Function-category.js

class Func {
  constructor(f) {
    // this.run = f
    this.run = x => f(x)
    
    // this :: Cat (x ↣ y)
    // Cat (y ↣ z) -> Cat (x ↣ z)
    this.pipe = g => new Func(x => g.run(this.run(x)))
    
    // utility function that pipes Func to a normal function
    // this :: Cat (x ↣ y)
    // (y -> z) -> Cat (x ↣ z)
    this.pipeTo = g => new Func(x => g(this.run(x)))
  }
}
// Cat (x ↣ x)
Func.id = new Func(x => x)

Usage example: https://jsbin.com/kecoxa/edit?js,console

const operation = new Func(x => x + 1)
  .pipe(new Func(Math.sqrt))
  .pipe(new Func(x => x * 6))
  .pipeTo(x => x - 1)

const result = operation.run(48) // = 41