From 18e2d0d0c6ed9fcdeae8d9b411a468ab452ded43 Mon Sep 17 00:00:00 2001 From: Yuri Tatishchev Date: Thu, 12 Feb 2026 14:56:17 -0800 Subject: [PATCH] semantics-1: typst pt. 2 --- semantics-1/semantics-typst.pdf | 1747 ++++++++++++++++--------------- semantics-1/semantics.typ | 49 +- 2 files changed, 895 insertions(+), 901 deletions(-) diff --git a/semantics-1/semantics-typst.pdf b/semantics-1/semantics-typst.pdf index 2eb3714..5a3e7f0 100644 --- a/semantics-1/semantics-typst.pdf +++ b/semantics-1/semantics-typst.pdf @@ -5,7 +5,7 @@ << /Type /Pages /Count 2 - /Kids [189 0 R 193 0 R] + /Kids [191 0 R 195 0 R] >> endobj @@ -21,18 +21,18 @@ endobj >> /K [5 0 R] /ParentTree << - /Nums [0 71 0 R 1 3 0 R 2 26 0 R 3 23 0 R 4 4 0 R] + /Nums [0 72 0 R 1 3 0 R 2 26 0 R 3 23 0 R 4 4 0 R] >> /ParentTreeNextKey 5 >> endobj 3 0 obj -[153 0 R 152 0 R 152 0 R 152 0 R 151 0 R 150 0 R 150 0 R 149 0 R 147 0 R 147 0 R 148 0 R 147 0 R 144 0 R 144 0 R 142 0 R 138 0 R 136 0 R 132 0 R 130 0 R 126 0 R 124 0 R 120 0 R 120 0 R 119 0 R 118 0 R 118 0 R 118 0 R 117 0 R 116 0 R 116 0 R 116 0 R 115 0 R 113 0 R 109 0 R 109 0 R 108 0 R 106 0 R 102 0 R 102 0 R 101 0 R 99 0 R 96 0 R 96 0 R 94 0 R 90 0 R 88 0 R 84 0 R 82 0 R 78 0 R 76 0 R 146 0 R 71 0 R 67 0 R 67 0 R 70 0 R 67 0 R 69 0 R 67 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 68 0 R 67 0 R 67 0 R 63 0 R 63 0 R 63 0 R 66 0 R 63 0 R 65 0 R 63 0 R 64 0 R 63 0 R 62 0 R 62 0 R 61 0 R 61 0 R 61 0 R 58 0 R 60 0 R 58 0 R 59 0 R 58 0 R] +[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] endobj 4 0 obj -[54 0 R 55 0 R 55 0 R 55 0 R 53 0 R 51 0 R 51 0 R 51 0 R 51 0 R 48 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 46 0 R 43 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 41 0 R 38 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 36 0 R 33 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 57 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] +[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] endobj 5 0 obj @@ -40,7 +40,7 @@ endobj /Type /StructElem /S /Document /P 2 0 R - /K [153 0 R 152 0 R 151 0 R 150 0 R 149 0 R 147 0 R 72 0 R 67 0 R 63 0 R 62 0 R 61 0 R 58 0 R 27 0 R 25 0 R 21 0 R 20 0 R 15 0 R 6 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] >> endobj @@ -50,7 +50,7 @@ endobj /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 193 0 R + /Pg 195 0 R >> endobj @@ -60,7 +60,7 @@ endobj /S /Formula /P 6 0 R /K [139] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -70,7 +70,7 @@ endobj /S /Formula /P 6 0 R /K [137] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -80,7 +80,7 @@ endobj /S /Formula /P 6 0 R /K [133 134 135] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -90,7 +90,7 @@ endobj /S /Formula /P 6 0 R /K [130 131] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -100,7 +100,7 @@ endobj /S /Formula /P 6 0 R /K [124 125 126] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -110,7 +110,7 @@ endobj /S /Formula /P 6 0 R /K [121 122] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -120,7 +120,7 @@ endobj /S /Formula /P 6 0 R /K [119] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -130,7 +130,7 @@ endobj /S /Formula /P 6 0 R /K [116] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -140,7 +140,7 @@ endobj /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 193 0 R + /Pg 195 0 R >> endobj @@ -150,7 +150,7 @@ endobj /S /Formula /P 15 0 R /K [108] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -160,7 +160,7 @@ endobj /S /Formula /P 15 0 R /K [105] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -170,7 +170,7 @@ endobj /S /Formula /P 15 0 R /K [102 103] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -180,7 +180,7 @@ endobj /S /Formula /P 15 0 R /K [97 98] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -190,7 +190,7 @@ endobj /S /P /P 5 0 R /K [92 93] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -200,7 +200,7 @@ endobj /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 193 0 R + /Pg 195 0 R >> endobj @@ -210,7 +210,7 @@ endobj /S /Em /P 21 0 R /K [81] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -221,10 +221,10 @@ endobj /P 21 0 R /K [78 << /Type /OBJR - /Pg 193 0 R - /Obj 192 0 R + /Pg 195 0 R + /Obj 194 0 R >>] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -234,7 +234,7 @@ endobj /S /Formula /P 21 0 R /K [76] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -244,7 +244,7 @@ endobj /S /P /P 5 0 R /K [26 0 R 71 72] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -255,10 +255,10 @@ endobj /P 25 0 R /K [70 << /Type /OBJR - /Pg 193 0 R - /Obj 191 0 R + /Pg 195 0 R + /Obj 193 0 R >>] - /Pg 193 0 R + /Pg 195 0 R >> endobj @@ -267,7 +267,7 @@ endobj /Type /StructElem /S /Div /P 5 0 R - /K [56 0 R 28 0 R] + /K [57 0 R 28 0 R] >> endobj @@ -280,16 +280,16 @@ endobj /O /Layout /Placement /Block >>] - /K [54 0 R 49 0 R 44 0 R 39 0 R 34 0 R 29 0 R] + /K [29 0 R] >> endobj 29 0 obj << /Type /StructElem - /S /Div + /S /P /P 28 0 R - /K [32 0 R 30 0 R] + /K [55 0 R 50 0 R 45 0 R 40 0 R 35 0 R 30 0 R] >> endobj @@ -298,53 +298,53 @@ endobj /Type /StructElem /S /Div /P 29 0 R - /K [31 0 R] + /K [33 0 R 31 0 R] >> endobj 31 0 obj << /Type /StructElem - /S /Formula + /S /Div /P 30 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [60 61 62 63 64 65 66 67 68] - /Pg 193 0 R + /K [32 0 R] >> endobj 32 0 obj << /Type /StructElem - /S /Div - /P 29 0 R - /K [33 0 R] + /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 >> endobj 33 0 obj << /Type /StructElem - /S /Span - /P 32 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [59] - /Pg 193 0 R + /S /Div + /P 30 0 R + /K [34 0 R] >> endobj 34 0 obj << /Type /StructElem - /S /Div - /P 28 0 R - /K [37 0 R 35 0 R] + /S /Span + /P 33 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [59] + /Pg 195 0 R >> endobj @@ -352,54 +352,54 @@ endobj << /Type /StructElem /S /Div - /P 34 0 R - /K [36 0 R] + /P 29 0 R + /K [38 