MetaUtils.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MetaUtils\n",
    "\n",
    "* Author: Gen Kuroki\n",
    "* Date: 2020-10-11～2020-10-17, 2021-03-20～2021-03-26, 2021-06-07\n",
    "* Repository: https://github.com/genkuroki/MetaUtils.jl\n",
    "* File: https://nbviewer.jupyter.org/github/genkuroki/MetaUtils.jl/blob/master/MetaUtils.ipynb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Explanatory-examples\" data-toc-modified-id=\"Explanatory-examples-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Explanatory examples</a></span></li><li><span><a href=\"#Miscellaneous-examples-of-@show_texpr,-etc.\" data-toc-modified-id=\"Miscellaneous-examples-of-@show_texpr,-etc.-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Miscellaneous examples of @show_texpr, etc.</a></span><ul class=\"toc-item\"><li><span><a href=\"#for-loop\" data-toc-modified-id=\"for-loop-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>for loop</a></span></li><li><span><a href=\"#subtype-trees\" data-toc-modified-id=\"subtype-trees-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>subtype trees</a></span></li><li><span><a href=\"#function-definition\" data-toc-modified-id=\"function-definition-2.3\"><span class=\"toc-item-num\">2.3&nbsp;&nbsp;</span>function definition</a></span></li><li><span><a href=\"#macro-and-LineNumberNode\" data-toc-modified-id=\"macro-and-LineNumberNode-2.4\"><span class=\"toc-item-num\">2.4&nbsp;&nbsp;</span>macro and LineNumberNode</a></span></li><li><span><a href=\"#QuoteNode\" data-toc-modified-id=\"QuoteNode-2.5\"><span class=\"toc-item-num\">2.5&nbsp;&nbsp;</span>QuoteNode</a></span></li></ul></li><li><span><a href=\"#Evaluation-of-Lisp-like-tuple-expressions\" data-toc-modified-id=\"Evaluation-of-Lisp-like-tuple-expressions-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Evaluation of Lisp-like tuple expressions</a></span></li><li><span><a href=\"#Plot-example\" data-toc-modified-id=\"Plot-example-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Plot example</a></span></li><li><span><a href=\"#Documents\" data-toc-modified-id=\"Documents-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>Documents</a></span></li></ul></div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "v\"1.7.0-DEV.1133\""
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "VERSION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m  Activating\u001b[22m\u001b[39m project at `C:\\Users\\genkuroki\\OneDrive\\work\\MetaUtils.jl`\n"
     ]
    }
   ],
   "source": [
    "if isfile(\"Project.toml\")\n",
    "    using Pkg\n",
    "    Pkg.activate(\".\")\n",
    "    using Revise\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "using MetaUtils"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explanatory examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:call, :+, (:call, :*, 2, :x), 1)"
     ]
    }
   ],
   "source": [
    "@show_sexpr 2x+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 10; (:call, :+, (:call, :*, 2, :x), 1) |> teval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr(:call)\n",
      "├─ :+\n",
      "├─ Expr(:call)\n",
      "│  ├─ :*\n",
      "│  ├─ 2\n",
      "│  └─ :x\n",
      "└─ 1\n"
     ]
    }
   ],
   "source": [
    "@show_tree 2x+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr(:call)\n",
      "├─ :+\n",
      "├─ Expr(:call)\n",
      "│  ├─ :*\n",
      "│  ├─ 2\n",
      "│  └─ :x\n",
      "└─ 1\n"
     ]
    }
   ],
   "source": [
    "show_tree(:(2x + 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AbstractRange\n",
      "├─ LinRange\n",
      "├─ OrdinalRange\n",
      "│  ├─ AbstractUnitRange\n",
      "│  │  ├─ Base.IdentityUnitRange\n",
      "│  │  ├─ Base.OneTo\n",
      "│  │  ├─ Base.Slice\n",
      "│  │  └─ UnitRange\n",
      "│  └─ StepRange\n",
      "└─ StepRangeLen\n"
     ]
    }
   ],
   "source": [
    "print_subtypes(AbstractRange)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr(:call, :f, :x, \n",
      "    Expr(:call, :g, :y, :z))"
     ]
    }
   ],
   "source": [
    "show_expr(:(f(x, g(y, z))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr(:call, :+, \n",
      "    Expr(:call, :*, 2, :x), 1)"
     ]
    }
   ],
   "source": [
    "@show_expr 2x+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 10; Expr(:call, :+, \n",
    "    Expr(:call, :*, 2, :x), 1) |> eval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:call, :f, :x, \n",
      "    (:call, :g, :y, :z))"
     ]
    }
   ],
   "source": [
    "show_texpr(:(f(x, g(y, z))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:call, :+, \n",
      "    (:call, :*, 2, :x), 1)"
     ]
    }
   ],
   "source": [
    "@show_texpr 2x+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 10; (:call, :+, \n",
    "    (:call, :*, 2, :x), 1) |> teval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":(sin(π / 6))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "texpr2expr((:call, :sin, (:call, :/, π, 6)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.49999999999999994"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(:call, :sin, (:call, :/, π, 6)) |> teval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.49999999999999994"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@teval (:call, :sin, (:call, :/, π, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ":(sin(π / 6))\n",
      "→ 0.49999999999999994\n"
     ]
    }
   ],
   "source": [
    "MetaUtils.@t (:call, :sin, (:call, :/, π, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:call, :sin, (:call, :/, π, 6))\n",
      "→ (:call, :sin, \n",
      "    (:call, :/, π, 6))\n",
      "→ :(sin(π / 6))\n",
      "→ 0.49999999999999994\n"
     ]
    }
   ],
   "source": [
    "MetaUtils.@T (:call, :sin, (:call, :/, π, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.49999999999999994"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(:sin, (:/, π, 6)) |> teval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.49999999999999994"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@teval (:sin, (:/, π, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ":(sin(π / 6))\n",
      "→ 0.49999999999999994\n"
     ]
    }
   ],
   "source": [
    "MetaUtils.@t (:sin, (:/, π, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:sin, (:/, π, 6))\n",
      "→ (:call, :sin, \n",
      "    (:call, :/, π, 6))\n",
      "→ :(sin(π / 6))\n",
      "→ 0.49999999999999994\n"
     ]
    }
   ],
   "source": [
    "MetaUtils.@T (:sin, (:/, π, 6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Miscellaneous examples of @show_texpr, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### for loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:for, \n",
      "    (:(=), :k, \n",
      "        (:call, :(:), 1, 10)), \n",
      "    (:block, \n",
      "        (:(=), :x, \n",
      "            (:call, :÷, \n",
      "                (:call, :*, :k, \n",
      "                    (:call, :+, :k, 1)), 2)), \n",
      "        (:call, :println, \"k(k+1)/2 = \", :x)))"
     ]
    }
   ],
   "source": [
    "@show_texpr for k in 1:10\n",
    "    x = k*(k+1) ÷ 2\n",
    "    println(\"k(k+1)/2 = \", x)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:for, \n",
      "    (:(=), :k, \n",
      "        (:call, :(:), 1, 10)), \n",
      "    (:block, LineNumberNode(2, Symbol(\"In[25]\")), \n",
      "        (:(=), :x, \n",
      "            (:call, :÷, \n",
      "                (:call, :*, :k, \n",
      "                    (:call, :+, :k, 1)), 2)), LineNumberNode(3, Symbol(\"In[25]\")), \n",
