diff --git a/semantics-1/semantics-typst.pdf b/semantics-1/semantics-typst.pdf index 5a3e7f0..ba0ba42 100644 --- a/semantics-1/semantics-typst.pdf +++ b/semantics-1/semantics-typst.pdf @@ -4,8 +4,8 @@ 1 0 obj << /Type /Pages - /Count 2 - /Kids [191 0 R 195 0 R] + /Count 3 + /Kids [267 0 R 271 0 R 273 0 R] >> endobj @@ -19,58 +19,52 @@ endobj /Strong /Span /Em /Span >> - /K [5 0 R] + /K [6 0 R] /ParentTree << - /Nums [0 72 0 R 1 3 0 R 2 26 0 R 3 23 0 R 4 4 0 R] + /Nums [0 120 0 R 1 3 0 R 2 53 0 R 3 50 0 R 4 4 0 R 5 5 0 R] >> - /ParentTreeNextKey 5 + /ParentTreeNextKey 6 >> endobj 3 0 obj -[155 0 R 154 0 R 154 0 R 154 0 R 153 0 R 152 0 R 152 0 R 151 0 R 149 0 R 149 0 R 150 0 R 149 0 R 146 0 R 146 0 R 144 0 R 140 0 R 138 0 R 134 0 R 132 0 R 128 0 R 126 0 R 122 0 R 122 0 R 121 0 R 120 0 R 120 0 R 120 0 R 119 0 R 118 0 R 118 0 R 118 0 R 117 0 R 115 0 R 111 0 R 111 0 R 110 0 R 108 0 R 104 0 R 104 0 R 103 0 R 101 0 R 98 0 R 98 0 R 96 0 R 92 0 R 90 0 R 86 0 R 84 0 R 80 0 R 78 0 R 148 0 R 72 0 R 68 0 R 68 0 R 71 0 R 68 0 R 70 0 R 68 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 68 0 R 68 0 R 64 0 R 64 0 R 64 0 R 67 0 R 64 0 R 66 0 R 64 0 R 65 0 R 64 0 R 63 0 R 63 0 R 62 0 R 62 0 R 62 0 R 59 0 R 61 0 R 59 0 R 60 0 R 59 0 R] +[231 0 R 230 0 R 230 0 R 230 0 R 229 0 R 228 0 R 228 0 R 228 0 R 228 0 R 228 0 R 227 0 R 226 0 R 225 0 R 224 0 R 223 0 R 221 0 R 221 0 R 222 0 R 221 0 R 218 0 R 218 0 R 216 0 R 212 0 R 210 0 R 206 0 R 204 0 R 200 0 R 198 0 R 194 0 R 194 0 R 193 0 R 192 0 R 192 0 R 192 0 R 191 0 R 190 0 R 190 0 R 190 0 R 189 0 R 187 0 R 183 0 R 183 0 R 182 0 R 180 0 R 176 0 R 176 0 R 175 0 R 173 0 R 169 0 R 169 0 R 168 0 R 166 0 R 163 0 R 163 0 R 161 0 R 157 0 R 155 0 R 151 0 R 149 0 R 145 0 R 143 0 R 140 0 R 140 0 R 138 0 R 134 0 R 132 0 R 128 0 R 126 0 R 220 0 R 120 0 R 112 0 R 112 0 R 119 0 R 112 0 R 118 0 R 112 0 R 117 0 R 112 0 R 116 0 R 116 0 R 116 0 R 116 0 R 116 0 R 116 0 R 112 0 R 112 0 R 115 0 R 115 0 R 112 0 R 114 0 R 114 0 R 112 0 R 113 0 R 113 0 R 112 0 R 112 0 R 102 0 R 111 0 R 102 0 R 110 0 R 110 0 R 110 0 R 110 0 R 110 0 R 102 0 R 109 0 R 102 0 R 108 0 R 102 0 R 102 0 R 107 0 R 102 0 R 106 0 R 102 0 R 102 0 R 102 0 R 105 0 R 102 0 R 104 0 R 102 0 R 103 0 R 102 0 R 99 0 R 101 0 R 99 0 R 100 0 R 99 0 R] endobj 4 0 obj -[55 0 R 56 0 R 56 0 R 56 0 R 54 0 R 52 0 R 52 0 R 52 0 R 52 0 R 49 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 44 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 39 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 34 0 R 32 0 R 32 0 R 32 0 R 32 0 R 32 0 R 32 0 R 32 0 R 32 0 R 32 0 R 58 0 R 26 0 R 25 0 R 25 0 R 21 0 R 21 0 R 21 0 R 24 0 R 21 0 R 23 0 R 21 0 R 21 0 R 22 0 R 21 0 R 21 0 R 21 0 R 21 0 R 21 0 R 21 0 R 21 0 R 21 0 R 21 0 R 21 0 R 20 0 R 20 0 R 15 0 R 15 0 R 15 0 R 19 0 R 19 0 R 15 0 R 15 0 R 15 0 R 18 0 R 18 0 R 15 0 R 17 0 R 15 0 R 15 0 R 16 0 R 15 0 R 15 0 R 15 0 R 15 0 R 6 0 R 6 0 R 6 0 R 14 0 R 6 0 R 6 0 R 13 0 R 6 0 R 12 0 R 12 0 R 6 0 R 11 0 R 11 0 R 11 0 R 6 0 R 6 0 R 6 0 R 10 0 R 10 0 R 6 0 R 9 0 R 9 0 R 9 0 R 6 0 R 8 0 R 6 0 R 7 0 R 6 0 R] +[98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 98 0 R 97 0 R 96 0 R 96 0 R 95 0 R 95 0 R 95 0 R 95 0 R 95 0 R 95 0 R 95 0 R 91 0 R 94 0 R 91 0 R 93 0 R 91 0 R 92 0 R 91 0 R 87 0 R 88 0 R 88 0 R 88 0 R 88 0 R 88 0 R 88 0 R 88 0 R 86 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 84 0 R 81 0 R 79 0 R 79 0 R 79 0 R 79 0 R 79 0 R 79 0 R 79 0 R 79 0 R 79 0 R 79 0 R 79 0 R 79 0 R 79 0 R 79 0 R 79 0 R 76 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 74 0 R 71 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 69 0 R 66 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 64 0 R 61 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 59 0 R 90 0 R 53 0 R 52 0 R 44 0 R 44 0 R 44 0 R 51 0 R 44 0 R 50 0 R 44 0 R 44 0 R 49 0 R 44 0 R 44 0 R 48 0 R 44 0 R 44 0 R 44 0 R 47 0 R 47 0 R 47 0 R 47 0 R 47 0 R 44 0 R 46 0 R 44 0 R 44 0 R 45 0 R 45 0 R 45 0 R 45 0 R 45 0 R 44 0 R 39 0 R 39 0 R 39 0 R 39 0 R 39 0 R 43 0 R 39 0 R 39 0 R 42 0 R 39 0 R 41 0 R 41 0 R 39 0 R 40 0 R 40 0 R 40 0 R 40 0 R 40 0 R 39 0 R 36 0 R 36 0 R 38 0 R 36 0 R 37 0 R 37 0 R 36 0 R 30 0 R 30 0 R 30 0 R 35 0 R 35 0 R 30 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 34 0 R 30 0 R 33 0 R 33 0 R 30 0 R 32 0 R 32 0 R 32 0 R 32 0 R 32 0 R 32 0 R 30 0 R 30 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 30 0 R 30 0 R 30 0 R 24 0 R 29 0 R 24 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 28 0 R 24 0 R 27 0 R 27 0 R 27 0 R 27 0 R 27 0 R 24 0 R 24 0 R 26 0 R 26 0 R 26 0 R 26 0 R 26 0 R 24 0 R 24 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 25 0 R 24 0 R] endobj 5 0 obj -<< - /Type /StructElem - /S /Document - /P 2 0 R - /K [155 0 R 154 0 R 153 0 R 152 0 R 151 0 R 149 0 R 73 0 R 68 0 R 64 0 R 63 0 R 62 0 R 59 0 R 27 0 R 25 0 R 21 0 R 20 0 R 15 0 R 6 0 R] ->> +[11 0 R 11 0 R 11 0 R 23 0 R 11 0 R 22 0 R 22 0 R 22 0 R 22 0 R 22 0 R 11 0 R 21 0 R 21 0 R 11 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 20 0 R 11 0 R 11 0 R 19 0 R 19 0 R 19 0 R 11 0 R 18 0 R 18 0 R 18 0 R 18 0 R 18 0 R 11 0 R 17 0 R 17 0 R 11 0 R 16 0 R 16 0 R 16 0 R 16 0 R 16 0 R 11 