This table shows information about the rendering of the ProofPower special characters in HTML.

ProofPower uses a special 8-bit character set in which the characters below 128 are ascii and those above are a special encoding of a suitable selection of logical or mathematical characters, many of them to represent the characters used in the Z specification language.

ProofPower comes with support for editing documents encoded in this way suitable for providing specification and proof scripts which can be processed by ProofPower, and for processing these documents using LaTeX to give postscript or PDF files. It does not come with any support for rendering such documents in HTML. The RBJones.com web site does make use of documents which are prepared in XML for processing by ProofPower and for presentation via HTML. This was a hack supporting only the subset of characters which happen to have been needed for the material used at RBJones.com, rather than a full implementation of HTML support for ProofPower sources, however, it is gradually getting more comprehensive.

The following table has been prepared to assist in occasional enhancement of this hack and shows which of the ProofPower special characters can be rendered in HTML by each of three methods.

The three methods are:

It would also be possible to select characters from named fonts, but success would depend on what fonts were available on the machine on which the browser was running, so I didn't think this line worth investigating. The present translation algorithms use the first method whenever an image is available, because the other two methods work only on some browsers. If no image is available the bald UNICODE character code is used, because inspection of results on a random selection of browsers suggests that the UNICODE character codes are implemented whenever the corresponding HTML4 entity is but not always vice-versa. Below is also presented information from pp-symbol.ent which consists of the entitiy definitions required for processing XML files including ProofPower source used to generate this web site.
ProofPower Special Character Renderings
codegifentityunicode
200subesube⊆2286⊆subset of or equal to
201! ! 2A65⩥range antirestriction
202! ! 228E⊎multiset union
203dsu! 1D54C𝕌double struck U
204udeltaDeltaΔ0394ΔGreek capital delta
205! ! ! [not in use?]
206upsiPhiΦ03A6ΦGreek capital phi
207utauGammaΓ0393ΓGreek capital gamma
210! ! ! bottom left corner
211! ! 22CE⋎curly logical or
212! ThetaΘ0398Θgreek capital theta
213! ! ! distributed concatenation
214ulambdaLambdaΛ039BΛgreek capital lambda
215isinisin∈2208∈element of
216notinnotin∉2209∉not an element of
217urarrtlRarrtl⤖2916⤖bijection space constructor
220upiPiΠ03A0Πgreek capital letter pi
221qqml! ! ML quote (left ceiling?)
222! ! 25B7▷range restriction (or x22B3 ⊳?)
223usigmaSigmaΣ03A3Σgreek capital letter sigma
224qqco! ! type quote (top left crop?)
225! upsihϒ03D2ϒgreek upsilon (with hook?)
226dsb! 1d539𝔹double struck B
227uomegaOmegaΩ03A9Ωgreek capital letter omega
230uchiXiΞ039EΞgreek capital letter Xi
231! PsiΨ03A8Ψgreek capital letter Psi
232emptyempty∅2205∅empty set
233! ! 22CF⋏curly logical and
234! ! 2550═bold horizontal double line
235! ! ! top left corner with double horizontal
236nnrarrtl! 2915⤕finite injection space constructor
237nnrarr! 21FB⇻finite function space constructor
240subsub⊂2282⊂subset of
241capcap∩2229∩intersecion
242! rang⟩232A〉right angled bracket (or x3009 〉?)
243! ! 2296⊖circled minus
244equivhArr⇔21D4⇔equivalent to
245lcap! 22C2⋂n-ary intersection (large cap)
246! ! ! defined as (equal + hat)
247! lang⟨2329〈left angled bracket (or x3008 〈?)
250! ! 2987⦇left half moon bracket
251! ! 2988⦈right half moon bracket
252leftrightarrowharr↔2194↔relation space constructor
253! ! 2295⊕relational override (o + +)
254qqtel! 231C⌜top left quine corner
255rarrrarr→2192→rightwards arrow
256qqter! 231D⌝top right quine corner
257dsr! 211Dℝthe set of real numbers
260! ! 220E∎end of proof (black box)
261andand∧2227∧logical and
262oror∨2228∨logical or
263notnot¬00AC¬not
264ruarrrArr⇒21D2⇒implies
265forallforall∀2200∀universal quantification
266existexist∃2203∃existential quantification
267bullbull•2022•bullet (or x2981 ⦁?)