      "        (:call, :println, \"k(k+1)/2 = \", :x)))"
     ]
    }
   ],
   "source": [
    "@show_texpr for k in 1:10\n",
    "    x = k*(k+1) ÷ 2\n",
    "    println(\"k(k+1)/2 = \", x)\n",
    "end true"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr(:for)\n",
      "├─ Expr(:(=))\n",
      "│  ├─ :k\n",
      "│  └─ Expr(:call)\n",
      "│     ⋮\n",
      "│     \n",
      "└─ Expr(:block)\n",
      "   ├─ Expr(:(=))\n",
      "   │  ⋮\n",
      "   │  \n",
      "   └─ Expr(:call)\n",
      "      ⋮\n",
      "      \n"
     ]
    }
   ],
   "source": [
    "@show_tree for k in 1:10\n",
    "    x = k*(k+1) ÷ 2\n",
    "    println(\"k(k+1)/2 = \", x)\n",
    "end 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr(:for)\n",
      "├─ Expr(:(=))\n",
      "│  ├─ :k\n",
      "│  └─ Expr(:call)\n",
      "│     ├─ :(:)\n",
      "│     ├─ 1\n",
      "│     └─ 10\n",
      "└─ Expr(:block)\n",
      "   ├─ Expr(:(=))\n",
      "   │  ├─ :x\n",
      "   │  └─ Expr(:call)\n",
      "   │     ├─ :÷\n",
      "   │     ├─ Expr(:call)\n",
      "   │     │  ├─ :*\n",
      "   │     │  ├─ :k\n",
      "   │     │  └─ Expr(:call)\n",
      "   │     │     ├─ :+\n",
      "   │     │     ├─ :k\n",
      "   │     │     └─ 1\n",
      "   │     └─ 2\n",
      "   └─ Expr(:call)\n",
      "      ├─ :println\n",
      "      ├─ \"k(k+1)/2 = \"\n",
      "      └─ :x\n"
     ]
    }
   ],
   "source": [
    "@show_tree for k in 1:10\n",
    "    x = k*(k+1) ÷ 2\n",
    "    println(\"k(k+1)/2 = \", x)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr(:for)\n",
      "├─ Expr(:(=))\n",
      "│  ├─ :k\n",
      "│  └─ Expr(:call)\n",
      "│     ├─ :(:)\n",
      "│     ├─ 1\n",
      "│     └─ 10\n",
      "└─ Expr(:block)\n",
      "   ├─ :(#= In[28]:2 =#)\n",
      "   ├─ Expr(:(=))\n",
      "   │  ├─ :x\n",
      "   │  └─ Expr(:call)\n",
      "   │     ├─ :÷\n",
      "   │     ├─ Expr(:call)\n",
      "   │     │  ├─ :*\n",
      "   │     │  ├─ :k\n",
      "   │     │  └─ Expr(:call)\n",
      "   │     │     ├─ :+\n",
      "   │     │     ├─ :k\n",
      "   │     │     └─ 1\n",
      "   │     └─ 2\n",
      "   ├─ :(#= In[28]:3 =#)\n",
      "   └─ Expr(:call)\n",
      "      ├─ :println\n",
      "      ├─ \"k(k+1)/2 = \"\n",
      "      └─ :x\n"
     ]
    }
   ],
   "source": [
    "@show_tree for k in 1:10\n",
    "    x = k*(k+1) ÷ 2\n",
    "    println(\"k(k+1)/2 = \", x)\n",
    "end 10 true"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr\n",
      "  head: Symbol for\n",
      "  args: Array{Any}((2,))\n",
      "    1: Expr\n",
      "      head: Symbol =\n",
      "      args: Array{Any}((2,))\n",
      "        1: Symbol k\n",
      "        2: Expr\n",
      "          head: Symbol call\n",
      "          args: Array{Any}((3,))\n",
      "            1: Symbol :\n",
      "            2: Int64 1\n",
      "            3: Int64 10\n",
      "    2: Expr\n",
      "      head: Symbol block\n",
      "      args: Array{Any}((4,))\n",
      "        1: LineNumberNode\n",
      "          line: Int64 2\n",
      "          file: Symbol In[29]\n",
      "        2: Expr\n",
      "          head: Symbol =\n",
      "          args: Array{Any}((2,))\n",
      "            1: Symbol x\n",
      "            2: Expr\n",
      "              head: Symbol call\n",
      "              args: Array{Any}((3,))\n",
      "                1: Symbol ÷\n",
      "                2: Expr\n",
      "                3: Int64 2\n",
      "        3: LineNumberNode\n",
      "          line: Int64 3\n",
      "          file: Symbol In[29]\n",
      "        4: Expr\n",
      "          head: Symbol call\n",
      "          args: Array{Any}((3,))\n",
      "            1: Symbol println\n",
      "            2: String \"k(k+1)/2 = \"\n",
      "            3: Symbol x\n"
     ]
    }
   ],
   "source": [
    "Meta.@dump for k in 1:10\n",
    "    x = k*(k+1) ÷ 2\n",
    "    println(\"k(k+1)/2 = \", x)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr(:for, \n",
      "    Expr(:(=), :k, \n",
      "        Expr(:call, :(:), 1, 10)), \n",
      "    Expr(:block, \n",
      "        Expr(:(=), :x, \n",
      "            Expr(:call, :÷, \n",
      "                Expr(:call, :*, :k, \n",
      "                    Expr(:call, :+, :k, 1)), 2)), \n",
      "        Expr(:call, :println, \"k(k+1)/2 = \", :x)))"
     ]
    }
   ],
   "source": [
    "@show_expr for k in 1:10\n",
    "    x = k*(k+1) ÷ 2\n",
    "    println(\"k(k+1)/2 = \", x)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:for, \n",
      "    (:(=), :k, \n",
      "        (:call, :(:), 1, 10)), \n",
      "    (:block, \n",
      "        (:(=), :x, \n",
      "            (:call, :÷, \n",
      "                (:call, :*, :k, \n",
      "                    (:call, :+, :k, 1)), 2)), \n",
      "        (:call, :println, \"k(k+1)/2 = \", :x)))"
     ]
    }
   ],
   "source": [
    "@show_texpr for k in 1:10\n",
    "    x = k*(k+1) ÷ 2\n",
    "    println(\"k(k+1)/2 = \", x)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### subtype trees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AbstractRange\n",
      "├─ LinRange\n",
      "├─ OrdinalRange\n",
      "│  ├─ AbstractUnitRange\n",
      "│  │  ├─ Base.IdentityUnitRange\n",
      "│  │  ├─ Base.OneTo\n",
      "│  │  ├─ Base.Slice\n",
      "│  │  └─ UnitRange\n",
      "│  └─ StepRange\n",
      "└─ StepRangeLen\n"
     ]
    }
   ],
   "source": [
    "print_subtypes(AbstractRange)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number\n",
      "├─ Complex\n",
      "└─ Real\n",
      "   ├─ AbstractFloat\n",
      "   │  ├─ BigFloat\n",
      "   │  ├─ Float16\n",
      "   │  ├─ Float32\n",
      "   │  └─ Float64\n",
      "   ├─ AbstractIrrational\n",
      "   │  └─ Irrational\n",
      "   ├─ Integer\n",
      "   │  ├─ Bool\n",
      "   │  ├─ Signed\n",
      "   │  │  ├─ BigInt\n",
      "   │  │  ├─ Int128\n",
      "   │  │  ├─ Int16\n",
      "   │  │  ├─ Int32\n",
      "   │  │  ├─ Int64\n",
      "   │  │  └─ Int8\n",
      "   │  └─ Unsigned\n",
      "   │     ├─ UInt128\n",
      "   │     ├─ UInt16\n",
      "   │     ├─ UInt32\n",
      "   │     ├─ UInt64\n",
      "   │     └─ UInt8\n",
      "   └─ Rational\n"
     ]
    }
   ],
   "source": [
    "print_subtypes(Number)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AbstractVector\n",
      "├─ AbstractRange\n",
      "│  ├─ LinRange\n",
      "│  ├─ OrdinalRange\n",
      "│  │  ├─ AbstractUnitRange\n",
      "│  │  │  ├─ Base.IdentityUnitRange\n",
      "│  │  │  ├─ Base.OneTo\n",
      "│  │  │  ├─ Base.Slice\n",
      "│  │  │  └─ UnitRange\n",
      "│  │  └─ StepRange\n",
      "│  └─ StepRangeLen\n",
      "├─ Base.ExceptionStack\n",
      "├─ Base.LogicalIndex\n",
      "├─ Base.MethodList\n",
      "├─ Base.ReinterpretArray{T, 1, S, A} where {T, S, A<:(AbstractArray{S})}\n",
      "├─ Base.ReshapedArray{T, 1} where T\n",
      "├─ BitVector\n",
      "├─ CartesianIndices{1, R} where R<:Tuple{OrdinalRange{Int64, Int64}}\n",
      "├─ Core.Compiler.AbstractRange\n",
      "│  ├─ Core.Compiler.LinRange\n",
      "│  ├─ Core.Compiler.OrdinalRange\n",
      "│  │  ├─ Core.Compiler.AbstractUnitRange\n",
      "│  │  │  ├─ Core.Compiler.IdentityUnitRange\n",
      "│  │  │  ├─ Core.Compiler.OneTo\n",
      "│  │  │  ├─ Core.Compiler.Slice\n",
      "│  │  │  ├─ Core.Compiler.StmtRange\n",
      "│  │  │  └─ Core.Compiler.UnitRange\n",
      "│  │  └─ Core.Compiler.StepRange\n",
      "│  └─ Core.Compiler.StepRangeLen\n",
