From 061ea0e0d3e532ae3b71c652a3e94a4d3f680714 Mon Sep 17 00:00:00 2001 From: Joshua Moerman Date: Mon, 1 Feb 2021 11:36:47 +0100 Subject: [PATCH] Moore machines --- moore/README.md | 5 ++ moore/Setup.hs | 2 + moore/app/Main.hs | 11 +++ moore/moore.cabal | 28 ++++++ moore/output.7z | Bin 0 -> 1740042 bytes moore/src/Crossword.hs | 152 +++++++++++++++++++++++++++++++++ moore/src/Gridworld.hs | 171 +++++++++++++++++++++++++++++++++++++ moore/src/Lib.hs | 6 ++ moore/src/Registerworld.hs | 79 +++++++++++++++++ moore/stack.yaml | 4 + 10 files changed, 458 insertions(+) create mode 100644 moore/README.md create mode 100644 moore/Setup.hs create mode 100644 moore/app/Main.hs create mode 100644 moore/moore.cabal create mode 100644 moore/output.7z create mode 100644 moore/src/Crossword.hs create mode 100644 moore/src/Gridworld.hs create mode 100644 moore/src/Lib.hs create mode 100644 moore/src/Registerworld.hs create mode 100644 moore/stack.yaml diff --git a/moore/README.md b/moore/README.md new file mode 100644 index 0000000..5b9e4df --- /dev/null +++ b/moore/README.md @@ -0,0 +1,5 @@ +Moore machines +============== + +Some code to generate Moore machines. Especially the ones +by the Rivest and Schapire papers. Enjoy! diff --git a/moore/Setup.hs b/moore/Setup.hs new file mode 100644 index 0000000..9a994af --- /dev/null +++ b/moore/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/moore/app/Main.hs b/moore/app/Main.hs new file mode 100644 index 0000000..f5f24b2 --- /dev/null +++ b/moore/app/Main.hs @@ -0,0 +1,11 @@ +module Main where + +import Gridworld (dotgraph) +import Registerworld (dotgraph) +import Crossword (dotgraph) + +main :: IO () +main = do + --mapM_ (\n -> writeFile ("output/register" ++ show n ++ ".dot") (Registerworld.dotgraph n)) [2..16] + --mapM_ (\(w,h) -> writeFile ("output/grid" ++ show w ++ "x" ++ show h ++ ".dot") (Gridworld.dotgraph w h)) [(2,2), (2,3), (2,4), (2,5), (3,3), (3,4)] + mapM_ (\(w,h) -> writeFile ("output/crossword" ++ show w ++ "x" ++ show h ++ ".dot") (Crossword.dotgraph w h)) . fmap (\x -> (x, x)) $ [2..12] diff --git a/moore/moore.cabal b/moore/moore.cabal new file mode 100644 index 0000000..6195903 --- /dev/null +++ b/moore/moore.cabal @@ -0,0 +1,28 @@ +cabal-version: 2.2 +name: moore +version: 0.1.0.0 +author: Joshua Moerman + +extra-source-files: + README.md + +common stuff + default-language: Haskell2010 + ghc-options: -O2 -Wall + build-depends: + base >= 4.8 && < 5, + containers + +library + import: stuff + hs-source-dirs: src + exposed-modules: + Gridworld, + Registerworld, + Crossword + +executable moore + import: stuff + main-is: Main.hs + hs-source-dirs: app + build-depends: moore diff --git a/moore/output.7z b/moore/output.7z new file mode 100644 index 0000000000000000000000000000000000000000..4d9472e653c019a49c68a5f82fd8bacfe8a6b780 GIT binary patch literal 1740042 zcmV(!K;^$Tdc3bE8~_A`R+O#Aj2Zv{0000a000000002+ni9JI`<9`kT>vr~NgAR> zX2ZZ0H5!rVDIt0VHV}lL1ZApMwUydhkGu`nc%%deL*TZ|s^_aqUBOMEoeN#P107c) zI{8ugya}G->1igk+O@b|ym=HZFR-fbvvue7Ao@4|WG$XF*az@YXBA8wO|CvwUngTt znx1m;dA|k6leBQ3)>lvR^xMy^y#o<5q)KM_n1UZE;N2SH-S9S?MTqaWQLdX!j6r&l zw<`G=j`Vyx!