Equivalence

The Equivalence module provides a way to define equivalence relations between values in TypeScript. An equivalence relation is a binary relation that is reflexive, symmetric, and transitive, establishing a formal notion of when two values should be considered equivalent.

What is Equivalence?

An Equivalence<A> represents a function that compares two values of type A and determines if they are equivalent. This is more flexible and customizable than simple equality checks using ===.

Here’s the structure of an Equivalence:

interface Equivalence<A> {
  (self: A, that: A): boolean
}

Using Built-in Equivalences

The module provides several built-in equivalence relations for common data types:

Equivalence	Description
`string`	Uses strict equality (`===`) for strings
`number`	Uses strict equality (`===`) for numbers
`boolean`	Uses strict equality (`===`) for booleans
`symbol`	Uses strict equality (`===`) for symbols
`bigint`	Uses strict equality (`===`) for bigints
`Date`	Compares `Date` objects by their timestamps

Example (Using Built-in Equivalences)

1
import { import Equivalence
Equivalence } from "effect"
2

3
namespace console
var console: ConsoleThe `console` module provides a simple debugging console that is similar to the
JavaScript console mechanism provided by web browsers.

The module exports two specific components:

* A `Console` class with methods such as `console.log()`, `console.error()` and `console.warn()` that can be used to write to any Node.js stream.
* A global `console` instance configured to write to [`process.stdout`](https://nodejs.org/docs/latest-v22.x/api/process.html#processstdout) and
[`process.stderr`](https://nodejs.org/docs/latest-v22.x/api/process.html#processstderr). The global `console` can be used without importing the `node:console` module.

_**Warning**_: The global console object's methods are neither consistently
synchronous like the browser APIs they resemble, nor are they consistently
asynchronous like all other Node.js streams. See the [`note on process I/O`](https://nodejs.org/docs/latest-v22.x/api/process.html#a-note-on-process-io) for
more information.

Example using the global `console`:

```js
console.log('hello world');
// Prints: hello world, to stdout
console.log('hello %s', 'world');
// Prints: hello world, to stdout
console.error(new Error('Whoops, something bad happened'));
// Prints error message and stack trace to stderr:
//   Error: Whoops, something bad happened
//     at [eval]:5:15
//     at Script.runInThisContext (node:vm:132:18)
//     at Object.runInThisContext (node:vm:309:38)
//     at node:internal/process/execution:77:19
//     at [eval]-wrapper:6:22
//     at evalScript (node:internal/process/execution:76:60)
//     at node:internal/main/eval_string:23:3

const name = 'Will Robinson';
console.warn(`Danger ${name}! Danger!`);
// Prints: Danger Will Robinson! Danger!, to stderr
```

Example using the `Console` class:

```js
const out = getStreamSomehow();
const err = getStreamSomehow();
const myConsole = new console.Console(out, err);

myConsole.log('hello world');
// Prints: hello world, to out
myConsole.log('hello %s', 'world');
// Prints: hello world, to out
myConsole.error(new Error('Whoops, something bad happened'));
// Prints: [Error: Whoops, something bad happened], to err

const name = 'Will Robinson';
myConsole.warn(`Danger ${name}! Danger!`);
// Prints: Danger Will Robinson! Danger!, to err
```
console.(method) Console.log(message?: any, ...optionalParams: any[]): voidPrints to `stdout` with newline. Multiple arguments can be passed, with the
first used as the primary message and all additional used as substitution
values similar to [`printf(3)`](http://man7.org/linux/man-pages/man3/printf.3.html)
(the arguments are all passed to [`util.format()`](https://nodejs.org/docs/latest-v22.x/api/util.html#utilformatformat-args)).

```js
const count = 5;
console.log('count: %d', count);
// Prints: count: 5, to stdout
console.log('count:', count);
// Prints: count: 5, to stdout
```

See [`util.format()`](https://nodejs.org/docs/latest-v22.x/api/util.html#utilformatformat-args) for more information.
log(import Equivalence
Equivalence.const string: Equivalence.Equivalence
(self: string, that: string) => boolean
string("apple", "apple"))
4
// Output: true
5

6
namespace console
var console: ConsoleThe `console` module provides a simple debugging console that is similar to the
JavaScript console mechanism provided by web browsers.

The module exports two specific components:

* A `Console` class with methods such as `console.log()`, `console.error()` and `console.warn()` that can be used to write to any Node.js stream.
* A global `console` instance configured to write to [`process.stdout`](https://nodejs.org/docs/latest-v22.x/api/process.html#processstdout) and
[`process.stderr`](https://nodejs.org/docs/latest-v22.x/api/process.html#processstderr). The global `console` can be used without importing the `node:console` module.