      "├─ Core.Compiler.BitArray{1}\n",
      "├─ Core.Compiler.ExceptionStack\n",
      "├─ Core.Compiler.LinearIndices{1, R} where R<:Tuple{Core.Compiler.AbstractUnitRange{Int64}}\n",
      "├─ Core.Compiler.MethodList\n",
      "├─ DenseVector\n",
      "│  ├─ Base.CodeUnits\n",
      "│  ├─ Base.Experimental.Const{T, 1} where T\n",
      "│  ├─ Random.UnsafeView\n",
      "│  ├─ SharedArrays.SharedVector\n",
      "│  └─ Vector\n",
      "├─ LinearIndices{1, R} where R<:Tuple{AbstractUnitRange{Int64}}\n",
      "├─ PermutedDimsArray{T, 1} where T\n",
      "├─ SparseArrays.AbstractSparseVector\n",
      "│  └─ SparseArrays.SparseVector\n",
      "├─ SubArray{T, 1} where T\n",
      "├─ Test.GenericArray{T, 1} where T\n",
      "└─ ZMQ.Message\n"
     ]
    }
   ],
   "source": [
    "print_subtypes(AbstractVector)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### function definition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:function, \n",
      "    (:where, \n",
      "        (:call, :f, \n",
      "            (:(::), :x, :T)), \n",
      "        (:<:, :T, :Number)), \n",
      "    (:block, \n",
      "        (:call, :sin, :x)))"
     ]
    }
   ],
   "source": [
    "@show_texpr function f(x::T) where T<:Number\n",
    "    sin(x)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr(:function)\n",
      "├─ Expr(:where)\n",
      "│  ├─ Expr(:call)\n",
      "│  │  ├─ :f\n",
      "│  │  └─ Expr(:(::))\n",
      "│  │     ├─ :x\n",
      "│  │     └─ :T\n",
      "│  └─ Expr(:<:)\n",
      "│     ├─ :T\n",
      "│     └─ :Number\n",
      "└─ Expr(:block)\n",
      "   └─ Expr(:call)\n",
      "      ├─ :sin\n",
      "      └─ :x\n"
     ]
    }
   ],
   "source": [
    "@show_tree function f(x::T) where T<:Number\n",
    "    sin(x)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr(:function, \n",
      "    Expr(:where, \n",
      "        Expr(:call, :f, \n",
      "            Expr(:(::), :x, :T)), \n",
      "        Expr(:<:, :T, :Number)), \n",
      "    Expr(:block, \n",
      "        Expr(:call, :sin, :x)))"
     ]
    }
   ],
   "source": [
    "@show_expr function f(x::T) where T<:Number\n",
    "    sin(x)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:function, \n",
      "    (:where, \n",
      "        (:call, :f, \n",
      "            (:(::), :x, :T)), \n",
      "        (:<:, :T, :Number)), \n",
      "    (:block, \n",
      "        (:call, :sin, :x)))"
     ]
    }
   ],
   "source": [
    "@show_texpr function f(x::T) where T<:Number\n",
    "    sin(x)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### macro and LineNumberNode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr(:macrocall)\n",
      "├─ Symbol(\"@show\")\n",
      "├─ :(#= In[39]:1 =#)\n",
      "└─ Expr(:call)\n",
      "   ├─ :float\n",
      "   └─ :π\n"
     ]
    }
   ],
   "source": [
    "@show_tree @show float(π)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:macrocall, Symbol(\"@show\"), :(#= In[40]:1 =#), (:call, :float, :π))"
     ]
    }
   ],
   "source": [
    "@show_sexpr @show float(π)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "float(π) = 3.141592653589793\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@teval (:macrocall, Symbol(\"@show\"), :(#= In[34]:1 =#), (:call, :float, :π))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr(:macrocall, Symbol(\"@show\"), LineNumberNode(1, Symbol(\"In[42]\")), \n",
      "    Expr(:call, :float, :π))"
     ]
    }
   ],
   "source": [
    "@show_expr @show float(π)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expr(:macrocall, Symbol(\"@show\"), LineNumberNode(1, Symbol(\"In[43]\")), \n",
      "    Expr(:call, :float, :π))"
     ]
    }
   ],
   "source": [
    "Expr(:macrocall, Symbol(\"@show\"), LineNumberNode(@__LINE__, @__FILE__), \n",
    "    Expr(:call, :float, :π)) |> show_expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "float(π) = 3.141592653589793\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Expr(:macrocall, Symbol(\"@show\"), LineNumberNode(@__LINE__, @__FILE__), \n",
    "    Expr(:call, :float, :π)) |> eval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:macrocall, Symbol(\"@show\"), LineNumberNode(1, Symbol(\"In[45]\")), \n",
      "    (:call, :float, :π))"
     ]
    }
   ],
   "source": [
    "@show_texpr @show float(π)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "float(π) = 3.141592653589793\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(:macrocall, Symbol(\"@show\"), LineNumberNode(@__LINE__, @__FILE__), \n",
    "    (:call, :float, :π)) |> teval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "float(π) = 3.141592653589793\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@teval (:macrocall, Symbol(\"@show\"), LineNumberNode(@__LINE__, @__FILE__),  \n",
    "    (:call, :float, :π))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### QuoteNode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":($(QuoteNode(:(sin(x)))))"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QuoteNode(:(sin(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:quote, #QuoteNode\n",
      "  (:call, :sin, :x)\n",
      ")"
     ]
    }
   ],
   "source": [
    "QuoteNode(:(sin(x))) |> Meta.show_sexpr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "QuoteNode(\n",
      "    Expr(:call, :sin, :x))"
     ]
    }
   ],
   "source": [
    "QuoteNode(:(sin(x))) |> show_expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "QuoteNode(\n",
      "    (:call, :sin, :x))"
     ]
    }
   ],
   "source": [
    "QuoteNode(:(sin(x))) |> show_texpr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "QuoteNode(\n",
    "    (:call, :sin, :x)) |> texpr2expr == QuoteNode(:(sin(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":(sin(x))"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@teval QuoteNode(\n",
    "    (:call, :sin, :x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation of Lisp-like tuple expressions\n",
    "\n",
    "If you want more Lisp-like examamples, see [LispLikeEval.ipynb](https://nbviewer.jupyter.org/github/genkuroki/LispLikeEval.jl/blob/master/LispLikeEval.ipynb)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "using MetaUtils: @t, @T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ":(f(x) = sin(x))\n",
      "→ f\n",
      "\n",
      ":(f(π / 6))\n",
      "→ 0.49999999999999994\n"
     ]
    }
   ],
   "source": [
    "# Define and run a function f(x) = sin(x)\n",
    "\n",
    "@t (:(=), :(f(x)), (:sin, :x))\n",
    "println()\n",
    "@t (:f, (:/, π, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:(=), :(f(x)), (:sin, :x))\n",
      "→ (:(=), \n",
      "    (:call, :f, :x), \n",
      "    (:call, :sin, :x))\n",
      "→ :(f(x) = sin(x))\n",
      "→ f\n",
      "\n",
      "(:f, (:/, π, 6))\n",
      "→ (:call, :f, \n",
      "    (:call, :/, π, 6))\n",
      "→ :(f(π / 6))\n",
      "→ 0.49999999999999994\n"
     ]
    }
   ],
   "source": [
    "# Define and run a function f(x) = sin(x)\n",
    "\n",
    "@T (:(=), :(f(x)), (:sin, :x))\n",
    "println()\n",
    "@T (:f, (:/, π, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "quote\n",
      "    function g(x)\n",
      "        sin(x)\n",
      "    end\n",
      "    g(π / 6)\n",
      "end\n",
      "→ 0.49999999999999994\n"
     ]
    }
   ],
   "source": [
    "# Define and run a function g(x) = sin(x)\n",
    "\n",
    "@t (:block,\n",
    "    (:function, :(g(x)), (:sin, :x)),\n",
    "    (:call, :g, (:/, π, 6)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:block, (:function, :(g(x)), (:sin, :x)), (:call, :g, (:/, π, 6)))\n",
