{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Examples (and some documentation) for the Words in the Library"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stack Chatter\n",
    "This is what I like to call the functions that just rearrange things on the stack.  (One thing I want to mention is that during a hypothetical compilation phase these \"stack chatter\" words effectively disappear, because we can map the logical stack locations to registers that remain static for the duration of the computation.  This remains to be done but it's \"off the shelf\" technology.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `clear`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 1 3 1 2 3"
     ]
    }
   ],
   "source": [
    "1 2 3 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    }
   ],
   "source": [
    "clear"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `dup` `dupd`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 3 3"
     ]
    }
   ],
   "source": [
    "1 2 3 dup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    }
   ],
   "source": [
    "clear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 2 3"
     ]
    }
   ],
   "source": [
    "1 2 3 dupd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    }
   ],
   "source": [
    "clear"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `enstacken` `disenstacken` `stack` `unstack`\n",
    "\n",
    "Replace the stack with a quote of itself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 2 1]"
     ]
    }
   ],
   "source": [
    "1 2 3 enstacken"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    }
   ],
   "source": [
    "clear"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unpack a list onto the stack."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4 5 6 [3 2 1] unstack"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get the stack on the stack."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 3 [3 2 1]"
     ]
    }
   ],
   "source": [
    "1 2 3 stack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    }
   ],
   "source": [
    "clear"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Replace the stack with the list on top.\n",
    "The items appear reversed but they are not,\n",
    "is on the top of both the list and the stack."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6 5 4"
     ]
    }
   ],
   "source": [
    "1 2 3 [4 5 6] disenstacken"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `pop` `popd` `popop`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 2 3 pop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 3"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 2 3 popd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 2 3 popop"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `roll<` `rolldown` `roll>` `rollup`\n",
    "The \"down\" and \"up\" refer to the movement of two of the top three items (displacing the third.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 3 1"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 2 3 roll<"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 1 2"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 2 3 roll>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `swap`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 3 2"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 2 3 swap"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `tuck` `over`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 3 2 3"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 2 3 tuck"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 3 2"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 2 3 over"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `unit` `quoted` `unquoted`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 [3]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 2 3 unit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 [2] 3"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 2 3 quoted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 3"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 [2] 3 unquoted"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unquoting evaluates.  Be aware."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 1 3"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 [dup] 3 unquoted"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# List words"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `concat` `swoncat` `shunt`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 4 5 6]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3] [4 5 6] concat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4 5 6 1 2 3]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3] [4 5 6] swoncat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[6 5 4 1 2 3]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3] [4 5 6] shunt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `cons` `swons` `uncons`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 [2 3] cons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[2 3] 1 swons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 [2 3]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3] uncons"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `first` `second` `third` `rest`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3 4] first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3 4] second"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3 4] third"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 3 4]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3 4] rest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `flatten`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 [3] 4 5 6]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[[1] [2 [3] 4] [5 6]] flatten"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `getitem` `at` `of` `drop` `take`\n",
    "\n",
    "`at` and `getitem` are the same function. `of == swap at`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[10 11 12 13 14] 2 getitem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3 4] 0 at"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3"
     ]
    }
   ],
   "source": [
    "clear\n",
    "2 [1 2 3 4] of"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 4]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3 4] 2 drop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 1]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3 4] 2 take"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " `take` reverses the order."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`reverse` could be defines as `reverse == dup size take`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `remove`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 3 1 4]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3 1 4] 1 remove"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `reverse`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4 3 2 1]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3 4] reverse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `size`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 1 1 1] size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `swaack`\n",
