From b7f2c3b87d7d5812c66f0643d84a2d98bffdf50b Mon Sep 17 00:00:00 2001 From: "ajeffrey@roblox.com" Date: Mon, 21 Aug 2023 14:10:02 -0500 Subject: [PATCH] Responding to treferee comments on the HATRA 23 paper --- papers/hatra23/hatra23.pdf | Bin 399315 -> 415900 bytes papers/hatra23/hatra23.tex | 52 ++++++++++++++++++++++++++++++++----- 2 files changed, 45 insertions(+), 7 deletions(-) diff --git a/papers/hatra23/hatra23.pdf b/papers/hatra23/hatra23.pdf index 60201e651322b49b8097d3f533d5da0869124dd4..32e83b9ba8770868167b4160dfaa159a54bd6a6c 100644 GIT binary patch delta 138659 zcmZsCQ*bT}uw-o8wr%6Ywr$(_V%yeKh>6I-*cyh94~9|J%-+J)l8BXsl{sB$ADjwMqOIk!#ew4gT9;7l@!gai+FV(42v4*$=$3Dn{7#faN@^IK1XdeJ1M_#*u3GYgX*J+s`X@OW6nZG&3|q>^pVHd@v&CL zeR85qB9r5nJxO@`B2~E4E_ymm)-Nt^C>n=Ep=rDnE6aJ&LZNOuOEWjDeK#i947tkC ztG^3z9RGBGUuw2MDwD8unMust(E7t63QOo9xo@ldPq@3YP4IH)WKY$MsGrme9{~oQ;=3 zV*~aX^AJ*keMH$dKqs*>?~WNtjCXXf{Qjx6^iDr!o9Phd1Obs(Y#L?>VuS(sy3+H< zVZH-*u&LzadQu*Drv8#6Ow5RrD`aN(R3!fJABqkuM5Q%igXaM2JA1LZuayh6338T{ z=F^JEq8C4g#zH-MV%NI8G!D_+*@ODqk@TiopfjDMCa3Zu`YbfhCRX-W6Cw}B30SSw z{gT?WHo~WsVHmHg*=&SD9;O)pPWW~BCjg~Q*4Np2oHdHnj%24cUUF9753LA!M0hiH zxCTL@-e0EIzK94C8OwNoty2_n6{x+8yuoen*1FRv_x+hHcZHr%c zC(%)ep5?=eD(LaGZW$C2A;ky>h<;e}{0ZcePz0N1cX`V2tK7881}_63B^ePe-L0}D zIh6w;AwLi>t?wOd0vsN(pJWlw$A$e-R>40-A)3qs(_dR!X=BKbm4bW{?J|jE2tkY+ zvsB?6(>GS`KhAzx0qgj329QN)8p!H z)$}_^pR_MI3oL1%8Fn6kNGi>wE@uT@O%$bR8bF1DskCLpv+|({LR?}rv3=-T&htPA zSs*p840N4Pt(DaIhB=oM4KT92tCO{$OZfr*$vrHK1_1kp6+U5;jDQ=rm`fr54%F$f z{^T*-*U1VD_EuGgBGIWLTsOXu1|ucl4-D<1(BH}mnIahrpOFIeV#A9|=2`iOk|>nt zmFpCzN`js)fUeOR`2(>$%<-NQXSjH0%$rENZVs-N7Mery`q#4> zIOp?HX6DE7S6!k|Q|u7X<@JnT z@o2zrpj_hA)#(8cdjsiQE>%QAia~X)CDcx`7s>^)fe&JV&e;=abuXEq(RfjO4EKFB z`{(JE#$=gsE}3OPH{l847z!Y^l`&w071`Ft>Kdb{k%HUF+&L5OwRy(5q4_CO#Yv+@ zKWv&x&wmUTfjT9{jS&$+L93;&%pnhNp3f0oIufHFOR)iyP)J`a=*`MZYh59j#JR6L zQv*=_rg&_*?OGXMbf23de`?X)26r8y;k8TtB<9OhJR4QfHU5>K^hXA3qk!Qi&jxf7^Y+Pd=33%wNJ*rm8ew;f0e3;f+Gxa=Ibo&do3yS0BIe(WIiy znNyd0#;wQ{6{=A}<(o4s!R>oxe>2l;lcg+J>6E#$>j6S+zGJloMZ|F@~H;gHw zODouK2Gj?XtsTrpJBUfvhHfcUl=`k)rGF=~Uln`>pL8t4MgW<*Ga zzq}!_{EVUL@*uC7s0 z%!mOH&5S`UfzB71)MAUJFd5-k|E2>^N$Y8RutK0vqg50qdg zJ$DVdKW{D$K0dJB=pS(uT&N1K@J z56!Xmo|k$9h6niyd~05D^)T}#XA|n>0~`R-2LkQ{ms3{jG5Ve6^;FI!q2tLZ$2nQ_ zS*8$b$g04{9MCbQOrg4sYZULYYbt$Lig8@4a-@S5gq{6U+xu|yNHg4Q=ziR3$=32T ziUlf0WW?K5!-LohZMhNUYOt~bBs}$G7e#^_d3G5L@^H<X`8q-SiS;qPYK+zK&YdUs1NjNg9gO(a$l;w`EmFMkA6JBs7 zl43Y|FQS(wtHB;ge?|Cvl~<0iqyJ@E=6l!nb{uG14VaQlMNcZ=ld2V}V?kksk1u)T zr3_j(5BJMhJQ(cE>!GsCEJ;v^PI3UuoqK(cf|{6!RodMdf<7^6`&^Ff_1Hm3g*q$jRrDyOPE#+!aZCsyv%={EB;uxOg*sc{H{o!VPnIQJdCJ*|Cb3 z0pjYA)%S)3+{QL^QFG%ZaT5UALP@t0QlJSi>e1m>g7|+g+OjDt&HIg+-&rDYwZ=w; z8zBfN4QLi*2kD3i5Gjec7kg5Q=)$|{m-cm2A|Nqu=m7nL*(w<#or6cgE$WrDc+Fes ztBQ~ivE*4Q0WY*)mCCS)zW!SR%yc;5jSB=1wqZ|WeqFs)&06pM+cy9zOC;jo7Krfc zN9D_R<<8a9PpPR?Or$hMaJQMy&Gfw0V~N!t4bsUdhg;oYrFX~`Q@N=sLm5Py7nRPx z?#0=hP}$V1)mNNd5Ep9~J+&{TxiR^1l0>TsTx68?f*(`Tx-hlQnrZ7>(&CNpG-ewh ze%t6z<1dp}n&QMGh5mq7+01|FMO+p)p|jFk-!6VXjBicS!D#Q?$R7Qvp9d$yjErgh z#Ii(eC)s|F2dDA-CqOnd+AtBA@!l3q$n75n30QfT)6dZWdg>!ZC(tKIklrpsktnj2 z%bCCW%K0NqAh7)`op;Zd6dS&q!0VZJaa6bF3r_&*bqGgioD0A&=s1zygJ-f#nvh&k z-G=ETl3?gdzVCDpbn5k<|5Vf1+`1m2xP%0v1#K0uoN&ZC z^bgDE`SbK%;y9j=jV<1MBT7|E`94FDYv~WP$5C~;!~bL!1qX5AvW2O(FXFj1 z4+cAY-EDLf6D9{@=p+hBvRK%{KU*%GiH9(i@^d;6wd%9v>i3QT^=@NSGweg=J0#}l zg(+VMJ;EE~F1;0i$(XrVIQ|PJdLuJ)PI@+TQxkeF=Kp}r z#EgxD#n{;RzoJRsHxU+#gX{lexHy@({;%Ph#`({1wY=-~8dLf~wf+rtyn7P0FclY2 z=5#kJ@vrAsv6iaIxJtT6N-4_xdGqgs3;+_7YDu1Y64pNWxq&T+o(^KrC*Ttl zJ>70UJE!*7-Z}V%3ie(UR+Wy{*?