      "→ (:block, \n",
      "    (:function, \n",
      "        (:call, :g, :x), \n",
      "        (:call, :sin, :x)), \n",
      "    (:call, :g, \n",
      "        (:call, :/, π, 6)))\n",
      "→ quote\n",
      "    function g(x)\n",
      "        sin(x)\n",
      "    end\n",
      "    g(π / 6)\n",
      "end\n",
      "→ 0.49999999999999994\n"
     ]
    }
   ],
   "source": [
    "# Define and run a function g(x) = sin(x)\n",
    "\n",
    "@T (:block,\n",
    "    (:function, :(g(x)), (:sin, :x)),\n",
    "    (:call, :g, (:/, π, 6)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "quote\n",
      "    function pi_mc(N)\n",
      "        c = 0\n",
      "        for i = 1:N\n",
      "            c += ifelse(rand() ^ 2 + rand() ^ 2 ≤ 1, 1, 0)\n",
      "        end\n",
      "        (4c) / N\n",
      "    end\n",
      "    pi_mc(10 ^ 8)\n",
      "end\n",
      "→ 3.14178092\n"
     ]
    }
   ],
   "source": [
    "# Calculation of pi by the Monte Carlo method\n",
    "\n",
    "@t (:block, \n",
    "    (:function, :(pi_mc(N)), \n",
    "        (:block, \n",
    "            (:(=), :c, 0), \n",
    "            (:for, (:(=), :i, (:(:), 1, :N)), \n",
    "                (:block, \n",
    "                    (:+=, :c, \n",
    "                        (:call, :ifelse, \n",
    "                            (:≤, (:+, (:^, (:rand,), 2), (:^, (:rand,), 2)), 1), \n",
    "                            1, 0)))), \n",
    "            (:/, (:*, 4, :c), :N))), \n",
    "    (:call, :pi_mc, (:^, 10, 8)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ":($(Expr(:quote, :(sin(x)))))\n",
      "→ :(sin(x))\n"
     ]
    }
   ],
   "source": [
    "# quote\n",
    "\n",
    "@t (:quote, (:sin, :x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ":((1, 2, 3))\n",
      "→ (1, 2, 3)\n"
     ]
    }
   ],
   "source": [
    "# tuple\n",
    "\n",
    "@t (:tuple, 1, 2, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
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       "  1071.73,1104.85 1076.83,1099.41 1081.93,1093.92 1087.04,1088.38 1092.14,1082.8 1097.25,1077.17 1102.35,1071.49 1107.46,1065.78 1112.56,1060.02 1117.66,1054.22 \n",
       "  1122.77,1048.37 1127.87,1042.49 1132.98,1036.58 1138.08,1030.62 1143.19,1024.63 1148.29,1018.6 1153.39,1012.54 1158.5,1006.44 1163.6,1000.32 1168.71,994.162 \n",
       "  1173.81,987.975 1178.92,981.76 1184.02,975.516 1189.12,969.246 1194.23,962.951 1199.33,956.63 1204.44,950.286 1209.54,943.92 1214.65,937.532 1219.75,931.123 \n",
       "  1224.85,924.695 1229.96,918.249 1235.06,911.785 1240.17,905.305 1245.27,898.81 1250.38,892.3 1255.48,885.777 1260.59,879.242 1265.69,872.697 1270.79,866.141 \n",
       "  1275.9,859.575 1281,853.002 1286.11,846.423 1291.21,839.837 1296.32,833.246 1301.42,826.651 1306.52,820.054 1311.63,813.455 1316.73,806.855 1321.84,800.256 \n",
       "  1326.94,793.658 1332.05,787.063 1337.15,780.471 1342.25,773.883 1347.36,767.301 1352.46,760.726 1357.57,754.158 1362.67,747.599 1367.78,741.05 1372.88,734.512 \n",
       "  1377.98,727.985 1383.09,721.471 1388.19,714.971 1393.3,708.486 1398.4,702.017 1403.51,695.565 1408.61,689.131 1413.71,682.716 1418.82,676.322 1423.92,669.948 \n",
       "  1429.03,663.597 1434.13,657.269 1439.24,650.965 1444.34,644.687 1449.44,638.435 1454.55,632.211 1459.65,626.015 1464.76,619.848 1469.86,613.712 1474.97,607.608 \n",
       "  1480.07,601.537 1485.18,595.499 1490.28,589.495 1495.38,583.528 1500.49,577.597 1505.59,571.704 1510.7,565.851 1515.8,560.037 1520.91,554.264 1526.01,548.533 \n",
       "  1531.11,542.845 1536.22,537.201 1541.32,531.602 1546.43,526.05 1551.53,520.545 1556.64,515.088 1561.74,509.68 1566.84,504.323 1571.95,499.017 1577.05,493.763 \n",
       "  1582.16,488.563 1587.26,483.418 1592.37,478.328 1597.47,473.295 1602.57,468.319 1607.68,463.402 1612.78,458.545 1617.89,453.749 1622.99,449.014 1628.1,444.342 \n",
       "  1633.2,439.734 1638.3,435.191 1643.41,430.714 1648.51,426.304 1653.62,421.963 1658.72,417.69 1663.83,413.487 1668.93,409.356 1674.03,405.296 1679.14,401.31 \n",
       "  1684.24,397.399 1689.35,393.563 1694.45,389.803 1699.56,386.12 1704.66,382.516 1709.77,378.992 1714.87,375.548 1719.97,372.186 1725.08,368.906 1730.18,365.71 \n",
       "  1735.29,362.599 1740.39,359.573 1745.5,356.635 1750.6,353.784 1755.7,351.022 1760.81,348.35 1765.91,345.769 1771.02,343.28 1776.12,340.884 1781.23,338.582 \n",
       "  1786.33,336.375 1791.43,334.265 1796.54,332.252 1801.64,330.337 1806.75,328.521 1811.85,326.806 1816.96,325.192 1822.06,323.68 1827.16,322.272 1832.27,320.969 \n",
       "  1837.37,319.771 1842.48,318.68 1847.58,317.696 1852.69,316.821 1857.79,316.056 1862.89,315.401 1868,314.858 1873.1,314.429 1878.21,314.113 1883.31,313.912 \n",
       "  1888.42,313.827 1893.52,313.859 1898.62,314.009 1903.73,314.278 1908.83,314.667 1913.94,315.178 1919.04,315.81 1924.15,316.566 1929.25,317.447 1934.36,318.452 \n",
       "  1939.46,319.584 1944.56,320.844 1949.67,322.232 1954.77,323.749 1959.88,325.397 1964.98,327.177 1970.09,329.089 1975.19,331.135 1980.29,333.316 1985.4,335.632 \n",
       "  1990.5,338.085 1995.61,340.676 2000.71,343.406 2005.82,346.276 2010.92,349.287 2016.02,352.44 2021.13,355.736 2026.23,359.176 2031.34,362.761 2036.44,366.493 \n",
       "  2041.55,370.371 2046.65,374.398 2051.75,378.575 2056.86,382.901 2061.96,387.379 2067.07,392.009 2072.17,396.793 2077.28,401.732 2082.38,406.826 2087.48,412.076 \n",
       "  2092.59,417.484 2097.69,423.051 2102.8,428.778 2107.9,434.665 2113.01,440.714 2118.11,446.926 2123.21,453.302 2128.32,459.843 2133.42,466.55 2138.53,473.424 \n",
       "  2143.63,480.466 2148.74,487.677 2153.84,495.058 2158.94,502.61 2164.05,510.335 2169.15,518.233 2174.26,526.305 2179.36,534.552 2184.47,542.976 2189.57,551.577 \n",
       "  2194.68,560.357 2199.78,569.316 2204.88,578.456 2209.99,587.778 2215.09,597.282 2220.2,606.97 2225.3,616.842 2230.41,626.9 2235.51,637.145 2240.61,647.578 \n",
       "  2245.72,658.2 2250.82,669.012 2255.93,680.015 2261.03,691.209 2266.14,702.597 2271.24,714.179 2276.34,725.956 2281.45,737.929 2286.55,750.1 2291.66,762.468 \n",
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      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "begin\n",
    "    using Plots\n",
    "    n = 20\n",
    "    x = range(-π, π; length=20)\n",
    "    noise = 0.3randn(n)\n",
    "    y = sin.(x) + noise\n",
    "    X = x .^ (0:3)'\n",
    "    b = X\\y\n",
    "    f(x) = evalpoly(x, b)\n",
    "    xs = range(-π, π; length=400)\n",
    "    plot(; legend=:topleft)\n",
    "    scatter!(x, y; label=\"sample\")\n",
    "    plot!(xs, sin.(xs); label=\"sin(x)\", color=:blue, ls=:dash)\n",
    "    plot!(xs, f.(xs); label=\"degree-3 polynomial\", color=:red, lw=2)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(:block, \n",
      "    (:using, \n",
      "        (:., :Plots)), \n",
      "    (:(=), :n, 20), \n",
      "    (:(=), :x, \n",
      "        (:call, :range, \n",
      "            (:parameters, \n",
      "                (:kw, :length, 20)), \n",
      "            (:call, :-, :π), :π)), \n",
      "    (:(=), :noise, \n",
      "        (:call, :*, 0.3, \n",
      "            (:call, :randn, :n))), \n",
      "    (:(=), :y, \n",
      "        (:call, :+, \n",
      "            (:., :sin, \n",
      "                (:tuple, :x)), :noise)), \n",
      "    (:(=), :X, \n",
      "        (:call, :.^, :x, \n",
      "            (Symbol(\"'\"), \n",