0 R 36 0 R] >> endobj 36 0 obj << /Type /StructElem - /S /Formula + /S /Div /P 35 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [50 51 52 53 54 55 56 57 58] - /Pg 193 0 R + /K [37 0 R] >> endobj 37 0 obj << /Type /StructElem - /S /Div - /P 34 0 R - /K [38 0 R] + /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 >> endobj 38 0 obj << /Type /StructElem - /S /Span - /P 37 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [49] - /Pg 193 0 R + /S /Div + /P 35 0 R + /K [39 0 R] >> endobj 39 0 obj << /Type /StructElem - /S /Div - /P 28 0 R - /K [42 0 R 40 0 R] + /S /Span + /P 38 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [49] + /Pg 195 0 R >> endobj @@ -407,54 +407,54 @@ endobj << /Type /StructElem /S /Div - /P 39 0 R - /K [41 0 R] + /P 29 0 R + /K [43 0 R 41 0 R] >> endobj 41 0 obj << /Type /StructElem - /S /Formula + /S /Div /P 40 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 193 0 R + /K [42 0 R] >> endobj 42 0 obj << /Type /StructElem - /S /Div - /P 39 0 R - /K [43 0 R] + /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 >> endobj 43 0 obj << /Type /StructElem - /S /Span - /P 42 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [29] - /Pg 193 0 R + /S /Div + /P 40 0 R + /K [44 0 R] >> endobj 44 0 obj << /Type /StructElem - /S /Div - /P 28 0 R - /K [47 0 R 45 0 R] + /S /Span + /P 43 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [29] + /Pg 195 0 R >> endobj @@ -462,54 +462,54 @@ endobj << /Type /StructElem /S /Div - /P 44 0 R - /K [46 0 R] + /P 29 0 R + /K [48 0 R 46 0 R] >> endobj 46 0 obj << /Type /StructElem - /S /Formula + /S /Div /P 45 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 193 0 R + /K [47 0 R] >> endobj 47 0 obj << /Type /StructElem - /S /Div - /P 44 0 R - /K [48 0 R] + /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 >> endobj 48 0 obj << /Type /StructElem - /S /Span - /P 47 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [9] - /Pg 193 0 R + /S /Div + /P 45 0 R + /K [49 0 R] >> endobj 49 0 obj << /Type /StructElem - /S /Div - /P 28 0 R - /K [52 0 R 50 0 R] + /S /Span + /P 48 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [9] + /Pg 195 0 R >> endobj @@ -517,108 +517,107 @@ endobj << /Type /StructElem /S /Div - /P 49 0 R - /K [51 0 R] + /P 29 0 R + /K [53 0 R 51 0 R] >> endobj 51 0 obj << /Type /StructElem - /S /Formula + /S /Div /P 50 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [5 6 7 8] - /Pg 193 0 R + /K [52 0 R] >> endobj 52 0 obj << /Type /StructElem - /S /Div - /P 49 0 R - /K [53 0 R] + /S /Formula + /P 51 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [5 6 7 8] + /Pg 195 0 R >> endobj 53 0 obj << /Type /StructElem - /S /Span - /P 52 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [4] - /Pg 193 0 R + /S /Div + /P 50 0 R + /K [54 0 R] >> endobj 54 0 obj << /Type /StructElem - /S /P - /P 28 0 R - /K [0 55 0 R] - /Pg 193 0 R + /S /Span + /P 53 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [4] + /Pg 