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terasakisatoshi/OOPMacro.ipynb

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OOPMacro.ipynb
{
"cells": [
{
"cell_type": "markdown",
"id": "d0c99e3d",
"metadata": {},
"source": [
"# OOPMacro.jl のお話し\n",
"\n",
"- このノートブックはどうしてもOOPスタイルに固執する哀れな人々を対象に Julia パッケージ OOPMacro.jl を使うことで OOP ようのな表記スタイルで記述することを示す. その過程を通して OOP に固執しなくても良い Julia らしい書き方を紹介する.\n",
"\n",
"## 背景\n",
"\n",
"- C++, Python などある程度プログラミング経験者が Julia への移行の際に出現する心理的障壁として Julia の文法・視覚的な表記が伝統的な OOP(Object Oriented Programming) と異なる点が挙げられる. 学習履歴を管理する脳内のリポジトリを `git checkout <初期の段階>` に戻し unlearning してプログラミングを学習すればそのような容易に障壁を避けて学習ができる．しかしながら，悲しいことに脳内にリポジトリがない，そもそも思考・学習履歴をバージョン管理する概念の取得，訓練を受ける教育の機会を得られなかった人々が多いようである. ここでは悲劇の中にある人々からある種の心理的障壁を取り除くカウンセリングを狙う.\n",
"\n",
"\n",
"# メソッドの記述について\n",
"\n",
"## Julia の場合\n",
"\n",
"- Julia では `obj.method(args)` のように特定のメソッドが注目しているオブジェクトに紐づいているようなイメージを彷彿させるスタイルではなく `method(obj, args)` のように注目しているオブジェクトと引数を平等に扱うスタイルで書いていく. \n",
"\n",
"### 自然な演算子の実装\n",
"\n",
"- 一旦プログラミングのことは忘れて例えばある種の代数系 $X$ における演算子 $\\otimes$ を定義することを考える. $\\otimes$ はさらに二項演算であるとしよう. この場合「数学の世界だと $x, y \\in X$ に対して $x\\otimes y$ を ... のように定義する」のように書くだろう. これをプログラミングの世界で実現する（＝実装する）ことを考える. 素直に考えると\n",
"\n",
"```julia\n",
"⊗(x::MyObject, y::MyObject) = ... # 関数定義\n",
"x = MyObject(args_for_x)\n",
"y = MyObject(args_for_y)\n",
"z = ⊗(x, y) # その言語が中置演算の表記を採用しているとすれば x ⊗ y と書いても良いだろう\n",
"# あとは色々論理を展開する\n",
"```\n",
"\n",
"のように表現するだろう. OOP のスタイルを採用するとどうしても 第一引数 `x` 側を特別扱いすることになる.\n",
"\n",
"```python\n",
"def MyObject(args):\n",
" def __init__(self):\n",
" # 初期化のロジックを組む\n",
" ⊗(self, y):\n",
" # メソッドの定義\n",
"\n",
"x = MyObject(args_for_x)\n",
"y = MyObject(args_for_y)\n",
"x.⊗(y)\n",
"```\n",
"\n",
"数学の世界において(主に二項の)演算子の定義では無意識に引数を対等に扱っているはずである. 特定のオブジェクトにメソッドが紐づいているという考えを持ちながら代数学をはじめとする数学の分野を履修していなかったはずだ. そういう意味で `x.method(y)` のような典型的な OOP スタイルに比べると `method(x, y)` のような表記を採用するのが数理のバックグラウンドを持つ人間にとって優しい設計に見えるだろう. \n",
"\n",
"- `x.method(y)` のスタイルをやめて `method(x, y)` というスタイルを採用するとその `method` が `x` の型のために設計したというプログラマーの意図を潰してしまいそうに見える. それは心配ない Julia は後述する多重ディスパッチでその心配事を解決してくれる.\n",
"\n",
"### 多重ディスパッチ\n",
"\n",
"- Julia では 多重ディスパッチ(Multiple dispatch) を採用するプログラミング言語である, 入力に受け取る引数の数，引数の型の情報をもとに関数の振る舞いを切り替えることができる. このような機構を多重ディスパッチと呼んでいる. 例えば可視化ライブラリ Plots.jl では `plot` 関数で多くのことを実現できる:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "93b4d9e1",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:54:55.726000+09:00",
"start_time": "2021-12-29T10:54:51.710Z"
}
},
"outputs": [
{
"data": {
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]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Plots\n",
"\n",
"p11 = plot([3,2,1])\n",
"p12 = plot([1,2,3], [3,2,1])\n",
"p21 = plot(-pi:0.01:pi, sin.(-pi:0.01:pi))\n",
"p22 = plot(sin, xlims=(-pi, pi))\n",
"\n",
"plot(p11, p12, p21, p22, layout=(2,2))"
]
},
{
"cell_type": "markdown",
"id": "a3df67e4",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T19:31:46.218000+09:00",
"start_time": "2021-12-26T10:31:46.162Z"
}
},
"source": [
"`plot` 関数は入力として色々なものを受け付けてそれ相応の結果を表示することができる. 各々の入力のケースに対してどのような動作をさせるかはプログラマーが実装を決めることができる. プログラムの実行中は\n",
"Julia が入力する型を調べそれに対するメソッドを探し見つけてくれる. 見つからない場合はもちろんエラーを起こす. \n",
"\n",
"このように多重ディスパッチでは同じ名前の関数で入力のインターフェースを柔軟に設計できるメリットがある．\n",
