From 870bdff6cb4b12ca5131e0b644c806f9fef43042 Mon Sep 17 00:00:00 2001
From: Michael Leuschel <leuschel@uni-duesseldorf.de>
Date: Tue, 15 Oct 2024 13:36:51 +0200
Subject: [PATCH] add more examples and an image
---
logic_programming/2_IntroProlog.ipynb | 567 ++++++++++++++++++--------
logic_programming/img/simple_tree.png | Bin 0 -> 17748 bytes
2 files changed, 395 insertions(+), 172 deletions(-)
create mode 100644 logic_programming/img/simple_tree.png
diff --git a/logic_programming/2_IntroProlog.ipynb b/logic_programming/2_IntroProlog.ipynb
index ffca183..06d4722 100644
--- a/logic_programming/2_IntroProlog.ipynb
+++ b/logic_programming/2_IntroProlog.ipynb
@@ -786,6 +786,15 @@
"?- edge(A,B,C)."
]
},
+ {
+ "cell_type": "markdown",
+ "id": "c137912e",
+ "metadata": {},
+ "source": [
+ "By calling jupyter:print_transition_graph(PredSpec, FromIdx, ToIdx, LabelIdx),\n",
+ "a transition graph can be created (FromIdx is the number of argument specifying the origin, ToIdx the destination and LabelIdx the label)."
+ ]
+ },
{
"cell_type": "code",
"execution_count": 68,
@@ -1213,64 +1222,14 @@
},
{
"cell_type": "code",
- "execution_count": 73,
+ "execution_count": 44,
"id": "12f78859",
"metadata": {
"vscode": {
"languageId": "prolog"
}
},
- "outputs": [
- {
- "data": {
- "text/html": [
- "\n",
- " <style>\n",
- " details {\n",
- " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
- " }\n",
- "\n",
- " details > summary {\n",
- " cursor: pointer;\n",
- " }\n",
- " </style>\n",
- " <details><summary>Previously defined clauses of user:edge/2 were retracted (click to expand)</summary><pre>:- dynamic edge/2.\n",
- "\n",
- "edge(a, b).\n",
- "edge(a, c).\n",
- "edge(b, d).\n",
- "edge(c, d).\n",
- "edge(d, e).\n",
- "edge(f, g).\n",
- "</pre></details>"
- ],
- "text/plain": [
- "Previously defined clauses of user:edge/2 were retracted:\n",
- ":- dynamic edge/2.\n",
- "\n",
- "edge(a, b).\n",
- "edge(a, c).\n",
- "edge(b, d).\n",
- "edge(c, d).\n",
- "edge(d, e).\n",
- "edge(f, g).\n"
- ]
- },
- "metadata": {
- "application/json": {}
- },
- "output_type": "display_data"
- },
- {
- "data": {
- "text/plain": [
- "% Asserting clauses for user:edge/2\n"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "outputs": [],
"source": [
"edge(a,b). edge(a,c).\n",
"edge(b,d). edge(c,d).\n",
@@ -1288,7 +1247,7 @@
},
{
"cell_type": "code",
- "execution_count": 74,
+ "execution_count": 45,
"id": "99bfae95",
"metadata": {
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@@ -1418,6 +1377,28 @@
"jupyter:print_transition_graph(edge/2, 1, 2,0)."
]
},
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "b400c8fa",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[1;31mERROR: call/1: Unknown procedure: jupyter:print_transition_graph/1\n",
+ "ERROR: However, there are definitions for:\n",
+ "ERROR: jupyter:print_transition_graph/4\n"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "jupyter:print_transition_graph(edge/2)."