270crosscross✗00D7×runic cross punctuation
271! ! 24C8Ⓢcircled latin capital letter s
272! ! ! type constraint
273! fwsemico&fwsemico;2A1F⨟Z schema composition (or x2A3E ⨾?)
274lele≤2264≤less than or equal to
275nene≠2260≠not equal to
276gege≥2265≥greater-than or equal to
277dss! 1D54A𝕊double struck S
300cupcup∪222A∪union
301alphaalphaα03B1αsmall greek alpha
302betabetaβ03B2βsmall greek beta
303! ! ! square less than or equal
304deltadeltaδ03B4δsmall greek delta
305epsilonepsilonε03B5εsmall greek epsilon
306phiphiφ03C6φsmall greek phi
307! gammaγ03B3γsmall greek gamma
310! etaη03B7ηsmall greek eta
311iotaiotaι03B9ιsmall greek iota
312thetathetaθ03B8θsmall greek theta
313! kappaκ03BAκsmall greek kappa
314lambdalambdaλ03BBλsmall greek lambda
315mumuμ03BCμsmall greek mu
316! nuν03BDνsmall greek nu
317nurarr! 2900⤀partial surjection space constructor
320pipiπ03C0πsmall greek pi
321! chiχ03C7χsmall greek chi
322! rhoρ03C1ρsmall greek rho
323! sigmaσ03C3σsmall greek sigma
324tautauτ03C4τsmall greek tau
325! ! 03C5υsmall greek upsilon?
326dsc! 2102ℂdouble struck C
327omegaomegaω03C9ωomega
330! xiξ03BEξsmall greek xi
331! psiψ03C8ψsmall greek psi
332! zetaζ03B6ζsmall greek zeta
333! ! ! left indexing bracket
334! ! 2577╷vertical bar
335! ! ! right indexing bracket
336lcup! 22C3⋃distributed ("n-ary") union
337nrightarrow! 21F8⇸partial function space constructor (or x219B ↛?)
340rarrtl! 21A3↣injection space constructor
341! ! 2A64⩤domain co-restriction
342bottomperp⊥22A5⊥bottom or up tack
343! lArr⇐21D0⇐left double arrow
344! sup⊃2283⊃superset
345! supe⊇2287⊇superset or equal
346fset! 1D53D𝔽finite_subsets *fset
347! ! 2197↗superscript, north east arrow
350! ! 2198↘subscript, south east arrow
351equiv2equivalent&equivalent;2261≡*ppequiv
352! sboth&sboth;! endsubsupscript *ppesss
353! ! 2040⁀concatenate, slur, character tie
354! ! 21BF↿sequence extraction, up harpoon with barb left
355mapsto! 21A6↦maplet, rightward arrow from bar
356natnat&nat;2115ℕnatural_number *ppnat
357urarrRarr↠21A0↠surjection
360pset! 2119ℙpowerset (entity should be dsP?)
361! ! ! leftquinecornerz *qqtelz
362dr! 25C1◁domain restriction (or x22B2 ⊲?)
363dsq! 211Aℚdouble struck Q
364turnstil! 22A2⊢turnstile (right tack)
365! ! ! [not in use?]
366! ! ! [not in use?]
366! ! ! [not in use?]
371! ! 21BE↾schema projection (or x2A21 ⨡?)
372dsz! 2124ℤset of integers
373! ! ! double left square bracket
374! ! ! horizontal for box
375! ! ! double right square bracket
376nrarrtl! 2914⤔partial injection space constructor
377qqtel! 250F┏box top left corner *qqtel

The following table shows the character entities used in XML source for ProofPower pages on this site. This is in fact the HTML4 entities plus entities for some of the ProofPower symbols which don't appear in HTML4. Not all of these have sensible values, when there is no corresponding UNICODE character or when I just havn't found it yet, and even where I have identified a UNICODE character it is likely not to display correctly in HTML. The ProofPower special entities come first, followed by the HTML4 entities (of which the first is "nbsp").

