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# Introduction to MATHS

## Why

This set of notes gives you a way to prepare formal or mathematical statements in ASCII. MATHS is very simple. It relies on smart interpreters to render it for presentation and analysis - there is a prototype tool for producing HTML for example. There experiemntal searching tools for it.

If you want an easy to learn technique and do not need complex mathematical formula, but you do want to structure your document and incclude some formulae, then MATHS may help you.

## Sample

` 		. Subsection heading`
` 		paragraph...`

` 		paragraph...`
` 		. Subsection heading`
` 		paragraph...`

` 		paragraph...`
Formal Parts
` 		 defined_term::=expression`
` 			formula`
` 		(Evidence)|- (label): Conclusion`
` 		.See Universal_Resource_Locator`
` 			... \$term ...`
Structures
` 		.Set`
` 			item`
` 			item`
` 		.Close.Set`

` 		.Box`
` 			item`
` 			item`
` 		.Close.Box`

` 		.Open Section`
` 		paragraph...`

` 		paragraph...`

` 		.Close Section`
Logical Net of pieces and properties
` 		.Net`
` 			item`
` 			item`
` 		.Close.Net`
Experiment with Some Assumptions
` 		.Let`
` 			Assumptions`
` 			Derived formulae`
` 		.Close.Let`
` 		()|- Conclusion`

## Introduction

As a rule MATHS documents have definitions, declarations, assumptions, and theorems.
` 	::=	Indicates a definition (like in BNF and EBNF)`
` 	::	Indicates a declaration`
` 	|-	Indicates a theorem, axiom or other assertion.`
The definitions, declarations, and formulae (quoted, proved, or unproven) are surrounded by comments. This should be informal and help the reader understand what is going on.

A document is often split up into sections. This is done by directives. A directive starts with a period(.) as the first character in a line. Sections can be further split up into subsections. Ultimately a piece of documentation is a series of paragraphs(separated by blank lines), Definitions and declarations (see above), and formulae (Starting with 'For' or indented one or more tapbs or spaces. Some sections can indicate a prefered format: Set, Box, etc.

Any collection of definitions, declarations, etc can be bracketed together and given a name using this syntax:

`	NAME::=Net{`
`		Any documentation`
`	}=::NAME.`
There is an alternative syntax:
`	NAME::=following.`
` 	.Net`
`		Any documentation`
`	.Close.Net`
These are just definitions, linking a NAME to a meaning. The meaning in this case being the contents. The NAME can the be used both formally and informally elsewhere to refer to the contents. The word "Net" was chosen because it is a short English word indicating a collection of interconnected objects. The word "Web" is already in use in computing for interconnected texts. A net is for interconnected ideas. Alternative forms include unordered Sets, Boxes, arguments (Lets), and Tables.

Nets are a way of defining record structures, sets and classes of objects: [ intro_records.html ]

The raw form of MATHS uses simple notations to show structure and links:

` 	.Open Header`
` 	section`
` 	.Close Header`
Sections can be nested. A section can be made of simple headers and paragraphs.
` 	. Header2`
` 	paragraph`

` 	paragraph`
` 	...`

Cross references are shown like this

` 	.See NAME`
`		where NAME is defined to be a "Net{.....}"`
`			or any labeled formula`
` 	.See Header`
`		where Header is any section header in the file`
` 	.See Any Universal Resource locator`
`		proticol://host/path/file#anchor`

The raw (foo.mth) from is translated to the WWW form (foo.html) automatically by the UNIX script [ mth2html ] that in turn needs a compiled ANSI C program [ ascii2html.c ] to handle the character conversions.

## This Document in MATHS & HTML

The raw form of this document is in [ intro_documentation.mth ] and the WWW form can be seen by viewing the source of this document in your browser options

. . . . . . . . . ( end of section Introduction to MATHS) <<Contents | Index>>