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Tue Sep 18 15:18:56 PDT 2007


    An Overview of the MATHS Notation

      This document

      [ notn_00_README.html ]

      Quick Introduction

      [ into_characters.html ]

      A Lexicon

      [ 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.


        [ notn_13_Docn_Syntax.html ]


        [ notn_14_Docn_Semantics.html ]

        Naming pieces of Documentation

        [ notn_15_Naming_Documentn.html ]

        Re-using Documentation

        [ notn_4_Re_Use_.html ]


        [ notn_3_Conveniences.html ]

        Classification and Ontologies

        [ notn_16_Classification.html ]


        [ notn_14_Docn_Semantics.html ]

      . . . . . . . . . ( end of section Documentation in MATHS) <<Contents | End>>

      Structure of a Document

      [ notn_2_Structure.html ]


      [ 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 ]

    Notes on the Underlying Logic of MATHS

    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

  1. STANDARD::= See http://www.csci.csusb.edu/dick/maths/math_11_STANDARD.html


  2. 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).
  3. given::reason="I've been told that...", used to describe a problem.
  4. given::variable="I'll be given a value or object like this...", used to describe a problem.
  5. goal::theorem="The result I'm trying to prove right now".
  6. goal::variable="The value or object I'm trying to find or construct".
  7. 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.
  8. hyp::reason="I assumed this in my last Let/Case/Po/...".
  9. QED::conclusion="Quite Easily Done" or "Quod Erat Demonstrandum", indicates that you have proved what you wanted to prove.
  10. QEF::conclusion="Quite Easily Faked", -- indicate that you have proved that the object you constructed fitted the goal you were given.
  11. RAA::conclusion="Reducto Ad Absurdum". This allows you to discard the last assumption (let) that you introduced.