Piping and Function Composition Equivalence

By Xah Lee. Date: . Last updated: .

Had a divine revelation, that is, how pipe operator is equivalent to function composition.

Here's background.

Pipe operator, e.g. in unix | or as dot operator in ruby etc, is very useful.

In general, operators can be considered as a function. (in many function languages, operators can be used with function call syntax.)

I want to write a pipe function in my JavaScript library, e.g. Pipe(x,f,g):=g(f(x))

But there's also function composition, i.e.

pipe(x,f,g) == compose(f,g)(x)

function compose is also quite useful. But, pipe and compose seems very similar. I wish not to have to write both, because it seems redundant.

(Note, between pipe and function composition, pipe is far more useful.)

The Problem

So, the problem is, is there a way to consider pipe and function composition as equivalent , so that you can implement just one function in a programing language library, and it can be practically use for both piping and compose?

Note: pipe, is mathematically the same as nested function call.

Thought for 1 hour, and found an answer that's mathematically sane!

Solution

the math sane answer is, just write a function composition function. Allow each argument to be a non-function e.g. 3. When a non-function argument is encountered, treat it as constant function, i.e. 3 is a function that always returns 3. This way, pipe(x,f,g) is same as compose(g,f,x) .

So, when x is a non-function value such as 3, the whole compose(g,f,x) also returns a non-function value.

Note, this works fine in languages that's not strictly typed. compose(g,f,x) return a function or a value, depending on whether x is a function or a value.

But in strictly typed languages, you may not have a return value whose type depends on input parameters. But such languages have ways to resolve that. e.g. a type defined to be or.

#haskell #ocaml #clojure

treating data (such as number) as (constant) function is a powerful idea. Because it lets you treat function and data in a uniform way.

Unix Pipe, Dot Notation, Postfix Notation

  1. OOP Dot Notation, Dot Before Data or After?
  2. OOP Dot Notation, is Object Data or Namespace?
  3. Unix Pipe as Functional Language
  4. Method Chaining, Postfix Operator, and OOP
  5. JavaScript Language Design: Dot Notation be Namespace or Object System
  6. Ontology of Postfix Notation, Method Chaining, and Unix Pipe
  7. Piping and Function Composition Equivalence

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