195 0 R >> endobj 55 0 obj << /Type /StructElem - /S /Formula - /P 54 0 R - /K [1 2 3] - /Pg 193 0 R + /S /P + /P 29 0 R + /K [0 56 0 R] + /Pg 195 0 R >> endobj 56 0 obj << /Type /StructElem - /S /Caption - /P 27 0 R - /K [57 0 R] + /S /Formula + /P 55 0 R + /K [1 2 3] + /Pg 195 0 R >> endobj 57 0 obj << /Type /StructElem - /S /Span - /P 56 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [69] - /Pg 193 0 R + /S /Caption + /P 27 0 R + /K [58 0 R] >> endobj 58 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [80 60 0 R 82 59 0 R 84] - /Pg 189 0 R + /S /Span + /P 57 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [69] + /Pg 195 0 R >> endobj 59 0 obj << /Type /StructElem - /S /Formula - /P 58 0 R - /K [83] - /Pg 189 0 R + /S /P + /P 5 0 R + /K [80 61 0 R 82 60 0 R 84] + /Pg 191 0 R >> endobj @@ -626,13 +625,23 @@ endobj << /Type /StructElem /S /Formula - /P 58 0 R - /K [81] - /Pg 189 0 R + /P 59 0 R + /K [83] + /Pg 191 0 R >> endobj 61 0 obj +<< + /Type /StructElem + /S /Formula + /P 59 0 R + /K [81] + /Pg 191 0 R +>> +endobj + +62 0 obj << /Type /StructElem /S /Formula @@ -642,17 +651,7 @@ endobj /Placement /Block >>] /K [77 78 79] - /Pg 189 0 R ->> -endobj - -62 0 obj -<< - /Type /StructElem - /S /P - /P 5 0 R - /K [75 76] - /Pg 189 0 R + /Pg 191 0 R >> endobj @@ -661,18 +660,18 @@ endobj /Type /StructElem /S /P /P 5 0 R - /K [66 67 68 66 0 R 70 65 0 R 72 64 0 R 74] - /Pg 189 0 R + /K [75 76] + /Pg 191 0 R >> endobj 64 0 obj << /Type /StructElem - /S /Formula - /P 63 0 R - /K [73] - /Pg 189 0 R + /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 >> endobj @@ -680,9 +679,9 @@ endobj << /Type /StructElem /S /Formula - /P 63 0 R - /K [71] - /Pg 189 0 R + /P 64 0 R + /K [73] + /Pg 191 0 R >> endobj @@ -690,29 +689,29 @@ endobj << /Type /StructElem /S /Formula - /P 63 0 R - /K [69] - /Pg 189 0 R + /P 64 0 R + /K [71] + /Pg 191 0 R >> endobj 67 0 obj << /Type /StructElem - /S /P - /P 5 0 R - /K [71 0 R 52 53 70 0 R 55 69 0 R 57 68 0 R 64 65] - /Pg 189 0 R + /S /Formula + /P 64 0 R + /K [69] + /Pg 191 0 R >> endobj 68 0 obj << /Type /StructElem - /S /Formula - /P 67 0 R - /K [58 59 60 61 62 63] - /Pg 189 0 R + /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 >> endobj @@ -720,9 +719,9 @@ endobj << /Type /StructElem /S /Formula - /P 67 0 R - /K [56] - /Pg 189 0 R + /P 68 0 R + /K [58 59 60 61 62 63] + /Pg 191 0 R >> endobj @@ -730,32 +729,33 @@ endobj << /Type /StructElem /S /Formula - /P 67 0 R - /K [54] - /Pg 189 0 R + /P 68 0 R + /K [56] + /Pg 191 0 R >> endobj 71 0 obj << /Type /StructElem - /S /Link - /P 67 0 R - /K [51 << - /Type /OBJR - /Pg 189 0 R - /Obj 188 0 R - >>] - /Pg 189 0 R + /S /Formula + /P 68 0 R + /K [54] + /Pg 191 0 R >> endobj 72 0 obj << /Type /StructElem - /S /Div - /P 5 0 R - /K [145 0 R 73 0 R] + /S /Link + /P 68 0 R + /K [51 << + /Type /OBJR + /Pg 191 0 R + /Obj 190 0 R + >>] + /Pg 191 0 R >> endobj @@ -763,12 +763,8 @@ endobj << /Type /StructElem /S /Div - /P 72 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [140 0 R 134 0 R 128 0 R 122 0 R 111 0 R 104 0 R 97 0 R 92 0 R 86 0 R 80 0 R 74 0 R] + /P 5 0 R + /K [147 0 R 74 0 R] >> endobj @@ -777,30 +773,29 @@ endobj /Type /StructElem /S /Div /P 73 0 R - /K [79 0 R 77 0 R 75 0 R] + /A [<< + /O /Layout + /Placement /Block + >>] + /K [75 0 R] >> endobj 75 0 obj << /Type /StructElem - /S /Div + /S /P /P 74 0 R - /K [76 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] >> endobj 76 0 obj << /Type /StructElem - /S /Span + /S /Div /P 75 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [49] - /Pg 189 0 R + /K [81 0 R 79 0 R 77 0 R] >> endobj @@ -808,7 +803,7 @@ endobj << /Type /StructElem /S /Div - /P 74 0 R + /P 76 0 R /K [78 0 R] >> endobj @@ -816,14 +811,14 @@ endobj 78 0 obj << /Type /StructElem - /S /Formula + /S /Span /P 77 0 R /A [<< /O /Layout /Placement /Block >>] - /K [48] - /Pg 189 0 R + /K [49] + /Pg 191 0 R >> endobj @@ -831,17 +826,22 @@ endobj << /Type /StructElem /S /Div - /P 74 0 R - /K [] + /P 76 0 R + /K [80 0 R] >> endobj 80 0 obj << /Type /StructElem - /S /Div - /P 73 0 R - /K [85 0 R 83 0 R 81 0 R] + /S /Formula + /P 79 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [48] + /Pg 191 0 R >> endobj @@ -849,22 +849,17 @@ endobj << /Type /StructElem /S /Div - /P 80 0 R - /K [82 0 R] + /P 76 0 R + /K [] >> endobj 82 0 obj << /Type /StructElem - /S /Span - /P 81 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [47] - /Pg 189 0 R + /S /Div + /P 75 0 R + /K [87 0 R 85 0 R 83 0 R] >> endobj @@ -872,7 +867,7 @@ endobj << /Type /StructElem /S /Div - /P 80 0 R + /P 82 0 R /K [84 0 R] >> endobj @@ -886,8 +881,8 @@ endobj /O /Layout /Placement /Block >>] - /K [46] - /Pg 189 0 R + /K [47] + /Pg 191 0 R >> endobj @@ -895,17 +890,22 @@ endobj << /Type /StructElem /S /Div - /P 80 0 R - /K [] + /P 82 0 R + /K [86 0 R] >> endobj 86 0 obj << /Type /StructElem - /S /Div - /P 73 0 R - /K [91 0 R 89 0 R 87 0 R] + /S /Span + /P 85 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [46] + /Pg 191 0 R >> endobj @@ -913,22 +913,17 @@ endobj << /Type /StructElem /S /Div - /P 86 0 R - /K [88 0 R] + /P 82 0 R + /K [] >> endobj 88 0 obj << /Type /StructElem - /S /Span - /P 87 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [45] - /Pg 189 0 R + /S /Div + /P 75 0 R + /K [93 0 R 91 0 R 89 0 R] >> endobj @@ -936,7 +931,7 @@ endobj << /Type /StructElem /S /Div - /P 86 0 R + /P 88 0 R /K [90 0 R] >> endobj @@ -950,8 +945,8 @@ endobj /O /Layout /Placement /Block >>] - /K [44] - /Pg 189 0 R + /K [45] + /Pg 191 0 R >> endobj @@ -959,17 +954,22 @@ endobj << /Type /StructElem /S /Div - /P 86 0 R - /K [] + /P 88 0 R + /K [92 0 R] >> endobj 92 0 obj << /Type /StructElem - /S /Div - /P 73 0 R - /K [95 0 R 93 0 R] + /S /Span + /P 91 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [44] + /Pg 191 0 R >> endobj @@ -977,22 +977,17 @@ endobj << /Type /StructElem /S /Div - /P 92 0 R - /K [94 0 R] + /P 