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

Xah Lee, 2009-08

This page is a index of essays on subjects of math notations, syntax, formalism, in programing languages and math.

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

Notations

• 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

• The Problems of Traditional Math Notation
• The TeX Pestilence (or, the problems of TeX/LaTex)
• The Moronicities of Typography
• the Moronicity of the Expositions of Common Mathematicians (rant)
• Math Typesetting, Mathematica, MathML

• A Notation for Plane Geometry

• 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

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 and Complexities?
• Java's Abuse of the Jargon “Interface” and API
• Jargons of Info Tech Industry
• The Term Currying in Computer Science
• What is Currying in a Computer Language?
• Why You should Not Use The Jargon Lisp1 and Lisp2
• 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, at http://www.stephenwolfram.com/publications/recent/mathml/index.html.
• 〈Functional Mathematics〉, by Raymond Boute, 2006. http://www.funmath.be/
• 〈Formalized Mathematics〉, by John Harrison, 1996-08-13. http://www.rbjones.com/rbjpub/logic/jrh0100.htm
• 〈How Computing Science created a new mathematical style〉 (1990), by Edsger W Dijkstra. EWD1073
• 〈Under the spell of Leibniz's dream〉 (2000), by Edsger W Dijkstra. EWD1298
• Abuse of notation
• Formal system