Редактирование: Изображение:Pvs tree.png

Материал из eSyr's wiki.

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Автор: Василий Мерзляков.

Исходный dot-файл:
<pre>
digraph PVSTree {
    "node0" [
        label = "{ |[1] FORALL (i : nat) : (i \> 7) IMPLIES EXIST (t : nat, f : nat) : i = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node1" [
        label = "(induct \"i\")"
    ]
    "node0" -> "node1"
    "node2" [
        label = "{[-1] i = 0|[1] (i \> 7) IMPLIES EXIST (t : nat, f : nat) : i = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node1" -> "node2" [label = "базис индукции"]
    "node3" [
        label = "(flatten 1)"
    ]
    "node2" -> "node3"
    "node4" [
        label = "{[-1] i \> 7\n[-2] i = 0|[1] EXIST (t : nat, f : nat) : i = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node3" -> "node4"
    "node5" [
        label = "(replace -2)"
    ]
    "node4" -> "node5"
    "node6" [
        label = "{[-1] 0 \> 7\n[-2] i = 0|[1] EXIST (t : nat, f : nat) : i = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node5" -> "node6"
    "node7" [
        label = "(assert)"
        style = "filled"
        fillcolor = "green"
    ]
    "node6" -> "node7"
    "node8" [
        label = "{ |[1] FORALL (j : nat) :\n(j \> 7) IMPLIES EXIST (t : nat, f : nat) : j = 3 * t + 5 * f\nIMPLIES\n(j + 1 \> 7) IMPLIES EXIST (t : nat, f : nat) : j + 1 = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node1" -> "node8" [label = "индуктивный переход"]
    "node9" [
        label = "(skolem! 1)"
    ]
    "node8" -> "node9"
    "node10" [
        label = "{ |[1] (j!1 \> 7) IMPLIES EXIST (t : nat, f : nat) : j!1 = 3 * t + 5 * f\nIMPLIES\n(j!1 + 1 \> 7) IMPLIES EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node9" -> "node10"
    "node11" [
        label = "(flatten 1)"
    ]
    "node10" -> "node11"
    "node12" [
        label = "{[-1] (j!1 \> 7) IMPLIES EXIST (t : nat, f : nat) : j!1 = 3 * t + 5 * f|[1] (j!1 + 1 \> 7) IMPLIES EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node11" -> "node12"
    "node13" [
        label = "(flatten 1)"
    ]
    "node12" -> "node13"
    "node14" [
        label = "{[-1] j!1 + 1 \> 7\n[-2] (j!1 \> 7) IMPLIES EXIST (t : nat, f : nat) : j!1 = 3 * t + 5 * f|[1] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node13" -> "node14"
    "node15" [
        label = "(split -2)"
    ]
    "node14" -> "node15"
    "node16" [
        label = "{[-1] EXIST (t : nat, f : nat) : j!1 = 3 * t + 5 * f\n[-2] j!1 + 1 \> 7|[1] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node15" -> "node16" [label = "следствие в антецеденты"]
    "node17" [
        label = "(skolem! -1)"
    ]
    "node16" -> "node17"
    "node18" [
        label = "{[-1] j!1 = 3 * t!1 + 5 * f!1\n[-2] j!1 + 1 \> 7|[1] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node17" -> "node18"
    "node19" [
        label = "(case \"f!1 = 0\")"
    ]
    "node18" -> "node19"
    "node20" [
        label = "{[-1] f!1 = 0\n[-2] j!1 = 3 * t!1 + 5 * f!1\n[-3] j!1 + 1 \> 7|[1] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node19" -> "node20"