=!to5YCD$9 zL4T^)Kzq^2Hao7+_fiGK^DzL*;xAH_cU*BF-Wn~UO(Xj0e;WOKmaFUTnl8`+y@y!) zm{G+n(KhXwlwm&7v5wnSKk8wZiz^uu|C`cj1@6b*Y?WoHHFhh<7@Z6)+kYIk&$T-3 z1*x^v5c{b7rbgdb8{k+5(#gnZ_bAQ8&~QGQP>$s7F=c>-K}xBj8({%Y?KtRQjT%ZY zkP|klZz$ub)*t5c67l+c=49rf0COiqmbHL@hqpxm!h^UpN-MUPF~qt06keQ@8*(a2 z?&BZ*%i8N~f1t!Ze)`?hr{zt0NIA29`_?4Wq&x2h8|Uic`Vg`Lh@FAP?m>24C=WUL z^1XUlEh^*Ep_!D_F&DrZBe=&6*|LLs(y9>p>Pt& z@pxF2(TLb2(ZnO`=8t-HGYC*oEDYGBvLAUwE%{U5G{vNoEgkoWGHZpuL=_#E{XiuE zJ*iZD%;fn5IVPk>6f^k~aTv-EpjDsdvXNfG`gv`_*nWFdT95< zlFkp?s}Q7AmiZ2iRT5jFh##A|yeZiXXo?0yizUKBWr|US72KO`B~zNr8livp4XF$!ELIX z**p#?eeFQiZY`j7x&xcZ(WDk^506vd2*aP>(%YrM5~L~0AXPj*&A%w+V(@WFD+RR_F4P(CH;?rh8+l6hO%P+zj z5hO`vAh39cr@|thh+a)~4(RPRZ-T=Trt4u9569NVhSKF6#vF}zreu*RiXT!>nka)M z$3Fr*R2uS$OwJ+sb6SzJG~{^r-}#_O20wL3ybORiL};oZiEC&jaZ&L z#QH#CFQXSc`TmgXi|_B_=25%ZhJpFHWPkDrF#b0Xg;Sy3=r%Z38Me5N6O3vQkQq2M zf(Z{aNS$mMndZAbD)`wHvOp~6Q>7Zs94=th+`T7oZByJ)$1;K$$pS^CyS zsB*KO$E#V+3{HReW>ugq|Zb=B)8gAZr+o{hXh@&_sn zMqccsxbRUPDQ>cNW;Vk+x@LwCiH|^F0#35UBtrhiY};Tk-aZYp0FC;UPGSr)V;_Lq zvD+VU5N{%uR|dQ$ydc%T&`@VKi01!D4Ut$ODJx7s{I1SC_RbPZs+J;8Y(`6>b#L8p z9`^0k==YF;)N|NO_TlX+E`}d>hAte~ZR*N-qu>h|9*V3m? 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zMoJ?ql_AK5ghy_RjjCEJ@o^*Zb+K?h2|>rietqxVK!YJtH@uf;o5JxaSVSB83|Va| zZJ@a4k|y(rXiV{8?f=1KB-=^by8el@6V*~_eyoU(DtG#uvD48=^!dJ3fDVJ>6N^+4 zPckT*nuO-VmrALjzM_p|3eUp>j80jZ`#j`_Ys@!%iVdasn+q$i0J5dLVVsF|jp08=#qaI|t%CZh7e$Qtmz5{z1%8{yA`_of7!^=VqswR7KC2|pK@-0~?oH71fY z9~?EbpV}oHLz!Ky|KP4=25c9pDrIqv58xsOZf;km8csi>Z%xH=E(keCy^VvK!>bJ34lrCAd)EK_u@c2d1LGWAStCrQr=XH?AKtcuR%IrL%g7} zfsz-Zw8d4SIhk;B3Fy1*09;+q_pp{ zrqMZ(I;# 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 @@ -94,8 +110,30 @@ 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. Error suppression is in production Luau, and is -mechanically verified~\cite{BJ23:agda-typeck}. +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}