0 R 11 0 R 11 0 R 11 0 R 15 0 R 15 0 R 11 0 R 14 0 R 14 0 R 14 0 R 14 0 R 14 0 R 14 0 R 14 0 R 11 0 R 13 0 R 11 0 R 12 0 R 12 0 R 12 0 R 12 0 R 12 0 R 11 0 R 7 0 R 10 0 R 7 0 R 7 0 R 9 0 R 7 0 R 7 0 R 8 0 R 7 0 R] endobj 6 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [113 114 115 14 0 R 117 118 13 0 R 120 12 0 R 123 11 0 R 127 128 129 10 0 R 132 9 0 R 136 8 0 R 138 7 0 R 140] - /Pg 195 0 R + /S /Document + /P 2 0 R + /K [231 0 R 230 0 R 229 0 R 228 0 R 227 0 R 226 0 R 225 0 R 224 0 R 223 0 R 221 0 R 121 0 R 112 0 R 102 0 R 99 0 R 98 0 R 97 0 R 96 0 R 95 0 R 91 0 R 54 0 R 52 0 R 44 0 R 39 0 R 36 0 R 30 0 R 24 0 R 11 0 R 7 0 R] >> endobj 7 0 obj << /Type /StructElem - /S /Formula + /S /P /P 6 0 R - /K [139] - /Pg 195 0 R + /K [64 10 0 R 66 67 9 0 R 69 70 8 0 R 72] + /Pg 273 0 R >> endobj 8 0 obj << /Type /StructElem - /S /Formula - /P 6 0 R - /K [137] - /Pg 195 0 R + /S /Em + /P 7 0 R + /K [71] + /Pg 273 0 R >> endobj @@ -78,9 +72,9 @@ endobj << /Type /StructElem /S /Formula - /P 6 0 R - /K [133 134 135] - /Pg 195 0 R + /P 7 0 R + /K [68] + /Pg 273 0 R >> endobj @@ -88,19 +82,19 @@ endobj << /Type /StructElem /S /Formula - /P 6 0 R - /K [130 131] - /Pg 195 0 R + /P 7 0 R + /K [65] + /Pg 273 0 R >> endobj 11 0 obj << /Type /StructElem - /S /Formula + /S /P /P 6 0 R - /K [124 125 126] - /Pg 195 0 R + /K [0 1 2 23 0 R 4 22 0 R 10 21 0 R 13 20 0 R 21 22 19 0 R 26 18 0 R 32 17 0 R 35 16 0 R 41 42 43 44 15 0 R 47 14 0 R 55 13 0 R 57 12 0 R 63] + /Pg 273 0 R >> endobj @@ -108,9 +102,9 @@ endobj << /Type /StructElem /S /Formula - /P 6 0 R - /K [121 122] - /Pg 195 0 R + /P 11 0 R + /K [58 59 60 61 62] + /Pg 273 0 R >> endobj @@ -118,9 +112,9 @@ endobj << /Type /StructElem /S /Formula - /P 6 0 R - /K [119] - /Pg 195 0 R + /P 11 0 R + /K [56] + /Pg 273 0 R >> endobj @@ -128,19 +122,19 @@ endobj << /Type /StructElem /S /Formula - /P 6 0 R - /K [116] - /Pg 195 0 R + /P 11 0 R + /K [48 49 50 51 52 53 54] + /Pg 273 0 R >> endobj 15 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [94 95 96 19 0 R 99 100 101 18 0 R 104 17 0 R 106 107 16 0 R 109 110 111 112] - /Pg 195 0 R + /S /Formula + /P 11 0 R + /K [45 46] + /Pg 273 0 R >> endobj @@ -148,9 +142,9 @@ endobj << /Type /StructElem /S /Formula - /P 15 0 R - /K [108] - /Pg 195 0 R + /P 11 0 R + /K [36 37 38 39 40] + /Pg 273 0 R >> endobj @@ -158,9 +152,9 @@ endobj << /Type /StructElem /S /Formula - /P 15 0 R - /K [105] - /Pg 195 0 R + /P 11 0 R + /K [33 34] + /Pg 273 0 R >> endobj @@ -168,9 +162,9 @@ endobj << /Type /StructElem /S /Formula - /P 15 0 R - /K [102 103] - /Pg 195 0 R + /P 11 0 R + /K [27 28 29 30 31] + /Pg 273 0 R >> endobj @@ -178,136 +172,129 @@ endobj << /Type /StructElem /S /Formula - /P 15 0 R - /K [97 98] - /Pg 195 0 R + /P 11 0 R + /K [23 24 25] + /Pg 273 0 R >> endobj 20 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [92 93] - /Pg 195 0 R + /S /Formula + /P 11 0 R + /K [14 15 16 17 18 19 20] + /Pg 273 0 R >> endobj 21 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [73 74 75 24 0 R 77 23 0 R 79 80 22 0 R 82 83 84 85 86 87 88 89 90 91] - /Pg 195 0 R + /S /Formula + /P 11 0 R + /K [11 12] + /Pg 273 0 R >> endobj 22 0 obj << /Type /StructElem - /S /Em - /P 21 0 R - /K [81] - /Pg 195 0 R + /S /Formula + /P 11 0 R + /K [5 6 7 8 9] + /Pg 273 0 R >> endobj 23 0 obj << /Type /StructElem - /S /Link - /P 21 0 R - /K [78 << - /Type /OBJR - /Pg 195 0 R - /Obj 194 0 R - >>] - /Pg 195 0 R + /S /Formula + /P 11 0 R + /K [3] + /Pg 273 0 R >> endobj 24 0 obj << /Type /StructElem - /S /Formula - /P 21 0 R - /K [76] - /Pg 195 0 R + /S /P + /P 6 0 R + /K [271 29 0 R 273 28 0 R 281 27 0 R 287 288 26 0 R 294 295 25 0 R 309] + /Pg 271 0 R >> endobj 25 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [26 0 R 71 72] - /Pg 195 0 R + /S /Formula + /P 24 0 R + /K [296 297 298 299 300 301 302 303 304 305 306 307 308] + /Pg 271 0 R >> endobj 26 0 obj << /Type /StructElem - /S /Link - /P 25 0 R - /K [70 << - /Type /OBJR - /Pg 195 0 R - /Obj 193 0 R - >>] - /Pg 195 0 R + /S /Formula + /P 24 0 R + /K [289 290 291 292 293] + /Pg 271 0 R >> endobj 27 0 obj << /Type /StructElem - /S /Div - /P 5 0 R - /K [57 0 R 28 0 R] + /S /Formula + /P 24 0 R + /K [282 283 284 285 286] + /Pg 271 0 R >> endobj 28 0 obj << /Type /StructElem - /S /Div - /P 27 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [29 0 R] + /S /Formula + /P 24 0 R + /K [274 275 276 277 278 279 280] + /Pg 271 0 R >> endobj 29 0 obj << /Type /StructElem - /S /P - /P 28 0 R - /K [55 0 R 50 0 R 45 0 R 40 0 R 35 0 R 30 0 R] + /S /Em + /P 24 0 R + /K [272] + /Pg 271 0 R >> endobj 30 0 obj << /Type /StructElem - /S /Div - /P 29 0 R - /K [33 0 R 31 0 R] + /S /P + /P 6 0 R + /K [239 240 241 35 0 R 244 34 0 R 251 33 0 R 254 32 0 R 261 262 31 0 R 268 269 270] + /Pg 271 0 R >> endobj 31 0 obj << /Type /StructElem - /S /Div + /S /Formula /P 30 0 R - /K [32 0 R] + /K [263 264 265 266 267] + /Pg 271 0 R >> endobj @@ -315,54 +302,49 @@ endobj << /Type /StructElem /S /Formula - /P 31 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [60 61 62 63 64 65 66 67 68] - /Pg 195 0 R + /P 30 0 R + /K [255 256 257 258 259 260] + /Pg 271 0 R >> endobj 33 0 obj << /Type /StructElem - /S /Div + /S /Formula /P 30 0 R - /K [34 0 R] + /K [252 253] + /Pg 271 0 R >> endobj 34 0 obj << /Type /StructElem - /S /Span - /P 33 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [59] - /Pg 195 0 R + /S /Formula + /P 30 0 R + /K [245 246 247 248 249 250] + /Pg 271 0 R >> endobj 35 0 obj << /Type /StructElem - /S /Div - /P 29 0 R - /K [38 0 R 36 0 R] + /S /Formula + /P 30 0 R + /K [242 243] + /Pg 271 0 R >> endobj 36 0 obj << /Type /StructElem - /S /Div - /P 35 0 R - /K [37 0 R] + /S /P + /P 6 0 R + /K [232 233 38 0 R 235 37 0 R 238] + /Pg 271 0 R >> endobj @@ -371,53 +353,48 @@ endobj /Type /StructElem /S /Formula /P 36 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [50 51 52 53 54 55 56 57 58] - /Pg 195 0 R + /K [236 237] + /Pg 271 0 R >> endobj 38 0 obj << /Type /StructElem - /S /Div - /P 35 0 R - /K [39 0 R] + /S /Em + /P 36 0 R + /K [234] + /Pg 271 0 R >> endobj 39 0 obj << /Type /StructElem - /S /Span - /P 38 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [49] - /Pg 195 0 R + /S /P + /P 6 0 R + /K [213 214 215 216 217 43 0 R 219 220 42 0 R 222 41 0 R 225 40 0 R 231] + /Pg 271 0 R >> endobj 40 0 obj << /Type /StructElem - /S /Div - /P 29 0 R - /K [43 0 R 41 0 R] + /S /Formula + /P 39 0 R + /K [226 227 228 229 230] + /Pg 271 0 R >> endobj 41 0 obj << /Type /StructElem - /S /Div - /P 40 0 R - /K [42 0 R] + /S /Formula + /P 39 0 R + /K [223 224] + /Pg 271 0 R >> endobj @@ -425,54 +402,49 @@ endobj << /Type /StructElem /S /Formula - /P 41 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48] - /Pg 195 0 R + /P 39 0 R + /K [221] + /Pg 271 0 R >> endobj 43 0 obj << /Type /StructElem - /S /Div - /P 40 0 R - /K [44 0 R] + /S /Formula + /P 39 0 R + /K [218] + /Pg 271 0 R >> endobj 44 0 obj << /Type /StructElem - /S /Span - /P 43 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [29] - /Pg 195 0 R + /S /P + /P 6 0 R + /K [183 184 185 51 0 R 187 50 0 R 189 190 49 0 R 192 193 48 0 R 195 196 197 47 0 R 203 46 0 R 205 206 45 0 R 212] + /Pg 271 0 R >> endobj 45 0 obj << /Type /StructElem - /S /Div - /P 29 0 R - /K [48 0 R 46 0 R] + /S /Formula + /P 44 0 R + /K [207 208 209 210 211] + /Pg 271 0 R >> endobj 46 0 obj << /Type /StructElem - /S /Div - /P 45 0 R - /K [47 0 R] + /S /Formula + /P 44 0 R + /K [204] + /Pg 271 0 R >> endobj @@ -480,238 +452,236 @@ endobj << /Type /StructElem /S /Formula - /P 46 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28] - /Pg 195 0 R + /P 44 0 R + /K [198 199 200 201 202] + /Pg 271 0 R >> endobj 48 0 obj << /Type /StructElem - /S /Div - /P 45 0 R - /K [49 0 R] + /S /Formula + /P 44 0 R + /K [194] + /Pg 271 0 R >> endobj 49 0 obj << /Type /StructElem - /S /Span - /P 48 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [9] - /Pg 195 0 R + /S /Em + /P 44 0 R + /K [191] + /Pg 271 0 R >> endobj 50 0 obj << /Type /StructElem - /S /Div - /P 29 0 R - /K [53 0 R 51 0 R] + /S /Link + /P 44 0 R + /K [188 << + /Type /OBJR + /Pg 271 0 R + /Obj 270 0 R + >>] + /Pg 271 0 R >> endobj 51 0 obj << /Type /StructElem - /S /Div - /P 50 0 R - /K [52 0 R] + /S /Formula + /P 44 0 R + /K [186] + /Pg 271 0 R >> endobj 52 0 obj << /Type /StructElem - /S /Formula - /P 51 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [5 6 7 8] - /Pg 195 0 R + /S /P + /P 6 0 R + /K [53 0 R 182] + /Pg 271 0 R >> endobj 53 0 obj << /Type /StructElem - /S /Div - /P 50 0 R - /K [54 0 R] + /S /Link + /P 52 0 R + /K [181 << + /Type /OBJR + /Pg 271 0 R + /Obj 269 0 R + >>] + /Pg 271 0 R >> endobj 54 0 obj << /Type /StructElem - /S /Span - /P 53 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [4] - /Pg 195 0 R + /S /Div + /P 6 0 R + /K [89 0 R 55 0 R] >> endobj 55 0 obj << /Type /StructElem - /S /P - /P 29 0 R - /K [0 56 0 R] - /Pg 195 0 R + /S /Div + /P 54 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [56 0 R] >> endobj 56 0 obj << /Type /StructElem - /S /Formula + /S /P /P 55 0 R - /K [1 2 3] - /Pg 195 0 R + /K [87 0 R 82 0 R 77 0 R 72 0 R 67 0 R 62 0 R 57 0 R] >> endobj 57 0 obj << /Type /StructElem - /S /Caption - /P 27 0 R - /K [58 0 R] + /S /Div + /P 56 0 R + /K [60 0 R 58 0 R] >> endobj 58 0 obj << /Type /StructElem - /S /Span + /S /Div /P 57 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [69] - /Pg 195 0 R + /K [59 0 R] >> endobj 59 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [80 61 0 R 82 60 0 R 84] - /Pg 191 0 R + /S /Formula + /P 58 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179] + /Pg 271 0 R >> endobj 60 0 obj << /Type /StructElem - /S /Formula - /P 59 0 R - /K [83] - /Pg 191 0 R + /S /Div + /P 57 0 R + /K [61 0 R] >> endobj 61 0 obj << /Type /StructElem - /S /Formula - /P 59 0 R - /K [81] - /Pg 191 0 R + /S /Span + /P 60 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [162] + /Pg 271 0 R >> endobj 62 0 obj << /Type /StructElem - /S /Formula - /P 5 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [77 78 79] - /Pg 191 0 R + /S /Div + /P 56 0 R + /K [65 0 R 63 0 R] >> endobj 63 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [75 76] - /Pg 191 0 R + /S /Div + /P 62 0 R + /K [64 0 R] >> endobj 64 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [66 67 68 67 0 R 70 66 0 R 72 65 0 R 74] - /Pg 191 