    "node21" [
        label = "(inst 1 \"t!1 - 3\" \"2\")"
    ]
    "node20" -> "node21"
    "node22" [
        label = "{[-1] f!1 = 0\n[-2] j!1 = 3 * t!1 + 5 * f!1\n[-3] j!1 + 1 \> 7|[1] j!1 + 1 = 3 * (t!1 - 3) + 5 * 2}"
        shape = "record"
    ]
    "node21" -> "node22"
    "node23" [
        label = "(replace -1)"
    ]
    "node22" -> "node23"
    "node24" [
        label = "{[-1] j!1 = 3 * t!1 + 5 * 0\n[-2] f!1 = 0\n[-3] j!1 + 1 \> 7|[1] j!1 + 1 = 3 * (t!1 - 3) + 5 * 2}"
        shape = "record"
    ]
    "node23" -> "node24"
    "node25" [
        label = "(assert)"
        style = "filled"
        fillcolor = "green"
    ]
    "node24" -> "node25"
    "node26" [
        label = "{[-1] f!1 = 0\n[-2] j!1 = 3 * t!1 + 5 * f!1\n[-3] j!1 + 1 \> 7|[1] t!1 - 3 \>= 0}"
        shape = "record"
    ]
    "node21" -> "node26"
    "node27" [
        label = "(assert)"
        style = "filled"
        fillcolor = "green"
    ]
    "node26" -> "node27"
    "node28" [
        label = "{[-1] f!1 /= 0\n[-2] j!1 = 3 * t!1 + 5 * f!1\n[-3] j!1 + 1 \> 7|[1] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node19" -> "node28"
    "node29" [
        label = "(inst 1 \"t!1 + 2\" \"f!1 - 1\")"
    ]
    "node28" -> "node29"
    "node30" [
        label = "{[-1] f!1 /= 0\n[-2] j!1 = 3 * t!1 + 5 * f!1\n[-3] j!1 + 1 \> 7|[1] j!1 + 1 = 3 * (t!1 + 2) + 5 * (f!1 - 1)}"
        shape = "record"
    ]
    "node29" -> "node30"
    "node31" [
        label = "(assert)"
        style = "filled"
        fillcolor = "green"
    ]
    "node30" -> "node31"
    "node32" [
        label = "{[-1] f!1 /= 0\n[-2] j!1 = 3 * t!1 + 5 * f!1\n[-3] j!1 + 1 \> 7|[1] f!1 - 1 \>= 0}"
        shape = "record"
    ]
    "node29" -> "node32"
    "node33" [
        label = "(assert)"
        style = "filled"
        fillcolor = "green"
    ]
    "node32" -> "node33"
    "node34" [
        label = "{[-1] j!1 + 1 \> 7|[1] j!1 \> 7\n[2] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node15" -> "node34" [label = "посылку в консеквенты"]
    "node35" [
        label = "(case \"j!1 = 7\")"
    ]
    "node34" -> "node35"
    "node36" [
        label = "{[-1] j!1 = 7\n[-2] j!1 + 1 \> 7|[1] j!1 \> 7\n[2] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node35" -> "node36"
    "node37" [
        label = "(inst 2 \"1\" \"1\")"
    ]
    "node36" -> "node37"
    "node38" [
        label = "{[-1] j!1 = 7\n[-2] j!1 + 1 \> 7|[1] j!1 \> 7\n[2] j!1 + 1 = 3 * 1 + 5 * 1}"
        shape = "record"
    ]
    "node37" -> "node38"
    "node39" [
        label = "(assert)"
        style = "filled"
        fillcolor = "green"
    ]
    "node38" -> "node39"
    "node40" [
        label = "{[-1] j!1 /= 7\n[-2] j!1 + 1 \> 7|[1] j!1 \> 7\n[2] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
        shape = "record"
    ]
    "node35" -> "node40"
    "node41" [
        label = "(assert)"
        style = "filled"
        fillcolor = "green"
    ]
    "node40" -> "node41"
}
</pre>

