diff --git a/papers/.gitignore b/papers/.gitignore
deleted file mode 100644
index 86338e14..00000000
--- a/papers/.gitignore
+++ /dev/null
@@ -1,12 +0,0 @@
-*.aux
-*.bbl
-*.blg
-*.dvi
-*.fdb_latexmk
-*.fls
-*.log
-*.out
-*.xcp
-*.nav
-*.snm
-*.toc
diff --git a/papers/hatra21/Logo-Roblox-Black-Full.png b/papers/hatra21/Logo-Roblox-Black-Full.png
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index a792fd0b..00000000
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diff --git a/papers/hatra21/README.md b/papers/hatra21/README.md
deleted file mode 100644
index 3105bb5b..00000000
--- a/papers/hatra21/README.md
+++ /dev/null
@@ -1,45 +0,0 @@
-# HATRA 21 position paper
-
-A position paper on Luau for [Human Aspects of Types and Reasoning Assistants](https://2021.splashcon.org/home/hatra-2021) (HATRA) 2021.
-
-## Installing latexmk
-
-First install  basictex
-```
-sudo brew install basictex
-```
-
-Then install the dependencies for the paper (sigh, by hand):
-
-```
-sudo tlmgr update --all
-sudo tlmgr install acmart
-sudo tlmgr install iftex
-sudo tlmgr install xstring
-sudo tlmgr install environ
-sudo tlmgr install totpages
-sudo tlmgr install trimspaces
-sudo tlmgr install manyfoot
-sudo tlmgr install ncctools
-sudo tlmgr install comment
-sudo tlmgr install balance
-sudo tlmgr install preprint
-sudo tlmgr install libertine
-sudo tlmgr install inconsolata
-sudo tlmgr install newtx
-sudo tlmgr install latexmk
-sudo tlmgr install montserrat
-sudo tlmgr install ly1
-```
-
-## Building the paper
-
-To build the paper:
-```
-latexmk --pdf hatra21
-```
-
-To run latexmk in watching mode (where it rebuilds the PDF on each change):
-```
-latexmk --pdf --pvc hatra21
-```
diff --git a/papers/hatra21/bibliography.bib b/papers/hatra21/bibliography.bib
deleted file mode 100644
index 3c193618..00000000
--- a/papers/hatra21/bibliography.bib
+++ /dev/null
@@ -1,177 +0,0 @@
-@Misc{Roblox,
-  author =    {Roblox},
-  title =     {What is {Roblox}},
-  year = 2021,
-  url = {https://corp.roblox.com},
-}
-
-@Misc{Luau,
-  author =    {Roblox},
-  title =        {The {Luau} Programming Language},
-  year = 2021,
-  url = {https://luau-lang.org},
-}
-
-@Misc{Lua,
-  author =    {Lua.org and {PUC}-Rio},
-  title =        {The {Lua} Programming Language},
-  year = 2021,
-  url = {https://lua.org},
-}
-
-@Misc{AllEducators,
-  author =       {Roblox},
-  title =        {Roblox Education: All Educators},
-  year =         {2021},
-  url =          {https://education.roblox.com/en-us/educators},
-}
-
-@Misc{RobloxDevelopers,
-  author =       {Roblox},
-  title =        {Roblox Developers Expected to Earn Over \$250 Million in 2020; Platform Now Has Over 150 Million Monthly Active Users
-},
-  year =         {2020},
-  url =          {https://corp.roblox.com/2020/07/roblox-developers-expected-earn-250-million-2020-platform-now-150-million-monthly-active-users/},
-}
-
-@Book{TAPL,
-  author =       {Benjamin C. Pierce},
-  title =        {Types and Programming Languages},
-  publisher =    {{MIT} Press},
-  year =         {2002},
-  isbn =         {0-262-16209-1},
-}
-
-@Book{TDDIdris,
-  author =       {Edwin Brady},
-  title =        {Type-Driven Development with {Idris}},
-  publisher =    {Manning},
-  year =         {2017},
-  isbn =         {9781617293023},
-}
-
-@PhdThesis{TopQuality,
-  author =       {Bastiaan J. Heeren},
-  title =        {Top Quality Type Error Messages},
-  school =       {U. Utrecht},
-  year =         {2005},
-}
-
-@PhdThesis{RepairingTypeErrors,
-  author =       {Bruce J. McAdam},
-  title =        {Repairing Type Errors in Functional Programs},
-  school =       {U. Edinburgh},
-  year =         {2002},
-}
-
-@InProceedings{GradualTyping,
-  author =       {Jeremy G. Siek and Walid Taha},
-  title =        {Gradual Typing for Functional Languages},
-  booktitle =    {Proc. Scheme and Functional Programming Workshop},
-  year =         {2006},
-  pages =        {81-92},
-}
-
-@InProceedings{WellTyped,
-  author =       {Philip Wadler and Robert B. Findler},
-  title =        {Well-typed Programs Can’t be Blamed},
-  booktitle =    {Proc. European Symp. Programming},
-  year =         {2009},
-  pages =        {1-16},
-}
-
-@InProceedings{Contracts,
-  author =       {Robert B. Findler and Matthias Felleisen},
-  title =        {Contracts for Higher-order Functions},
-  booktitle =    {Proc. Int. Conf. Functional Programming},
-  year =         {2002},
-  pages =        {48-59},
-}
-
-@inproceedings{SuccessTyping,
-  author = {Lindahl, Tobias and Sagonas, Konstantinos},
-  title = {Practical Type Inference Based on Success Typings},
-  year = {2006},
-  booktitle = {Proc. Int. Conf. Principles and Practice of Declarative Programming},
-  pages = {167–178},
-}
-
-@InProceedings{IncorrectnessLogic,
-  author = {O'Hearn, Peter W.},
-  title = {Incorrectness Logic},
-  year = {2020},
-  booktitle = {Proc. Symp. Principles of Programming Languages},
-  articleno = {10},
-  pages = {1-32},
-}
-
-@Misc{HowToDrawAnOwl,
-  author =       {Know Your Meme},
-  title =        {How To Draw An Owl},
-  year =         {2010},
-  url =    {https://knowyourmeme.com/memes/how-to-draw-an-owl},
-}
-
-@Misc{RustBook,
-  author = {Klabnik, Steve and Nichols, Carol and the Rust Community},
-  title = {The Rust Programming Language},
-  year = {2021},
-  url = {https://doc.rust-lang.org/book/},
-}
-
-@article{TypeClasses,
-author = {Hall, Cordelia V. and Hammond, Kevin and Peyton Jones, Simon L. and Wadler, Philip L.},
-title = {Type Classes in Haskell},