0 R + /S /Formula + /P 63 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161] + /Pg 271 0 R >> endobj 65 0 obj << /Type /StructElem - /S /Formula - /P 64 0 R - /K [73] - /Pg 191 0 R + /S /Div + /P 62 0 R + /K [66 0 R] >> endobj 66 0 obj << /Type /StructElem - /S /Formula - /P 64 0 R - /K [71] - /Pg 191 0 R + /S /Span + /P 65 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [144] + /Pg 271 0 R >> endobj 67 0 obj << /Type /StructElem - /S /Formula - /P 64 0 R - /K [69] - /Pg 191 0 R + /S /Div + /P 56 0 R + /K [70 0 R 68 0 R] >> endobj 68 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [72 0 R 52 53 71 0 R 55 70 0 R 57 69 0 R 64 65] - /Pg 191 0 R + /S /Div + /P 67 0 R + /K [69 0 R] >> endobj @@ -720,42 +690,44 @@ endobj /Type /StructElem /S /Formula /P 68 0 R - /K [58 59 60 61 62 63] - /Pg 191 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143] + /Pg 271 0 R >> endobj 70 0 obj << /Type /StructElem - /S /Formula - /P 68 0 R - /K [56] - /Pg 191 0 R + /S /Div + /P 67 0 R + /K [71 0 R] >> endobj 71 0 obj << /Type /StructElem - /S /Formula - /P 68 0 R - /K [54] - /Pg 191 0 R + /S /Span + /P 70 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [106] + /Pg 271 0 R >> endobj 72 0 obj << /Type /StructElem - /S /Link - /P 68 0 R - /K [51 << - /Type /OBJR - /Pg 191 0 R - /Obj 190 0 R - >>] - /Pg 191 0 R + /S /Div + /P 56 0 R + /K [75 0 R 73 0 R] >> endobj @@ -763,39 +735,45 @@ endobj << /Type /StructElem /S /Div - /P 5 0 R - /K [147 0 R 74 0 R] + /P 72 0 R + /K [74 0 R] >> endobj 74 0 obj << /Type /StructElem - /S /Div + /S /Formula /P 73 0 R /A [<< /O /Layout /Placement /Block >>] - /K [75 0 R] + /K [69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105] + /Pg 271 0 R >> endobj 75 0 obj << /Type /StructElem - /S /P - /P 74 0 R - /K [142 0 R 136 0 R 130 0 R 124 0 R 113 0 R 106 0 R 99 0 R 94 0 R 88 0 R 82 0 R 76 0 R] + /S /Div + /P 72 0 R + /K [76 0 R] >> endobj 76 0 obj << /Type /StructElem - /S /Div + /S /Span /P 75 0 R - /K [81 0 R 79 0 R 77 0 R] + /A [<< + /O /Layout + /Placement /Block + >>] + /K [68] + /Pg 271 0 R >> endobj @@ -803,54 +781,54 @@ endobj << /Type /StructElem /S /Div - /P 76 0 R - /K [78 0 R] + /P 56 0 R + /K [80 0 R 78 0 R] >> endobj 78 0 obj << /Type /StructElem - /S /Span + /S /Div /P 77 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [49] - /Pg 191 0 R + /K [79 0 R] >> endobj 79 0 obj << /Type /StructElem - /S /Div - /P 76 0 R - /K [80 0 R] + /S /Formula + /P 78 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [53 54 55 56 57 58 59 60 61 62 63 64 65 66 67] + /Pg 271 0 R >> endobj 80 0 obj << /Type /StructElem - /S /Formula - /P 79 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [48] - /Pg 191 0 R + /S /Div + /P 77 0 R + /K [81 0 R] >> endobj 81 0 obj << /Type /StructElem - /S /Div - /P 76 0 R - /K [] + /S /Span + /P 80 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [52] + /Pg 271 0 R >> endobj @@ -858,8 +836,8 @@ endobj << /Type /StructElem /S /Div - /P 75 0 R - /K [87 0 R 85 0 R 83 0 R] + /P 56 0 R + /K [85 0 R 83 0 R] >> endobj @@ -875,14 +853,14 @@ endobj 84 0 obj << /Type /StructElem - /S /Span + /S /Formula /P 83 0 R /A [<< /O /Layout /Placement /Block >>] - /K [47] - /Pg 191 0 R + /K [44 45 46 47 48 49 50 51] + /Pg 271 0 R >> endobj @@ -904,34 +882,36 @@ endobj /O /Layout /Placement /Block >>] - /K [46] - /Pg 191 0 R + /K [43] + /Pg 271 0 R >> endobj 87 0 obj << /Type /StructElem - /S /Div - /P 82 0 R - /K [] + /S /P + /P 56 0 R + /K [35 88 0 R] + /Pg 271 0 R >> endobj 88 0 obj << /Type /StructElem - /S /Div - /P 75 0 R - /K [93 0 R 91 0 R 89 0 R] + /S /Formula + /P 87 0 R + /K [36 37 38 39 40 41 42] + /Pg 271 0 R >> endobj 89 0 obj << /Type /StructElem - /S /Div - /P 88 0 R + /S /Caption + /P 54 0 R /K [90 0 R] >> endobj @@ -945,81 +925,82 @@ endobj /O /Layout /Placement /Block >>] - /K [45] - /Pg 191 0 R + /K [180] + /Pg 271 0 R >> endobj 91 0 obj << /Type /StructElem - /S /Div - /P 88 0 R - /K [92 0 R] + /S /P + /P 6 0 R + /K [28 94 0 R 30 93 0 R 32 92 0 R 34] + /Pg 271 0 R >> endobj 92 0 obj << /Type /StructElem - /S /Span + /S /Formula /P 91 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [44] - /Pg 191 0 R + /K [33] + /Pg 271 0 R >> endobj 93 0 obj << /Type /StructElem - /S /Div - /P 88 0 R - /K [] + /S /Formula + /P 91 0 R + /K [31] + /Pg 271 0 R >> endobj 94 0 obj << /Type /StructElem - /S /Div - /P 75 0 R - /K [97 0 R 95 0 R] + /S /Formula + /P 91 0 R + /K [29] + /Pg 271 0 R >> endobj 95 0 obj << /Type /StructElem - /S /Div - /P 94 0 R - /K [96 0 R] + /S /Formula + /P 6 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [21 22 23 24 25 26 27] + /Pg 271 0 R >> endobj 96 0 obj << /Type /StructElem - /S /Em - /P 95 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [43] - /Pg 191 0 R + /S /P + /P 6 0 R + /K [19 20] + /Pg 271 0 R >> endobj 97 0 obj << /Type /StructElem - /S /Div - /P 94 0 R - /K [98 0 R] + /S /P + /P 6 0 R + /K [18] + /Pg 271 0 R >> endobj @@ -1027,54 +1008,53 @@ endobj << /Type /StructElem /S /Formula - /P 97 0 R + /P 6 0 R /A [<< /O /Layout /Placement /Block >>] - /K [41 42] - /Pg 191 0 R + /K [0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17] + /Pg 271 0 R >> endobj 99 0 obj << /Type /StructElem - /S /Div - /P 75 0 R - /K [105 0 R 102 0 R 100 0 R] + /S /P + /P 6 0 R + /K [122 101 0 R 124 100 0 R 126] + /Pg 267 0 R >> endobj 100 0 obj << /Type /StructElem - /S /Div + /S /Formula /P 99 0 R - /K [101 0 R] + /K [125] + /Pg 267 0 R >> endobj 101 0 obj << /Type /StructElem - /S /Span - /P 100 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [40] - /Pg 191 0 R + /S /Em + /P 99 0 R + /K [123] + /Pg 267 0 R >> endobj 102 0 obj << /Type /StructElem - /S /Div - /P 99 0 R - /K [104 0 R 103 0 R] + /S /P + /P 6 0 R + /K [96 111 0 R 98 110 0 R 104 109 0 R 106 108 0 R 108 109 107 0 R 111 106 0 R 113 114 115 105 0 R 117 104 0 R 119 103 0 R 121] + /Pg 267 0 R >> endobj @@ -1083,76 +1063,68 @@ endobj /Type /StructElem /S /Formula /P 102 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [39] - /Pg 191 0 R + /K [120] + /Pg 267 0 R >> endobj 104 0 obj << /Type /StructElem - /S /Span + /S /Formula /P 102 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [37 38] - /Pg 191 0 R + /K [118] + /Pg 267 0 R >> endobj 105 0 obj << /Type /StructElem - /S /Div - /P 99 0 R - /K [] + /S /Formula + /P 102 0 R + /K [116] + /Pg 267 0 R >> endobj 106 0 obj << /Type /StructElem - /S /Div - /P 75 0 R - /K [112 0 R 109 0 R 107 0 R] + /S /Formula + /P 102 0 R + /K [112] + /Pg 267 0 R >> endobj 107 0 obj << /Type /StructElem - /S /Div - /P 106 0 R - /K [108 0 R] + /S /Formula + /P 102 0 R + /K [110] + /Pg 267 0 R >> endobj 108 0 obj << /Type /StructElem - /S /Span - /P 107 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [36] - /Pg 191 0 R + /S /Formula + /P 102 0 R + /K [107] + /Pg 267 0 R >> endobj 109 0 obj << /Type /StructElem - /S /Div - /P 106 0 R - /K [111 0 R 110 0 R] + /S /Formula + /P 102 0 R + /K [105] + /Pg 267 0 R >> endobj @@ -1160,77 +1132,69 @@ endobj << /Type /StructElem /S /Formula - /P 109 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [35] - /Pg 191 0 R + /P 102 0 R + /K [99 100 101 102 103] + /Pg 267 0 R >> endobj 111 0 obj << /Type /StructElem - /S /Span - /P 109 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [33 34] - /Pg 191 0 R + /S /Em + /P 102 0 R + /K [97] + /Pg 267 0 R >> endobj 112 0 obj << /Type /StructElem - /S /Div - /P 106 0 R - /K [] + /S /P + /P 6 0 R + /K [120 0 R 70 71 119 0 R 73 118 0 R 75 117 0 R 77 116 0 R 84 85 115 0 R 88 114 0 R 91 113 0 R 94 95] + /Pg 267 0 R >> endobj 113 0 obj << /Type /StructElem - /S /Div - /P 75 0 R - /K [123 0 R 116 0 R 114 0 R] + /S /Formula + /P 112 0 R + /K [92 93] + /Pg 267 0 R >> endobj 114 0 obj << /Type /StructElem - /S /Div - /P 113 0 R - /K [115 0 R] + /S /Formula + /P 112 0 R + /K [89 90] + /Pg 267 0 R >> endobj 115 0 obj << /Type /StructElem - /S /Span - /P 114 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [32] - /Pg 191 0 R + /S /Formula + /P 112 0 R + /K [86 87] + /Pg 267 0 R >> endobj 116 0 obj << /Type /StructElem - /S /Div - /P 113 0 R - /K [122 0 R 121 0 R 120 0 R 119 0 R 118 0 R 117 0 R] + /S /Formula + /P 112 0 R + /K [78 79 80 81 82 83] + /Pg 267 0 R >> endobj @@ -1238,27 +1202,19 @@ endobj << /Type /StructElem /S /Formula - /P 116 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [31] - /Pg 191 0 R + /P 112 0 R + /K [76] + /Pg 267 0 R >> endobj 118 0 obj << /Type /StructElem - /S /Span - /P 116 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [28 29 30] - /Pg 191 0 R + /S /Formula + /P 112 0 R + /K [74] + /Pg 267 0 R >> endobj @@ -1266,64 +1222,54 @@ endobj << /Type /StructElem /S /Formula - /P 116 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [27] - /Pg 191 0 R + /P 112 0 R + /K [72] + /Pg 267 0 R >> endobj 120 0 obj << /Type /StructElem - /S /Span - /P 116 0 R - /A [<< - /O /Layout - /Placement /Block + /S /Link + /P 112 0 R + /K [69 << + /Type /OBJR + /Pg 267 0 R + /Obj 266 0 R >>] - /K [24 25 26] - /Pg 191 0 R + /Pg 267 0 R >> endobj 121 0 obj << /Type /StructElem - /S /Formula - /P 116 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [23] - /Pg 191 0 R + /S /Div + /P 6 0 R + /K [219 0 R 122 0 R] >> endobj 122 0 obj << /Type /StructElem - /S /Span - /P 116 0 R + /S /Div + /P 121 0 R /A [<< /O /Layout /Placement /Block >>] - /K [21 22] - /Pg 191 0 R + /K [123 0 R] >> endobj 123 0 obj << /Type /StructElem - /S /Div - /P 113 0 R - /K [] + /S /P + /P 122 0 R + /K [214 0 R 208 0 R 202 0 R 196 0 R 185 0 R 178 0 R 171 0 R 164 0 R 159 0 R 153 0 R 147 0 R 141 0 R 136 0 R 130 0 R 124 0 R] >> endobj @@ -1331,7 +1277,7 @@ endobj << /Type /StructElem /S /Div - /P 75 0 R + /P 123 0 R /K [129 0 R 127 0 R 125 0 R] >> endobj @@ -1354,8 +1300,8 @@ endobj /O /Layout /Placement /Block >>] - /K [20] - /Pg 191 0 R + /K [67] + /Pg 267 0 R >> endobj @@ -1377,8 +1323,8 @@ endobj /O /Layout /Placement /Block >>] - /K [19] - /Pg 191 0 R + /K [66] + /Pg 267 0 R >> endobj @@ -1395,7 +1341,7 @@ endobj << /Type /StructElem /S /Div - /P 75 0 R + /P 123 0 R /K [135 0 R 133 0 R 131 0 R] >> endobj @@ -1418,8 +1364,8 @@ endobj /O /Layout /Placement /Block >>] - /K [18] - /Pg 191 0 R + /K [65] + /Pg 267 0 R >> endobj @@ -1435,14 +1381,14 @@ endobj 134 0 obj << /Type /StructElem - /S /Span + /S /Formula /P 133 0 R /A [<< /O /Layout /Placement /Block >>] - /K [17] - /Pg 191 0 R + /K [64] + /Pg 267 0 R >> endobj @@ -1459,8 +1405,8 @@ endobj << /Type /StructElem /S /Div - /P 75 0 R - /K [141 0 R 139 0 R 137 0 R] + /P 123 0 R + /K [139 0 R 137 0 R] >> endobj @@ -1476,14 +1422,14 @@ endobj 138 0 obj << /Type /StructElem - /S /Span + /S /Em /P 137 0 R /A [<< /O /Layout /Placement /Block >>] - /K [16] - /Pg 191 0 R + /K [63] + /Pg 267 0 R >> endobj @@ -1499,14 +1445,14 @@ endobj 140 0 obj << /Type /StructElem - /S /Span + /S /Formula /P 139 0 R /A [<< /O /Layout /Placement /Block >>] - /K [15] - /Pg 191 0 R + /K [61 62] + /Pg 267 0 R >> endobj @@ -1514,8 +1460,8 @@ endobj << /Type /StructElem /S /Div - /P 136 0 R - /K [] + /P 123 0 R + /K [146 0 R 144 0 R 142 0 R] >> endobj @@ -1523,170 +1469,1024 @@ endobj << /Type /StructElem /S /Div - /P 75 0 R - /K [145 0 R 143 0 R] + /P 141 0 R + /K [143 0 R] >> endobj 143 0 obj << /Type /StructElem - /S /Div + /S /Span /P 142 0 R - /K [144 0 R] + /A [<< + /O /Layout + /Placement /Block + >>] + /K [60] + /Pg 267 0 R >> endobj 144 0 obj << /Type /StructElem - /S /Em - /P 143 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [14] - /Pg 191 0 R + /S /Div + /P 141 0 R + /K [145 0 R] >> endobj 145 0 obj << /Type /StructElem - /S /Div - /P 142 0 R - /K [146 0 R] + /S /Formula + /P 144 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [59] + /Pg 267 0 R >> endobj 146 0 obj << /Type /StructElem - /S /Formula - /P 145 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [12 13] - /Pg 191 0 R + /S /Div + /P 141 0 R + /K [] >> endobj 147 0 obj << /Type /StructElem - /S /Caption - /P 73 0 R - /K [148 0 R] + /S /Div + /P 123 0 R + /K [152 0 R 150 0 R 148 0 R] >> endobj 148 0 obj << /Type /StructElem - /S /Span + /S /Div /P 147 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [50] - /Pg 191 0 R + /K [149 0 R] >> endobj 149 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [8 9 150 0 R 11] - /Pg 191 0 R + /S /Span + /P 148 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [58] + /Pg 267 0 R >> endobj 150 0 obj << /Type /StructElem - /S /Em - /P 149 0 R - /K [10] - /Pg 191 0 R + /S /Div + /P 147 0 R + /K [151 0 R] >> endobj 151 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [7] - /Pg 191 0 R + /S /Span + /P 150 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [57] + /Pg 267 0 R >> endobj 152 0 obj << /Type /StructElem - /S /Span - /P 5 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [5 6] - /Pg 191 0 R + /S /Div + /P 147 0 R + /K [] >> endobj 153 0 obj << /Type /StructElem - /S /Strong - /P 5 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [4] - /Pg 191 0 R + /S /Div + /P 123 0 R + /K [158 0 R 156 0 R 154 0 R] >> endobj 154 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [1 2 3] - /Pg 191 0 R + /S /Div + /P 153 0 R + /K [155 0 R] >> endobj 155 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [0] - /Pg 191 0 R + /S /Span + /P 154 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [56] + /Pg 267 0 R >> endobj 156 0 obj << - /Type /Font - /Subtype /Type0 - /BaseFont /QHEWSS+LibertinusSerif-Bold-Identity-H - /Encoding /Identity-H - /DescendantFonts [157 0 R] - /ToUnicode 160 0 R + /Type /StructElem + /S /Div + /P 153 0 R + /K [157 0 R] >> endobj 157 0 obj +<< + /Type /StructElem + /S /Span + /P 156 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [55] + /Pg 267 0 R +>> +endobj + +158 0 obj +<< + /Type /StructElem + /S /Div + /P 153 0 R + /K [] +>> +endobj + +159 0 obj +<< + /Type /StructElem + /S /Div + /P 123 0 R + /K [162 0 R 160 0 R] +>> +endobj + +160 0 obj +<< + /Type /StructElem + /S /Div + /P 159 0 R + /K [161 0 R] +>> +endobj + +161 0 obj +<< + /Type /StructElem + /S /Em + /P 160 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [54] + /Pg 267 0 R +>> +endobj + +162 0 obj +<< + /Type /StructElem + /S /Div + /P 159 0 R + /K [163 0 R] +>> +endobj + +163 0 obj +<< + /Type /StructElem + /S /Formula + /P 162 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [52 53] + /Pg 267 0 R +>> +endobj + +164 0 obj +<< + /Type /StructElem + /S /Div + /P 123 0 R + /K [170 0 R 167 0 R 165 0 R] +>> +endobj + +165 0 obj +<< + /Type /StructElem + /S /Div + /P 164 0 R + /K [166 0 R] +>> +endobj + +166 0 obj +<< + /Type /StructElem + /S /Span + /P 165 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [51] + /Pg 267 0 R +>> +endobj + +167 0 obj +<< + /Type /StructElem + /S /Div + /P 164 0 R + /K [169 0 R 168 0 R] +>> +endobj + +168 0 obj +<< + /Type /StructElem + /S /Formula + /P 167 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [50] + /Pg 267 0 R +>> +endobj + +169 0 obj +<< + /Type /StructElem + /S /Span + /P 167 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [48 49] + /Pg 267 0 R +>> +endobj + +170 0 obj +<< + /Type /StructElem + /S /Div + /P 164 0 R + /K [] +>> +endobj + +171 0 obj +<< + /Type /StructElem + /S /Div + /P 123 0 R + /K [177 0 R 174 0 R 172 0 R] +>> +endobj + +172 0 obj +<< + /Type /StructElem + /S /Div + /P 171 0 R + /K [173 0 R] +>> +endobj + +173 0 obj +<< + /Type /StructElem + /S /Span + /P 172 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [47] + /Pg 267 0 R +>> +endobj + +174 0 obj +<< + /Type /StructElem + /S /Div + /P 