      "                (:call, :(:), 0, 3)))), \n",
      "    (:(=), :b, \n",
      "        (:call, :\\, :X, :y)), \n",
      "    (:(=), \n",
      "        (:call, :f, :x), \n",
      "        (:block, \n",
      "            (:call, :evalpoly, :x, :b))), \n",
      "    (:(=), :xs, \n",
      "        (:call, :range, \n",
      "            (:parameters, \n",
      "                (:kw, :length, 400)), \n",
      "            (:call, :-, :π), :π)), \n",
      "    (:call, :plot, \n",
      "        (:parameters, \n",
      "            (:kw, :legend, QuoteNode(:topleft)))), \n",
      "    (:call, :scatter!, \n",
      "        (:parameters, \n",
      "            (:kw, :label, \"sample\")), :x, :y), \n",
      "    (:call, :plot!, \n",
      "        (:parameters, \n",
      "            (:kw, :label, \"sin(x)\"), \n",
      "            (:kw, :color, QuoteNode(:blue)), \n",
      "            (:kw, :ls, QuoteNode(:dash))), :xs, \n",
      "        (:., :sin, \n",
      "            (:tuple, :xs))), \n",
      "    (:call, :plot!, \n",
      "        (:parameters, \n",
      "            (:kw, :label, \"degree-3 polynomial\"), \n",
      "            (:kw, :color, QuoteNode(:red)), \n",
      "            (:kw, :lw, 2)), :xs, \n",
      "        (:., :f, \n",
      "            (:tuple, :xs))))"
     ]
    }
   ],
   "source": [
    "@show_texpr begin\n",
    "    using Plots\n",
    "    n = 20\n",
    "    x = range(-π, π; length=20)\n",
    "    noise = 0.3randn(n)\n",
    "    y = sin.(x) + noise\n",
    "    X = x .^ (0:3)'\n",
    "    b = X\\y\n",
    "    f(x) = evalpoly(x, b)\n",
    "    xs = range(-π, π; length=400)\n",
    "    plot(; legend=:topleft)\n",
    "    scatter!(x, y; label=\"sample\")\n",
    "    plot!(xs, sin.(xs); label=\"sin(x)\", color=:blue, ls=:dash)\n",
    "    plot!(xs, f.(xs); label=\"degree-3 polynomial\", color=:red, lw=2)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
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       "  1837.37,315.972 1842.48,316.352 1847.58,316.859 1852.69,317.494 1857.79,318.258 1862.89,319.152 1868,320.177 1873.1,321.334 1878.21,322.624 1883.31,324.049 \n",
       "  1888.42,325.609 1893.52,327.306 1898.62,329.141 1903.73,331.115 1908.83,333.228 1913.94,335.483 1919.04,337.879 1924.15,340.419 1929.25,343.103 1934.36,345.933 \n",
       "  1939.46,348.909 1944.56,352.033 1949.67,355.305 1954.77,358.728 1959.88,362.301 1964.98,366.026 1970.09,369.905 1975.19,373.938 1980.29,378.126 1985.4,382.471 \n",
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/></svg>\n"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@teval (:block, \n",
    "    (:using, (:., :Plots)), \n",
    "    (:(=), :n, 20), \n",
    "    (:(=), :x, (:range, (:parameters, (:kw, :length, 20)), (:-, :π), :π)), \n",
    "    (:(=), :noise, (:*, 0.3, (:randn, :n))), \n",
    "    (:(=), :y, (:+, (:., :sin, (:tuple, :x)), :noise)), \n",
    "    (:(=), :X, (:call, :.^, :x, (Symbol(\"'\"), (:call, :(:), 0, 3)))),  \n",
    "    (:(=), :b, (:\\, :X, :y)), \n",
    "    (:(=), (:call, :f, :x), (:block, (:call, :evalpoly, :x, :b))),\n",
    "    (:(=), :xs, (:range, (:parameters, (:kw, :length, 400)), (:-, :π), :π)), \n",
    "    (:plot, (:parameters, (:kw, :legend, QuoteNode(:topleft)))), \n",
    "    (:scatter!, (:parameters, (:kw, :label, \"sample\")), :x, :y), \n",
    "    (:plot!, (:parameters, \n",
    "            (:kw, :label, \"sin(x)\"), \n",
    "            (:kw, :color, QuoteNode(:blue)), \n",
    "            (:kw, :ls, QuoteNode(:dash))), \n",
    "        :xs, (:., :sin, (:tuple, :xs))), \n",
    "    (:plot!, (:parameters, \n",
    "            (:kw, :label, \"degree-3 polynomial\"), \n",
    "            (:kw, :color, QuoteNode(:red)), \n",
    "            (:kw, :lw, 2)), \n",
    "        :xs, (:., :f, (:tuple, :xs))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "```julia\n",
       "begin\n",
       "    using Plots\n",
       "    n = 20\n",
       "    x = range(-π, π; length = 20)\n",
       "    noise = 0.3 * randn(n)\n",
       "    y = sin.(x) + noise\n",
       "    X = x .^ var\"'\"(0:3)\n",
       "    b = X \\ y\n",
       "    f(x) = begin\n",
       "            evalpoly(x, b)\n",
       "        end\n",
       "    xs = range(-π, π; length = 400)\n",
       "    plot(; legend = :topleft)\n",
       "    scatter!(x, y; label = \"sample\")\n",
       "    plot!(xs, sin.(xs); label = \"sin(x)\", color = :blue, ls = :dash)\n",
       "    plot!(xs, f.(xs); label = \"degree-3 polynomial\", color = :red, lw = 2)\n",
       "end\n",
       "```"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(:block, \n",
    "    (:using, (:., :Plots)), \n",
    "    (:(=), :n, 20), \n",
    "    (:(=), :x, (:range, (:parameters, (:kw, :length, 20)), (:-, :π), :π)), \n",
    "    (:(=), :noise, (:*, 0.3, (:randn, :n))), \n",
    "    (:(=), :y, (:+, (:., :sin, (:tuple, :x)), :noise)), \n",
    "    (:(=), :X, (:call, :.^, :x, (Symbol(\"'\"), (:call, :(:), 0, 3)))),  \n",
    "    (:(=), :b, (:\\, :X, :y)), \n",
    "    (:(=), (:call, :f, :x), (:block, (:call, :evalpoly, :x, :b))),\n",
    "    (:(=), :xs, (:range, (:parameters, (:kw, :length, 400)), (:-, :π), :π)), \n",
    "    (:plot, (:parameters, (:kw, :legend, QuoteNode(:topleft)))), \n",
    "    (:scatter!, (:parameters, (:kw, :label, \"sample\")), :x, :y), \n",
    "    (:plot!, (:parameters, \n",
    "            (:kw, :label, \"sin(x)\"), \n",
    "            (:kw, :color, QuoteNode(:blue)), \n",
    "            (:kw, :ls, QuoteNode(:dash))), \n",
    "        :xs, (:., :sin, (:tuple, :xs))), \n",
    "    (:plot!, (:parameters, \n",
    "            (:kw, :label, \"degree-3 polynomial\"), \n",
    "            (:kw, :color, QuoteNode(:red)), \n",
    "            (:kw, :lw, 2)), \n",
    "        :xs, (:., :f, (:tuple, :xs)))) |> texpr2expr |> \n",
    "x -> display(\"text/markdown\", \"```julia\\n$x\\n```\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Documents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "MetaUtils\n",
       "\\end{verbatim}\n",
       "contains utilities for metaprogramming in Julia.\n",
       "\n",
       "\\begin{verbatim}\n",
       "export @show_sexpr, \n",
       "    show_tree, @show_tree, \n",
       "    print_subtypes, \n",
       "    show_expr, @show_expr, \n",
       "    show_texpr, @show_texpr, \n",
       "    texpr2expr, teval, @teval\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "MetaUtils\n",
       "```\n",
       "\n",
       "contains utilities for metaprogramming in Julia.\n",
       "\n",
       "```julia\n",
       "export @show_sexpr, \n",
       "    show_tree, @show_tree, \n",
       "    print_subtypes, \n",
       "    show_expr, @show_expr, \n",
       "    show_texpr, @show_texpr, \n",
       "    texpr2expr, teval, @teval\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  MetaUtils\u001b[39m\n",
       "\n",
       "  contains utilities for metaprogramming in Julia.\n",
       "\n",
       "\u001b[36m  export @show_sexpr, \u001b[39m\n",
       "\u001b[36m      show_tree, @show_tree, \u001b[39m\n",
       "\u001b[36m      print_subtypes, \u001b[39m\n",
       "\u001b[36m      show_expr, @show_expr, \u001b[39m\n",
       "\u001b[36m      show_texpr, @show_texpr, \u001b[39m\n",
       "\u001b[36m      texpr2expr, teval, @teval\u001b[39m"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@doc MetaUtils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "@show_sexpr(expr, linenums=false)\n",
       "\\end{verbatim}\n",
