Minor docs edits.
This commit is contained in:
Simon Forman
+45
-127
@@ -4,7 +4,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Treating Trees I\n",
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"# Treating Trees I: Ordered Binary Trees\n",
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"\n",
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"Although any expression in Joy can be considered to describe a [tree](https://en.wikipedia.org/wiki/Tree_structure) with the quotes as compound nodes and the non-quote values as leaf nodes, in this page I want to talk about [ordered binary trees](https://en.wikipedia.org/wiki/Binary_search_tree) and how to make and use them.\n",
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"\n",
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@@ -92,7 +92,15 @@
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"['k' 'v' [] []]\n"
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]
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}
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],
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"source": [
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"J('\"v\" \"k\" Tree-new')"
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]
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@@ -521,7 +529,7 @@
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"metadata": {},
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"source": [
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"## Interlude: `cmp` combinator\n",
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"Instead of mucking about with nested `ifte` combinators let's just go whole hog and define `cmp` which takes two values and three quoted programs on the stack and runs one of the three depending on the results of comparing the two values:\n",
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"Instead of mucking about with nested `ifte` combinators let's use `cmp` which takes two values and three quoted programs on the stack and runs one of the three depending on the results of comparing the two values:\n",
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"\n",
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" a b [G] [E] [L] cmp\n",
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" ------------------------- a > b\n",
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@@ -540,43 +548,6 @@
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"cell_type": "code",
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"execution_count": 20,
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"metadata": {},
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"outputs": [],
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"source": [
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"from joy.library import FunctionWrapper\n",
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"from joy.utils.stack import pushback\n",
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"from notebook_preamble import D\n",
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"\n",
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"\n",
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"@FunctionWrapper\n",
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"def cmp_(stack, expression, dictionary):\n",
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" '''\n",
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" cmp takes two values and three quoted programs on the stack and runs\n",
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" one of the three depending on the results of comparing the two values:\n",
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"\n",
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" a b [G] [E] [L] cmp\n",
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" ------------------------- a > b\n",
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" G\n",
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"\n",
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" a b [G] [E] [L] cmp\n",
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" ------------------------- a = b\n",
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" E\n",
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"\n",
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" a b [G] [E] [L] cmp\n",
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" ------------------------- a < b\n",
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" L\n",
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" '''\n",
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" L, (E, (G, (b, (a, stack)))) = stack\n",
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" expression = pushback(G if a > b else L if a < b else E, expression)\n",
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" return stack, expression, dictionary\n",
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"\n",
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"\n",
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"D['cmp'] = cmp_"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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@@ -592,7 +563,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"execution_count": 21,
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"metadata": {},
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"outputs": [
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{
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@@ -609,7 +580,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"execution_count": 22,
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"metadata": {},
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"outputs": [
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{
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@@ -674,7 +645,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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"execution_count": 23,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -713,7 +684,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"execution_count": 24,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -722,7 +693,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"execution_count": 25,
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"metadata": {
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"scrolled": false
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},
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@@ -865,7 +836,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"execution_count": 26,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -881,7 +852,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 28,
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"execution_count": 27,
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"metadata": {},
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"outputs": [
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{
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@@ -898,7 +869,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 29,
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"execution_count": 28,
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"metadata": {},
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"outputs": [
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{
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@@ -915,7 +886,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 30,
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"execution_count": 29,
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"metadata": {},
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"outputs": [
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{
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@@ -940,7 +911,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 31,
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"execution_count": 30,
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"metadata": {},
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"outputs": [
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{
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@@ -957,7 +928,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 32,
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"execution_count": 31,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -966,7 +937,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 33,
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"execution_count": 32,
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"metadata": {},
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"outputs": [
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{
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@@ -990,7 +961,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 34,
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"execution_count": 33,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -999,7 +970,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 35,
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"execution_count": 34,
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"metadata": {
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"scrolled": true
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},
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@@ -1117,7 +1088,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 36,
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"execution_count": 35,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -1141,7 +1112,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 37,
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"execution_count": 36,
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"metadata": {},
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"outputs": [
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{
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@@ -1160,7 +1131,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Parameterizing the `[F]` function is left as an exercise for the reader (for now.)"
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"Parameterizing the `[F]` function is left as an exercise for the reader."