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Описание изменений:

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Получено с http://esyr.org/wiki/%D0%98%D0%B7%D0%BE%D0%B1%D1%80%D0%B0%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5:Pvs_tree.png

Редактирование: Изображение:Pvs tree.png

Материал из eSyr's wiki.

Просмотры

Личные инструменты

Навигация

инструменты

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Спецкурсы

9 семестр

7 семестр

5 семестр

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Поиск

Инструменты

@@ Строка 1: / Строка 1: @@
-Автор: Игорь Бронштейн.
+Автор: Василий Мерзляков.
 Исходный dot-файл:
@@ Строка 13: / Строка 13: @@
     "node0" -> "node1"
     "node2" [
-        label = "{ |[1] (0 \> 7) IMPLIES EXIST (t : nat, f : nat) : 0 = 3 * t + 5 * f}"
+        label = "{[-1] i = 0|[1] (i \> 7) IMPLIES EXIST (t : nat, f : nat) : i = 3 * t + 5 * f}"
         shape = "record"
     ]
@@ Строка 22: / Строка 22: @@
     "node2" -> "node3"
     "node4" [
-        label = "{[-1] 0 \> 7|[1] EXIST (t : nat, f : nat) : 0 = 3 * t + 5 * f}"
+        label = "{[-1] i \> 7\n[-2] i = 0|[1] EXIST (t : nat, f : nat) : i = 3 * t + 5 * f}"
         shape = "record"
     ]
     "node3" -> "node4"
+    "node5" [
+        label = "(replace -2)"
+    ]
+    "node4" -> "node5"
+    "node6" [
+        label = "{[-1] 0 \> 7\n[-2] i = 0|[1] EXIST (t : nat, f : nat) : i = 3 * t + 5 * f}"
+        shape = "record"
+    ]
+    "node5" -> "node6"
     "node7" [
         label = "(assert)"
@@ Строка 31: / Строка 40: @@
         fillcolor = "green"
     ]
-    "node4" -> "node7"
+    "node6" -> "node7"
     "node8" [
         label = "{ |[1] FORALL (j : nat) :\n(j \> 7) IMPLIES EXIST (t : nat, f : nat) : j = 3 * t + 5 * f\nIMPLIES\n(j + 1 \> 7) IMPLIES EXIST (t : nat, f : nat) : j + 1 = 3 * t + 5 * f}"
@@ Строка 105: / Строка 114: @@
     "node22" -> "node23"
     "node24" [
-        label = "{[-1] j!1 = 3 * t!1 + 5 * 0\n[-2] j!1 + 1 \> 7|[1] j!1 + 1 = 3 * (t!1 - 3) + 5 * 2}"
+        label = "{[-1] j!1 = 3 * t!1 + 5 * 0\n[-2] f!1 = 0\n[-3] j!1 + 1 \> 7|[1] j!1 + 1 = 3 * (t!1 - 3) + 5 * 2}"
         shape = "record"
     ]
@@ Строка 121: / Строка 130: @@
     "node21" -> "node26"
     "node27" [
-        label = "(replace -1)"
+        label = "(assert)"
+        style = "filled"
+        fillcolor = "green"
     ]
     "node26" -> "node27"
     "node28" [
-        label = "{[-1] j!1 = 3 * t!1 + 5 * 0\n[-2] j!1 + 1 \> 7|[1] t!1 - 3 \>= 0}"
+        label = "{[-1] f!1 /= 0\n[-2] j!1 = 3 * t!1 + 5 * f!1\n[-3] j!1 + 1 \> 7|[1] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
         shape = "record"
     ]
-    "node27" -> "node28"
+    "node19" -> "node28"
     "node29" [
-        label = "(assert)"
+        label = "(inst 1 \"t!1 + 2\" \"f!1 - 1\")"
-        style = "filled"
-        fillcolor = "green"
     ]
     "node28" -> "node29"
     "node30" [
-        label = "{[-1] j!1 = 3 * t!1 + 5 * f!1\n[-2] j!1 + 1 \> 7|[1] f!1 = 0\n[2] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