       "shows the lisp style S-expression of \\texttt{expr} and prints the line number nodes if \\texttt{linenums} is true.  This is the macro version of \\texttt{Meta.show\\_sexpr}.\n",
       "\n",
       "\\subsection{Example}\n",
       "\\begin{verbatim}\n",
       "julia> @show_sexpr 2x+1\n",
       "(:call, :+, (:call, :*, 2, :x), 1)\n",
       "\\end{verbatim}\n",
       "\\texttt{teval} function can evaluate the output of \\texttt{@show\\_sexpr}. \n",
       "\n",
       "\\begin{verbatim}\n",
       "julia> x = 10; (:call, :+, (:call, :*, 2, :x), 1) |> teval\n",
       "21\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "@show_sexpr(expr, linenums=false)\n",
       "```\n",
       "\n",
       "shows the lisp style S-expression of `expr` and prints the line number nodes if `linenums` is true.  This is the macro version of `Meta.show_sexpr`.\n",
       "\n",
       "## Example\n",
       "\n",
       "```julia\n",
       "julia> @show_sexpr 2x+1\n",
       "(:call, :+, (:call, :*, 2, :x), 1)\n",
       "```\n",
       "\n",
       "`teval` function can evaluate the output of `@show_sexpr`. \n",
       "\n",
       "```julia\n",
       "julia> x = 10; (:call, :+, (:call, :*, 2, :x), 1) |> teval\n",
       "21\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  @show_sexpr(expr, linenums=false)\u001b[39m\n",
       "\n",
       "  shows the lisp style S-expression of \u001b[36mexpr\u001b[39m and prints the line number nodes\n",
       "  if \u001b[36mlinenums\u001b[39m is true. This is the macro version of \u001b[36mMeta.show_sexpr\u001b[39m.\n",
       "\n",
       "\u001b[1m  Example\u001b[22m\n",
       "\u001b[1m  =========\u001b[22m\n",
       "\n",
       "\u001b[36m  julia> @show_sexpr 2x+1\u001b[39m\n",
       "\u001b[36m  (:call, :+, (:call, :*, 2, :x), 1)\u001b[39m\n",
       "\n",
       "  \u001b[36mteval\u001b[39m function can evaluate the output of \u001b[36m@show_sexpr\u001b[39m.\n",
       "\n",
       "\u001b[36m  julia> x = 10; (:call, :+, (:call, :*, 2, :x), 1) |> teval\u001b[39m\n",
       "\u001b[36m  21\u001b[39m"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@doc @show_sexpr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "@show_tree(expr, maxdepth=10, linenums=false)\n",
       "\\end{verbatim}\n",
       "shows the tree form of the expression \\texttt{expr} with maxdepth and prints the line number nodes if \\texttt{linenums} is true.\n",
       "\n",
       "\\subsection{Example}\n",
       "\\begin{verbatim}\n",
       "julia> @show_tree 2x+1\n",
       "Expr(:call)\n",
       "├─ :+\n",
       "├─ Expr(:call)\n",
       "│  ├─ :*\n",
       "│  ├─ 2\n",
       "│  └─ :x\n",
       "└─ 1\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "@show_tree(expr, maxdepth=10, linenums=false)\n",
       "```\n",
       "\n",
       "shows the tree form of the expression `expr` with maxdepth and prints the line number nodes if `linenums` is true.\n",
       "\n",
       "## Example\n",
       "\n",
       "```julia\n",
       "julia> @show_tree 2x+1\n",
       "Expr(:call)\n",
       "├─ :+\n",
       "├─ Expr(:call)\n",
       "│  ├─ :*\n",
       "│  ├─ 2\n",
       "│  └─ :x\n",
       "└─ 1\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  @show_tree(expr, maxdepth=10, linenums=false)\u001b[39m\n",
       "\n",
       "  shows the tree form of the expression \u001b[36mexpr\u001b[39m with maxdepth and prints the line\n",
       "  number nodes if \u001b[36mlinenums\u001b[39m is true.\n",
       "\n",
       "\u001b[1m  Example\u001b[22m\n",
       "\u001b[1m  =========\u001b[22m\n",
       "\n",
       "\u001b[36m  julia> @show_tree 2x+1\u001b[39m\n",
       "\u001b[36m  Expr(:call)\u001b[39m\n",
       "\u001b[36m  ├─ :+\u001b[39m\n",
       "\u001b[36m  ├─ Expr(:call)\u001b[39m\n",
       "\u001b[36m  │  ├─ :*\u001b[39m\n",
       "\u001b[36m  │  ├─ 2\u001b[39m\n",
       "\u001b[36m  │  └─ :x\u001b[39m\n",
       "\u001b[36m  └─ 1\u001b[39m"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@doc @show_tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "show_tree(expr) = AbstractTrees.print_tree(expr)\n",
       "\\end{verbatim}\n",
       "can be regarded as the function version of \\texttt{@show\\_tree}.\n",
       "\n"
      ],
      "text/markdown": [
       "```\n",
       "show_tree(expr) = AbstractTrees.print_tree(expr)\n",
       "```\n",
       "\n",
       "can be regarded as the function version of `@show_tree`.\n"
      ],
      "text/plain": [
       "\u001b[36m  show_tree(expr) = AbstractTrees.print_tree(expr)\u001b[39m\n",
       "\n",
       "  can be regarded as the function version of \u001b[36m@show_tree\u001b[39m."
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@doc show_tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "print_subtypes(T::Type; kwargs...)\n",
       "print_subtypes(io::IO, T::Type; kwargs...)\n",
       "print_subtypes(f, io::IO, T::Type; kwargs...)\n",
       "\\end{verbatim}\n",
       "prints the subtypes of \\texttt{T} by \\texttt{AbstractTrees.print\\_tree}.\n",
       "\n",
       "\\subsection{Example}\n",
       "\\begin{verbatim}\n",
       "julia> print_subtypes(AbstractRange)\n",
       "AbstractRange\n",
       "├─ LinRange\n",
       "├─ OrdinalRange\n",
       "│  ├─ AbstractUnitRange\n",
       "│  │  ├─ Base.IdentityUnitRange\n",
       "│  │  ├─ Base.OneTo\n",
       "│  │  ├─ Base.Slice\n",
       "│  │  └─ UnitRange\n",
       "│  └─ StepRange\n",
       "└─ StepRangeLen\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "print_subtypes(T::Type; kwargs...)\n",
       "print_subtypes(io::IO, T::Type; kwargs...)\n",
       "print_subtypes(f, io::IO, T::Type; kwargs...)\n",
       "```\n",
       "\n",
       "prints the subtypes of `T` by `AbstractTrees.print_tree`.\n",
       "\n",
       "## Example\n",
       "\n",
       "```julia\n",
       "julia> print_subtypes(AbstractRange)\n",
       "AbstractRange\n",
       "├─ LinRange\n",
       "├─ OrdinalRange\n",
       "│  ├─ AbstractUnitRange\n",
       "│  │  ├─ Base.IdentityUnitRange\n",
       "│  │  ├─ Base.OneTo\n",
       "│  │  ├─ Base.Slice\n",
       "│  │  └─ UnitRange\n",
       "│  └─ StepRange\n",
       "└─ StepRangeLen\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  print_subtypes(T::Type; kwargs...)\u001b[39m\n",
       "\u001b[36m  print_subtypes(io::IO, T::Type; kwargs...)\u001b[39m\n",
       "\u001b[36m  print_subtypes(f, io::IO, T::Type; kwargs...)\u001b[39m\n",
       "\n",
       "  prints the subtypes of \u001b[36mT\u001b[39m by \u001b[36mAbstractTrees.print_tree\u001b[39m.\n",
       "\n",
       "\u001b[1m  Example\u001b[22m\n",
       "\u001b[1m  =========\u001b[22m\n",
       "\n",
       "\u001b[36m  julia> print_subtypes(AbstractRange)\u001b[39m\n",
       "\u001b[36m  AbstractRange\u001b[39m\n",
       "\u001b[36m  ├─ LinRange\u001b[39m\n",
       "\u001b[36m  ├─ OrdinalRange\u001b[39m\n",
       "\u001b[36m  │  ├─ AbstractUnitRange\u001b[39m\n",
       "\u001b[36m  │  │  ├─ Base.IdentityUnitRange\u001b[39m\n",
       "\u001b[36m  │  │  ├─ Base.OneTo\u001b[39m\n",
       "\u001b[36m  │  │  ├─ Base.Slice\u001b[39m\n",
       "\u001b[36m  │  │  └─ UnitRange\u001b[39m\n",
       "\u001b[36m  │  └─ StepRange\u001b[39m\n",
       "\u001b[36m  └─ StepRangeLen\u001b[39m"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@doc print_subtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "show_expr([io::IO,], ex)\n",
       "\\end{verbatim}\n",
       "shows expression \\texttt{ex} as a Julia style expression.\n",
       "\n",
       "\\section{Examples}\n",
       "\\begin{verbatim}\n",
