Immutability and Mathematical Notation

Mathematical notation relies on immutability.

If you have immutability, you can replace patterns with impunity.

Note that I’m not describing all of mathematics, just the notation part1.

Search and Replace

The notation part of mathematics boils down to a simple set of principles

  1. find a pattern
  2. replace the pattern
  3. repeat.


Word® does search and replace.

Can Word® do mathematical manipulation for us?

Recursive Search and Replace

It is easier if your searcher-and-replacer works recursively.

REGEX is flat (non-recursive).

Parsers are recursive.


PEG1 does recursive parsing and is “better” than REGEX in that regard.

UNIX® Immutability

Immutability is, actually, isolation.

You can re-arrange things if you can guarantee that rearranging doesn’t cause unintended side-effects.

UNIX® provides isolation.

Using C, yet.

UNIX® commands are completely stand-alone. If you change the source for cat.c, the operation of sed.c doesn’t change.

UNIX® creates isolation at runtime by piping (isolated) commands together.

What’s Inside?

Who cares what’s inside?

Do we care if a UNIX® command is written in C or in Haskell?


We only care that the commands are isolated from each other. We can make the internals of the commands better, later.

Achieving isolation - immutability - at compile-time is just icing-on-the-cake (aka optimization).

See Also

Table of Contents

  1. Ohm-JS is currently my favourite form of PEG.  2