Listing of Entities in pp-symbol.ent
bbox#x220e∎ black box - end of proof -->
circS#x24c8Ⓢ circled capital S -->
cross#x00d7× circled capital S -->
dr#x22b2⊲ domain restriction -->
cr#x22b3⊳ codomain restriction -->
lcap#x22c2⋂ distributed intersection -->
lcup#x22c3⋃ distributed union -->
mapsto#x21a6↦ maplet or order pair constructor, right arrow from bar -->
qqco#x0020 left quine quote with colon (type quotation) -->
qqml#x0020 left quine quote with ML (ML quotation) -->
qqtel#x231C⌜ left quine quote (term quotation) -->
qqter#x231D⌝ right quine quote (end quotation) -->
turnstil#x22a2⊢ turnstile -->
dsA#x1D538𝔸 double struck capital A -->
dsB#x1D539𝔹 double struck capital B -->
dsC#x2102ℂ double struck capital C (the set of complex numbers) -->
dsF#8230… double struck capital F (finite sets) -->
fset#8230… double struck capital F (finite sets) -->
dsH#x210dℍ double struck capital H (latin capital letter h) -->
nat#x2115ℕ double struck capital N (the set of natural numbers) -->
dsP#x2119ℙ double struck capital P (power set) -->
dsQ#x211aℚ double struck capital Q (the set of rational numbers) -->
dsR#x211dℝ double struck capital R (the set of real numbers) -->
dsS#x1D54A𝕊 double struck capital S -->
dsU#x1D54C𝕌 double struck capital U -->
dsZ#x2124ℤ double struck capital Z (the set of integers) -->
nbsp#160  no-break space = non-breaking space,
iexcl#161¡ inverted exclamation mark, U+00A1 ISOnum -->
cent#162¢ cent sign, U+00A2 ISOnum -->
pound#163£ pound sign, U+00A3 ISOnum -->
curren#164¤ currency sign, U+00A4 ISOnum -->
yen#165¥ yen sign = yuan sign, U+00A5 ISOnum -->
brvbar#166¦ broken bar = broken vertical bar,
sect#167§ section sign, U+00A7 ISOnum -->
uml#168¨ diaeresis = spacing diaeresis,
copy#169© copyright sign, U+00A9 ISOnum -->
ordf#170ª feminine ordinal indicator, U+00AA ISOnum -->
laquo#171« left-pointing double angle quotation mark
not#172¬ not sign = angled dash,
shy#173­ soft hyphen = discretionary hyphen,
reg#174® registered sign = registered trade mark sign,
macr#175¯ macron = spacing macron = overline
deg#176° degree sign, U+00B0 ISOnum -->
plusmn#177± plus-minus sign = plus-or-minus sign,
sup2#178² superscript two = superscript digit two
sup3#179³ superscript three = superscript digit three
acute#180´ acute accent = spacing acute,
micro#181µ micro sign, U+00B5 ISOnum -->
para#182 pilcrow sign = paragraph sign,
middot#183· middle dot = Georgian comma
cedil#184¸ cedilla = spacing cedilla, U+00B8 ISOdia -->
sup1#185¹ superscript one = superscript digit one,
ordm#186º masculine ordinal indicator,
raquo#187» right-pointing double angle quotation mark
frac14#188¼ vulgar fraction one quarter
frac12#189½ vulgar fraction one half
frac34#190¾ vulgar fraction three quarters
iquest#191¿ inverted question mark
Agrave#192À latin capital letter A with grave
Aacute#193Á latin capital letter A with acute,
Acirc#194Â latin capital letter A with circumflex,
Atilde#195Ã latin capital letter A with tilde,
Auml#196Ä latin capital letter A with diaeresis,
Aring#197Å latin capital letter A with ring above
AElig#198Æ latin capital letter AE
Ccedil#199Ç latin capital letter C with cedilla,
Egrave#200È latin capital letter E with grave,