-year = {1996},
-volume = {18},
-number = {2},
-journal = {ACM Trans. Program. Lang. Syst.},
-pages = {109–138},
-}
-
-@InProceedings{Hazel,
-  author =       {Cyrus Omar and Ian Voysey and Ravi Chugh and Matthew Hammer},
-  title =        {Live Functional Programming with Typed Holes},
-  booktitle =    {Proc. Symp. Principles of Programming Languages},
-  year =         {2019},
-  pages =        {14:1-14:28},
-}
-
-@InProceedings{MigratoryTyping,
-  author =       {Sam Tobin-Hochstadt and Matthias Felleisen and Robert Bruce Findler and Matthew Flatt and Ben Greenman and Andrew M. Kent and Vincent St-Amour and T. Stephen Strickland and Asumu Takikawa},
-  title =        {Migratory Typing: Ten Years Later},
-  booktitle =    {Proc. Summit on Advances in Programming Languages},
-  year =         {2017},
-}
-
-@InProceedings{LinkingTypes,
-  author =       {Daniel Patterson and Amal Ahmed},
-  title =        {Linking Types for Multi-Language Software: Have Your Cake and Eat It Too},
-  booktitle =    {Proc. Summit on Advances in Programming Languages},
-  year =         {2017},
-}
-
-@InProceedings{QuickLook,
-author = {Serrano, Alejandro and Hage, Jurriaan and Peyton Jones, Simon and Vytiniotis, Dimitrios},
-title = {A quick look at impredicativity},
-booktitle = {Proc. Int. Conf. Functional Programming},
-year = {2020},
-}
-
-@InProceedings{Boehm85,
-  author =       {Partial polymorphic type inference is undecidable},
-  title =        {Hans-J. Boehm},
-  booktitle =    {Proc. Symp. Foundations of Computer Science},
-  year =         {1985},
-  pages =        {339-345},
-}
-
-@article{LocalTypeInference,
-author = {Pierce, Benjamin C. and Turner, David N.},
-title = {Local Type Inference},
-year = {2000},
-volume = {22},
-number = {1},
-journal = {ACM Trans. Program. Lang. Syst.},
-pages = {1–44},
-}
\ No newline at end of file
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-\documentclass[acmsmall]{acmart}
-
-\setcopyright{rightsretained}
-\copyrightyear{2021}
-\acmYear{2021}
-\acmConference[HATRA '21]{Human Aspects of Types and Reasoning Assistants}{October 2021}{Chicago, IL}
-\acmBooktitle{HATRA '21: Human Aspects of Types and Reasoning Assistants}
-\acmDOI{}
-\acmISBN{}
-\expandafter\def\csname @copyrightpermission\endcsname{\raisebox{-1ex}{\includegraphics[height=3.5ex]{cc-by}} This work is licensed under a Creative Commons Attribution 4.0 International License.}
-\expandafter\def\csname @copyrightowner\endcsname{Roblox.}
-
-\newcommand{\squnder}[1]{\color{red}\underline{{\color{black}#1}}\color{black}}
-\newcommand{\infer}[2]{\frac{\textstyle#1}{\textstyle#2}}
-\newcommand{\erase}{\mathrm{erase}}
-\newcommand{\evCtx}{\mathcal{E}}
-\newcommand{\NIL}{\mathsf{nil}}
-\newcommand{\ANY}{\mathsf{any}}
-\newcommand{\TRUE}{\mathsf{true}}
-\newcommand{\FALSE}{\mathsf{false}}
-\newcommand{\NUMBER}{\mathsf{number}}
-\newcommand{\STRING}{\mathsf{string}}
-\newcommand{\ERROR}{\mathsf{error}}
-\newcommand{\IF}{\mathsf{if}\,}
-\newcommand{\LOCAL}{\mathsf{local}\,}
-\newcommand{\THEN}{\,\mathsf{then}\,}
-\newcommand{\ELSE}{\,\mathsf{else}\,}
-\newcommand{\END}{\,\mathsf{end}}
-\newcommand{\FUNCTION}{\mathsf{function}\,}
-\newcommand{\RETURN}{\mathsf{return}\,}
-\newcommand{\FIND}{\mathsf{find}}
-\newcommand{\PRINT}{\mathsf{print}}
-\newcommand{\strlit}[1]{\mbox{``#1''}}
-
-\begin{document}
-
-\title{Position Paper: Goals of the Luau Type System}
-
-\author{Lily Brown}
-\author{Andy Friesen}
-\author{Alan Jeffrey}
-\affiliation{
-  \institution{Roblox}
-  \city{San Mateo}
-  \state{CA}
-  \country{USA}
-}
-
-\begin{abstract}
-  Luau is the scripting language that powers user-generated experiences on the
-  Roblox platform. It is a statically-typed language, based on the
-  dynamically-typed Lua language, with type inference. These types are used for providing
-  editor assistance in Roblox Studio, the IDE for authoring Roblox experiences.
-  Due to Roblox's uniquely heterogeneous developer community, Luau must operate
-  in a somewhat different fashion than a traditional statically-typed language.
-  In this paper, we describe some of the goals of the Luau type system,
-  focusing on where the goals differ from those of other type systems.
-\end{abstract}
-
-\maketitle
-
-\section{Introduction}
-
-The Roblox platform allows anyone to create shared,
-immersive, 3D experiences.  As of July 2021, there are
-approximately 20~million experiences available on Roblox, created
-by 8~million developers~\cite{Roblox}.  Roblox creators are often young: there are
-over 200~Roblox kids' coding camps in 65~countries
-listed by the company as education resources~\cite{AllEducators}.
-The Luau programming language~\cite{Luau} is the scripting language
-used by creators of Roblox experiences. Luau is derived from the Lua
-programming language~\cite{Lua}, with additional capabilities,
-including a type inference engine.
-
-This paper will discuss some of the goals of the Luau type system, such
-as supporting goal-driven learning, non-strict typing semantics, and
-mixing strict and non-strict types.  Particular focus is placed on how
-these goals differ from traditional type systems' goals.
-
-\section{Needs of the Roblox platform}
-\subsection{Heterogeneous developer community}
-
-Need: \emph{a language that is powerful enough to support professional users, yet accessible to beginners}
-
-Quoting a Roblox 2020 report \cite{RobloxDevelopers}:
-\begin{itemize}
-\item \emph{Adopt Me!} now has over 10 billion plays and surpassed 1.6 million concurrent users earlier this year.