"\n",
"### 関数 と メソッド\n",
"\n",
"- ここで関数とメソッドという言葉を用いていることに注意しよう. 平たくいうと関数(function)は入力を与えるとそれに対する出力を与える機構を表すものでメソッド(method)はその関数を呼び出したときの具体的な実装を指すことが多い. 数学で言えば「関数」は抽象的な写像で「メソッド」は特定の数学的対象に対して具体的に構成する方法のを述べていると思えば良い. 例えば次のような `func` という関数を定義しよう."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "8202aba4",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:54:56.152000+09:00",
"start_time": "2021-12-29T10:54:51.875Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"func (generic function with 3 methods)"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"func(x) = identity(x) # A\n",
"func(x, y) = x + y # B\n",
"func(x, y, z) = x + y + z # C"
]
},
{
"cell_type": "markdown",
"id": "f0271416",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T19:39:29.705000+09:00",
"start_time": "2021-12-26T10:39:29.698Z"
}
},
"source": [
"上記のセルを実行することによって3つのメソッドができたことになる. 例えば `func(2, 3)` とすれば `# B` とコメントしたメソッドが呼び出されることになる. もちろん結果は `2 + 3` を計算した 5 が得られる."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "6b67ba70",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:54:56.628000+09:00",
"start_time": "2021-12-29T10:54:51.935Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"5"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"func(2, 3)"
]
},
{
"cell_type": "markdown",
"id": "e0d02528",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T19:40:33.919000+09:00",
"start_time": "2021-12-26T10:40:33.908Z"
}
},
"source": [
"`func(1,2,3)` を実行すると `# C` とコメントした同じ行のメソッドが呼び出される. もちろん結果は `1 + 2 + 3` を計算した 6 を出力する"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "90324a43",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:54:56.634000+09:00",
"start_time": "2021-12-29T10:54:51.983Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"6"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"func(1,2,3)"
]
},
{
"cell_type": "markdown",
"id": "d9322b0b",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T19:45:15.481000+09:00",
"start_time": "2021-12-26T10:45:15.471Z"
}
},
"source": [
"上記の例は `func` という名前の関数が呼び出された時に引数の数によってどのメソッドを選択するかを制御できるかを説明した例である. \n",
"Julia では引数の個数が同じでも入力に受け付ける型が異なる場合それらに対応するメソッドを実装することによって動作を制御できる. 下記のような `⊗` 関数を実装してみよう:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "50db10af",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:54:56.818000+09:00",
"start_time": "2021-12-29T10:54:52.033Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"⊗ (generic function with 2 methods)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"⊗(x::Int, y::Int) = x * y # A\n",
"⊗(x::String, y::String) = x * y # B"
]
},
{
"cell_type": "markdown",
"id": "93594d8e",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T19:49:11.837000+09:00",
"start_time": "2021-12-26T10:49:11.829Z"
}
},
"source": [
"プログラマーは下記のように結合する意図を込めた実装をしている:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "b1ad876b",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:54:57.756000+09:00",
"start_time": "2021-12-29T10:54:52.077Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3 ⊗ 4 = 12\n",
"\"Hello\" ⊗ \"World\" = \"HelloWorld\"\n"
]
},
{
"data": {
"text/plain": [
"\"HelloWorld\""
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@show ⊗(3, 4)\n",
"@show ⊗(\"Hello\", \"World\")"
]
},
{
"cell_type": "markdown",