Eacute#201É latin capital letter E with acute,
Ecirc#202Ê latin capital letter E with circumflex,
Euml#203Ë latin capital letter E with diaeresis,
Igrave#204Ì latin capital letter I with grave,
Iacute#205Í latin capital letter I with acute,
Icirc#206Î latin capital letter I with circumflex,
Iuml#207Ï latin capital letter I with diaeresis,
ETH#208Ð latin capital letter ETH, U+00D0 ISOlat1 -->
Ntilde#209Ñ latin capital letter N with tilde,
Ograve#210Ò latin capital letter O with grave,
Oacute#211Ó latin capital letter O with acute,
Ocirc#212Ô latin capital letter O with circumflex,
Otilde#213Õ latin capital letter O with tilde,
Ouml#214Ö latin capital letter O with diaeresis,
times#215× multiplication sign, U+00D7 ISOnum -->
Oslash#216Ø latin capital letter O with stroke
Ugrave#217Ù latin capital letter U with grave,
Uacute#218Ú latin capital letter U with acute,
Ucirc#219Û latin capital letter U with circumflex,
Uuml#220Ü latin capital letter U with diaeresis,
Yacute#221Ý latin capital letter Y with acute,
THORN#222Þ latin capital letter THORN,
szlig#223ß latin small letter sharp s = ess-zed,
agrave#224à latin small letter a with grave
aacute#225á latin small letter a with acute,
acirc#226â latin small letter a with circumflex,
atilde#227ã latin small letter a with tilde,
auml#228ä latin small letter a with diaeresis,
aring#229å latin small letter a with ring above
aelig#230æ latin small letter ae
ccedil#231ç latin small letter c with cedilla,
egrave#232è latin small letter e with grave,
eacute#233é latin small letter e with acute,
ecirc#234ê latin small letter e with circumflex,
euml#235ë latin small letter e with diaeresis,
igrave#236ì latin small letter i with grave,
iacute#237í latin small letter i with acute,
icirc#238î latin small letter i with circumflex,
iuml#239ï latin small letter i with diaeresis,
eth#240ð latin small letter eth, U+00F0 ISOlat1 -->
ntilde#241ñ latin small letter n with tilde,
ograve#242ò latin small letter o with grave,
oacute#243ó latin small letter o with acute,
ocirc#244ô latin small letter o with circumflex,
otilde#245õ latin small letter o with tilde,
ouml#246ö latin small letter o with diaeresis,
divide#247÷ division sign, U+00F7 ISOnum -->
oslash#248ø latin small letter o with stroke,
ugrave#249ù latin small letter u with grave,
uacute#250ú latin small letter u with acute,
ucirc#251û latin small letter u with circumflex,
uuml#252ü latin small letter u with diaeresis,
yacute#253ý latin small letter y with acute,
thorn#254þ latin small letter thorn,
yuml#255ÿ latin small letter y with diaeresis,
quot#34" quotation mark, U+0022 ISOnum -->
gt#62> greater-than sign, U+003E ISOnum -->
apos#39' apostrophe = APL quote, U+0027 ISOnum -->
OElig#338Œ latin capital ligature OE,
oelig#339œ latin small ligature oe, U+0153 ISOlat2 -->
Scaron#352Š latin capital letter S with caron,
scaron#353š latin small letter s with caron,
Yuml#376Ÿ latin capital letter Y with diaeresis,
circ#710ˆ modifier letter circumflex accent,
tilde#732˜ small tilde, U+02DC ISOdia -->
ensp#8194  en space, U+2002 ISOpub -->
emsp#8195  em space, U+2003 ISOpub -->
thinsp#8201  thin space, U+2009 ISOpub -->
zwnj#8204‌ zero width non-joiner,
zwj#8205‍ zero width joiner, U+200D NEW RFC 2070 -->
