From 67195be048d9ec4b2d19890abd61700ff7b112d1 Mon Sep 17 00:00:00 2001
From: Michael Leuschel <leuschel@uni-duesseldorf.de>
Date: Thu, 30 Apr 2020 10:57:35 +0200
Subject: [PATCH] add Grammar G2
---
info4/kapitel-1/Grammatiken.ipynb | 550 ++++++++++++++++++++++++++----
1 file changed, 482 insertions(+), 68 deletions(-)
diff --git a/info4/kapitel-1/Grammatiken.ipynb b/info4/kapitel-1/Grammatiken.ipynb
index afe1ca1..92625bb 100644
--- a/info4/kapitel-1/Grammatiken.ipynb
+++ b/info4/kapitel-1/Grammatiken.ipynb
@@ -161,25 +161,62 @@
},
{
"cell_type": "code",
- "execution_count": 44,
+ "execution_count": 75,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Loaded machine: Grammatik"
+ ]
+ },
+ "execution_count": 75,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "::load\n",
+ "MACHINE Grammatik\n",
+ "SETS ΣN = {a,b,c, S}\n",
+ "CONSTANTS Σ, N, P\n",
+ "ABSTRACT_CONSTANTS abl\n",
+ "PROPERTIES\n",
+ " Σ = {a,b,c} ∧\n",
+ " Σ ∩ N = {} ∧\n",
+ " Σ ∪ N = ΣN ∧\n",
+ " S ∈ N ∧\n",
+ " P ⊆ seq1(ΣN) × seq(ΣN) ∧\n",
+ " \n",
+ " // Die Beispiel Grammatik G1 von den Folien\n",
+ " P = { [S] ↦ [],\n",
+ " [S] ↦ [a,S,b]\n",
+ " }\n",
+ " \n",
+ " ∧ \n",
+ " abl = {u,v | ∃(x,z,p,q).( p↦q ∈ P ∧ u = x^p^z ∧ v = x^q^z )}\n",
+ "DEFINITIONS SET_PREF_PP_SEQUENCES == TRUE\n",
+ "END"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 76,
"metadata": {},
"outputs": [
{
"data": {
- "text/markdown": [
- "$\\newcommand{\\qdot}{\\mathord{\\mkern1mu\\cdot\\mkern1mu}}/*@symbolic*/ \\{\\mathit{u},\\mathit{v}\\mid\\exists(\\mathit{x},\\mathit{z},\\mathit{p},\\mathit{q})\\qdot(\\mathit{p} \\mapsto \\mathit{q} \\in \\{([S]\\mapsto []),([S]\\mapsto [a,\\mathit{S},b])\\} \\land \\mathit{u} = \\mathit{x} ⌒ \\mathit{p} ⌒ \\mathit{z} \\land \\mathit{v} = \\mathit{x} ⌒ \\mathit{q} ⌒ \\mathit{z})\\}$"
- ],
"text/plain": [
- "/*@symbolic*/ {u,v∣∃(x,z,p,q)·(p ↦ q ∈ {([S]↦[]),([S]↦[a,S,b])} ∧ u = x ⌒ p ⌒ z ∧ v = x ⌒ q ⌒ z)}"
+ "Machine constants set up using operation 0: $setup_constants()"
]
},
- "execution_count": 44,
+ "execution_count": 76,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- ":let abl {u,v | ∃(x,z,p,q).( p↦q ∈ P ∧ u = x^p^z ∧ v = x^q^z )}"
+ ":constants"
]
},
{
@@ -604,67 +641,7 @@
}
],
"source": [
- "UNION(i).(i:0..4|iterate(abl,i)[ {[S]} ]) /\\ seq(Σ)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 62,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "Loaded machine: Grammatik"
- ]
- },
- "execution_count": 62,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "::load\n",
- "MACHINE Grammatik\n",
- "SETS ΣN = {a,b,c, S}\n",
- "CONSTANTS Σ, N, P\n",
- "ABSTRACT_CONSTANTS abl\n",
- "PROPERTIES\n",
- " Σ = {a,b,c} ∧\n",
- " Σ ∩ N = {} ∧\n",
- " Σ ∪ N = ΣN ∧\n",
- " S ∈ N ∧\n",
- " P ⊆ seq1(ΣN) × seq(ΣN) ∧\n",
- " \n",
- " // Die Beispiel Grammatik G1 von den Folien\n",
- " P = { [S] ↦ [],\n",
- " [S] ↦ [a,S,b]\n",