_**Warning**_: The global console object's methods are neither consistently
synchronous like the browser APIs they resemble, nor are they consistently
asynchronous like all other Node.js streams. See the [`note on process I/O`](https://nodejs.org/docs/latest-v22.x/api/process.html#a-note-on-process-io) for
more information.

Example using the global `console`:

```js
console.log('hello world');
// Prints: hello world, to stdout
console.log('hello %s', 'world');
// Prints: hello world, to stdout
console.error(new Error('Whoops, something bad happened'));
// Prints error message and stack trace to stderr:
//   Error: Whoops, something bad happened
//     at [eval]:5:15
//     at Script.runInThisContext (node:vm:132:18)
//     at Object.runInThisContext (node:vm:309:38)
//     at node:internal/process/execution:77:19
//     at [eval]-wrapper:6:22
//     at evalScript (node:internal/process/execution:76:60)
//     at node:internal/main/eval_string:23:3

const name = 'Will Robinson';
console.warn(`Danger ${name}! Danger!`);
// Prints: Danger Will Robinson! Danger!, to stderr
```

Example using the `Console` class:

```js
const out = getStreamSomehow();
const err = getStreamSomehow();
const myConsole = new console.Console(out, err);

myConsole.log('hello world');
// Prints: hello world, to out
myConsole.log('hello %s', 'world');
// Prints: hello world, to out
myConsole.error(new Error('Whoops, something bad happened'));
// Prints: [Error: Whoops, something bad happened], to err

const name = 'Will Robinson';
myConsole.warn(`Danger ${name}! Danger!`);
// Prints: Danger Will Robinson! Danger!, to err
```
console.(method) Console.log(message?: any, ...optionalParams: any[]): voidPrints to `stdout` with newline. Multiple arguments can be passed, with the
first used as the primary message and all additional used as substitution
values similar to [`printf(3)`](http://man7.org/linux/man-pages/man3/printf.3.html)
(the arguments are all passed to [`util.format()`](https://nodejs.org/docs/latest-v22.x/api/util.html#utilformatformat-args)).

```js
const count = 5;
console.log('count: %d', count);
// Prints: count: 5, to stdout
console.log('count:', count);
// Prints: count: 5, to stdout
```

See [`util.format()`](https://nodejs.org/docs/latest-v22.x/api/util.html#utilformatformat-args) for more information.
log(import Equivalence
Equivalence.const string: Equivalence.Equivalence
(self: string, that: string) => boolean
string("apple", "orange"))
7
// Output: false
8

9
namespace console
var console: ConsoleThe `console` module provides a simple debugging console that is similar to the
JavaScript console mechanism provided by web browsers.

The module exports two specific components:

* A `Console` class with methods such as `console.log()`, `console.error()` and `console.warn()` that can be used to write to any Node.js stream.
* A global `console` instance configured to write to [`process.stdout`](https://nodejs.org/docs/latest-v22.x/api/process.html#processstdout) and
[`process.stderr`](https://nodejs.org/docs/latest-v22.x/api/process.html#processstderr). The global `console` can be used without importing the `node:console` module.

_**Warning**_: The global console object's methods are neither consistently
synchronous like the browser APIs they resemble, nor are they consistently
asynchronous like all other Node.js streams. See the [`note on process I/O`](https://nodejs.org/docs/latest-v22.x/api/process.html#a-note-on-process-io) for
more information.

Example using the global `console`:

```js
console.log('hello world');
// Prints: hello world, to stdout
console.log('hello %s', 'world');
// Prints: hello world, to stdout
console.error(new Error('Whoops, something bad happened'));
// Prints error message and stack trace to stderr:
//   Error: Whoops, something bad happened
//     at [eval]:5:15
//     at Script.runInThisContext (node:vm:132:18)
//     at Object.runInThisContext (node:vm:309:38)
//     at node:internal/process/execution:77:19
//     at [eval]-wrapper:6:22
//     at evalScript (node:internal/process/execution:76:60)
//     at node:internal/main/eval_string:23:3

const name = 'Will Robinson';
console.warn(`Danger ${name}! Danger!`);
// Prints: Danger Will Robinson! Danger!, to stderr
```