"id": "89b5d101",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T19:52:48.009000+09:00",
"start_time": "2021-12-26T10:52:47.998Z"
}
},
"source": [
"整数に対しては 3, 4 の乗算を実行し 12 を得る. 文字列同士に対しては `Hello` と `World` を結合させた `HelloWorld` を得る. このように\n",
"入力として受け付ける引数は同じでも入力の型に応じて動作を制御できていることがわかる."
]
},
{
"cell_type": "markdown",
"id": "39598ef9",
"metadata": {},
"source": [
"### 共通のインターフェースを定義する\n",
"\n",
"- 引数の型によって動作を制御できるので `x.method(y)` のように `x` の型に紐づいている動作を定義するためには `method` の引数に型を指定すれば良い. \n",
"- 例えば図形オブジェクトの面積を計算する機能を実現したいとする. Julia では下記のように実現できる."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "cd88e174",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:54:57.940000+09:00",
"start_time": "2021-12-29T10:54:52.169Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"area (generic function with 2 methods)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"struct 円\n",
" 半径\n",
"end\n",
"\n",
"area(c::円) = c.半径^2 * π\n",
"\n",
"struct 長方形\n",
" 横\n",
" 縦\n",
"end\n",
"\n",
"area(r::長方形) = r.縦 * r.横"
]
},
{
"cell_type": "markdown",
"id": "271152c6",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T20:04:09.452000+09:00",
"start_time": "2021-12-26T11:04:09.446Z"
}
},
"source": [
"`area` という面積を求める関数を用意し `円` に対するものと `長方形` に対するメソッドを実装した. 実は日本語も識別子として使える. (普通は使わないが)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "02825014",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:54:58.003000+09:00",
"start_time": "2021-12-29T10:54:52.204Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"6"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c = 円(3)\n",
"area(c)\n",
"r = 長方形(2, 3)\n",
"area(r)"
]
},
{
"cell_type": "markdown",
"id": "69cab62d",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T20:06:52.586000+09:00",
"start_time": "2021-12-26T11:06:52.577Z"
}
},
"source": [
"これによって特定のオブジェクトに対するメソッドの実装を実件することができた. `obj.method` ののように呼び出せる副次的なメリットとしてエディタの補完機能でメソッドの一覧を表示できるなどの検索性があるが, Julia では `methodswith` 関数を使うと良い. 例えば上記で定義した `円` 構造体に関するメソッドとして `area` があるがその情報を得られることがわかる."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "2f92f3e5",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:51.247000+09:00",
"start_time": "2021-12-29T10:54:52.236Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"1-element Vector{Method}:<ul><li> area(c::<b>円</b>) in Main at In[7]:5</ul>"
],
"text/plain": [
"[1] area(c::円) in Main at In[7]:5"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"methodswith(円)"
]
},
{
"cell_type": "markdown",
"id": "0496f3ec",
"metadata": {},
"source": [
"# 継承の実現 について\n",
"\n",
"- `obj.method(args)` のスタイルは `method(obj, args)` のように機械的に変換できるので OOP 信者でも渋々と移行できるはずだ. \n",
"- では継承はどう実現するのか？ これついては抽象型を定義しそれのサブタイプとして具体型を定義し必要に応じてその型に対するメソッドを実装していけば良い. 共通の振る舞いは抽象型を型アノテーションしたメソッドを実装すれば良い"
]
},
{
"cell_type": "markdown",
"id": "ba9607ee",
"metadata": {},
"source": [
"### 具体型・具象型\n",
"\n",
"Concrete types の日本語訳である. `typeof` 関数を用いるとその `1, 1.0, rand(2,2)` などの値，自作構造体の型を知ることができる. その戻り値は具体型である.\n",
"`Base.isconcretetype` で確かめられる. `typeof(Int)` は `DataType` である. これも具体型である."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "c282b0d8",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:51.850000+09:00",
"start_time": "2021-12-29T10:54:52.357Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"true"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Base.isconcretetype(typeof(Int))"
