Also features the Mathematical Definition of the TEA, Transforming Executable Alphabet computer programming language.

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[fut.][prof.] J. WILLRICH LUTALO | Inventor | TEA language | the mathematics of Transformatics | Nuchwezi Research | GARUGA, *UGANDA.*

20251023

PhD-Research--Reviewing:

Tree Algorithm Algebras Thesis --- Prof.Jeremy Gibbons (1991);

@phdthesis{gibbons1991algebras,
  title={Algebras for tree algorithms},
  author={Gibbons, Jeremy},
  year={1991},
  school={University of Oxford}
}

REVIEWER: Joseph Willrich (Nuchwezi Research)

TITLE: A Comparative Review and Critique of Tree Algebras: Revisiting Gibbons (1991) Thesis in Light of Contemporary Modern Transformatics

IN-BRIEF:

This is a review of the orginal PhD thesis of Prof. Jeremy Gibbons (Oxford University) by his potential PhD student, J. Willrich Lutalo. It is a critical and comparative review of tree algebras vis-a-vis contemporary Transformatics Theory and its applications in the TEA programming language.

[PREPRINT]DOI: https://doi.org/10.6084/m9.figshare.30445721

TAGS: #Mathematics, #ComputerScience, #Trees, #TreeAlgebras, #SequenceAlgebras, #Transformatics, #HigherOrderSequences, #ThesisReview

Notes from further analysis of both the abstract and introduction of Prof. Jeremy Gibbons' 1991 PhD thesis on Tree Algebras by fut.prof. JWL

#notes #analysis #review #paper #thesis

First VERDICT:

Further, after analyzing both the abstract and introduction of Jeremy Gibbons' thesis on Tree Algebras, we find that not only is it that the claim that "trees are fundamental" is arguably misleading (at least in the most general mathematical sense), but that, actually trees are just a higher abstraction over sets (set theory) or, and for the case of my work on TRANSFORMATICS, an abstraction over [ordered] sequences (themselves an abstraction over sets), and thus, one can comfortably argue that both trees and graphs (since trees are essentially graphs), are less fundamental than both sequences and sets. So that studying Tree Algebra, much as it is useful and very applicable in domains such as Software Engineering, Design and Processing/Analysis of Networks and many problems involving dealing with hierarchical structure mathematical objects, is less fundamental than Study of sequences or the theory and computations based on just sequences and sets such as Transformatics and the computer language based on it; TEA, treat of.

Talking of reviewing supervisors/professors at Oxford.. Have already found many telling signs that my mathematical theory of TRANSFORMATICS underlies more problems than Prof. Jeremy's work. But more about this later.. (or in the actual review paper)

👆🏼🔆 BUT, his work did lay some interesting, indeed important foundations for many practical & theoretical problems in computer science (not much for [general] mathematics though)

Such as heavy use of the Feijen-Dijkstra equational proof format, also adopted into the Bird-Meertens calculus for program construction and proofs. I have found that transformatics calculus somewhat generalizes this formalism much further too.. and correctly so.

He also [obviously] studied trees a lot. However, I again find that my theories of Transformatics and sequence algebras are more fundamental than #TreeAlgebras, BUT they are indeed closely related since trees, just like graphs, can be reduced to [higher-order] sequences which is the stuff we are dealing with in my #Transformatics and the #TEAlanguage ✓

#oxford #universityofoxford #nuchweziresearch reviewing #jeremygibbons

The Global INTERNET Community now has a public chatroom at the WEB TEA IDE | https://tea.nuchwezi.com

<1 < 2 < 3 >>> 
⇅ [[de]amalgam-spliter]
<1 < 2, 3>>
⇅ [[de]glue-spliter]
<<1>, <2>, <3>>
⇅ [[de]flat-transformer]
<1, 2, 3>

Transfomatics applied to Trees; a case of lossless shape alternators/shifters on equivalent codon expression structures/shapes #definitions

Researcher: Prof. J. Willrich Lutalo (Nuchwezi Research)

REF: https://bit.ly/transformatics101book

#transformatics #treealgebras #sequencetrees
#CREATED:Oct 25, 2025 19:00:36