- " }\n",
- " \n",
- " ∧ \n",
- " abl = {u,v | ∃(x,z,p,q).( p↦q ∈ P ∧ u = x^p^z ∧ v = x^q^z )}\n",
- "DEFINITIONS SET_PREF_PP_SEQUENCES == TRUE\n",
- "END"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 63,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "Machine constants set up using operation 0: $setup_constants()"
- ]
- },
- "execution_count": 63,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- ":constants"
+ "UNION(i).(i:0..4|iterate(abl,i)[ {[S]} ]) ∩ seq(Σ)"
]
},
{
@@ -845,6 +822,443 @@
":dot expr_as_graph (\"abl\",SF <| abl |> SF)"
]
},
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Die Grammatik G2 können wir wie folgt umsetzen:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 79,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Loaded machine: Grammatik2"
+ ]
+ },
+ "execution_count": 79,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "::load\n",
+ "MACHINE Grammatik2\n",
+ "SETS ΣN = {a,b,c, S, B,C}\n",
+ "CONSTANTS Σ, N, P\n",
+ "ABSTRACT_CONSTANTS abl\n",
+ "PROPERTIES\n",
+ " Σ = {a,b,c} ∧\n",
+ " Σ ∩ N = {} ∧\n",
+ " Σ ∪ N = ΣN ∧\n",
+ " S ∈ N ∧\n",
+ " P ⊆ seq1(ΣN) × seq(ΣN) ∧\n",
+ " \n",
+ " // Die Beispiel Grammatik G1 von den Folien\n",
+ " P = { [S] ↦ [a,B,C],\n",
+ " [S] ↦ [a,S,B,C],\n",
+ " [C,B] ↦ [B,C],\n",
+ " [a,B] ↦ [a,b],\n",
+ " [b,B] ↦ [b,b],\n",
+ " [b,C] ↦ [b,c],\n",
+ " [c,C] ↦ [c,c]\n",
+ " }\n",
+ " \n",
+ " ∧ \n",
+ " abl = {u,v | ∃(x,z,p,q).( p↦q ∈ P ∧ u = x^p^z ∧ v = x^q^z )}\n",
+ "DEFINITIONS SET_PREF_PP_SEQUENCES == TRUE\n",
+ "END"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 80,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Machine constants set up using operation 0: $setup_constants()"
+ ]
+ },
+ "execution_count": 80,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":constants"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 81,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\{[S],[a,\\mathit{b},c],[a,\\mathit{b},C],[a,\\mathit{S},\\mathit{B},C],[a,\\mathit{B},C],[a,\\mathit{a},\\mathit{b},\\mathit{c},\\mathit{B},C],[a,\\mathit{a},\\mathit{b},\\mathit{C},\\mathit{B},C],[a,\\mathit{a},\\mathit{b},\\mathit{B},\\mathit{C},C],[a,\\mathit{a},\\mathit{B},\\mathit{C},\\mathit{B},C],[a,\\mathit{a},\\mathit{B},\\mathit{B},\\mathit{C},C],[a,\\mathit{a},\\mathit{S},\\mathit{B},\\mathit{C},\\mathit{B},C],[a,\\mathit{a},\\mathit{S},\\mathit{B},\\mathit{B},\\mathit{C},C],[a,\\mathit{a},\\mathit{a},\\mathit{S},\\mathit{B},\\mathit{C},\\mathit{B},\\mathit{B},\\mathit{C},C],[a,\\mathit{a},\\mathit{a},\\mathit{S},\\mathit{B},\\mathit{B},\\mathit{C},\\mathit{C},\\mathit{B},C],[a,\\mathit{a},\\mathit{a},\\mathit{S},\\mathit{B},\\mathit{C},\\mathit{B},\\mathit{C},\\mathit{B},C],[a,\\mathit{a},\\mathit{a},\\mathit{B},\\mathit{B},\\mathit{C},\\mathit{C},\\mathit{B},C],[a,\\mathit{a},\\mathit{a},\\mathit{b},\\mathit{C},\\mathit{B},\\mathit{C},\\mathit{B},C],[a,\\mathit{a},\\mathit{a},\\mathit{B},\\mathit{C},\\mathit{B},\\mathit{B},\\mathit{C},C],[a,\\mathit{a},\\mathit{a},\\mathit{B},\\mathit{C},\\mathit{B},\\mathit{C},\\mathit{B},C],[a,\\mathit{a},\\mathit{a},\\mathit{a},\\mathit{B},\\mathit{C},\\mathit{B},\\mathit{C},\\mathit{B},\\mathit{C},\\mathit{B},C],[a,\\mathit{a},\\mathit{a},\\mathit{a},\\mathit{S},\\mathit{B},\\mathit{C},\\mathit{B},\\mathit{C},\\mathit{B},\\mathit{C},\\mathit{B},C]\\}$"
+ ],
+ "text/plain": [
+ "{[S],[a,b,c],[a,b,C],[a,S,B,C],[a,B,C],[a,a,b,c,B,C],[a,a,b,C,B,C],[a,a,b,B,C,C],[a,a,B,C,B,C],[a,a,B,B,C,C],[a,a,S,B,C,B,C],[a,a,S,B,B,C,C],[a,a,a,S,B,C,B,B,C,C],[a,a,a,S,B,B,C,C,B,C],[a,a,a,S,B,C,B,C,B,C],[a,a,a,B,B,C,C,B,C],[a,a,a,b,C,B,C,B,C],[a,a,a,B,C,B,B,C,C],[a,a,a,B,C,B,C,B,C],[a,a,a,a,B,C,B,C,B,C,B,C],[a,a,a,a,S,B,C,B,C,B,C,B,C]}"
+ ]
+ },
+ "execution_count": 81,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":let SF UNION(i).(i:0..4|iterate(abl,i)[ {[S]} ])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 84,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\{[a,\\mathit{b},c]\\}$"
+ ],
+ "text/plain": [
+ "{[a,b,c]}"
+ ]
+ },
+ "execution_count": 84,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "SF ∩ seq(Σ)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 82,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Preference changed: DOT_DECOMPOSE_NODES = FALSE\n"
+ ]
+ },
+ "execution_count": 82,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":pref DOT_DECOMPOSE_NODES=FALSE"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 83,
+ "metadata": {},
+ "outputs": [
+ {
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+ "</g>\n",
+ "<!-- [S]->[a,B,C] -->\n",
+ "<g id=\"edge44\" class=\"edge\"><title>[S]->[a,B,C]</title>\n",
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+ "</g>\n",
+ "</g>\n",
+ "</svg>"
+ ],
+ "text/plain": [
+ "<Dot visualization: expr_as_graph [SFSF={[S],[a,b,c],[a,b,C],[a,S,B,C],[a,B,C],[a,a,b,c,B,C],[a,a,b,C,B,C],[a,a,b,B,C,C],[a,a,B,C,B,C],[a,a,B,B,C,C],[a,a,S,B,C,B,C],[a,a,S,B,B,C,C],[a,a,a,S,B,C,B,B,C,C],[a,a,a,S,B,B,C,C,B,C],[a,a,a,S,B,C,B,C,B,C],[a,a,a,B,B,C,C,B,C],[a,a,a,b,C,B,C,B,C],[a,a,a,B,C,B,B,C,C],[a,a,a,B,C,B,C,B,C],[a,a,a,a,B,C,B,C,B,C,B,C],[a,a,a,a,S,B,C,B,C,B,C,B,C]}(\"abl\",SF<|abl|>SF)]>"
+ ]
+ },
+ "execution_count": 83,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ ":dot expr_as_graph (\"abl\",SF <| abl |> SF)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 87,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\{[a,\\mathit{b},c],[a,\\mathit{a},\\mathit{b},\\mathit{b},\\mathit{c},c]\\}$"
+ ],
+ "text/plain": [
+ "{[a,b,c],[a,a,b,b,c,c]}"
+ ]
+ },
+ "execution_count": 87,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": []
+ },
{
"cell_type": "code",
"execution_count": null,
--
GitLab