diff --git a/docs/Trees.ipynb b/docs/Trees.ipynb
index d9afaff..51580f2 100644
--- a/docs/Trees.ipynb
+++ b/docs/Trees.ipynb
@@ -133,11 +133,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [],
    "source": [
-    "from notebook_preamble import J, V, define"
+    "from notebook_preamble import D, J, V, define, DefinitionWrapper"
    ]
   },
   {
@@ -906,7 +906,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -917,6 +917,22 @@
     "\n",
     "@FunctionWrapper\n",
     "def cmp_(stack, expression, dictionary):\n",
+    "    '''\n",
+    "    cmp takes two values and three quoted programs on the stack and runs\n",
+    "    one of the three depending on the results of comparing the two values:\n",
+    "\n",
+    "           a b [G] [E] [L] cmp\n",
+    "        ------------------------- a > b\n",
+    "                G\n",
+    "\n",
+    "           a b [G] [E] [L] cmp\n",
+    "        ------------------------- a = b\n",
+    "                    E\n",
+    "\n",
+    "           a b [G] [E] [L] cmp\n",
+    "        ------------------------- a < b\n",
+    "                        L\n",
+    "    '''\n",
     "    L, (E, (G, (b, (a, stack)))) = stack\n",
     "    expression = pushback(G if a > b else L if a < b else E, expression)\n",
     "    return stack, expression, dictionary\n",
@@ -925,6 +941,55 @@
     "D['cmp'] = cmp_"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from joy.library import FunctionWrapper, S_ifte\n",
+    "\n",
+    "\n",
+    "@FunctionWrapper\n",
+    "def cond(stack, expression, dictionary):\n",
+    "  '''\n",
+    "  like a case statement; works by rewriting into a chain of ifte.\n",
+    "\n",
+    "  [..[[Bi] Ti]..[D]] -> ...\n",
+    "\n",
+    "\n",
+    "        [[[B0] T0] [[B1] T1] [D]] cond\n",
+    "  -----------------------------------------\n",
+    "     [B0] [T0] [[B1] [T1] [D] ifte] ifte\n",
+    "\n",
+    "  '''\n",
+    "  conditions, stack = stack\n",
+    "  if conditions:\n",
+    "    expression = _cond(conditions, expression)\n",
+    "    try:\n",
+    "      # Attempt to preload the args to first ifte.\n",
+    "      (P, (T, (E, expression))) = expression\n",
+    "    except ValueError:\n",
+    "      # If, for any reason, the argument to cond should happen to contain\n",
+    "      # only the default clause then this optimization will fail.\n",
+    "      pass\n",
+    "    else:\n",
+    "      stack = (E, (T, (P, stack)))\n",
+    "  return stack, expression, dictionary\n",
+    "\n",
+    "\n",
+    "def _cond(conditions, expression):\n",
+    "  (clause, rest) = conditions\n",
+    "  if not rest:  # clause is [D]\n",
+    "    return clause\n",
+    "  P, T = clause\n",
+    "  return (P, (T, (_cond(rest, ()), (S_ifte, expression))))\n",
+    "\n",
+    "\n",
+    "\n",
+    "D['cond'] = cond"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 31,
@@ -1415,17 +1480,16 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# TODO: BTree-delete\n",
+    "# BTree-delete\n",
     "\n",
-    "Then, once we have add, get, and delete we can see about abstracting them.\n",
     "\n",
-    "       tree key [E] BTree-delete\n",
-    "    ---------------------------- key in tree\n",
+    "       tree key [Er] BTree-delete\n",
+    "    -------------------------------- key in tree\n",
     "           tree\n",
     "\n",
-    "       tree key [E] BTree-delete\n",
-    "    ---------------------------- key not in tree\n",
-    "             tree key E"
+    "       tree key [Er] BTree-delete\n",
+    "    ----------------------    ------ key not in tree\n",
+    "             tree key Er"
    ]
   },
   {
@@ -1434,26 +1498,16 @@
    "source": [
     "So:\n",
     "\n",
-    "    BTree-delete == [pop not] [] [R0] [R1] genrec\n",
-    "\n",
-    "And:\n",
-    "\n",
-    "    [n_key n_value left right] key R0              [BTree-get] R1\n",
-    "    [n_key n_value left right] key [dup first] dip [BTree-get] R1\n",
-    "    [n_key n_value left right] n_key key           [BTree-get] R1\n",
-    "    [n_key n_value left right] n_key key           [BTree-get] roll> [T>] [E] [T<] cmp\n",
-    "    [n_key n_value left right] [BTree-get] n_key key                 [T>] [E] [T<] cmp\n",
-    "\n",
-    "    BTree-delete == [pop not] swap [[dup first] dip] [roll> [T>] [E] [T<] cmp] genrec"
+    "    BTree-Delete == [pop not] swap [R0] [R1] genrec\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "    [n_key n_value left right] [BTree-get] T>\n",
-    "    [n_key n_value left right] [BTree-get] E\n",
-    "    [n_key n_value left right] [BTree-get] T<"
+    "                 [Er] BTree-delete\n",
+    "    -------------------------------------\n",
+    "       [pop not] [Er] [R0] [R1] genrec"
    ]
   },
   {
@@ -1466,32 +1520,493 @@
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
+   "cell_type": "markdown",
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "source": [
+    "Now we get to figure out the recursive case:\n",
+    "\n",
+    "    w/ D == [pop not] [Er] [R0] [R1] genrec\n",
+    "\n",
+    "    [node_key node_value left right] key R0                  [D] R1\n",
+    "    [node_key node_value left right] key over first swap dup [D] R1\n",
+    "    [node_key node_value left right] node_key key key        [D] R1\n",
+    "\n",
+    "And then:\n",
+    "\n",
+    "    [node_key node_value left right] node_key key key [D] R1\n",
+    "    [node_key node_value left right] node_key key key [D] cons roll> [T>] [E] [T<] cmp\n",
+    "    [node_key node_value left right] node_key key [key D]      roll> [T>] [E] [T<] cmp\n",
+    "    [node_key node_value left right] [key D] node_key key            [T>] [E] [T<] cmp"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now this:;\n",
+    "\n",
+    "    [node_key node_value left right] [key D] node_key key [T>] [E] [T<] cmp\n",
+    "\n",
+    "Becomes one of these three:;\n",
+    "\n",
+    "    [node_key node_value left right] [key D] T>\n",
+    "    [node_key node_value left right] [key D] E\n",
+    "    [node_key node_value left right] [key D] T<"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Greater than case and less than case\n",
+    "\n",
+    "       [node_key node_value left right] [key D] T>\n",
+    "    -------------------------------------------------\n",
+    "       [node_key node_value left key D right]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "First:\n",
+    "\n",
+    "    right left       node_value node_key [key D] dipd\n",
+    "    right left key D node_value node_key\n",
+    "    right left'      node_value node_key"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Ergo:\n",
+    "\n",
+    "    [node_key node_value left right] [key D] [dipd] cons infra"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "So:\n",
+    "\n",
+    "    T> == [dipd] cons infra\n",
+    "    T< == [dipdd] cons infra"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### The else case\n",
+    "\n",
+    "    [node_key node_value left right] [key D] E\n",
+    "\n",
+    "We have to handle three cases, so let's use `cond`."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The first two cases are symmetrical, if we only have one non-empty child node return it.\n",
+    "\n",
+    "    E == [\n",
+    "        [[pop third not] pop fourth]\n",
+    "        [[pop fourth not] pop third]\n",
+    "        [default]\n",
+    "    ] cond"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "(If both child nodes are empty return an empty node.)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The initial structure of the default function:\n",
+    "\n",
+    "    default == [E'] cons infra\n",
+    "\n",
+    "    [node_key node_value left right] [key D] default\n",
+    "    [node_key node_value left right] [key D] [E'] cons infra\n",
+    "    [node_key node_value left right] [[key D] E']      infra\n",
+    "\n",
+    "    right left node_value node_key [key D] E'"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "If both child nodes are non-empty, we find the highest node in our lower sub-tree, take its key and value to replace (delete) our own, then get rid of it by recursively calling delete() on our lower sub-node with our new key.\n",
+    "\n",
+    "(We could also find the lowest node in our higher sub-tree and take its key and value and delete it. I only implemented one of these two symmetrical options. Over a lot of deletions this might make the tree more unbalanced.  Oh well.)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "First things first, we no longer need this node's key and value:\n",
+    "\n",
+    "    right left node_value node_key [key D] roll> popop E''\n",
+    "    right left [key D] node_value node_key       popop E''\n",
+    "    right left [key D]                                 E''"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Then we have to we find the highest (right-most) node in our lower (left) sub-tree:\n",
+    "\n",
+    "    right left [key D] E''"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Ditch the key:\n",
+    "\n",
+    "    right left [key D] rest E'''\n",
+    "    right left     [D]      E'''"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Find the right-most node:\n",
+    "\n",
+    "    right left        [D] [dup W] dip E''''\n",
+    "    right left dup  W [D]             E''''\n",
+    "    right left left W [D]             E''''"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Consider:\n",
+    "\n",
+    "    left W"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We know left is not empty:\n",
+    "\n",
+    "    [L_key L_value L_left L_right] W"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We want to keep extracting the right node as long as it is not empty:\n",
+    "\n",
+    "    left [P] [B] while W'"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The predicate:\n",
+    "\n",
+    "    [L_key L_value L_left L_right] P\n",
+    "    [L_key L_value L_left L_right] fourth\n",
+    "                          L_right\n",
+    "                          \n",
+    "(This has a bug, can run on `[]` so must be guarded:\n",
+    "\n",
+    "    if_not_empty == [] swap [] ifte\n",
+    "    ?fourth == [fourth] if_not_empty\n",
+    "    W.rightmost == [?fourth] [fourth] while"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The body is also `fourth`:\n",
+    "\n",
+    "    left [fourth] [fourth] while W'\n",
+    "    rightest                     W'"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We know rightest is not empty:\n",
+    "\n",
+    "    [R_key R_value R_left R_right] W'\n",
+    "    [R_key R_value R_left R_right] uncons uncons pop\n",
+    "    R_key [R_value R_left R_right]        uncons pop\n",
+    "    R_key R_value [R_left R_right]               pop\n",
+    "    R_key R_value"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "So:\n",
+    "\n",
+    "    W == [fourth] [fourth] while uncons uncons pop"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "And:\n",
+    "\n",
+    "    right left left W        [D] E''''\n",
+    "    right left R_key R_value [D] E''''"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Final stretch.  We want to end up with something like:\n",
+    "\n",
+    "    right left [R_key D] i R_value R_key\n",
+    "    right left  R_key D    R_value R_key\n",
+    "    right left'            R_value R_key"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "If we adjust our definition of `W` to include `over` at the end:\n",
+    "\n",
+    "    W == [fourth] [fourth] while uncons uncons pop over"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "That will give us:\n",
+    "\n",
+    "    right left R_key R_value R_key [D] E''''\n",
+    "\n",
+    "    right left         R_key R_value R_key [D] cons dipdd E'''''\n",
+    "    right left         R_key R_value [R_key D]      dipdd E'''''\n",
+    "    right left R_key D R_key R_value                      E'''''\n",
+    "    right left'        R_key R_value                      E'''''\n",
+    "    right left'        R_key R_value                      swap\n",
+    "    right left' R_value R_key"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "So:\n",
+    "\n",
+    "    E' == roll> popop E''\n",
+    "\n",
+    "    E'' == rest E'''\n",
+    "\n",
+    "    E''' == [dup W] dip E''''\n",
+    "\n",
+    "    E'''' == cons dipdd swap"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Substituting:\n",
+    "\n",
+    "    W == [fourth] [fourth] while uncons uncons pop over\n",
+    "    E' == roll> popop rest [dup W] dip cons dipdd swap\n",
+    "    E == [\n",
+    "        [[pop third not] pop fourth]\n",
+    "        [[pop fourth not] pop third]\n",
+    "        [[E'] cons infra]\n",
+    "    ] cond"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Minor rearrangement:\n",
+    "\n",
+    "    W == dup [fourth] [fourth] while uncons uncons pop over\n",
+    "    E' == roll> popop rest [W] dip cons dipdd swap\n",
+    "    E == [\n",
+    "        [[pop third not] pop fourth]\n",
+    "        [[pop fourth not] pop third]\n",
+    "        [[E'] cons infra]\n",
+    "    ] cond"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Refactoring\n",
+    "\n",
+    "    W.rightmost == [fourth] [fourth] while\n",
+    "    W.unpack == uncons uncons pop\n",
+    "    E.clear_stuff == roll> popop rest\n",
+    "    E.delete == cons dipdd\n",
+    "    W == dup W.rightmost W.unpack over\n",
+    "    E.0 == E.clear_stuff [W] dip E.delete swap\n",
+    "    E == [\n",
+    "        [[pop third not] pop fourth]\n",
+    "        [[pop fourth not] pop third]\n",
+    "        [[E.0] cons infra]\n",
+    "    ] cond\n",
+    "    T> == [dipd] cons infra\n",
+    "    T< == [dipdd] cons infra\n",
+    "    R0 == over first swap dup\n",
+    "    R1 == cons roll> [T>] [E] [T<] cmp\n",
+    "    BTree-Delete == [pop not] swap [R0] [R1] genrec\n",
+    "\n",
+    "By the standards of the code I've written so far, this is a *huge* Joy program."
