---
title: Fixed Array in TypeScript
description: Fixed Array in TypeScript
image:
tags: typescript
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lang: zh
dir: ltr
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GA: UA-168653916-1
disqus: hackmd
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---
# Fixed Array in TypeScript
## 簡介
近期在研究如何用透過型別推斷定義出固定長度的陣列
本篇將嘗試解釋給大家聽
## 研究案例
先提這次的研究案例有兩個如下 (其實只有一個):
- 定義型別為 從 0 到 指定數值的陣列型別
```typescript
export type Sequence<N extends number, R extends unknown[] = []> =
R['length'] extends N
? R
: Sequence<N, [R['length'], ...R]>;
// example
const a: Sequence<5> = [0, 1, 2, 3, 4]; // typeof a is [0,1,2,3,4]
const b: Sequence<3> = [0, 1, 2]; // typeof a is [0,1,2]
// how to use
// ex: define type is 10 | 11| 12| 13| .... | 19
type ArrayToUnion<T> = T extends any[] ? T[number] : T; // [1,2,3,4] to 1 | 2 | 3 | 4
type UnionSequence<T extends number> = ArrayToUnion<Sequence<T>>;
// 0 - 19 union exclude 0 - 9 union should be 10 - 19 union
type Example = Exclude<UnionSequence<20>, UnionSequence<10>>
```
- 定義一個固定長度且自訂型別的陣列與矩陣
```typescript
type Fixed<N extends number, P = number, R extends P[] = []> =
R['length'] extends N
? R
: Sequence<N, P, [P, ...R]>;
// example
const a: Fixed<3> = [0,0,0]; //typeof a is [number, number, number]
const b: Fixed<4, string> = ['','','',''] //typeof b is [string, string, string, string]
// how to use
type Matrix<X extends number, Y extends number, T = number> = Fixed<X, Fixed<Y, T>>;
const m1: Matrix<2, 3> = [[0,0,0],[1,2,2]];
const m2: Matrix<3, 2, string> = [['0','0'],['1','2'],['','']];
```
想跳過解說直接使用的可以從這裡取得相關語法
[playground](https://www.typescriptlang.org/play?#code/C4TwDgpgBAyhCOBXCA7AxhAPAOShAHsKgCYDOUKiAtgEYQBOANFAEp6EnmIoDWKA9gHcUAbQC6UALxRxAPilQAUFFYiA5ABtUAc2AALNRIJEUZKLmUqrKgPysl16wC5YCZOizZmIgHR+WzCzqWii6BmJisgDcigD0sewAhlRgWopo-CikwFCJLnBIqBiYAKzy0iIADMwAjMwATMwAzMwALGJRUPFQoJD8AGa5UACW5FWMdY0t7emZ2VA0+W5FWE3lMtVQdVD1HV0JvRADQ6MbE4y7cQl6Qj38UIikEFfsLsQQ-cMo0Icj5DWVKAAHy2NRBNXq4KaIL8fmBWwAnEpfgBBej0RIgAAq-AAqihhplMFj1lj2CYzIkUCBxFA7FiRJRaAwJC4sZ1uiJJoxphJgPcavD6vCmvDWopfvjCSgCu5imTjJwKNQ6PR1miMdi8QSibKVsTZNElN1AQBaREPHUodhoDSId5QM1QJHcaVQUg3RAaYgLaAAqDmmouq0S8DQACi+GSqWg0kjtvtWClmT1Hkw9UqsmYyZlyzTAMNxtippLpbL5Yrlar1Zrtbr1cUocgUAAYsN8BBiDhyUqmarmAAFBR9hiBHumcgD2kVSIKSxBTQ6fSGcdmCyOKx2NiWDcuNsdrteKAD7ywgLHyIxboEaNaJQZLI5NB79udzBrBTjaqVPbxQ7HRI-hkEcmGVZlQJAsRZkfKBiBfA9MFaZhsnoL5tHWdQ1EYNQsJw7CVz-MNjhoICRBQtDkOAVDQko6jtFotCoO6G5BDuB4nibaAAFlEio9tMAADVXcgQOYABNYSwP7KAyWkED1n3N8BOYRSuzE5gSWiaD5ioGoXB4vj8HTZoMK-Rgf0YLkLguCIYgfHT6n03jUKMlodgY0JTLUSpcJ8sRLLUGpcPqQwAtwwwOiAA)
### 已知問題
這個做法目前仍存在上限問題
因為是依靠遞迴完成 所以 上限目前貌似為 999 個索引
如果要考量接續應用他們的話 大約是 900 個索引
也就是 如果寫 ```Sequence<1000>``` 會在開發階段就跳出 stackoverflow 的錯誤
後續遇到會再詳細解釋問題點
### 詳解
這個做法主要是利用 v3.7 所更新時
允許使用 recursive 來定義型別
以及 ```Array<T>.length``` 來產生數列
尤其是後者 想出這個方法的人真的是天才
在 typescript 中如果要宣告一個值的型別為 數字 1
通常就必須先行定義出該型別
這導致可能必須先進行一串 像是宣告 keyboard code 的靜態字串
而這裡不需要這樣做
但會有一點代價 請參考已知問題
---
這裡的型別定義宣告為
```typescript
type Sequence<N extends number, R extends unknown[] = []> =
