‹ob› Mathematical Structure Articles
Job Jar & Diary
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‹ob› Mathematical Structure Articles |
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| done | 2024-02-09 |
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| 2024-06-12 | For obreps we need to be cautious about whether or not there is a (canonical) bidirectional mapping of interpretations in ob. It would seem to be cheating if we cannot do that. | ||
| 2024-06-12 | index.md for starters: Tie down the treatment of obs as being entirely about theoretical entities and the only notion of computation has to do with operation in the theory to establish any definite result of functions given definite operand values. This is in accord with the treatment in [Rogers1987] and we will borrow it for the ob structure. We don't deal directly with computational interpretation although we can deflect that question to obap. We also point to the obreps on the matter.. | ||
| 2024-06-12 | obtheory.txt: In reviewing obtheory.txt just now, I realize that denumerability and effectiveness are challenged when certain kinds of individuals are derived from obs. This is a case where obs can precede individuals. This applies to any extensions of that sort, so I need to look at that case. It looks like ob9(g) leaves this open. The extension individuals are not elemental. Ob7 might need slight adjustment also. | ||
| 2024-02-11 | These matters seem to be about concrete expression and I will need to somehow move the focus to oFrugal (and any persistent forms other than UTF-8 text), and keep the treatment here informal, with a hat-tip to the rigorous case - that is, concrete digital texts. | ||
| 2024-02-11 | A problem with lindies may be difficulties with regard to different ways to enter the same text. I believe there is a kind of Unicode normalization that reduces the redundant but different forms and that will need to be applied along with i18n. | ||
| 2024-02-11 | There needs to be some allowance for Arabic (and Hebrew) scripts. There is a good account of Arabic Script on Wikipedia, with a nice Unicode tabulation of Arabic forms. Persian is supported on Wikipedia. فارسی (fārsī) This needs to be hinted at and included in the sketch example. The "fa" language code is used, https://fa.wikipedia.org/wiki/%D8%B2%D8%A8%D8%A7%D9%86_%D9%81%D8%A7%D8%B1%D8%B3%DB%8C. And UTF-8 :). | ||
| 2024-02-11 | I need to be careful to distinguish the semi-(quasi-)formal theoretical formulation, the Frugalese mechanical language, and the concrete writing of Frugalese in digital files and input-output. I am unclear where to put that. | ||
| 2024-02-10 | I do need to know if Windows Terminal VT arrangement does admit of bidirectional encoding and then there is the question of IME handling too. | ||
| 2024-02-10 | I am over-thinking this business about lindy encoding. This needs to be formalized with oFrugal lexical structures. Move over later when I have article structure there. | ||
| 2024-02-10 | There are locale-dependent uses of dead keys and over-striking that may be considered different expressions of the same single code point. I don't know how to cope with that, at this point, and I wonder how I can delimit things with relaxations later. I still want to support portability of oFrugal scripts and that may be the controlling factor. | ||
| 2024-02-10 | It seems that it might be easier to determine what code points are excluded in C11 Annex D, not included. | ||
| 2024-02-10 | The whole matter of encoding CFob and hence lindies is a big deal. It becomes a lexical structure matter and we intend for it to be encoded and transported with great fidelity. This extends to oFrugal, of course, but there can be more accomodations there than in the idea of comparability of CFob texts. | ||
| 2024-02-10 | I am hoping that the C Language provision for Universal Character Names would help me. I don't have the identifier rule about non-digit initial characters. I don't quite understand the C11 6.4.3 limitation about $, @, and `, but it has me think I don't want to give those characters any significance in oFrugal. The C Language restriction (6.4.2.1) refers to a range D.1, with the initial characters that are excluded are in ranges specified in D.2. It is not clear what these are in reference to, unless it is in ISO/IEC 10646. In the C99 rationale, there seems to be an Annex I that limits extended characters and extended digits. There is reference to ISO/IEC TR 10176. I did find D.1 and D.2 in Annex D of C11 finally. It contradicts the statement about allowance of $, @, and `. This may have something to do with external identifiers and perhaps not a concern for Miser. I need to compare with the XML list of alphanumerics as well. | ||
| 2024-02-10 | lindies: In allowing characters beyond the C printables, I need to determine how matters such as composed characters, directional reading, etc., are handled. I intend to rely on the XML alphanumerics and I need to know exactly what that entails and what the entering/rendering considerations are. I also need to cope with escaping in order to introduce and convey large categories of Unicode code points, ones for which there may be no font or other presentation provisions. In early releases of oMiser and oFrugal, I might need to confine things to the ISO/IEC 646 C Language locale set of printables. I think I may have to punt and stick with the C locale until I am prepared to cope with writing direction, etc. However, I have used more-extensive character glyphs in the sketch. | ||
| 2024-02-10 | lindies: I am musing about the introduction of lindies at ‹ob› rather than with obap. It is a pragmatic (and significant) provision, and I suppose I need to be emphatic about them being uninterpreted symbols in which any significance is not to be found in ‹ob› itself. | ||
| 2024-02-09 | Scavenge notebooks for additional items to account for here. Perhaps there needs to be a history article at some level. Probably at Miser level, so maybe under about/ or vision/. | ||
| 2024-02-09 | Find and reference more about that in the 2024-01-06 note. Also, maybe a general treatment of structures as characterized for Miser belongs in obreps. | ||