-\item \emph{Piggy}, launched in January 2020, has close to 5 billion visits in just over six months.
-\item There are now 345,000 developers on the platform who are monetizing their games.
-\end{itemize}
-This demonstrates the heterogeneity of the Roblox developer community:
-developers of experiences with billions of plays are on the same
-platform as children first learning to code. Both of these groups are important to
-support: the professional development studios bring high-quality experiences to the
-platform, and the beginning creators contribute to the energetic creative community,
-forming the next generation of developers.
-
-\subsection{Goal-driven learning}
-
-Need: \emph{organic learning for achieving specific goals}
-
-All developers are goal-driven, but this is especially true for
-learners. A learner will download Roblox Studio
-(the creation environment for the Roblox platform) with an
-experience in mind, such as designing an obstacle course
-to play in with their friends.
-
-The user experience of developing a Roblox experience is primarily a
-3D interactive one, seen in Fig.~\ref{fig:studio}(a). The user designs
-and deploys 3D assets such as terrain, parts and joints, providing
-them with physics attributes such as mass and orientation. The user
-can interact with the experience in Studio, and deploy it to a Roblox
-server so anyone with the Roblox app can play it. Physics, rendering
-and multiplayer are all immediately accessible to creators.
-
-\begin{figure}
-\includegraphics[width=0.48\textwidth]{studio-mow.png}
-\includegraphics[width=0.48\textwidth]{studio-script-editor.png}
-\caption{Roblox Studio's 3D environment editor (a), and script editor (b)}
-\label{fig:studio}
-\end{figure}
-
-At some point during experience design, the experience creator has a need
-that can't be met by the game engine alone, such as ``the stairs should
-light up when a player walks on them'' or ``a firework is set off
-every few seconds''. At this point, they will discover the script
-editor, seen in Fig.~\ref{fig:studio}(b).
-
-This onboarding experience is different from many initial exposures to
-programming, in that by the time the user first opens the script
-editor, they have already built much of their creation, and have a
-very specific concrete aim. As such, Luau must allow users to perform a
-specific task with as much help as possible from tools.
-
-A common workflow for getting started is to Google the task, then
-cut-and-paste the resulting code, adapting it as needed.  Since this
-is so common, backward compatibility of Luau with existing code is
-important, even for learners who do not have an existing code base to
-maintain.
-
-Type-driven tools are useful to all creators, in as much as they help
-them achieve their current goals. For example type-driven
-autocomplete, or type-driven API documentation, are of immediate
-benefit. Traditional typechecking can be useful, for example for
-catching spelling mistakes, but for most goal-driven developers, the
-type system should help or get out of the way.
-
-\subsection{Type-driven development}
-
-Need: \emph{a language that supports large-scale codebases and defect detection}
-
-Professional development studios are also goal-directed (though the
-goals may be more abstract, such as ``decrease user churn'' or
-``improve frame rate'') but have additional needs:
-\begin{itemize}
-
-\item \emph{Code planning}:
-  code spends much of its time in an incomplete state, with holes
-  that will be filled in later.
-
-\item \emph{Code refactoring}:
-  code evolves over time, and it is easy for changes to
-  break previously-held invariants.
-
-\item \emph{Defect detection}:
-  code has errors, and detecting these at runtime (for example by crash telemetry)
-  can be expensive and recovery can be time-consuming.
-  
-\end{itemize}
-Detecting defects ahead-of-time is a traditional goal of type systems,
-resulting in an array of techniques for establishing safety results,
-surveyed for example in~\cite{TAPL}. Supporting code planning and
-refactoring are some of the goals of \emph{type-driven
-development}~\cite{TDDIdris} under the slogan ``type, define,
-refine''.  A common use of type-driven development is renaming a
-property, which is achieved by changing the name in one place,
-and then fixing the resulting type errors---once the type system stops
-reporting errors, the refactoring is complete.
-
-To help support the transition from novice to experienced developer,
-types are introduced gradually, through API documentation and type discovery.
-Type inference provides many of the benefits of type-driven development
-even to creators who are not explicitly providing types.
-
-\section{Goals of the type system}
-\subsection{Infallible types}
-
-Goal: \emph{provide type information even for ill-typed or syntactically invalid programs.}
-
-Programs spend much of their time under development in an ill-typed or incomplete state, even if the
-final artifact is well-typed. If tools such as autocomplete and API documentation are type-driven,
-this means that tooling needs to rely on type information even for ill-typed
-or syntactically invalid programs. An analogy is infallible parsers, which perform error recovery and
-provide an AST for all input texts, even if they don't adhere to the parser's syntax.
-
-Program analysis can still flag type errors, which may be presented
-to the user with red squiggly underlining. Formalizing this, rather
-than a judgment
-$\Gamma\vdash M:T$, for an input term $M$, there is a judgment
-$\Gamma \vdash M \Rightarrow N : T$ where $N$ is an output term
-where some subterms are \emph{flagged} as having type errors, written $\squnder{N}$. Write $\erase(N)$
-for the result of erasing flaggings: $\erase(\squnder{N}) = \erase(N)$.
-
-For example, in Lua, the $\STRING.\FIND$ function expects two strings, and returns the
-offsets for that string:
-\[
-  \STRING.\FIND(\strlit{hello}, \strlit{ell}) \rightarrow (2, 4)
-\qquad
-  \STRING.\FIND(\strlit{world}, \strlit{ell}) \rightarrow (\NIL, \NIL)
-\]
-and in Luau it has the type:
-\[
-  \STRING.\FIND : (\STRING, \STRING) \rightarrow (\NUMBER?, \NUMBER?)
-\]
-In a conventional type system, there is no judgment for ill-typed terms
-such as $\STRING.\FIND(\strlit{hello}, 37)$ but in an infallible system we flag the error
-and approximate the type, for example:
-\[
-  {} \vdash
-  \STRING.\FIND(\strlit{hello}, 37)
-  \Rightarrow
-  \squnder{\STRING.\FIND(\strlit{hello}, 37)}
-  :
-  (\NUMBER?, \NUMBER?)
-\]
-The goal of infallible types is that every term has a typing judgment
-given by flagging ill-typed subterms:
-\begin{itemize}
-\item \emph{Typability}: for every $M$ and $\Gamma$,
-  there are $N$ and $T$ such that $\Gamma \vdash M \Rightarrow N : T$.
-\item \emph{Erasure}: if $\Gamma \vdash M \Rightarrow N : T$
-  then $\erase(M) = \erase(N)$ 
-\end{itemize}
-Some issues raised by infallible types:
-\begin{itemize}
-\item Which heuristics should be used to provide types for flagged programs? For example, could one
-  use minimal edit distance to correct for spelling mistakes in field names?