+   ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "DefinitionWrapper.add_definitions('''\n",
+    "first_two == uncons uncons pop\n",
+    "fourth == rest rest rest first\n",
+    "?fourth == [] [fourth] [] ifte\n",
+    "W.rightmost == [?fourth] [fourth] while\n",
+    "E.clear_stuff == roll> popop rest\n",
+    "E.delete == cons dipdd\n",
+    "W == dup W.rightmost first_two over\n",
+    "E.0 == E.clear_stuff [W] dip E.delete swap\n",
+    "E == [[[pop third not] pop fourth] [[pop fourth not] pop third] [[E.0] cons infra]] cond\n",
+    "T> == [dipd] cons infra\n",
+    "T< == [dipdd] cons infra\n",
+    "R0 == over first swap dup\n",
+    "R1 == cons roll> [T>] [E] [T<] cmp\n",
+    "BTree-Delete == [pop not] swap [R0] [R1] genrec''', D)"
+   ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 23,
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['a' 23 [] ['b' 88 [] []]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "J(\"['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'c' ['Er'] BTree-Delete \")"
+   ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 24,
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['a' 23 [] ['c' 44 [] []]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "J(\"['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'b' ['Er'] BTree-Delete \")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['b' 88 [] ['c' 44 [] []]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "J(\"['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'a' ['Er'] BTree-Delete \")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['a' 23 [] ['b' 88 [] ['c' 44 [] 'Er' 'der' []]]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "J(\"['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'der' ['Er'] BTree-Delete \")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['a' 23 [] ['b' 88 [] ['c' 44 [] []]]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "J(\"['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'der' [pop] BTree-Delete \")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "One bug, I forgot to put `not` in the first two clauses of the `cond`.\n",
+    "\n",
+    "The behavior of the `[Er]` function should maybe be different: either just silently fail, or maybe implement some sort of function that can grab the pending expression up to a sentinel value or something, allowing for a kind of \"except\"-ish control-flow?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Then, once we have add, get, and delete we can see about abstracting them.\n"
+   ]
   },
   {
    "cell_type": "markdown",
@@ -2161,7 +2676,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython2",
-   "version": "2.7.13"
+   "version": "2.7.12"
   }
  },
  "nbformat": 4,
diff --git a/docs/sphinx_docs/_build/html/index.html b/docs/sphinx_docs/_build/html/index.html
index 4a4ef75..4f0e5dc 100644
--- a/docs/sphinx_docs/_build/html/index.html
+++ b/docs/sphinx_docs/_build/html/index.html
@@ -132,6 +132,7 @@ interesting aspects.  It’s quite a treasure trove.</p>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="notebooks/index.html">Essays about Programming in Joy</a><ul>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/Developing.html">Developing a Program in Joy</a></li>
+<li class="toctree-l2"><a class="reference internal" href="notebooks/Replacing.html">Replacing Functions in the Dictionary</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/Trees.html">Treating Trees</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/Newton-Raphson.html">Newton’s method</a></li>
 <li class="toctree-l2"><a class="reference internal" href="notebooks/Quadratic.html">Quadratic formula</a></li>
diff --git a/docs/sphinx_docs/_build/html/notebooks/4. Replacing Functions in the Dictionary.html b/docs/sphinx_docs/_build/html/notebooks/4. Replacing Functions in the Dictionary.html
deleted file mode 100644
index 813ed5b..0000000
--- a/docs/sphinx_docs/_build/html/notebooks/4. Replacing Functions in the Dictionary.html	
+++ /dev/null
@@ -1,212 +0,0 @@
-
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
-  "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-
-<html xmlns="http://www.w3.org/1999/xhtml">
-  <head>
-    <meta http-equiv="X-UA-Compatible" content="IE=Edge" />
-    <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
-    <title>Replacing Functions in the Dictionary &#8212; Thun 0.1.1 documentation</title>
-    <link rel="stylesheet" href="../_static/alabaster.css" type="text/css" />
-    <link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
-    <script type="text/javascript" src="../_static/documentation_options.js"></script>
-    <script type="text/javascript" src="../_static/jquery.js"></script>
-    <script type="text/javascript" src="../_static/underscore.js"></script>
-    <script type="text/javascript" src="../_static/doctools.js"></script>
-    <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
-    <link rel="index" title="Index" href="../genindex.html" />
-    <link rel="search" title="Search" href="../search.html" />
-   
-  <link rel="stylesheet" href="../_static/custom.css" type="text/css" />
-  
-  
-  <meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />
-
-  </head><body>
-  
-
-    <div class="document">
-      <div class="documentwrapper">
-        <div class="bodywrapper">
-          <div class="body" role="main">
-            
-  <div class="section" id="replacing-functions-in-the-dictionary">
-<h1>Replacing Functions in the Dictionary<a class="headerlink" href="#replacing-functions-in-the-dictionary" title="Permalink to this headline">¶</a></h1>
-<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span>
-</pre></div>
-</div>
-<div class="section" id="a-long-trace">
-<h2>A long trace<a class="headerlink" href="#a-long-trace" title="Permalink to this headline">¶</a></h2>
-<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[23 18] average&#39;</span><span class="p">)</span>
-</pre></div>
-</div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                                  <span class="o">.</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="n">average</span>
-                          <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="n">average</span>
-                          <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="n">cleave</span> <span class="o">/</span>
-              <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="n">cleave</span> <span class="o">/</span>
-       <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="o">.</span> <span class="n">cleave</span> <span class="o">/</span>
-       <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">app2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-   <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">.</span> <span class="n">app2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-              <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                          <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                               <span class="mi">41</span> <span class="o">.</span> <span class="mf">1.0</span> <span class="o">*</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                           <span class="mi">41</span> <span class="mf">1.0</span> <span class="o">.</span> <span class="o">*</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                             <span class="mf">41.0</span> <span class="o">.</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                   <span class="mf">41.0</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="o">.</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                   <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="mf">41.0</span><span class="p">]</span> <span class="o">.</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                     <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="o">.</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-    <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="o">.</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                   <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                          <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="n">size</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                          <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                        <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mi">0</span> <span class="o">.</span> <span class="n">swap</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                        <span class="mi">0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-               <span class="mi">0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                    <span class="mi">0</span> <span class="mi">23</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                             <span class="mi">0</span> <span class="mi">23</span> <span class="o">.</span> <span class="n">pop</span> <span class="o">++</span> <span class="p">[</span><span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                                <span class="mi">0</span> <span class="o">.</span> <span class="o">++</span> <span class="p">[</span><span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                                <span class="mi">1</span> <span class="o">.</span> <span class="p">[</span><span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                           <span class="mi">1</span> <span class="p">[</span><span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                  <span class="mi">1</span> <span class="p">[</span><span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                    <span class="mi">1</span> <span class="mi">18</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                             <span class="mi">1</span> <span class="mi">18</span> <span class="o">.</span> <span class="n">pop</span> <span class="o">++</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                                <span class="mi">1</span> <span class="o">.</span> <span class="o">++</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                                <span class="mi">2</span> <span class="o">.</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                 <span class="mi">2</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="o">.</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                 <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                   <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="mi">2</span> <span class="o">.</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-            <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="mi">2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="o">/</span>
-                     <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="o">.</span> <span class="n">popd</span> <span class="mi">2</span> <span class="o">/</span>
-                             <span class="mf">41.0</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">/</span>
-                           <span class="mf">41.0</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">/</span>
-                             <span class="mf">20.5</span> <span class="o">.</span>
-</pre></div>
-</div>
-</div>
-<div class="section" id="replacing-size-with-a-python-version">
-<h2>Replacing <code class="docutils literal notranslate"><span class="pre">size</span></code> with a Python Version<a class="headerlink" href="#replacing-size-with-a-python-version" title="Permalink to this headline">¶</a></h2>
-<p>Both <code class="docutils literal notranslate"><span class="pre">sum</span></code> and <code class="docutils literal notranslate"><span class="pre">size</span></code> each convert a sequence to a single value.</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="nb">sum</span> <span class="o">==</span> <span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">step</span>
-<span class="n">size</span> <span class="o">==</span> <span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span>
-</pre></div>
-</div>
-<p>An efficient <code class="docutils literal notranslate"><span class="pre">sum</span></code> function is already in the library.  But for <code class="docutils literal notranslate"><span class="pre">size</span></code> we can use
-a “compiled” version hand-written in Python to speed up evaluation and make the trace more readable.</p>
-<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="k">import</span> <span class="n">SimpleFunctionWrapper</span>
-<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="k">import</span> <span class="n">iter_stack</span>
-
-
-<span class="nd">@SimpleFunctionWrapper</span>
-<span class="k">def</span> <span class="nf">size</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
-    <span class="sd">&#39;&#39;&#39;Return the size of the sequence on the stack.&#39;&#39;&#39;</span>
-    <span class="n">sequence</span><span class="p">,</span> <span class="n">stack</span> <span class="o">=</span> <span class="n">stack</span>
-    <span class="n">n</span> <span class="o">=</span> <span class="mi">0</span>
-    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="n">iter_stack</span><span class="p">(</span><span class="n">sequence</span><span class="p">):</span>
-        <span class="n">n</span> <span class="o">+=</span> <span class="mi">1</span>
-    <span class="k">return</span> <span class="n">n</span><span class="p">,</span> <span class="n">stack</span>
-</pre></div>
-</div>
-<p>Now we replace the old version in the dictionary with the new version,
-and re-evaluate the expression.</p>
-<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">D</span><span class="p">[</span><span class="s1">&#39;size&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">size</span>
-</pre></div>
-</div>
-</div>
-<div class="section" id="a-shorter-evaluation">
-<h2>A Shorter Evaluation<a class="headerlink" href="#a-shorter-evaluation" title="Permalink to this headline">¶</a></h2>
-<p>You can see that <code class="docutils literal notranslate"><span class="pre">size</span></code> and <code class="docutils literal notranslate"><span class="pre">sum</span></code> now execute in a single step.</p>
-<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">&#39;[23 18] average&#39;</span><span class="p">)</span>
-</pre></div>
-</div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>                                  <span class="o">.</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="n">average</span>
-                          <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="n">average</span>
-                          <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="n">cleave</span> <span class="o">/</span>
-              <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="n">cleave</span> <span class="o">/</span>
-       <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="o">.</span> <span class="n">cleave</span> <span class="o">/</span>
