Math Notation, Computer Language Syntax, and the “Form” in Formalism

This page is a index of essays related to {math notations, syntax, formalism, programing languages}. For example, {calculational proofs, automated proof languages, computer algebra systems}.

Introduction: Math Notation, Proof System, Computer Algebra, in One Language

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
• Pattern Matching vs Grammar Specification
• Logical Operators, Truth Table, Unicode
• What is Function, What is Operator?
• What is the Difference Between BNF, EBNF, ABNF?
• 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

• Abuse of Math Notation
• The Problems of Traditional Math Notation
• The TeX Pestilence: Why TeX LaTeX Sucks
• Math Typesetting, Mathematica, MathML
• Tools to Display Math on Web

• A Notation for Plane Geometry

• Math Writing Style: Use of the Term “Linear Operator” vs “Linear Function”

• Modeling Math Problem Into a Question in Formal Language

Unicode

• Unicode: Math Symbols π² ∞ ∫
• Unicode: Arrows → ➵ ➛ ➲ ➤
• Unicode: Brackets, Quotes 「」【】《》
• Unicode: Math Font ℤ

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

• Importance of Terminology's Quality in Computer Languages
• Object Oriented Programing (OOP) Jargons and Complexities
• Official Java Tutorial on Interface, the Inanity
• Jargons of Software 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 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)

misc

Mathematical Notation: Past and Future

Reference

• 〔Mathematica Notation: Past and Future 2000-10-20 By Stephen Wolfram. At http://www.stephenwolfram.com/publications/mathematical-notation-past-future/ , accessed on 2015-09-30〕
• Functional Mathematics 2010-12-18 By Raymond Boute. At http://www.funmath.be/
• Formalized Mathematics 1996-08-13 By John Harrison. At http://www.rbjones.com/rbjpub/logic/jrh0100.htm
• How Computing Science created a new mathematical style By Edsger W. Dykstra (EWD 1073) 1990-12-30 By Edsger W Dijkstra. At EWD1073.html
• Under the spell of Leibniz's dream 2000-11-19 By Edsger W Dijkstra. At http://www.cs.utexas.edu/users/EWD/transcriptions/EWD12xx/EWD1298.html
• Abuse of notation
• Formal system