{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------------------------------------------------------------------------\n",
    "\n",
    "Haskell\n",
    "=======\n",
    "\n",
    "Syntactic elements\n",
    "------------------\n",
    "\n",
    "-   A Haskell program (basically) consists of *expressions* and\n",
    "    *declarations*\n",
    "\n",
    "Expressions\n",
    "-----------\n",
    "\n",
    "-   Literals\n",
    "-   Arithmetic expressions\n",
    "-   Function applications\n",
    "-   Conditionals\n",
    "-   Identifiers (names)\n",
    "\n",
    "Declarations\n",
    "------------\n",
    "\n",
    "-   Bind expressions to names\n",
    "-   Use the operator `=`\n",
    "-   Top-level bindings\n",
    "-   Local bindings\n",
    "\n",
    "------------------------------------------------------------------------\n",
    "\n",
    "Expressions\n",
    "===========\n",
    "\n",
    "Literals\n",
    "--------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "42\n",
    "\"Arthur Dent\"\n",
    "[1, 2, 3]\n",
    "(42, \"fortytwo\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Evaluates to the value itself\n",
    "\n",
    "Arithmetic\n",
    "----------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "(1 + 2) * 3\n",
    "3.14 * 2 * 17\n",
    "3^2 + 4^2 == 5^2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Evaluates to the result of the operation\n",
    "\n",
    "Function invocation\n",
    "-------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "max 23 42\n",
    "length [1, 2, 3]\n",
    "triple 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Evaluates to the function value returned\n",
    "\n",
    "------------------------------------------------------------------------\n",
    "\n",
    "Declarations\n",
    "============\n",
    "\n",
    "Bind expressions\n",
    "----------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "answer = 42\n",
    "crew = [\"Kirk\", \"Spock\", \"McCoy\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-   Value `42` is bound to name `answer`\n",
    "-   List of crew members is bound to name `crew`\n",
    "-   Identifiers `answer` and `crew` can be used in other expression\n",
    "-   They evaluate to the bound values\n",
    "\n",
    "Bind functions\n",
    "--------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "triple x = x + x + x\n",
    "hello name = \"Hello \" ++ name"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-   Functions of one parameter are bound to names `triple` and `hello`\n",
    "-   Functions `triple` and `hello` can be invoked in other expressions\n",
    "-   They evaluate to the computed function value\n",
    "\n",
    "------------------------------------------------------------------------\n",
    "\n",
    "Special expression syntax\n",
    "=========================\n",
    "\n",
    "Conditional `if` expression\n",
    "---------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = 1\n",
    "if x < 2 then \"Smaller than two\" else \"Bigger than 2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`if` expression in a function declaration\n",
    "-----------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "max a b = if a > b then a else b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------------------------------------------------------------------------\n",
    "\n",
    "Function declaration\n",
    "====================\n",
    "\n",
    "3 Examples\n",
    "----------\n",
    "\n",
    "``` {.haskell}\n",
    "seven = 7\n",
    "triple x = x + x + x\n",
    "max a b = if a > b then a else b\n",
    "```\n",
    "\n",
    "Components\n",
    "----------\n",
    "\n",
    "-   Function names (`seven`, `triple`, `max`)\n",
    "-   Zero or more function parameters (`a`, `b`, `x`)\n",
    "-   Function expression with identifiers bound to the function\n",
    "    parameters\n",
    "\n",
    "Function and parameter names\n",
    "----------------------------\n",
    "\n",
    "-   Must start with a *lower-case* character\n",
    "-   Consist of *alpha-numeric* characters only\n",
    "\n",
    "------------------------------------------------------------------------\n",
    "\n",
    "Function example\n",
    "================\n",
    "\n",
    "Consider these expressions\n",
    "--------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "label": "Haskell"
   },
   "outputs": [],
   "source": [
    "3.141 * 5 * 5\n",
    "3.141 * 42 * 42\n",
    "3.141 * 17 * 17"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Try to abstract that into a function\n",
    "------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "label": "Haskell"
   },
   "outputs": [],
   "source": [
    "circleArea r = 3.141 * r ^ 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------------------------------------------------------------------------\n",
    "\n",
    "Recursive operations on lists\n",
    "=============================\n",
    "\n",
    "Task: Calculate the arithmetic mean of a list of numbers\n",
    "--------------------------------------------------------\n",
    "\n",
    "$$\n",
    "\\bar{x} = \\frac{1}{n}\\left (\\sum_{i=1}^n{x_i}\\right ) = \\frac{x_1+x_2+\\cdots +x_n}{n}\n",
    "$$\n",
    "\n",
    "The mean function\n",
    "-----------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "label": "Haskell"
   },
   "outputs": [],
   "source": [
    "mean list = totalSum list / count list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Now implement `count` and `totalSum`]{.fragment}\n",
    "\n",
    "------------------------------------------------------------------------\n",
    "\n",
    "Recursive operations on lists\n",
    "=============================\n",
    "\n",
    "Task: Calculate the number of elements in a list\n",
    "------------------------------------------------\n",
    "\n",
    "The function `count`\n",
    "--------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "label": "Haskell"
   },
   "outputs": [],
   "source": [
    "count list =\n",
    "  if null list\n",
    "    then 0\n",
    "    else 1 + count (tail list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------------------------------------------------------------------------\n",
    "\n",
    "Recursive operations on lists\n",
    "=============================\n",
    "\n",
    "Task: Calculate the sum of elements in a list of numbers\n",
    "--------------------------------------------------------\n",
    "\n",
    "The function `totalSum`\n",
    "-----------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "label": "Haskell"
   },
   "outputs": [],
   "source": [
    "totalSum list =\n",
    "  if null list \n",
    "    then 0\n",
    "    else head list + totalSum (tail list)"
   ]
  }
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