Math Notations, Computer Languages, and the “Form” in Formalism

Xah Lee, 2009-08-30

This page is a index of essays on subjects of math notations, syntax, formalism, in programing languages and math. For example, calculational proofs and automated proof languages. For latest articles, subscribe: Xah's Math Blog, Xah's Programing Blog.

Main introduction of the issues: Math Notations, Computer Languages, and the “Form” in Formalism

Notations, Syntax, Logicism, Symbols

• The Codification of Mathematics
• What is the Difference of Symbolic Logic System, Hilbert's Formalism, Russell's Logicism, Axiomatic System?
• State of Theorem Proving Systems 2008
• Logical Operators, Truth Table, Unicode
• What's Function, What's Operator?
• Pattern Matching vs Lexical Grammar Specification
• Fundamental Problems of Lisp (see section 1, on the importance for regularity of syntax)
• The Concepts and Confusions of Prefix, Infix, Postfix and Fully Functional Notations

• The Problems of Traditional Math Notation
• The TeX Pestilence (the problems of TeX/LaTeX)
• The Moronicities of Typography
• Math Typesetting, Mathematica, MathML
• Tools to Display Math on Web

• A Notation for Plane Geometry

• Modeling Math Problem Into a Question in Formal Language

Unicode

• Math Symbols in Unicode
• Arrows in Unicode
• Matching Brackets in Unicode
• Math Font, Unicode, Gothic Letters, Double Struck, 𝔄 𝔅 ℭ

Jargons

Math

• Math Terminology and Naming of Things
• Math Jargons Explained
• Politics and the English Language, 1946, by George Orwell.

Harm Of Bad Terminologies In Computing Languages

• The Importance of Terminology's Quality In A Computer Language
• What are OOP's Jargons ＆ Complexities?
• Java's Abuse of the Jargon “Interface” and API
• Jargons of Info Tech Industry
• The Term Currying in Computer Science
• Why You should Not Use the Jargons lisp-1 lisp-2
• The Jargon “Tail Recursion”
• What is Closure in a Programing Language?
• Jargons and High Level Languages (unpolished essay)
• Why You Should Avoid the Jargon Tail Recursion
• I Can Not Find A Word Better Than “CAR”

Harm of Mixing Concept of Syntax and Formatting

• The Harm of hard-wrapping Lines (harm of confusing syntax with formatting)
• Tabs versus Spaces in Source Code (harm of treating syntax as formatting instead of syntax)

Applications of Regular Syntax

• A Text Editor Feature: Syntax Tree Walk (application of syntax)
• A Simple Lisp Code Formatter (application of syntax regularity)

References

• Mathematica Notation: Past and FutureMathematica Notation: Past and Future 2000-10-20 By Stephen Wolfram. @ www.stephenwolfram.com…
• Functional Mathematics 2010-12-18 By Raymond Boute. @ www.funmath.be…
• Formalized Mathematics 1996-08-13 By John Harrison. @ www.rbjones.com…
• How Computing Science created a new mathematical style 1990-12-30 By Edsger W Dijkstra. @ EWD1…
• Under the spell of Leibniz's dream 2000-11-19 By Edsger W Dijkstra. @ www.cs.utexas.edu…
• Abuse of notation
• Formal system