utensil.tngl.sh
A series of experiments with Julia and Python
Begin experimenting @rules
author
Utensil
date
(May 19, 2023, 2:18 PM UTC)
commit
abb3c65b
abb3c65b3b30de98947a9051a59cd1b6a9a556ec
parent
ed988ec6
ed988ec624ed11941882e98bb14fc2d40b2386aa
+637
+637
GARules.jl/scratch.ipynb
+637
GARules.jl/scratch.ipynb
···
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"using GARules"
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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": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Hello GARules!"
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]
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}
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],
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"source": [
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"GARules.greet()"
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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": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"using SymbolicUtils"
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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": 5,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(w, z, α, β)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"@syms w z α::Real β::Real"
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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": 6,
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"metadata": {},
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"outputs": [],
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"source": [
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"using SymbolicUtils: symtype"
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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": 7,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(Number, Number, Real, Real)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"symtype(w), symtype(z), symtype(α), symtype(β)"
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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": 8,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"w isa Number = false\n",
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"α isa Real = false\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"false"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"@show w isa Number\n",
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"@show α isa Real"
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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": 9,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"typeof(w) = SymbolicUtils.BasicSymbolic{Number}\n",
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"typeof(α) = SymbolicUtils.BasicSymbolic{Real}\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"SymbolicUtils.BasicSymbolic{Real}"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"@show typeof(w)\n",
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"@show typeof(α)"
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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": 10,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"α*(sin(w)^2) + β*(sin(w)^2) + α*(cos(z)^2) + β*(cos(z)^2)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"expr1 = α*sin(w)^2 + β*cos(z)^2\n",
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"expr2 = α*cos(z)^2 + β*sin(w)^2\n",
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"\n",
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"expr1 + expr2"
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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": 11,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"α + 5w - 3z"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"2w + 3w - 3z + α"
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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": 12,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(w + z)*(α + β)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"(z + w)*(α + β)"
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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": 13,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(4//3) + α + 5w + (1//2)*β - 3z"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"5 + 2w - 3z + α - (β + 5//3) + 3w - 2 + 3//2 * β"
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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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{
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"data": {
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"text/plain": [
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"(f, g)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"using SymbolicUtils\n",
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"@syms f(x) g(x::Real, y::Real)::Real"
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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": 15,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"sin(w) + f(z) + g(1, α)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"f(z) + g(1, α) + sin(w)"
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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": 16,
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"metadata": {},
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"outputs": [
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{
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"ename": "ErrorException",
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"evalue": "Tuple{Int64, Number} is not a subtype of Tuple{Real, Real}.",
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"output_type": "error",
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"traceback": [
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"Tuple{Int64, Number} is not a subtype of Tuple{Real, Real}.\n",
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"\n",
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"Stacktrace:\n",
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" [1] error(s::String)\n",
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" @ Base ./error.jl:35\n",
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" [2] promote_symtype(::SymbolicUtils.BasicSymbolic{SymbolicUtils.FnType{Tuple{Real, Real}, Real}}, ::Type, ::Type)\n",
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" @ SymbolicUtils ~/.julia/packages/SymbolicUtils/H684H/src/types.jl:901\n",
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" [3] (::SymbolicUtils.BasicSymbolic{SymbolicUtils.FnType{Tuple{Real, Real}, Real}})(::Int64, ::Vararg{Any})\n",
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" @ SymbolicUtils ~/.julia/packages/SymbolicUtils/H684H/src/types.jl:879\n",
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" [4] top-level scope\n",
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" @ /workspaces/julia-playground/GARules.jl/scratch.ipynb:1"
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]
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}
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],
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"source": [
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"g(1, z)"
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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": 17,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"g(2//5, g(1, β))"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"g(2//5, g(1, β))"
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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": 18,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"2(α + β + 2w + cos(z)^2 + sin(z)^2 - 1)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"ex1 = 2 * (w+w+α+β + sin(z)^2 + cos(z)^2 - 1)"
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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": 19,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"2(α + β + 2w)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"ex1 |> simplify"
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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": 20,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"false"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"SymbolicUtils.show_simplified[] = false"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"α + 5w - 3z"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"2w + 3w - 3z + α"
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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": 22,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(w + z)*(α + β)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"(z + w)*(α + β)"
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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": 23,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"sin(2 * ~x) => (2 * sin(~x)) * cos(~x)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"r1 = @rule sin(2(~x)) => 2sin(~x)*cos(~x)"
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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": 25,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"2cos(z)*sin(z)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"r1(sin(2z))"
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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": 26,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"true"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"r1(sin(3z)) === nothing"
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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": 27,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"2cos(w - z)*sin(w - z)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"r1(sin(2*(w-z)))"
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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": 28,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"true"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"r1(sin(2*(w+z)*(α+β))) === nothing"
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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": 29,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"sin(~x + ~y) => sin(~x) * cos(~y) + cos(~x) * sin(~y)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"r2 = @rule sin(~x + ~y) => sin(~x)*cos(~y) + cos(~x)*sin(~y)"
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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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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"sin(α)*cos(β) + cos(α)*sin(β)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"r2(sin(α+β))"
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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": 34,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(x, y, z)"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"@syms x y z"
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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": 36,
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"metadata": {},
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"outputs": [
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{
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"ename": "LoadError",
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"evalue": "LoadError: UndefVarError: @slots not defined\nin expression starting at /workspaces/julia-playground/GARules.jl/scratch.ipynb:1",
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"output_type": "error",
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+
"traceback": [
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+
"LoadError: UndefVarError: @slots not defined\n",
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+
"in expression starting at /workspaces/julia-playground/GARules.jl/scratch.ipynb:1\n"
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]
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}
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],
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+
"source": [
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"r3 = @slots x y z @rule x(y + z) --> x*y + x*z"
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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": 41,
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+
"metadata": {},
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+
"outputs": [
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+
{
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+
"data": {
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"text/plain": [
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+
"+(~(~xs)) => ~(~xs)"
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+
]
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+
},
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+
"metadata": {},
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"output_type": "display_data"
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+
}
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+
],
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"source": [
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"r4 = @rule +(~~xs) => ~~xs"
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]
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},
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{
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"cell_type": "code",
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+
"execution_count": 42,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"3-element view(::Vector{Any}, 1:3) with eltype Any:\n",
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" x\n",
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" y\n",
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" z"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
609
+
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{
614
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615
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616
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617
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618
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619
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620
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623
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