption{Input Syntax with optional type annotations}\label{fig:miniJavaSyntax}
|
||||
\end{figure}
|
||||
|
||||
|
||||
% v.m(v, v.f, this.id(v));
|
||||
|
||||
% let x1 = v, x2 = v, x3 = v.f, x4 = |this.id(v)| in x1.m(x2, x3, x4)
|
||||
We explain the process using the following example input.
|
||||
The classes \texttt{List} and \texttt{Id} are already fully typed and we want to create constraints for the class
|
||||
\texttt{CExample} now.
|
||||
|
||||
\begin{lstlisting}{java}
|
||||
class Id{
|
||||
@ -361,7 +388,7 @@ class Id{
|
||||
}
|
||||
|
||||
class List<X> {
|
||||
List<X> concat(List<X> l){ ... }
|
||||
<Y extends X> List<X> concat(List<Y> l){ ... }
|
||||
}
|
||||
|
||||
class CExample{
|
||||
@ -371,7 +398,7 @@ class CExample{
|
||||
}
|
||||
\end{lstlisting}
|
||||
|
||||
At first we assign a type placeholder to every expression in the input program.
|
||||
The first step of constraint generation is to assign type placeholders to every expression in the input program.
|
||||
Type placeholders also fill in for missing type annotations in method headers.
|
||||
|
||||
\begin{lstlisting}{java}
|
||||
@ -394,16 +421,28 @@ The type of local variable expressions like \expr{p1} and \expr{p2} is already k
|
||||
$\expr{p1}:\tv{b}$ and $\expr{p2}:\tv{c}$ in this case.
|
||||
The method call to \texttt{id} gets the fresh type placeholder $\tv{d}$ as type and the method call to \texttt{concat} is assigned the placeholder $\tv{e}$.
|
||||
|
||||
Afterwards a method type environment $\mtypeEnvironment$ containing all method declarations is created.
|
||||
Note how type placeholders are used for the \texttt{example} method:
|
||||
Afterwards we create a method type environment $\mtypeEnvironment$ containing all method declarations.
|
||||
Each entry has the form $\texttt{m} : \generics{\ol{X \triangleleft N}} \ol{T} \to \type{T}$.
|
||||
The type arguments of the surrounding class and the type arguments of each method are merged together
|
||||
leading to the list $\generics{\type{X}, \type{Y} \triangleleft \type{X}}$ for the \texttt{concat} method
|
||||
($\triangleleft$ is short for \texttt{extends}).
|
||||
Also the type of the surrounding class is added to the parameter list of the method.
|
||||
This leads to the \texttt{id} method having two arguments.
|
||||
One is the \texttt{Id} class itself and the second one is the actual arguemnt of the method.
|
||||
|
||||
$\mtypeEnvironment{} = \left\{ \begin{array}{l}
|
||||
\texttt{id} : \generics{\type{X}}\type{Id},\type{X} \to \type{X}, \\
|
||||
\texttt{concat} : \generics{\type{X}}\exptype{List}{\type{X}},\exptype{List}{\type{X}} \to \exptype{List}{\type{X}}, \\
|
||||
\texttt{concat} : \generics{\type{X}, \type{Y} \triangleleft \type{X}}\exptype{List}{\type{X}},\exptype{List}{\type{Y}} \to \exptype{List}{\type{X}}, \\
|
||||
\texttt{example} : \type{CExample},\tv{b},\tv{c} \to \tv{a}, \\
|
||||
\end{array} \right\}
|
||||
$
|
||||
|
||||
Note: type placeholders are used for the \texttt{example} method.
|
||||
|
||||
Our constraint generation rules have the form:
|
||||
$\mtypeEnvironment \vdash \expr{e} : \tv{a} \implies C$,
|
||||
that given a method environment $\mtypeEnvironment$ and an expression $\expr{e}$ with type $\tv{a}$ generates the constraint set $C$.
|
||||
|
||||
\begin{mathpar}
|
||||
\inferrule[Method-Cons]{
|
||||
\mtypeEnvironment \vdash \expr{e} : \tv{e} \implies C \\
|
||||
@ -415,8 +454,39 @@ $
|
||||
}{
|
||||
\mtypeEnvironment \vdash \expr{e}.\texttt{m}(\overline{\expr{e}}) : \tv{a} \implies C \cup \overline{C} \cup C_m
|
||||
}
|
||||
\and
|
||||
% \inferrule[Field-Cons]{
|
||||
% \mtypeEnvironment \vdash \expr{e} : \tv{e} \implies C \\
|
||||
% C_f = \set{}
|
||||
% }{
|
||||
% \mtypeEnvironment \vdash \expr{e}.\texttt{f} : \tv{a} \implies C \cup C_f \\
|
||||
% }
|
||||
% \and
|
||||
\inferrule[Var-Cons]{
|
||||
}{
|
||||
\mtypeEnvironment \vdash \expr{x} : \tv{a} \implies \emptyset
|
||||
}
|
||||
\and
|
||||
\inferrule[Elvis-Cons]{
|
||||
\mtypeEnvironment \vdash \expr{e}_1 : \tv{e}_1 \implies C_1 \\
|
||||
\mtypeEnvironment \vdash \expr{e}_2 : \tv{e}_2 \implies C_2
|
||||
}{
|
||||
\mtypeEnvironment \vdash \expr{e}_1 \elvis{} \expr{e}_2 : \tv{a} \implies C_1 \cup C_2 \cup \set{\tv{e}_1 \lessdot \tv{a}, \tv{e}_2 \lessdot \tv{a}}
|
||||
}
|
||||
\and
|
||||
\inferrule[New-Cons]{
|
||||
\overline{\mtypeEnvironment \vdash \expr{e} : \tv{e} \implies C} \\
|
||||
\texttt{class} \ \exptype{D}{\ol{X \triangleleft N}} \set{ \ol{T\ f}; \ldots }
|
||||
}{
|
||||
\mtypeEnvironment \vdash \texttt{new}\ \type{D}(\ol{e}) : \tv{a} \implies \overline{C} \cup [\ol{\wtv{b}}/\ol{X}]\set{ \overline{\tv{e} \lessdot \type{T}}, \exptype{D}{\ol{X}} \lessdot \tv{a}, \ol{X \lessdot N} }
|
||||
}
|
||||
\end{mathpar}
|
||||
|
||||
According to the Method-Cons rule the constraints generated by the call to \texttt{id} are:
|
||||
$\mtypeEnvironment \vdash (p1:\tv{b}).id(p2:\tv{c}):\tv{d} \implies \set{\tv{b} \lessdot \tv{x}_1, \tv{c} \lessdot \tv{x}_2, \tv{x}_1 \lessdotCC \type{Id},
|
||||
\tv{x}_2 \lessdotCC \wtv{b}, \wtv{b} \lessdot \tv{d}}$.
|
||||
|
||||
\subsection{Or-Constraints}
|
||||
In case the input program contains multiple method declarations holding the same name and same amount of parameters then so called Or-Constraints must be generated.
|
||||
Usually Java is able to determine which method to call based on the argument's types passed to the method. %'
|
||||
During the constraint generation step the argument types are unknown and we have to assume multiple methods as invocation target.
|
||||
|
||||
Loading…
Reference in New Issue
Block a user