       "julia> show_expr(:(f(x, g(y, z))))\n",
       "Expr(:call, :f, :x, \n",
       "    Expr(:call, :g, :y, :z))\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "show_expr([io::IO,], ex)\n",
       "```\n",
       "\n",
       "shows expression `ex` as a Julia style expression.\n",
       "\n",
       "# Examples\n",
       "\n",
       "```julia\n",
       "julia> show_expr(:(f(x, g(y, z))))\n",
       "Expr(:call, :f, :x, \n",
       "    Expr(:call, :g, :y, :z))\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  show_expr([io::IO,], ex)\u001b[39m\n",
       "\n",
       "  shows expression \u001b[36mex\u001b[39m as a Julia style expression.\n",
       "\n",
       "\u001b[1m  Examples\u001b[22m\n",
       "\u001b[1m  ≡≡≡≡≡≡≡≡≡≡\u001b[22m\n",
       "\n",
       "\u001b[36m  julia> show_expr(:(f(x, g(y, z))))\u001b[39m\n",
       "\u001b[36m  Expr(:call, :f, :x, \u001b[39m\n",
       "\u001b[36m      Expr(:call, :g, :y, :z))\u001b[39m"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@doc show_expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "@show_expr(expr, linenums=false)\n",
       "\\end{verbatim}\n",
       "shows the Juia style expression of \\texttt{expr} and prints the line number nodes if \\texttt{linenums} is true.  This is the macro version of \\texttt{show\\_expr}.\n",
       "\n",
       "\\subsection{Example}\n",
       "\\begin{verbatim}\n",
       "julia> @show_expr 2x+1\n",
       "Expr(:call, :+, \n",
       "    Expr(:call, :*, 2, :x), 1)\n",
       "\\end{verbatim}\n",
       "\\texttt{eval} function can evaluate the output of \\texttt{@show\\_expr}. \n",
       "\n",
       "\\begin{verbatim}\n",
       "julia> x = 10; Expr(:call, :+, \n",
       "    Expr(:call, :*, 2, :x), 1) |> eval\n",
       "21\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "@show_expr(expr, linenums=false)\n",
       "```\n",
       "\n",
       "shows the Juia style expression of `expr` and prints the line number nodes if `linenums` is true.  This is the macro version of `show_expr`.\n",
       "\n",
       "## Example\n",
       "\n",
       "```julia\n",
       "julia> @show_expr 2x+1\n",
       "Expr(:call, :+, \n",
       "    Expr(:call, :*, 2, :x), 1)\n",
       "```\n",
       "\n",
       "`eval` function can evaluate the output of `@show_expr`. \n",
       "\n",
       "```julia\n",
       "julia> x = 10; Expr(:call, :+, \n",
       "    Expr(:call, :*, 2, :x), 1) |> eval\n",
       "21\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  @show_expr(expr, linenums=false)\u001b[39m\n",
       "\n",
       "  shows the Juia style expression of \u001b[36mexpr\u001b[39m and prints the line number nodes if\n",
       "  \u001b[36mlinenums\u001b[39m is true. This is the macro version of \u001b[36mshow_expr\u001b[39m.\n",
       "\n",
       "\u001b[1m  Example\u001b[22m\n",
       "\u001b[1m  =========\u001b[22m\n",
       "\n",
       "\u001b[36m  julia> @show_expr 2x+1\u001b[39m\n",
       "\u001b[36m  Expr(:call, :+, \u001b[39m\n",
       "\u001b[36m      Expr(:call, :*, 2, :x), 1)\u001b[39m\n",
       "\n",
       "  \u001b[36meval\u001b[39m function can evaluate the output of \u001b[36m@show_expr\u001b[39m.\n",
       "\n",
       "\u001b[36m  julia> x = 10; Expr(:call, :+, \u001b[39m\n",
       "\u001b[36m      Expr(:call, :*, 2, :x), 1) |> eval\u001b[39m\n",
       "\u001b[36m  21\u001b[39m"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@doc @show_expr"
   ]
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   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "show_texpr([io::IO,], ex)\n",
       "\\end{verbatim}\n",
       "Yet another \\texttt{Meta.show\\_sexpr}.  It shows expression \\texttt{ex} as a lisp style expression.\n",
       "\n",
       "Remark: The indentation is different from \\texttt{Meta.show\\_sexpr}.\n",
       "\n",
       "\\section{Examples}\n",
       "\\begin{verbatim}\n",
       "julia> show_texpr(:(f(x, g(y, z))))\n",
       "Expr(:call, :f, :x, \n",
       "    Expr(:call, :g, :y, :z))\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "show_texpr([io::IO,], ex)\n",
       "```\n",
       "\n",
       "Yet another `Meta.show_sexpr`.  It shows expression `ex` as a lisp style expression.\n",
       "\n",
       "Remark: The indentation is different from `Meta.show_sexpr`.\n",
       "\n",
       "# Examples\n",
       "\n",
       "```julia\n",
       "julia> show_texpr(:(f(x, g(y, z))))\n",
       "Expr(:call, :f, :x, \n",
       "    Expr(:call, :g, :y, :z))\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  show_texpr([io::IO,], ex)\u001b[39m\n",
       "\n",
       "  Yet another \u001b[36mMeta.show_sexpr\u001b[39m. It shows expression \u001b[36mex\u001b[39m as a lisp style\n",
       "  expression.\n",
       "\n",
       "  Remark: The indentation is different from \u001b[36mMeta.show_sexpr\u001b[39m.\n",
       "\n",
       "\u001b[1m  Examples\u001b[22m\n",
       "\u001b[1m  ≡≡≡≡≡≡≡≡≡≡\u001b[22m\n",
       "\n",
       "\u001b[36m  julia> show_texpr(:(f(x, g(y, z))))\u001b[39m\n",
       "\u001b[36m  Expr(:call, :f, :x, \u001b[39m\n",
       "\u001b[36m      Expr(:call, :g, :y, :z))\u001b[39m"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@doc show_texpr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "@show_texpr(expr, linenums=false)\n",
       "\\end{verbatim}\n",
       "Yet another \\texttt{@show\\_sexpr}.  It shows the lisp style S-expression of \\texttt{expr} and prints the line number nodes if \\texttt{linenums} is true.\n",
       "\n",
       "Remark: The indentation is different from \\texttt{@show\\_sexpr}.\n",
       "\n",
       "\\subsection{Example}\n",
       "\\begin{verbatim}\n",
       "julia> @show_texpr 2x+1\n",
       "(:call, :+, \n",
       "    (:call, :*, 2, :x), 1)\n",
       "\\end{verbatim}\n",
       "\\texttt{teval} function can evaluate the output of \\texttt{@show\\_texpr}.\n",
       "\n",
       "\\begin{verbatim}\n",
       "julia> x = 10; (:call, :+, \n",
       "    (:call, :*, 2, :x), 1) |> teval\n",
       "21\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "@show_texpr(expr, linenums=false)\n",
       "```\n",
       "\n",
       "Yet another `@show_sexpr`.  It shows the lisp style S-expression of `expr` and prints the line number nodes if `linenums` is true.\n",
       "\n",
       "Remark: The indentation is different from `@show_sexpr`.\n",
       "\n",
       "## Example\n",
       "\n",
       "```julia\n",
       "julia> @show_texpr 2x+1\n",
       "(:call, :+, \n",
       "    (:call, :*, 2, :x), 1)\n",
       "```\n",
       "\n",
       "`teval` function can evaluate the output of `@show_texpr`.\n",
       "\n",
       "```julia\n",
       "julia> x = 10; (:call, :+, \n",
       "    (:call, :*, 2, :x), 1) |> teval\n",
       "21\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  @show_texpr(expr, linenums=false)\u001b[39m\n",
       "\n",
       "  Yet another \u001b[36m@show_sexpr\u001b[39m. It shows the lisp style S-expression of \u001b[36mexpr\u001b[39m and\n",
       "  prints the line number nodes if \u001b[36mlinenums\u001b[39m is true.\n",
       "\n",
       "  Remark: The indentation is different from \u001b[36m@show_sexpr\u001b[39m.\n",
       "\n",
       "\u001b[1m  Example\u001b[22m\n",
       "\u001b[1m  =========\u001b[22m\n",
       "\n",
       "\u001b[36m  julia> @show_texpr 2x+1\u001b[39m\n",
       "\u001b[36m  (:call, :+, \u001b[39m\n",
       "\u001b[36m      (:call, :*, 2, :x), 1)\u001b[39m\n",
       "\n",
       "  \u001b[36mteval\u001b[39m function can evaluate the output of \u001b[36m@show_texpr\u001b[39m.\n",