R['length'] extends N
? R
: Sequence<N, [R['length'], ...R]>;
```
1. 除了 數列長度 ```N``` 之外 還宣告了一個陣列 ```R``` 並給予預設值空陣列
而這個空陣列就是用來產生數列的主要功臣
2. 判斷邏輯為 如果陣列 R 的長度是 N 就回傳陣列 R
否則回傳 ```Sequence<N, [R['length'], ...R]>```
```[R['length'], ...R]``` 這段語法的意思是
把陣列 ```R``` 前面再加上一個數字做為新的泛型參數帶回 ```Sequence<N, R>``` 的 ```R```
而有趣的事情就發生了
此時因為陣列 ```R``` 多了一個元素 導致下一個 ```R['length']``` 比前一次多了 1
使得這段語法會在 typescript 的 編譯器中進行遞迴
使陣列 ```R``` 持續增加元素直到他的長度等於 ```R```
這樣我們就可以透過 ```Sequence<N>``` 來取得指定長度的數列了
有了這個 就可以做很多過去不好處理的型別或判斷
### 好處
1. 在參數傳遞上 如果需要 指定個數的元素陣列時 不用在刻死一個專用的型別 來限制
ex:
```typescript
//old
let numb5: [number,number,number,number,number] = [1,2,3,4,5];
function matrixAdd<T extends [[number, number], [number, number]]>(left: T, right: T);
//new
let numb5: Fixed<5> = [1,2,3,4,5];
function matrixAdd<X extends number, Y extends number>(left: Matrix<X, Y>, right: Matrix<X, Y>);
```
2. 減少 runtime 繁瑣的結構判斷, 改成於 designTime 就進行約定加以限制 以提升執行效能
ex:
```typescript
//old
function runNumb5(num5: number[]) {
if(num5.length === 5) return;
///....
}
//new
function runNumb5(num5: Fixed<5>) {
// num5 length exactly equals 5 without condition
///....
}
```
....more
還有很多可能性都可以從這個點延伸
## 後記
我當初想做的其實就是 ```Matrix<X, Y>```
當然在更早之前其實就已經開始思考該怎麼做
只是以前無法實現
而且這件事情對於對數理 數字有興趣的人
應該都可以腦洞大開
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.ui-toc-dropdown .nav>.active:hover>a,
.ui-toc-dropdown .nav>.active>a {
color: #7bf;
border-left-color: #7bf;
}
.ui-toc-dropdown .nav>li>a:focus,
.ui-toc-dropdown .nav>li>a:hover {
color: #7bf;
border-left-color: #7bf;
}
.ui-toc-dropdown.dropdown-menu {
background: #333;
}
.toc-menu a {
color: #ddd;
}
.toc-menu a:focus,
.toc-menu a:hover {
color: #7bf;
}
.cm-m-markdown {
color: #ddd;
}
.cm-s-one-dark .cm-header,
.cm-m-xml.cm-attribute {
color: #ffa653;
}
.cm-s-one-dark .cm-string,
.cm-s-one-dark .cm-variable-2 {
color: #7bf;
}
.cm-m-markdown.cm-variable-3 {
color: #ff7e7e;
}
.cm-s-one-dark .cm-link {
color: #b0ee83;
}
.cm-s-one-dark .CodeMirror-linenumber {
color: #666;
}
.cm-strong {
color: #f4511e;
}
.cm-s-one-dark .cm-comment {
color: #a9a9a9;
}
.cm-matchhighlight {
color: #ffea00;
}
.cm-positive {
color: #11bf64;
}
.cm-negative {
color: #ff3e3e;
}
.dropdown-menu.CodeMirror-other-cursor {
border: 2px solid #4d4d4d;
background-color: #202020;
}
.dropdown-menu.CodeMirror-other-cursor li a {
color: #ececec;
}
.topbar {
background: #1e1e1e;
}
.btn.focus,
.btn:focus,
.btn:hover {
color: #aaa;
}
.summary {
background: #1e1e1e;
}
.summary,
.toolbar {
background: #1e1e1e !important;
border-color: #4d4d4d !important;
}
.toolbar i {
color: #fff;
}
.summary h1,
.summary h2,
.summary h3 .summary hr {
color: #ddd;
border-color: #777 !important;
}
.summary .nav>li>a {
color: #7bf;
}
.summary .nav-pills>li.active>a,
.summary .nav-pills>li.active>a:focus,
.summary .nav-pills>li.active>a:hover {
color: #ff9100;
}
.ui-summary-search {
font-size: 16px;
border: 1px solid #6D6D6D;
background-color: #333;
color: #FFF;
}
.summary h1,
.summary h2,
.summary h3,
.summary h4,
.summary h5,
.summary h6 {
border-color: #454545;