lrm#8206‎ left-to-right mark, U+200E NEW RFC 2070 -->
rlm#8207‏ right-to-left mark, U+200F NEW RFC 2070 -->
ndash#8211– en dash, U+2013 ISOpub -->
mdash#8212— em dash, U+2014 ISOpub -->
lsquo#8216‘ left single quotation mark,
rsquo#8217’ right single quotation mark,
sbquo#8218‚ single low-9 quotation mark, U+201A NEW -->
ldquo#8220“ left double quotation mark,
rdquo#8221” right double quotation mark,
bdquo#8222„ double low-9 quotation mark, U+201E NEW -->
dagger#8224† dagger, U+2020 ISOpub -->
Dagger#8225‡ double dagger, U+2021 ISOpub -->
permil#8240‰ per mille sign, U+2030 ISOtech -->
lsaquo#8249‹ single left-pointing angle quotation mark,
rsaquo#8250› single right-pointing angle quotation mark,
euro#8364€ euro sign, U+20AC NEW -->
fnof#402ƒ latin small letter f with hook = function
Alpha#913Α greek capital letter alpha, U+0391 -->
Beta#914Β greek capital letter beta, U+0392 -->
Gamma#915Γ greek capital letter gamma,
Delta#916Δ greek capital letter delta,
Epsilon#917Ε greek capital letter epsilon, U+0395 -->
Zeta#918Ζ greek capital letter zeta, U+0396 -->
Eta#919Η greek capital letter eta, U+0397 -->
Theta#920Θ greek capital letter theta,
Iota#921Ι greek capital letter iota, U+0399 -->
Kappa#922Κ greek capital letter kappa, U+039A -->
Lambda#923Λ greek capital letter lamda,
Mu#924Μ greek capital letter mu, U+039C -->
Nu#925Ν greek capital letter nu, U+039D -->
Xi#926Ξ greek capital letter xi, U+039E ISOgrk3 -->
Omicron#927Ο greek capital letter omicron, U+039F -->
Pi#928Π greek capital letter pi, U+03A0 ISOgrk3 -->
Rho#929Ρ greek capital letter rho, U+03A1 -->
Sigma#931Σ greek capital letter sigma,
Tau#932Τ greek capital letter tau, U+03A4 -->
Upsilon#933Υ greek capital letter upsilon,
Phi#934Φ greek capital letter phi,
Chi#935Χ greek capital letter chi, U+03A7 -->
Psi#936Ψ greek capital letter psi,
Omega#937Ω greek capital letter omega,
alpha#945α greek small letter alpha,
beta#946β greek small letter beta, U+03B2 ISOgrk3 -->
gamma#947γ greek small letter gamma,
delta#948δ greek small letter delta,
epsilon#949ε greek small letter epsilon,
zeta#950ζ greek small letter zeta, U+03B6 ISOgrk3 -->
eta#951η greek small letter eta, U+03B7 ISOgrk3 -->
theta#952θ greek small letter theta,
iota#953ι greek small letter iota, U+03B9 ISOgrk3 -->
kappa#954κ greek small letter kappa,
lambda#955λ greek small letter lamda,
mu#956μ greek small letter mu, U+03BC ISOgrk3 -->
nu#957ν greek small letter nu, U+03BD ISOgrk3 -->
xi#958ξ greek small letter xi, U+03BE ISOgrk3 -->
omicron#959ο greek small letter omicron, U+03BF NEW -->
pi#960π greek small letter pi, U+03C0 ISOgrk3 -->
rho#961ρ greek small letter rho, U+03C1 ISOgrk3 -->
sigmaf#962ς greek small letter final sigma,
sigma#963σ greek small letter sigma,
tau#964τ greek small letter tau, U+03C4 ISOgrk3 -->
upsilon#965υ greek small letter upsilon,
phi#966φ greek small letter phi, U+03C6 ISOgrk3 -->
chi#967χ greek small letter chi, U+03C7 ISOgrk3 -->
psi#968ψ greek small letter psi, U+03C8 ISOgrk3 -->
omega#969ω greek small letter omega,
thetasym#977ϑ greek theta symbol,
upsih#978ϒ greek upsilon with hook symbol,
piv#982ϖ greek pi symbol, U+03D6 ISOgrk3 -->
bull#8226• bullet = black small circle,