-\item How can we avoid cascading type errors, where a developer is
-  faced with type errors that are artifacts of the heuristics, rather
-  than genuine errors?
-\item How can the goals of an infallible type system be formalized?
-\end{itemize}
-\emph{Related work}:
-there is a large body of work on type error reporting
-(see, for example, the survey in~\cite[Ch.~3]{TopQuality})
-and on type-directed program repair
-(see, for example, the survey in~\cite[Ch.~3]{RepairingTypeErrors}),
-but less on type repair.
-The closest work is Hazel's~\cite{Hazel} \emph{typed holes}
-where $\squnder{N}$ is treated as a partially-filled hole in the program,
-though in that work partially-filled holes are not erased at run-time.
-Many compilers perform
-error recovery during typechecking, but do not provide a semantics
-for programs with type errors.
-
-\subsection{Strict types}
-
-Goal: \emph{no false negatives.}
-
-For developers who are interested in defect detection, Luau provides a \emph{strict mode},
-which acts much like a traditional, sound, type system. This has the goal of ``no false negatives''
-where any possible run-time error is flagged. This is formalized using:
-\begin{itemize}
-\item \emph{Operational semantics}: a reduction judgment $M \rightarrow N$ on terms.
-\item \emph{Values}: a subset of terms representing a successfully completed evaluation.
-\end{itemize}
-Error states at runtime are represented as stuck states (terms that are not
-values but cannot reduce), and showing that no well-typed program is
-stuck. This is not true if typing is infallible, but can fairly
-straightforwardly be adapted. We extend the operational semantics to flagged terms,
-where $M \rightarrow M'$ implies $\squnder{M} \rightarrow \squnder{M'}$, and
-for any value $V$ we have $\squnder{V} \rightarrow V$, then show:
-\begin{itemize}
-\item \emph{Progress}: if ${} \vdash M \Rightarrow N : T$, then either $N \rightarrow N'$ or $N$ is a value or $N$ has a flagged subterm.
-\item \emph{Preservation}: if ${} \vdash M \Rightarrow N : T$ and $N \rightarrow N'$ then  $M \rightarrow^*M'$ and ${} \vdash M' \Rightarrow N' : T$.
-\end{itemize}
-For example in typechecking the program:
-\[
-  \LOCAL (i,j) = \STRING.\FIND(x, y);
-  \IF i \THEN \PRINT(j-i) \END
-\]
-the interesting case is $i-j$ in a context where  $i$ has type
-$\NUMBER$ (since it is guarded by the $\IF$) but $j$ has type
-$\NUMBER?$. Since subtraction has type $(\NUMBER, \NUMBER) \rightarrow \NUMBER$,
-this is a type error, so the relevant typing judgment is:
-\[\begin{array}{r@{}l}
-  x: \STRING, y: \STRING \vdash {}&
-  (\LOCAL (i,j) = \STRING.\FIND(x, y);
-  \IF i \THEN \PRINT(j-i) \END) \\
-  \Rightarrow {}&
-  (\LOCAL (i,j) = \STRING.\FIND(x, y);
-  \IF i \THEN \PRINT(\squnder{j-i}) \END)
-\end{array}\]
-Some issues raised by soundness for infallible types:
-\begin{itemize}
-\item How should the judgments and their metatheory be set up?
-\item How should type inference and generic functions be handled?
-\item Is the operational semantics of flagged values
-  ($\squnder{V} \rightarrow V$) the right one?
-\end{itemize}
-\emph{Related work}: gradual typing and blame analysis, e.g.~\cite{GradualTyping,WellTyped,Contracts}.
-The main difference between this approach and that of migratory typing~\cite{MigratoryTyping}
-is that (due to backward compatibility with existing Lua) we cannot introduce
-extra code during migration.
-
-\subsection{Nonstrict types}
-
-Goal: \emph{no false positives.}
-
-For developers who are not interested in defect detection, type-driven
-tools and techniques such as autocomplete, API documentation
-and type-driven refactoring are still useful.
-For such developers, Luau provides a
-\emph{nonstrict mode}, which we hope will eventually be useful for all
-developers.  This non-strict typing mode is particularly useful when
-adopting Luau types in pre-existing code that was not authored with
-the type system in mind.  Non-strict mode does \emph{not} aim for
-soundness, but instead has the goal of ``no false positives``, in the
-sense that any flagged code is guaranteed to produce a runtime error
-when executed.
-
-Our previous example was, in fact, a false positive since a programmer
-can make use of the fact that $\STRING.\FIND(x, y)$ is either $\NIL$
-in both results or neither, so if $i$ is non-$\NIL$ then so is $j$.
-This is discussed in the English-language documentation but not reflected
-in the type. So flagging $(i - j)$ is a false positive.
-
-On the face of it, detecting all errors without false positives is undecidable, since a program such as
-$(\IF f() \THEN \ERROR \END)$ will produce a runtime error when $f()$ is
-$\TRUE$. Instead we can aim for a weaker property: that all flagged code
-is either dead code or will produce an error. Either of these is a
-defect, so deserves flagging, even if the tool does not know
-which reason applies.
-
-We can formalize this by defining an \emph{evaluation context}
-$\evCtx[\bullet]$, and saying $M$ is \emph{incorrectly flagged}
-if it is of the form $\evCtx[\squnder{V}]$. We can then define:
-\begin{itemize}
-\item \emph{Correct flagging}: if ${} \vdash M \Rightarrow N : T$
-  then $N$ is correctly flagged.
-\end{itemize}
-Some issues raised by nonstrict types:
-\begin{itemize}
-
-\item Will nonstrict types result in errors being flagged in function call sites
-  rather than definitions?
-
-\item In Luau, ill-typed property update of most tables succeeds
-  (the property is inserted if it did not exist), and so functions which
-  update properties cannot be flagged. Can we still provide meaningful
-  error messages in such cases?
-
-\item Does nonstrict typing require whole program analysis,
-  to find all the possible types a property might be updated with?
-
-\item The natural formulation of function types in a nonstrict setting
-  is that of~\cite{SuccessTyping}: if $f: T \rightarrow U$ and $f(V) \rightarrow^* W$
-  then $V:T$ and $W:U$. This formulation is \emph{covariant} in $T$,
-  not \emph{contravariant}; what impact does this have?
-  
-\end{itemize}
-\emph{Related work}: success types~\cite{SuccessTyping} and incorrectness logic~\cite{IncorrectnessLogic}.
