Virtual Library
Formal Methods
Z Notation
Proposed extensions in HTML for Z
This document includes information on the display of the
Z notation in
World Wide Web pages and
hyperlinks to related resources.
Note:
The Z characters below will not display correctly on
standard HTML browsers like
Netscape although a number of
ISO symbols are supported.
Mathematical extensions to HTML
This section summarizes
early work undertaken by
Phillip M. Hallam-Baker
at
CERN
on
mathematical extensions to HTML including
support for Z by
WWW browsers.
Special Characters
The following characters are required to typeset Z but are not present
in the HTML entity sets. Characters not present in the
SGML
ISO entity sets are marked *.
- Blackboard bold characters.
&bbF;* &bbN;* &bbP;* &bbZ;*
- Maplet
↦
- Functions
↣ ↠ ⤖
- Partial Functions
↛ &nrarrtl; &nRarr;
- Finite Functions
&Nrarr; &Narrtl;
- Harpoons
↿ ↾
- Relational Image
&Lpar; &Rpar;
- Bag display
&Lbrack; &Rbrack;
- Sequence display
〈 〉
- Binding Formation
⟪ ⟫
- Distributed Union and intersection
∪ ∩
- Semantic and Syntactic turnstiles
⊧ ⊢
- Domain and Codomain Restriction and and anti restriction
◃ ▹
&triangleleftbar; &trianglerightbar;
Free Types
[Name, Date]
Schemas
-------------------------
|AddBirthday
|Delta BirthdayBook
|name? : Name
|date? : Date
|---
|name? ∉ known
|birthday' = birthday ∪ {name ↦ date}
-------------------------
Generic Schemas
===[X,Y]=================
| _ ⊕ _ : (X ↛ Y) × (X ↛ Y) → (X ↛ Y)
|---
|∀ f, g: X ↛ Y •
| f ⊕ g = ((dom g) &trianglerightbar; f) ∩ g
-------------------------
Axiomatic Descriptions
|Declaration
|--------
|Predicate
(La)TeX links
Of related interest:
HyperTeX, a defacto standard for inclusion of hyperlink
information in TeX (and LaTeX) documents.
Other links
-
Z Browser Plug-in for viewing Z using WWW browsers such as
Netscape Navigation under
Windows 95 and Windows NT, and the associated
Z Browser for use under Windows on PCs.
-
Math markup in HTML information from the
W3C World Wide Web Consortium.
-
Character entity references for symbols, mathematical symbols,
and Greek letters in the
HTML 4.0 specification.
-
Z on the Web using Java:
Presentation of Z specifications on the World Wide Web
using
Java, a student project by
David Chippington,
Department of Computer Science,
The University of Reading,
supervised by
Jonathan Bowen.
-
Implementing displets by
Fabio Vitali et al.
See
examples,
including Spivey's
Birthday Book.
-
HTML Math Overview from
W3C, including
Mathematical Markup Language (MathML),
based on
XML.
See
Amaya, W3C's Browser/Editor
including a
demonstration of MathML.
See also
XML FAQ including
Can I do mathematics using XML?.
-
IDVI, a Java DVI viewer,
(see
demo of IDVI features)
and
nDVI,
a Unix plug-in DVI viewer.
-
WebEQ: Java applets for mathematics in Web pages.
(Slow!)
-
The MINSE project: mathematical expressions in Web pages
using a CGI program to generate GIF images.
Works well with
small mathematical expressions.
-
Mathematical symbols as GIF images available as part of the
MacTutor History of Mathematics archive.
-
Webify PostScript to HTML/JPEG image converter.
See a Z example:
Undefinedness in Z
(example
slide).
Download Webify C source for Unix.
-
IBM techexplorer Hypermedia Browser
a plug-in to display documents marked up
using a well-defined subset of TeX and LaTeX,
including mathematics.
(Windows 95/NT and IBM/Sun/SGI Unix.)
-
MapleExplorer:
techexplorer and
Maple V.
Supports a subset of
MathML 1.0.
-
Swift, an equation editor in Java.
-
Dynamic Font Support from
Netscape.
See also
Bitstream dynamic fonts, including
maths equation example.
-
Greek font help, if you like Greek symbols.
-
Comparative Review of World-Wide-Web Mathematics Renderers
by Ian Hutchinson. Covers Netscape, Amaya and e-Lite.
Last updated
9 February 2000.
Page maintained by
Jonathan Bowen.