+        label = "{[-1] f!1 /= 0\n[-2] j!1 = 3 * t!1 + 5 * f!1\n[-3] j!1 + 1 \> 7|[1] j!1 + 1 = 3 * (t!1 + 2) + 5 * (f!1 - 1)}"
         shape = "record"
     ]
-    "node19" -> "node30"
+    "node29" -> "node30"
     "node31" [
-        label = "(inst 2 \"t!1 + 2\" \"f!1 - 1\")"
+        label = "(assert)"
+        style = "filled"
+        fillcolor = "green"
     ]
     "node30" -> "node31"
     "node32" [
-        label = "{[-1] j!1 = 3 * t!1 + 5 * f!1\n[-2] j!1 + 1 \> 7|[1] j!1 + 1 = 3 * (t!1 + 2) + 5 * (f!1 - 1)\n[2] f!1 = 0}"
+        label = "{[-1] f!1 /= 0\n[-2] j!1 = 3 * t!1 + 5 * f!1\n[-3] j!1 + 1 \> 7|[1] f!1 - 1 \>= 0}"
         shape = "record"
     ]
-    "node31" -> "node32"
+    "node29" -> "node32"
     "node33" [
         label = "(assert)"
@@ Строка 156: / Строка 167: @@
     "node32" -> "node33"
     "node34" [
-        label = "{[-1] j!1 = 3 * t!1 + 5 * f!1\n[-2] j!1 + 1 \> 7|[1] f!1 - 1 \>= 0\n[2] f!1 = 0}"
+        label = "{[-1] j!1 + 1 \> 7|[1] j!1 \> 7\n[2] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
         shape = "record"
     ]
-    "node31" -> "node34"
+    "node15" -> "node34" [label = "посылку в консеквенты"]
     "node35" [
-        label = "(assert)"
+        label = "(case \"j!1 = 7\")"
-        style = "filled"
-        fillcolor = "green"
     ]
     "node34" -> "node35"
     "node36" [
-        label = "{[-1] j!1 + 1 \> 7|[1] j!1 \> 7\n[2] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
+        label = "{[-1] j!1 = 7\n[-2] j!1 + 1 \> 7|[1] j!1 \> 7\n[2] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
         shape = "record"
     ]
-    "node15" -> "node36" [label = "посылку в консеквенты"]
+    "node35" -> "node36"
     "node37" [
-        label = "(case \"j!1 = 7\")"
+        label = "(inst 2 \"1\" \"1\")"
     ]
     "node36" -> "node37"
     "node38" [
-        label = "{[-1] j!1 = 7\n[-2] j!1 + 1 \> 7|[1] j!1 \> 7\n[2] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
+        label = "{[-1] j!1 = 7\n[-2] j!1 + 1 \> 7|[1] j!1 \> 7\n[2] j!1 + 1 = 3 * 1 + 5 * 1}"
         shape = "record"
     ]
     "node37" -> "node38"
     "node39" [
-        label = "(inst 2 \"1\" \"1\")"
+        label = "(assert)"
+        style = "filled"
+        fillcolor = "green"
     ]
     "node38" -> "node39"
     "node40" [
-        label = "{[-1] j!1 = 7\n[-2] j!1 + 1 \> 7|[1] j!1 \> 7\n[2] j!1 + 1 = 3 * 1 + 5 * 1}"
+        label = "{[-1] j!1 /= 7\n[-2] j!1 + 1 \> 7|[1] j!1 \> 7\n[2] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
         shape = "record"
     ]
-    "node39" -> "node40"
+    "node35" -> "node40"
     "node41" [
         label = "(assert)"
@@ Строка 195: / Строка 206: @@
     ]
     "node40" -> "node41"
-    "node42" [
-        label = "{[-1] j!1 + 1 \> 7|[1] j!1 = 7\n[2] j!1 \> 7\n[3] EXIST (t : nat, f : nat) : j!1 + 1 = 3 * t + 5 * f}"
-        shape = "record"
-    ]
-    "node37" -> "node42"
-    "node43" [
-        label = "(assert)"
-        style = "filled"
-        fillcolor = "green"
-    ]
-    "node42" -> "node43"
 }
 </pre>