Remove Same rule. SameW rule is for both constraints
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Andreas Stadelmeier
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@ -560,23 +560,44 @@ During the course of the \unify{} algorithm more and more types emerge.
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As soon as enough type information is given \unify{} can conduct a capture conversion if needed.
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The constraints where this is possible are marked as capture constraints.
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Type information flows top down.
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Argument types of a method invocation impact its return type.
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But knowing the return type does not imply distinct argument types.
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We know from the argument types of \texttt{receive} -which are given- that the \texttt{copy} method
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needs to return a type of the form $\exptype{Pair}{\type{X}, \type{Y}}$
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where \type{X} and \type{Y} can be any types as long as \type{Y} is a subtype of \type{X}.
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Without wildcards this would leave us with a clue what the type should look like.
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\section{Discussion Pair Example}
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We can make it work with a special rule in the \unify{}.
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But this will only help in this specific example and not generally solve the issue.
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A type $\exptype{Pair}{\rwildcard{X}, \rwildcard{X}}$ has atleast two immediate supertypes:
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$\wctype{\rwildcard{X}}{Pair}{\rwildcard{X}, \rwildcard{X}}$ and
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$\wctype{\rwildcard{X}, \rwildcard{Y}}{Pair}{\rwildcard{X}, \rwildcard{Y}}$.
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Imagine a type $\exptype{Triple}{\rwildcard{X},\rwildcard{X},\rwildcard{X}}$ already has
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% TODO: how many supertypes are there?
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X.Triple<X,X,X> <: X,Y.Triple<X,Y,X> <:
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X,Y,Z.Triple<X,Y,Z>
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%TODO: simplify this example. lSpeial <. List<x> and List<x> <. id is sufficient
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% The unify algorithm needs to resolve l <c List<x?> to l <. X.List<X>, X.List<X> <c List<x?>
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\begin{verbatim}
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<X> Pair<X,X> make(List<X> l){ ... }
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<X> boolean compare(Pair<X,X> p) { ... }
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% this is not complete:
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l <c Pair<x?, y?>
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l <. X,Y.Pair<X,Y>, X,Y.Pair<X,Y> <. Pair<x?, y?>
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List<?> l;
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Pair<?,?> p;
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compare(make(l)); // Valid
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compare(p); // Error
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\end{verbatim}
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Our type inference algorithm is not able to solve this example.
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When we convert this to \TamedFJ{} and generate constraints we end up with:
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%TODO: Finish this example! does it work?
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\begin{lstlisting}[style=tamedfj]
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let x = l in let m = make(x) in compare(m)
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\end{lstlisting}
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\begin{constraints}
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\end{constraints}
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%TODO
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\begin{lstlisting}[style=letfj]
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let x : (*@$\wctype{\rwildcard{X}}{List}{\rwildcard{X}}$@*) = l in let m = make(x) in compare(m)
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\end{lstlisting}
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% if a x =. y emerge:
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X =. Y, which will delete both wildcards
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\end{itemize}
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59
unify.tex
59
unify.tex
@ -402,23 +402,8 @@ which are used for the upper and lower bounds.
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% \end{array}
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% \end{displaymath}
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%TODO new rules:
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% b <. List<x?>
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% ----------------
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% b =. bot | b <. List<x>
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% b <. List<X>
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% ----------------
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% b =. bot | XU =. XL, a =. XU [a/X]C
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% b =. C<X>
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% --------------
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% b =. X.C<X>
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% TODO: SameW rule can also be applied to normal type variables, because we have the contract rule now:
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% a <c List<x?>
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% --------------
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% a <. X.List<X>, X.List<X> <c List<x?>
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% if there are a <. List<x?> constraints remaining in the end, then this can be a sign of a irregular input constraint set.
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\begin{figure}
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\begin{center}
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@ -905,35 +890,35 @@ $\set{\tv{a} \doteq \type{N}} \in C$ with $\text{fv}(\type{N}) \cap \Delta_{in}
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\begin{center}
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\fbox{
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\begin{tabular}[t]{l@{~}l}
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\rulename{SameW}
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& $
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\begin{array}[c]{l}
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\wildcardEnv \vdash
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C \cup \type{G} \lessdot \wtv{a}\\
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\hline
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\wildcardEnv \vdash
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C \cup \set{
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\wtv{a} \doteq \type{G}
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}
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\end{array}
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$
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\\\\
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\cdashline{1-2} \\
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\rulename{Same}
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& $
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\begin{array}[c]{l}
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\wildcardEnv \cup \set{\overline{\wildcard{A}{\type{U}}{\type{L}}}} \vdash
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C \cup \wctype{\Delta'}{C}{\ol{X}} \lessdot \ntv{a}\\
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\wildcardEnv \vdash
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C \cup \type{G} \lessdot \tv{a}\\
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\hline
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\wildcardEnv \cup \set{\overline{\wildcard{A}{\type{U}}{\type{L}}}} \vdash
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\wildcardEnv \vdash
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C \cup \set{
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\ntv{a} \doteq \wctype{\Delta',\overline{\wildcard{A}{\type{U}}{\type{L}}}}{C}{\ol{X}}
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\tv{a} \doteq \type{G}
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}
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\end{array} \quad \begin{array}[c]{l}
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\text{fv}(\wctype{\Delta'}{C}{\ol{X}}) / \Delta_{in} = \overline{\rwildcard{A}}
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\end{array}
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$
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\\\\
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% \cdashline{1-2} \\
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% \rulename{Same}
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% & $
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% \begin{array}[c]{l}
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% \wildcardEnv \cup \set{\overline{\wildcard{A}{\type{U}}{\type{L}}}} \vdash
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% C \cup \wctype{\Delta'}{C}{\ol{X}} \lessdot \ntv{a}\\
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% \hline
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% \wildcardEnv \cup \set{\overline{\wildcard{A}{\type{U}}{\type{L}}}} \vdash
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% C \cup \set{
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% \ntv{a} \doteq \wctype{\Delta',\overline{\wildcard{A}{\type{U}}{\type{L}}}}{C}{\ol{X}}
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% }
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% \end{array} \quad \begin{array}[c]{l}
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% \text{fv}(\wctype{\Delta'}{C}{\ol{X}}) / \Delta_{in} = \overline{\rwildcard{A}}
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% \end{array}
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% $
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% \\\\
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\cdashline{1-2} \\
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\rulename{\generalizeRule}
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& $
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@ -981,7 +966,7 @@ $\set{\tv{a} \doteq \type{N}} \in C$ with $\text{fv}(\type{N}) \cap \Delta_{in}
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% $
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\\\\
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\cdashline{1-2} \\
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\rulename{\generalizeRule{}W}
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\rulename{\generalizeRule{}W} %TODO: Change description for step 2!
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& $
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\begin{array}[c]{l}
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\wildcardEnv \vdash C \cup \wctype{\Delta}{C}{\ol{T}} \lessdot \wtv{a}\\
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