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0.0.1 2024-01-17T21:53Z |
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An important capability of ‹ob› = 〈Ob,Of,Ot〉is the ability to identify interpretations of other mathematical structures in ‹ob›. There are three informative cases for starters.
First, the interpretation of Boolean algebras establishes a wide case of applicability from one mathematical structure to another via a simulation representation. The “=” in Boolean algebras does not carry over to “=” in ‹ob› but representation is assured by isomorphism of canonical forms. This is an important situation for obtaining computational interpretations of structures via computational interpretation of ‹ob›.
Secondly, the interpretation of Combinators via ‹ob› relies on the correspondence of the obap.ap function with the apply operation of structure ‹ca› (and hence of the λ-calculus also). There is no “=” for ‹ca› and no prospect of a canonical form for the interpretation in ‹ob›. This points at theoretical limitations of computation and of powerful mathematical theories.
Connection of ‹ob› with number theory is via the Z2adic interpretations, among many alternative approaches. This is important with regard to demonstration of Church-Turing completeness by expression of number theoretical functions and their computation. This is the neighborhood of mathematics around which the Church-Turing hypothesis arose. Z2adic is demonstration that oMiser attains the Church-Turing level, as well as providing an usable arithmetic.
There will be additional interpretations that further this appreciation, including a Turing Machines simulation.
Catalog (Specimen, rYYMMNN Content TBD)
This placeholder links to raw materials and notes, including text files. There will be organized folios of content as consolidation of documentation on the web progresses.
| ID | Status | Started | Topic |
|---|---|---|---|
| boole | 0.5.6 2024-01-15 | 2018-11-13 | Interpretation of Boolean Algebras in ‹ob› |
| combinators | 0.1.7 2024-01-15 | 2018-02-10 | Interpretation of Combinators in ‹obap› |
| Z2adic | 0.0.8 2024-01-17 | 2023-01-30 | Z 2’S Complement Arithmetic Implementation |
| Diary & Job Jar | undated | 2023-11-12 | Notes until there is better narrative material |
I invite discussion about Miser Project topics in the Discussion section. Improvements and removal of defects in this particular documentation can be reported and addressed in the Issues section. There are also relevant projects from time to time.
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created 2024-01-13 by orcmid |