-
-\subsection{Mixing types}
-
-Goal: \emph{support mixed strict/nonstrict development}.
-
-Like every active software community, Roblox developers share code
-with one another constantly.  First- and third-party developers alike
-frequently share entire software packages written in Luau.  To add to
-this, many Roblox experiences are authored by a team.  It is therefore
-crucial that we offer first-class support for mixing code written in
-strict and nonstrict modes.
-
-Some questions raised by mixed-mode types:
-\begin{itemize}
-
-\item How much feedback can we offer for a nonstrict script that is
-  importing strict-mode code?
-
-\item In strict mode, how do we talk about values and types that are
-  drawn from nonstrict code?
-
-\item How can we combine the goals of strict and nonstrict types?
-
-\item Can we have strict and non-strict mode infer the same types,
-  only with different flagging?
-
-\item Is strict-mode code sound when it relies on non-strict code,
-  which has weaker invariants?
-
-\item How can we avoid introducing function wrappers in higher-order code
-  at the strict/nonstrict boundary?
-
-\end{itemize}
-\emph{Related work}: there has been work on interoperability between different type systems,
-notably~\cite{LinkingTypes}, but there the overall goals of the systems were similar safety properties.
-In our case, the two type systems have different goals.
-
-\subsection{Type inference}
-
-Goal: \emph{infer types to allow gradual adoption of type annotations.}
-
-Since backward compatibility with existing code is important, we have
-to provide types for code without explicit annotations. Moreover, we
-want to make use of type-directed tools such as autocomplete, so we
-cannot adopt the common strategy of treating all untyped variables as
-having type $\ANY$. This leads us to type inference.
-
-To make use of type-driven technologies for programs
-without explicit type annotations, we use a type inference algorithm.
-Since Luau includes System~F, type inference is undecidable~\cite{Boehm85},
-but we can still make use of heuristics such as local type inference~\cite{LocalTypeInference}.
-
-It remains to be seen if type inference can satisfy the goals of
-strict and non-strict types. The current Luau system
-infers different types in the two modes, which is unsatisfactory as it
-makes changing mode a non-local breaking change. In addition,
-non-strict inference is currently too imprecise to support
-type-directed tools such as autocomplete.
-
-Some questions raised by type inference:
-\begin{itemize}
-
-\item How many cases in strict mode cannot be inferred by the type inference system? Minimizing
-  this kind of error is desirable, to make the type system as unobtrusive as possible.
-\item Can something like the Rust traits system~\cite{RustBook} or Haskell classes~\cite{TypeClasses} be used to provide types for overloaded operators, without hopelessly confusing learners?
-\item Type inference currently infers monotypes for unannotated
-  functions, in contrast to QuickLook~\cite{QuickLook}, which can infer generic types.
-  Will this be good enough for idiomatic Luau scripts?
-\item Can type inference be used to infer the same types in strict and nonstrict mode, to ease migrating between modes, with the only difference being error reporting?
-\end{itemize}
-\emph{Related work}: there is a large body of work on type inference, largely summarized in~\cite{TAPL}.
-
-\section{Conclusions}
-
-In this paper, we have presented some of the goals of the Luau type
-system, and how they map to the needs of the Roblox creator
-community. We have also explored how these goals differ from traditional
-type systems, where it is necessary to accommodate the unique needs of
-the Roblox platform. We have sketched what a solution might look like;
-all that remains is to draw the owl~\cite{HowToDrawAnOwl}.
-
-\bibliographystyle{ACM-Reference-Format} \bibliography{bibliography}
-
-\end{document}
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+++ /dev/null
@@ -1,203 +0,0 @@
-\documentclass[aspectratio=169]{beamer}
-
-\usecolortheme{whale}
-\setbeamertemplate{navigation symbols}{}
-\definecolor{background}{rgb}{0.945,0.941,0.96}
-\definecolor{bluish}{rgb}{0.188,0.455,0.863}
-\usepackage{montserrat}
-\setbeamerfont{frametitle}{size=\Large,series=\bfseries}
-\setbeamerfont{title}{size=\Huge,series=\bfseries}
-\setbeamerfont{date}{shape=\itshape}
-\setbeamercolor{title}{bg=bluish}
-\setbeamercolor{frametitle}{bg=bluish}
-\setbeamercolor{background canvas}{bg=background}
-\setbeamercolor{itemize item}{fg=bluish}
-\setbeamercolor{part name}{fg=background}
-\setbeamercolor{part title}{bg=bluish}
-\setbeamertemplate{footline}[text line]{\hfill\raisebox{5ex}{\insertshorttitle~~~~\insertframenumber/\inserttotalframenumber~~~~\includegraphics[width=5em]{Logo-Roblox-Black-Full.png}}}
-\AtBeginPart{{\setbeamertemplate{footline}{}\frame{\partpage}}}
-
-\newcommand{\erase}{\mathsf{erase}}
-
-\title{Goals of the Luau~Type~System}
-\author{Lily Brown \and Andy Friesen \and Alan Jeffrey}
-\institute[Roblox]{\includegraphics[width=15em]{Logo-Roblox-Black-Full.png}}
-\date[HATRA '21]{\textit{Human Aspects of Types and Reasoning Assistants} 2021}
-
-\begin{document}
-
-{\setbeamertemplate{footline}{}\frame{\titlepage}}
-
-\part{Creator Goals}
-
-\begin{frame}
-
-\frametitle{Roblox}
-
-A platform for creating shared immersive 3D experiences: 
-\begin{itemize}
-  \item \textbf{Many}: 20 million experiences, 8 million creators.
-  \item \textbf{At scale}: e.g.~\emph{Adopt Me!} has 10 billion plays.
-  \item \textbf{Learners}: e.g.~200+ kids' coding camps in 65+ countries.
-  \item \textbf{Professional}: 345k creators monetizing experiences.
-\end{itemize}
-A very heterogeneous community.
-
-\end{frame}
-
-\begin{frame}
-
-\frametitle{Roblox developer community}
-
-All developers are important:
-\begin{itemize}
-  \item \textbf{Learners}: energetic creative community.
-  \item \textbf{Professionals}: high-quality experiences.
-  \item \textbf{Everyone inbetween}: some learners become professionals!
-\end{itemize}
-Satisfying everyone is sometimes challenging.
-
-\end{frame}
-
-\begin{frame}
-
-\frametitle{Roblox Studio}
-
-Demo time!
