An Overview of the MATHS Notation
This document
[ notn_00_README.html ]
Quick Introduction
[ into_characters.html ]
[ notn_10_Lexicon.html ]
Names in MATHS
[ notn_11_Names.html ]
Expressions in MATHS
[ notn_12_Expressions.html ]
Documentation in MATHS
A document is made of pieces of documentation.... of
varying degress of formallity.
Syntax
[ notn_13_Docn_Syntax.html ]
Semantics
[ notn_14_Docn_Semantics.html ]
Naming pieces of Documentation
[ notn_15_Naming_Documentn.html ]
Re-using Documentation
[ notn_4_Re_Use_.html ]
Conveniences
[ notn_3_Conveniences.html ]
Classification and Ontologies
[ notn_16_Classification.html ]
[ notn_14_Docn_Semantics.html ]
. . . . . . . . . ( end of section Documentation in MATHS) <<Contents | End>>
[ notn_2_Structure.html ]
Formatting
[ notn_5_Form.html ]
Documenting Evidence
[ notn_8_Evidence.html ]
Abstract Algebra in MATHS
[ notn_6_Algebra.html ]
[ notn_7_OO_vs_Algebra.html ]
Design for a Lexical Analyser
[ notn_dlex.d.html ]
Notes on MATHS Notation
Special characters are defined in
[ intro_characters.html ]
that also outlines the syntax of expressions and a document.
Proofs follow a natural deduction style that start with
assumptions ("Let") and continue to a consequence ("Close Let")
and then discard the assumptions and deduce a conclusion. Look
here
[ Block Structure in logic_25_Proofs ]
for more on the structure and rules.
The notation also allows you to create a new network of variables
and constraints. A "Net" has a number of variables (including none) and
a number of properties (including none) that connect variables.
You can give them a name and then reuse them. The schema, formal system,
or an elementary piece of documentation starts with "Net" and finishes "End of Net".
For more, see
[ notn_13_Docn_Syntax.html ]
for these ways of defining and reusing pieces of logic and algebra
in your documents. A quick example: a circle = Net{radius:Positive Real, center:Point}.
For a complete listing of pages in this part of my site by topic see
[ home.html ]
The notation used here is a formal language with syntax
and a semantics described using traditional formal logic
[ logic_0_Intro.html ]
plus sets, functions, relations, and other mathematical extensions.
For a more rigorous description of the standard notations
see
- STANDARD::= See http://www.csci.csusb.edu/dick/maths/math_11_STANDARD.html
Glossary
- above::reason="I'm too lazy to work out which of the above statements I need here", often the last 3 or 4 statements.
The previous and previous but one statments are shown as (-1) and (-2).
- given::reason="I've been told that...", used to describe a problem.
- given::variable="I'll be given a value or object like this...", used to describe a problem.
- goal::theorem="The result I'm trying to prove right now".
- goal::variable="The value or object I'm trying to find or construct".
- let::reason="For the sake of argument let...", introduces a temporary hypothesis that survives until the end of the surrounding "Let...Close.Let" block or Case.
- hyp::reason="I assumed this in my last Let/Case/Po/...".
- QED::conclusion="Quite Easily Done" or "Quod Erat Demonstrandum", indicates that you have proved what you wanted to prove.
- QEF::conclusion="Quite Easily Faked", -- indicate that you have proved that the object you constructed fitted the goal you were given.
- RAA::conclusion="Reducto Ad Absurdum". This allows you to discard the last
assumption (let) that you introduced.