]
},
{
"cell_type": "markdown",
"id": "ea6595e7",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T20:18:00.003000+09:00",
"start_time": "2021-12-26T11:17:59.998Z"
}
},
"source": [
"### 抽象型\n",
"\n",
"abstract types の日本語訳である. 抽象型は類似したいくつかの型をまとめたグループを表現するために使われる. 例えば `AbstractFloat` は抽象型であり `typeof` で調べると `DataType` となる. 従ってこれも型の一つである."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "0a45c1ba",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:52.524000+09:00",
"start_time": "2021-12-29T10:54:52.405Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"DataType"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"typeof(AbstractFloat)"
]
},
{
"cell_type": "markdown",
"id": "93787f42",
"metadata": {},
"source": [
"`AbstractFloat` は浮動小数点数を表す具体型 `Float16`, `Float32`, `Float64`, `BigFloat` を取りまとめている. \n",
"取りまとめられている型と取りまとめる抽象型の関係を次のように表現する\n",
"\n",
"> `Float64` は `AbstractFloat` のサブタイプである\n",
"\n",
"上記の関係を `Float64 <: AbstractFloat` と書く\n",
"\n",
"抽象型が何を取りまとめているかは `subtypes` 関数を用いて調べることができる."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "c82ce65e",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:54.383000+09:00",
"start_time": "2021-12-29T10:54:52.445Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"4-element Vector{Any}:\n",
" BigFloat\n",
" Float16\n",
" Float32\n",
" Float64"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"subtypes(AbstractFloat)"
]
},
{
"cell_type": "markdown",
"id": "fc05d172",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T20:35:23.727000+09:00",
"start_time": "2021-12-26T11:35:23.718Z"
}
},
"source": [
"関数の具体的な動作は入力の引数に型アノテーションを付与することで具体的な振る舞いを指定できた. 抽象型に対しても同様である. 例えば浮動小数点に対して3乗を計算する関数を実装したいとしよう:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "8a271ed2",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:54.613000+09:00",
"start_time": "2021-12-29T10:54:52.486Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"cube (generic function with 1 method)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cube(x::Float64) = x^3"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "5210f28e",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:55.131000+09:00",
"start_time": "2021-12-29T10:54:52.492Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"19.683000000000003"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cube(2.7)"
]
},
{
"cell_type": "markdown",
"id": "7803942a",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T20:50:22.644000+09:00",
"start_time": "2021-12-26T11:50:22.633Z"
}
},
"source": [
"どうやら計算できそうだ. しかし `2.7f0` という 32 ビット精度の浮動小数点は受け付けてくれず, 実行時にエラーを与える.\n",
"\n",
"```julia\n",
"julia> invcube(2.7f0)\n",
"MethodError: no method matching invcube(::Float32)\n",
"```"
]
},
{
"cell_type": "markdown",
"id": "85b10faf",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T20:52:02.548000+09:00",
"start_time": "2021-12-26T11:52:02.542Z"
}
},
"source": [
"汎用な機能にもかかわらず，プログラマーが 64 ビットの精度のものしか受け付けないという強い意志がない限りこのような実装は止めるべきである. `浮動小数`というのが大事である場合は下記のようにすれば良い."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "212cbc83",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:55.133000+09:00",