-
-\end{frame}
-
-\begin{frame}
-
-\frametitle{Learners have immediate goals}
-
-E.g. ``when a player steps on the button, advance the slide''.
-\begin{itemize}
-  \item \textbf{3D scene editor} meets most goals, e.g.~model parts.
-  \item \textbf{Programming} is needed for reacting to events, e.g.~collisions.
-  \item \textbf{Onboarding} is very different from ``let's learn to program''.
-  \item \textbf{Google Stack Overflow} is a common workflow.
-  \item \textbf{Type-driven tools} are useful, e.g.~autocomplete or API help.
-  \item \textbf{Type errors} may be useful (e.g.~catching typos) but some are not.
-\end{itemize}
-Type systems should help or get out of the way.
-
-\end{frame}
-
-\begin{frame}
-
-\frametitle{Professionals have long-term goals}
-
-E.g. ``decrease user churn'' or ``improve frame rate''.
-\begin{itemize}
-\item \textbf{Code planning}: programs are incomplete.
-\item \textbf{Code refactoring}: programs change.
-\item \textbf{Defect detection}: programs have bugs.
-\end{itemize}
-Type-driven development is a useful technique!
-
-\end{frame}
-
-\part{Luau Type System}
-
-\begin{frame}
-
-\frametitle{Infallible types}
-
-Goal: \emph{support type-driven tools (e.g. autocomplete) for all programs.}
-\begin{itemize}
-\item \textbf{Traditional typing judgment} says nothing about ill-typed terms.
-\item \textbf{Infallible judgment}: every term gets a type.
-\item \textbf{Flag type errors}: elaboration introduces \emph{flagged} subterms.
-\end{itemize}
-
-\emph{Related work}:
-\begin{itemize}
-\item Type error reporting, program repair.
-\item Typed holes (e.g. in Hazel).
-\end{itemize}
-
-\end{frame}
-
-\begin{frame}
-
-\frametitle{Strict types}
-
-Goal: \emph{no false negatives}.
-
-\begin{itemize}
-\item \textbf{Strict mode} enabled by developers who want defect detection.
-\item \textbf{Business as usual} soundness via progress + preservation.
-\item \textbf{Gradual types} for programs with flagged type errors.
-\end{itemize}
-
-\emph{Related work}:
-\begin{itemize}
-\item Lots and lots for type safety.
-\item Gradual typing, blame analysis, migratory types\dots
-\end{itemize}
-
-\end{frame}
-
-\begin{frame}
-
-\frametitle{Nonstrict types}
-
-Goal: \emph{no false positives}.
-
-\begin{itemize}
-\item \textbf{Nonstrict mode} enabled by developers who want type-drive tools.
-\item \textbf{Victory condition} does not have an obvious definition!
-\item \textbf{A shot at it}: a program is \emph{incorrectly flagged} if it contains
-  a flagged value (i.e.~a flagged program has successfully terminated).
-\item \textbf{Progress + correct flagging} is what we want???
-\end{itemize}
-
-\emph{Related work}:
-\begin{itemize}
-\item Success types (e.g. Erlang Dialyzer).
-\item Incorrectness Logic.
-\end{itemize}
-
-\end{frame}
-
-\begin{frame}
-
-\frametitle{Mixing types}
-
-Goal: \emph{support mixed strict/nonstrict development}.
-
-\begin{itemize}
-\item \textbf{Per-module} strict/nonstrict mode.
-\item \textbf{Combined} progress + preservation with progress + correct flagging?
-\end{itemize}
-
-\emph{Related work}:
-\begin{itemize}
-\item Some on mixed languages, but with shared safety properties.
-\end{itemize}
-  
-\end{frame}
-
-\begin{frame}
-
-\frametitle{Type inference}
-
-Goal: \emph{provide benefits of type-directed tools to everyone}.
-
-\begin{itemize}
-\item \textbf{Infer types} for all variables.  Resist the urge to give up and ascribe a top type when an error is encountered.
-\item \textbf{System F} is in Luau, so everything is undecidable. Yay heuristics!
-\item \textbf{Different modes} currently infer different types. Boo!
-\end{itemize}
-
-\emph{Related work}:
-\begin{itemize}
-\item Lots, though not on mixed modes.
-\end{itemize}
-
-\end{frame}
-
-\part{Thank you!\\Roblox is hiring!}
-
-\end{document}
diff --git a/papers/hatra23/bibliography.bib b/papers/hatra23/bibliography.bib
deleted file mode 100644
index 3fbae85e..00000000
--- a/papers/hatra23/bibliography.bib
+++ /dev/null
@@ -1,69 +0,0 @@
-@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},
-}
\ No newline at end of file
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--- a/papers/hatra23/hatra23.tex
+++ /dev/null
@@ -1,156 +0,0 @@
-\documentclass[acmsmall]{acmart}
-
-\setcopyright{rightsretained}
-\copyrightyear{2023}
-\acmYear{2023}
-\acmConference[HATRA '23]{Human Aspects of Types and Reasoning Assistants}{October 2023}{Portugal, Spain}
-\acmBooktitle{HATRA '23: Human Aspects of Types and Reasoning Assistants}
-\acmDOI{}
-\acmISBN{}
-\expandafter\def\csname @copyrightpermission\endcsname{\raisebox{-1ex}{\includegraphics[height=3.5ex]{cc-by}} This work is licensed under a Creative Commons Attribution 4.0 International License.}
-\expandafter\def\csname @copyrightowner\endcsname{Roblox.}
-
-\newcommand{\ANY}{\mathtt{any}}
-\newcommand{\ERROR}{\mathtt{error}}
-\newcommand{\NUMBER}{\mathtt{number}}
-
-\begin{document}
-
-\title{Goals of the Luau Type System, Two Years On}
-
-\author{Lily Brown}
-\author{Andy Friesen}
-\author{Alan Jeffrey}
-\affiliation{
-  \institution{Roblox}
-  \city{San Mateo}
-  \state{CA}
-  \country{USA}
-}
-
-\begin{abstract}
-In HATRA 2021, we presented \emph{The Goals Of The Luau Type System},
-describing the human factors of a type system for a
-language with a heterogeneous developer community. In this extended
-abstract we provide a progress report, focusing on
-the unexpected aspects: semantic subtyping and type error
-suppression.
-\end{abstract}
-
-\maketitle
-
-\section{Recap}
-
-Luau~\cite{Luau} is the scripting language used by the
-Roblox~\cite{Roblox} platform for shared immersive experiences.  Luau extends
-the Lua~\cite{Lua} language, notably by providing type-driven tooling
-such as autocomplete and API documentation (as well as traditional type
-error reporting). Roblox has hundreds of millions of users, and
-millions of creators, ranging from children learning to program for
-the first time to professional development studios.
