Editing Trees; implemented BTree-Delete.
This commit is contained in:
Simon Forman
parent
c3a3f5a527
commit
aafecdc035
587
docs/Trees.ipynb
587
docs/Trees.ipynb
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@ -133,11 +133,11 @@
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 6,
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"metadata": {},
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"outputs": [],
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"source": [
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"from notebook_preamble import J, V, define"
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"from notebook_preamble import D, J, V, define, DefinitionWrapper"
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]
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},
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{
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@ -906,7 +906,7 @@
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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": 11,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -917,6 +917,22 @@
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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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@ -925,6 +941,55 @@
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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": 14,
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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": "code",
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"execution_count": 31,
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@ -1415,17 +1480,16 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# TODO: BTree-delete\n",
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"# BTree-delete\n",
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"\n",
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"Then, once we have add, get, and delete we can see about abstracting them.\n",
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"\n",
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" tree key [E] BTree-delete\n",
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" ---------------------------- key in tree\n",
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" tree key [Er] BTree-delete\n",
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" -------------------------------- key in tree\n",
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" tree\n",
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"\n",
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" tree key [E] BTree-delete\n",
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" tree key [Er] BTree-delete\n",
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" ---------------------- ------ key not in tree\n",
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" tree key E"
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" tree key Er"
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]
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},
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{
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@ -1434,26 +1498,16 @@
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"source": [
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"So:\n",
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"\n",
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" BTree-delete == [pop not] [] [R0] [R1] genrec\n",
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"\n",
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"And:\n",
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"\n",
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" [n_key n_value left right] key R0 [BTree-get] R1\n",
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" [n_key n_value left right] key [dup first] dip [BTree-get] R1\n",
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" [n_key n_value left right] n_key key [BTree-get] R1\n",
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" [n_key n_value left right] n_key key [BTree-get] roll> [T>] [E] [T<] cmp\n",
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" [n_key n_value left right] [BTree-get] n_key key [T>] [E] [T<] cmp\n",
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"\n",
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" BTree-delete == [pop not] swap [[dup first] dip] [roll> [T>] [E] [T<] cmp] genrec"
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" BTree-Delete == [pop not] swap [R0] [R1] genrec\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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" [n_key n_value left right] [BTree-get] T>\n",
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" [n_key n_value left right] [BTree-get] E\n",
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" [n_key n_value left right] [BTree-get] T<"
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" [Er] BTree-delete\n",
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" -------------------------------------\n",
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" [pop not] [Er] [R0] [R1] genrec"
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]
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},
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{
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@ -1466,32 +1520,493 @@
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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": null,
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"cell_type": "markdown",
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"metadata": {},
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"outputs": [],
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"source": []
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"source": [
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"Now we get to figure out the recursive case:\n",
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"\n",
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" w/ D == [pop not] [Er] [R0] [R1] genrec\n",
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"\n",
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" [node_key node_value left right] key R0 [D] R1\n",
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" [node_key node_value left right] key over first swap dup [D] R1\n",
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" [node_key node_value left right] node_key key key [D] R1\n",
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"\n",
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"And then:\n",
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"\n",
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" [node_key node_value left right] node_key key key [D] R1\n",
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" [node_key node_value left right] node_key key key [D] cons roll> [T>] [E] [T<] cmp\n",
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" [node_key node_value left right] node_key key [key D] roll> [T>] [E] [T<] cmp\n",
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" [node_key node_value left right] [key D] node_key key [T>] [E] [T<] cmp"
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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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"Now this:;\n",
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"\n",
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" [node_key node_value left right] [key D] node_key key [T>] [E] [T<] cmp\n",
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"\n",
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"Becomes one of these three:;\n",
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"\n",
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" [node_key node_value left right] [key D] T>\n",
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" [node_key node_value left right] [key D] E\n",
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" [node_key node_value left right] [key D] T<"
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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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"### Greater than case and less than case\n",
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"\n",
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" [node_key node_value left right] [key D] T>\n",
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" -------------------------------------------------\n",
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" [node_key node_value left key D right]"
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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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"First:\n",
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"\n",
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" right left node_value node_key [key D] dipd\n",
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" right left key D node_value node_key\n",
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" right left' node_value node_key"
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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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"Ergo:\n",
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"\n",
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" [node_key node_value left right] [key D] [dipd] cons infra"
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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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"So:\n",
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"\n",
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" T> == [dipd] cons infra\n",
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" T< == [dipdd] cons infra"
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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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"### The else case\n",
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"\n",
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" [node_key node_value left right] [key D] E\n",
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"\n",
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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": "markdown",
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"metadata": {},
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"source": [
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"The first two cases are symmetrical, if we only have one non-empty child node return it.\n",
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"\n",
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" E == [\n",
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" [[pop third not] pop fourth]\n",
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" [[pop fourth not] pop third]\n",
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" [default]\n",
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" ] 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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"source": [
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"(If both child nodes are empty return an empty node.)"
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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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"The initial structure of the default function:\n",
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"\n",
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" default == [E'] cons infra\n",
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"\n",
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" [node_key node_value left right] [key D] default\n",
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" [node_key node_value left right] [key D] [E'] cons infra\n",
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" [node_key node_value left right] [[key D] E'] infra\n",
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"\n",
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" right left node_value node_key [key D] E'"
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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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"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",
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"\n",
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"(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.)"