-       <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">app2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-   <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">.</span> <span class="n">app2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-              <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                          <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                               <span class="mi">41</span> <span class="o">.</span> <span class="mf">1.0</span> <span class="o">*</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                           <span class="mi">41</span> <span class="mf">1.0</span> <span class="o">.</span> <span class="o">*</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                             <span class="mf">41.0</span> <span class="o">.</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                   <span class="mf">41.0</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="o">.</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                   <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="mf">41.0</span><span class="p">]</span> <span class="o">.</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                     <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="o">.</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-    <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="o">.</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                   <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                          <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="n">size</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                                <span class="mi">2</span> <span class="o">.</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                 <span class="mi">2</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="o">.</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                 <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-                   <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="mi">2</span> <span class="o">.</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
-            <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="mi">2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="o">/</span>
-                     <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="o">.</span> <span class="n">popd</span> <span class="mi">2</span> <span class="o">/</span>
-                             <span class="mf">41.0</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">/</span>
-                           <span class="mf">41.0</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">/</span>
-                             <span class="mf">20.5</span> <span class="o">.</span>
-</pre></div>
-</div>
-</div>
-</div>
-
-
-          </div>
-        </div>
-      </div>
-      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
-        <div class="sphinxsidebarwrapper">
-  <h3><a href="../index.html">Table Of Contents</a></h3>
-  <ul>
-<li><a class="reference internal" href="#">Replacing Functions in the Dictionary</a><ul>
-<li><a class="reference internal" href="#a-long-trace">A long trace</a></li>
-<li><a class="reference internal" href="#replacing-size-with-a-python-version">Replacing <code class="docutils literal notranslate"><span class="pre">size</span></code> with a Python Version</a></li>
-<li><a class="reference internal" href="#a-shorter-evaluation">A Shorter Evaluation</a></li>
-</ul>
-</li>
-</ul>
-<div class="relations">
-<h3>Related Topics</h3>
-<ul>
-  <li><a href="../index.html">Documentation overview</a><ul>
-  </ul></li>
-</ul>
-</div>
-  <div role="note" aria-label="source link">
-    <h3>This Page</h3>
-    <ul class="this-page-menu">
-      <li><a href="../_sources/notebooks/4. Replacing Functions in the Dictionary.rst.txt"
-            rel="nofollow">Show Source</a></li>
-    </ul>
-   </div>
-<div id="searchbox" style="display: none" role="search">
-  <h3>Quick search</h3>
-    <div class="searchformwrapper">
-    <form class="search" action="../search.html" method="get">
-      <input type="text" name="q" />
-      <input type="submit" value="Go" />
-      <input type="hidden" name="check_keywords" value="yes" />
-      <input type="hidden" name="area" value="default" />
-    </form>
-    </div>
-</div>
-<script type="text/javascript">$('#searchbox').show(0);</script>
-        </div>
-      </div>
-      <div class="clearer"></div>
-    </div>
-    <div class="footer" role="contentinfo">
-<a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">
-<img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" />
-</a>
-<br />
-<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
-      Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
-    </div>
-
-  </body>
-</html>
\ No newline at end of file
diff --git a/docs/sphinx_docs/_build/html/notebooks/Developing.html b/docs/sphinx_docs/_build/html/notebooks/Developing.html
index 4880165..c6cd960 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Developing.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Developing.html
@@ -16,7 +16,7 @@
     <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
-    <link rel="next" title="Treating Trees" href="Trees.html" />
+    <link rel="next" title="Replacing Functions in the Dictionary" href="Replacing.html" />
     <link rel="prev" title="Essays about Programming in Joy" href="index.html" />
    
   <link rel="stylesheet" href="../_static/custom.css" type="text/css" />
@@ -689,7 +689,7 @@ is just:</p>
   <li><a href="../index.html">Documentation overview</a><ul>
   <li><a href="index.html">Essays about Programming in Joy</a><ul>
       <li>Previous: <a href="index.html" title="previous chapter">Essays about Programming in Joy</a></li>
-      <li>Next: <a href="Trees.html" title="next chapter">Treating Trees</a></li>
+      <li>Next: <a href="Replacing.html" title="next chapter">Replacing Functions in the Dictionary</a></li>
   </ul></li>
   </ul></li>
 </ul>
diff --git a/docs/sphinx_docs/_build/html/notebooks/Trees.html b/docs/sphinx_docs/_build/html/notebooks/Trees.html
index dfb9141..d420f7a 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Trees.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Trees.html
@@ -17,7 +17,7 @@
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
     <link rel="next" title="Newton’s method" href="Newton-Raphson.html" />
-    <link rel="prev" title="Developing a Program in Joy" href="Developing.html" />
+    <link rel="prev" title="Replacing Functions in the Dictionary" href="Replacing.html" />
    
   <link rel="stylesheet" href="../_static/custom.css" type="text/css" />
   
@@ -967,37 +967,102 @@ because there’s no value to discard. Now we have to derive the branches:</p>
 </div>
 <div class="section" id="todo-btree-delete">
 <h2>TODO: BTree-delete<a class="headerlink" href="#todo-btree-delete" title="Permalink to this headline">¶</a></h2>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>   <span class="n">tree</span> <span class="n">key</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="n">BTree</span><span class="o">-</span><span class="n">delete</span>
-<span class="o">----------------------------</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">tree</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>   <span class="n">tree</span> <span class="n">key</span> <span class="p">[</span><span class="n">Er</span><span class="p">]</span> <span class="n">BTree</span><span class="o">-</span><span class="n">delete</span>
+<span class="o">--------------------------------</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">tree</span>
        <span class="n">tree</span>
 
-   <span class="n">tree</span> <span class="n">key</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="n">BTree</span><span class="o">-</span><span class="n">delete</span>
-<span class="o">----------------------------</span> <span class="n">key</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">tree</span>
-         <span class="n">tree</span> <span class="n">key</span> <span class="n">E</span>
+   <span class="n">tree</span> <span class="n">key</span> <span class="p">[</span><span class="n">Er</span><span class="p">]</span> <span class="n">BTree</span><span class="o">-</span><span class="n">delete</span>
+<span class="o">--------------------------------</span> <span class="n">key</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">tree</span>
+         <span class="n">tree</span> <span class="n">key</span> <span class="n">Er</span>
 </pre></div>
 </div>
 <p>So:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">BTree</span><span class="o">-</span><span class="n">delete</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">R0</span><span class="p">]</span> <span class="p">[</span><span class="n">R1</span><span class="p">]</span> <span class="n">genrec</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">BTree</span><span class="o">-</span><span class="n">Delete</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="ow">not</span><span class="p">]</span> <span class="n">swap</span> <span class="p">[</span><span class="n">R0</span><span class="p">]</span> <span class="p">[</span><span class="n">R1</span><span class="p">]</span> <span class="n">genrec</span>
 </pre></div>
 </div>
-<p>And:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">n_key</span> <span class="n">n_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">key</span> <span class="n">R0</span>              <span class="p">[</span><span class="n">BTree</span><span class="o">-</span><span class="n">get</span><span class="p">]</span> <span class="n">R1</span>
-<span class="p">[</span><span class="n">n_key</span> <span class="n">n_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">key</span> <span class="p">[</span><span class="n">dup</span> <span class="n">first</span><span class="p">]</span> <span class="n">dip</span> <span class="p">[</span><span class="n">BTree</span><span class="o">-</span><span class="n">get</span><span class="p">]</span> <span class="n">R1</span>
-<span class="p">[</span><span class="n">n_key</span> <span class="n">n_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">n_key</span> <span class="n">key</span>           <span class="p">[</span><span class="n">BTree</span><span class="o">-</span><span class="n">get</span><span class="p">]</span> <span class="n">R1</span>
-<span class="p">[</span><span class="n">n_key</span> <span class="n">n_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">n_key</span> <span class="n">key</span>           <span class="p">[</span><span class="n">BTree</span><span class="o">-</span><span class="n">get</span><span class="p">]</span> <span class="n">roll</span><span class="o">&gt;</span> <span class="p">[</span><span class="n">T</span><span class="o">&gt;</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="o">&lt;</span><span class="p">]</span> <span class="nb">cmp</span>
-<span class="p">[</span><span class="n">n_key</span> <span class="n">n_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">BTree</span><span class="o">-</span><span class="n">get</span><span class="p">]</span> <span class="n">n_key</span> <span class="n">key</span>                 <span class="p">[</span><span class="n">T</span><span class="o">&gt;</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="o">&lt;</span><span class="p">]</span> <span class="nb">cmp</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>             <span class="p">[</span><span class="n">Er</span><span class="p">]</span> <span class="n">BTree</span><span class="o">-</span><span class="n">delete</span>
+<span class="o">------------------------------------</span>
+   <span class="p">[</span><span class="n">pop</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">Er</span><span class="p">]</span> <span class="p">[</span><span class="n">R0</span><span class="p">]</span> <span class="p">[</span><span class="n">R1</span><span class="p">]</span> <span class="n">genrec</span>
+</pre></div>
+</div>
+<p>Now we get to figure out the recursive case:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">D</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">Er</span><span class="p">]</span> <span class="p">[</span><span class="n">R0</span><span class="p">]</span> <span class="p">[</span><span class="n">R1</span><span class="p">]</span> <span class="n">genrec</span>
 
-<span class="n">BTree</span><span class="o">-</span><span class="n">delete</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="ow">not</span><span class="p">]</span> <span class="n">swap</span> <span class="p">[[</span><span class="n">dup</span> <span class="n">first</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="p">[</span><span class="n">roll</span><span class="o">&gt;</span> <span class="p">[</span><span class="n">T</span><span class="o">&gt;</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="o">&lt;</span><span class="p">]</span> <span class="nb">cmp</span><span class="p">]</span> <span class="n">genrec</span>
+<span class="p">[</span><span class="n">node_key</span> <span class="n">node_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">key</span> <span class="n">R0</span>                  <span class="p">[</span><span class="n">D</span><span class="p">]</span> <span class="n">R1</span>
+<span class="p">[</span><span class="n">node_key</span> <span class="n">node_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">key</span> <span class="n">over</span> <span class="n">first</span> <span class="n">swap</span> <span class="n">dup</span> <span class="p">[</span><span class="n">D</span><span class="p">]</span> <span class="n">R1</span>
+<span class="p">[</span><span class="n">node_key</span> <span class="n">node_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">node_key</span> <span class="n">key</span> <span class="n">key</span>        <span class="p">[</span><span class="n">D</span><span class="p">]</span> <span class="n">R1</span>
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">n_key</span> <span class="n">n_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">BTree</span><span class="o">-</span><span class="n">get</span><span class="p">]</span> <span class="n">T</span><span class="o">&gt;</span>
-<span class="p">[</span><span class="n">n_key</span> <span class="n">n_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">BTree</span><span class="o">-</span><span class="n">get</span><span class="p">]</span> <span class="n">E</span>
-<span class="p">[</span><span class="n">n_key</span> <span class="n">n_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">BTree</span><span class="o">-</span><span class="n">get</span><span class="p">]</span> <span class="n">T</span><span class="o">&lt;</span>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">node_key</span> <span class="n">node_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">node_key</span> <span class="n">key</span> <span class="n">key</span> <span class="p">[</span><span class="n">D</span><span class="p">]</span> <span class="n">R1</span>
+<span class="p">[</span><span class="n">node_key</span> <span class="n">node_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">node_key</span> <span class="n">key</span> <span class="n">key</span> <span class="p">[</span><span class="n">D</span><span class="p">]</span> <span class="n">cons</span> <span class="n">roll</span><span class="o">&gt;</span> <span class="p">[</span><span class="n">T</span><span class="o">&gt;</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="o">&lt;</span><span class="p">]</span> <span class="nb">cmp</span>