-
-In HATRA 2021, we presented a position paper on the \emph{Goals Of The Luau Type
-System}~\cite{BFJ21:GoalsLuau}, describing the human factors issues
-with designing a type system for a language with a heterogeneous
-developer community. The design flows from the needs of the different
-communities: beginners are focused on immediate goals (``the stairs
-should light up when a player walks on them'') and less on the code
-quality concerns of more experienced developers; for all users
-type-driven tooling is important for productivity. These needs result in a design with two modes:
-\begin{itemize}
-\item \emph{non-strict mode}, aimed at non-professionals, focused on
-  minimizing false positives (that is, in non-strict mode, any program with a type error has a defect), and
-\item \emph{strict mode}, aimed at professionals, focused on
-  minimizing false negatives (that is, in strict mode, any program with a defect has a type error).
-\end{itemize}
-%% For both communities, type-driven tooling is important, so we
-%% provide \emph{infallible type inference}, which infers types
-%% even for ill-typed or syntactically invalid programs.
-
-\section{Progress}
-
-In the two years since the position paper, we have been making changes
-to the Luau type system to achieve the goals we set out. Most of the
-changes were straightforward, but two were large changes in how we
-thought about the design of the type system: replacing the existing
-syntactic subtyping algorithm by \emph{semantic subtyping}, and
-treating gradual typing as \emph{type error suppression}.
-
-Semantic subtyping
-interprets types as sets of values, and subtyping as set
-inclusion~\cite{GF05:GentleIntroduction}. This is aligned with the
-\emph{minimize false positives} goal of Luau non-strict mode, since
-semantic subtyping only reports a failure of subtyping when there is a
-value which inhabits the candidate subtype, but not the candidate
-supertype.
-For example, the program:
-\begin{verbatim}
-  local x : CFrame = CFrame.new()
-  local y : Vector3 | CFrame
-  if math.random() < 0.5 then y = CFrame.new() else y = Vector3.new() end
-  local z : Vector3 | CFrame = x * y
-\end{verbatim}
-cannot produce a run-time error, since multiplication of \verb|CFrame|s is overloaded:
-\begin{verbatim}
-  ((CFrame, CFrame) -> CFrame) & ((CFrame, Vector3) -> Vector3)
-\end{verbatim}
-In order to typecheck this program, we check that that type is a subtype of:
-\begin{verbatim}
-  (CFrame, Vector3 | CFrame) -> (Vector3 | CFrame)
-\end{verbatim}
-In the previous, syntax-driven, implementation of subtyping, this subtype check  would fail, resulting in a false positive.
-We have now released an implementation of semantic subtyping, which does not suffer from this defect.
-See our technical blog for more details~\cite{Jef22:SemanticSubtyping}.
-
-Rather than the gradual typing approach
-of Siek and Taha~\cite{ST07:GradualTyping}, which uses \emph{consistent
-subtyping} where $\ANY \lesssim T \lesssim \ANY$ for any type $T$, we
-adopt an approach based on \emph{error suppression}, where $\ANY$ is
-an error-suppressing type, and any failures of subtyping involving
-error-suppressing types are not reported. Users can explicitly
-suppress type errors by declaring variables with type $\ANY$, and
-since an expression with a type error has an error-suppressing type we
-avoid cascading errors.
-
-We do this by defining a \emph{infallible} typing judgment $\Gamma \vdash M : T$
-such that for any $\Gamma$ and $M$, there is a $T$ such that $\Gamma \vdash M : T$.
-For example the rule for addition (ignoring overloads for simplicity) is:
-\[
-  \frac{\Gamma \vdash M : T \quad \Gamma \vdash M : U}{\Gamma \vdash M+N : \NUMBER} 
-\]
-We define which judgments produce warnings, for example that rule produces a warning
-when
-\begin{itemize}
-  \item either $T \not<: \NUMBER$ and $T$ is not error-suppressing,
-  \item or $U \not<: \NUMBER$ and $U$ is not error-suppressing.
-\end{itemize}
-To retain type soundness (in the absence of user-supplied error-suppressing types)
-we  show that
-if $\Gamma \vdash M : T$ and $T$ is error-suppressing, then either
-\begin{itemize}
-  \item $\Gamma$ or $M$ contains an error-suppressing type, or
-  \item $\Gamma \vdash M : T$ produces a warning.
-\end{itemize}
-From this it is straightforward to show the usual ``well typed
-programs don't go wrong'' type soundness result for programs without explicit
-error-suppressing types~\cite{BJ23:agda-typeck}.
-
-\section{Further work}
-
-Currently the type inference system uses greedy inference, which is
-very sensitive to order of declarations, and can easily result in
-false positives. We plan to replace this by some form of local type
-inference~\cite{PT00:LocalTypeInference}.
-
-Currently, non-strict mode operates in the style of gradual type
-systems by inferring $\ANY$ as the type for local variables. This does
-not play well with type-directed tooling, for example $\ANY$ cannot
-provide autocomplete suggestions. Local type inference will infer more
-precise union types, and hence better type-driven tooling.
-
-At some point, we hope that error suppression will be the only difference
-between strict mode and non-strict mode.