hellip#8230… horizontal ellipsis = three dot leader,
prime#8242′ prime = minutes = feet, U+2032 ISOtech -->
Prime#8243″ double prime = seconds = inches,
oline#8254‾ overline = spacing overscore,
frasl#8260⁄ fraction slash, U+2044 NEW -->
weierp#8472℘ script capital P = power set
image#8465ℑ black-letter capital I = imaginary part,
real#8476ℜ black-letter capital R = real part symbol,
trade#8482™ trade mark sign, U+2122 ISOnum -->
alefsym#8501ℵ alef symbol = first transfinite cardinal,
larr#8592← leftwards arrow, U+2190 ISOnum -->
uarr#8593↑ upwards arrow, U+2191 ISOnum-->
rarr#8594→ rightwards arrow, U+2192 ISOnum -->
darr#8595↓ downwards arrow, U+2193 ISOnum -->
harr#8596↔ left right arrow, U+2194 ISOamsa -->
crarr#8629↵ downwards arrow with corner leftwards
lArr#8656⇐ leftwards double arrow, U+21D0 ISOtech -->
uArr#8657⇑ upwards double arrow, U+21D1 ISOamsa -->
rArr#8658⇒ rightwards double arrow,
dArr#8659⇓ downwards double arrow, U+21D3 ISOamsa -->
hArr#8660⇔ left right double arrow,
forall#8704∀ for all, U+2200 ISOtech -->
part#8706∂ partial differential, U+2202 ISOtech -->
exist#8707∃ there exists, U+2203 ISOtech -->
empty#8709∅ empty set = null set, U+2205 ISOamso -->
nabla#8711∇ nabla = backward difference,
isin#8712∈ element of, U+2208 ISOtech -->
notin#8713∉ not an element of, U+2209 ISOtech -->
ni#8715∋ contains as member, U+220B ISOtech -->
prod#8719∏ n-ary product = product sign,
sum#8721∑ n-ary summation, U+2211 ISOamsb -->
minus#8722− minus sign, U+2212 ISOtech -->
lowast#8727∗ asterisk operator, U+2217 ISOtech -->
radic#8730√ square root = radical sign,
prop#8733∝ proportional to, U+221D ISOtech -->
infin#8734∞ infinity, U+221E ISOtech -->
ang#8736∠ angle, U+2220 ISOamso -->
and#8743∧ logical and = wedge, U+2227 ISOtech -->
or#8744∨ logical or = vee, U+2228 ISOtech -->
cap#8745∩ intersection = cap, U+2229 ISOtech -->
cup#8746∪ union = cup, U+222A ISOtech -->
int#8747∫ integral, U+222B ISOtech -->
there4#8756∴ therefore, U+2234 ISOtech -->
sim#8764∼ tilde operator = varies with = similar to,
cong#8773≅ approximately equal to, U+2245 ISOtech -->
asymp#8776≈ almost equal to = asymptotic to,
ne#8800≠ not equal to, U+2260 ISOtech -->
equiv#8801≡ identical to, U+2261 ISOtech -->
le#8804≤ less-than or equal to, U+2264 ISOtech -->
ge#8805≥ greater-than or equal to,
sub#8834⊂ subset of, U+2282 ISOtech -->
sup#8835⊃ superset of, U+2283 ISOtech -->
nsub#8836⊄ not a subset of, U+2284 ISOamsn -->
sube#8838⊆ subset of or equal to, U+2286 ISOtech -->
supe#8839⊇ superset of or equal to,
oplus#8853⊕ circled plus = direct sum,
otimes#8855⊗ circled times = vector product,
perp#8869⊥ up tack = orthogonal to = perpendicular,
sdot#8901⋅ dot operator, U+22C5 ISOamsb -->
lceil#8968⌈ left ceiling = APL upstile,
rceil#8969⌉ right ceiling, U+2309 ISOamsc -->
lfloor#8970⌊ left floor = APL downstile,
rfloor#8971⌋ right floor, U+230B ISOamsc -->
lang#9001〈 left-pointing angle bracket = bra,
rang#9002〉 right-pointing angle bracket = ket,
loz#9674◊ lozenge, U+25CA ISOpub -->
spades#9824♠ black spade suit, U+2660 ISOpub -->
clubs#9827♣ black club suit = shamrock,
hearts#9829♥ black heart suit = valentine,
diams#9830♦ black diamond suit, U+2666 ISOpub -->