+<span class="p">[</span><span class="n">node_key</span> <span class="n">node_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">node_key</span> <span class="n">key</span> <span class="p">[</span><span class="n">key</span> <span class="n">D</span><span class="p">]</span>      <span class="n">roll</span><span class="o">&gt;</span> <span class="p">[</span><span class="n">T</span><span class="o">&gt;</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="o">&lt;</span><span class="p">]</span> <span class="nb">cmp</span>
+<span class="p">[</span><span class="n">node_key</span> <span class="n">node_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">key</span> <span class="n">D</span><span class="p">]</span> <span class="n">node_key</span> <span class="n">key</span>            <span class="p">[</span><span class="n">T</span><span class="o">&gt;</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="o">&lt;</span><span class="p">]</span> <span class="nb">cmp</span>
 </pre></div>
 </div>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">n_key</span> <span class="n">n_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">BTree</span><span class="o">-</span><span class="n">get</span><span class="p">]</span>
-<span class="p">[</span><span class="n">n_key</span> <span class="n">n_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">BTree</span><span class="o">-</span><span class="n">get</span><span class="p">]</span> <span class="n">E</span>
-<span class="p">[</span><span class="n">n_key</span> <span class="n">n_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">BTree</span><span class="o">-</span><span class="n">get</span><span class="p">]</span> <span class="n">T</span><span class="o">&lt;</span>
+<p>Now this:;</p>
+<blockquote>
+<div>[node_key node_value left right] [key D] node_key key [T&gt;] [E] [T&lt;] cmp</div></blockquote>
+<p>Becomes one of these three:;</p>
+<blockquote>
+<div>[node_key node_value left right] [key D] T&gt;
+[node_key node_value left right] [key D] E
+[node_key node_value left right] [key D] T&lt;</div></blockquote>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>   <span class="p">[</span><span class="n">node_key</span> <span class="n">node_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">key</span> <span class="n">D</span><span class="p">]</span> <span class="n">T</span><span class="o">&gt;</span>
+<span class="o">-------------------------------------------------</span>
+   <span class="p">[</span><span class="n">node_key</span> <span class="n">node_value</span> <span class="n">left</span> <span class="n">key</span> <span class="n">D</span> <span class="n">right</span><span class="p">]</span>
+
+
+<span class="n">right</span> <span class="n">left</span> <span class="n">node_value</span> <span class="n">node_key</span> <span class="p">[</span><span class="n">key</span> <span class="n">D</span><span class="p">]</span> <span class="n">dipd</span>
+
+<span class="p">[</span><span class="n">node_key</span> <span class="n">node_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">key</span> <span class="n">D</span><span class="p">]</span> <span class="p">[</span><span class="n">dipd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">T</span><span class="o">&gt;</span> <span class="o">==</span> <span class="p">[</span><span class="n">dipd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span>
+<span class="n">T</span><span class="o">&lt;</span> <span class="o">==</span> <span class="p">[</span><span class="n">dipdd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">node_key</span> <span class="n">node_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">key</span> <span class="n">D</span><span class="p">]</span> <span class="n">E</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">delete</span><span class="p">(</span><span class="n">node</span><span class="p">,</span> <span class="n">key</span><span class="p">):</span>
+  <span class="sd">&#39;&#39;&#39;</span>
+<span class="sd">  Return a tree with the value (and key) removed or raise KeyError if</span>
+<span class="sd">  not found.</span>
+<span class="sd">  &#39;&#39;&#39;</span>
+  <span class="k">if</span> <span class="ow">not</span> <span class="n">node</span><span class="p">:</span>
+    <span class="k">raise</span> <span class="ne">KeyError</span><span class="p">,</span> <span class="n">key</span>
+
+  <span class="n">node_key</span><span class="p">,</span> <span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="p">(</span><span class="n">lower</span><span class="p">,</span> <span class="p">(</span><span class="n">higher</span><span class="p">,</span> <span class="n">_</span><span class="p">)))</span> <span class="o">=</span> <span class="n">node</span>
+
+  <span class="k">if</span> <span class="n">key</span> <span class="o">&lt;</span> <span class="n">node_key</span><span class="p">:</span>
+    <span class="k">return</span> <span class="n">node_key</span><span class="p">,</span> <span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="p">(</span><span class="n">delete</span><span class="p">(</span><span class="n">lower</span><span class="p">,</span> <span class="n">key</span><span class="p">),</span> <span class="p">(</span><span class="n">higher</span><span class="p">,</span> <span class="p">())))</span>
+
+  <span class="k">if</span> <span class="n">key</span> <span class="o">&gt;</span> <span class="n">node_key</span><span class="p">:</span>
+    <span class="k">return</span> <span class="n">node_key</span><span class="p">,</span> <span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="p">(</span><span class="n">lower</span><span class="p">,</span> <span class="p">(</span><span class="n">delete</span><span class="p">(</span><span class="n">higher</span><span class="p">,</span> <span class="n">key</span><span class="p">),</span> <span class="p">())))</span>
+
+  <span class="c1"># So, key == node_key, delete this node itself.</span>
+
+  <span class="c1"># If we only have one non-empty child node return it.  If both child</span>
+  <span class="c1"># nodes are empty return an empty node (one of the children.)</span>
+  <span class="k">if</span> <span class="ow">not</span> <span class="n">lower</span><span class="p">:</span>
+    <span class="k">return</span> <span class="n">higher</span>
+  <span class="k">if</span> <span class="ow">not</span> <span class="n">higher</span><span class="p">:</span>
+    <span class="k">return</span> <span class="n">lower</span>
+
+  <span class="c1"># If both child nodes are non-empty, we find the highest node in our</span>
+  <span class="c1"># lower sub-tree, take its key and value to replace (delete) our own,</span>
+  <span class="c1"># then get rid of it by recursively calling delete() on our lower</span>
+  <span class="c1"># sub-node with our new key.</span>
+  <span class="c1"># (We could also find the lowest node in our higher sub-tree and take</span>
+  <span class="c1"># its key and value and delete it. I only implemented one of these</span>
+  <span class="c1"># two symmetrical options. Over a lot of deletions this might make</span>
+  <span class="c1"># the tree more unbalanced.  Oh well.)</span>
+  <span class="n">node</span> <span class="o">=</span> <span class="n">lower</span>
+  <span class="k">while</span> <span class="n">node</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]:</span>
+    <span class="n">node</span> <span class="o">=</span> <span class="n">node</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+  <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="o">=</span> <span class="n">node</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">node</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+
+  <span class="k">return</span> <span class="n">key</span><span class="p">,</span> <span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="p">(</span><span class="n">delete</span><span class="p">(</span><span class="n">lower</span><span class="p">,</span> <span class="n">key</span><span class="p">),</span> <span class="p">(</span><span class="n">higher</span><span class="p">,</span> <span class="p">())))</span>
 </pre></div>
 </div>
 </div>
@@ -1507,7 +1572,7 @@ because lookup happens at evaluation, not parsing. E.g.:</p>
 <ul>
   <li><a href="../index.html">Documentation overview</a><ul>
   <li><a href="index.html">Essays about Programming in Joy</a><ul>
-      <li>Previous: <a href="Developing.html" title="previous chapter">Developing a Program in Joy</a></li>
+      <li>Previous: <a href="Replacing.html" title="previous chapter">Replacing Functions in the Dictionary</a></li>
       <li>Next: <a href="Newton-Raphson.html" title="next chapter">Newton’s method</a></li>
   </ul></li>
   </ul></li>
diff --git a/docs/sphinx_docs/_build/html/notebooks/index.html b/docs/sphinx_docs/_build/html/notebooks/index.html
index 9c81313..a75d684 100644
--- a/docs/sphinx_docs/_build/html/notebooks/index.html
+++ b/docs/sphinx_docs/_build/html/notebooks/index.html
@@ -44,6 +44,12 @@
 <li class="toctree-l2"><a class="reference internal" href="Developing.html#the-simplest-program">The Simplest Program</a></li>
 </ul>
 </li>
+<li class="toctree-l1"><a class="reference internal" href="Replacing.html">Replacing Functions in the Dictionary</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="Replacing.html#a-long-trace">A long trace</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Replacing.html#replacing-size-with-a-python-version">Replacing <code class="docutils literal notranslate"><span class="pre">size</span></code> with a Python Version</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Replacing.html#a-shorter-trace">A shorter trace</a></li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="Trees.html">Treating Trees</a><ul>
 <li class="toctree-l2"><a class="reference internal" href="Trees.html#a-function-to-traverse-a-btree">A Function to Traverse a BTree</a></li>
 <li class="toctree-l2"><a class="reference internal" href="Trees.html#adding-nodes-to-the-btree">Adding Nodes to the BTree</a></li>
diff --git a/docs/sphinx_docs/_build/html/objects.inv b/docs/sphinx_docs/_build/html/objects.inv
index e1e7db6..8ec420f 100644
Binary files a/docs/sphinx_docs/_build/html/objects.inv and b/docs/sphinx_docs/_build/html/objects.inv differ
diff --git a/docs/sphinx_docs/_build/html/searchindex.js b/docs/sphinx_docs/_build/html/searchindex.js
index c099fb7..fb36beb 100644
--- a/docs/sphinx_docs/_build/html/searchindex.js
+++ b/docs/sphinx_docs/_build/html/searchindex.js
@@ -1 +1 @@
-Search.setIndex({docnames:["index","joy","lib","library","notebooks/4. Replacing Functions in the Dictionary","notebooks/Advent of Code 2017 December 1st","notebooks/Advent of Code 2017 December 2nd","notebooks/Advent of Code 2017 December 3rd","notebooks/Advent of Code 2017 December 4th","notebooks/Advent of Code 2017 December 5th","notebooks/Advent of Code 2017 December 6th","notebooks/Categorical","notebooks/Developing","notebooks/Generator Programs","notebooks/Hylo-, Ana-, Cata-, and Para-morphisms - Recursion Combinators","notebooks/Intro","notebooks/Newton-Raphson","notebooks/NoUpdates","notebooks/Quadratic","notebooks/Trees","notebooks/Zipper","notebooks/index","parser","pretty","stack"],envversion:52,filenames:["index.rst","joy.rst","lib.rst","library.rst","notebooks/4. Replacing Functions in the Dictionary.rst","notebooks/Advent of Code 2017 December 1st.rst","notebooks/Advent of Code 2017 December 2nd.rst","notebooks/Advent of Code 2017 December 3rd.rst","notebooks/Advent of Code 2017 December 4th.rst","notebooks/Advent of Code 2017 December 5th.rst","notebooks/Advent of Code 2017 December 6th.rst","notebooks/Categorical.rst","notebooks/Developing.rst","notebooks/Generator Programs.rst","notebooks/Hylo-, Ana-, Cata-, and Para-morphisms - Recursion Combinators.rst","notebooks/Intro.rst","notebooks/Newton-Raphson.rst","notebooks/NoUpdates.rst","notebooks/Quadratic.rst","notebooks/Trees.rst","notebooks/Zipper.rst","notebooks/index.rst","parser.rst","pretty.rst","stack.rst"],objects:{"joy.joy":{joy:[1,1,1,""],repl:[1,1,1,""],run:[1,1,1,""]},"joy.library":{"void":[3,1,1,""],BinaryBuiltinWrapper:[3,1,1,""],DefinitionWrapper:[3,2,1,""],FunctionWrapper:[3,1,1,""],SimpleFunctionWrapper:[3,1,1,""],UnaryBuiltinWrapper:[3,1,1,""],add_aliases:[3,1,1,""],app1:[3,1,1,""],app2:[3,1,1,""],app3:[3,1,1,""],b:[3,1,1,""],branch:[3,1,1,""],choice:[3,1,1,""],clear:[3,1,1,""],concat:[3,1,1,""],cons:[3,1,1,""],dip:[3,1,1,""],dipd:[3,1,1,""],dipdd:[3,1,1,""],divmod_:[3,1,1,""],drop:[3,1,1,""],dup:[3,1,1,""],dupd:[3,1,1,""],dupdip:[3,1,1,""],first:[3,1,1,""],floor:[3,1,1,""],genrec:[3,1,1,""],getitem:[3,1,1,""],help_:[3,1,1,""],i:[3,1,1,""],id_:[3,1,1,""],ifte:[3,1,1,""],infra:[3,1,1,""],initialize:[3,1,1,""],inscribe:[3,1,1,""],loop:[3,1,1,""],map_:[3,1,1,""],max_:[3,1,1,""],min_:[3,1,1,""],over:[3,1,1,""],parse:[3,1,1,""],pm:[3,1,1,""],pop:[3,1,1,""],popd:[3,1,1,""],popdd:[3,1,1,""],popop:[3,1,1,""],pred:[3,1,1,""],remove:[3,1,1,""],rest:[3,1,1,""],reverse:[3,1,1,""],rolldown:[3,1,1,""],rollup:[3,1,1,""],select:[3,1,1,""],sharing:[3,1,1,""],shunt:[3,1,1,""],sort_:[3,1,1,""],sqrt:[3,1,1,""],stack_:[3,1,1,""],step:[3,1,1,""],succ:[3,1,1,""],sum_:[3,1,1,""],swaack:[3,1,1,""],swap:[3,1,1,""],take:[3,1,1,""],times:[3,1,1,""],tuck:[3,1,1,""],uncons:[3,1,1,""],unique:[3,1,1,""],unstack:[3,1,1,""],warranty:[3,1,1,""],words:[3,1,1,""],x:[3,1,1,""],zip_:[3,1,1,""]},"joy.library.DefinitionWrapper":{add_def:[3,3,1,""],add_definitions:[3,3,1,""],parse_definition:[3,3,1,""]},"joy.parser":{ParseError:[22,4,1,""],Symbol:[22,2,1,""],text_to_expression:[22,1,1,""]},"joy.utils":{pretty_print:[23,0,0,"-"],stack:[24,0,0,"-"]},"joy.utils.pretty_print":{TracePrinter:[23,2,1,""]},"joy.utils.pretty_print.TracePrinter":{go:[23,5,1,""],viewer:[23,5,1,""]},"joy.utils.stack":{expression_to_string:[24,1,1,""],iter_stack:[24,1,1,""],list_to_stack:[24,1,1,""],pick:[24,1,1,""],pushback:[24,1,1,""],stack_to_string:[24,1,1,""]},joy:{joy:[1,0,0,"-"],library:[3,0,0,"-"],parser:[22,0,0,"-"]}},objnames:{"0":["py","module","Python module"],"1":["py","function","Python function"],"2":["py","class","Python class"],"3":["py","classmethod","Python class method"],"4":["py","exception","Python exception"],"5":["py","method","Python