-
-\bibliographystyle{ACM-Reference-Format} \bibliography{bibliography}
-
-\end{document}
diff --git a/papers/incorrectness24/bibliography.bib b/papers/incorrectness24/bibliography.bib
deleted file mode 100644
index a5724f6b..00000000
--- a/papers/incorrectness24/bibliography.bib
+++ /dev/null
@@ -1,122 +0,0 @@
-@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
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-\documentclass[sigplan]{acmart}
-
-\setcopyright{rightsretained}
-\copyrightyear{2024}
-\acmYear{2024}
-\acmConference[Incorrectness '24]{Formal Methods for Incorrectness}{January 2024}{London, UK}
-\acmBooktitle{Incorrectness '24: Formal Methods for Incorrectness}
-\acmDOI{}
-\acmISBN{}
-\expandafter\def\csname @copyrightpermission\endcsname{\raisebox{-2ex}{\includegraphics[width=.2\linewidth]{cc-by}} \parbox{.7\linewidth}{\raggedright This work is licensed under a Creative Commons Attribution 4.0 International License.}}
-\expandafter\def\csname @copyrightowner\endcsname{Roblox.}
-\newcommand{\infer}[2]{\frac{\displaystyle\begin{array}{@{}l@{}}#1\end{array}}{\displaystyle#2}}
-\newcommand{\LOCAL}{\mathop{\mathsf{local}}}
-\newcommand{\FUNCTION}{\mathop{\mathsf{function}}}
-\newcommand{\IF}{\mathop{\mathsf{if}}}
-\newcommand{\THEN}{\mathbin{\mathsf{then}}}
-\newcommand{\ELSE}{\mathbin{\mathsf{else}}}
-\newcommand{\END}{\mathop{\mathsf{end}}}
-\newcommand{\NEVER}{\mathsf{never}}
-\newcommand{\ERROR}{\mathsf{error}}
-\newcommand{\UNKNOWN}{\mathsf{unknown}}
-\newcommand{\STRING}{\mathsf{string}}
-\newcommand{\NUMBER}{\mathsf{number}}
-\newcommand{\MATH}{\mathsf{math}}
-\newcommand{\ABS}{\mathsf{abs}}
-\newcommand{\LOWER}{\mathsf{lower}}
-\newcommand{\fun}{\mathbin{\rightarrow}}
-
-\begin{document}
-
-\title{Towards an Unsound But Complete Type System}
-\subtitle{Work In Progress on New Non-Strict Mode for Luau}
-
-\author{Lily Brown}
-\author{Andy Friesen}
-\author{Alan Jeffrey}
-\author{Vighnesh Vijay}
-\affiliation{
-  \institution{Roblox}
-  \city{San Mateo}
-  \state{CA}
-  \country{USA}
-}
-
-\begin{abstract}
-In HATRA 2021, we presented \emph{The Goals Of The Luau Type System},
-describing the human factors of a type system for a language with a
-heterogeneous developer community.  One of the goals was the design of
-type system for bug detection, where we have high confidence that type
-errors identify genuine software defects, and that false positives are
-minimized. Such a type system is, by necessity, unsound, but we can ask
-instead that it is complete. This paper presents a work-in-progress report
-on the design and implementation of the new unsound type system for Luau.
-\end{abstract}
-
-\maketitle
-
-\section{Introduction}
-
-Luau~\cite{Luau} is the scripting language used by the
-Roblox~\cite{Roblox} platform for shared immersive experiences.  Luau extends
-the Lua~\cite{Lua} language, notably by providing type-driven tooling
-such as autocomplete and API documentation (as well as traditional type
-error reporting). Roblox has hundreds of millions of users, and
-millions of creators, ranging from children learning to program for
-the first time to professional development studios.
-
-In HATRA 2021, we presented a position paper on the \emph{Goals Of The Luau Type
-System}~\cite{BFJ21:GoalsLuau}, describing the human factors issues
-with designing a type system for a language with a heterogeneous
-developer community. The design flows from the needs of the different
-communities: beginners are focused on immediate goals (``the stairs
-should light up when a player walks on them'') and less on the code
-quality concerns of more experienced developers; for all users
-type-driven tooling is important for productivity. These needs result in a design with two modes:
-\begin{itemize}
-\item \emph{non-strict mode}, aimed at non-professionals, which
-  minimizes false positives (that is, in non-strict mode, any program with a type error has a defect), and
-\item \emph{strict mode}, aimed at professionals, which
-  minimizes false negatives (that is, in strict mode, any program with a defect has a type error).
-\end{itemize}
-The focus of this extended abstract is the design of non-strict mode: what constitutes
-a defect, and how can we design a complete type system for detecting them.
-(The words ``sound'' and ``complete'' in this sense are far from ideal,
-but ``sound type system'' has a well-established meaning, and ``complete''
-is well-established as the dual of ``sound'', so here we are.)
-
-The closest work to ours is success typing~\cite{SuccessTyping}, used
-in Erlang Dialyzer~\cite{Dialyzer}.  The new feature of our work is
-that strict and non-strict mode have to interact, whereas Dialyzer only has
-the equivalent of non-strict mode.
-
-New non-strict mode is specified in a Luau Request For
-Comment~\cite{NewNonStrictRFC}, and is currently being implemented.
-We expect it (and other new type checking features) to be available in
-2024. This extended abstract is based on the RFC, but written in
-``Greek letters and horizontal lines'' rather than ``monospaced text''.
-
-\section{Code defects}
-
-The main goal of non-strict mode is to identify defects, but this requires
-deciding what a defect is. Run-time errors are an obvious defect:
-\begin{verbatim}
-  local hi = "hi"
-  print(math.abs(hi))
-\end{verbatim}
-but we also want to catch common mistakes such as mis-spelling a property name,
-even though Luau returns \verb|nil| for missing property accesses.
-For this reason, we consider a larger class of defects:
-\begin{itemize}
-\item run-time errors,
-\item expressions guaranteed to be \verb|nil|, and
-\item writing to a table property that is never read.
-\end{itemize}
-
-\subsection{Run-time errors}
-
-Run-time errors occur due to run-time type mismatches (such as \verb|5("hi")|)
-or incorrect built-in function calls (such as \verb|math.abs("hi")|).
-Precisely identifying run-time errors is undecidable, for example:
-\begin{verbatim}
-  if cond() then
-    math.abs(“hi”)
-  end
-\end{verbatim}
-We cannot be sure that this code produces a run-time
-error, but we do know that if \verb|math.abs("hi")| is executed, it
-will produce an error, so we consider this to be a defect.
-
-\subsection{Expressions guaranteed to be nil}
-
-Luau tables do not error when a missing property is accessed (though embeddings may). So
-\begin{verbatim}
-  local t = { Foo = 5 }
-  local x = t.Fop
-\end{verbatim}
-does not produce a run-time error, but is more likely than not a
-programmer error. If the programmer intended to
-initialize \verb|x| as \verb|nil|, they could have written
-\verb|x = nil|.  For this reason, we consider it a code defect to use
-an expression that the type system infers is of type \verb|nil|, other
-than the \verb|nil| literal.
-
-\subsection{Writing properties that are never read}
-
-There is a matching problem with misspelling properties when writing. For example
-\begin{verbatim}
-  function f()
-    local t = {}
-    t.Foo = 5
-    t.Fop = 7
-    print(t.Foo)
-  end
-\end{verbatim}
-does not produce a run-time error, but is more likely than not a
-programmer error, since \verb|t.Fop| is written but never read. We can use
-read-only and write-only table properties types for this, and consider it an
-code defect to create a write-only property.
-
-We have to be careful about this though, because if \verb|f| ended
-with \verb|return t|, then it would be a perfectly sensible function
-with type \verb|() -> { Foo: number, Fop: number }|. 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}