From 497dd1bad412dfd63a0219f5a7ccd36503a41efb Mon Sep 17 00:00:00 2001 From: Alan Jeffrey <403333+asajeffrey@users.noreply.github.com> Date: Mon, 9 Oct 2023 19:00:31 -0500 Subject: [PATCH] Incorrectness 2024 paper (#1048) --- papers/incorrectness24/bibliography.bib | 122 +++++++ papers/incorrectness24/cc-by.png | Bin 0 -> 12588 bytes papers/incorrectness24/incorrectness24.pdf | Bin 0 -> 405978 bytes papers/incorrectness24/incorrectness24.tex | 366 +++++++++++++++++++++ 4 files changed, 488 insertions(+) create mode 100644 papers/incorrectness24/bibliography.bib create mode 100644 papers/incorrectness24/cc-by.png create mode 100644 papers/incorrectness24/incorrectness24.pdf create mode 100644 papers/incorrectness24/incorrectness24.tex diff --git a/papers/incorrectness24/bibliography.bib b/papers/incorrectness24/bibliography.bib new file mode 100644 index 00000000..a5724f6b --- /dev/null +++ b/papers/incorrectness24/bibliography.bib @@ -0,0 +1,122 @@ +@InProceedings{BFJ21:GoalsLuau, + author = {L. Brown and A. Friesen and A. S. A. Jeffrey}, + title = {Position Paper: Goals of the Luau Type System}, + booktitle = {Proc. Human Aspects of Types and Reasoning Assistants}, + year = {2021}, + url = {https://asaj.org/papers/hatra21.pdf}, +} + +@Misc{Roblox, + author = {Roblox}, + title = {Reimagining the way people come together}, + year = 2023, + url = {https://corp.roblox.com}, +} + +@Misc{Luau, + author = {Roblox}, + title = {The {Luau} Programming Language}, + year = 2023, + url = {https://luau-lang.org}, +} + +@Misc{Lua, + author = {Lua.org and {PUC}-Rio}, + title = {The {Lua} Programming Language}, + year = 2023, + url = {https://lua.org}, +} + +@Misc{Jef22:SemanticSubtyping, + author = {A. S. A. Jeffrey}, + title = {Semantic Subtyping in Luau}, + howpublished = {Roblox Technical Blog}, + year = {2022}, + url = {https://blog.roblox.com/2022/11/semantic-subtyping-luau/}, +} + +@InProceedings{GF05:GentleIntroduction, + author = {G. Castagna and A. Frisch}, + title = {A Gentle Introduction to Semantic Subtyping}, + booktitle = {Proc. Principles and Practice of Declarative Programming}, + year = {2005}, +} + +@InProceedings{ST07:GradualTyping, + author = {J. G. Siek and W. Taha}, + title = {Gradual Typing for Objects}, + booktitle = {Proc. European Conf Object-Oriented Programming}, + year = {2007}, + pages = {2-27}, +} + +@Misc{BJ23:agda-typeck, + author = {L. Brown and A. S. A. Jeffrey}, + title = {Luau Prototype Typechecker}, + year = {2023}, + OPTnote = {}, + url = {https://github.com/luau-lang/agda-typeck} +} + +@article{PT00:LocalTypeInference, +author = {Pierce, B. C. and Turner, D. N.}, +title = {Local Type Inference}, +year = {2000}, +volume = {22}, +number = {1}, +journal = {ACM Trans. Program. Lang. Syst.}, +pages = {1–44}, +} + +@inproceedings{SuccessTyping, + author = {Lindahl, T. and Sagonas, K.