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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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"First things first, we no longer need this node's key and value:\n",
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"\n",
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" right left node_value node_key [key D] roll> popop E''\n",
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" right left [key D] node_value node_key popop E''\n",
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" right left [key D] E''"
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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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"Then we have to we find the highest (right-most) node in our lower (left) sub-tree:\n",
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"\n",
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" right left [key D] E''"
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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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"Ditch the key:\n",
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"\n",
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" right left [key D] rest E'''\n",
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" right left [D] E'''"
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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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"Find the right-most node:\n",
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"\n",
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" right left [D] [dup W] dip E''''\n",
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" right left dup W [D] E''''\n",
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" right left left W [D] E''''"
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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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"Consider:\n",
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"\n",
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" left W"
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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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"We know left is not empty:\n",
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"\n",
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" [L_key L_value L_left L_right] W"
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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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"We want to keep extracting the right node as long as it is not empty:\n",
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"\n",
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" left [P] [B] while W'"
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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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"The predicate:\n",
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"\n",
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" [L_key L_value L_left L_right] P\n",
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" [L_key L_value L_left L_right] fourth\n",
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" L_right\n",
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" \n",
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"(This has a bug, can run on `[]` so must be guarded:\n",
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"\n",
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" if_not_empty == [] swap [] ifte\n",
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" ?fourth == [fourth] if_not_empty\n",
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" W.rightmost == [?fourth] [fourth] while"
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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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"The body is also `fourth`:\n",
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"\n",
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" left [fourth] [fourth] while W'\n",
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" rightest W'"
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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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"We know rightest is not empty:\n",
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"\n",
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" [R_key R_value R_left R_right] W'\n",
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" [R_key R_value R_left R_right] uncons uncons pop\n",
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" R_key [R_value R_left R_right] uncons pop\n",
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" R_key R_value [R_left R_right] pop\n",
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" R_key R_value"
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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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"So:\n",
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"\n",
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" W == [fourth] [fourth] while uncons uncons pop"
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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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"And:\n",
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"\n",
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" right left left W [D] E''''\n",
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" right left R_key R_value [D] E''''"
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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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"Final stretch. We want to end up with something like:\n",
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"\n",
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" right left [R_key D] i R_value R_key\n",
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" right left R_key D R_value R_key\n",
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" right left' R_value R_key"
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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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"If we adjust our definition of `W` to include `over` at the end:\n",
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"\n",
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" W == [fourth] [fourth] while uncons uncons pop over"
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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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"That will give us:\n",
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"\n",
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" right left R_key R_value R_key [D] E''''\n",
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"\n",
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" right left R_key R_value R_key [D] cons dipdd E'''''\n",
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" right left R_key R_value [R_key D] dipdd E'''''\n",
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" right left R_key D R_key R_value E'''''\n",
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" right left' R_key R_value E'''''\n",
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" right left' R_key R_value swap\n",
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" right left' R_value R_key"
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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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"So:\n",
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"\n",
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" E' == roll> popop E''\n",
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"\n",
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" E'' == rest E'''\n",
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"\n",
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" E''' == [dup W] dip E''''\n",
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"\n",
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" E'''' == cons dipdd swap"
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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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"Substituting:\n",
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||||
"\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,
|
||||
|
|
|
|||
|
|
@ -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>
|
||||
|
|
|
|||
|
|
@ -1,212 +0,0 @@
|
|||
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml">
|
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<head>
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<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
|
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
|
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<title>Replacing Functions in the Dictionary — Thun 0.1.1 documentation</title>
|
||||
<link rel="stylesheet" href="../_static/alabaster.css" type="text/css" />
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</head><body>
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<div class="document">
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<div class="documentwrapper">
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<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">'[23 18] average'</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">'''Return the size of the sequence on the stack.'''</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">'size'</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">'[23 18] average'</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>
|
||||
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|
||||
<li><a href="../index.html">Documentation overview</a><ul>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<h3>This Page</h3>
|
||||
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|
||||
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||||
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|
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<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>.
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|
@ -16,7 +16,7 @@
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|
@ -689,7 +689,7 @@ is just:</p>
|
|||
<li><a href="../index.html">Documentation overview</a><ul>
|
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<li><a href="index.html">Essays about Programming in Joy</a><ul>
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@ -17,7 +17,7 @@
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||||
|
|
@ -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">></span> <span class="p">[</span><span class="n">T</span><span class="o">></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"><</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">></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"><</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">></span> <span class="p">[</span><span class="n">T</span><span class="o">></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"><</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">></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"><</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">></span> <span class="p">[</span><span class="n">T</span><span class="o">></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"><</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">></span> <span class="p">[</span><span class="n">T</span><span class="o">></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"><</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">></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"><</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"><</span>
|
||||
<p>Now this:;</p>
|
||||
<blockquote>
|
||||
<div>[node_key node_value left right] [key D] node_key key [T>] [E] [T<] cmp</div></blockquote>
|
||||
<p>Becomes one of these three:;</p>
|
||||
<blockquote>
|
||||
<div>[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<</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">></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">></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"><</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">'''</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"> '''</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"><</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">></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>
|
||||
|
|
|
|||
|
|
@ -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>
|
||||
|
|
|
|||
Binary file not shown.
File diff suppressed because one or more lines are too long
|
|
@ -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.
|
||||
|
|
@ -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.
|
||||
=================================
|
||||
|
|
|
|||
|
|
@ -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
|
||||
|
|
|
|||
Loading…
Reference in New Issue