"start_time": "2021-12-29T10:54:52.566Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"cube (generic function with 2 methods)"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cube(x::AbstractFloat) = x^3"
]
},
{
"cell_type": "markdown",
"id": "5081b54d",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T20:54:39.300000+09:00",
"start_time": "2021-12-26T11:54:39.283Z"
}
},
"source": [
"このようにすると入力として `cube(2.7f0)` という使い方もできるようになる."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "0953bd0d",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:55.704000+09:00",
"start_time": "2021-12-29T10:54:52.601Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"19.683002f0"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cube(2.7f0)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "0907830d",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:56.216000+09:00",
"start_time": "2021-12-29T10:54:52.605Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"Float16(19.67)"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cube(Float16(2.7))"
]
},
{
"cell_type": "markdown",
"id": "070a66cc",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T20:56:56.806000+09:00",
"start_time": "2021-12-26T11:56:56.797Z"
}
},
"source": [
"cube は単に３乗すればいいので条件を緩めて実数であれば計算はできるはずである. その場合は AbstractFloat の代わりに数学で言うところの実数を表す Real という抽象型を使えば良い.\n",
"\n",
"```julia\n",
"cube(x::Real) = x^3\n",
"```"
]
},
{
"cell_type": "markdown",
"id": "dce8a0ff",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T20:59:55.574000+09:00",
"start_time": "2021-12-26T11:59:55.569Z"
}
},
"source": [
"乗算であれば複素数でも構わないはずなので数をあらわす Number という抽象型を使えば良い\n",
"\n",
"```julia\n",
"cube(x::Number) = x^3\n",
"```"
]
},
{
"cell_type": "markdown",
"id": "26efb99c",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:18:07.677000+09:00",
"start_time": "2021-12-26T12:18:07.661Z"
}
},
"source": [
"### 抽象型と多重ディスパッチによる継承の実現\n",
"\n",
"- N次元ユークリッド空間上の頂点を表すオブジェクトとそれらに関する何かしらの演算の実装を行いたいとする. OOPの基底クラス相当する抽象型を定義し派生型に相当する具体型をちまちま実装してみよう:"
]
},
{
"cell_type": "markdown",
"id": "e07ec0a8",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:36:30.180000+09:00",
"start_time": "2021-12-26T12:36:30.085Z"
}
},
"source": [
"下記のようにして抽象型を定義できる. 抽象型は field を持たないので下記のように素朴になる:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "5b8ae35f",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:56.247000+09:00",
"start_time": "2021-12-29T10:54:52.838Z"
}
},
"outputs": [],
"source": [
"abstract type PointND end"
]
},
{
"cell_type": "markdown",
"id": "08caf7e5",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:37:57.321000+09:00",
"start_time": "2021-12-26T12:37:56.948Z"
}
},
"source": [
"OOPの派生型に相当するものとして２次元と３次元用の頂点構造体を定義しよう. PointND のサブタイプとして定義する:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "52e47df1",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:56.291000+09:00",
"start_time": "2021-12-29T10:54:52.886Z"
}
},
"outputs": [],
"source": [
"struct Point2D <: PointND\n",
" x::Float64\n",
" y::Float64\n",
"end\n",
"\n",
"struct Point3D <: PointND\n",
" x::Float64\n",
" y::Float64\n",
" z::Float64\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "b074605c",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:38:41.468000+09:00",
"start_time": "2021-12-26T12:38:41.462Z"
}
},
"source": [
"頂点オブジェクトがどの次元のものかを確かめたい. 例えば二次元頂点は二次元平面上にあるものとみなす."