method"]},objtypes:{"0":"py:module","1":"py:function","2":"py:class","3":"py:classmethod","4":"py:exception","5":"py:method"},terms:{"0b11100111011011":12,"10m":14,"10n":14,"4ac":18,"5bkei":19,"\u03b5":16,"abstract":[15,19],"boolean":[2,3,15,19],"break":[10,15],"byte":12,"case":[2,3,6,10,14,24],"class":[3,15,22,23,24],"default":[3,9,13,24],"export":[3,22],"final":[2,7,14],"float":[3,15,20,22],"function":[0,1,5,6,7,8,9,11,12,13,17,20,21,22,23,24],"g\u00e9rard":20,"import":[2,4,5,6,7,8,9,10,12,13,14,16,18,19,20],"int":[7,13,14,15,20,22,24],"new":[2,3,4,7,13,14,15,16,17,19],"public":17,"return":[1,3,4,6,7,9,10,12,14,15,16,18,19,22,23,24],"short":18,"static":[2,17],"switch":2,"true":[2,3,6,7,12,14,19],"try":[7,13,14],"void":[0,3],"while":[3,7,9,10,15,22,24],Adding:[15,21],And:[5,7,12,13,14,16,19,20,24],But:[0,4,6,11,12,14,15,19],CPS:15,For:[2,3,5,6,7,8,9,13,14,19,21,24],Going:6,Has:3,Its:3,Not:7,One:[2,15],RHS:19,TOS:[2,3,14],That:[12,14,19],The:[0,1,2,3,5,6,7,8,9,11,13,16,17,18,20,21,22,24],Then:[2,3,6,9,18,19],There:[7,9,14,19,24],These:[21,24],Use:[3,14,16],Using:[7,14,16,19],With:[5,14,16],__str__:23,_within_b:16,_within_p:16,_within_r:16,aaa:8,abbrevi:19,abl:18,about:[0,7,9,15,19,20,24],abov:[0,7,12,16,18,19],abs:[7,16],absolut:[7,15],accept:[1,2,3,12,14,15,16,19,20],access:[7,9],accomplish:18,accordingli:19,accumul:12,across:[7,9],act:16,action:[15,20],actual:[2,7,12,15,19],adapt:21,add:[3,5,6,7,12,13,15,18,23],add_alias:3,add_def:3,add_definit:[3,9,14,19],add_if_match:5,add_valu:9,added:[11,19],adding:[7,17],addit:[0,2,3,9,12,14,15,19],admit:7,advantag:14,after:[5,7,9,12,13,15],afterward:15,again:[2,3,7,9,12,15,16,19],against:[6,7],aggreg:[3,20],aka:[15,20],albrecht:0,algebra:19,algorithm:15,alia:3,alias:[3,15],align:[15,23],all:[3,5,6,12,13,14,15,19,23],alloc:7,allow:[14,17,19],almost:19,along:[14,15,18],alphabet:3,alreadi:[4,7,16,20],also:[0,12,14,15,24],altern:[11,19],although:[5,11,19],altogeth:13,alwai:[7,12,14,17],amort:19,amount:7,analysi:[11,21],anamorph:15,ani:[9,11,12,15,17,19,20,22],annual:15,anonym:19,anoth:[5,14,19,24],answer:7,anyth:[2,3,15],aoc20017:6,aoc20173:7,aoc2017:[5,6,7,8,9,10],api:17,app1:3,app2:[3,4,6,15,18],app3:3,app:15,appear:[2,8,11,12,19],append:9,appli:[2,3,6,12,19],applic:13,approach:[12,18],approxim:21,archiv:0,aren:20,arg:[2,3],argument:[2,3,13,14,15,16,23,24],arithmet:2,ariti:2,around:[12,24],arrai:9,arrang:9,arriv:[13,19],articl:[0,11],ask:[7,11,13],aspect:[0,7],assembl:9,assert:[7,10],assign:24,associ:19,assum:[5,6,8,9,16],asterisk:19,attack:15,attempt:[0,1],attribut:3,automat:[11,14,21],avail:[0,8],averag:[4,15],avoid:19,awar:2,awkward:19,azur:21,back:[7,9,19],backward:[17,19],bag:15,banana:[14,19],bank:10,barb:14,base:[0,2,3,6,10,14,17],basic:[1,2,3,5,7,15,19],bear:9,beat:9,becaus:[2,3,5,6,7,9,14,15,19,20,24],becom:[5,18,19,24],been:[14,16,17,19,20],befor:[6,9,13,14,15,19],begin:[7,14,19],behavior:[17,19],behaviour:[0,1],behind:9,being:0,belong:9,below:[2,3,7,12,13,19,20],bespok:15,best:0,better:[7,12,13,19],between:[0,6,7,12],biannual:15,big:[7,9,19],binari:[0,13,15,19],binary_search_tre:19,binarybuiltinwrapp:3,bind:15,bingo:20,bit:[7,12,13,19],block:[10,12],bodi:[2,15,19],body_text:3,bool:[6,14],borrow:15,both:[2,4,7,9,12,14,15,18,24],bottom:13,boundari:7,bracket:[7,15,22],branch:[3,5,6,9,12,13,19],breakpoint:15,bring:[12,15],btree:21,buck:19,bug:[0,15],build:[14,15,19,20,24],built:[14,18],bundl:[2,3],burgeon:15,calcul:7,calculu:11,call:[2,14,15,16,17,18,23,24],caller:19,came:[9,19],can:[0,2,3,4,5,6,7,11,12,13,14,15,16,17,18,20,21,24],candid:6,captur:15,card:15,care:[7,12,24],carefulli:[19,20],carri:[5,7,14],cartesian:11,categor:[0,18,21],categori:11,ccc:11,ccon:19,ceil:7,certain:[15,24],certainli:19,chang:[2,7,9,17,19,20],charact:20,chat:15,chatter:0,cheat:10,check:[6,13,14],checksum:6,child0:19,childn:19,children:19,choic:[3,14],choos:[17,19],circuit:11,circular:[5,19],cite_not:19,classmethod:3,clear:[3,7,12,15],cleav:[4,5,6,8,15,18],close:[0,1,11],clunki:12,cmp:21,cmp_:19,code:[0,1,11,14,19],collaps:14,collect:[11,13,15],column:7,combin:[0,3,8,12,13,15,16,18,20,21],come:[7,9,15],command:[5,15,18,19],common:[2,12,14],compar:[7,11],comparison:0,compel:11,compil:[2,4,9,11,14,15],complet:11,complex:[3,20],compos:14,compound:19,comput:[2,6,7,9,11,12,15,18],con:[3,6,9,10,12,13,14,15,16,18,20,24],conal:11,concat:[3,5,13,14,15,19],concaten:0,concatin:[0,3,24],concis:7,concret:14,concurr:2,condit:[9,15],condition:6,confid:7,conflict:19,cons2:19,consecut:[13,21],consid:[9,12,13,14,19,20],consist:[2,7,15,19],constant:19,constitu:14,consum:[6,14],contain:[0,2,3,7,8,13,14,15],context:2,continu:[0,6,14,20],control:15,conveni:11,convert:[4,14,19,22,24],cook:14,cool:19,copi:[2,3,5,12,14,19,21],copyright:15,corner:7,correct:7,correctli:19,correspond:11,could:[2,7,9,11,12,14,15,17,19,20],count:[3,7,8,13],count_stat:10,counter:12,cours:[7,9,12,14,19],cover:7,cpu:7,crack:19,crap:21,crash:19,creat:[0,2,3,5,12,13,14,16,19],crude:[19,22],current:[2,3,9,14,15,20,23],custom:17,cycl:[12,13],cython:15,dai:[14,15],data:[2,3,7,21],datastructur:[0,2,14,20,22,24],datatyp:24,ddididi:20,deal:[0,5,19],debugg:14,decid:19,decor:3,decoupl:14,decreas:7,decrement:3,deduc:12,deeper:0,deepli:11,def:[3,4,7,9,10,14,15,18,19,24],defi:3,defin:[2,3,5,6,7,8,9,10,11,12,13,14,15,16,17,20],definit:[2,3,8,9,12,13,14,15,16,17,19,21],definitionwrapp:[3,9,14,19],deleg:15,delet:21,demonstr:[11,14],depend:[14,19],deposit:19,dequot:[5,14],deriv:[2,3,5,6,12,15,16,21],descend:6,describ:[3,11,14,19,22],descript:[12,15,19],design:[2,3,6,19],desir:[7,15,19],destruct:19,detail:[7,15,19],detect:[6,13,14,19],determin:[6,7],develop:[0,13,15,21],diagram:12,dialect:1,dict:[1,3],dictionari:[1,3,15,16,18,19],did:7,didn:14,differ:[0,6,8,11,12,14,16,18,19,24],differenti:11,dig:20,digit:[5,12],dimension:7,dinfrirst:15,dip:[3,4,6,7,9,10,12,13,14,15,16,18,19],dipd:[3,9,13,14,15,18,19,20],dipdd:[3,19],direco:[10,16],direct:15,directli:[7,12,19,24],disappear:2,discard:[3,13,14,16,19],discov:6,disenstacken:[15,19],disk:15,displac:2,distanc:7,distribut:10,ditch:19,div:[3,15],dive:19,divid:6,divis:[6,19],divisor:6,divmod:[3,6],divmod_:3,doc:[2,3,15],document:[21,22,24],doe:[0,1,6,7,9,11,14,15,21,23],doesn:[5,9,12,14,17,19,24],dog:19,doing:[7,11,12,14,15,20],domain:[7,11],don:[6,7,9,12,15,19],done:[2,12,13,15,17],doodl:7,door:15,dot:23,doubl:[12,15],down:[2,3,7,9,16,20],down_to_zero:15,downward:9,dozen:15,draft:[10,11,17],dream:15,drive:13,driven:[12,16],driver:13,drop:[3,5,19],dudipd:15,due:5,dummi:6,dup:[3,5,6,7,9,10,12,13,14,15,16,18,19,20,24],dupd:3,dupdip:[3,6,7,12,14,18,19],duplic:[3,8,14,19],durat:2,dure:[2,14],each:[2,3,4,5,6,7,9,11,12,14,15,19,23],easi:[0,7,19,20],easier:[3,5,19],easili:11,edit:21,effect:[2,3,15,20],effici:[4,7,9,20],either:[1,2,3,6,14,19],eleg:[9,15,18,19],element:[2,3],elliott:11,els:[2,3,5,6,9,10,14],embed:[11,19,20],empti:[3,6,15,24],encapsul:15,enclos:15,encod:[9,13],encount:9,end:[7,9,12,14,24],endless:13,enforc:[2,15],engend:15,enlarg:7,enough:[7,14,15,18,23],enstacken:[13,15],ensur:8,enter:15,entir:24,entri:[3,20,23],epsilon:16,equal:[12,24],equat:[7,15,16],ergo:[7,14,19],err:19,error:[7,15,22],escap:9,essai:0,etc:[3,7,20,22],euler:21,eval:0,evalu:[1,2,3,5,14,15,16,18,19],even:9,evenli:6,eventu:[7,18],everi:13,everyth:[3,19],evolv:17,exactli:14,exampl:[0,3,5,6,7,8,9,12,13,14,16,19,22,24],exce:13,except:[15,19,22],execut:[0,1,2,3,4,6,15,20,24],exist:11,exit:9,expect:[2,3,6,14,19,24],experi:15,experiment:7,explan:15,explor:15,express:[0,1,2,3,4,11,14,19,20,23,24],expression_to_str:24,extend:7,extra:[5,6,12],extrem:15,extrememli:15,facet:0,facil:15,fact:[19,22],factor:[2,12,15,21],fail:[2,3,6,19,22],fals:[2,3,6,10,12,14],far:[9,14,16,19],fascin:0,fast:7,faster:7,favorit:18,fear:19,feel:7,few:[7,12,15],fewer:[3,15],fib:13,fib_gen:13,figur:[2,3,7,19],filter:19,fin:12,find:[2,3,5,6,12,13,19,21],finder:16,fine:[0,12,19],finish:18,first:[3,4,5,6,7,9,10,13,14,15,16,18,19,20,21],fit:[12,15,18],five:[12,14,15],fix:[2,3],flag:6,flatten:[15,19],flexibl:19,floor:[3,7],floordiv:12,flow:15,follow:[0,2,3,6,9,14,15,16,17,20],foo:[15,17,19],foo_ii:17,form:[2,3,6,8,11,12,13,21,24],forman:15,format:[21,23],formula:[0,7,12,21],forth:[5,9,15,19],fortun:9,forum:0,forward:[6,9],found:[9,10,15,19],four:[2,3,7,9,12,13,15,19],fourteen:12,fourth:[2,3,5,19],fractal:15,fraction0:15,fraction:[2,15],framework:15,free:[11,15,19],freeli:[2,7],from:[0,1,2,3,4,5,6,7,8,9,10,12,13,15,16,18,19,20,21,24],front:[2,3],full:[8,12],fun:7,functionwrapp:[3,19],funtion:19,further:[16,21],futur:18,garbag:15,gari:19,gcd:15,gen:10,gener:[2,3,7,9,11,21,24],genrec:[3,6,9,14,15,19],geometr:12,geometri:19,get:[2,6,7,11,12,13,14,15,21],get_valu:9,getitem:3,getrecursionlimit:24,getsourc:15,ghc:11,give:[7,11,12,14,16,24],given:[2,3,5,6,7,9,10,12,13,16,20],glue:15,goal:9,going:[6,7,9,19,20],good:[9,12,19],grab:3,grammar:22,grand:15,graph:7,great:[0,5,7,15,21],greater:[7,24],grid:7,group:[0,7],gsra:16,guard:[6,7],had:[12,20],haiku:15,half:[12,20],half_of_s:5,halfwai:5,hand:[4,15,18,19,21],handi:16,handl:24,happen:[7,15,19],hard:20,hardli:14,hardwar:11,has:[0,2,6,7,9,13,14,15,16,17,19,20,24],haskel:11,have:[2,3,5,6,7,9,10,12,13,14,15,16,17,19,20,21,24],head:[6,14,24],help:[8,14,15,19],help_:3,helper:[3,6],herd:15,here:[7,12,13,14,18,19,20],heterogen:19,heurist:[5,9],hide:19,higher:[15,19],highest:6,highli:[15,19],hindsight:6,histori:23,hmm:19,hog:19,hoist:3,hold:12,hood:9,hope:[0,12,15,21],host:21,how:[0,7,8,9,11,14,19,20],html:[2,3,13,18,21],http:19,huet:20,hugh:[16,19],human:15,hypothet:2,id_:3,idea:[11,12,15,19],ident:[3,14],identifi:7,ift:[3,5,6,9,14,19],ignor:[3,19],illustr:14,imagin:20,immedi:[9,14],immut:[15,19],imper:14,implement:[0,1,2,3,7,10,11,14,15,17,18,19],impli:6,implicit:15,includ:[8,11],inclus:12,incom:24,incompat:17,incr_at:9,incr_step_count:9,incr_valu:9,increas:[7,9,12],increment:[3,11,12,17],index:[0,7,10,15,24],index_of:10,indexerror:24,indic:19,infil:19,infinit:7,inform:3,infra:[3,4,13,14,15,18],infrastructur:3,init:9,init_print:7,initi:[2,3,6,7,8,9,15,16,19],inlin:19,inner:6,input:[1,5,6,7,8,14,16],inscrib:3,inspect:15,instal:0,instanti:[11,23],instead:[7,12,13,14,19,20,24],instruct:9,integ:[2,3,5,6,7,8,9,13,14,15],integr:3,intend:[0,15],interact:[15,21],interest:[0,7,12,13,19],interlock:7,interlud:21,intermedi:14,intern:[0,23,24],interpret:[0,11,14,17,22,23],interrupt:15,interv:[11,12],introduc:17,introduct:0,invari:3,invers:3,investig:18,ipf:15,ipynb:13,isn:[14,20],item:[2,3,5,6,10,14,15,19,24],iter:[1,3,7,14,15,21,24],iter_stack:[4,10,24],its:[0,2,3,6,7,11,12,14,15,19,24],itself:[0,2,9,15,19],j05cmp:[2,3],jenni:19,job:[9,21],john:[16,19],joi:[2,4,5,6,8,9,10,11,16,17,18,19],joypi:[9,10,14,15,19,20],jump:9,jupyt:21,just:[0,2,3,5,6,7,9,13,14,15,17,20],keep:20,kei:21,kevin:0,key_n:19,keyerror:19,kind:[2,7,9,11,14,15,19],kleen:19,know:[7,12,14,19],known:11,labda:11,lambda:[11,14],lambdifi:7,languag:[11,15,17,18,19],larg:7,larger:[7,24],largest:[3,6,9],last:[5,9,12,14],lastli:[13,14],later:[9,15],law:2,lazi:16,lazili:16,lcm:12,lead:[9,15],leaf:19,lean:15,learn:[0,10],least:[2,7,9,12,14,24],least_fract:15,leav:[6,7,9,12,13,19],left:[7,13,14,15,20,23,24],leftov:14,legendari:9,legibl:9,len:10,length:[3,12,24],lens:14,less:[12,13,14,15,24],lesser:7,let:[5,6,7,9,13,14,16,18,19,20],level:[11,19],librari:[0,4,7,9,10,16,18,19],lieu:19,like:[2,3,6,7,10,12,14,15,16,18,22],line:[3,6,9,14,15,19,23],linear:24,link:0,linux:0,list:[0,3,5,6,8,9,10,12,15,16,20,21,23],list_to_stack:[9,10,24],liter:[1,19,20,22],littl:[7,9,19,21],live:21,lkei:19,load:[12,15],locat:[2,7],locu:23,log_2:19,logic:[0,12],longer:19,look:[7,13,15,16,19],lookup:[15,19],loop:[0,1,3,12],lot:[15,18,19,20],love:12,low:11,lower:12,lowest:6,machin:[0,19],machineri:19,macro:15,made:[0,6,15,19,20],mai:[2,9,14,19],mail:0,main:[0,3,5,15,20],mainloop:17,maintain:20,major:17,make:[2,3,4,5,11,12,14,15,20],make_distributor:10,make_gener:16,manfr:[0,2,3,11],manhattan:7,mani:[0,7,8,9,13,14,15],manipul:7,manual:[7,14],map:[1,3,12,14,15,17,18,19],map_:3,mark:[7,9],marker:15,mask:[12,13],match:[0,1,5],materi:0,math:[0,7,9,15,19],mathemat:[7,15],matter:[5,12,14,16,19],max:[6,7,10],max_:3,maximum:[3,19],maxmin:6,mayb:[14,19],maze:9,mean:[6,11,12,14,15,16,19,24],meant:[14,15,18,19],meantim:9,mem:9,member:[2,3,7],memori:7,mental:15,mention:2,mercuri:0,merg:19,meta:[15,19],methink:19,method:[0,3,7,15,21,23],mfloor:7,midpoint:12,might:[5,11,13,14,19],million:13,min:6,min_:3,mind:9,minimum:3,minu:[3,18],mirror:0,miscellan:[0,21],mistak:10,mix:15,mnemon:5,mod:3,model:[11,15],modern:0,modif:13,modifi:[9,15,20],modul:[0,1,3,15,22],modulu:15,monkei:7,month:15,more:[0,3,4,8,9,11,12,13,14,15,16,18,19,22,24],most:19,mostli:0,move:[5,7,9],movement:2,mrank_of:7,much:[7,9,12,14,19],muck:19,mul:[15,18,20,23],multi:3,multipl:[14,21],must:[2,3,6,7,8,12,14,17],mutabl:9,n_kei:19,n_rang:13,n_valu:19,nail:9,name:[1,3,5,15,17,20,21,22,24],natur:[12,13,19],navig:20,need:[2,3,5,6,7,9,10,12,13,14,16,17,19],neg:[3,9,18],nest:[15,19,20],network:15,never:17,newton:[0,21],next:[5,6,7,9,12,14,19],nice:[0,5,7,14,24],niether:2,node:21,non:[6,19],none:[1,3],normal:[8,14],notat:[15,19],note:[2,7,12,16,19,24],notebook:[12,15,20,21],notebook_preambl:[2,4,5,6,7,8,9,10,12,13,14,16,18,19,20],noth:[2,19],notic:12,now:[4,5,6,7,12,13,14,15,21],nth:[3,24],nullari:[6,9,10,15,19],number:[1,2,3,6,12,13,24],object:22,observ:12,obviou:13,obvious:[6,8,9],occur:19,odd:[12,13],off:[2,3,7,12,13,20],offset:9,offset_of:7,old:[2,4],omit:14,onc:[3,8,17,18,19],one:[2,3,5,6,7,8,9,12,13,14,18,19,23,24],ones:13,onli:[2,3,5,6,7,9,12,14,19,20,24],onto:[1,2,3,15,24],open:[8,15],oper:[3,6,14,15,19,24],oppos:5,option:[1,15,24],order:[2,3,5,6,14,15,21,24],org:[0,19],origin:[0,1,2,3,5,19,20],other:[0,2,3,6,7,11,14,15,19,24],otherwis:[3,6,12,13,19],our:[5,6,7,12,13,14,15,16],ourselv:14,out:[2,3,7,11,12,13,14,15,19,20],outcom:19,output:[7,14,16],outsid:[9,11],outward:7,over:[3,5,7,11,12,13,15,16,18,19,21],overhead:7,overkil:14,overshadow:7,own:[7,19],pack:[19,24],packag:[0,15],page:[0,18,19,24],pair:[2,3,5,6,12,13],pair_up:5,palidrom:12,palindrom:12,pam:[15,18],paper:[7,11,14,15,19,20],parallel:2,paramet:[1,2,3,9,14,22,23,24],paranthes:19,parenthes:[9,19,24],pariti:13,pars:[0,3,15,19],parse_definit:3,parseerror:22,parser:0,part:[2,3,6,9,14,16,18,19],partial:[7,14],particular:20,particularli:9,pass:[0,19,23],passphras:8,path:7,pattern:[7,12,19],payoff:14,pe1:[12,13],pe2:13,pearl:20,pend:[3,14,15,20,23],peopl:21,per:[7,15],perform:9,perhap:13,period:15,permit:[9,24],persist:19,phase:2,pick:[12,13,24],pickl:15,pictur:19,piec:14,pip:0,pita:10,place:[3,7,9,12,14,15],plai:0,plain:9,plane:7,plu:[3,7,18],plug:[13,14,19],point:[7,11,14,15,19],pointless:2,pop:[3,4,5,6,9,10,12,13,14,15,18,19,24],popd:[3,4,9,15,16],popdd:[3,6,13,18],popop:[3,5,6,9,10,12,13,14,15,16,19],port:7,posit:[3,9,12,14,15],possibilit:19,possibl:[6,19,21],post:[15,19],potenti:3,power:15,pragmat:12,pre:[9,14,19],preambl:16,precis:[0,1],pred:3,predic:[2,6,13,14],prefer:14,prefix:[14,23],prep:[6,19],prepar:[9,14],preprocessor:14,present:19,preserv:11,pretti:[7,18,19,23,24],pretty_print:0,prevent:14,previou:[7,9,15],prime:[6,16],primit:[2,3,9,18],primrec:[3,6,9,10,13,14,15,16],print:[0,1,2,3,7,14,23,24],probabl:[5,13,15,19],problem:[7,15,21],proc_curr:19,proc_left:19,proc_right:19,proce:[5,12],process:[9,14,15,23],processor:19,produc:[5,12,14,19],product:15,program:[0,2,3,5,6,7,9,13,15,16,20],project:21,prompt:15,proper:[2,3],properli:9,properti:0,provid:[0,3,11,15],prune:19,pun:[0,15],pure:[0,19],puriti:15,purpos:15,push:[2,3,14,15,20,24],pushback:[15,19,24],put:[1,2,13,15,24],puzzl:[5,6,7,8],pypi:0,pyramid:7,python:[0,2,3,7,9,14,18,19,20,22,24],quadrat:[0,7,21],queri:19,queu:14,quit:[0,1,7],quot:[0,3,13,14,15,16,18,19,20,23],quotat:[2,3],quotient:3,rais:[19,22,24],random:9,rang:[7,14,15],range_sum:14,range_to_zero:15,rank_and_offset:7,rank_of:7,raphson:16,rather:[12,14,15,19],ratio:15,reach:[9,12,13,14],read:[0,1,12,13,19,20],readabl:4,real:19,realiz:[5,9,11,19],realli:7,rearrang:[2,14],reason:[7,12,15],rebuild:20,rec1:[2,3],rec2:[2,3],recogn:22,record:[15,23],recur:14,recurs:[2,3,6,9,10,13,15,16,21,24],recus:15,recusr:19,redistribut:[3,15],reduc:2,redund:24,reexamin:19,refactor:[14,15,17],refer:[0,2],regist:2,regular:22,rel:[9,18],releas:17,relev:7,remain:[2,3,15,17],remaind:[3,16],remind:14,remov:[3,7,19,24],renam:19,render:[19,21],repeat:[5,7,12],repeatedli:12,repl:[0,1],replac:[2,3,13,14,20,24],repositori:0,repres:[2,15,19,22,23],represent:24