#69<#$T6(lvigqM$Svpi5j6}w9_7kpY18Hc;sAe{sd{!0s=T1)}@e$ z%J=^qO*}zTlJWm5TvojX1zQ3Mi4TY6{Cp5Pvc)Iv50-z=0JCHg{J7Eom(EDt>NC@b zE)T1BMc#zOqB3NxDyeJiQytV32lmJnG%#b+VF!&Nx|B@UFpo`5R{iWZR3d#hAJMEB z-`Pj-cNIcZU=-46?lucg$c)`O=wabM(~BjioXn*c0(c?D8O|~v-q_^8xX_>nFK=_4 zMv0?eFsSk2x^ESm0J%KIk0#woJTvKFj`IqTkX|uKY}(T-*^H;&vHLy>(=dhYUhbIx zDY8U1I~>^HX#|oA*!+!sT8bNz+1b4OL1G^&!W$YLd5qqZG~@&SN0YBXP|UHf%yJ2 zCjMeU*7x$xP*?ae3vlp;W7kIFZLJ_<$(R?u`&Bh75dD>Pb;N+!DkAk_ApWnT_B--0 zNXGLdGHy3QZG{HDyija{tiVk=A<(yI1{>hrONIxn%h%R+bc$|%d)R5#v!mwGu}#dL z_55&(=yn~JnNi?Bu8AIm#OWWii~Lf?$@D-d&Kt#RrmmrqAlSXQtahawA3GJR45LVY zD*7#4j@ECA%(j*m6&_gv!Kko+M?t_mS@M1|>oC@>E&pBpo2L_*fu+$Vg$sh_;kJe4 zydPl8a~sq#kQj3^%@j+Z2bCFAn9s9QDbuF9Y;?ZnBk61R>f?AWfUJ-`W736jG3uPQL z+^{X!I<5S@-rCi3xu1d@kel)@4Vr@+Q)vN#XvgW>!d56+P!Jx&HxGfmAqZ*t>CGHu zLOawRUj@9#Z8E{Z+eKEHqzz#y6OhT7v-);jq-69EP;t1H#^t{xaE?hCRl-`>Tz3uNH{Cqua$WivSww_WfZI$=|Dly?f+PAyhmTqNe5avoQ+~R8 zn3BVTni*aAZjagZ>79}Hzx$6mK_Jn-X2$zK)9pqQ6#EyCy3pL%R61PnQhMUKL3Ob1 zJ{JZQ+86a|m>ic)p-v3u}ptUs6b&Igci#1cDzJIP6vENm7hd82ZbSj zjnHO+J>Mn9We&>Tg`VEq_~BaeBO~(O zK-oR1>w2R6;?`SM;h9I~Jyku`N89{VUu3zi!as5nx@-FeZF>4c!x9Z0TZyVwrES3V zw#7E|tg<)TzuV1wCl&A|0D33LP)Hv!axr&Yp=c9F5!~oYi2MBZC_eW|gn74h_IwpE zJyaXQqcO;29Z=R>g-6q4MW7p(MyA5pGzECTT>uB`S7|aVz~83Rv~Ai`h0Nt^FMQ08 z+R*tTSa)|6c*UDNhb~vPPs7$Iw!}^44_-^wT~ry&Ruuo_MI|_JV`Y=YIAlksaR_Omoxn6B0(%Wr3sDwok(HN!`-Uq^F%S!RGE)Sd^>u>hyrT_c{*VTIq z>Os%J`^uAc4KH}B41&mHhro>E4gP~2}o`Fim`i5C$E=xy`(kVA(akVb=m@_LhE;KCuf2TuD zQHhH1H4kx^aNo9+17?Xm2KBK3XzaY0@QLvwdJhj<10v&0=6Pk!Nl!Hbn$KKSkReQ? zht*)jJxpN`=oWr7iQ*nGz$w6*#n4aYPF*4pSK)eh*Ig}|K?j=33sAh~83G%i{Mcw4 z7(Le3FtwoM6Ub3_4_6&SdU~5)rlqKD$cup1hPyL8#EdNJxH9MdhB2tzpeu!=7PaTV zaD*$P9o;#TMkj@pBaSdDe(5C(r2uV$z69YNB4teTEb%@90%~~;I8osP7ctjGdYG;A zv_f~v4$lyJiycj{aa*8R269!!vTLEm;%H>v0QQ>swruHA!=LCSNMto*<>CWia|%0^ z9Tj+5mRZz0NXe*@ZJOWp%Cx%)SP71LCzu`l3%#ZGVgRwSO=`Y z>ewQ|V>uF`OVvOGR{u)~l6`dxE-xhimlN&Hc*?QA+Of11<7b+89z+nhU&F5d?N2JZ z33vs`Q0O^PR5cH@gS%`CNkp$)uK7%pG2TOlHW7KoowqM^{pT#cxY`_&4$GOWhr|g( zV;VXUHprB?iq7L?@gfy#Oun;Livey{dP9;O;I56g$M71=#0;IJ)(vxFi(P#fZ%g~;nbxK#fRkM;bWWwueSu3?}*99;YOKgy^*%?Hb zooc}d^3}}TVZD$}4MVod*pIyLJ+Y`cX(|Ic2iC2DO+i|Aa-vI@ukqD3T|@KpAr`~_-UUR_EQsHV5hn?17{#P?=7ska?Dv{US2{2Bc`fAtVgA&K zc2d{(xt$5BuQi;wVA}5crr@tiCj(V8pS;zjf)g2Z_iydDr4b?xNElq%CT@@<>7yCXS0b?zyTl0X zI&>1CEEgJH)rN(TOC~0E^`Rsi_?k>9jyL?wy#3Sj{QfVpYlxi^4)wI>%6LIP7~AjA zP*cOw&_skQU4qZytfOlY%3U18%+DyZUuO-hwl@^zheoNS+p1>V<0cK6jjU5dFK>7aY_?6v|#g?bfw-I#wy#-T&-!6OM;vaa+_|+XO$n&=F98+&DX#K-E-;3qYYh7Zf@T7;aN7$t73RL zfrcUpWvkM$%$p!5kOH8$l>NM7^ij@3|~~}P@<9t*k+T3OipjW zZEv5s8h~@8s6D&Ag#1r5#rxHXWN24*pK}x_vd@#pFmzP^>gC_IrSKZM}n2>Kp!l31W2fi!gO5rS#tn#TTOBWQjO54MY>VywO8^H(AW z0WWmJD*N0L#H>K<(e@K$0Ugqr?2yRC&}fU1a<2;4x`$=7=0Bp7 z$EUN5@pzQ4nPz5z_AnPl8f(aZgvCO5sTdk)0Z>+|FW-V|NUR+eEk%a}DOqB3W4b(eD@;9Y|q(6~w zR~mUHvDc%cRMPZt@>x8E;B3gE$3c)1Y>7kcy9| z3_V9#3K)M9hw}m9Aq&!5G$21<)t(~71JzLwsE#FfRxII=48629;BFl!SGZ