}
div[class$=container-mask] {
background: #1e1e1e;
z-index: 1;
display: block;
}
.dropdown.ui-notification .ui-notification-label,
.dropdown.ui-invitee .ui-invitee-label {
color: #eee;
border-color: #6a6a6a;
}
.ui-notification .dropdown-menu {
border-top: 1px solid #555;
}
.modal-header {
background-color: #2a2a2a;
}
.panel-default {
border-color: #6d6d6d;
}
.panel-default>.panel-heading {
background-color: #2a2a2a;
color: #eee;
border-color: #6d6d6d;
}
.panel-body {
background: #2e2e2e;
}
.panel-body a {
color: #7bf;
}
.table>tbody>tr>td,
.table>tbody>tr>th,
.table>tfoot>tr>td,
.table>tfoot>tr>th,
.table>thead>tr>td,
.table>thead>tr>th {
border-color: #6d6d6d;
}
.ui-comment-container .ui-comment-header {
background-color: #2a2a2a;
color: #eee;
border-color: #6d6d6d;
}
.ui-comment-container {
background-color: #2e2e2e;
border-color: #6d6d6d;
}
.ui-comment-container .ui-comments-container .ui-comment .comment-author {
color: #eee;
}
.ui-comment-container .ui-comments-container .ui-comment .timestamp {
color: #aaa;
}
.ui-comment-container .ui-comments-container .ui-comment .comment-content {
color: #eee;
}
.ui-comment-container .ui-comments-container .ui-comment .comment-menu {
color: #eee;
}
.ui-comment-container .ui-comments-container .ui-comment .comment-menu .comment-dropdown-menu {
background: #222;
color: #eee;
border-color: #555;
}
.ui-comment-container .ui-comments-container .ui-comment .comment-menu .comment-dropdown-menu>div:hover {
background-color: #555555;
color: #eee;
}
.ui-comment-container .ui-comments-container .ui-comment .comment-menu:hover,
.ui-comment-container .ui-comments-container .ui-comment .comment-menu:active,
.ui-comment-container .ui-comments-container .ui-comment .comment-menu.active {
background-color: #737373;
color: #eee;
}
.ui-comment-container .ui-comment-input-container {
background-color: #3c3c3c;
}
.ui-comment-container textarea {
background-color: #3e4045;
color: #eee;
border: 1px solid #6d6d6d;
}
.ui-comment-container textarea::placeholder,
.ui-comment-container textarea::-webkit-input-placeholder,
.ui-comment-container textarea:-moz-placeholder,
.ui-comment-container textarea::-moz-placeholder,
.ui-comment-container textarea:-ms-input-placeholder {
color: #eee;
}
@keyframes highlight {
0% {
background-color: #3c3c3c;
}
30% {
background-color: #3c3c3c;
}
100% {
background-color: transparent;
}
}
.template-content .modal-header {
background: #2a2a2a;
}
.template-content .close {
color: #fff;
}
.template-content .modal-title {
color: #eee;
}
.template-content .ui-templates-container {
border-color: #6d6d6d;
}
.ui-templates-container .ui-create-template-btn {
background: #446fab;
color: #fff;
}
.ui-template-list-filter .ui-template-list-filter-label,
.ui-template-list-filter .ui-template-list-filter-label:hover {
color: #eee;
}
.ui-template-list .list-group-item.active {
background: #4d4d4d;
}
.ui-template-list .list-group-item.active:focus {
background: #4d4d4d !important;
}
.list-group-item.active,
.list-group-item.active:focus,
.list-group-item.active:hover {