    "\"Swap stack\" swap the list on the top of the stack for the stack, and put the old stack on top of the new one.  Think of it as a context switch.  Niether of the lists/stacks change their order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6 5 4 [3 2 1]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 2 3 [4 5 6] swaack"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `choice` `select`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9"
     ]
    }
   ],
   "source": [
    "clear\n",
    "23 9 true choice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23"
     ]
    }
   ],
   "source": [
    "clear\n",
    "23 9 false choice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[23 9 7] 1 select"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "scrolled": true
   },
   "source": [
    "(`select` is basically `getitem`, should retire it?)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[23 9 7] 0 select"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `zip`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[6 1] [5 2] [4 3]]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3] [6 5 4] zip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7 7 7]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3] [6 5 4] zip [sum] map"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Math words"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `+` `add`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "32"
     ]
    }
   ],
   "source": [
    "clear\n",
    "23 9 +"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `-` `sub`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14"
     ]
    }
   ],
   "source": [
    "clear\n",
    "23 9 -"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `*` `mul`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "207"
     ]
    }
   ],
   "source": [
    "clear\n",
    "23 9 *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `/` `div`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2"
     ]
    }
   ],
   "source": [
    "clear\n",
    "23 9 /"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2"
     ]
    }
   ],
   "source": [
    "clear\n",
    "23 9 div"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3"
     ]
    }
   ],
   "source": [
    "clear\n",
    "23 -9 div"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `%` `mod` `modulus` `rem` `remainder`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5"
     ]
    }
   ],
   "source": [
    "clear\n",
    "23 9 %"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `neg`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-23 5"
     ]
    }
   ],
   "source": [
    "clear\n",
    "23 neg -5 neg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### pow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1024"
     ]
    }
   ],
   "source": [
    "clear\n",
    "2 10 pow"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `sqr`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "529"
     ]
    }
   ],
   "source": [
    "clear\n",
    "23 sqr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `++` `succ` `--` `pred`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 ++"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0"
     ]
    }
   ],
   "source": [
    "clear\n",
    "1 --"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `<<` `lshift` `>>` `rshift`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16"
     ]
    }
   ],
   "source": [
    "clear\n",
    "8 1 <<"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4"
     ]
    }
   ],
   "source": [
    "clear\n",
    "8 1 >>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `range` `range_to_zero` `down_to_zero`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4 3 2 1 0]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "5 range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "5 range_to_zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 4 3 2 1 0"
     ]
    }
   ],
   "source": [
    "clear\n",
    "5 down_to_zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[5 down_to_zero] run"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `product`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "30"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3 5] product"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `sum`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3 5] sum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `min`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 3 5] min"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `gcd`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15"
     ]
    }
   ],
   "source": [
    "clear\n",
    "45 30 gcd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logic and Comparison"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `?` `truthy`\n",
    "Get the Boolean value of the item on the top of the stack."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true"
     ]
    }
   ],
   "source": [
    "clear\n",
    "23 bool"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "false"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[] bool"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "false"
     ]
    }
   ],
   "source": [
    "clear\n",
    "0 bool"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    ? == dup truthy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23 true"
     ]
    }
   ],
   "source": [
    "clear\n",
    "23 ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[] false"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[] ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 false"
     ]
    }
   ],
   "source": [
    "clear\n",
    "0 ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `&` `and` "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "false"
     ]
    }
   ],
   "source": [
    "clear\n",
    "true false &"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `!=` `<>` `ne`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true"
     ]
    }
   ],
   "source": [
    "clear\n",
    "23 9 !="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The usual suspects:\n",
    "- `<` `lt`\n",
    "- `<=` `le`  \n",
    "- `=` `eq`\n",
    "- `>` `gt`\n",
    "- `>=` `ge`\n",
    "- `not`\n",
    "- `or`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Miscellaneous"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `help`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==== Help on help ====\n",
      "\n",
      "Accepts a quoted symbol on the top of the stack and prints its docs.\n",
      "\n",
      "---- end ( help )\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[help] help"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `run`\n",
    "Evaluate a quoted Joy sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5]"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[1 2 dup + +] run"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Combinators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `app1` `app2` `app3`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==== Help on app1 ====\n",
