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The elaboration of universal computational functions for ‹ob› = 〈Ob,Of,Ot〉 is provided here. The essential characteristics of obs and reasoning (in Ot) about functions on obs (thereby in Of) is the foundation on which univerality is explained and expanded upon.
Two variants are defined, ap(p, x) and eval(s), with common reliance on supporting function ev(p, x, s).
Text file obaptheory is the authoritative specification.
1. Universal?
A simple notion of universality is that the specified function can deliver every computable function f(x) in Of by determination of an operand p of ap(p, x) such that
ap(p, x) = f(x)
For ‹ob›, this is a non-trivial requirement. It is satisfied in strong terms by establishing that ap is Church-Turing complete via demonstration of a Universal Turing Machine (UTM) simulation.
The confirming simulation and other characteristics are covered under the [Computation Theory] topic. Here ap and eval are formulated in way that leads directly to their computational interpretation.
Related Material
There will be organized folios of content as consolidation of documentation on the web progresses. The file obaptheory will remain the authoritative definition.
Accessions of subtopics are identified with codes of the form “APyymmnn”.
| ID | Status | Started | Topic |
|---|---|---|---|
| obaptheory | 1.7.1 2026-06-22 | 2017-09-11 | ‹ob› Universal Applicative Functions (authoritative) |
| Diary & Job Jar | undated | 2024-01-08 | Notes until there is better narrative material |
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created 2024-01-14 by orcmid |