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The robot has three actions available to it: it can step ahead one + square, or it can turn left or right by 90 degrees. The robot can only + occupy the white squares of the crossword puzzle; an attempt to move onto + a black square is a "no-op." Attempting to step beyond the boundaries of + the puzzle is also a no-op. Each of the four "walls" of the puzzle has + been painted a different color. The robot looks as far ahead as possible + in the direction it faces: if its view is obstructed by a black square, + then it sees "black;" otherwise, it sees the color of the wall it is + facing. Thus, the robot has five possible sensations. Since this + environment is essentially a maze, it may contain regions which are + difficult to reach or difficult to get out of. " + +-} + +import Data.List (delete) +import Data.Set (Set) +import qualified Data.Set as Set + +-- Four directions and blocked view +data Output = N | W | S | E | X + deriving (Show, Eq) + +data Alphabet = F | R | L + deriving (Show, Eq) + +-- Location and direction (taken from the Output type) +-- X is not a valid direction. Location is Row x Column +type Loc = (Int, Int) +type State = ((Int, Int), Output) + +-- We represent the walls and size of the world. Width x Height +type World = (Int, Int, Set Loc) +type WorldData = [[Bool]] + +t, f :: Bool +t = True +f = False + +-- The upper top-left 8x8 block is from the paper. The rest +-- I made up. However, the number of walls is correct for 12x12. +worldCxC :: WorldData +worldCxC = [ [ f, f, t, t, t, t, t, t, f, f, f, f ] + , [ t, t, t, t, f, t, t, t, f, t, f, f ] + , [ t, t, t, f, t, t, t, t, t, t, t, t ] + , [ t, f, t, t, t, f, t, t, t, f, t, t ] + , [ t, f, t, t, t, t, f, t, t, t, f, t ] + , [ t, t, f, t, t, t, f, t, t, t, f, t ] + , [ t, t, f, t, t, t, t, t, t, t, t, t ] + , [ f, t, t, t, t, t, t, t, t, t, t, t ] + + , [ f, t, t, t, t, t, t, t, t, t, t, t ] + , [ t, f, t, t, f, f, f, f, f, f, f, f ] + , [ t, f, t, t, f, f, f, f, f, f, f, t ] + , [ t, t, t, t, t, t, t, t, t, t, t, t ] + ] + +worldMap :: Int -> Int -> WorldData -> World +worldMap w h d = (w, h, Set.fromList walls) + where + widx = zipWith (\ridx row -> zipWith (\cidx cell -> ((ridx, cidx), cell)) [0..] row) [0..] d + widx2 = concat widx + walls = fmap fst . filter (not . snd) $ widx2 + +-- Subworld from above example +subWorld :: Int -> Int -> World -> World +subWorld w h (_, _, walls) = (w, h, Set.filter (\(r, c) -> r < h && c < w) walls) + +-- Initial states are not really given in the paper. +-- Only the picture (8x8) shows a specific state, we take that. +initialState :: Int -> Int -> State +initialState w h | w <= 6 && h <= 4 = ((1, 0), E) + | otherwise = ((6, 4), E) + +rotR :: Output -> Output +rotR N = E +rotR E = S +rotR S = W +rotR W = N +rotR x = x + +rotL :: Output -> Output +rotL E = N +rotL S = E +rotL W = S +rotL N = W +rotL x = x + +next :: Loc -> Output -> Loc +next (r, c) N = (r-1, c) +next (r, c) E = (r, c+1) +next (r, c) S = (r+1, c) +next (r, c) W = (r, c-1) + +isInBounds :: World -> Loc -> Bool +isInBounds (w, h, _) (r, c) = 