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Div ("",[],[]) [Para [Image ("fig:beside_church_haskell",[],[]) [Str "beside",Space,Str "church",Space,Str "haskell"] ("./.design-tools/4664407457353508916.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:random1",[],[]) [Str "Random",Space,Str "Tile",Space,Str "1"] ("./.design-tools/7276432862034232565.png","fig:")]] |
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CodeBlock ("",["haskell","ghci"],[]) "> zip [1,2,3,4] [5,6]\n[(1,5),(2,6)]\n\n\n" |
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CodeBlock ("",["haskell","ghci"],[]) "> fst $ step mempty (Just $ Number 1) (andThen (clue \"problem\" empty) $ points 5) >>= step mempty Nothing\nResults {rewards = fromOccurList [(Points 5,1)], clues = MonoidalMap {getMonoidalMap = fromList [(\"problem\",Completed)]}}\n\n\n" |
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Div ("",[],[]) [Para [Image ("fig:fmap_invert_color",[],[]) [Str "fmap",Space,Str "invert",Space,Str "$",Space,Str "color",Space,Str "1",Space,Str "0",Space,Str "1",Space,Str "1"] ("./.design-tools/1948340590216109650.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:quad_haskell_flipH_haskell_flipV_haskell_flipV_flipH_haskell_",[],[]) [Str "quad",Space,Str "haskell",Space,Str "(flipH",Space,Str "haskell)",Space,Str "(flipV",Space,Str "haskell)",Space,Str "(flipV",Space,Str "(flipH",Space,Str "haskell))"] ("./.design-tools/7680560819438423831.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:ex1",[],[]) [Str "Example",Space,Str "1"] ("./.design-tools/5129996169843890603.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:cw_cw_haskell_",[],[]) [Str "cw",Space,Str "(cw",Space,Str "haskell)"] ("./.design-tools/6186158070626338404.png","fig:")]] |
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(fromList [("andThen (andThen c c2) c3 = andThen c (andThen c2 c3)",15),("andThen (clue k bottom) c = clue k bottom",19),("andThen (gate f c) c2 = gate f (andThen c c2)",14),("andThen (reward r) (clue k empty) = clue k (reward r)",25),("andThen (reward r) (eitherC c empty) = eitherC c (reward r)",26),("andThen (reward r) (reward r2) = reward (r <> r2)",18),("andThen bottom c = bottom",6),("andThen c empty = c",5),("andThen empty c = c",7),("both (both c c2) c3 = both c (both c2 c3)",16),("both c (clue k (reward r)) = andThen (clue k (reward r)) c",29),("both c (clue k empty) = andThen (clue k empty) c",20),("both c (eitherC c2 empty) = andThen (eitherC c2 empty) c",21),("both c (reward r) = andThen (reward r) c",12),("both c bottom = andThen c bottom",8),("both c c2 = both c2 c",2),("both c empty = c",9),("clue k (andThen (reward r) c) = andThen (reward r) (clue k c)",28),("clue k (andThen c (reward r)) = andThen (clue k c) (reward r)",27),("eitherC (eitherC c c2) c3 = eitherC c (eitherC c2 c3)",17),("eitherC c (andThen (reward r) c2) = andThen (reward r) (eitherC c c2)",30),("eitherC c bottom = c",10),("eitherC c c2 = eitherC c2 c",3),("eitherC empty (both c c2) = eitherC c (eitherC c2 empty)",23),("eitherC empty (clue k empty) = clue k empty",24),("eitherC empty (gate f c) = empty",22),("eitherC empty (reward r) = reward r",13),("eitherC empty empty = empty",11),("empty = reward mempty",1),("gate f bottom = bottom",4)],CodeBlock ("",["haskell","ghci"],[]) "> quickSpec sig\n 1. empty = reward mempty\n 2. both c c2 = both c2 c\n 3. eitherC c c2 = eitherC c2 c\n 4. gate f bottom = bottom\n 5. andThen c empty = c\n 6. andThen bottom c = bottom\n 7. andThen empty c = c\n 8. both c bottom = andThen c bottom\n 9. both c empty = c\n 10. eitherC c bottom = c\n 11. eitherC empty empty = empty\n 12. both c (reward r) = andThen (reward r) c\n 13. eitherC empty (reward r) = reward r\n 14. andThen (gate f c) c2 = gate f (andThen c c2)\n 15. andThen (andThen c c2) c3 = andThen c (andThen c2 c3)\n 16. both (both c c2) c3 = both c (both c2 c3)\n 17. eitherC (eitherC c c2) c3 = eitherC c (eitherC c2 c3)\n 18. andThen (reward r) (reward r2) = reward (r <> r2)\n 19. andThen (clue k bottom) c = clue k bottom\n 20. both c (clue k empty) = andThen (clue k empty) c\n 21. both c (eitherC c2 empty) = andThen (eitherC c2 empty) c\n 22. eitherC empty (gate f c) = empty\n 23. eitherC empty (both c c2) = eitherC c (eitherC c2 empty)\n 24. eitherC empty (clue k empty) = clue k empty\n 25. andThen (reward r) (clue k empty) = clue k (reward r)\n 26. andThen (reward r) (eitherC c empty) = eitherC c (reward r)\n 27. clue k (andThen c (reward r)) = andThen (clue k c) (reward r)\n 28. clue k (andThen (reward r) c) = andThen (reward r) (clue k c)\n 29. both c (clue k (reward r)) = andThen (clue k (reward r)) c\n 30. eitherC c (andThen (reward r) c2) = andThen (reward r) (eitherC c c2)\n\n\n\n") |
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Div ("",[],[]) [Para [Image ("fig:color_orange",[],[]) [Str "color",Space,Str "1",Space,Str "0.8",Space,Str "0",Space,Str "1"] ("./.design-tools/2840229242405223662.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:applicative",[],[]) [Str "let",Space,Str "p1",Space,Str "=",Space,Str "pure",Space,Str "const;",Space,Str "p2",Space,Str "=",Space,Str "pure",Space,Str "$",Space,Str "flip",Space,Str "const;",Space,Str "x",Space,Str "=",Space,Str "quad",Space,Str "p1",Space,Str "p2",Space,Str "p2",Space,Str "p1;",Space,Str "xx",Space,Str "=",Space,Str "quad",Space,Str "x",Space,Str "x",Space,Str "x",Space,Str "x",Space,Str "in",Space,Str "behind",Space,Str "(beside",Space,Str "(color",Space,Str "0",Space,Str "0.8",Space,Str "0.9",Space,Str "1)",Space,Str "(color",Space,Str "0.8",Space,Str "0.6",Space,Str "0.2",Space,Str "1))",Space,Str "$",Space,Str "quad",Space,Str "xx",Space,Str "xx",Space,Str "xx",Space,Str "xx",Space,Str "<*>",Space,Str "church",Space,Str "<*>",Space,Str "flipH",Space,Str "church"] ("./.design-tools/8078323629900372753.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:cw_cw_cw_cw_haskell_",[],[]) [Str "cw",Space,Str "(cw",Space,Str "(cw",Space,Str "(cw",Space,Str "haskell)))"] ("./.design-tools/4917384761228999492.png","fig:")]] |
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CodeBlock ("",["haskell","ghci"],[]) "> :t sample\nsample :: Tile a -> Double -> Double -> a\n\n\n" |
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Div ("",[],[]) [Para [Image ("fig:above_exercise",[],[]) [Str "Recreate",Space,Str "this",Space,Str "tile"] ("./.design-tools/1302609340661756360.png","fig:")]] |
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CodeBlock ("",["haskell","ghci"],[]) "> quickSpec $ sig <> withPrintStyle ForQuickCheck <> withMaxTests 1000000 <> withMaxTestSize 20 <> withMaxTermSize 2\nquickspec_laws :: [(String, Property)]\nquickspec_laws =\n [ ( \"empty = mempty\"\n , property $ (empty :: Tile [Word8]) =~= mempty)\n , ( \"pure mempty = mempty\"\n , property $\n (pure mempty :: Tile [Word8]) =~= mempty)\n , ( \"ccw mempty = mempty\"\n , property $\n (ccw mempty :: Tile [Word8]) =~= mempty)\n , ( \"cw mempty = mempty\"\n , property $ (cw mempty :: Tile [Word8]) =~= mempty)\n , ( \"flipH mempty = mempty\"\n , property $\n (flipH mempty :: Tile [Word8]) =~= mempty)\n , ( \"flipV mempty = mempty\"\n , property $\n (flipV mempty :: Tile [Word8]) =~= mempty)\n , ( \"swirl mempty = mempty\"\n , property $\n (swirl mempty :: Tile [Word8]) =~= mempty)\n ]\n\n\n\n" |
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Div ("",[],[]) [Para [Image ("fig:color_blue",[],[]) [Str "color",Space,Str "0",Space,Str "0.67",Space,Str "0.87",Space,Str "0.5"] ("./.design-tools/6413152465481316551.png","fig:")]] |
