Swift Custom Operators for Mathematical Notation

Related tags

Math swift playground math notation operator
Overview

Euler

Build Status License Swift Version

Euler uses custom operators in the "Math Symbols" character set to implement functions using traditional mathematical notation.

Please keep in mind that this is not intended or recommended for production. Custom operators of any breed are ripe for misuse and abuse, and should be used with as much care and caution as you would something like method swizzling or complex macros.

Euler is much better-suited to a Playground, where it could be used for teaching and learning logic and mathematics using a more vernacular notation.

Euler is named after Leonhard Euler, the Swiss mathematician credited for the popularization of modern mathematical notation such as the Greek letters Σ for summation & π for the ratio of a circle's circumference to its diameter, the letters e to denote the base of the natural logarithm & i to denote the imaginary unit, sin & cos for trigonometric functions, and f(x) to denote the function f with argument x.

Example Usage

import Foundation
import Euler
import PlaygroundSupport

𝑒 // 2.718281828459045

¬true // false

3 × 4 // 12

let prime = [2, 3, 5, 7, 11]
let fibonacci = [1, 1, 2, 3, 5, 8, 13]
prime ∩ fibonacci // {2, 3, 5}

∑[1, 2, 3, 4, 5] // 15

[1, 2] ⋅ [3, 4] // 11

7 ≠ 9 // true

var f: (Double) -> Double = sin
let g: (Double) -> Double = cos

for x in stride(from: 0, to: 4 * π, by: π / 8) {
    (f ∘ g)(x) // ∿∿∿
}

(f′)(π) // -1

Inventory

Mathematical Constants

Logic

Arithmetic

Sets

Sequences

Vectors

Comparison

Calculus

Functions

License

MIT

Contact

Mattt (@mattt)

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Comments
  • `SignedInteger & UnsignedInteger` is probably the wrong bounds

    `SignedInteger & UnsignedInteger` is probably the wrong bounds

    What I assume was meant was one of (the non-existent) P | Q, duplicating the functions for SignedInteger and UnsignedInteger separately, or use BinaryInteger.

    This is because no type does, should, or is semantically permitted to conform to both SignedInteger & UnsignedInteger.

    opened by Dante-Broggi 1
  • Update for Swift 2.0

    Update for Swift 2.0

    This updates Euler for Swift 2.0, converting collection function calls to methods, and lets the function composition operator work on functions with different parameter and return types, so you can compose Double -> Int with Int -> String, yielding a Double -> String function.

    opened by natecook1000 1
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