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]
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},
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{
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@@ -1310,7 +1281,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 38,
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"execution_count": 37,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -1333,7 +1304,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 39,
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"execution_count": 38,
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"metadata": {},
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"outputs": [
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{
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@@ -1350,7 +1321,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 40,
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"execution_count": 39,
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"metadata": {},
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"outputs": [
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{
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@@ -1367,7 +1338,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 41,
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"execution_count": 40,
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"metadata": {},
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"outputs": [
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{
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@@ -1390,7 +1361,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 52,
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"execution_count": 41,
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"metadata": {},
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"outputs": [
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{
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@@ -1552,55 +1523,6 @@
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"We have to handle three cases, so let's use `cond`."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 42,
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"metadata": {},
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"outputs": [],
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"source": [
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"from joy.library import FunctionWrapper, S_ifte\n",
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"\n",
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"\n",
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"@FunctionWrapper\n",
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"def cond(stack, expression, dictionary):\n",
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" '''\n",
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" like a case statement; works by rewriting into a chain of ifte.\n",
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"\n",
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" [..[[Bi] Ti]..[D]] -> ...\n",
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"\n",
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"\n",
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" [[[B0] T0] [[B1] T1] [D]] cond\n",
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" -----------------------------------------\n",
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" [B0] [T0] [[B1] [T1] [D] ifte] ifte\n",
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"\n",
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" '''\n",
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" conditions, stack = stack\n",
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" if conditions:\n",
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" expression = _cond(conditions, expression)\n",
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" try:\n",
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" # Attempt to preload the args to first ifte.\n",
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" (P, (T, (E, expression))) = expression\n",
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" except ValueError:\n",
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" # If, for any reason, the argument to cond should happen to contain\n",
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" # only the default clause then this optimization will fail.\n",
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" pass\n",
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" else:\n",
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" stack = (E, (T, (P, stack)))\n",
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" return stack, expression, dictionary\n",
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"\n",
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"\n",
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"def _cond(conditions, expression):\n",
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" (clause, rest) = conditions\n",
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" if not rest: # clause is [D]\n",
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" return clause\n",
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" P, T = clause\n",
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" return (P, (T, (_cond(rest, ()), (S_ifte, expression))))\n",
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"\n",
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"\n",
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"\n",
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"D['cond'] = cond"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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@@ -1860,7 +1782,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Minor rearrangement:\n",
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"Minor rearrangement, move `dup` into `W`:\n",
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"\n",
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" W == dup [fourth] [fourth] while uncons uncons pop over\n",
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" E′ == roll> popop rest [W] dip cons dipd swap\n",
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@@ -1879,9 +1801,9 @@
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"\n",
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" W.rightmost == [fourth] [fourth] while\n",
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" W.unpack == uncons uncons pop\n",
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" W == dup W.rightmost W.unpack over\n",
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" E.clear_stuff == roll> popop rest\n",
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" E.delete == cons dipd\n",
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" W == dup W.rightmost W.unpack over\n",
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" E.0 == E.clear_stuff [W] dip E.delete swap\n",
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" E == [\n",
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" [[pop third not] pop fourth]\n",
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@@ -1899,7 +1821,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 43,
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"execution_count": 42,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -1917,12 +1839,13 @@
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"T< == [dipdd] cons infra\n",
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"R0 == over first swap dup\n",
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"R1 == cons roll> [T>] [E] [T<] cmp\n",
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"Tree-Delete == [pop not] [pop] [R0] [R1] genrec''', D)"
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"Tree-Delete == [pop not] [pop] [R0] [R1] genrec\n",
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"''', D)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 44,
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"execution_count": 43,
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"metadata": {},
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"outputs": [
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{
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@@ -1939,7 +1862,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 45,
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"execution_count": 44,
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"metadata": {},
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"outputs": [
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{
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@@ -1956,7 +1879,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 46,
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"execution_count": 45,
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"metadata": {},
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"outputs": [
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{
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@@ -1973,7 +1896,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 47,
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"execution_count": 46,
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"metadata": {},
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"outputs": [
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{
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@@ -1990,7 +1913,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 48,
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"execution_count": 47,
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"metadata": {},
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"outputs": [
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{
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@@ -2007,7 +1930,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 49,
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"execution_count": 48,
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"metadata": {},
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"outputs": [
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{
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@@ -2024,7 +1947,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 50,
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"execution_count": 49,
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"metadata": {
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"scrolled": true
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},
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@@ -2099,11 +2022,6 @@
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" Tree-delete == [pop not] [pop] [_Tree_delete_R0] [_Tree_delete_R1] genrec\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": []
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}
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],
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"metadata": {
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