color: #eee;
}
.ui-template-list .list-group-item .list-group-item-heading {
color: #eee;
}
.ui-template-list .list-group-item.active .list-group-item-heading {
color: #eee;
}
.ui-template-list .list-group-item:hover {
background: #4d4d4d !important;
}
.ui-template-item-menu {
color: #eee !important;
}
.ui-template-list .list-group-item {
color: #fff;
}
.ui-template-list .list-group-item .dropdown-container.open {
background-color: #2a2a2a;
}
.ui-template-list .list-group-item .dropdown-container:hover {
background-color: #2a2a2a !important;
}
.template-menu .more-template {
border-color: #6d6d6d;
}
.template-menu .more-template:hover {
color: #eee;
border-color: #6d6d6d;
}
.modal-content {
background: #1f2226;
}
.modal-header {
border-bottom: 1px solid #46484f;
}
.modal-footer {
border-top: 1px solid #46484f;
}
a.list-group-item {
background: #1f2226;
color: #ddd;
border: 1px solid #46484f;
}
a.list-group-item .list-group-item-heading {
color: #ddd;
}
a.list-group-item:focus,
a.list-group-item:hover {
background: #434651;
color: #ddd;
}
button.close {
color: #ddd;
opacity: .5;
}
.close:focus, .close:hover {
color: #fff;
opacity: .8;
}
.CodeMirror {
background: #1f2226;
}
.CodeMirror-gutters {
background: #1f2226;
border-right: 1px solid rgba(204, 217, 255, 0.1);
}
.cm-s-default .cm-comment {
color: #888;
}
.cm-s-default .cm-quote {
color: #ddd;
}
.cm-s-default .cm-header {
color: #ffa653;
}
.cm-s-default .cm-link {
color: #b0ee83;
}
.cm-s-default .cm-string,
.cm-s-default .cm-variable-2 {
color: #7bf;
}
.cm-s-default .cm-def {
color: #c678dd;
}
.cm-s-default .cm-number,
.cm-s-default .cm-attribute,
.cm-s-default .cm-qualifier,
.cm-s-default .cm-plus,
.cm-s-default .cm-atom {
color: #eda35e;
}
.cm-s-default .cm-property,
.cm-s-default .cm-variable,
.cm-s-default .cm-variable-3,
.cm-s-default .cm-operator,
.cm-s-default .cm-bracket {
color: #f76e79;
}
.cm-s-default .cm-keyword,
.cm-s-default .cm-builtin,
.cm-s-default .cm-tag {
color: #98c379;
}
.modal-title {
color: #ccc;
}
.modal-body {
color: #ccc !important;
}
div[contenteditable]:empty:not(:focus):before {
color: #aaa;
}
.CodeMirror pre {
color: #ddd;
}
.CodeMirror pre span[style^="background-color: rgb(221, 251, 230)"] {
background-color: #288c27 !important;
}
.CodeMirror pre span[style^="background-color: rgb(249, 215, 220)"] {
background-color: #a52721 !important;
}
.hljs {
background: #1E1E1E;
color: #DCDCDC;
}
.hljs-keyword,
.hljs-literal,
.hljs-symbol,
.hljs-name {
color: #569CD6;
}
.hljs-link {
color: #569CD6;
text-decoration: underline;
}
.hljs-built_in,
.hljs-type {
color: #4EC9B0;
}
.hljs-number,
.hljs-class {
color: #B8D7A3;
}
.hljs-string,
.hljs-meta-string {
color: #D69D85;
}
.hljs-regexp,
.hljs-template-tag {
color: #d16969;
}
.hljs-title {
color: #dcdcaa;
}
.hljs-subst,
.hljs-function,
.hljs-formula {
color: #DCDCDC;
}
.hljs-comment,
.hljs-quote {
color: #57A64A;
}
.hljs-doctag {
color: #608B4E;
}
.hljs-meta,
.hljs-meta-keyword,
.hljs-tag {
color: #9B9B9B;
}
.hljs-variable,
.hljs-template-variable {