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "19cccfd5",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:56.294000+09:00",
"start_time": "2021-12-29T10:54:52.928Z"
}
},
"outputs": [],
"source": [
"Base.ndims(p::PointND) = fieldcount(typeof(p))"
]
},
{
"cell_type": "markdown",
"id": "0905ca84",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:42:58.633000+09:00",
"start_time": "2021-12-26T12:42:58.623Z"
}
},
"source": [
"これで共通の振る舞いを定義できている"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "3d55ce00",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:56.385000+09:00",
"start_time": "2021-12-29T10:54:52.969Z"
}
},
"outputs": [],
"source": [
"p2d = Point2D(1,2)\n",
"p3d = Point3D(3,4,5)\n",
"\n",
"@assert ndims(p2d) == 2\n",
"@assert ndims(p3d) == 3"
]
},
{
"cell_type": "markdown",
"id": "c39a8c33",
"metadata": {},
"source": [
"頂点間の距離を計算するロジックを作る."
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "0d222484",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:56.599000+09:00",
"start_time": "2021-12-29T10:54:53.008Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"dist (generic function with 1 method)"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function dist(p::T, q::T) where T <: PointND\n",
" d = 0.\n",
" for f in fieldnames(T)\n",
" d += (getproperty(p, f) - getproperty(q, f))^2\n",
" end\n",
" d\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "59e33242",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:49:18.162000+09:00",
"start_time": "2021-12-26T12:49:18.156Z"
}
},
"source": [
"上記の関数宣言の意味は `where T <: PointND` の部分は PointND のサブタイプ `T` を型にもつ `p` と `q` を入力として受け付けると言う意味になる. もちろん \n",
"\n",
"```julia\n",
"dist(p::Point2D, q::Point2D) = ...\n",
"dist(p::Point3D, q::Point3D) = ...\n",
"```\n",
"\n",
"のように各々の具体型に対して実装もできるが `where T <: PointND` を使った表記の方が今後，機能を拡張する際に無用なコードを増やさずに済む"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "5db31369",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:56.619000+09:00",
"start_time": "2021-12-29T10:54:53.063Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"5.0"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dist(Point2D(0, 0), Point2D(1, 2))"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "7b349eca",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:56.648000+09:00",
"start_time": "2021-12-29T10:54:53.067Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"14.0"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dist(Point3D(0, 0, 0), Point3D(1, 2, 3))"
]
},
{
"cell_type": "markdown",
"id": "e085f0ca",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:52:39.632000+09:00",
"start_time": "2021-12-26T12:52:39.627Z"
}
},
"source": [
"簡単な例だが，多重ディスパッチと抽象型を組み合わせることによってある種の継承のようなことができている."
]
},
{
"cell_type": "markdown",
"id": "7972fe81",
"metadata": {},
"source": [
"### 補足: 型の階層関係\n",
"\n",
"- Number, Real, AbstractFloat という抽象型を導入してきた. 実は下記のようなサブタイプの関係にある:\n",
"\n",
"```julia\n",
"AbstractFloat <: Real <: Number \n",
"```\n",
"\n",
"抽象型にもその抽象度によって階層が作られていることがわかる. Real は AbstractType のスーパータイプになっている.\n",
"Number は Real のスーパータイプになっている.\n",
"\n",
"これを木構造によって表現してみよう."
]
},
{
"cell_type": "markdown",
"id": "5f8e49cd",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:06:15.672000+09:00",
"start_time": "2021-12-26T12:06:15.667Z"
}
},
"source": [
"AbstractFloat の場合は既に調べたが `AbstractTrees.jl` を用いてある程度視覚化できる:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "a4ba5fe5",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:57.891000+09:00",
"start_time": "2021-12-29T10:54:53.201Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"AbstractFloat\n",
"├─ BigFloat\n",
"├─ Float16\n",
"├─ Float32\n",
"└─ Float64\n"
]
}
],
"source": [
"using AbstractTrees\n",
"AbstractTrees.children(x::Type) = subtypes(x)\n",
"print_tree(AbstractFloat)"
]
},
{
"cell_type": "markdown",
"id": "a66b00d3",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:06:29.857000+09:00",
"start_time": "2021-12-26T12:06:29.852Z"
}
},
"source": [
"Real は実数を抱えていることがよくわかる."