171 0 R + /K [176 0 R 175 0 R] +>> +endobj + +175 0 obj +<< + /Type /StructElem + /S /Formula + /P 174 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [46] + /Pg 267 0 R +>> +endobj + +176 0 obj +<< + /Type /StructElem + /S /Span + /P 174 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [44 45] + /Pg 267 0 R +>> +endobj + +177 0 obj +<< + /Type /StructElem + /S /Div + /P 171 0 R + /K [] +>> +endobj + +178 0 obj +<< + /Type /StructElem + /S /Div + /P 123 0 R + /K [184 0 R 181 0 R 179 0 R] +>> +endobj + +179 0 obj +<< + /Type /StructElem + /S /Div + /P 178 0 R + /K [180 0 R] +>> +endobj + +180 0 obj +<< + /Type /StructElem + /S /Span + /P 179 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [43] + /Pg 267 0 R +>> +endobj + +181 0 obj +<< + /Type /StructElem + /S /Div + /P 178 0 R + /K [183 0 R 182 0 R] +>> +endobj + +182 0 obj +<< + /Type /StructElem + /S /Formula + /P 181 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [42] + /Pg 267 0 R +>> +endobj + +183 0 obj +<< + /Type /StructElem + /S /Span + /P 181 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [40 41] + /Pg 267 0 R +>> +endobj + +184 0 obj +<< + /Type /StructElem + /S /Div + /P 178 0 R + /K [] +>> +endobj + +185 0 obj +<< + /Type /StructElem + /S /Div + /P 123 0 R + /K [195 0 R 188 0 R 186 0 R] +>> +endobj + +186 0 obj +<< + /Type /StructElem + /S /Div + /P 185 0 R + /K [187 0 R] +>> +endobj + +187 0 obj +<< + /Type /StructElem + /S /Span + /P 186 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [39] + /Pg 267 0 R +>> +endobj + +188 0 obj +<< + /Type /StructElem + /S /Div + /P 185 0 R + /K [194 0 R 193 0 R 192 0 R 191 0 R 190 0 R 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n +0000079169 00000 n +0000080255 00000 n trailer << - /Size 200 - /Root 199 0 R - /Info 197 0 R - /ID [(JKzMzsxU1w5V2hNWCgOlzw==) (JKzMzsxU1w5V2hNWCgOlzw==)] + /Size 278 + /Root 277 0 R + /Info 275 0 R + /ID [(9xE079YG4wV/143ktBCKmg==) (9xE079YG4wV/143ktBCKmg==)] >> startxref -60083 +80474 %%EOF \ No newline at end of file diff --git a/semantics-1/semantics.typ b/semantics-1/semantics.typ index dbbc8af..928113f 100644 --- a/semantics-1/semantics.typ +++ b/semantics-1/semantics.typ @@ -17,8 +17,17 @@ #let ife(e1, e2, e3) = [#kw[if] #e1 #kw[then] #e2 #kw[else] #e3] #let suc(e) = [#kw[succ] #e] #let prd(e) = [#kw[pred] #e] +#let sec(e) = [#kw[secret] #e] -// Big-step evaluation relation: e ⇓ v +// Security labels +#let lH = $upright(H)$ +#let lL = $upright(L)$ +#let ljoin = $union.sq$ + +// Labeled value: (v, ℓ) +#let lval(v, l) = $(#v, #l)$ + +// Big-step evaluation relation: e ⇓ (v, ℓ) #let bstep(e, v) = $#e arrow.b.double #v$ // Rule name label in small-caps @@ -75,6 +84,9 @@ #set text(size: 10pt) *Abstract.* In this paper, we will provide a review of the big-step operational semantics for the BoolInt\* language we discussed in class. + We extend the language with a #kw[secret] construct and security labels + ($#lH$ for private, $#lL$ for public) to track information flow + and prevent secret leakage. ] ] @@ -94,7 +106,7 @@ expressions always will.) // ----- Figure 1: language definition ------------------------ #figure( - box(width: 80%, inset: (left: 2em))[ + box(width: 85%, inset: (left: 2em))[ #set align(left) #mydefhead[$e ::=$ #h(6em)][Expressions] #mydefcase(tr, [true value]) @@ -103,6 +115,7 @@ expressions always will.) #mydefcase(ife[$e$][$e$][$e$], [conditional expressions]) #mydefcase(suc[$e$], [successor]) #mydefcase(prd[$e$], [predecessor]) + #mydefcase(sec[$e$], [secret]) #v(0.5em) @@ -110,71 +123,120 @@ expressions always will.) #mydefcase(tr, [true value]) #mydefcase(fl, [false value]) #mydefcase($i$, [integers]) + + #v(0.5em) + + #mydefhead[$ell ::=$ #h(6em)][Security Labels] + #mydefcase($#lL$, [low / public]) + #mydefcase($#lH$, [high / private]) ], - caption: [The BoolInt\* language], + caption: [The BoolInt\* language with security labels], ) -@fig:lang shows the list of expressions and values for the BoolInt\* language. +@fig:lang shows the list of expressions, values, and security labels for the BoolInt\* language. Expressions can be the value $#tr$, the value $#fl$, -or the conditional expression $#ife[$e$][$e$][$e$]$. +integers $i$, +the conditional expression $#ife[$e$][$e$][$e$]$, +arithmetic operations $#suc[$e$]$ and $#prd[$e$]$, +and the security construct $#sec[$e$]$. Note that conditional expressions have a recursive structure, with 3 sub-expressions. -After evaluating a program, we should be able to produce a value in this language. +After evaluating a program, we produce a _labeled value_ $#lval[$v$][$ell$]$, +where $v$ is the value and $ell$ is a security label +indicating whether the result is public ($#lL$) or private ($#lH$). (In other languages, we might hit a bad situation and need to crash instead; that won't happen in this language.) The valid values for BoolInt\* are $#tr$, $#fl$, and $i$. +We define a _join_ operation $#ljoin$ on security labels as follows: +$ #lL #ljoin #lL = #lL #h(3em) #lL #ljoin #lH = #lH #ljoin #lL = #lH #ljoin #lH = #lH $ +Intuitively, any interaction with a private value taints the result as private. + With our expressions and values