Example using the `Console` class:

```js
const out = getStreamSomehow();
const err = getStreamSomehow();
const myConsole = new console.Console(out, err);

myConsole.log('hello world');
// Prints: hello world, to out
myConsole.log('hello %s', 'world');
// Prints: hello world, to out
myConsole.error(new Error('Whoops, something bad happened'));
// Prints: [Error: Whoops, something bad happened], to err

const name = 'Will Robinson';
myConsole.warn(`Danger ${name}! Danger!`);
// Prints: Danger Will Robinson! Danger!, to err
```
console.(method) Console.log(message?: any, ...optionalParams: any[]): voidPrints to `stdout` with newline. Multiple arguments can be passed, with the
first used as the primary message and all additional used as substitution
values similar to [`printf(3)`](http://man7.org/linux/man-pages/man3/printf.3.html)
(the arguments are all passed to [`util.format()`](https://nodejs.org/docs/latest-v22.x/api/util.html#utilformatformat-args)).

```js
const count = 5;
console.log('count: %d', count);
// Prints: count: 5, to stdout
console.log('count:', count);
// Prints: count: 5, to stdout
```

See [`util.format()`](https://nodejs.org/docs/latest-v22.x/api/util.html#utilformatformat-args) for more information.
log(import Equivalence
Equivalence.const Date: Equivalence.Equivalence
(self: Date, that: Date) => boolean
Date(new var Date: DateConstructor
new (year: number, monthIndex: number, date?: number, hours?: number, minutes?: number, seconds?: number, ms?: number) => Date (+3 overloads)Creates a new Date.
Date(2023, 1, 1), new var Date: DateConstructor
new (year: number, monthIndex: number, date?: number, hours?: number, minutes?: number, seconds?: number, ms?: number) => Date (+3 overloads)Creates a new Date.
Date(2023, 1, 1)))
10
// Output: true
11

12
namespace console
var console: ConsoleThe `console` module provides a simple debugging console that is similar to the
JavaScript console mechanism provided by web browsers.

The module exports two specific components:

* A `Console` class with methods such as `console.log()`, `console.error()` and `console.warn()` that can be used to write to any Node.js stream.
* A global `console` instance configured to write to [`process.stdout`](https://nodejs.org/docs/latest-v22.x/api/process.html#processstdout) and
[`process.stderr`](https://nodejs.org/docs/latest-v22.x/api/process.html#processstderr). The global `console` can be used without importing the `node:console` module.

_**Warning**_: The global console object's methods are neither consistently
synchronous like the browser APIs they resemble, nor are they consistently
asynchronous like all other Node.js streams. See the [`note on process I/O`](https://nodejs.org/docs/latest-v22.x/api/process.html#a-note-on-process-io) for
more information.

Example using the global `console`:

```js
console.log('hello world');
// Prints: hello world, to stdout
console.log('hello %s', 'world');
// Prints: hello world, to stdout
console.error(new Error('Whoops, something bad happened'));
// Prints error message and stack trace to stderr:
//   Error: Whoops, something bad happened
//     at [eval]:5:15
//     at Script.runInThisContext (node:vm:132:18)
//     at Object.runInThisContext (node:vm:309:38)
//     at node:internal/process/execution:77:19
//     at [eval]-wrapper:6:22
//     at evalScript (node:internal/process/execution:76:60)
//     at node:internal/main/eval_string:23:3

const name = 'Will Robinson';
console.warn(`Danger ${name}! Danger!`);
// Prints: Danger Will Robinson! Danger!, to stderr
```

Example using the `Console` class:

```js
const out = getStreamSomehow();
const err = getStreamSomehow();
const myConsole = new console.Console(out, err);

myConsole.log('hello world');
// Prints: hello world, to out
myConsole.log('hello %s', 'world');
// Prints: hello world, to out
myConsole.error(new Error('Whoops, something bad happened'));
// Prints: [Error: Whoops, something bad happened], to err

const name = 'Will Robinson';
myConsole.warn(`Danger ${name}! Danger!`);
// Prints: Danger Will Robinson! Danger!, to err
```
console.(method) Console.log(message?: any, ...optionalParams: any[]): voidPrints to `stdout` with newline. Multiple arguments can be passed, with the
first used as the primary message and all additional used as substitution
values similar to [`printf(3)`](http://man7.org/linux/man-pages/man3/printf.3.html)
(the arguments are all passed to [`util.format()`](https://nodejs.org/docs/latest-v22.x/api/util.html#utilformatformat-args)).

```js
const count = 5;
console.log('count: %d', count);
// Prints: count: 5, to stdout
console.log('count:', count);
// Prints: count: 5, to stdout
```

See [`util.format()`](https://nodejs.org/docs/latest-v22.x/api/util.html#utilformatformat-args) for more information.
log(import Equivalence
Equivalence.const Date: Equivalence.Equivalence
(self: Date, that: Date) => boolean
Date(new var Date: DateConstructor
new (year: number, monthIndex: number, date?: number, hours?: number, minutes?: number, seconds?: number, ms?: number) => Date (+3 overloads)Creates a new Date.
Date(2023, 1, 1), new var Date: DateConstructor
new (year: number, monthIndex: number, date?: number, hours?: number, minutes?: number, seconds?: number, ms?: number) => Date (+3 overloads)Creates a new Date.
Date(2023, 10, 1)))
13
// Output: false

Deriving Equivalences

For more complex data structures, you may need custom equivalences. The Equivalence module lets you derive new Equivalence instances from existing ones with the Equivalence.mapInput function.

