Remove Same rule. SameW rule is for both constraints

introduction.tex

@@ -560,23 +560,44 @@ During the course of the \unify{} algorithm more and more types emerge.
 As soon as enough type information is given \unify{} can conduct a capture conversion if needed.
 The constraints where this is possible are marked as capture constraints.
 
-Type information flows top down.
+\section{Discussion Pair Example}
-Argument types of a method invocation impact its return type.
+We can make it work with a special rule in the \unify{}.
-But knowing the return type does not imply distinct argument types.
+But this will only help in this specific example and not generally solve the issue.
-We know from the argument types of \texttt{receive} -which are given- that the \texttt{copy} method
+A type $\exptype{Pair}{\rwildcard{X}, \rwildcard{X}}$ has atleast two immediate supertypes:
-needs to return a type of the form $\exptype{Pair}{\type{X}, \type{Y}}$
+$\wctype{\rwildcard{X}}{Pair}{\rwildcard{X}, \rwildcard{X}}$ and
-where \type{X} and \type{Y} can be any types as long as \type{Y} is a subtype of \type{X}.
+$\wctype{\rwildcard{X}, \rwildcard{Y}}{Pair}{\rwildcard{X}, \rwildcard{Y}}$.
-Without wildcards this would leave us with a clue what the type should look like.
+Imagine a type $\exptype{Triple}{\rwildcard{X},\rwildcard{X},\rwildcard{X}}$ already has 
+% TODO: how many supertypes are there?
+X.Triple<X,X,X> <: X,Y.Triple<X,Y,X> <: 
+X,Y,Z.Triple<X,Y,Z>
 
-%TODO: simplify this example. lSpeial <. List<x> and List<x> <. id is sufficient
+\begin{verbatim}
-% The unify algorithm needs to resolve l <c List<x?> to l <. X.List<X>, X.List<X> <c List<x?>
+<X> Pair<X,X> make(List<X> l){ ... }
+<X> boolean compare(Pair<X,X> p) { ... }
 
-% this is not complete:
+List<?> l;
-l <c Pair<x?, y?>
+Pair<?,?> p;
-l <. X,Y.Pair<X,Y>, X,Y.Pair<X,Y> <. Pair<x?, y?>
+
+compare(make(l)); // Valid
+compare(p); // Error
+\end{verbatim}
+
+Our type inference algorithm is not able to solve this example.
+When we convert this to \TamedFJ{} and generate constraints we end up with:
+%TODO: Finish this example! does it work?
+\begin{lstlisting}[style=tamedfj]
+let x = l in let m = make(x) in compare(m)
+\end{lstlisting}
+\begin{constraints}
+
+\end{constraints}
+
+%TODO
+
+\begin{lstlisting}[style=letfj]
+let x : (*@$\wctype{\rwildcard{X}}{List}{\rwildcard{X}}$@*) = l in let m = make(x) in compare(m)
+\end{lstlisting}
 
-% if a x =. y emerge:
-X =. Y, which will delete both wildcards
 
 
 \end{itemize}

unify.tex

@@ -402,23 +402,8 @@ which are used for the upper and lower bounds.
 %     \end{array}
 % \end{displaymath}
 
-%TODO new rules:
-% b <. List<x?>
-% ----------------
-% b =. bot   | b <. List<x>
 
-% b <. List<X>
+% if there are a <. List<x?> constraints remaining in the end, then this can be a sign of a irregular input constraint set.
-% ----------------
-% b =. bot | XU =. XL, a =. XU [a/X]C
-
-% b =. C<X>
-% --------------
-% b =. X.C<X>
-% TODO: SameW rule can also be applied to normal type variables, because we have the contract rule now:
-
-% a <c List<x?>
-% --------------
-% a <. X.List<X>, X.List<X> <c List<x?>
 
 \begin{figure}
   \begin{center}
@@ -905,35 +890,35 @@ $\set{\tv{a} \doteq \type{N}} \in C$ with $\text{fv}(\type{N}) \cap \Delta_{in}
   \begin{center}
           \fbox{
           \begin{tabular}[t]{l@{~}l}
-            \rulename{SameW}
+            \rulename{Same}
             & $
             \begin{array}[c]{l}
               \wildcardEnv \vdash
-              C \cup \type{G} \lessdot \wtv{a}\\
+              C \cup \type{G} \lessdot \tv{a}\\
               \hline
               \wildcardEnv \vdash
               C \cup \set{
-                \wtv{a} \doteq \type{G}
+                \tv{a} \doteq \type{G}
             }
             \end{array}
               $
           \\\\
-          \cdashline{1-2} \\
+        %   \cdashline{1-2} \\
-          \rulename{Same}
+        %   \rulename{Same}
-          & $
+        %   & $
-          \begin{array}[c]{l}
+        %   \begin{array}[c]{l}
-            \wildcardEnv \cup \set{\overline{\wildcard{A}{\type{U}}{\type{L}}}} \vdash
+        %     \wildcardEnv \cup \set{\overline{\wildcard{A}{\type{U}}{\type{L}}}} \vdash
-            C \cup \wctype{\Delta'}{C}{\ol{X}} \lessdot \ntv{a}\\
+        %     C \cup \wctype{\Delta'}{C}{\ol{X}} \lessdot \ntv{a}\\
-            \hline
+        %     \hline
-            \wildcardEnv \cup \set{\overline{\wildcard{A}{\type{U}}{\type{L}}}} \vdash
+        %     \wildcardEnv \cup \set{\overline{\wildcard{A}{\type{U}}{\type{L}}}} \vdash
-            C \cup \set{
+        %     C \cup \set{
-              \ntv{a} \doteq \wctype{\Delta',\overline{\wildcard{A}{\type{U}}{\type{L}}}}{C}{\ol{X}}
+        %       \ntv{a} \doteq \wctype{\Delta',\overline{\wildcard{A}{\type{U}}{\type{L}}}}{C}{\ol{X}}
-          }
+        %   }
-          \end{array} \quad \begin{array}[c]{l}
+        %   \end{array} \quad \begin{array}[c]{l}
-            \text{fv}(\wctype{\Delta'}{C}{\ol{X}}) / \Delta_{in} = \overline{\rwildcard{A}}
+        %     \text{fv}(\wctype{\Delta'}{C}{\ol{X}}) / \Delta_{in} = \overline{\rwildcard{A}}
-          \end{array}
+        %   \end{array}
-            $
+        %     $
-        \\\\
+        % \\\\
         \cdashline{1-2} \\
             \rulename{\generalizeRule}
             & $
@@ -981,7 +966,7 @@ $\set{\tv{a} \doteq \type{N}} \in C$ with $\text{fv}(\type{N}) \cap \Delta_{in}
               %   $
             \\\\
             \cdashline{1-2} \\
-                \rulename{\generalizeRule{}W}
+                \rulename{\generalizeRule{}W} %TODO: Change description for step 2!
                 & $
                 \begin{array}[c]{l}
                   \wildcardEnv \vdash C \cup \wctype{\Delta}{C}{\ol{T}} \lessdot \wtv{a}\\