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "4a9db246",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:58.164000+09:00",
"start_time": "2021-12-29T10:54:53.251Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Real\n",
"├─ AbstractFloat\n",
"│ ├─ BigFloat\n",
"│ ├─ Float16\n",
"│ ├─ Float32\n",
"│ └─ Float64\n",
"├─ AbstractIrrational\n",
"│ └─ Irrational\n",
"├─ FixedPoint\n",
"│ ├─ Fixed\n",
"│ └─ Normed\n",
"├─ Integer\n",
"│ ├─ Bool\n",
"│ ├─ OffsetInteger\n",
"│ ├─ ChainedVectorIndex\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",
"├─ SimpleRatio\n",
"├─ PValue\n",
"└─ TestStat\n"
]
}
],
"source": [
"print_tree(Real)"
]
},
{
"cell_type": "markdown",
"id": "71af91c6",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:06:59.772000+09:00",
"start_time": "2021-12-26T12:06:59.763Z"
}
},
"source": [
"`Number` は `Real` と複素数を表す Complex 型を取りまとめている."
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "ad7b4c56",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:58.462000+09:00",
"start_time": "2021-12-29T10:54:53.296Z"
}
},
"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",
" ├─ FixedPoint\n",
" │ ├─ Fixed\n",
" │ └─ Normed\n",
" ├─ Integer\n",
" │ ├─ Bool\n",
" │ ├─ OffsetInteger\n",
" │ ├─ ChainedVectorIndex\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",
" ├─ SimpleRatio\n",
" ├─ PValue\n",
" └─ TestStat\n"
]
}
],
"source": [
"print_tree(Number)"
]
},
{
"cell_type": "markdown",
"id": "8c328f5a",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:12:11.639000+09:00",
"start_time": "2021-12-26T12:12:11.627Z"
}
},
"source": [
"AbstractFloat のスーパタイプの系列は `Base.show_supertypes` を使って抽象度が高い順に並べることができる."
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "46ee3d20",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:59.868000+09:00",
"start_time": "2021-12-29T10:54:53.345Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"AbstractFloat <: Real <: Number <: Any"
]
}
],
"source": [
"Base.show_supertypes(AbstractFloat)"
]
},
{
"cell_type": "markdown",
"id": "96376873",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:07:47.094000+09:00",
"start_time": "2021-12-26T12:07:47.087Z"
}
},
"source": [
"実は `Number` の上には `Any` という抽象型がある. この `Any` は Julia の任意のスーパータイプとなる抽象型である."
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "3cfa9999",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:55:59.870000+09:00",
"start_time": "2021-12-29T10:54:53.408Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"true"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Number <: Any"
]
},
{
"cell_type": "markdown",
"id": "fcf7bb7f",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:13:30.743000+09:00",
"start_time": "2021-12-26T12:13:30.736Z"
}
},
"source": [
"実は `f(x)` は `f(x::Any)` と同じである. つまり型アノテーションを付与していない引数には `::Any` が暗黙のうちに付与されていることになる. `Any` は任意の型のスーパータイプなので `f(x)` は任意の具体型の値 `x` を受け付ける関数と理解することもできる."
]
},
{
"cell_type": "markdown",
"id": "f2c6602e",
"metadata": {},
"source": [
"# OOPMacro の使い方\n",
"\n",
"頭の良い読者であればもう OOP スタイル以外の書き方を知ることができただろう. しかし，どうしても OOP でやりたい場合は OOPMacro.jl を使う方法もある. ただし，あまりメンテナンスされていないようなので，どうしてもOOPが素晴らしいと感じる人は OOPMacro.jl をメンテしていくと良いだろう..."
