Mathematics consists of 2 main parts:

  1. the mechanics of manipulating symbols
  2. the hard-won knowledge of what works and what doesn’t (algorithms, laws, principles, etc.).

Part 1 is simple text manipulation.

Mathematics was invented when the only tools were pen and paper.

The UNIX people almost got part 1 by producing a set of utilities for manipulating symbols in the form of text.

The “problem” with the UNIX notation was that text was only text up to end-of-line.

Newline is special in UNIX

Lisp almost got part 1, except that the symbols must be arranged as lists (CONS cells).

New Math Manipulation

We need a way to manipulate symbols in a way that doesn’t make newlines and CONS cells special.

Computers like to think in terms of bytes.

PEG

How can we manipulate raw bytes?

Parsers.

PEG parsing makes parsing easier.

PEG is a DSL for parsing.

Ohm-JS is improved PEG.

Diagrams

Why stop at characters?

We can manipulate diagrams using computers.

How can we draw diagrams and then manipulate them?

A beginning might be:

  • draw.io
  • SVG
  • d2f.

See Also

d2f - Diagram to Text Converter
Ohm-JS (see, also, my articles on PEG and Ohm-JS)

See Also

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