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CodeBlock ("",["haskell","ghci"],[]) "> [(+1), (*8)] <*> [1, 5]\n[2,6,8,40]\n\n\n> getZipList $ ZipList [(+1), (*8)] <*> ZipList [1, 5]\n[2,40]\n\n\n" |
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CodeBlock ("",["haskell","ghci"],[]) "> fst $ step mempty (Just $ Number 1) (andThen (clue \"problem\" empty) $ points 5) >>= step mempty\nLeaving GHCi.\n\n\n" |
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CodeBlock ("",["haskell","ghci"],[]) "> fst $ stepFix mempty (Just $ Number 1) $ andThen (clue \"no problem\" empty) $ points 5\nResults {rewards = fromOccurList [(Points 5,1)], clues = MonoidalMap {getMonoidalMap = fromList [(\"no problem\",Completed)]}}\n\n\n" |
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CodeBlock ("",["haskell","ghci"],[]) "> quickCheck $ cw @Bool . cw . cw . cw =~= id\n+++ OK, passed 100 tests.\n\n\n" |
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Div ("",[],[]) [Para [Image ("fig:quad",[],[]) [Str "above",Space,Str "(beside",Space,Str "(cw",Space,Str "haskell)",Space,Str "(cw",Space,Str "(cw",Space,Str "church)))",Space,Str "(beside",Space,Str "church",Space,Str "(ccw",Space,Str "haskell))"] ("./.design-tools/5147171614754537735.png","fig:")]] |
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(fromList [("always = notF never",2),("andF (andF x y) z = andF x (andF y z)",13),("andF (exactly n) (exactly n) = exactly n",17),("andF (exactly n) (notF (exactly n)) = never",20),("andF (exactly n) (orF x (exactly n)) = exactly n",24),("andF (notF x) (notF y) = notF (orF x y)",18),("andF x always = x",7),("andF x never = never",8),("andF x y = andF y x",3),("matches (andF x (exactly n)) (Number n2) = matches (andF x (exactly n2)) (Number n)",23),("matches (exactly n) (Number n)",16),("matches (exactly n) (Number n2) = matches (exactly n2) (Number n)",15),("matches (notF x) i = not (matches x i)",12),("matches always i",5),("matches never i = False",6),("matches x i && matches y i = matches (andF x y) i",21),("matches x i || matches y i = matches (orF x y) i",22),("never = notF always",1),("notF (notF x) = x",11),("orF (exactly n) (andF x (exactly n)) = exactly n",25),("orF (exactly n) (exactly n) = exactly n",19),("orF (orF x y) z = orF x (orF y z)",14),("orF x always = always",9),("orF x never = x",10),("orF x y = orF y x",4)],CodeBlock ("",["haskell","ghci"],[]) "> quickSpec sig_filters\n 1. never = notF always\n 2. always = notF never\n 3. andF x y = andF y x\n 4. orF x y = orF y x\n 5. matches always i\n 6. matches never i = False\n 7. andF x always = x\n 8. andF x never = never\n 9. orF x always = always\n 10. orF x never = x\n 11. notF (notF x) = x\n 12. matches (notF x) i = not (matches x i)\n 13. andF (andF x y) z = andF x (andF y z)\n 14. orF (orF x y) z = orF x (orF y z)\n 15. matches (exactly n) (Number n2) = matches (exactly n2) (Number n)\n 16. matches (exactly n) (Number n)\n 17. andF (exactly n) (exactly n) = exactly n\n 18. andF (notF x) (notF y) = notF (orF x y)\n 19. orF (exactly n) (exactly n) = exactly n\n 20. andF (exactly n) (notF (exactly n)) = never\n 21. matches x i && matches y i = matches (andF x y) i\n 22. matches x i || matches y i = matches (orF x y) i\n 23. matches (andF x (exactly n)) (Number n2) = matches (andF x (exactly n2)) (Number n)\n 24. andF (exactly n) (orF x (exactly n)) = exactly n\n 25. orF (exactly n) (andF x (exactly n)) = exactly n\n\n\n\n") |
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Div ("",[],[]) [Para [Image ("fig:haskell",[],[]) [Str "haskell"] ("./.design-tools/685647680873084625.png","fig:")]] |