}, + title = {Practical Type Inference Based on Success Typings}, + year = {2006}, + booktitle = {Proc. Int. Conf. Principles and Practice of Declarative Programming}, + pages = {167–178}, +} + +@InProceedings{Dialyzer, +author="Lindahl, T. and Sagonas, K.", +title="Detecting Software Defects in Telecom Applications Through Lightweight Static Analysis: A War Story", +booktitle="Proc. Asian Symp. Programming Languages and Systems", +year="2004", +pages="91--106", +} + +@Misc{NewNonStrictRFC, + author = {A. S. A. Jeffrey}, + title = {{RFC} For New Non-strict Mode}, + howpublished = {Luau Request For Comment}, + year = {2023}, + note = {\url{https://github.com/Roblox/luau/pull/1037}}, +} + +@Inbook{Nielson1999, +author="Nielson, F. +and Nielson, H. R.", +title="Type and Effect Systems", +bookTitle="Correct System Design: Recent Insights and Advances", +year="1999", +publisher="Springer", +pages="114--136", +isbn="978-3-540-48092-1", +} + +@Misc{DesignElixir, + author = {G. Castagna and G. Duboc and J. Valim}, + title = {The Design Principles of the {Elixir} Type System}, + year = {2023}, + note = {\url{https://doi.org/10.48550/arXiv.2306.06391}}, +} + +@article{BidirectionalTyping, +author = {Dunfield, J. and Krishnaswami, N.}, +title = {Bidirectional Typing}, +year = {2022}, +volume = {54}, +number = {5}, +journal = {ACM Comput. Surv.}, +articleno = {98}, +numpages = {38}, +} \ No newline at end of file diff --git a/papers/incorrectness24/cc-by.png b/papers/incorrectness24/cc-by.png new file mode 100644 index 0000000000000000000000000000000000000000..c8473a24786ab016d9c3e717a380910f7cbb0fff GIT binary patch literal 12588 zcmXY21ys}R+a8ECNOyOalu|OfrKB5FI;2xzv^0{^t@KNGhp2Q&cju(@d-$J^b8s8m zZ`)J%758PtTU9wMbTV`Z1cId?FRcNAAS8nO(WuDaUzdgyad3n5396ul3VwW1EyKZM zG$(nzPY?(f$I~wYwr#u}_#>&SjIOJu<9k;RGZ!m}hldB3wS(;^3o|DxE=QLS8AqaI z5C{!KL0VGF^V{K~m!Zn_Bg)APXG5Cz6_kbu*5aB>jBu$QB3vT(-%i zKB=J`SOT?pH7U?g#dr`&s3Ol>2tvPZV> z&77JHeIvU}8=sv(M#NJdtRUhBsw>z2nrgl}Ru|sXi|wC?~nY zkR)+n-LEiAX;X&pQSZ3Z?zrPc5k@78a&f^kkqj7bUT~${R*R>7Lpia(SGTvfKii!_ zDSA)YX*Z?lZiWY5Ag-$Z5cWbNtJwFZIt34Md9!S7V`F|=!^jYi177ia+`c@jZ#emllvMD) zp@Abs2*qB&_Gp99+1YskHKimDQZ5g;J33z-JI+k~iY3?Kh8vQTD8sxfCj+i$`8EQV z5n}YMiGg9(MPDh7+(+eF; z*2+QYOP-GwpQ*6L#wK!^51RkR2cSsPbG}Y<5~gTX4T#=GQ}E16`qKK%ke~)bT}ul# z@`DjWN=2odwkg#hJzq)3z_ofGktj;W;tZ+F#7c${${j`{%0SU4(}#D=Ex}DaLr3S# 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The only way to detect +that \verb|Fop| was never read would be whole-program analysis, which is +prohibitively expensive. + +\section{New Non-strict error reporting} + +The difficult part of non-strict mode error-reporting is predicting +run-time errors. We do this using an error-reporting +pass that synthesizes a type context $\Delta$ such that if any of the $x : T$ in +$\Delta$ are satisfied, then the program will +produce a type error. For example in the program +\begin{verbatim} + function h(x, y) + math.abs(x) + string.lower(y) + end +\end{verbatim} +an error is reported when \verb|x| isn’t a \verb|number|, or \verb|y| isn’t a \verb|string|, so the synthesized context is +\begin{verbatim} + x : ~number, y : ~string +\end{verbatim} +(\verb|~T| is Luau's concrete syntax for type negation.) +In: +\begin{verbatim} + function f(x) + math.abs(x) + string.lower(x) + end +\end{verbatim} +an error is reported when \verb|x| isn’t a \verb|number| or