defined, we can now specify the semantics for our language. To do so, we will use the following big-step evaluation relation: -$ #bstep[$e$][$v$] $ +$ #bstep[$e$][$#lval[$v$][$ell$]$] $ -The above line should be read as "the expression $e$ evaluates to the value $v$". +The above line should be read as +"the expression $e$ evaluates to the value $v$ with security label $ell$". // ----- Figure 2: big-step semantics ------------------------- #figure( - box(width: 80%, inset: (left: 1em))[ + box(width: 85%, inset: (left: 1em))[ #set align(left) - #text(weight: "bold")[Evaluation Rules:#h(1em)]#box(stroke: 0.5pt, inset: 4pt, $#bstep[$e$][$v$]$) + #text(weight: "bold")[Evaluation Rules:#h(1em)]#box(stroke: 0.5pt, inset: 4pt, $#bstep[$e$][$#lval[$v$][$ell$]$]$) #v(0.6em) - #bsrule("B-Value", $emptyset$, $#bstep[$v$][$v$]$) + #bsrule("B-Value", $emptyset$, $#bstep[$v$][$#lval[$v$][$#lL$]$]$) - #bsrule("B-IfTrue", $#bstep[$e_1$][$#tr$] #h(2em) #bstep[$e_2$][$v$]$, $#bstep[#ife[$e_1$][$e_2$][$e_3$]][$v$]$) + #bsrule("B-Secret", $#bstep[$e$][$#lval[$v$][$ell$]$]$, $#bstep[#sec[$e$]][$#lval[$v$][$#lH$]$]$) - #bsrule("B-IfFalse", $#bstep[$e_1$][$#fl$] #h(2em) #bstep[$e_3$][$v$]$, $#bstep[#ife[$e_1$][$e_2$][$e_3$]][$v$]$) + #bsrule( + "B-IfTrue", + $#bstep[$e_1$][$#lval[$#tr$][$ell_1$]$] #h(2em) #bstep[$e_2$][$#lval[$v$][$ell_2$]$]$, + $#bstep[#ife[$e_1$][$e_2$][$e_3$]][$#lval[$v$][$ell_1 #ljoin ell_2$]$]$, + ) - #bsrule("B-Succ", $#bstep[$e$][$i$]$, $#bstep[#suc[$e$]][$i + 1$]$) + #bsrule( + "B-IfFalse", + $#bstep[$e_1$][$#lval[$#fl$][$ell_1$]$] #h(2em) #bstep[$e_3$][$#lval[$v$][$ell_3$]$]$, + $#bstep[#ife[$e_1$][$e_2$][$e_3$]][$#lval[$v$][$ell_1 #ljoin ell_3$]$]$, + ) - #bsrule("B-Pred", $#bstep[$e$][$i$]$, $#bstep[#prd[$e$]][$i - 1$]$) + #bsrule("B-Succ", $#bstep[$e$][$#lval[$i$][$ell$]$]$, $#bstep[#suc[$e$]][$#lval[$i + 1$][$ell$]$]$) + + #bsrule("B-Pred", $#bstep[$e$][$#lval[$i$][$ell$]$]$, $#bstep[#prd[$e$]][$#lval[$i - 1$][$ell$]$]$) ], - caption: [Big-step semantics for BoolInt\*], + caption: [Big-step semantics for BoolInt\* with information flow], ) -@fig:bigstep shows the big-step evaluation rules for the BoolInt\* language. -Of course, there are additional possible rules. +@fig:bigstep shows the big-step evaluation rules for the BoolInt\* language +with information flow tracking. The #rel("B-Value") rule applies when the expression (to the left of "$arrow.b.double$") is also a value, as defined in @fig:lang. There are no premises for this rule (above the line), meaning that it is an _axiom_. -This rule states that a value evaluates to itself, -so that #tr evaluates to #tr and #fl evaluates to #fl. +This rule states that a bare value evaluates to itself with a public label $#lL$, +so that #tr evaluates to $#lval[$#tr$][$#lL$]$ and $3$ evaluates to $#lval[$3$][$#lL$]$. + +The #rel("B-Secret") rule handles the #kw[secret] construct. +It evaluates the sub-expression $e$ and forces the security label to $#lH$, +regardless of the original label. +For example, $#sec[$3$]$ evaluates to $#lval[$3$][$#lH$]$. Two different rules are needed for handling conditional expressions. Which rule applies depends on the premises. +Critically, both rules _join_ the condition's label $ell_1$ with the branch result's label. For the #rel("B-IfTrue") rule, -the premise states that $e_1$ evaluates to #tr -and $e_2$ evaluates to some value $v$. -If the premise holds, then the result of evaluating the expression is the value $v$. +the premise states that $e_1$ evaluates to $#lval[$#tr$][$ell_1$]$ +and $e_2$ evaluates to $#lval[$v$][$ell_2$]$. +The result carries $ell_1 #ljoin ell_2$ as its label. The structure of #rel("B-IfFalse") is similar. +This join is essential for preventing _implicit flows_. +Consider the expression $#ife[#sec[$#tr$]][$1$][$0$]$. +Without the join, this would produce $#lval[$1$][$#lL$]$ — leaking which branch was taken +and thus revealing the secret condition. +With the join, the condition evaluates to $#lval[$#tr$][$#lH$]$, +so the result becomes $#lval[$1$][$#lH #ljoin #lL$] = #lval[$1$][$#lH$]$, +correctly tainting the output as private. + We also have rules for handling the integer operations. -The #rel("B-Succ") rule states that if the operand $e$ evaluates to an integer $i$, -then the expression $#suc[$e$]$ evaluates to $i + 1$. -Similarly, #rel("B-Pred") evaluates $#prd[$e$]$ to $i - 1$ if $e$ evaluates to $i$. +The #rel("B-Succ") rule states that if the operand $e$ evaluates to $#lval[$i$][$ell$]$, +then the expression $#suc[$e$]$ evaluates to $#lval[$i + 1$][$ell$]$. +This propagates the security label faithfully. +For example, $#suc[#sec[$3$]]$ evaluates to $#lval[$4$][$#lH$]$, +whereas $#suc[$3$]$ evaluates to $#lval[$4$][$#lL$]$. +Similarly, #rel("B-Pred") evaluates $#prd[$e$]$ to $#lval[$i - 1$][$ell$]$ if $e$ evaluates to $#lval[$i$][$ell$]$. + +In summary, under these semantics, there is no expression an attacker +can write that produces an $#lL$-labeled value +whose content depends on any $#lH$-labeled (secret) input. +The join in the conditional rules ensures that even _implicit_ information flows +through branch selection are tracked and labeled private.