Cleanup
This commit is contained in:
Andreas Stadelmeier
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4eb7b1ce19
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3904304a1d
@ -138,7 +138,8 @@ For the example above a correct solution would be $\sigma(\tv{a}) = \wctype{\rwi
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\orCons\set{
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\set{ &
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\tv{r} \lessdotCC \exptype{C}{\ol{\wtv{a}}} ,
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[\overline{\wtv{a}}/\ol{X}]\type{T} \lessdot \tv{a} , \ol{\wtv{a}} \lessdot [\overline{\wtv{a}}/\ol{X}]\ol{N}
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[\overline{\wtv{a}}/\ol{X}]\type{T} \lessdot \tv{a} ,
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\ol{\wtv{a}} \lessdot [\overline{\wtv{a}}/\ol{X}]\ol{N}
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} \\
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& \quad \mid \mv{T}\ \mv{f} \in \texttt{class}\ \exptype{C}{\ol{X} \triangleleft \ol{N}} \set{ \ol{T\ f}; \ldots}
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, \, \overline{\wtv{a}} \text{ fresh}
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@ -154,14 +155,9 @@ The set of method assumptions returned by the \textit{mtypes} function is used t
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There are two kinds of method calls.
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The ones to already typed methods and calls to untyped methods.
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LetFJ version: %TODO: or use the old version with \lessdotCC constraints. then there is no problem with \Delta'
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% or only use the \lessdotCC with X.C<X> and C<X> on both sides
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% what to do with ? <c X constraints? Just ignore them! they result in X <. X and can be ignored
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% generate a function which converts method types and parameter types to constraints of the form a <. X.C<X>, C<X> <. C<x>
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% add the free variables to \Delta' proof that they cannot escape the scope (they have to be treated differently than \Delta')
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\begin{displaymath}
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\begin{array}{@{}l@{}l}
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\typeExpr{}' & ({\mtypeEnvironment} , \texttt{e}.\mathtt{m}(\overline{\texttt{e}})) = \\
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\typeExpr{}' & ({\mtypeEnvironment} , \texttt{e}.\mathtt{m}(\overline{\texttt{e}}), \tv{a}) = \\
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& \begin{array}{ll}
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\textbf{let}
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& \tv{r}, \ol{\tv{r}} \text{ fresh} \\
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@ -171,87 +167,19 @@ LetFJ version: %TODO: or use the old version with \lessdotCC constraints. then t
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& \begin{array}{@{}l@{}l}
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\constraint = \orCons\set{ &
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\begin{array}[t]{l}
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%TODO: add \ol{\wildcard{X}{\wtv{u}}{\wtv{l}}} to \Delta'
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[\overline{\wtv{a}}/\ol{X}] [\overline{\wtv{b}}/\ol{Y}] \{ \tv{r} \lessdot \wctype{\ol{\wildcard{X}{\wtv{u}}{\wtv{l}}}}{C}{\ol{X}}, \exptype{C}{\ol{X}} \lessdot \exptype{C}{\ol{X}},
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%[\overline{\wtv{a}}/\ol{X}] [\overline{\wtv{b}}/\ol{Y}] \{ \tv{r} \lessdotCC \exptype{C}{\ol{X}},
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\overline{\tv{r}} \lessdot \ol{T},
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\ol{X} \lessdot \ol{N},
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\ol{Y} \lessdot \ol{N'} \}
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\end{array}\\
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& \ |\
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(\exptype{C}{\ol{X} \triangleleft \ol{N}}.\texttt{m} : \generics{\ol{Y} \triangleleft \ol{N'}}\overline{\type{T}} \to \type{T}) \in
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{\mtypeEnvironment}, \, |\ol{T}| = |\ol{e}|
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, \, \overline{\wtv{a}} \text{ fresh}, \, \overline{\wtv{b}} \text{ fresh} }
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\end{array}\\
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\mathbf{in} & (\consSet_R \cup \overline{\consSet} \cup \constraint, \type{T})
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\end{array}
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\end{array}
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\end{displaymath}
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Java version:
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\begin{displaymath}
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\begin{array}{@{}l@{}l}
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\typeExpr{}' & ({\mtypeEnvironment} , \texttt{e}.\mathtt{m}(\overline{\texttt{e}})) = \\
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& \begin{array}{ll}
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\textbf{let}
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& \tv{r}, \ol{\tv{r}} \text{ fresh} \\
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& \consSet_R = \typeExpr(({\mtypeEnvironment} ;
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\overline{\localVarAssumption}), \texttt{e}, \tv{r})\\
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& \overline{\consSet} = \typeExpr({\mtypeEnvironment}, \ol{e}, \ol{\tv{r}}) \\
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& \begin{array}{@{}l@{}l}
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\constraint = \orCons\set{ &
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\begin{array}[t]{l}