0 <= r && r < h && 0 <= c && c <= w + +isValid :: World -> Loc -> Bool +isValid world@(w, h, walls) rc = isInBounds world rc && isValid1 + where + isValid1 = not (rc `Set.member` walls) + +observation :: World -> State -> Output +observation world (rc, dir) = if seesBoundary + then dir + else X + where + locs = takeWhile (isInBounds world) . iterate (`next` dir) $ rc + locs2 = takeWhile (isValid world) locs + seesBoundary = length locs == length locs2 + +step :: World -> State -> State +step world (rc, dir) = if isValid world nrc + then (nrc, dir) + else (rc, dir) + where + nrc = next rc dir + +delta :: World -> State -> Alphabet -> State +delta world st F = step world st +delta world (rc, d) R = (rc, rotR d) +delta world (rc, d) L = (rc, rotL d) + +dotgraph :: Int -> Int -> String +dotgraph w h = unlines ls + where + world = subWorld w h (worldMap 12 12 worldCxC) + allStates = takePutFront (initialState w h) . filter (isValid world . fst) $ [ ((r, c), d) | r <- [0..h-1], c <- [0..w-1], d <- [N, E, S, W]] + allSymbols = [F, R, L] + + stateName ((r, c), d) = "r" ++ show r ++ "c" ++ show c ++ "d" ++ show d + stateDescr st = stateName st ++ " [label=\"" ++ show (observation world st) ++ "\"];" + transDescr st a = stateName st ++ " -> " ++ stateName (delta world st a) ++ " [label=\"" ++ show a ++ "\"];" + + ls = [ "digraph crossword" ++ show w ++ "x" ++ show h ++ " {" ] + ++ [ emptyLine ] + ++ [ indent ++ stateDescr st | st <- allStates ] + ++ [ emptyLine ] + ++ [ indent ++ transDescr st a | st <- allStates, a <- allSymbols ] + ++ [ emptyLine ] + ++ [ "}" ] + + emptyLine = "" + indent = " " + takePutFront x xs = x : delete x xs + diff --git a/moore/src/Gridworld.hs b/moore/src/Gridworld.hs new file mode 100644 index 0000000..a55ce4b --- /dev/null +++ b/moore/src/Gridworld.hs @@ -0,0 +1,171 @@ +module Gridworld where + +{- + +From the Rivest and Schapire paper: + +" The n*n grid World. Consider a robot on an n X n square grid (with + “wraparound,” so that is is topologically a torus). The robot is on one of + the squares and is facing in one of the four possible directions. Each + square (except the one it currently occupies) is either red, green, or + blue. The robot can sense the color of the square it is facing. The + following actions are available to the robot: It can paint the square it + faces red, geen, or blue. The robot can turn left or right by 90 degrees, + or step forward one square in the direction it is facing. Stepping ahead + has the curious side effect of causeing the square it previously occupied + to be painted the color of the square it has just moved to, so moving + around causes the coloring to get scrabled up. " + +-} + +import Data.List (transpose, delete) +import Control.Monad (replicateM) + +-- X is never used, only in intermediate steps +data Output = Red | Green | Blue | X + deriving (Show, Eq) + +data Alphabet = F | R | L | P Output + deriving (Show, Eq) + +alphabet :: [Alphabet] +alphabet = [F, R, L, P Red, P Green, P Blue] + +-- all very inefficient, but