      "\n",
      "app1 ≡ grba infrst\n",
      "\n",
      "---- end ( app1 )\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[app1] help"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 160"
     ]
    }
   ],
   "source": [
    "clear\n",
    "10 4 [sqr *] app1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 90 160"
     ]
    }
   ],
   "source": [
    "clear\n",
    "10 3 4 [sqr *] app2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==== Help on app2 ====\n",
      "\n",
      "app2 ≡ [grba swap grba swap] dip [infrst] cons ii\n",
      "\n",
      "---- end ( app2 )\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "clear\n",
    "[app2] help"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "160 90 40"
     ]
    }
   ],
   "source": [
    "clear\n",
    "10 2 3 4 [sqr *] app3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Wait... is that... backwards?)\n",
    "\n",
    "It should be `40 90 160` shouldn't it?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40 90 160"
     ]
    }
   ],
   "source": [
    "clear\n",
    "10 2 3 4 [sqr *] 3 [grabN] codi map reverse disenstacken"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ah! See?  It needs `reverse` in there!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40 90 160 250"
     ]
    }
   ],
   "source": [
    "clear\n",
    "10 2 3 4 5 [sqr *] 4 [grabN] codi map reverse disenstacken"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `anamorphism`\n",
    "Given an initial value, a predicate function `[P]`, and a generator function `[G]`, the `anamorphism` combinator creates a sequence.\n",
    "\n",
    "       n [P] [G] anamorphism\n",
    "    ---------------------------\n",
    "              [...]\n",
    "\n",
    "Example, `range`:\n",
    "\n",
    "    range == [0 <=] [1 - dup] anamorphism"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('3 [0 <=] [1 - dup] anamorphism')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `branch`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('3 4 1 [+] [*] branch')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('3 4 0 [+] [*] branch')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `cleave`\n",
    "    ... x [P] [Q] cleave\n",
    "\n",
    "From the original Joy docs: \"The cleave combinator expects two quotations, and below that an item `x`\n",
    "It first executes `[P]`, with `x` on top, and saves the top result element.\n",
    "Then it executes `[Q]`, again with `x`, and saves the top result.\n",
    "Finally it restores the stack to what it was below `x` and pushes the two\n",
    "results P(X) and Q(X).\"\n",
    "\n",
    "Note that `P` and `Q` can use items from the stack freely, since the stack (below `x`) is restored.  `cleave` is a kind of *parallel* primitive, and it would make sense to create a version that uses, e.g. Python threads or something, to actually run `P` and `Q` concurrently.  The current implementation of `cleave` is a definition in terms of `app2`:\n",
    "\n",
    "    cleave == [i] app2 [popd] dip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('10 2 [+] [-] cleave')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `dip` `dipd` `dipdd`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 3 4 5 [+] dip')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 3 4 5 [+] dipd')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 3 4 5 [+] dipdd')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `dupdip`\n",
    "Expects a quoted program `[Q]` on the stack and some item under it, `dup` the item and `dip` the quoted program under it.\n",
    "\n",
    "    n [Q] dupdip == n Q n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V('23 [++] dupdip *')  # N(N + 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `genrec` `primrec`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[genrec] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('3 [1 <=] [] [dup --] [i *] genrec')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `i`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "V('1 2 3 [+ +] i')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `ifte`\n",
    "    [predicate] [then] [else] ifte"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 [1] [+] [*] ifte')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 [0] [+] [*] ifte')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `infra`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V('1 2 3 [4 5 6] [* +] infra')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `loop`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[loop] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V('3 dup [1 - dup] loop')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `map` `pam`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('10 [1 2 3] [*] map')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('10 5 [[*][/][+][-]] pam')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `nullary` `unary` `binary` `ternary`\n",
    "Run a quoted program enforcing [arity](https://en.wikipedia.org/wiki/Arity)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 3 4 5 [+] nullary')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 3 4 5 [+] unary')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 3 4 5 [+] binary')  # + has arity 2 so this is technically pointless..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 3 4 5 [+] ternary')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `step`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[step] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "V('0 [1 2 3] [+] step')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `times`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V('3 2 1 2 [+] times')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `b`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[b] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V('1 2 [3] [4] b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `while`\n",
    "    [predicate] [body] while"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('3 [0 >] [dup --] while')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `x`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[x] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V('1 [2] [i 3] x')  # Kind of a pointless example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# `void`\n",
    "Implements [**Laws of Form** *arithmetic*](https://en.wikipedia.org/wiki/Laws_of_Form#The_primary_arithmetic_.28Chapter_4.29) over quote-only datastructures (that is, datastructures that consist soley of containers, without strings or numbers or anything else.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[] void')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[[]] void')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[[][[]]] void')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[[[]][[][]]] void')"
   ]
  }
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