isn’t a \verb|string|, so the context is +\begin{verbatim} + x : ~number | ~string +\end{verbatim} +(\verb"T | U" is Luau's concrete syntax for type union.) +Since the type \verb"~number | ~string" is equivalent to the type \verb|unknown| (which contains every value), +non-strict mode can report a warning, since calling the function is guaranteed to throw a run-time error. +In contrast: +\begin{verbatim} + function g(x) + if cond() then + math.abs(x) + else + string.lower(x) + end + end +\end{verbatim} +synthesizes context +\begin{verbatim} + x : ~number & ~string +\end{verbatim} +(\verb|T & U| is Luau's concrete syntax for type intersection.) +Since \verb|~number & ~string| is not equivalent to \verb|unknown|, non-strict mode reports no warning. + +\begin{figure*} + \[\begin{array}{c} + \infer{ + \Gamma \vdash M : \NEVER \dashv \Delta_1 \\ + \Gamma, x : T \vdash B \dashv \Delta_2, x : U \\ + \mbox{(warn if $\UNKNOWN <: U$)} + }{ + \Gamma \vdash (\LOCAL x : T = M; B) \dashv (\Delta_1 \cup \Delta_2) + } + \quad + \infer{ + \Gamma \vdash M : \NEVER \dashv \Delta_1 \\ + \Gamma \vdash B \dashv \Delta_2 \\ + \Gamma \vdash C \dashv \Delta_3 + }{ + \Gamma \vdash (\IF M \THEN B \ELSE C \END) \dashv (\Delta_1 \cup (\Delta_2 \cap \Delta_3)) + } + \\[\bigskipamount] + \infer{}{ + \Gamma \vdash x : T \dashv (x : T) + } + \quad + \infer{ + \mbox{(warn if $k:T$)} + }{ + \Gamma \vdash k : T \dashv \emptyset + } + \quad + \infer{ + \Gamma, x:S \vdash B \dashv \Delta, x:U \\ + \mbox{(warn if $\UNKNOWN <: U$)}\\ + \mbox{(warn if ${\FUNCTION} <: T$)} + }{ + \Gamma \vdash (\FUNCTION (x : S) B \END) : T \dashv \Delta + } + \quad + \infer{ + \Gamma \vdash M : (S \fun \ERROR) \\ + \Gamma \vdash M : \neg{\FUNCTION} \dashv \Delta_1 \\ + \Gamma \vdash N : S \dashv \Delta_2 \\ + \mbox{(warn if $\Gamma \vdash M : (\UNKNOWN \fun (T \cup \ERROR))$)} + }{ + \Gamma \vdash M(N) : T \dashv \Delta_1 \cup \Delta_2 + } + \end{array}\] + \caption{Type context synthesis for blocks ($\Gamma \vdash B \dashv \Delta$) and expressions ($\Gamma \vdash M:T \dashv \Delta$)} + \label{fig:ctxtgen} +\end{figure*} + +\begin{figure*} + \[ + \infer{ + \begin{array}[b]{c} + \infer{}{\Gamma \vdash \MATH.\ABS : (\neg\NUMBER \fun \ERROR)} \\[\bigskipamount] + \infer{}{\Gamma \vdash \MATH.\ABS : \neg{\FUNCTION} \dashv \emptyset} + \end{array} + \infer{ + \Gamma \vdash \STRING.\LOWER : (\neg\STRING \fun \ERROR) \\ + \Gamma \vdash \STRING.\LOWER : \neg{\FUNCTION} \dashv \emptyset \\ + \Gamma \vdash x : \neg{\STRING} \dashv (x : \neg\STRING) \\ + \mbox{(warn since $\Gamma \vdash \STRING.\LOWER : \UNKNOWN \fun (\neg\NUMBER \cup \ERROR)$)} + }{\Gamma \vdash \STRING.\LOWER(x) : \neg{\NUMBER} \dashv (x : \neg\STRING)} + }{\Gamma \vdash (\MATH.\ABS(\STRING.