| 2024-02-09 | Check Smullyan for possibly something on structures. | ||
| 2024-01-15 | Regarding structures, we need to deal with the denumerable and the notion that despite our unwillingness to depend on comprehension of Ob as an entirety, we must cope with the idea of Of being of higher cardinality. We then can argue about the computable functions in Of and their being far fewer (in fact, at most denumerable) and this says some odd things about what can be grasped by computation. This has to do with some squirrely things about "higher-level" and abstraction, and also diversity of interpretation. | ||
| 2024-01-12 | The emergence of types is a big deal. So then comes the question of reasoning about such things and being able to abstract types and then the injection of implementations/simulations. This note is because I am wondering where that fits in. It starts out being meta- and then I want to make it operational in some manner with regard to substitutions and accelerators in the software. | ||
| 2024-01-12 | Although I am a bit dismayed at the complexity of (Z2adic) arithmetic in oMiser, I just reminded myself that it is still far/somewhat better than accomplishing the same thing on a Turing Machine tape. Looking for accelerators will be fascinating in this case though. It dawns on me that I may need to reason about types (representations) to get any farther. I.e., to see where vectors and even int can be inserted into applicative interpretations. The race is then between how much one can afford in abstraction of type and substitutions before having the substitutions in the working of things. I also need to have what I just said make sense to me on future readings. | ||
| in progress 2024-01-11 |
2024-01-06 | There may need to be a folio on structures and theories to ground some of this and connect it to (similar/related) treatments and usages. We want to align with model theory and even category theory, but carefully and not entirely. [dh:2024-01-11 (World Logic Day weekend): I just ran into a discussion about theories and structures on FOM. In this case Monroe Eskew points to the wikipedia account, <https://en.wikipedia.org/wiki/Theory_(mathematical_logic)>, for definition of mathematical theory and also some explanation of structures. I think I can tease out my use of structure, although I need to trace those definitions (from Curry it seems - I hope I still have that mathematical logic book. Yes, I have his "Foundations of Mathematical Logic") and see how to weave my practice into it, or else revise my terminology. I am also presenting "axiomatic systems" and starting with structures is considered a semantics thing. <https://en.wikipedia.org/wiki/Structure_(mathematical_logic)>, and also not necessarily a "mathematical model," <https://en.wikipedia.org/wiki/Mathematical_model>. When I speak of a model of computation, that is probably a case of mathematical model though. I think I am safe with structure, it is just making the associated theory explicit is a shift in notation. However, <https://en.wikipedia.org/wiki/Model_theory> suggests some rather abstruse matters goinng back to Tarski and, lately, <https://en.wikipedia.org/wiki/Stable_theory>. This is all rather murky and I wonder if confinement to denumerable domains is a saving grace in respect to models of computation and C-T "completeness." | |
| 2024-01-06 | The business about interpretation, representation, and manifestation might be at a different level. Likewise the transitive nature of computational interpretation. There is going have to be some clear distinction between logical and operational realms, no matter how strong the resemblance. | ||
| 2024-01-06 | Historical treatment of obs may also be appropriate | ||
| 2023-11-20 | Under bib/: Create a discussion of [McCarthy1960], include mention of Anatomy of LISP, Talking about Ivory Snow LISP, and also what I found discouraging about how LISP and the LISP reader were used. This needs other references. There are also the inspirations of LISP into a particular approach to natural language processing, knowledge representation, and languages such as Scheme inspired by LISP. Also Common Lisp and Interlisp. Also, both the MIT and the Stanford Handbooks on AI, the blur between AI methods (such as search schemes) and what would simply be algorithms and methods of Computer Science and programming. | ||
| 2023-11-13 | Under bib/There's a nice entry on Strachey on WIkipedia: https://en.wikipedia.org/wiki/Christopher_Strachey. It provides a link (dor) on McG. There is also a connection on the M4 processor that was a Unix tool. https://en.wikipedia.org/wiki/M4_(computer_language). I will refer to that, although I need to verify whatever the similarity is, apart from the inspiration by Kerighan and Ritchie in 1977. The connection to RATFOR is also cool from a Software Tools pespective. Rhapsodize about this, Dennis. Also, Strachey is a great example of Burge's observation that computer programmers and computer scientists are people who were almost something else. I need to tie this to Edward's observations about Strachey and the existence of non-computable functions. I wonder where I saw that argument by Strachey, and if it was in-person or not. This will be interesting to tie in. Also that Peter Landin was Strachey's assistant at one point. | ||
| 2023-11-13 | Under bib/ After adding the Strachey McG citation, add a note that accounts for my experience with the paper, the two fixes, and the idea of shrinking it to purely applicative. How this was used by the FP team, but I don't think it was done for ISWIM at Speryy Univac. Connect to the Unix Macro utility also. I eventually realized that using LISP-style representation was much easier with regard to constructions for Miser and, although I knew about LISP, the coin didn't drop until I saw a Dr.Dobb's description of LISPX for microprocessors.. | ||
| done | 2024-02-09 | c000000: Bring technical items here. | |
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created 2024-02-09T20:46Z by orcmid |
