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Commit e2fbc7f9 authored by Christoph Ruegge's avatar Christoph Ruegge
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Pipe all notebooks through clean filter

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exercises/02 first steps_exercise.ipynb
View file @ e2fbc7f9
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Exercises 02\n",
"## problem 1\n",
"\n",
"- start the notebook\n",
"- evaluate $2^{16}$\n",
"- write a statement which checks if $2^{23} - 1000$ is greater than $2^{22.9999}$ (what is the difference between `**` and `^`?)\n",
"- is $23 \\cdot 5 > 45 \\wedge ( 169/3 = 56 \\vee 4 = (53\\cdot3) \\% 5 )$ true or false?"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 2\n",
"\n",
"\n",
"write an own function `tenfoldIfLess30`, which multiplies numbers under 30 with 10. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 3\n",
"\n",
"Write a function `divbl2or3` which returns `True` for numbers which are dividable by 2 or 3 and `False` otherwise. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 4\n",
"\n",
"implement the following functions:\n",
"\n",
"$f : \\mathbb{N}^3 \\to \\mathbb{N}$ with $f(x,y,z)= (x+y+z)/3$\n",
"\n",
"$g : \\mathbb{N}^3 \\to \\mathbb{N}$ with $g(a,b,c)=\\begin{cases}a :\\quad a > b,c\\\\b :\\quad b > a,c\\\\c : \\quad c \\geq a,b\\end{cases}$\n",
"\n",
"$h : \\mathbb{N}^2 \\to \\mathbb{N}$ with $h(i,j)=\\begin{cases}i :\\quad j=0\\\\ succ(h(i,j-1)) : \\quad otherwise\\end{cases}$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 5\n",
"\n",
"- write your own implementation of `even'.\n",
"- Look up `even` in _Hoogle_ (<http://www.haskell.org/hoogle/>) and/or\n",
"\t_Hayoo!_ (<http://hayoo.fh-wedel.de/>) (`rem` is aquivalent to `mod` for positive numbers).\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 6\n",
"\n",
"the imaginary weather prediction module `Magic.Weather.Prediction` creates the variables \n",
"\n",
"\trainy :: Bool\n",
"\tcold :: Bool\n",
"\twindy :: Bool\n",
"\n",
"(assume that they are filled)\n",
"\n",
"Use `if ... then ... else` (and boolean operators) to return the following strings:\n",
"\n",
"- \"fly kites\" _(when windy but not rainy)_\n",
"- \"take your umbrella\"\t_(when rainy but not cold)_\n",
"- \"sit at the fireplace\" _(when rainy and cold)_\n",
"- \"enjoy the sun\" _(when not rainy or windy)_\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 7\n",
"\n",
"Brackets get very expensive. Try to reduce the number of brackets via using of the application operator `$` from the following expressions:\n",
"\n",
"- `max 23 (max 5 39)`\n",
"- `max 23 (5 * (succ 4))`\n",
"- `mod 23 (min 7 ((*) 2 3))`\n",
"- `min (max 23 44) (max 5 (negate (-39)))`\n",
"\n",
"Which brackets are redundant anyway? \n",
"Which expression is an identity?"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Haskell",
"language": "haskell",
"name": "haskell"
},
"language_info": {
"codemirror_mode": "ihaskell",
"file_extension": ".hs",
"name": "haskell",
"version": "7.10.3"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
\ No newline at end of file
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Exercises 02\n",
"## problem 1\n",
"\n",
"- start the notebook\n",
"- evaluate $2^{16}$\n",
"- write a statement which checks if $2^{23} - 1000$ is greater than $2^{22.9999}$ (what is the difference between `**` and `^`?)\n",
"- is $23 \\cdot 5 > 45 \\wedge ( 169/3 = 56 \\vee 4 = (53\\cdot3) \\% 5 )$ true or false?"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 2\n",
"\n",
"\n",
"write an own function `tenfoldIfLess30`, which multiplies numbers under 30 with 10. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 3\n",
"\n",
"Write a function `divbl2or3` which returns `True` for numbers which are dividable by 2 or 3 and `False` otherwise. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 4\n",
"\n",
"implement the following functions:\n",
"\n",
"$f : \\mathbb{N}^3 \\to \\mathbb{N}$ with $f(x,y,z)= (x+y+z)/3$\n",
"\n",
"$g : \\mathbb{N}^3 \\to \\mathbb{N}$ with $g(a,b,c)=\\begin{cases}a :\\quad a > b,c\\\\b :\\quad b > a,c\\\\c : \\quad c \\geq a,b\\end{cases}$\n",
"\n",
"$h : \\mathbb{N}^2 \\to \\mathbb{N}$ with $h(i,j)=\\begin{cases}i :\\quad j=0\\\\ succ(h(i,j-1)) : \\quad otherwise\\end{cases}$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 5\n",
"\n",
"- write your own implementation of `even'.\n",
"- Look up `even` in _Hoogle_ (<http://www.haskell.org/hoogle/>) and/or\n",
"\t_Hayoo!_ (<http://hayoo.fh-wedel.de/>) (`rem` is aquivalent to `mod` for positive numbers).\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 6\n",
"\n",
"the imaginary weather prediction module `Magic.Weather.Prediction` creates the variables \n",
"\n",
"\trainy :: Bool\n",
"\tcold :: Bool\n",
"\twindy :: Bool\n",
"\n",
"(assume that they are filled)\n",