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%[\overline{\wtv{a}}/\ol{X}] [\overline{\wtv{b}}/\ol{Y}] \{ \tv{r} \lessdot \wctype{\ol{\wildcard{X}{\ntv{u}}{\ntv{l}}}}{C}{\ol{X}}, \wctype{\ol{\wildcard{X}{\ntv{u}}{\ntv{l}}}}{C}{\ol{X}} \lessdotCC \exptype{C}{\ol{X}},
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[\overline{\wtv{a}}/\ol{X}] [\overline{\wtv{b}}/\ol{Y}] \{ \tv{r} \lessdotCC \exptype{C}{\ol{X}},
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\overline{\tv{r}} \lessdotCC \ol{T},
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\ol{X} \lessdot \ol{N},
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\ol{Y} \lessdot \ol{N'} \}
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\overline{\tv{r}} \lessdotCC \ol{T}, \type{T} \lessdot \tv{a},
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\ol{Y} \lessdot \ol{N} \}
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\end{array}\\
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& \ |\
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(\exptype{C}{\ol{X} \triangleleft \ol{N}}.\texttt{m} : \generics{\ol{Y} \triangleleft \ol{N'}}\overline{\type{T}} \to \type{T}) \in
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{\mtypeEnvironment}, \, |\ol{T}| = |\ol{e}|
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, \, \overline{\wtv{a}} \text{ fresh}, \, \overline{\wtv{b}} \text{ fresh} }
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(\texttt{m} : \generics{\ol{Y} \triangleleft \ol{N}}\overline{\type{T}} \to \type{T}) \in
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{\mtypeEnvironment} %, \, |\ol{T}| = |\ol{e}|
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, \, \overline{\wtv{a}} \text{ fresh}}
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\end{array}\\
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\mathbf{in} & (\consSet_R \cup \overline{\consSet} \cup \constraint, \type{T})
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\end{array}
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\end{array}
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\end{displaymath}
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% \begin{displaymath}
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% \typeExpr{}' ({\mtypeEnvironment} , \texttt{e}.\mathtt{m}(\overline{\texttt{e}}), \tv{a} ) = \
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% \typeExpr{} ({\mtypeEnvironment} , \texttt{e}.\mathtt{m}(\overline{\texttt{e}}), \wtv{b} ) \cup \set{ \wtv{b} \lessdot \tv{a}}
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% \end{displaymath}
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\begin{displaymath}
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\typeExpr{}' ({\mtypeEnvironment} , \texttt{return e;}, \tv{a} ) = \
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\typeExpr{} ({\mtypeEnvironment} , \texttt{e}, \wtv{b} ) \cup \set{ \wtv{b} \lessdot \tv{a}} \quad \quad \tv{a}, \wtv{b} \ \text{fresh}
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\end{displaymath}
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% \begin{displaymath}
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% \begin{array}{@{}l@{}l}
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% \typeExpr{} & ({\mtypeEnvironment} , \texttt{e}.\mathtt{m}(\overline{\texttt{e}}), \tv{a} ) = \\
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% & \begin{array}{ll}
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% \textbf{let}
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% & \tv{r}, \ol{\tv{r}} \text{ fresh} \\
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% & \consSet_R = \typeExpr(({\mtypeEnvironment} ;
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% \overline{\localVarAssumption}), \texttt{e}, \tv{r})\\
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% & \overline{\consSet} = \typeExpr({\mtypeEnvironment}, \ol{e}, \ol{\tv{r}}) \\
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% & \begin{array}{@{}l@{}l}
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% \constraint = \orCons\set{ &
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% \begin{array}[t]{l}
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% [\overline{\wtv{a}}/\ol{X}] [\overline{\wtv{b}}/\ol{Y}] \{ \tv{r} \lessdot \exptype{C}{\ol{X}},
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% \overline{\tv{r}} \lessdot \ol{T},
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% \type{T} \lessdot \tv{a},
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% \ol{X} \lessdot \ol{N},
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% \ol{Y} \lessdot \ol{N'} \}
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% \end{array}\\
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% & \ |\
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% (\exptype{C}{\ol{X} \triangleleft \ol{N}}.\texttt{m} : \generics{\ol{Y} \triangleleft \ol{N'}}\overline{\type{T}} \to \type{T}) \in
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% {\mtypeEnvironment}
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% , \, \overline{\wtv{a}} \text{ fresh}, \, \overline{\wtv{b}} \text{ fresh} }
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% \end{array}\\
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% \mathbf{in} & \consSet_R \cup \overline{\consSet} \cup \constraint
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% \end{array}
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% \end{array}
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% \end{displaymath}
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\\[1em]
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\noindent
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\textbf{Example:}
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75
tRules.tex
75
tRules.tex
@ -214,68 +214,19 @@ $\begin{array}{l}
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\triangle | \Gamma \vdash \texttt{new}\ \type{C}(\ol{t}) : \exptype{C}{\ol{T}}
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\end{array}
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\end{array}$
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\\[1em] % TODO: we need subtyping for FJ without let statements. Problem is \Delta \vdash T witnessed. The \Delta here contains all the let statements beforehand.