\LOWER(x)) : \NEVER \dashv (x : \neg\STRING)} + \] + \caption{Example warning} + \label{fig:example} +\end{figure*} + +In Figure~\ref{fig:ctxtgen} we provide some of the inference rules for +context synthesis, and the warnings that it +produces. These are run after type inference, so they can assume that +all code is fully typed. + +In the judgment $\Gamma \vdash M : T \dashv +\Delta$, the type context $\Gamma$ is the usual \emph{checked} type +context and $\Delta$ is the \emph{synthesized} context used to predict +run-time errors (following the terminology of bidirectional +typing~\cite{BidirectionalTyping}). + +\begin{conjecture}\label{conj:complete}% +If $\Gamma \vdash M : T \dashv \Delta, x:U$ and $\sigma$ is a closing +substitution where $\sigma(x) : U$ and $M[\sigma] \rightarrow^* v$, +then $v : T$. +\end{conjecture} + +\begin{corollary}\label{cor:complete}% +If $\Gamma \vdash M : \NEVER \dashv \Delta, x:\UNKNOWN$ and $\sigma$ is a closing +substitution, then $M[\sigma]$ does not terminate successfully. +\end{corollary} + +\section{Checked functions} + +The crucial aspect of this type system is that we have a type $\ERROR$ +inhabited by no values, and by expressions which may throw a run-time exception. +(This is essentially a very simple type and effect system~\cite{Nielson1999} +with one effect.) + +The rule for function application $M(N)$ +has two dependencies on the type for $M$: +\[\begin{array}{c} + \Gamma \vdash M : (S \fun \ERROR) + \\[\jot] + \Gamma \vdash M : (\UNKNOWN \fun (T \cup \ERROR)) +\end{array}\] +Since Luau is based on semantic subtyping~\cite{GF05:GentleIntroduction,Jef22:SemanticSubtyping} and supports +intersection types, this is equivalent to asking for $M$ to be an +overloaded function, where one overload has argument type $\UNKNOWN$, and +one has result type $\ERROR$. For example: +\[ + \MATH.\ABS : (\NUMBER \fun \NUMBER) \cap (\neg\NUMBER \fun \ERROR) +\] +and so (by subsumption): +\[\begin{array}{c} + \MATH.\ABS : (\neg\NUMBER \fun \ERROR) + \\[\jot] + \MATH.\ABS : (\UNKNOWN \fun (\NUMBER \cup \ERROR)) +\end{array}\] +This is a common enough idiom it is worth naming it: +we call any function of type +\[ + (S \fun T) \cap (\neg S \fun \ERROR) +\] +a \emph{checked} function, since it performs a run-time check +on its argument. They are called \emph{strong arrows} +in Elixir~\cite{DesignElixir}. + +Note that this type system has the usual subtyping rule for +functions: contravariant in their argument type, and +covariant in their result type. In contrast, checked functions +are invariant in their argument type, since one overload +$S \fun T$ is contravariant in $S$, and the other $\neg S \fun \ERROR$ +is covariant. + +This system is also different from success +typings~\cite{SuccessTyping}, which has functions +$(\neg S \fun \ERROR) \cap (\UNKNOWN \fun (T \cup \ERROR))$, +in our system, which are covariant in both $S$ and $T$. + +\section{Future work} + +This type system is still in the design phase~\cite{NewNonStrictRFC}, though we hope +the implementation will be ready by the end of 2023. This will include +testing the implementation on our unit tests, and on large code bases. + +There is an Agda development of a core of strict mode~\cite{BJ23:agda-typeck}. It +should extend to non-strict mode, at which point +Conjecture~\ref{conj:complete} (or something like it) +will be mechanically verified. + +\bibliographystyle{ACM-Reference-Format} \bibliography{bibliography} + +\end{document}