88 0 R + /K [] >> endobj 94 0 obj << /Type /StructElem - /S /Em - /P 93 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [43] - /Pg 189 0 R + /S /Div + /P 75 0 R + /K [97 0 R 95 0 R] >> endobj @@ -1000,7 +995,7 @@ endobj << /Type /StructElem /S /Div - /P 92 0 R + /P 94 0 R /K [96 0 R] >> endobj @@ -1008,14 +1003,14 @@ endobj 96 0 obj << /Type /StructElem - /S /Formula + /S /Em /P 95 0 R /A [<< /O /Layout /Placement /Block >>] - /K [41 42] - /Pg 189 0 R + /K [43] + /Pg 191 0 R >> endobj @@ -1023,31 +1018,31 @@ endobj << /Type /StructElem /S /Div - /P 73 0 R - /K [103 0 R 100 0 R 98 0 R] + /P 94 0 R + /K [98 0 R] >> endobj 98 0 obj << /Type /StructElem - /S /Div + /S /Formula /P 97 0 R - /K [99 0 R] + /A [<< + /O /Layout + /Placement /Block + >>] + /K [41 42] + /Pg 191 0 R >> endobj 99 0 obj << /Type /StructElem - /S /Span - /P 98 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [40] - /Pg 189 0 R + /S /Div + /P 75 0 R + /K [105 0 R 102 0 R 100 0 R] >> endobj @@ -1055,26 +1050,12 @@ endobj << /Type /StructElem /S /Div - /P 97 0 R - /K [102 0 R 101 0 R] + /P 99 0 R + /K [101 0 R] >> endobj 101 0 obj -<< - /Type /StructElem - /S /Formula - /P 100 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [39] - /Pg 189 0 R ->> -endobj - -102 0 obj << /Type /StructElem /S /Span @@ -1083,26 +1064,45 @@ endobj /O /Layout /Placement /Block >>] - /K [37 38] - /Pg 189 0 R + /K [40] + /Pg 191 0 R +>> +endobj + +102 0 obj +<< + /Type /StructElem + /S /Div + /P 99 0 R + /K [104 0 R 103 0 R] >> endobj 103 0 obj << /Type /StructElem - /S /Div - /P 97 0 R - /K [] + /S /Formula + /P 102 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [39] + /Pg 191 0 R >> endobj 104 0 obj << /Type /StructElem - /S /Div - /P 73 0 R - /K [110 0 R 107 0 R 105 0 R] + /S /Span + /P 102 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [37 38] + /Pg 191 0 R >> endobj @@ -1110,22 +1110,17 @@ endobj << /Type /StructElem /S /Div - /P 104 0 R - /K [106 0 R] + /P 99 0 R + /K [] >> endobj 106 0 obj << /Type /StructElem - /S /Span - /P 105 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [36] - /Pg 189 0 R + /S /Div + /P 75 0 R + /K [112 0 R 109 0 R 107 0 R] >> endobj @@ -1133,26 +1128,12 @@ endobj << /Type /StructElem /S /Div - /P 104 0 R - /K [109 0 R 108 0 R] + /P 106 0 R + /K [108 0 R] >> endobj 108 0 obj -<< - /Type /StructElem - /S /Formula - /P 107 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [35] - /Pg 189 0 R ->> -endobj - -109 0 obj << /Type /StructElem /S /Span @@ -1161,26 +1142,45 @@ endobj /O /Layout /Placement /Block >>] - /K [33 34] - /Pg 189 0 R + /K [36] + /Pg 191 0 R +>> +endobj + +109 0 obj +<< + /Type /StructElem + /S /Div + /P 106 0 R + /K [111 0 R 110 0 R] >> endobj 110 0 obj << /Type /StructElem - /S /Div - /P 104 0 R - /K [] + /S /Formula + /P 109 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [35] + /Pg 191 0 R >> endobj 111 0 obj << /Type /StructElem - /S /Div - /P 73 0 R - /K [121 0 R 114 0 