+ ]
+ },
{
"cell_type": "code",
"execution_count": 75,
@@ -2191,126 +2172,321 @@
},
{
"cell_type": "code",
- "execution_count": 86,
+ "execution_count": 13,
"id": "d4664fd8",
"metadata": {
"vscode": {
"languageId": "prolog"
}
},
+ "outputs": [],
+ "source": [
+ "\n",
+ "construct(Name,Department,employe(Name,Department)).\n",
+ "\n",
+ "get_name(employe(Name,_),Name).\n",
+ "get_dept(employe(_,Dept),Dept)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "id": "08715fa2",
+ "metadata": {
+ "vscode": {
+ "languageId": "prolog"
+ }
+ },
"outputs": [
{
"data": {
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- "\n",
- " <style>\n",
- " details {\n",
- " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
- " }\n",
- "\n",
- " details > summary {\n",
- " cursor: pointer;\n",
- " }\n",
- " </style>\n",
- " <details><summary>Previously defined clauses of user:construct/3 were retracted (click to expand)</summary><pre>:- dynamic construct/3.\n",
- "\n",
- "construct(A, B, employe(A, B)).\n",
- "</pre></details>"
- ],
"text/plain": [
- "Previously defined clauses of user:construct/3 were retracted:\n",
- ":- dynamic construct/3.\n",
- "\n",
- "construct(A, B, employe(A, B)).\n"
+ "\u001b[1mE1 = employe(peter,cs),\n",
+ "E2 = employe(mary,cs),\n",
+ "N1 = peter,\n",
+ "D2 = cs"
]
},
- "metadata": {
- "application/json": {}
- },
+ "metadata": {},
"output_type": "display_data"
- },
+ }
+ ],
+ "source": [
+ "?- construct(peter,cs,E1), construct(mary,cs,E2), get_name(E1,N1), get_dept(E2,D2)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "43452d97",
+ "metadata": {},
+ "source": [
+ "Let us work out a small database example using such compound terms for data abstraction:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "id": "e9ff8860",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "% Facts for courses with time slot and location:\n",
+ "course(logic_programming,time(tuesday,1430,1600),location(25,'5F')).\n",
+ "course(sks,time(monday,1430,1600),location(25,'5G')).\n",
+ "course(drones,time(thursday,1430,1600),location(25,'12.O2.55')).\n",
+ "course(navigating_tomorrow,time(thursday,1430,1600),location(25,'12.O2.21')).\n",
+ "% separate facts about which programme the courses belong to (can be multiple):\n",
+ "programme(logic_programming,bachelor_cs).\n",
+ "programme(logic_programming,master_dsai).\n",
+ "programme(sks,master_cs).\n",
+ "programme(navigating_tomorrow,bachelor_cs).\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3dc100cb",
+ "metadata": {},
+ "source": [
+ "Let us try and write a predicate for:\n",
+ "- which courses take place on a particular day\n",
+ "- which courses take place in a particular building (e.g., 25)\n",
+ "- which courses are available for multiple programmes\n",
+ "- which courses are in conflict (time-wise)\n",
+ "- on which days there are courses a given programme (e.g., bachelor_cs)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "fbed4b05",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "7f506936",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c34b9d8c",
+ "metadata": {},
+ "source": [
+ "Here is a solution. You will see that the compound term encoding of times and buildings\n",
+ "has some advantages and drawbacks over a flatter representation such as course/6 with 6 arguments:\n",
+ "```\n",
+ "course(logic_programming,tuesday,1430,1600,25,'5F').\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "id": "74a9e660",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "day(Lect,Day) :- course(Lect,time(Day,_,_),_).\n",
+ "building(Lect,Bldg) :- course(Lect,_,location(Bldg,_)).\n",
+ "multi(Lect) :- course(Lect,_,_), programme(Lect,P1), programme(Lect,P2), P1\\=P2.\n",
+ "conflict(L1,L2) :- course(L1,T,_), course(L2,T,_), L1\\=L2.\n",
+ "lecture_day(Day,Progr) :- course(L1,time(Day,_,_),_), programme(L1,Progr)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "id": "3cddfd08",
+ "metadata": {},
+ "outputs": [
{
"data": {
"text/plain": [
- "% Asserting clauses for user:construct/3\n"
+ "\u001b[1mL = logic_programming"
]
},
"metadata": {},
"output_type": "display_data"
- },
+ }
+ ],
+ "source": [
+ "?- multi(L)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "id": "9271f0d7",
+ "metadata": {},
+ "outputs": [
{
"data": {
- "text/html": [
- "\n",
- " <style>\n",
- " details {\n",
- " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