who cares +-- The current position is left out, as the color will be swapped +type Row = [Output] +type World = [Row] + +r, g, b :: Output +r = Red +g = Green +b = Blue + +-- From the paper, but with current position top-left, +-- and facing the other direction. (It doesn't matter much.) +-- Note that n=5 gives 282'429'536'481 states +initialWorld5x5 :: World +initialWorld5x5 = [ [ b, b, g, g ] + , [ g, r, g, r, b ] + , [ r, g, b, r, g ] + , [ r, b, b, g, b ] + , [ g, r, r, b, r ] + ] + +-- Subworld from above example +subWorld :: Int -> Int -> World +subWorld w h = take (w-1) crow : fmap (take w) rest + where + sub1 = take h initialWorld5x5 + (crow:rest) = sub1 + +initialWorld2x2 :: World +initialWorld2x2 = [ [ b ] + , [ g, r ] + ] + +initialWorld2x3 :: World +initialWorld2x3 = [ [ b, b ] + , [ g, r, g ] + ] + +stepForward :: World -> World +stepForward world = world2 + where + (crow:frow:rest) = world + (facing:nrow) = frow + urow = facing:crow + world2 = nrow:rest ++ [urow] + +-- Reverse except the first. +reverse1 :: [a] -> [a] +reverse1 [] = [] +reverse1 (x:xs) = x:reverse xs + +-- Rotation is a transpose and reversing the columns. +rotateRight :: World -> World +rotateRight world = world2 + where + (w:orld) = world + worldX = (X:w):orld + worldXT = transpose worldX + worldXTR = fmap reverse1 worldXT + (_:w2):orld2 = worldXTR + world2 = w2:orld2 + +-- The other rotation is 3x the right one. +rotateLeft :: World -> World +rotateLeft = rotateRight . rotateRight . rotateRight + +paint :: World -> Output -> World +paint world n = world2 + where + (crow:frow:rest) = world + (_:nrow) = frow + lrow = n:nrow + world2 = crow:lrow:rest + +delta :: World -> Alphabet -> World +delta world F = stepForward world +delta world R = rotateRight world +delta world L = rotateLeft world +delta world (P c) = paint world c + +observation :: World -> Output +observation world = facing + where + (_:frow:_) = world + (facing:_) = frow + +allRows :: Int -> [Row] +allRows 0 = [] +allRows 1 = [[Red], [Green], [Blue]] +allRows n = do + fa <- [Red, Green, Blue] + ro <- allRows (n-1) + return (fa:ro) + +allWorlds :: Int -> Int -> [World] +allWorlds w h = do + crow <- allRows (w-1) + rest <- replicateM (h-1) (allRows w) + return (crow:rest) + +stateName :: World -> String +stateName w = "s" ++ fmap cname (concat w) + where + cname Red = 'R' + cname Green = 'G' + cname Blue = 'B' + cname X = 'X' + +stateDescr :: World -> String +stateDescr bs = stateName bs ++ " [label=\"" ++ clongname (observation bs) ++ "\"];" + where + clongname Red = "Red" + clongname Green = "Green" + clongname Blue = "Blue" + clongname X = "There is a bug in the generation" + +transDescr :: World -> Alphabet -> String +transDescr bs a = stateName bs ++ " -> " ++ stateName (delta bs a) ++ " [label=\"" ++ show2 a ++ "\"];" + where + show2 (P c) = 'P':show c + show2 x = show x + +dotgraph :: Int -> Int -> String +dotgraph w h = unlines ls + where + ls = [ "digraph grid" ++ show w ++ "x" ++ show h ++ " {" ] + ++ [ emptyLine ] + ++ [ indent ++ stateDescr bs | bs <- all ] + ++ [ emptyLine ] + ++ [ indent ++ transDescr bs a | bs <- all, a <- alphabet ] + ++ [ emptyLine ] + ++ [ "}" ] + all = if w <= 5 && h <= 5 + then takePutFront (subWorld w h) (allWorlds w h) + else allWorlds w h + emptyLine = "" + indent = " " + takePutFront x xs = x : delete x xs diff --git a/moore/src/Lib.hs b/moore/src/Lib.hs new file mode 100644 index 0000000..d36ff27 --- /dev/null +++ b/moore/src/Lib.hs @@ -0,0 +1,6 @@ +module Lib + ( someFunc + ) where + +someFunc :: IO () +someFunc = putStrLn "someFunc" diff --git a/moore/src/Registerworld.hs b/moore/src/Registerworld.hs new file mode 100644 index 0000000..5891c98 --- /dev/null +++ b/moore/src/Registerworld.hs @@ -0,0 +1,79 @@ +module Registerworld where + +import Prelude hiding (flip) + +{- + +From the Rivest and Schapire paper: + +" In this environment, the robot is able to read the leftmost bit of an n-bit + register, such as the 10-bit register depicted in Figure 1. Its actions allow + it to rotate the register left or right (with wraparound) or to flip the bit + it sees. Clearly, this automaton consists of 2“ global states, but its + diversity is only 2n since there is one test for each bit, and one for the + complement note that the register world is a permutation automaton. " + +-} + +-- Not very efficient, but who cares +type Bitstring = String + +data Alphabet = L | R | F + deriving Show + +rotateL :: Bitstring -> Bitstring +rotateL [] = [] +rotateL (x:xs) = xs ++ [x] + +rotateR :: Bitstring -> Bitstring +rotateR = reverse . rotateL . reverse + +flip :: Bitstring -> Bitstring +flip [] = [] +flip (x:xs) = flipBit x : xs + where + flipBit '0' = '1' + flipBit '1' = '0' + flipBit c = c + +delta :: Bitstring -> Alphabet -> Bitstring +delta bs L = rotateL bs +delta bs R = rotateR bs +delta bs F = flip bs + +observation :: Bitstring -> String +observation = pure . head + +allBitstrings :: Int -> [Bitstring] +allBitstrings 0 = [] +allBitstrings 1 = ["0", "1"] +allBitstrings n = do + b <- ['0', '1'] + bs <- allBitstrings (n-1) + return (b:bs) + +allSymbols :: [Alphabet] +allSymbols = [L, R, F] + +stateName :: Bitstring -> String +stateName bs = "state" ++ bs + +stateDescr :: Bitstring -> String +stateDescr bs = stateName bs ++ " [label=\"" ++ observation bs ++ "\"];" + +transDescr :: Bitstring -> Alphabet -> String +transDescr bs a = stateName bs ++ " -> " ++ stateName (delta bs a) ++ " [label=\"" ++ show a ++ "\"];" + +dotgraph :: Int -> String +dotgraph n = unlines ls + where + ls = [ "digraph register" ++ show n ++ " {" ] + ++ [ emptyLine ] + ++ [ indent ++ stateDescr bs | bs <- allbs ] + ++ [ emptyLine ] + ++ [ indent ++ transDescr bs a | bs <- allbs, a <- allSymbols ] + ++ [ emptyLine ] + ++ [ "}" ] + allbs = allBitstrings n + emptyLine = "" + indent = " " diff --git a/moore/stack.yaml b/moore/stack.yaml new file mode 100644 index 0000000..eda25cc --- /dev/null +++ b/moore/stack.yaml @@ -0,0 +1,4 @@ +resolver: lts-16.8 + +packages: +- .

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