,reprod:13,request:7,requir:[7,24],resembl:15,respect:12,rest:[3,6,10,12,13,15,19,20,21,24],restor:2,result:[1,2,3,6,12,13,14,18,19,20],resum:15,retir:2,retri:15,reus:19,revers:[3,5,6,12,13,14,20,24],rewrit:[9,15],rewritten:15,richard:19,right:[7,13,14,15,23,24],rightmost:12,rkei:19,role:19,roll:[3,6,8,9,14,16,18,19],rolldown:3,rollup:3,root:[3,7,18,21],rotate_seq:5,round:5,row:[6,7],row_valu:7,run:[0,1,3,7,12,14,15,16,19,20],runtim:7,runtimeerror:24,sai:19,same:[2,11,12,14,19,24],sandwich:[2,3],save:[2,12,15],scan:3,scanner:[15,22],scenario:20,scheme:[18,19],scope:[5,19],search:[0,7,19],second:[3,5,6,14,15,19,24],secur:8,see:[0,4,7,13,14,15,17,19,20,23],seem:[0,10,12,15,19],seen:20,select:[3,7],semant:[2,3,15,17,19],semi:15,send:15,sens:[0,2,12,20],separ:15,sequenc:[0,1,2,3,4,5,6,8,9,10,12,15,19,20,22],seri:[7,12,13,14,19,20],serv:14,set:[2,3,14],seven:[12,13],sever:[0,11,15],share:[3,7,15],shelf:2,shift:[12,13],shine:9,shortest:7,should:[2,6,12,14,19],shouldn:15,show:[7,11,19,20],shunt:[3,20],side:19,sign:7,signal:6,signifi:[15,19],silli:19,similar:19,simon:15,simpl:[7,14,15,24],simplefunctionwrapp:[3,4,9,10,18],simplest:21,simpli:11,simplifi:[7,12,19,20],sinc:[2,7,12,18,19],singl:[3,4,13,15,22],situ:19,situat:19,six:[12,13,15],sixti:[12,13],size:[5,8,9,10,15],skeptic:15,skip:[7,9],slight:16,slightli:[14,19],small:[5,19],smallest:[3,6],smart:[9,14],sneaki:7,softwar:15,solei:2,solut:[7,12],solv:7,solvabl:15,some:[2,3,6,7,9,13,14,15,19,21,24],somehow:19,someth:[2,5,9,17],sometim:19,somewher:[14,19,21],sophist:7,sort:[3,6,14,18,19],sort_:3,sourc:[0,1,3,22,23,24],space:[7,12,23],span:12,special:[13,14,19],specif:[0,11],speed:[4,7,9],sphinx:[21,24],spiral:7,spirit:[0,1,19],split_at:5,spreadsheet:6,sqr:[15,18,20],sqrt:[3,7,16,18],squar:[3,7,21,22],stack:[0,1,3,4,6,9,10,12,13,14,16,18,19,20,22,23],stack_:3,stack_to_str:24,stage:19,stai:[0,1],stand:11,standard:15,star:19,stare:19,start:[6,7,9,10,12,13,14,15,16,18,19],state:[6,9,15],step:[3,4,5,6,7,8,12,15,18,19,20],step_zero:[5,6,8],still:[7,9,14],stop:19,storag:[12,14,19],store:[7,12,14],stori:14,str:[1,22,23,24],straightforward:[1,5,7,13],strang:9,stream:[12,16],string:[1,2,3,5,15,20,22,23,24],strip:7,structur:[14,15,19,20,24],stuff:19,style:[0,11],sub:17,subclass:15,subject:20,subract:7,substitut:[7,14],subtract:[6,7,12],succ:3,success:16,suffici:[9,14],suggest:[6,11,19],suitabl:[3,11,12],sum:[3,4,5,6,13,14,15,18,19],sum_:3,summand:12,suppli:[14,19,22],support:[7,15,23,24],sure:[7,14],suspect:2,swaack:[3,4,14,18,19,20],swap:[3,4,5,6,7,8,10,12,13,14,15,16,19,20],swon:[3,10,13,14,15,19,20],swoncat:[9,10,13,14,15,16,19],symbol:[2,3,7,18,20,22],symmetr:12,sympi:18,syntact:15,syntax:[15,24],sys:[7,24],system:[7,8,15,19],tail:[6,19,24],take:[3,5,7,9,12,13,15,16,18,19,24],taken:9,talk:[15,19,24],target:[7,20],task:7,tast:11,tbd:15,technic:2,techniqu:[11,20],technolog:2,teh:19,temporari:20,ten:12,term:[1,2,6,9,10,14,15,16,22,24],termin:[2,3,6],ternari:15,test:[2,3],text:[0,1,3],text_to_express:[15,22],textual:15,than:[0,3,7,8,12,13,15,16,18,24],thei:[2,6,7,12,13,14,15,19,20,22,24],them:[2,3,6,7,12,13,14,19,20,21],theori:[2,3],therefor:[13,19],thi:[0,1,2,3,5,6,7,9,10,11,12,13,14,15,18,20,22,23,24],thing:[2,6,7,9,13,14,18,19,20,22,24],think:[2,9,12,14,15,19],third:[3,5,6,13,15,19],thirti:12,those:[2,3,6,7,9,14,19,21],though:[12,13,19],thought:15,thousand:12,thread:2,three:[2,3,9,12,15,19],through:[1,12,15,20,24],thu:5,thun:[2,3,11,17],thunder:15,tied:19,tile:7,time:[3,7,9,10,12,14,15,19,20],tini:19,to_set:19,todai:15,todo:[15,21,22],togeth:[13,15],token:22,toler:21,tommi:19,too:[14,19],took:7,tool:15,top:[2,3,15,23,24],total:[5,7,12],total_match:5,trace:[0,15,18,20,24],traceprint:23,track:20,tracker:0,trade:7,transform:[11,14],translat:[7,11,14],travers:[20,21],treasur:0,treat:[0,2,3,21],treatment:13,tree:[0,15,21],treemap:14,tri:12,trick:[12,19],tricki:[7,9],trivial:[6,9,19],trobe:0,trove:0,truediv:18,truthi:[3,15],ts0:[14,19],ts1:[14,19],tuck:[3,6,15,19],tupl:[3,15,24],turn:[2,3,7],twice:[7,14,19],two:[2,3,6,7,12,14,15,16,19,20,24],type:[1,11,14,15,21,22,23,24],typic:[2,3],unari:[9,14,15],unarybuiltinwrapp:3,unbalanc:22,uncon:[3,5,6,13,14,15,19,20],under:[2,3,9,15],understand:[0,7,19],undocu:15,unfortun:24,uniqu:[3,8,19],unit:[5,14,15,19],univers:[0,15],unless:[7,14],unlik:14,unnecessari:21,unpack:[2,3,24],unpair:12,unquot:[14,15,19],unstack:3,untangl:[13,14],until:[6,7,9,13],unus:12,unusu:19,updat:[0,21],upward:9,usag:15,use:[0,2,3,4,7,9,11,12,13,15,16,17,18,19,20,24],used:[3,11,14,15,19,20,22,24],useful:0,user:7,uses:[2,6,12,14],using:[3,6,7,13,14,18,19,20],usual:[0,2],util:[0,4,9,10,19],valid:8,valu:[2,3,4,6,7,12,14,15,16,21,24],value_n:19,valueerror:24,vanilla:9,variabl:[14,21],variat:14,varient:19,varieti:[11,15],variou:0,vener:24,verbos:11,veri:[0,1,7,11,15,19,24],versa:2,version:[0,1,2,13,17,18,20,21],via:15,vice:2,view:21,viewer:[1,15,17,23],von:[0,2,3,11],wai:[0,2,3,5,7,9,11,12,14,15,19],walk:19,wall:7,want:[2,7,9,12,13,16,19],warranti:[3,15],wash:15,wast:15,web:24,websit:[0,12],welcom:15,well:[0,5,6,7,11,15,19,22],were:[7,9,14,15,20],what:[2,3,6,9,10,11,14,15,18,19,23],whatev:[2,3,13,19,24],when:[12,13,14,15,16,19,20,22,24],where:[2,3,5,6,9,14,15,19,21,24],whether:14,which:[0,1,3,6,7,9,12,14,15,16,18,19,20,24],whole:[2,3,6,12,19],whose:13,why:[7,16,19],wiki:19,wikipedia:[0,19,20],wildli:15,wind:15,winner:7,wire:14,wit:9,within:[15,19,21],without:[2,15,19],won:[19,24],word:[0,3,5,6,8,12,13,15,19,20],work:[0,5,6,7,9,12,13,14,15,19,20,24],worth:[7,12],would:[2,6,7,8,9,10,12,13,14,15,16,19,20,24],wouldn:9,wrap:[3,7,15],write:[5,7,9,11,13,14,16,19,20,21,24],written:[0,1,4,9,16,18,24],wrong:2,wtf:14,wtfmorphism:14,year:15,yet:[9,14,19,20],yield:[2,3,24],you:[0,2,3,4,6,7,9,12,13,14,15,17,19,20,23,24],your:[2,3,5,6,7,8,15],yourself:[15,19],zero:[3,6,7,9,14,19,22,24],zip:[5,12],zip_:3,zstr:20},titles:["Thun 0.1.1 Documentation","Joy Interpreter","Functions Grouped by, er, Function with Examples","Function Reference","Replacing Functions in the Dictionary","Advent of Code 2017","Advent of Code 2017","Advent of Code 2017","Advent of Code 2017","Advent of Code 2017","Advent of Code 2017","Categorical Programming","Developing a Program in Joy","Using <code class=\"docutils literal notranslate\"><span class=\"pre\">x</span></code> to Generate Values","Hylomorphism","Thun: Joy in Python","Newton\u2019s method","No Updates","Quadratic formula","Treating Trees","Preamble","Essays about Programming in Joy","Parsing Text into Joy Expressions","Tracing Joy Execution","Stack or Quote or Sequence or List\u2026"],titleterms:{"1st":5,"2nd":6,"3rd":7,"4th":8,"5th":9,"6th":10,"case":[16,19],"final":6,"function":[2,3,4,10,14,15,16,18,19],"long":4,"void":2,"while":2,Adding:19,One:13,The:[12,14,15,19],There:15,Use:19,Using:13,about:21,abov:14,add:[2,9,19],adding:19,address:20,advent:[5,6,7,8,9,10],all:[7,9],ana:14,analysi:[7,12],anamorph:[2,14],app1:2,app2:2,app3:2,appendix:14,approxim:16,automat:19,averag:2,base:[16,19],befor:10,better:14,binari:2,block:6,branch:2,breakdown:9,btree:19,can:19,cata:14,catamorph:14,categor:11,chatter:2,check:18,child:19,choic:2,cleanup:18,clear:2,cleav:2,cmp:19,code:[5,6,7,8,9,10,15],combin:[2,14,19],compar:19,comparison:2,compil:13,comput:16,con:[2,19],concat:2,consecut:16,continu:15,count:[9,10],crap:19,current:19,data:19,datastructur:[15,19],decemb:[5,6,7,8,9,10],defin:[18,19],definit:18,delet:19,deriv:[14,18,19],determin:20,develop:12,dialect:0,dictionari:4,dip:[2,20],dipd:2,dipdd:2,direco:13,disenstacken:2,div:2,document:0,doe:19,down:6,down_to_zero:2,drive:10,drop:2,dup:2,dupd:2,dupdip:2,els:19,empti:19,enstacken:2,equal:19,essai:21,euler:[12,13],eval:15,evalu:4,even:13,exampl:[2,15],execut:23,express:[15,22],extract:[14,19],factor:[14,19],factori:14,fibonacci:13,filter:12,find:[7,14,16],first:[2,12],five:13,flatten:2,floordiv:2,form:[14,19],formula:18,four:14,from:14,ftw:5,fun:14,further:12,fusion:14,gcd:2,gener:[10,12,13,14,16,19],genrec:2,get:[9,19],getitem:2,given:[14,19],gotten:9,greater:19,group:2,help:2,host:0,how:[10,12,13],hylo:14,hylomorph:14,ift:2,increment:9,index:9,indic:0,inform:0,infra:[2,19,20],integ:12,interlud:19,intern:22,interpret:[1,15],isn:19,item:20,iter:[12,19],joi:[0,1,3,7,12,14,15,20,21,22,23,24],just:[12,19],kei:19,languag:0,law:14,least_fract:2,left:19,less:19,let:12,librari:[3,15],like:19,list:[2,14,19,24],literari:15,littl:12,logic:2,loop:[2,6,15],lshift:2,make:[16,19],mani:[10,12],map:2,math:2,method:16,min:2,miscellan:[2,19],mod:2,modif:19,modulu:2,mul:2,multipl:[12,13],must:19,name:[18,19],nativ:18,neg:2,newton:16,next:16,node:[14,19],now:[9,19],nullari:2,number:[7,14],offset:7,one:15,onli:15,order:19,osdn:0,our:19,out:6,over:2,pack:12,pam:2,paper:6,para:14,paramet:19,parameter:[14,19],paramorph:14,pars:[2,22],parser:[15,22],pass:15,path:20,pattern:14,per:19,piec:6,pop:2,popd:2,popop:2,pow:2,power:13,preambl:[9,14,20],pred:2,predic:[9,12,16,19],pretty_print:23,primrec:2,print:15,problem:[12,13],process:19,product:2,program:[10,11,12,14,18,19,21],project:[0,12,13],pure:15,put:[7,19],python:[4,15],quadrat:18,quick:0,quot:[2,24],rang:[2,12],range_to_zero:2,rank:7,read:15,recal:10,recur:[16,19],recurs:[14,19],redefin:19,refactor:[5,12,19],refer:3,regular:15,rem:2,remaind:2,remov:2,render:12,repeat:10,repl:15,replac:4,rescu:7,reset:13,rest:[2,14],revers:2,right:[19,20],roll:2,rolldown:2,rollup:2,root:16,rshift:2,run:[2,13],sat:6,second:2,select:2,sequenc:[13,24],set:[9,16,19],shorter:4,should:15,shunt:2,simplest:12,simplifi:18,size:[2,4],slight:19,sqr:2,sqrt:2,squar:16,stack:[2,15,24],start:0,state:10,step:[2,9,14],style:15,sub:2,succ:2,sum:[2,12],swaack:2,swap:2,swon:2,swoncat:2,symbol:[14,15],sympi:7,tabl:0,tail:14,take:2,term:[12,13,19],ternari:2,text:22,than:[14,19],thi:19,think:6,third:2,three:13,thun:[0,15],time:[2,13],todo:19,togeth:[7,9,19],toi:19,token:15,toler:16,trace:[4,23],traceprint:15,travers:19,treat:19,tree:[14,19,20],treestep:[14,19],triangular:14,tricki:6,truediv:2,truthi:2,tuck:2,two:13,type:19,unari:2,uncon:2,unfinish:14,unit:2,unnecessari:12,unquot:2,unstack:2,updat:17,use:14,usual:14,util:[23,24],valu:[9,13,19],variabl:18,version:[4,7,12,19],view:15,want:6,within:16,word:2,write:18,xor:2,zero:13,zip:2,zipper:20}})
\ No newline at end of file
+Search.setIndex({docnames:["index","joy","lib","library","notebooks/Advent of Code 2017 December 1st","notebooks/Advent of Code 2017 December 2nd","notebooks/Advent of Code 2017 December 3rd","notebooks/Advent of Code 2017 December 4th","notebooks/Advent of Code 2017 December 5th","notebooks/Advent of Code 2017 December 6th","notebooks/Categorical","notebooks/Developing","notebooks/Generator Programs","notebooks/Hylo-, Ana-, Cata-, and Para-morphisms - Recursion Combinators","notebooks/Intro","notebooks/Newton-Raphson","notebooks/NoUpdates","notebooks/Quadratic","notebooks/Replacing","notebooks/Trees","notebooks/Zipper","notebooks/index","parser","pretty","stack"],envversion:52,filenames:["index.rst","joy.rst","lib.rst","library.rst","notebooks/Advent of Code 2017 December 1st.rst","notebooks/Advent of Code 2017 December 2nd.rst","notebooks/Advent of Code 2017 December 3rd.rst","notebooks/Advent of Code 2017 December 4th.rst","notebooks/Advent of Code 2017 December 5th.rst","notebooks/Advent of Code 2017 December 6th.rst","notebooks/Categorical.rst","notebooks/Developing.rst","notebooks/Generator Programs.rst","notebooks/Hylo-, Ana-, Cata-, and Para-morphisms - Recursion Combinators.rst","notebooks/Intro.rst","notebooks/Newton-Raphson.rst","notebooks/NoUpdates.rst","notebooks/Quadratic.rst","notebooks/Replacing.rst","notebooks/Trees.rst","notebooks/Zipper.rst","notebooks/index.rst","parser.rst","pretty.rst","stack.rst"],objects:{"joy.joy":{joy:[1,1,1,""],repl:[1,1,1,""],run:[1,1,1,""]},"joy.library":{"void":[3,1,1,""],BinaryBuiltinWrapper:[3,1,1,""],DefinitionWrapper:[3,2,1,""],FunctionWrapper:[3,1,1,""],SimpleFunctionWrapper:[3,1,1,""],UnaryBuiltinWrapper:[3,1,1,""],add_aliases:[3,1,1,""],app1:[3,1,1,""],app2:[3,1,1,""],app3:[3,1,1,""],b:[3,1,1,""],branch:[3,1,1,""],choice:[3,1,1,""],clear:[3,1,1,""],concat:[3,1,1,""],cons:[3,1,1,""],dip:[3,1,1,""],dipd:[3,1,1,""],dipdd:[3,1,1,""],divmod_:[3,1,1,""],drop:[3,1,1,""],dup:[3,1,1,""],dupd:[3,1,1,""],dupdip:[3,1,1,""],first:[3,1,1,""],floor:[3,1,1,""],genrec:[3,1,1,""],getitem:[3,1,1,""],help_:[3,1,1,""],i:[3,1,1,""],id_:[3,1,1,""],ifte:[3,1,1,""],infra:[3,1,1,""],initialize:[3,1,1,""],inscribe:[3,1,1,""],loop:[3,1,1,""],map_:[3,1,1,""],max_:[3,1,1,""],min_:[3,1,1,""],over:[3,1,1,""],parse:[3,1,1,""],pm:[3,1,1,""],pop:[3,1,1,""],popd:[3,1,1,""],popdd:[3,1,1,""],popop:[3,1,1,""],pred:[3,1,1,""],remove:[3,1,1,""],rest:[3,1,1,""],reverse:[3,1,1,""],rolldown:[3,1,1,""],rollup:[3,1,1,""],select:[3,1,1,""],sharing:[3,1,1,""],shunt:[3,1,1,""],sort_:[3,1,1,""],sqrt:[3,1,1,""],stack_:[3,1,1,""],step:[3,1,1,""],succ:[3,1,1,""],sum_:[3,1,1,""],swaack:[3,1,1,""],swap:[3,1,1,""],take:[3,1,1,""],times:[3,1,1,""],tuck:[3,1,1,""],uncons:[3,1,1,""],unique:[3,1,1,""],unstack:[3,1,1,""],warranty:[3,1,1,""],words:[3,1,1,""],x:[3,1,1,""],zip_:[3,1,1,""]},"joy.library.DefinitionWrapper":{add_def:[3,3,1,""],add_definitions:[3,3,1,""],parse_definition:[3,3,1,""]},"joy.parser":{ParseError:[22,4,1,""],Symbol:[22,2,1,""],text_to_expression:[22,1,1,""]},"joy.utils":{pretty_print:[23,0,0,"-"],stack:[24,0,0,"-"]},"joy.utils.pretty_print":{TracePrinter:[23,2,1,""]},"joy.utils.pretty_print.TracePrinter":{go:[23,5,1,""],viewer:[23,5,1,""]},"joy.utils.stack":{expression_to_string:[24,1,1,""],iter_stack:[24,1,1,""],list_to_stack:[24,1,1,""],pick:[24,1,1,""],pushback:[24,1,1,""],stack_to_string:[24,1,1,""]},joy:{joy:[1,0,0,"-"],library:[3,0,0,"-"],parser:[22,0,0,"-"]}},objnames:{"0":["py","module","Python module"],"1":["py","function","Python function"],"2":["py","class","Python class"],"3":["py","classmethod","Python class method"],"4":["py","exception","Python exception"],"5":["py","method","Python