R 112 0 R] + /S /Span + /P 109 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [33 34] + /Pg 191 0 R >> endobj @@ -1188,22 +1188,17 @@ endobj << /Type /StructElem /S /Div - /P 111 0 R - /K [113 0 R] + /P 106 0 R + /K [] >> endobj 113 0 obj << /Type /StructElem - /S /Span - /P 112 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [32] - /Pg 189 0 R + /S /Div + /P 75 0 R + /K [123 0 R 116 0 R 114 0 R] >> endobj @@ -1211,26 +1206,12 @@ endobj << /Type /StructElem /S /Div - /P 111 0 R - /K [120 0 R 119 0 R 118 0 R 117 0 R 116 0 R 115 0 R] + /P 113 0 R + /K [115 0 R] >> endobj 115 0 obj -<< - /Type /StructElem - /S /Formula - /P 114 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [31] - /Pg 189 0 R ->> -endobj - -116 0 obj << /Type /StructElem /S /Span @@ -1239,8 +1220,17 @@ endobj /O /Layout /Placement /Block >>] - /K [28 29 30] - /Pg 189 0 R + /K [32] + /Pg 191 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] >> endobj @@ -1248,13 +1238,13 @@ endobj << /Type /StructElem /S /Formula - /P 114 0 R + /P 116 0 R /A [<< /O /Layout /Placement /Block >>] - /K [27] - /Pg 189 0 R + /K [31] + /Pg 191 0 R >> endobj @@ -1262,13 +1252,13 @@ endobj << /Type /StructElem /S /Span - /P 114 0 R + /P 116 0 R /A [<< /O /Layout /Placement /Block >>] - /K [24 25 26] - /Pg 189 0 R + /K [28 29 30] + /Pg 191 0 R >> endobj @@ -1276,13 +1266,13 @@ endobj << /Type /StructElem /S /Formula - /P 114 0 R + /P 116 0 R /A [<< /O /Layout /Placement /Block >>] - /K [23] - /Pg 189 0 R + /K [27] + /Pg 191 0 R >> endobj @@ -1290,31 +1280,41 @@ endobj << /Type /StructElem /S /Span - /P 114 0 R + /P 116 0 R /A [<< /O /Layout /Placement /Block >>] - /K [21 22] - /Pg 189 0 R + /K [24 25 26] + /Pg 191 0 R >> endobj 121 0 obj << /Type /StructElem - /S /Div - /P 111 0 R - /K [] + /S /Formula + /P 116 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [23] + /Pg 191 0 R >> endobj 122 0 obj << /Type /StructElem - /S /Div - /P 73 0 R - /K [127 0 R 125 0 R 123 0 R] + /S /Span + /P 116 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [21 22] + /Pg 191 0 R >> endobj @@ -1322,22 +1322,17 @@ endobj << /Type /StructElem /S /Div - /P 122 0 R - /K [124 0 R] + /P 113 0 R + /K [] >> endobj 124 0 obj << /Type /StructElem - /S /Span - /P 123 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [20] - /Pg 189 0 R + /S /Div + /P 75 0 R + /K [129 0 R 127 0 R 125 0 R] >> endobj @@ -1345,7 +1340,7 @@ endobj << /Type /StructElem /S /Div - /P 122 0 R + /P 124 0 R /K [126 0 R] >> endobj @@ -1353,14 +1348,14 @@ endobj 126 0 obj << /Type /StructElem - /S /Formula + /S /Span /P 125 0 R /A [<< /O /Layout /Placement /Block >>] - /K [19] - /Pg 189 0 R + /K [20] + /Pg 191 0 R >> endobj @@ -1368,17 +1363,22 @@ endobj << /Type /StructElem /S /Div - /P 122 0 R - /K [] + /P 124 0 R + /K [128 0 R] >> endobj 128 0 obj << /Type /StructElem - /S /Div - /P 73 0 R - /K [133 0 R 131 0 R 129 0 R] + /S /Formula + /P 127 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [19] + /Pg 