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CodeBlock ("",["haskell","ghci"],[]) "" |
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Div ("",[],[]) [Para [Image ("fig:ccw_haskell",[],[]) [Str "ccw",Space,Str "haskell"] ("./.design-tools/1814190580623256108.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:random3",[],[]) [Str "Random",Space,Str "Tile",Space,Str "3"] ("./.design-tools/2878904624674742461.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:flipH_haskell",[],[]) [Str "flipH",Space,Str "haskell"] ("./.design-tools/8743731100880087760.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:ex2",[],[]) [Str "Swirling",Space,Str "mathematicians"] ("./.design-tools/5144871656302002968.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:cw_haskell",[],[]) [Str "cw",Space,Str "haskell"] ("./.design-tools/8434207368872788858.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:lt",[],[]) [Str "Example"] ("./.design-tools/6397363250693265987.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:beside_haskell_beside_haskell_haskell_",[],[]) [Str "beside",Space,Str "haskell",Space,Str "(beside",Space,Str "haskell",Space,Str "haskell)"] ("./.design-tools/7369113312797069228.png","fig:")]] |
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(fromList [("above (beside t t2) mempty = quad t t2 mempty mempty",39),("above (cw t) (cw t2) = cw (beside t t2)",37),("above (cw t) mempty = cw (beside t mempty)",23),("above (flipH t) (flipH t2) = flipH (above t t2)",38),("above (flipH t) mempty = flipH (above t mempty)",24),("above (pure x) (pure x) = pure x",36),("above mempty (beside t t2) = quad mempty mempty t t2",35),("above mempty (cw t) = cw (beside mempty t)",21),("above mempty (flipH t) = flipH (above mempty t)",22),("above mempty mempty = mempty",9),("behind t t2 = t2 <> t",8),("beside (above t t2) mempty = quad t mempty t2 mempty",43),("beside (flipV t) (flipV t2) = flipV (beside t t2)",42),("beside (pure x) (pure x) = pure x",41),("beside mempty (above t t2) = quad mempty t mempty t2",40),("beside mempty mempty = mempty",10),("ccw (cw t) = t",12),("ccw (pure x) = pure x",11),("ccw mempty = mempty",3),("ccw t <*> ccw t2 = ccw (t <*> t2)",44),("ccw t <*> mempty = ccw (t <*> mempty)",25),("ccw t <> ccw t2 = ccw (t <> t2)",31),("cw (ccw t) = t",14),("cw (cw t) = ccw (ccw t)",15),("cw (flipH t) = ccw (flipV t)",16),("cw (pure x) = pure x",13),("cw mempty = mempty",4),("empty = mempty",1),("flipH (ccw t) = ccw (flipV t)",18),("flipH (flipH t) = t",19),("flipH (pure x) = pure x",17),("flipH (swirl (ccw t)) = cw (swirl (flipH t))",28),("flipH mempty = mempty",5),("flipH t <*> flipH t2 = flipH (t <*> t2)",45),("flipH t <*> mempty = flipH (t <*> mempty)",26),("flipH t <> flipH t2 = flipH (t <> t2)",32),("flipV mempty = mempty",6),("flipV t <*> flipV t2 = flipV (t <*> t2)",46),("flipV t <> flipV t2 = flipV (t <> t2)",33),("pure mempty = mempty",2),("pure x <> pure y = pure (x <> y)",30),("quad mempty mempty mempty mempty = mempty",29),("swirl (pure x) = pure x",20),("swirl mempty = mempty",7),("swirl t <*> mempty = swirl (t <*> mempty)",27),("swirl t <*> swirl t2 = swirl (t <*> t2)",47),("swirl t <> swirl t2 = swirl (t <> t2)",34)],CodeBlock ("",["haskell","ghci"],[]) "> quickSpec sig\n 1. empty = mempty\n 2. pure mempty = mempty\n 3. ccw mempty = mempty\n 4. cw mempty = mempty\n 5. flipH mempty = mempty\n 6. flipV mempty = mempty\n 7. swirl mempty = mempty\n 8. behind t t2 = t2 <> t\n 9. above mempty mempty = mempty\n 10. beside mempty mempty = mempty\n 11. ccw (pure x) = pure x\n 12. ccw (cw t) = t\n 13. cw (pure x) = pure x\n 14. cw (ccw t) = t\n 15. cw (cw t) = ccw (ccw t)\n 16. cw (flipH t) = ccw (flipV t)\n 17. flipH (pure x) = pure x\n 18. flipH (ccw t) = ccw (flipV t)\n 19. flipH (flipH t) = t\n 20. swirl (pure x) = pure x\n 21. above mempty (cw t) = cw (beside mempty t)\n 22. above mempty (flipH t) = flipH (above mempty t)\n 23. above (cw t) mempty = cw (beside t mempty)\n 24. above (flipH t) mempty = flipH (above t mempty)\n 25. ccw t <*> mempty = ccw (t <*> mempty)\n 26. flipH t <*> mempty = flipH (t <*> mempty)\n 27. swirl t <*> mempty = swirl (t <*> mempty)\n 28. flipH (swirl (ccw t)) = cw (swirl (flipH t))\n 29. quad mempty mempty mempty mempty = mempty\n 30. pure x <> pure y = pure (x <> y)\n 31. ccw t <> ccw t2 = ccw (t <> t2)\n 32. flipH t <> flipH t2 = flipH (t <> t2)\n 33. flipV t <> flipV t2 = flipV (t <> t2)\n 34. swirl t <> swirl t2 = swirl (t <> t2)\n 35. above mempty (beside t t2) = quad mempty mempty t t2\n 36. above (pure x) (pure x) = pure x\n 37. above (cw t) (cw t2) = cw (beside t t2)\n 38. above (flipH t) (flipH t2) = flipH (above t t2)\n 39. above (beside t t2) mempty = quad t t2 mempty mempty\n 40. beside mempty (above t t2) = quad mempty t mempty t2\n 41. beside (pure x) (pure x) = pure x\n 42. beside (flipV t) (flipV t2) = flipV (beside t t2)\n 43. beside (above t t2) mempty = quad t mempty t2 mempty\n 44. ccw t <*> ccw t2 = ccw (t <*> t2)\n 45. flipH t <*> flipH t2 = flipH (t <*> t2)\n 46. flipV t <*> flipV t2 = flipV (t <*> t2)\n 47. swirl t <*> swirl t2 = swirl (t <*> t2)\n\n\n\n") |
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Div ("",[],[]) [Para [Image ("fig:swirl_above_church_haskell_",[],[]) [Str "swirl",Space,Str "(above",Space,Str "church",Space,Str "haskell)"] ("./.design-tools/8680841579127703940.png","fig:")]] |
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CodeBlock ("",["haskell","ghci"],[]) "> take 25 $ getZipList $ pure 0\n[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]\n\n\n" |
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CodeBlock ("",["haskell","ghci"],[]) "> quickCheck $ \\t1 t2 -> cw @[Word8] t1 <> cw t2 =~= cw (t1 <> t2)\n+++ OK, passed 100 tests.\n\n\n" |
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Div ("",[],[]) [Para [Image ("fig:random2",[],[]) [Str "Random",Space,Str "Tile",Space,Str "2"] ("./.design-tools/2005873570172435013.png","fig:")]] |
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CodeBlock ("",["haskell","ghci"],[]) "> runTests\nLeaving GHCi.\n\n\n" |
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Div ("",[],[]) [Para [Image ("fig:beside_beside_haskell_haskell_beside_haskell_haskell_",[],[]) [Str "beside",Space,Str "(beside",Space,Str "haskell",Space,Str "haskell)",Space,Str "(beside",Space,Str "haskell",Space,Str "haskell)"] ("./.design-tools/3147986067790784650.png","fig:")]] |
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Div ("",[],[]) [Para [Str "Leaving",Space,Str "GHCi."]] |
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Div ("",[],[]) [Para [Image ("fig:behind_church_haskell",[],[]) [Str "behind",Space,Str "church",Space,Str "haskell"] ("./.design-tools/8571158314722189358.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:ex3",[],[]) [Str "Sierpinski",Space,Str "Carpet"] ("./.design-tools/5707412034355586966.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:inverted",[],[]) [Str "beside",Space,Str "(pure",Space,Str "id)",Space,Str "(pure",Space,Str "invert)",Space,Str "<*>",Space,Str "church"] ("./.design-tools/4981337960892639274.png","fig:")]] |
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Div ("",[],[]) [Para [Image ("fig:color_blue_alpha",[],[]) [Str "behind",Space,Str "church",Space,Str "(color",Space,Str "0",Space,Str "0.67",Space,Str "0.87",Space,Str "0.5)"] ("./.design-tools/1657305245304044224.png","fig:")]] |
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