- " }\n",
- "\n",
- " details > summary {\n",
- " cursor: pointer;\n",
- " }\n",
- " </style>\n",
- " <details><summary>Previously defined clauses of user:get_name/2 were retracted (click to expand)</summary><pre>:- dynamic get_name/2.\n",
- "\n",
- "get_name(employe(A, _), A).\n",
- "</pre></details>"
- ],
"text/plain": [
- "Previously defined clauses of user:get_name/2 were retracted:\n",
- ":- dynamic get_name/2.\n",
- "\n",
- "get_name(employe(A, _), A).\n"
+ "\u001b[1mX = drones,\n",
+ "Y = navigating_tomorrow"
]
},
- "metadata": {
- "application/json": {}
- },
+ "metadata": {},
"output_type": "display_data"
- },
+ }
+ ],
+ "source": [
+ "?- conflict(X,Y)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "id": "d7b8619e",
+ "metadata": {},
+ "outputs": [
{
"data": {
"text/plain": [
- "% Asserting clauses for user:get_name/2\n"
+ "\u001b[1mL = [tuesday,thursday]"
]
},
"metadata": {},
"output_type": "display_data"
- },
+ }
+ ],
+ "source": [
+ "?- findall(D,lecture_day(D,bachelor_cs),L)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e2ed5de7",
+ "metadata": {},
+ "source": [
+ "## Peano Arithmetic\n",
+ "\n",
+ "The arguments to a functor can in term also make use of a functor.\n",
+ "\n",
+ "We can also use functors of arity 1. (Functors of arity 0 are simply constants, i.e., atoms in Prolog terminology.)\n",
+ "This can be used to represent natural numbers:\n",
+ "- we can represent zero using the atom `zero/0`\n",
+ "- we can represent the successor of a number using a functor `s/1` \n",
+ "\n",
+ "Thus the number 1 is represented by the term `s(zero)` and the number 2 by `s(s(zero))`.\n",
+ "\n",
+ "How could one write predicates to check if a term is a valid natural number in that representation?\n",
+ "E.g., `s(zero)` is valid, `s(a)` is not.\n",
+ "How could one write addition and multiplication predicate to add or multiply two numbers?\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "7d1a7bf2",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "1735fe4c",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "id": "dbc89f40",
+ "metadata": {},
+ "source": [
+ "A possible solution is this one.\n",
+ "This is also called Peano arithmetic. Note, that contrary to built-in arithmetic (using is/2), these predicates are reversible"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 38,
+ "id": "d44c70af",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "nat(zero).\n",
+ "nat(s(X)) :- nat(X).\n",
+ "\n",
+ "plus(zero,X,X).\n",
+ "plus(s(X),Y,s(Z)) :- plus(X,Y,Z).\n",
+ "\n",
+ "mult(zero,_,zero).\n",
+ "mult(s(X),Y,Z) :- mult(X,Y,XY), plus(Y,XY,Z). % (x+1)*y = x*y + y\n",
+ "\n",
+ "exp(zero,s(_),zero).\n",
+ "exp(s(_),zero,s(zero)).\n",
+ "exp(Y,s(X),Z) :- exp(Y,X,YX), mult(YX,Y,Z)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 39,
+ "id": "6e96b7aa",
+ "metadata": {},
+ "outputs": [
{
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- " details {\n",
- " font-family: Menlo, Consolas, 'DejaVu Sans Mono', monospace; font-size: 13px;\n",
- " }\n",
- "\n",
- " details > summary {\n",
- " cursor: pointer;\n",
- " }\n",
- " </style>\n",
- " <details><summary>Previously defined clauses of user:get_dept/2 were retracted (click to expand)</summary><pre>:- dynamic get_dept/2.\n",
- "\n",
- "get_dept(employe(_, A), A).\n",
- "</pre></details>"
- ],
"text/plain": [
- "Previously defined clauses of user:get_dept/2 were retracted:\n",
- ":- dynamic get_dept/2.\n",
- "\n",
- "get_dept(employe(_, A), A).\n"
+ "\u001b[1mR = s(s(s(zero)))"
]
},
- "metadata": {
- "application/json": {}
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "?-plus(s(s(zero)),s(zero),R)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 40,
+ "id": "d119214f",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[1mR = s(s(s(s(s(s(zero))))))"
+ ]
},
+ "metadata": {},
"output_type": "display_data"
- },
+ }
+ ],
+ "source": [
+ "?-mult(s(s(zero)),s(s(s(zero))),R)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 41,
+ "id": "b3c9b644",
+ "metadata": {},
+ "outputs": [
{
"data": {
"text/plain": [
- "% Asserting clauses for user:get_dept/2\n"
+ "\u001b[1mR = s(s(s(s(s(s(s(s(zero))))))))"
]
},
"metadata": {},
@@ -2318,30 +2494,39 @@
}
],
"source": [
- "\n",
- "construct(Name,Department,employe(Name,Department)).\n",
- "\n",
- "get_name(employe(Name,_),Name).\n",
- "get_dept(employe(_,Dept),Dept)."