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "f98bdbc2",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:56:01.652000+09:00",
"start_time": "2021-12-29T10:54:53.632Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"dist (generic function with 2 methods)"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using OOPMacro\n",
"\n",
"@class Point begin\n",
" x::Float64\n",
" y::Float64\n",
" __init__(self, x, y) = begin\n",
" self.x = x\n",
" self.y = y\n",
" end\n",
" function dist(self, other::Point)\n",
" Δx = self.x - other.x\n",
" Δy = self.y - other.y\n",
" √(Δx^2 + Δy^2)\n",
" end\n",
" shift(self, x, y) = Point(self.x + x, self.y + y)\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "bfd0c8f5",
"metadata": {},
"source": [
"## Example"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "82d0ffa2",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:56:02.420000+09:00",
"start_time": "2021-12-29T10:54:53.684Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"Point(1.0, 2.0)"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p = Point(0, 0)\n",
"q = Point(1, 2)"
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "11ab69ea",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:56:02.470000+09:00",
"start_time": "2021-12-29T10:54:53.689Z"
}
},
"outputs": [],
"source": [
"@assert dist(p, q) ≈ √5\n",
"r = shift(q, -1, -2)\n",
"@assert r.x ≈ p.x\n",
"@assert r.y ≈ p.y"
]
},
{
"cell_type": "markdown",
"id": "93dddcd4",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:29:19.187000+09:00",
"start_time": "2021-12-26T12:29:19.179Z"
}
},
"source": [
"# oop macro を作る\n",
"\n",
"OOP っぽくクラスを作ったからと言って `obj.method(args)` 方式が使えるわけではない. そこでマクロを使ってよしなに変換してみよう. これぐらいならできそうである:"
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "699ed33e",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:56:02.689000+09:00",
"start_time": "2021-12-29T10:54:53.744Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"@oop (macro with 1 method)"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"macro oop(ex::Expr)\n",
" obj, qn = ex.args[1].args\n",
" method = qn.value\n",
" args = ex.args[2:end]\n",
" quote\n",
" ($method)($obj, $(args...))\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "8fcd2630",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:56:02.738000+09:00",
"start_time": "2021-12-29T10:54:53.747Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"2.23606797749979"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@oop p.dist(q)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "c2c4d1dc",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-29T19:56:02.752000+09:00",
"start_time": "2021-12-29T10:54:53.749Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"r.x = -1.0\n",
"r.y = -2.0\n"
]
},
{
"data": {
"text/plain": [
"-2.0"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"r = @oop p.shift(-1, -2)\n",
"@show r.x\n",
"@show r.y"
]
},
{
"cell_type": "markdown",
"id": "fe7dd874",
"metadata": {},
"source": [
"### 補足"
]
},
{
"cell_type": "markdown",
"id": "96fd0ca5",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:52:58.460000+09:00",
"start_time": "2021-12-26T12:52:58.451Z"
}
},
"source": [
"必要に応じて Classes.jl を参照せよ."
]
},
{
"cell_type": "markdown",
"id": "2c623cb8",
"metadata": {
"ExecuteTime": {
"end_time": "2021-12-26T21:54:28.619000+09:00",
"start_time": "2021-12-26T12:54:28.613Z"
}
},
"source": [
"# まとめ \n",
"\n",
"OOP と Julia の関係を説明することができた. OOPMacro.jl の使い方，メソッド呼び出しの工夫を人添えしたマクロも紹介した.\n",
"これで OOP スタイルにこだわらなくても実装ができる自信を掴んでもらえれば幸いである."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia-sys 1.7.1",
"language": "julia",
"name": "julia-sys-1.7"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.7.1"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
},
"varInspector": {
"cols": {
"lenName": 16,
"lenType": 16,
"lenVar": 40
},
"kernels_config": {
"python": {
"delete_cmd_postfix": "",
"delete_cmd_prefix": "del ",
"library": "var_list.py",
"varRefreshCmd": "print(var_dic_list())"
},
"r": {
"delete_cmd_postfix": ") ",
"delete_cmd_prefix": "rm(",
"library": "var_list.r",
"varRefreshCmd": "cat(var_dic_list()) "
}
},
"types_to_exclude": [
"module",
"function",
"builtin_function_or_method",
"instance",
"_Feature"
],
"window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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