method"]},objtypes:{"0":"py:module","1":"py:function","2":"py:class","3":"py:classmethod","4":"py:exception","5":"py:method"},terms:{"0b11100111011011":11,"10m":13,"10n":13,"4ac":17,"5bkei":19,"\u03b5":15,"abstract":[14,19],"boolean":[2,3,14,19],"break":[9,14],"byte":11,"case":[2,3,5,9,13,24],"class":[3,14,22,23,24],"default":[3,8,12,24],"export":[3,22],"final":[2,6,13],"float":[3,14,20,22],"function":[0,1,4,5,6,7,8,10,11,12,16,20,21,22,23,24],"g\u00e9rard":20,"import":[2,4,5,6,7,8,9,11,12,13,15,17,18,19,20],"int":[6,12,13,14,20,22,24],"long":21,"new":[2,3,6,12,13,14,15,16,18,19],"public":16,"return":[1,3,5,6,8,9,11,13,14,15,17,18,19,22,23,24],"short":17,"static":[2,16],"switch":2,"true":[2,3,5,6,11,13,19],"try":[6,12,13],"void":[0,3],"while":[3,6,8,9,14,19,22,24],Adding:[14,21],And:[4,6,11,12,13,15,19,20,24],But:[0,5,10,11,13,14,18,19],CPS:14,For:[2,3,4,5,6,7,8,12,13,19,21,24],Going:5,Has:3,Its:3,Not:6,One:[2,14],RHS:19,TOS:[2,3,13],That:[11,13,19],The:[0,1,2,3,4,5,6,7,8,10,12,15,16,17,20,21,22,24],Then:[2,3,5,8,17,19],There:[6,8,13,19,24],These:[21,24],Use:[3,13,15],Using:[6,13,15,19],With:[4,13,15],__str__:23,_within_b:15,_within_p:15,_within_r:15,aaa:7,abbrevi:19,abl:17,about:[0,6,8,14,19,20,24],abov:[0,6,11,15,17,19],abs:[6,15],absolut:[6,14],accept:[1,2,3,11,13,14,15,19,20],access:[6,8],accomplish:17,accordingli:19,accumul:11,across:[6,8],act:15,action:[14,20],actual:[2,6,11,14,19],adapt:21,add:[3,4,5,6,11,12,14,17,23],add_alias:3,add_def:3,add_definit:[3,8,13,19],add_if_match:4,add_valu:8,added:[10,19],adding:[6,16],addit:[0,2,3,8,11,13,14,19],admit:6,advantag:13,after:[4,6,8,11,12,14],afterward:14,again:[2,3,6,8,11,14,15,19],against:[5,6],aggreg:[3,20],aka:[14,20],albrecht:0,algebra:19,algorithm:14,alia:3,alias:[3,14],align:[14,23],all:[3,4,5,11,12,13,14,19,23],alloc:6,allow:[13,16,19],almost:19,along:[13,14,17],alphabet:3,alreadi:[6,15,18,20],also:[0,11,13,14,19,24],altern:[10,19],although:[4,10,19],altogeth:12,alwai:[6,11,13,16],amort:19,amount:6,analysi:[10,21],anamorph:14,ani:[8,10,11,14,16,19,20,22],annual:14,anonym:19,anoth:[4,13,19,24],answer:6,anyth:[2,3,14],aoc20017:5,aoc20173:6,aoc2017:[4,5,6,7,8,9],api:16,app1:3,app2:[3,5,14,17,18],app3:3,app:14,appear:[2,7,10,11,19],append:8,appli:[2,3,5,11,19],applic:12,approach:[11,17],approxim:21,archiv:0,aren:20,arg:[2,3],argument:[2,3,12,13,14,15,23,24],arithmet:2,ariti:2,around:[11,24],arrai:8,arrang:8,arriv:[12,19],articl:[0,10],ask:[6,10,12],aspect:[0,6],assembl:8,assert:[6,9],assign:24,associ:19,assum:[4,5,7,8,15],asterisk:19,attack:14,attempt:[0,1],attribut:3,automat:[10,13,21],avail:[0,7],averag:[14,18],avoid:19,awar:2,awkward:19,azur:21,back:[6,8,19],backward:[16,19],bag:14,banana:[13,19],bank:9,barb:13,base:[0,2,3,5,9,13,16],basic:[1,2,3,4,6,14,19],bear:8,beat:8,becaus:[2,3,4,5,6,8,13,14,19,20,24],becom:[4,17,19,24],been:[13,15,16,19,20],befor:[5,8,12,13,14,19],begin:[6,13,19],behavior:[16,19],behaviour:[0,1],behind:8,being:0,belong:8,below:[2,3,6,11,12,19,20],bespok:14,best:0,better:[6,11,12,19],between:[0,5,6,11],biannual:14,big:[6,8,19],binari:[0,12,14,19],binary_search_tre:19,binarybuiltinwrapp:3,bind:14,bingo:20,bit:[6,11,12,19],block:[9,11],bodi:[2,14,19],body_text:3,bool:[5,13],borrow:14,both:[2,6,8,11,13,14,17,18,19,24],bottom:12,boundari:6,bracket:[6,14,22],branch:[3,4,5,8,11,12,19],breakpoint:14,bring:[11,14],btree:21,buck:19,bug:[0,14],build:[13,14,19,20,24],built:[13,17],bundl:[2,3],burgeon:14,calcul:6,calculu:10,call:[2,13,14,15,16,17,19,23,24],caller:19,came:[8,19],can:[0,2,3,4,5,6,10,11,12,13,14,15,16,17,18,20,21,24],candid:5,captur:14,card:14,care:[6,11,24],carefulli:[19,20],carri:[4,6,13],cartesian:10,categor:[0,17,21],categori:10,ccc:10,ccon:19,ceil:6,certain:[14,24],certainli:19,chang:[2,6,8,16,19,20],charact:20,chat:14,chatter:0,cheat:9,check:[5,12,13],checksum:5,child0:19,childn:19,children:19,choic:[3,13],choos:[16,19],circuit:10,circular:[4,19],cite_not:19,classmethod:3,clear:[3,6,11,14],cleav:[4,5,7,14,17,18],close:[0,1,10],clunki:11,cmp:21,cmp_:19,code:[0,1,10,13,19],collaps:13,collect:[10,12,14],column:6,combin:[0,3,7,11,12,14,15,17,20,21],come:[6,8,14],command:[4,14,17,19],common:[2,11,13],compar:[6,10],comparison:0,compel:10,compil:[2,8,10,13,14,18],complet:10,complex:[3,20],compos:13,compound:19,comput:[2,5,6,8,10,11,14,17],con:[3,5,8,9,11,12,13,14,15,17,20,24],conal:10,concat:[3,4,12,13,14,19],concaten:0,concatin:[0,3,24],concis:6,concret:13,concurr:2,condit:[8,14],condition:5,confid:6,conflict:19,cons2:19,consecut:[12,21],consid:[8,11,12,13,19,20],consist:[2,6,14,19],constant:19,constitu:13,consum:[5,13],contain:[0,2,3,6,7,12,13,14],context:2,continu:[0,5,13,20],control:14,conveni:10,convert:[13,18,19,22,24],cook:13,cool:19,copi:[2,3,4,11,13,19,21],copyright:14,corner:6,correct:6,correctli:19,correspond:10,could:[2,6,8,10,11,13,14,16,19,20],count:[3,6,7,12],count_stat:9,counter:11,cours:[6,8,11,13,19],cover:6,cpu:6,crack:19,crap:21,crash:19,creat:[0,2,3,4,11,12,13,15,19],crude:[19,22],current:[2,3,8,13,14,20,23],custom:16,cycl:[11,12],cython:14,dai:[13,14],data:[2,3,6,21],datastructur:[0,2,13,20,22,24],datatyp:24,ddididi:20,deal:[0,4,19],debugg:13,decid:19,decor:3,decoupl:13,decreas:6,decrement:3,deduc:11,deeper:0,deepli:10,def:[3,6,8,9,13,14,17,18,19,24],defi:3,defin:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,20],definit:[2,3,7,8,11,12,13,14,15,16,19,21],definitionwrapp:[3,8,13,19],deleg:14,delet:21,demonstr:[10,13],depend:[13,19],deposit:19,dequot:[4,13],deriv:[2,3,4,5,11,14,15,21],descend:5,describ:[3,10,13,19,22],descript:[11,14,19],design:[2,3,5,19],desir:[6,14,19],destruct:19,detail:[6,14,19],detect:[5,12,13,19],determin:[5,6],develop:[0,12,14,21],diagram:11,dialect:1,dict:[1,3],dictionari:[0,1,3,14,15,17,19,21],did:6,didn:13,differ:[0,5,7,10,11,13,15,17,19,24],differenti:10,dig:20,digit:[4,11],dimension:6,dinfrirst:14,dip:[3,5,6,8,9,11,12,13,14,15,17,18,19],dipd:[3,8,12,13,14,17,19,20],dipdd:[3,19],direco:[9,15],direct:14,directli:[6,11,19,24],disappear:2,discard:[3,12,13,15,19],discov:5,disenstacken:[14,19],disk:14,displac:2,distanc:6,distribut:9,ditch:19,div:[3,14],dive:19,divid:5,divis:[5,19],divisor:5,divmod:[3,5],divmod_:3,doc:[2,3,14],document:[21,22,24],doe:[0,1,5,6,8,10,13,14,21,23],doesn:[4,8,11,13,16,19,24],dog:19,doing:[6,10,11,13,14,20],domain:[6,10],don:[5,6,8,11,14,19],done:[2,11,12,14,16],doodl:6,door:14,dot:23,doubl:[11,14],down:[2,3,6,8,15,20],down_to_zero:14,downward:8,dozen:14,draft:[9,10,16],dream:14,drive:12,driven:[11,15],driver:12,drop:[3,4,19],dudipd:14,due:4,dummi:5,dup:[3,4,5,6,8,9,11,12,13,14,15,17,19,20,24],dupd:3,dupdip:[3,5,6,11,13,17,19],duplic:[3,7,13,19],durat:2,dure:[2,13],each:[2,3,4,5,6,8,10,11,13,14,18,19,23],easi:[0,6,19,20],easier:[3,4,19],easili:10,edit:21,effect:[2,3,14,20],effici:[6,8,18,20],either:[1,2,3,5,13,19],eleg:[8,14,17,19],element:[2,3],elliott:10,els:[2,3,4,5,8,9,13],embed:[10,19,20],empti:[3,5,14,24],encapsul:14,enclos:14,encod:[8,12],encount:8,end:[6,8,11,13,24],endless:12,enforc:[2,14],engend:14,enlarg:6,enough:[6,13,14,17,23],enstacken:[12,14],ensur:7,enter:14,entir:24,entri:[3,20,23],epsilon:15,equal:[11,24],equat:[6,14,15],ergo:[6,13,19],err:19,error:[6,14,22],escap:8,essai:0,etc:[3,6,20,22],euler:21,eval:0,evalu:[1,2,3,4,13,14,15,17,18,19],even:8,evenli:5,eventu:[6,17],everi:12,everyth:[3,19],evolv:16,exactli:13,exampl:[0,3,4,5,6,7,8,11,12,13,15,19,22,24],exce:12,except:[14,19,22],execut:[0,1,2,3,5,14,18,20,24],exist:10,exit:8,expect:[2,3,5,13,19,24],experi:14,experiment:6,explan:14,explor:14,express:[0,1,2,3,10,13,18,19,20,23,24],expression_to_str:24,extend:6,extra:[4,5,11],extrem:14,extrememli:14,facet:0,facil:14,fact:[19,22],factor:[2,11,14,21],fail:[2,3,5,19,22],fals:[2,3,5,9,11,13],far:[8,13,15,19],fascin:0,fast:6,faster:6,favorit:17,fear:19,feel:6,few:[6,11,14],fewer:[3,14],fib:12,fib_gen:12,figur:[2,3,6,19],filter:19,fin:11,find:[2,3,4,5,11,12,19,21],finder:15,fine:[0,11,19],finish:17,first:[3,4,5,6,8,9,12,13,14,15,17,18,19,20,21],fit:[11,14,17],five:[11,13,14],fix:[2,3],flag:5,flatten:[14,19],flexibl:19,floor:[3,6],floordiv:11,flow:14,follow:[0,2,3,5,8,13,14,15,16,20],foo:[14,16,19],foo_ii:16,form:[2,3,5,7,10,11,12,21,24],forman:14,format:[21,23],formula:[0,6,11,21],forth:[4,8,14,19],fortun:8,forum:0,forward:[5,8],found:[8,9,14,19],four:[2,3,6,8,11,12,14,19],fourteen:11,fourth:[2,3,4,19],fractal:14,fraction0:14,fraction:[2,14],framework:14,free:[10,14,19],freeli:[2,6],from:[0,1,2,3,4,5,6,7,8,9,11,12,14,15,17,18,19,20,21,24],front:[2,3],full:[7,11],fun:6,functionwrapp:[3,19],funtion:19,further:[15,21],futur:17,garbag:14,gari:19,gcd:14,gen:9,gener:[2,3,6,8,10,21,24],genrec:[3,5,8,13,14,19],geometr:11,geometri:19,get:[2,5,6,10,11,12,13,14,21],get_valu:8,getitem:3,getrecursionlimit:24,getsourc:14,ghc:10,give:[6,10,11,13,15,24],given:[2,3,4,5,6,8,9,11,12,15,20],glue:14,goal:8,going:[5,6,8,19,20],good:[8,11,19],grab:3,grammar:22,grand:14,graph:6,great:[0,4,6,14,21],greater:[6,24],grid:6,group:[0,6],gsra:15,guard:[5,6],had:[11,20],haiku:14,half:[11,20],half_of_s:4,halfwai:4,hand:[14,17,18,19,21],handi:15,handl:24,happen:[6,14,19],hard:20,hardli:13,hardwar:10,has:[0,2,5,6,8,12,13,14,15,16,19,20,24],haskel:10,have:[2,3,4,5,6,8,9,11,12,13,14,15,16,19,20,21,24],head:[5,13,24],help:[7,13,14,19],help_:3,helper:[3,5],herd:14,here:[6,11,12,13,17,19,20],heterogen:19,heurist:[4,8],hide:19,higher:[14,19],highest:[5,19],highli:[14,19],hindsight:5,histori:23,hmm:19,hog:19,hoist:3,hold:11,hood:8,hope:[0,11,14,21],host:21,how:[0,6,7,8,10,13,19,20],html:[2,3,12,17,21],http:19,huet:20,hugh:[15,19],human:14,hypothet:2,id_:3,idea:[10,11,14,19],ident:[3,13],identifi:6,ift:[3,4,5,8,13,19],ignor:[3,19],illustr:13,imagin:20,immedi:[8,13],immut:[14,19],imper:13,implement:[0,1,2,3,6,9,10,13,14,16,17,19],impli:5,implicit:14,includ:[7,10],inclus:11,incom:24,incompat:16,incr_at:8,incr_step_count:8,incr_valu:8,increas:[6,8,11],increment:[3,10,11,16],index:[0,6,9,14,24],index_of:9,indexerror:24,indic:19,infil:19,infinit:6,inform:3,infra:[3,12,13,14,17,18],infrastructur:3,init:8,init_print:6,initi:[2,3,5,6,7,8,14,15,19],inlin:19,inner:5,input:[1,4,5,6,7,13,15],inscrib:3,inspect:14,instal:0,instanti:[10,23],instead:[6,11,12,13,19,20,24],instruct:8,integ:[2,3,4,5,6,7,8,12,13,14],integr:3,intend:[0,14],interact:[14,21],interest:[0,6,11,12,19],interlock:6,interlud:21,intermedi:13,intern:[0,23,24],interpret:[0,10,13,16,22,23],interrupt:14,interv:[10,11],introduc:16,introduct:0,invari:3,invers:3,investig:17,ipf:14,ipynb:12,isn:[13,20],item:[2,3,4,5,9,13,14,19,24],iter:[1,3,6,13,14,21,24],iter_stack:[9,18,24],its:[0,2,3,5,6,10,11,13,14,19,24],itself:[0,2,8,14,19],j05cmp:[2,3],jenni:19,job:[8,21],john:[15,19],joi:[2,4,5,7,8,9,10,15,16,17,18,19],joypi:[8,9,13,14,19,20],jump:8,jupyt:21,just:[0,2,3,4,5,6,8,12,13,14,16,20],keep:20,kei:21,kevin:0,key_n:19,keyerror:19,kind:[2,6,8,10,13,14,19],kleen:19,know:[6,11,13,19],known:10,labda:10,lambda:[10,13],lambdifi:6,languag:[10,14,16,17,19],larg:6,larger:[6,24],largest:[3,5,8],last:[4,8,11,13],lastli:[12,13],later:[8,14],law:2,lazi:15,lazili:15,lcm:11,lead:[8,14],leaf:19,lean:14,learn:[0,9],least:[2,6,8,11,13,24],least_fract:14,leav:[5,6,8,11,12,19],left:[6,12,13,14,20,23,24],leftov:13,legendari:8,legibl:8,len:9,length:[3,11,24],lens:13,less:[11,12,13,14,24],lesser:6,let:[4,5,6,8,12,13,15,17,19,20],level:[10,19],librari:[0,6,8,9,15,17,18,19],lieu:19,like:[2,3,5,6,9,11,13,14,15,17,22],line:[3,5,8,13,14,19,23],linear:24,link:0,linux:0,list:[0,3,4,5,7,8,9,11,14,15,20,21,23],list_to_stack:[8,9,24],liter:[1,19,20,22],littl:[6,8,19,21],live:21,lkei:19,load:[11,14],locat:[2,6],locu:23,log_2:19,logic:[0,11],longer:19,look:[6,12,14,15,19],lookup:[14,19],loop:[0,1,3,11],lot:[14,17,19,20],love:11,low:10,lower:[11,19],lowest:[5,19],machin:[0,19],machineri:19,macro:14,made:[0,5,14,19,20],mai:[2,8,13,19],mail:0,main:[0,3,4,14,20],mainloop:16,maintain:20,major:16,make:[2,3,4,10,11,13,14,18,20],make_distributor:9,make_gener:15,manfr:[0,2,3,10],manhattan:6,mani:[0,6,7,8,12,13,14],manipul:6,manual:[6,13],map:[1,3,11,13,14,16,17,19],map_:3,mark:[6,8],marker:14,mask:[11,12],match:[0,1,4],materi:0,math:[0,6,8,14,19],mathemat:[6,14],matter:[4,11,13,15,19],max:[5,6,9],max_:3,maximum:[3,19],maxmin:5,mayb:[13,19],maze:8,mean:[5,10,11,13,14,15,19,24],meant:[13,14,17,19],meantim:8,mem:8,member:[2,3,6],memori:6,mental:14,mention:2,mercuri:0,merg:19,meta:[14,19],methink:19,method:[0,3,6,14,21,23],mfloor:6,midpoint:11,might:[4,10,12,13,19],million:12,min:5,min_:3,mind:8,minimum:3,minu:[3,17],mirror:0,miscellan:[0,21],mistak:9,mix:14,mnemon:4,mod:3,model:[10,14],modern:0,modif:12,modifi:[8,14,20],modul:[0,1,3,14,22],modulu:14,monkei:6,month:14,more:[0,3,7,8,10,11,12,13,14,15,17,18,19,22,24],most:19,mostli:0,move:[4,6,8],movement:2,mrank_of:6,much:[6,8,11,13,19],muck:19,mul:[14,17,20,23],multi:3,multipl:[13,21],must:[2,3,5,6,7,11,13,16],mutabl:8,n_rang:12,nail:8,name:[1,3,4,14,16,20,21,22,24],natur:[11,12,19],navig:20,need:[2,3,4,5,6,8,9,11,12,13,15,16,19],neg:[3,8,17],nest:[14,19,20],network:14,never:16,newton:[0,21],next:[4,5,6,8,11,13,19],nice:[0,4,6,13,24],niether:2,node:21,node_kei:19,node_valu:19,non:[5,19],none:[1,3],normal:[7,13],notat:[14,19],note:[2,6,11,15,19,24],notebook:[11,14,20,21],notebook_preambl:[2,4,5,6,7,8,9,11,12,13,15,17,18,19,20],noth:[2,19],notic:11,now:[4,5,6,11,12,13,14,18,21],nth:[3,24],nullari:[5,8,9,14,19],number:[1,2,3,5,11,12,24],object:22,observ:11,obviou:12,obvious:[5,7,8],occur:19,odd:[11,12],off:[2,3,6,11,12,20],offset:8,offset_of:6,old:[2,18],omit:13,onc:[3,7,16,17,19],one:[2,3,4,5,6,7,8,11,12,13,17,19,23,24],ones:12,onli:[2,3,4,5,6,8,11,13,19,20,24],onto:[1,2,3,14,24],open:[7,14],oper:[3,5,13,14,19,24],oppos:4,option:[1,14,19,24],order:[2,3,4,5,13,14,21,24],org:[0,19],origin:[0,1,2,3,4,19,20],other:[0,2,3,5,6,10,13,14,19,24],otherwis:[3,5,11,12,19],our:[4,5,6,11,12,13,14,15],ourselv:13,out:[2,3,6,10,11,12,13,14,19,20],outcom:19,output:[6,13,15],outsid:[8,10],outward:6,over:[3,4,6,10,11,12,14,15,17,19,21],overhead:6,overkil:13,overshadow:6,own:[6,19],pack:[19,24],packag:[0,14],page:[0,17,19,24],pair:[2,3,4,5,11,12],pair_up:4,palidrom:11,palindrom:11,pam:[14,17],paper:[6,10,13,14,19,20],parallel:2,paramet:[1,2,3,8,13,22,23,24],paranthes:19,parenthes:[8,19,24],pariti:12,pars:[0,3,14,19],parse_definit:3,parseerror:22,parser:0,part:[2,3,5,8,13,15,17,19],partial:[6,13],particular:20,particularli:8,pass:[0,19,23],passphras:7,path:6,pattern:[6,11,19],payoff:13,pe1:[11,12],pe2:12,pearl:20,pend:[3,13,14,20,23],peopl:21,per:[6,14],perform:8,perhap:12,period:14,permit:[8,24],persist:19,phase:2,pick:[11,12,24],pickl:14,pictur:19,piec:13,pip:0,pita:9,place:[3,6,8,11,13,14],plai:0,plain:8,plane:6,plu:[3,6,17],plug:[12,13,19],point:[6,10,13,14,19],pointless:2,pop:[3,4,5,8,9,11,12,13,14,17,18,19,24],popd:[3,8,14,15,18],popdd:[3,5,12,17],popop:[3,4,5,8,9,11,12,13,14,15,19],port:6,posit:[3,8,11,13,14],possibilit:19,possibl:[5,19,21],post:[14,19],potenti:3,power:14,pragmat:11,pre:[8,13,19],preambl:15,precis:[0,1],pred:3,predic:[2,5,12,13],prefer:13,prefix:[13,23],prep:[5,19],prepar:[8,13],preprocessor:13,present:19,preserv:10,pretti:[6,17,19,23,24],pretty_print:0,prevent:13,previou:[6,8,14],prime:[5,15],primit:[2,3,8,17],primrec:[3,5,8,9,12,13,14,15],print:[0,1,2,3,6,13,23,24],probabl:[4,12,14,19],problem:[6,14,21],proc_curr:19,proc_left:19,proc_right:19,proce:[4,11],process:[8,13,14,23],processor:19,produc:[4,11,13,19],product:14,program:[0,2,3,4,5,6,8,12,14,15,20],project:21,prompt:14,proper:[2,3],properli:8,properti:0,provid:[0,3,10,14],prune:19,pun:[0,14],pure:[0,19],puriti:14,purpos:14,push:[2,3,13,14,20,24],pushback:[14,19,24],put:[1,2,12,14,24],puzzl:[4,5,6,7],pypi:0,pyramid:6,python:[0,2,3,6,8,13,17,19,20,21,22,24],quadrat:[0,6,21],queri:19,queu:13,quit:[0,1,6],quot:[0,3,12,13,14,15,17,19,20,23],quotat:[2,3],quotient:3,rais:[19,22,24],random:8,rang:[6,13,14],range_sum:13,range_to_zero:14,rank_and_offset:6,rank_of:6,raphson:15,rather:[11,13,14,19],ratio:14,reach:[8,11,12,13],read:[0,1,11,12,19,20],readabl:18,real:19,realiz:[4,8,10,19],realli:6,rearrang:[2,13],reason:[6,11,14],rebuild:20,rec1:[2,3],rec2:[2,3],recogn:22,record:[14,23],recur:13,recurs:[2,3,5,8,9,12,14,15,21,24],recus:14,recusr:19,redistribut:[3,14],reduc:2,redund:24,reexamin:19,refactor:[13,14,16],refer:[0,2],regist:2,regular:22,rel:[8,17],releas:16,relev:6,remain:[2,3,14,16],remaind:[3,15],remind:13,remov:[3,6,19,24],renam:19,render:[19,21],repeat:[4,6,11],repeatedli:11,repl:[0,1],replac:[0,2,3,12,13,19,20,21,24],repositori:0,repres:[2,14,19,22,23],represent:24,reprod:12,request:6,requir:[6,24],resembl:14,respect:11,rest:[3,5,9,11,12,14,19,20,21,24],restor:2,result:[1,2,3,5,11,12,13,17,19,20],resum:14,retir:2,retri:14,reus:19,revers:[3,4,5,11,12,13,20,24],rewrit:[8,14],rewritten:14,richard:19,rid:19,right:[6,12,13,14,23,24],rightmost:11,rkei:19,role:19,roll:[3,5,7,8,13,15,17,19],rolldown:3,rollup:3,root:[3,6,17,21],rotate_seq:4,round:4,row:[5,6],row_valu:6,run:[0,1,3,6,11,13,14,15,19,20],runtim:6,runtimeerror:24,sai:19,same:[2,10,11,13,19,24],sandwich:[2,3],save:[2,11,14],scan:3,scanner:[14,22],scenario:20,scheme:[17,19],scope:[4,19],search:[0,6,19],second:[3,4,5,13,14,19,24],secur:7,see:[0,6,12,13,14,16,18,19,20,23],seem:[0,9,11,14,19],seen:20,select:[3,6],semant:[2,3,14,16,19],semi:14,send:14,sens:[0,2,11,20],separ:14,sequenc:[0,1,2,3,4,5,7,8,9,11,14,18,19,20,22],seri:[6,11,12,13,19,20],serv:13,set:[2,3,13],seven:[11,12],sever:[0,10,14],share:[3,6,14],shelf:2,shift:[11,12],shine:8,shorter:21,shortest:6,should:[2,5,11,13,19],shouldn:14,show:[6,10,19,20],shunt:[3,20],side:19,sign:6,signal:5,signifi:[14,19],silli:19,similar:19,simon:14,simpl:[6,13,14,24],simplefunctionwrapp:[3,8,9,17,18],simplest:21,simpli:10,simplifi:[6,11,19,20],sinc:[2,6,11,17,19],singl:[3,12,14,18,22],situ:19,situat:19,six:[11,12,14],sixti:[11,12],size:[4,7,8,9,14,21],skeptic:14,skip:[6,8],slight:15,slightli:[13,19],small:[4,19],smallest:[3,5],smart:[8,13],sneaki:6,softwar:14,solei:2,solut:[6,11],solv:6,solvabl:14,some:[2,3,5,6,8,12,13,14,19,21,24],somehow:19,someth:[2,4,8,16],sometim:19,somewher:[13,19,21],sophist:6,sort:[3,5,13,17,19],sort_:3,sourc:[0,1,3,22,23,24],space:[6,11,23],span:11,special:[12,13,19],specif:[0,10],speed:[6,8,18],sphinx:[21,24],spiral:6,spirit:[0,1,19],split_at:4,spreadsheet:5,sqr:[14,17,20],sqrt:[3,6,15,17],squar:[3,6,21,22],stack:[0,1,3,5,8,9,11,12,13,15,17,18,19,20,22,23],stack_:3,stack_to_str:24,stage:19,stai:[0,1],stand:10,standard:14,star:19,stare:19,start:[5,6,8,9,11,12,13,14,15,17,19],state:[5,8,14],step:[3,4,5,6,7,11,14,17,18,19,20],step_zero:[4,5,7],still:[6,8,13],stop:19,storag:[11,13,19],store:[6,11,13],stori:13,str:[1,22,23,24],straightforward:[1,4,6,12],strang:8,stream:[11,15],string:[1,2,3,4,14,20,22,23,24],strip:6,structur:[13,14,19,20,24],stuff:19,style:[0,10],sub:[16,19],subclass:14,subject:20,subract:6,substitut:[6,13],subtract:[5,6,11],succ:3,success:15,suffici:[8,13],suggest:[5,10,19],suitabl:[3,10,11],sum:[3,4,5,12,13,14,17,18,19],sum_:3,summand:11,suppli:[13,19,22],support:[6,14,23,24],sure:[6,13],suspect:2,swaack:[3,13,17,18,19,20],swap:[3,4,5,6,7,9,11,12,13,14,15,18,19,20],swon:[3,9,12,13,14,19,20],swoncat:[8,9,12,13,14,15,19],symbol:[2,3,6,17,20,22],symmetr:[11,19],sympi:17,syntact:14,syntax:[14,24],sys:[6,24],system:[6,7,14,19],tail:[5,19,24],take:[3,4,6,8,11,12,14,15,17,19,24],taken:8,talk:[14,19,24],target:[6,20],task:6,tast:10,tbd:14,technic:2,techniqu:[10,20],technolog:2,teh:19,temporari:20,ten:11,term:[1,2,5,8,9,13,14,15,22,24],termin:[2,3,5],ternari:14,test:[2,3],text:[0,1,3],text_to_express:[14,22],textual:14,than:[0,3,6,7,11,12,14,15,17,24],thei:[2,5,6,11,12,13,14,19,20,22,24],them:[2,3,5,6,11,12,13,19,20,21],theori:[2,3],therefor:[12,19],thi:[0,1,2,3,4,5,6,8,9,10,11,12,13,14,17,20,22,23,24],thing:[2,5,6,8,12,13,17,19,20,22,24],think:[2,8,11,13,14,19],third:[3,4,5,12,14,19],thirti:11,those:[2,3,5,6,8,13,19,21],though:[11,12,19],thought:14,thousand:11,thread:2,three:[2,3,8,11,14,19],through:[1,11,14,20,24],thu:4,thun:[2,3,10,16],thunder:14,tied:19,tile:6,time:[3,6,8,9,11,13,14,19,20],tini:19,to_set:19,todai:14,todo:[14,21,22],togeth:[12,14],token:22,toler:21,tommi:19,too:[13,19],took:6,tool:14,top:[2,3,14,23,24],total:[4,6,11],total_match:4,trace:[0,14,17,20,21,24],traceprint:23,track:20,tracker:0,trade:6,transform:[10,13],translat:[6,10,13],travers:[20,21],treasur:0,treat:[0,2,3,21],treatment:12,tree:[0,14,21],treemap:13,tri:11,trick:[11,19],tricki:[6,8],trivial:[5,8,19],trobe:0,trove:0,truediv:17,truthi:[3,14],ts0:[13,19],ts1:[13,19],tuck:[3,5,14,19],tupl:[3,14,24],turn:[2,3,6],twice:[6,13,19],two:[2,3,5,6,11,13,14,15,19,20,24],type:[1,10,13,14,21,22,23,24],typic:[2,3],unari:[8,13,14],unarybuiltinwrapp:3,unbalanc:[19,22],uncon:[3,4,5,12,13,14,19,20],under:[2,3,8,14],understand:[0,6,19],undocu:14,unfortun:24,uniqu:[3,7,19],unit:[4,13,14,19],univers:[0,14],unless:[6,13],unlik:13,unnecessari:21,unpack:[2,3,24],unpair:11,unquot:[13,14,19],unstack:3,untangl:[12,13],until:[5,6,8,12],unus:11,unusu:19,updat:[0,21],upward:8,usag:14,use:[0,2,3,6,8,10,11,12,14,15,16,17,18,19,20,24],used:[3,10,13,14,19,20,22,24],useful:0,user:6,uses:[2,5,11,13],using:[3,5,6,12,13,17,19,20],usual:[0,2],util:[0,8,9,18,19],valid:7,valu:[2,3,5,6,11,13,14,15,18,21,24],value_n:19,valueerror:24,vanilla:8,variabl:[13,21],variat:13,varient:19,varieti:[10,14],variou:0,vener:24,verbos:10,veri:[0,1,6,10,14,19,24],versa:2,version:[0,1,2,12,16,17,20,21],via:14,vice:2,view:21,viewer:[1,14,16,23],von:[0,2,3,10],wai:[0,2,3,4,6,8,10,11,13,14,19],walk:19,wall:6,want:[2,6,8,11,12,15,19],warranti:[3,14],wash:14,wast:14,web:24,websit:[0,11],welcom:14,well:[0,4,5,6,10,14,19,22],were:[6,8,13,14,20],what:[2,3,5,8,9,10,13,14,17,19,23],whatev:[2,3,12,19,24],when:[11,12,13,14,15,19,20,22,24],where:[2,3,4,5,8,13,14,19,21,24],whether:13,which:[0,1,3,5,6,8,11,13,14,15,17,19,20,24],whole:[2,3,5,11,19],whose:12,why:[6,15,19],wiki:19,wikipedia:[0,19,20],wildli:14,wind:14,winner:6,wire:13,wit:8,within:[14,19,21],without:[2,14,19],won:[19,24],word:[0,3,4,5,7,11,12,14,19,20],work:[0,4,5,6,8,11,12,13,14,19,20,24],worth:[6,11],would:[2,5,6,7,8,9,11,12,13,14,15,19,20,24],wouldn:8,wrap:[3,6,14],write:[4,6,8,10,12,13,15,19,20,21,24],written:[0,1,8,15,17,18,24],wrong:2,wtf:13,wtfmorphism:13,year:14,yet:[8,13,19,20],yield:[2,3,24],you:[0,2,3,5,6,8,11,12,13,14,16,18,19,20,23,24],your:[2,3,4,5,6,7,14],yourself:[14,19],zero:[3,5,6,8,13,19,22,24],zip:[4,11],zip_:3,zstr:20},titles:["Thun 0.1.1 Documentation","Joy Interpreter","Functions Grouped by, er, Function with Examples","Function Reference","Advent of Code 2017","Advent of Code 2017","Advent of Code 2017","Advent of Code 2017","Advent of Code 2017","Advent of Code 2017","Categorical Programming","Developing a Program in Joy","Using <code class=\"docutils literal notranslate\"><span class=\"pre\">x</span></code> to Generate Values","Hylomorphism","Thun: Joy in Python","Newton\u2019s method","No Updates","Quadratic formula","Replacing Functions in the Dictionary","Treating Trees","Preamble","Essays about Programming in Joy","Parsing Text into Joy Expressions","Tracing Joy Execution","Stack or Quote or Sequence or List\u2026"],titleterms:{"1st":4,"2nd":5,"3rd":6,"4th":7,"5th":8,"6th":9,"case":[15,19],"final":5,"function":[2,3,9,13,14,15,17,18,19],"long":18,"void":2,"while":2,Adding:19,One:12,The:[11,13,14,19],There:14,Use:19,Using:12,about:21,abov:13,add:[2,8,19],adding:19,address:20,advent:[4,5,6,7,8,9],all:[6,8],ana:13,analysi:[6,11],anamorph:[2,13],app1:2,app2:2,app3:2,appendix:13,approxim:15,automat:19,averag:2,base:[15,19],befor:9,better:13,binari:2,block:5,branch:2,breakdown:8,btree:19,can:19,cata:13,catamorph:13,categor:10,chatter:2,check:17,child:19,choic:2,cleanup:17,clear:2,cleav:2,cmp:19,code:[4,5,6,7,8,9,14],combin:[2,13,19],compar:19,comparison:2,compil:12,comput:15,con:[2,19],concat:2,consecut:15,continu:14,count:[8,9],crap:19,current:19,data:19,datastructur:[14,19],decemb:[4,5,6,7,8,9],defin:[17,19],definit:17,delet:19,deriv:[13,17,19],determin:20,develop:11,dialect:0,dictionari:18,dip:[2,20],dipd:2,dipdd:2,direco:12,disenstacken:2,div:2,document:0,doe:19,down:5,down_to_zero:2,drive:9,drop:2,dup:2,dupd:2,dupdip:2,els:19,empti:19,enstacken:2,equal:19,essai:21,euler:[11,12],eval:14,even:12,exampl:[2,14],execut:23,express:[14,22],extract:[13,19],factor:[13,19],factori:13,fibonacci:12,filter:11,find:[6,13,15],first:[2,11],five:12,flatten:2,floordiv:2,form:[13,19],formula:17,four:13,from:13,ftw:4,fun:13,further:11,fusion:13,gcd:2,gener:[9,11,12,13,15,19],genrec:2,get:[8,19],getitem:2,given:[13,19],gotten:8,greater:19,group:2,help:2,host:0,how:[9,11,12],hylo:13,hylomorph:13,ift:2,increment:8,index:8,indic:0,inform:0,infra:[2,19,20],integ:11,interlud:19,intern:22,interpret:[1,14],isn:19,item:20,iter:[11,19],joi:[0,1,3,6,11,13,14,20,21,22,23,24],just:[11,19],kei:19,languag:0,law:13,least_fract:2,left:19,less:19,let:11,librari:[3,14],like:19,list:[2,13,19,24],literari:14,littl:11,logic:2,loop:[2,5,14],lshift:2,make:[15,19],mani:[9,11],map:2,math:2,method:15,min:2,miscellan:[2,19],mod:2,modif:19,modulu:2,mul:2,multipl:[11,12],must:19,name:[17,19],nativ:17,neg:2,newton:15,next:15,node:[13,19],now:[8,19],nullari:2,number:[6,13],offset:6,one:14,onli:14,order:19,osdn:0,our:19,out:5,over:2,pack:11,pam:2,paper:5,para:13,paramet:19,parameter:[13,19],paramorph:13,pars:[2,22],parser:[14,22],pass:14,path:20,pattern:13,per:19,piec:5,pop:2,popd:2,popop:2,pow:2,power:12,preambl:[8,13,20],pred:2,predic:[8,11,15,19],pretty_print:23,primrec:2,print:14,problem:[11,12],process:19,product:2,program:[9,10,11,13,17,19,21],project:[0,11,12],pure:14,put:[6,19],python:[14,18],quadrat:17,quick:0,quot:[2,24],rang:[2,11],range_to_zero:2,rank:6,read:14,recal:9,recur:[15,19],recurs:[13,19],redefin:19,refactor:[4,11,19],refer:3,regular:14,rem:2,remaind:2,remov:2,render:11,repeat:9,repl:14,replac:18,rescu:6,reset:12,rest:[2,13],revers:2,right:[19,20],roll:2,rolldown:2,rollup:2,root:15,rshift:2,run:[2,12],sat:5,second:2,select:2,sequenc:[12,24],set:[8,15,19],shorter:18,should:14,shunt:2,simplest:11,simplifi:17,size:[2,18],slight:19,sqr:2,sqrt:2,squar:15,stack:[2,14,24],start:0,state:9,step:[2,8,13],style:14,sub:2,succ:2,sum:[2,11],swaack:2,swap:2,swon:2,swoncat:2,symbol:[13,14],sympi:6,tabl:0,tail:13,take:2,term:[11,12,19],ternari:2,text:22,than:[13,19],thi:19,think:5,third:2,three:12,thun:[0,14],time:[2,12],todo:19,togeth:[6,8,19],toi:19,token:14,toler:15,trace:[18,23],traceprint:14,travers:19,treat:19,tree:[13,19,20],treestep:[13,19],triangular:13,tricki:5,truediv:2,truthi:2,tuck:2,two:12,type:19,unari:2,uncon:2,unfinish:13,unit:2,unnecessari:11,unquot:2,unstack:2,updat:16,use:13,usual:13,util:[23,24],valu:[8,12,19],variabl:17,version:[6,11,18,19],view:14,want:5,within:15,word:2,write:17,xor:2,zero:12,zip:2,zipper:20}})
\ No newline at end of file
diff --git a/docs/sphinx_docs/notebooks/4. Replacing Functions in the Dictionary.rst b/docs/sphinx_docs/notebooks/Replacing.rst
similarity index 99%
rename from docs/sphinx_docs/notebooks/4. Replacing Functions in the Dictionary.rst
rename to docs/sphinx_docs/notebooks/Replacing.rst
index 76bdad7..62ea07f 100644
--- a/docs/sphinx_docs/notebooks/4. Replacing Functions in the Dictionary.rst	
+++ b/docs/sphinx_docs/notebooks/Replacing.rst
@@ -99,7 +99,7 @@ and re-evaluate the expression.
     D['size'] = size
 
 
-A Shorter Evaluation
+A shorter trace
 ~~~~~~~~~~~~~~~~~~~~
 
 You can see that ``size`` and ``sum`` now execute in a single step.
diff --git a/docs/sphinx_docs/notebooks/Trees.rst b/docs/sphinx_docs/notebooks/Trees.rst
index 6c81411..7f87ef4 100644
--- a/docs/sphinx_docs/notebooks/Trees.rst
+++ b/docs/sphinx_docs/notebooks/Trees.rst
@@ -1210,43 +1210,144 @@ TODO: BTree-delete
 
 ::
 
-       tree key [E] BTree-delete
-    ---------------------------- key in tree
+       tree key [Er] BTree-delete
+    -------------------------------- key in tree
            tree
 
-       tree key [E] BTree-delete
-    ---------------------------- key not in tree
-             tree key E
+       tree key [Er] BTree-delete
+    -------------------------------- key not in tree
+             tree key Er
 
-So:
+So::
+
+    BTree-Delete == [pop not] swap [R0] [R1] genrec
 
 ::
 
-    BTree-delete == [pop not] [] [R0] [R1] genrec
+                 [Er] BTree-delete
+    ------------------------------------
+       [pop not] [Er] [R0] [R1] genrec
 
-And:
+
+Now we get to figure out the recursive case::
+
+    D == [pop not] [Er] [R0] [R1] genrec
+
+    [node_key node_value left right] key R0                  [D] R1
+    [node_key node_value left right] key over first swap dup [D] R1
+    [node_key node_value left right] node_key key key        [D] R1
 
 ::
 
-    [n_key n_value left right] key R0              [BTree-get] R1
-    [n_key n_value left right] key [dup first] dip [BTree-get] R1
-    [n_key n_value left right] n_key key           [BTree-get] R1
-    [n_key n_value left right] n_key key           [BTree-get] roll> [T>] [E] [T<] cmp
-    [n_key n_value left right] [BTree-get] n_key key                 [T>] [E] [T<] cmp
+    [node_key node_value left right] node_key key key [D] R1
+    [node_key node_value left right] node_key key key [D] cons roll> [T>] [E] [T<] cmp
+    [node_key node_value left right] node_key key [key D]      roll> [T>] [E] [T<] cmp
+    [node_key node_value left right] [key D] node_key key            [T>] [E] [T<] cmp
+
+Now this:;
+
+    [node_key node_value left right] [key D] node_key key [T>] [E] [T<] cmp
+
+Becomes one of these three:;
+
+    [node_key node_value left right] [key D] T>
+    [node_key node_value left right] [key D] E
+    [node_key node_value left right] [key D] T<
 
-    BTree-delete == [pop not] swap [[dup first] dip] [roll> [T>] [E] [T<] cmp] genrec
 
 ::
 
-    [n_key n_value left right] [BTree-get] T>
-    [n_key n_value left right] [BTree-get] E
-    [n_key n_value left right] [BTree-get] T<
+       [node_key node_value left right] [key D] T>
+    -------------------------------------------------
+       [node_key node_value left key D right]
+
+
+    right left node_value node_key [key D] dipd
+
+    [node_key node_value left right] [key D] [dipd] cons infra
 
 ::
 
-    [n_key n_value left right] [BTree-get] 
-    [n_key n_value left right] [BTree-get] E
-    [n_key n_value left right] [BTree-get] T<
+    T> == [dipd] cons infra
+    T< == [dipdd] cons infra
+
+
+::
+
+    [node_key node_value left right] [key D] E
+
+::
+
+
+    def delete(node, key):
+      '''
+      Return a tree with the value (and key) removed or raise KeyError if
+      not found.
+      '''
+      if not node:
+        raise KeyError, key
+
+      node_key, (value, (lower, (higher, _))) = node
+
+      if key < node_key:
+        return node_key, (value, (delete(lower, key), (higher, ())))
+
+      if key > node_key:
+        return node_key, (value, (lower, (delete(higher, key), ())))
+
+      # So, key == node_key, delete this node itself.
+
+      # If we only have one non-empty child node return it.  If both child
+      # nodes are empty return an empty node (one of the children.)
+      if not lower:
+        return higher
+      if not higher:
+        return lower
+
+      # If both child nodes are non-empty, we find the highest node in our
+      # lower sub-tree, take its key and value to replace (delete) our own,
+      # then get rid of it by recursively calling delete() on our lower
+      # sub-node with our new key.
+      # (We could also find the lowest node in our higher sub-tree and take
+      # its key and value and delete it. I only implemented one of these
+      # two symmetrical options. Over a lot of deletions this might make
+      # the tree more unbalanced.  Oh well.)
+      node = lower
+      while node[1][1][1][0]:
+        node = node[1][1][1][0]
+      key, value = node[0], node[1][0]
+
+      return key, (value, (delete(lower, key), (higher, ())))
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
 
 Tree with node and list of trees.
 =================================
diff --git a/docs/sphinx_docs/notebooks/index.rst b/docs/sphinx_docs/notebooks/index.rst
index a6a7605..660fd8c 100644
--- a/docs/sphinx_docs/notebooks/index.rst
+++ b/docs/sphinx_docs/notebooks/index.rst
@@ -9,6 +9,7 @@ These essays are adapted from Jupyter notebooks.  I hope to have those hosted so
    :maxdepth: 2
 
    Developing
+   Replacing
    Trees
    Newton-Raphson
    Quadratic