.Open MATHS To Do List Any help will be appreciated... .Hole .Open To Be Done to mth2html and m2h index N & S if diff below: .As_is N::lexeme= "S"... Use a formally derived lexical analyzer to recognize terms and link them to their definitions. Use a formally derived parser to distinguish formal from informal statements Implement the MATHS->diagram mapping algorithm to produce GIFs from formulae Link formulae to their GIFs .Close .Open To Be Done to Content (PM *35.354) |- For R:@(X,Y), A:@Y, S:@(Y,Z), (R; A); S = R; (A; S) Expand and correct intro*mth...pages. Link to other pages. Add Bernstein's lemma? create sample/logic_base and link to intro_logic and logic_*: university perhaps?? or Roman Relations?? Base on Leech's ontologies? Include a diagram of domain with sets/types/functions. Perhaps include Prolog and Java code? Expand notes on probability and give some examples -- penguins in urns? Bayesian Busses. Check and revize notes on matching partitions. Add notes on reducing data sets: Given A:#Sets, R:@ (>< (A)), for a in A(f[a]:A(a)->B(a), find structure of R/f??? also image of data set under equivalences on attributes, or deleting certain attributes (rough sets). Check and revize notes on rough sets. Extract subsections, "nets", proofs on this web site into separate pages. .Close .Open To be done to the submission system When POSTed nothing, hole.php should output hole.html OR nothing but a form or a topic ?? Create specialized versions for cs375 and samples. .Close .Open To Be Done to Definition of MATHS Note use of "lexeme'' as a type. Formalize the relation between variables and expressions .Net Define variables as a map :expression->#(id, {free, bound }, type ( | , value)) free ::expression->@id, free ::LPC.wff->@id,... .Close.Net Strengthen GRAMMAR so that we can refer to newbib.section(N).paragraph(i). State idea that unambiguous syntax determines default parsing and logical structure. eg. if A:=#B then a part of type A has parts B(1), B(2), ... B(|B|). If A:= B C B D then there four parts numbered 1,2,3,4 and also parts called B(1), C(1), B(2), D(1). Hence part B=(B(1), B(2)). Can add explicit `parsers` as functions: parse(b1 c b2 d)::=(b1, c, b2, d) Strengthen formal DOM . In general, syntax determines DOM. Provide access to sections indexed by section header: document[header]. Do NOT index by number! Note:only if header not unique, number the occurences(how?). DOM: doc->%piece, piece=... | para. para->#sentence->#item->#word->#char. d.piece[3].item[2].word[1] .Net section = headline #paragraph section ::= | [h:header] (headline(h) #paragraph(h) | openline(h) #paragraph(h) closeline(h) ), headline(h) ::= ". " h eoln. M::syntax ->semantics, M(h ps)= h+> ><[p:ps]M(p). .Close.Net Don't parse into a tree but into a data base! Define a 3NF data base for storing MATHS. Define a standard mapping into XML. .Close .Open Problems Clumsy!!. Model checking??. proof checking. how to [sub] & ^(sup) in *formula only*. Inconsistent nets and undefinitions .Open The metalinguistic barrier how to express in syntax that a string in the object language should be used as an identifier for a part. For example bibliography uses headers to label items and may want to refer (and change them by label). Defining extensions to the parsing of MATHS .But This may introduce paradoxes -- review Frank Plumpton Ramsey! `F`(F) .Close.But .Close When can m2h send to mailing list? When to move to F/OSS, SourceForge?? .Close .Open Partly Baked Ideas Elementary nets = Net{v: T} & Combining nets. Use in data normalization and design. add .[ and .] . How to escape in `sed` RegExs? Semantics of .{...} and .[ ... .]? Sell as a tool for: mathematics vs ADA, EMail, and RFCs. Distinguish: subtypes, extensions, & subsets Include YAML?? Explore !? Notation for OO design. Should records be partial maps: (a=>1, b=>2) =~= ("a"+>1 | "b"+>2), Towards a UnifiedPC! LPC is generic for objects of a single type. But MATHS needs expressions that involve objects of many types. Therefore .Net extend LPC syntax to allow types. For all T x, P(x) (Q(x)) For some T x, P(x) (Q(x)). Each T has an ontology. Sets @T. ==>,&,~, | . T is one of \coPi[i:I]S[i], or tuples ><[i:I]S[i], or T/eqrela'. Use Nets to define new Types. Model Typed/unified PC in LPC?? .Close.Net Universes of discourse do not overlap. Don't define a `domain` as a universe of discourse that is co-product. .Open Add to set ?? (s.l !=n) ::= (s'=s~l|(l ! n) Perhaps need a loose match, find and replace: bib.id'=bib.id~{x:bib.id. "Duck" substring x}|"Dick Botting". ??for P:@S, (s.P'=n) ::= (s'=s~P|n) ?? newbib.id."Duck" .substring ' ="Dick Botting". Suppose set s is a partial map Id(0..)-(0..1)Data and i:Id, and we want to change s(i) to value v: s.{ (i,d). for some d}' = (i,v). s.(i>