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% TODO: maybe do a rule which adds let statements at any place! Goal: a program which Unify calculates a type for is also correct under our type laws and can be converted to LefFJ
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% motivation: do not use normal types as intermediate types. Keep a Pair<X,X> as that and not convert to X,Y.Pair<X,Y>
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% it is possible because the parameters of the method are normal types. we can start capture converting them
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% is it possible to say there exists any \Delta which makes the method body possible?
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$\begin{array}{l}
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\typerule{T-Call}\\
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\begin{array}{@{}c}
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\Delta \vdash \type{T}, \wcNtype{\Delta'}{N}, \overline{\type{T}} \ \ok \quad \quad
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\Delta \vdash \ol{\type{N}} <: [\ol{S}/\ol{X}]\ol{U} \quad \quad
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\generics{\ol{X \triangleleft U'}} \type{N} \to \ol{U} \to \type{U} \in \Pi(\texttt{m}) \quad \quad
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\Delta, \Delta', \overline{\Delta} \vdash \ol{S} <: [\ol{S}/\ol{X}]\ol{U'}
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\\
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\Delta, \Delta', \overline{\Delta} \vdash \ol{S} \ \ok \quad \quad
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\Delta | \Gamma \vdash \texttt{e} : \type{T}_r \mid \Delta_G \quad \quad
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\Delta | \Gamma \vdash \ol{e} : \ol{T} \mid \overline{\Delta_G} \quad \quad
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\Delta \vdash \type{T}_r <: \wcNtype{\Delta'}{N} \quad \quad
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\Delta \vdash \ol{T} <: \overline{\wcNtype{\Delta}{N}}
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\\
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\overline{\Delta_G}, \Delta_G, \Delta, \Delta', \overline{\Delta} \vdash [\ol{S}/\ol{X}]\type{U} <: \type{T} \quad \quad
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\text{dom}(\Delta') \subseteq \text{fv}(\type{N}) \quad \quad
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\overline{\text{dom}(\Delta) \subseteq \text{fv}(\type{N})}
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\\
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\hline
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\vspace*{-0.3cm}\\
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\Delta | \Gamma \vdash \texttt{e}.\texttt{m}(\ol{e}) : \type{T} \mid \Delta', \overline{\Delta}
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\end{array}
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\end{array}$
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\\[1em]
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$\begin{array}{l}
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\typerule{T-Call}\\
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\begin{array}{@{}c}
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\Delta \vdash \ol{\type{N}} <: [\ol{S}/\ol{X}]\ol{U} \quad \quad
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\generics{\ol{X \triangleleft U'}}\ol{U} \to \type{U} \in \Pi(\texttt{m}) \quad \quad
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\Delta \vdash \ol{S} <: [\ol{S}/\ol{X}]\ol{U'}
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\\
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\Delta \vdash \ol{S} \ \ok \quad \quad
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\Delta | \Gamma \vdash \texttt{e}, \ol{e} : \ol{T} \mid \overline{\Delta'} \quad \quad
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\Delta \vdash \ol{T} <: \overline{\wcNtype{\Delta}{N}} \quad \quad
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\Delta \vdash [\ol{S}/\ol{X}]\type{U} <: \type{T}
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\\
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\hline
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\vspace*{-0.3cm}\\
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\Delta | \Gamma \vdash \texttt{e}.\texttt{m}(\ol{e}) : \type{T} \mid \overline{\Delta}, \overline{\Delta'}
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\end{array}
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\end{array}$
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% \Delta is not allowed to have wildcards depending on eachother. X^Y, Y^T for example
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\\[1em]
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$\begin{array}{l}
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\typerule{T-Call}\\
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\begin{array}{@{}c}
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\Delta, \Delta', \overline{\Delta} \vdash \ol{\type{N}} <: [\ol{S}/\ol{X}]\ol{U} \quad \quad
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\generics{\ol{X \triangleleft U'}} \type{N} \to \ol{U} \to \type{U} \in \Pi(\texttt{m}) \quad \quad
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\generics{\ol{X \triangleleft U'}} \ol{U} \to \type{U} \in \Pi(\texttt{m}) \quad \quad
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\Delta, \Delta', \overline{\Delta} \vdash \ol{S} <: [\ol{S}/\ol{X}]\ol{U'}
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\\
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\Delta, \Delta', \overline{\Delta} \vdash \ol{S} \ \ok \quad \quad
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\Delta | \Gamma \vdash \texttt{e} : \type{T}_r \quad \quad