"\n",
"Use `if ... then ... else` (and boolean operators) to return the following strings:\n",
"\n",
"- \"fly kites\" _(when windy but not rainy)_\n",
"- \"take your umbrella\"\t_(when rainy but not cold)_\n",
"- \"sit at the fireplace\" _(when rainy and cold)_\n",
"- \"enjoy the sun\" _(when not rainy or windy)_\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 7\n",
"\n",
"Brackets get very expensive. Try to reduce the number of brackets via using of the application operator `$` from the following expressions:\n",
"\n",
"- `max 23 (max 5 39)`\n",
"- `max 23 (5 * (succ 4))`\n",
"- `mod 23 (min 7 ((*) 2 3))`\n",
"- `min (max 23 44) (max 5 (negate (-39)))`\n",
"\n",
"Which brackets are redundant anyway? \n",
"Which expression is an identity?"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Haskell",
"language": "haskell",
"name": "haskell"
},
"language_info": {
"codemirror_mode": "ihaskell",
"file_extension": ".hs",
"name": "haskell",
"version": "7.10.3"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
exercises/03 lists and tuples_exercise.ipynb
View file @ e2fbc7f9
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Exercises 03\n",
"\n",
"## problem 1\n",
"\n",
"```haskell\n",
" alphabet = ['a'..'z']\n",
"```\n",
"\n",
"get the following information from `alphabet`:\n",
"\n",
"- length\n",
"- first 3 characters\n",
"- the 12th character\n",
"- the 7-10th character\n",
"- the last 5 characters\n",
"\n",
"and then create an `aLPHABET` with upper case characters and add it to the existing one\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 2\n",
"implement a function `hasVowel` which checks if a string contains a vowel character. Test the function with \"foo\", \"bar\" and \"bz\".\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 3\n",
"\n",
"use list comprehensions for creating the following sets in haskell\n",
"\n",
"\n",
"- $A = \\{ x \\,:\\, x \\in \\mathbb{N},\\, x \\text{ odd}\\}$ (only showing the first 5 elements)\n",
"- $B = \\{ -x \\,:\\, x \\in \\mathbb{N},\\, 3|x ,\\, x < 10\\}$ ($3|x$ : 3 is a divisor of x)\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 4 \n",
"\n",
"Create the set of all odd numbers smaller than 500, which are dividable through 5 and 7.\n",
"\n",
"$S=\\{x : x \\neq 0 \\land 5|x \\land 7|x\\}$\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# problem 5\n",
"\n",
"Let $A=\\{1,2,3\\}$, $B=\\{3,4,5\\}$. Calculate the intersection and the union of $A$ and $B$."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 6\n",
"\n",
"Let `less` and `greater` be functions which have a value `v` and a list of values `l` of the same type as `v`. Return a list of all values which are less or greater as `v`.\n",
"\n",
"$\\text{less}(v,l) = \\{x : x \\in l, x < v\\}$\n",
"\n",
"Implement the functions using list comprehensions.\n",
"\n",
"Test: `5 [1..10]`\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 7\n",
"\n",
"the list generated with `[0.1,0.3..0.9]` has problems with precision (has roundingerror). Do it better via using list comprehensions. (Tip: ranges of integral types do not have rounding errors).\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Haskell",
"language": "haskell",
"name": "haskell"
},
"language_info": {
"codemirror_mode": "ihaskell",
"file_extension": ".hs",
"name": "haskell",
"version": "7.10.3"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
\ No newline at end of file
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Exercises 03\n",
"\n",
"## problem 1\n",
"\n",
"```haskell\n",
" alphabet = ['a'..'z']\n",
"```\n",
"\n",
"get the following information from `alphabet`:\n",
"\n",
"- length\n",
"- first 3 characters\n",
"- the 12th character\n",
"- the 7-10th character\n",
"- the last 5 characters\n",
"\n",
"and then create an `aLPHABET` with upper case characters and add it to the existing one\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 2\n",
"implement a function `hasVowel` which checks if a string contains a vowel character. Test the function with \"foo\", \"bar\" and \"bz\".\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 3\n",
"\n",
"use list comprehensions for creating the following sets in haskell\n",
"\n",
"\n",
"- $A = \\{ x \\,:\\, x \\in \\mathbb{N},\\, x \\text{ odd}\\}$ (only showing the first 5 elements)\n",
"- $B = \\{ -x \\,:\\, x \\in \\mathbb{N},\\, 3|x ,\\, x < 10\\}$ ($3|x$ : 3 is a divisor of x)\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## problem 4 \n",
"\n",
"Create the set of all odd numbers smaller than 500, which are dividable through 5 and 7.\n",
"\n",
"$S=\\{x : x \\neq 0 \\land 5|x \\land 7|x\\}$\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# problem 5\n",
"\n",
"Let $A=\\{1,2,3\\}$, $B=\\{3,4,5\\}$. Calculate the intersection and the union of $A$ and $B$."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false