color: #BD63C5;
}
.hljs-params,
.hljs-attr,
.hljs-attribute,
.hljs-builtin-name {
color: #9CDCFE;
}
.hljs-section {
color: gold;
}
.hljs-emphasis {
font-style: italic;
}
.hljs-strong {
font-weight: bold;
}
.hljs-code {
font-family:'Monospace';
}
.hljs-bullet,
.hljs-selector-tag,
.hljs-selector-id,
.hljs-selector-class,
.hljs-selector-attr,
.hljs-selector-pseudo {
color: #D7BA7D;
}
.hljs-addition {
background-color: #155a36;
color: #dfdfdf;
display: inline-block;
width: 100%;
}
.hljs-deletion {
background-color: #872e2e;
color: #dfdfdf;
display: inline-block;
width: 100%;
}
code[class*="language-"],
pre[class*="language-"] {
color: #DCDCDC;
}
:not(pre)>code[class*="language-"],
pre[class*="language-"] {
background: #1E1E1E;
}
.token.comment,
.token.block-comment,
.token.prolog,
.token.cdata {
color: #57A64A;
}
.token.doctype,
.token.punctuation {
color: #9B9B9B;
}
.token.tag,
.token.entity {
color: #569CD6;
}
.token.attr-name,
.token.namespace,
.token.deleted,
.token.property,
.token.builtin {
color: #9CDCFE;
}
.token.function,
.token.function-name {
color: #dcdcaa;
}
.token.boolean,
.token.keyword,
.token.important {
color: #569CD6;
}
.token.number {
color: #B8D7A3;
}
.token.class-name,
.token.constant {
color: #4EC9B0;
}
.token.symbol {
color: #f8c555;
}
.token.rule {
color: #c586c0;
}
.token.selector {
color: #D7BA7D;
}
.token.atrule {
color: #cc99cd;
}
.token.string,
.token.attr-value {
color: #D69D85;
}
.token.char {
color: #7ec699;
}
.token.variable {
color: #BD63C5;
}
.token.regex {
color: #d16969;
}
.token.operator {
color: #DCDCDC;
background: transparent;
}
.token.url {
color: #67cdcc;
}
.token.important,
.token.bold {
font-weight: bold;
}
.token.italic {
font-style: italic;
}
.token.entity {
cursor: help;
}
.token.inserted {
color: green;
}
.gist .gist-file {
border: 1px solid #555;
}
.gist .gist-data {
background-color: #1e1e1e;
border-bottom: 1px solid #555;
}
.gist .gist-meta {
background-color: #424a55;
color: #eee;
}
.gist .gist-meta a {
color: #eee;
}
.gist .highlight {
color: #eee;
background-color: #1e1e1e;
}
.gist .blob-num {
color: #afafaf;
}
.gist .blob-code-inner {
color: #dfdfdf;
}
.pl-mb {
color: #fff !important;
}
.pl-c {
color: #57A64A !important;
}
.pl-ent {
color: #569CD6 !important;
}
.pl-e {
color: #9CDCFE !important;
}
.pl-en {
color: #4EC9B0 !important;
}
.pl-smi {
color: #9CDCFE !important;
}
.pl-k {
color: #569cd6 !important;
}
.pl-c1,
.pl-s .pl-v {
color: #4EC9B0 !important;
}
.pl-pds,
.pl-s,
.pl-s .pl-pse .pl-s1,
.pl-sr,
.pl-sr .pl-cce,
.pl-sr .pl-sra,
.pl-sr .pl-sre,
.pl-s .pl-s1 {
color: #D69D85 !important;
}
.pl-s .pl-s1 .pl-pse {
color: #c5dbff !important;
}
.diff-table .pl-c,
.diff-table .pl-ent,
.diff-table .pl-e,
.diff-table .pl-en,
.diff-table .pl-pds,
.diff-table .pl-s,
.diff-table .pl-s .pl-s1,
.diff-table .pl-s .pl-pse .pl-s1,
.diff-table .pl-sr,
.diff-table .pl-sr .pl-cce,
.diff-table .pl-sr .pl-sra,
.diff-table .pl-sr .pl-sre,
.diff-table .pl-k,
.diff-table .pl-smi,
.diff-table .pl-c1,
.diff-table .pl-v {
color: #eee !important;
}
</style>