191 0 R >> endobj @@ -1386,22 +1386,17 @@ endobj << /Type /StructElem /S /Div - /P 128 0 R - /K [130 0 R] + /P 124 0 R + /K [] >> endobj 130 0 obj << /Type /StructElem - /S /Span - /P 129 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [18] - /Pg 189 0 R + /S /Div + /P 75 0 R + /K [135 0 R 133 0 R 131 0 R] >> endobj @@ -1409,7 +1404,7 @@ endobj << /Type /StructElem /S /Div - 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fl = kw[false] #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] @@ -28,13 +28,10 @@ // premises (content), conclusion (content) #let bsrule(name, premises, conclusion) = { grid( - columns: (auto, 1fr), + columns: (auto, auto), column-gutter: 1em, align: (right + horizon, left + horizon), - rel(name), - math.equation(block: true, numbering: none, - math.frac(premises, conclusion) - ), + rel(name), math.equation(block: true, numbering: none, math.frac(premises, conclusion)), ) v(0.4em) } @@ -42,16 +39,17 @@ // Definition head: "e ::= ..." with label #let mydefhead(lhs, label) = { grid( - columns: (1fr, auto), - [#lhs], - emph(label), + columns: (auto, auto), + column-gutter: 1fr, + [#lhs], emph(label), ) } // Definition case: indented alternative with description #let mydefcase(alt, desc) = { grid( - columns: (2em, 1fr, auto), + columns: (2em, auto, auto), + column-gutter: 1fr, [], [#alt], [#desc], ) } @@ -96,7 +94,7 @@ expressions always will.) // ----- Figure 1: language definition ------------------------ #figure( - block(inset: (left: 2em))[ + box(width: 80%, inset: (left: 2em))[ #set align(left) #mydefhead[$e ::=$ #h(6em)][Expressions] #mydefcase(tr, [true value]) @@ -138,36 +136,21 @@ The above line should be read as "the expression $e$ evaluates to the value $v$" // ----- Figure 2: big-step semantics ------------------------- #figure( - block(inset: (left: 1em))[ + box(width: 80%, inset: (left: 1em))[ #set align(left) #text(weight: "bold")[Evaluation Rules:#h(1em)]#box(stroke: 0.5pt, inset: 4pt, $#bstep[$e$][$v$]$) #v(0.6em) - #bsrule("B-Value", - $emptyset$, - $#bstep[$v$][$v$]$, - ) + #bsrule("B-Value", $emptyset$, $#bstep[$v$][$v$]$) - #bsrule("B-IfTrue", - $#bstep[$e_1$][$#tr$] #h(2em) #bstep[$e_2$][$v$]$, - $#bstep[#ife[$e_1$][$e_2$][$e_3$]][$v$]$, - ) + #bsrule("B-IfTrue", $#bstep[$e_1$][$#tr$] #h(2em) #bstep[$e_2$][$v$]$, $#bstep[#ife[$e_1$][$e_2$][$e_3$]][$v$]$) - #bsrule("B-IfFalse", - $#bstep[$e_1$][$#fl$] #h(2em) #bstep[$e_3$][$v$]$, - $#bstep[#ife[$e_1$][$e_2$][$e_3$]][$v$]$, - ) + #bsrule("B-IfFalse", $#bstep[$e_1$][$#fl$] #h(2em) #bstep[$e_3$][$v$]$, $#bstep[#ife[$e_1$][$e_2$][$e_3$]][$v$]$) - #bsrule("B-Succ", - $#bstep[$e$][$i$]$, - $#bstep[#suc[$e$]][$i + 1$]$, - ) + #bsrule("B-Succ", $#bstep[$e$][$i$]$, $#bstep[#suc[$e$]][$i + 1$]$) - #bsrule("B-Pred", - $#bstep[$e$][$i$]$, - $#bstep[#prd[$e$]][$i - 1$]$, - ) + #bsrule("B-Pred", $#bstep[$e$][$i$]$, $#bstep[#prd[$e$]][$i - 1$]$) ], caption: [Big-step semantics for BoolInt\*], )