+ "?-exp(s(s(zero)),s(s(s(zero))),R)."
]
},
{
"cell_type": "code",
- "execution_count": 87,
- "id": "08715fa2",
- "metadata": {
- "vscode": {
- "languageId": "prolog"
+ "execution_count": 42,
+ "id": "e61cc47b",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[1mX = s(zero)"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
}
- },
+ ],
+ "source": [
+ "?-plus(X,s(zero),s(s(zero)))."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "id": "747d23d1",
+ "metadata": {},
"outputs": [
{
"data": {
"text/plain": [
- "\u001b[1mE1 = employe(a,cs),\n",
- "E2 = employe(b,cs),\n",
- "N1 = a,\n",
- "D2 = cs"
+ "\u001b[1mX = s(s(zero))"
]
},
"metadata": {},
@@ -2349,21 +2534,24 @@
}
],
"source": [
- "?- construct(a,cs,E1), construct(b,cs,E2), get_name(E1,N1), get_dept(E2,D2)."
+ "?-mult(X,s(zero),s(s(zero)))."
]
},
{
"cell_type": "markdown",
- "id": "e2ed5de7",
+ "id": "15942ef6",
"metadata": {},
"source": [
- "The arguments to a functor can in term also make use of a functor.\n",
+ "## Recursive Data Structures\n",
+ "\n",
+ "Compound terms can be used the represent complex data structures, as will see below.\n",
+ "First, think on how one could represent a list of objects, say a list of length 2 containing `a` and `b`.\n",
"\n",
- "One could thus for example represent a list in Prolog by using\n",
+ "One could for example represent a list in Prolog by using\n",
"a functor `cons/2` to denote a non-empty list and `nil/0` to denote\n",
"an empty list.\n",
- "Note that a functor of arity 0 is simply a constant (aka atom in Prolog).\n",
- "So a list of length two with a and b as elements is represented as follows:"
+ "(Remember, a functor of arity 0 is simply a constant (aka atom in Prolog).)\n",
+ "So a list of length two with a and b as elements can be represented as follows:"
]
},
{
@@ -2826,6 +3014,30 @@
"?- last0(X,cons(a,cons(b,nil)))."
]
},
+ {
+ "cell_type": "markdown",
+ "id": "34c38129",
+ "metadata": {},
+ "source": [
+ "Exercise: write predicates prefix/2 and suffix/2 which is true if the first argument is a prefix or suffix of the second one."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "9a65d023",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "df88c4bd",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
{
"cell_type": "markdown",
"id": "5f251e4d",
@@ -2839,7 +3051,10 @@
"- the left sub-tree\n",
"- the information at the root of the tree\n",
"- the right sub-tree\n",
- "We also need the empty tree, which we represent by `nil`."
+ "We also need the empty tree, which we represent by `nil`.\n",
+ "\n",
+ "For example, how would you represent this tree:\n",
+ ""
]
},
{
@@ -2866,6 +3081,14 @@
"?- Mytree = tree( tree(nil,a,nil), b, tree(nil,c,tree(nil,d,nil)))."
]
},
+ {
+ "cell_type": "markdown",
+ "id": "8ac0d99f",
+ "metadata": {},
+ "source": [
+ "Let us now try to write a predicate which reverses (mirrors) the tree, swapping left and right children:"
+ ]
+ },
{
"cell_type": "code",
"execution_count": 104,
diff --git a/logic_programming/img/simple_tree.png b/logic_programming/img/simple_tree.png
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GitLab