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\Delta | \Gamma \vdash \ol{e} : \ol{T} \quad \quad
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\Delta \vdash \type{T}_r <: \wcNtype{\Delta'}{N} \quad \quad
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\Delta | \Gamma \vdash \texttt{e}, \ol{e} : \ol{T} \quad \quad
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\Delta \vdash \ol{T} <: \overline{\wcNtype{\Delta}{N}}
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\\
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\Delta \vdash \type{T}, \wcNtype{\Delta'}{N}, \overline{\wcNtype{\Delta}{N}} \ \ok \quad \quad
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\Delta \vdash \type{T}, \overline{\wcNtype{\Delta}{N}} \ \ok \quad \quad
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\Delta, \Delta', \overline{\Delta} \vdash [\ol{S}/\ol{X}]\type{U} <: \type{T} \quad \quad
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\text{dom}(\Delta') \subseteq \text{fv}(\type{N}) \quad \quad
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\overline{\text{dom}(\Delta) \subseteq \text{fv}(\type{N})}
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@ -286,26 +237,6 @@ $\begin{array}{l}
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\end{array}
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\end{array}$
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\\[1em]
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$\begin{array}{l}
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\typerule{T-Call}\\
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\begin{array}{@{}c}
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\Delta, \Delta', \overline{\Delta} \vdash \ol{\type{N}} <: [\ol{S}/\ol{X}]\ol{U} \quad \quad
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\generics{\ol{X \triangleleft U'}} \type{N} \to \ol{U} \to \type{U} \in \Pi(\texttt{m}) \quad \quad
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\Delta, \Delta', \overline{\Delta} \vdash \ol{S} <: [\ol{S}/\ol{X}]\ol{U'} \quad \quad
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\Delta, \Delta', \overline{\Delta} \vdash \ol{S} \ \ok
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\\
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\Delta | \Gamma \vdash \ol{e} : \ol{T} \quad \quad
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\Delta \vdash \ol{T} <: \overline{\wcNtype{\Delta}{N}} \quad \quad
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\Delta \vdash \type{T}, \overline{\wcNtype{\Delta}{N}} \ \ok \quad \quad
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\Delta, \Delta', \overline{\Delta} \vdash [\ol{S}/\ol{X}]\type{U} <: \type{T} \quad \quad
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\overline{\text{dom}(\Delta) \subseteq \text{fv}(\type{N})}
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\\
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\hline
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\vspace*{-0.3cm}\\
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\Delta | \Gamma \vdash \texttt{m}(\ol{e}) : \type{T}
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\end{array}
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\end{array}$
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\\[1em]
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$\begin{array}{l}
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\typerule{T-Elvis}\\
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\begin{array}{@{}c}
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19
unify.tex
19
unify.tex
@ -1,12 +1,29 @@
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% TODO: unify changes
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% a? <. T can be deleted in the last step
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% remove lessdotCC constraints completely
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% delete wildcard tphs a? when needed
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% aswell ass free variables:
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% a <. T with fv(T) not empty and not in \Delta' must be removed by U = L
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% also in T <. T constraints no free variables are allowed on both sides
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% the algorithm only removes wildcards, never adds them
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% lessdotCC constraint cannot be removed. we do not know what to capture
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% example <X> add(List<X> l, X v)
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% here we need to generate constraints p1 <c List<x>, p2 <c x
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% because x can become List<a?>:
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% class Box<X>{}
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% class Test{
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% static <X> Box<X> add(Box<X> b, X x){return null;}
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% static <X> Box<X> empty(){return null;}
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% static <X> Box<Box<X>> empty2(){return null;}
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% public static void main(String args[]){
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% Box<?> b = null;
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% Box<? extends Box<?>> b2 = add(empty2(), b);
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% }
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% }
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\section{Unify}\label{sec:unify}
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%TODO: Remove lessdotC constraints. those have to be handeld during constraint generation
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