05 - Boolean Values and Operators.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Boolean Values and Boolean Operators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The three basic boolean operators are `and`, `or` and `not`. There are others, but for now let's stick to these three."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should already know how these work in languages such as Java.\n",
    "\n",
    "The `and` and `or` operators are **binary** operators (they take two operands), while `not` is a **unary** operator (it only has one operand).\n",
    "\n",
    "In all cases, the operands are boolean values, and return a boolean value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 1,
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     "output_type": "execute_result"
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   ],
   "source": [
    "True or False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "True and False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "not True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So Python works the same way when the operands are boolean types, for example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 10\n",
    "b = 5\n",
    "\n",
    "a > b and not(a == b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But Python can actually handle non-boolean operands too!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Python **every** object has an **associated truth value** - often referred to as the **truthyness** of the object.\n",
    "\n",
    "By default, any non-zero number is considered `True`, while any zero number is considered `False`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(False, True, True, True)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bool(0), bool(-1), bool(1), bool(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `None` object is always considered `False`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bool(None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Empty container types are considered falsy, while non-empty containers are considered truthy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(False, True)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bool([]), bool([0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bool({})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bool({'a': 1})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since strings are container types, the same holds for strings - empty strings are considered falsy, and truthy otherwise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(False, True)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bool(''), bool('a')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that if a container contains any item, even other empty containers, it is still considered truthy (it contains something):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(True, True)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bool(['']), bool([()])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we understand associated truth values, we can start to understand how the `and` and `or` operators actually work in Python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start with the `or` operator and think of short-circuit evaluation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the expression `a or b`, if `a` is `True`, then there is no need to evaluate `b`, since the result ius always `True`. So, with plain boolean values, if `a` is `True`, immediately return `True`. On the other hand, if `a` is `False`, then the result of the operation **must** rely on whether `b` is `True` or `False`, and in fact the result of the calculation is `b` itself (`True` or `False`).\n",
    "\n",
    "So, for `a or b`, return `a` if `a` is `True`, otherwise return `b`.\n",
    "\n",
    "And that's exactly how Python handles non-boolean values - it looks at the truthyness of `a` and `b` and returns `a` if `a` is *truthy*, otherwise it returns `b`.\n",
    "\n",
    "Let's look at some examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(True, 10, True)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "True or False, 10 or 0, bool(10 or 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(True, 10, True)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "False or True, 0 or 10, bool(0 or 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(False, 0, False)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "False or False, 0 or 0, bool(0 or 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the same works with other objects too:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'test'"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'test' or 'N/A'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'N/A'"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'' or 'N/A'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1, 2] or 'empty'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'empty'"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[] or 'empty'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Something similar happens with `and`.\n",
    "\n",
    "Again let's examine it in the context of shorty circuiting:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For `a and b`, \n",
    "- if `a` is `False`, then the result is always `False`, so just return `False` (`a`) right away\n",
    "- if `a` is `True`, then the result depends entirely on `b` - return `True` if `b` id `True` and `False` if `b` is `False`\n",
    "\n",
    "In other words:\n",
    "- if `a` is `False`, return `a`\n",
    "- if `a` is `True`, return `b`\n",
    "\n",
    "Of course, with associated truth values, Python can now handle non-boolean operands:\n",
    "- return `a` if `a` is falsy\n",
    "- return `b` if `a` is truthy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are some examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(False, '', False)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "False and True, '' and 'abc', bool('' and 'abc')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(False, [], False)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "False and False, [] and '', bool([] and '')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(True, 'abc', True)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "True and True, 100 and 'abc', bool(100 and 'abc')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(False, '', False)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "True and False, 100 and '', bool(100 and '')"
   ]
  }
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