       "\n",
       "\u001b[36m  julia> x = 10; (:call, :+, \u001b[39m\n",
       "\u001b[36m      (:call, :*, 2, :x), 1) |> teval\u001b[39m\n",
       "\u001b[36m  21\u001b[39m"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@doc @show_texpr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "teval(texpr, m::Module=Main)\n",
       "\\end{verbatim}\n",
       "evaluates the lisp-like tuple expression \\texttt{texpr}.\n",
       "\n",
       "Example: Calculation of \\texttt{sin(π/6)}\n",
       "\n",
       "\\begin{verbatim}\n",
       "julia> (:call, :sin, (:call, :/, π, 6)) |> teval\n",
       "0.49999999999999994\n",
       "\\end{verbatim}\n",
       "In some cases, you can omit \\texttt{:call}.\n",
       "\n",
       "\\begin{verbatim}\n",
       "julia> (:sin, (:/, π, 6)) |> teval\n",
       "0.49999999999999994\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "teval(texpr, m::Module=Main)\n",
       "```\n",
       "\n",
       "evaluates the lisp-like tuple expression `texpr`.\n",
       "\n",
       "Example: Calculation of `sin(π/6)`\n",
       "\n",
       "```julia\n",
       "julia> (:call, :sin, (:call, :/, π, 6)) |> teval\n",
       "0.49999999999999994\n",
       "```\n",
       "\n",
       "In some cases, you can omit `:call`.\n",
       "\n",
       "```julia\n",
       "julia> (:sin, (:/, π, 6)) |> teval\n",
       "0.49999999999999994\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  teval(texpr, m::Module=Main)\u001b[39m\n",
       "\n",
       "  evaluates the lisp-like tuple expression \u001b[36mtexpr\u001b[39m.\n",
       "\n",
       "  Example: Calculation of \u001b[36msin(π/6)\u001b[39m\n",
       "\n",
       "\u001b[36m  julia> (:call, :sin, (:call, :/, π, 6)) |> teval\u001b[39m\n",
       "\u001b[36m  0.49999999999999994\u001b[39m\n",
       "\n",
       "  In some cases, you can omit \u001b[36m:call\u001b[39m.\n",
       "\n",
       "\u001b[36m  julia> (:sin, (:/, π, 6)) |> teval\u001b[39m\n",
       "\u001b[36m  0.49999999999999994\u001b[39m"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@doc teval"
   ]
  },
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   "execution_count": 76,
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    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "@teval texpr\n",
       "\\end{verbatim}\n",
       "evaluates the lisp-like tuple expression \\texttt{texpr}.\n",
       "\n",
       "Example: Calculation of \\texttt{sin(π/6)}\n",
       "\n",
       "\\begin{verbatim}\n",
       "julia> @teval (:call, :sin, (:call, :/, π, 6))\n",
       "0.49999999999999994\n",
       "\\end{verbatim}\n",
       "In some cases, you can omit \\texttt{:call}.\n",
       "\n",
       "\\begin{verbatim}\n",
       "julia> @teval (:sin, (:/, π, 6))\n",
       "0.49999999999999994\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "@teval texpr\n",
       "```\n",
       "\n",
       "evaluates the lisp-like tuple expression `texpr`.\n",
       "\n",
       "Example: Calculation of `sin(π/6)`\n",
       "\n",
       "```julia\n",
       "julia> @teval (:call, :sin, (:call, :/, π, 6))\n",
       "0.49999999999999994\n",
       "```\n",
       "\n",
       "In some cases, you can omit `:call`.\n",
       "\n",
       "```julia\n",
       "julia> @teval (:sin, (:/, π, 6))\n",
       "0.49999999999999994\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  @teval texpr\u001b[39m\n",
       "\n",
       "  evaluates the lisp-like tuple expression \u001b[36mtexpr\u001b[39m.\n",
       "\n",
       "  Example: Calculation of \u001b[36msin(π/6)\u001b[39m\n",
       "\n",
       "\u001b[36m  julia> @teval (:call, :sin, (:call, :/, π, 6))\u001b[39m\n",
       "\u001b[36m  0.49999999999999994\u001b[39m\n",
       "\n",
       "  In some cases, you can omit \u001b[36m:call\u001b[39m.\n",
       "\n",
       "\u001b[36m  julia> @teval (:sin, (:/, π, 6))\u001b[39m\n",
       "\u001b[36m  0.49999999999999994\u001b[39m"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@doc @teval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "MetaUtils.@t texpr\n",
       "\\end{verbatim}\n",
       "shows the Julia expression and the value of the lisp-like tuple expression \\texttt{texpr}.\n",
       "\n",
       "Example:\n",
       "\n",
       "\\begin{verbatim}\n",
       "julia> MetaUtils.@t (:call, :sin, (:call, :/, π, 6))\n",
       ":(sin(π / 6))\n",
       "→ 0.49999999999999994\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "MetaUtils.@t texpr\n",
       "```\n",
       "\n",
       "shows the Julia expression and the value of the lisp-like tuple expression `texpr`.\n",
       "\n",
       "Example:\n",
       "\n",
       "```julia\n",
       "julia> MetaUtils.@t (:call, :sin, (:call, :/, π, 6))\n",
       ":(sin(π / 6))\n",
       "→ 0.49999999999999994\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  MetaUtils.@t texpr\u001b[39m\n",
       "\n",
       "  shows the Julia expression and the value of the lisp-like tuple expression\n",
       "  \u001b[36mtexpr\u001b[39m.\n",
       "\n",
       "  Example:\n",
       "\n",
       "\u001b[36m  julia> MetaUtils.@t (:call, :sin, (:call, :/, π, 6))\u001b[39m\n",
       "\u001b[36m  :(sin(π / 6))\u001b[39m\n",
       "\u001b[36m  → 0.49999999999999994\u001b[39m"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@doc MetaUtils.@t"
   ]
  },
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   "execution_count": 78,
   "metadata": {},
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    {
     "data": {
      "text/latex": [
       "\\begin{verbatim}\n",
       "MetaUtils.@T texpr\n",
       "\\end{verbatim}\n",
       "shows \\texttt{show(texpr)}, \\texttt{show\\_texpr(texpr)}, the Julia expression, and the value of the lisp-like tuple expression \\texttt{texpr}.\n",
       "\n",
       "Example:\n",
       "\n",
       "\\begin{verbatim}\n",
       "julia> MetaUtils.@T (:call, :sin, (:call, :/, π, 6))\n",
       "(:call, :sin, (:call, :/, π, 6))\n",
       "→ (:call, :sin, \n",
       "    (:call, :/, π, 6))\n",
       "→ :(sin(π / 6))\n",
       "→ 0.49999999999999994\n",
       "\\end{verbatim}\n"
      ],
      "text/markdown": [
       "```\n",
       "MetaUtils.@T texpr\n",
       "```\n",
       "\n",
       "shows `show(texpr)`, `show_texpr(texpr)`, the Julia expression, and the value of the lisp-like tuple expression `texpr`.\n",
       "\n",
       "Example:\n",
       "\n",
       "```julia\n",
       "julia> MetaUtils.@T (:call, :sin, (:call, :/, π, 6))\n",
       "(:call, :sin, (:call, :/, π, 6))\n",
       "→ (:call, :sin, \n",
       "    (:call, :/, π, 6))\n",
       "→ :(sin(π / 6))\n",
       "→ 0.49999999999999994\n",
       "```\n"
      ],
      "text/plain": [
       "\u001b[36m  MetaUtils.@T texpr\u001b[39m\n",
       "\n",
       "  shows \u001b[36mshow(texpr)\u001b[39m, \u001b[36mshow_texpr(texpr)\u001b[39m, the Julia expression, and the value of\n",
       "  the lisp-like tuple expression \u001b[36mtexpr\u001b[39m.\n",
       "\n",
       "  Example:\n",
       "\n",
       "\u001b[36m  julia> MetaUtils.@T (:call, :sin, (:call, :/, π, 6))\u001b[39m\n",
       "\u001b[36m  (:call, :sin, (:call, :/, π, 6))\u001b[39m\n",
       "\u001b[36m  → (:call, :sin, \u001b[39m\n",
       "\u001b[36m      (:call, :/, π, 6))\u001b[39m\n",
       "\u001b[36m  → :(sin(π / 6))\u001b[39m\n",
       "\u001b[36m  → 0.49999999999999994\u001b[39m"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@doc MetaUtils.@T"
   ]
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