Example (Creating a Custom Equivalence for Objects)

1
import { import Equivalence
Equivalence } from "effect"
2

3
interface interface User
User {
4
  readonly (property) User.id: number
id: number
5
  readonly (property) User.name: string
name: string
6
}
7

8
// Create an equivalence that compares User objects based only on the id
9
const const equivalence: Equivalence.Equivalence<User>
equivalence = import Equivalence
Equivalence.const mapInput: <number, User>(self: Equivalence.Equivalence<number>, f: (b: User) => number) => Equivalence.Equivalence<User> (+1 overload)
mapInput(
10
  import Equivalence
Equivalence.const number: Equivalence.Equivalence<number>
number, // Base equivalence for comparing numbers
11
  ((parameter) user: User
user: interface User
User) => (parameter) user: User
user.(property) User.id: number
id // Function to extract the id from a User
12
)
13

14
// Compare two User objects: they are equivalent if their ids are the same
15
namespace console
var console: ConsoleThe `console` module provides a simple debugging console that is similar to the
JavaScript console mechanism provided by web browsers.

The module exports two specific components:

* A `Console` class with methods such as `console.log()`, `console.error()` and `console.warn()` that can be used to write to any Node.js stream.
* A global `console` instance configured to write to [`process.stdout`](https://nodejs.org/docs/latest-v22.x/api/process.html#processstdout) and
[`process.stderr`](https://nodejs.org/docs/latest-v22.x/api/process.html#processstderr). The global `console` can be used without importing the `node:console` module.

_**Warning**_: The global console object's methods are neither consistently
synchronous like the browser APIs they resemble, nor are they consistently
asynchronous like all other Node.js streams. See the [`note on process I/O`](https://nodejs.org/docs/latest-v22.x/api/process.html#a-note-on-process-io) for
more information.

Example using the global `console`:

```js
console.log('hello world');
// Prints: hello world, to stdout
console.log('hello %s', 'world');
// Prints: hello world, to stdout
console.error(new Error('Whoops, something bad happened'));
// Prints error message and stack trace to stderr:
//   Error: Whoops, something bad happened
//     at [eval]:5:15
//     at Script.runInThisContext (node:vm:132:18)
//     at Object.runInThisContext (node:vm:309:38)
//     at node:internal/process/execution:77:19
//     at [eval]-wrapper:6:22
//     at evalScript (node:internal/process/execution:76:60)
//     at node:internal/main/eval_string:23:3

const name = 'Will Robinson';
console.warn(`Danger ${name}! Danger!`);
// Prints: Danger Will Robinson! Danger!, to stderr
```

Example using the `Console` class:

```js
const out = getStreamSomehow();
const err = getStreamSomehow();
const myConsole = new console.Console(out, err);

myConsole.log('hello world');
// Prints: hello world, to out
myConsole.log('hello %s', 'world');
// Prints: hello world, to out
myConsole.error(new Error('Whoops, something bad happened'));
// Prints: [Error: Whoops, something bad happened], to err

const name = 'Will Robinson';
myConsole.warn(`Danger ${name}! Danger!`);
// Prints: Danger Will Robinson! Danger!, to err
```
console.(method) Console.log(message?: any, ...optionalParams: any[]): voidPrints to `stdout` with newline. Multiple arguments can be passed, with the
first used as the primary message and all additional used as substitution
values similar to [`printf(3)`](http://man7.org/linux/man-pages/man3/printf.3.html)
(the arguments are all passed to [`util.format()`](https://nodejs.org/docs/latest-v22.x/api/util.html#utilformatformat-args)).

```js
const count = 5;
console.log('count: %d', count);
// Prints: count: 5, to stdout
console.log('count:', count);
// Prints: count: 5, to stdout
```

See [`util.format()`](https://nodejs.org/docs/latest-v22.x/api/util.html#utilformatformat-args) for more information.
log(const equivalence: Equivalence.Equivalence
(self: User, that: User) => boolean
equivalence({ (property) User.id: number
id: 1, (property) User.name: string
name: "Alice" }, { (property) User.id: number
id: 1, (property) User.name: string
name: "Al" }))
16
// Output: true

The Equivalence.mapInput function takes two arguments:

The existing Equivalence you want to use as a base (Equivalence.number in this case, for comparing numbers).
A function that extracts the value used for the equivalence check from your data structure ((user: User) => user.id in this case).