{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Haskell exercise sheet 2\n",
    "\n",
    "## Basic list processing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Functions on lists\n",
    "\n",
    "Implement some general functions on lists such that the following expressions evaluate to `True`. Some of them can be found in the Prelude. Of course, do not use them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "myLast ['a', 'b', 'c', 'd'] == 'd'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "myElementAt ['a', 'b', 'c', 'd'] 1 == 'b'\n",
    "myElementAt ['a', 'b', 'c', 'd'] 2 == 'c'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate a list\n",
    "\n",
    "Use a list as an accumulator to build up the list by prepending elements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "myRange 0 3 == [0, 1, 2, 3]\n",
    "myRange 5 12 == [5, 6, 7, 8, 9, 10, 11, 12]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "myDuplicate ['a', 'b', 'c'] == ['a', 'a', 'b', 'b', 'c', 'c']\n",
    "myDuplicate [1, 2, 3] == [1, 1, 2, 2, 3, 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "myMulticate ['a', 'b', 'c'] 2 == ['a', 'a', 'b', 'b', 'c', 'c']\n",
    "myMulticate [1, 2, 3] 3 == [1, 1, 1, 2, 2, 2, 3, 3, 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "myEven [5, 6, 7, 8, 9, 10, 11, 12] == [6, 8, 10, 12]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mySplitAt [5, 6, 7, 8, 9, 10, 11, 12] 3 = ([5, 6, 7], [8, 9, 10, 11, 12])\n",
    "mySplitAt ['a', 'b', 'c', 'd'] 2 == (['a', 'b'], ['c', 'd'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Query a list\n",
    "\n",
    "Consider the following list of numbers and write functions that answer a few questions about the numbers in that list. Do not use existing functions from the Prelude, except `head`, `tail` and `(:)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "z = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How many numbers are greater than five?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the smallest number greater than 5?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the average value of the numbers that come after a 5?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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