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Dev - #308
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…thematical formatting
…entity-component relationships
…s and formalize state definition
…orage and manipulation
Master thesis
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Pull request overview
This PR extends the German LaTeX master document by adding a dedicated “Notation und Begriffe” chapter plus a new “Notation” section inside the concurrency appendix, including formal mathematical definitions, grammar formalization, and supporting macros/packages and bibliography entries.
Changes:
- Adds LaTeX preamble support for theorem environments, additional math/symbol packages, and tcolorbox styling/macros for formal notation.
- Introduces new notation content (math glossary, Core ECS notation sections, grammar formalization) and wires it into the German document index and concurrency appendix.
- Adds new bibliography entry used by the newly introduced grammar section.
Reviewed changes
Copilot reviewed 16 out of 18 changed files in this pull request and generated 7 comments.
Show a summary per file
| File | Description |
|---|---|
| docs/latex/helios_master/helios_master_de.tex | Adds packages/macros/styles (theorems, symbols, tcolorbox style, notation macros) used by new formal sections. |
| docs/latex/helios_master/helios_master.bib | Adds VW16 reference used in the grammar/notation text. |
| docs/latex/helios_master/content/de/notation/mathematik.tex | New “Mathematische Definitionen und Begriffe” glossary-like section. |
| docs/latex/helios_master/content/de/notation/index.tex | New “Notation und Begriffe” chapter entry point. |
| docs/latex/helios_master/content/de/notation.tex | Removes previous (now replaced) notation stub chapter. |
| docs/latex/helios_master/content/de/index.tex | Enables the new notation chapter in the German content index. |
| docs/latex/helios_master/content/de/appendix/concurrency_paper/notation/einleitung.tex | New intro for the appendix notation section. |
| docs/latex/helios_master/content/de/appendix/concurrency_paper/notation/komponenten.tex | New formal definition/description of components and component schemas. |
| docs/latex/helios_master/content/de/appendix/concurrency_paper/notation/entitaeten.tex | New formal section on entities incl. theorems/proofs. |
| docs/latex/helios_master/content/de/appendix/concurrency_paper/notation/zustand.tex | New formal section defining “state” notation. |
| docs/latex/helios_master/content/de/appendix/concurrency_paper/notation/existierende_entitaeten.tex | New section defining “live entities” and relating it to SparseSet implementations. |
| docs/latex/helios_master/content/de/appendix/concurrency_paper/notation/grammatik.tex | New formal grammar section for Core ECS, citing VW16. |
| docs/latex/helios_master/content/de/appendix/concurrency_paper/notation/index.tex | New index file wiring all appendix-notation subsections together. |
| docs/latex/helios_master/content/de/appendix/concurrency_paper/notation/img/sparse_sets.png | Adds illustration used by the “Existierende Entitäten” excursus. |
| docs/latex/helios_master/content/de/appendix/concurrency_paper/notation/img/sparse_set_domain.png | Adds illustration used by the “Existierende Entitäten” excursus. |
| docs/latex/helios_master/content/de/appendix/concurrency_paper/index.tex | Wires the new notation section and the new “erste Betrachtung” section into the appendix chapter. |
| docs/latex/helios_master/content/de/appendix/concurrency_paper/erste_betrachtung_concurrency.tex | New section discussing concurrency vs. parallelism terminology and setup for further content. |
| docs/latex/helios_master/content/de/appendix/concurrency_paper/einleitung.tex | Refactors ECS intro; adds explanations of queries/state/program and a tcolorbox example. |
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| \subsection*{Abgrenzung Nebenläufigkeit und Paralellität} | ||
| Wie Oechsle in~\cite{Oec22} anmerkt, wird in der Literatur oft nicht genau zwischen \textit{Nebenläufigkeit} und \textit{Paralellität} unterschieden. |
| \item \textbf{Systeme} (\textit{System}/\textit{Systems}, $S$): Funktionen {bzw.} Programmteile, die einzelne Komponenten lesend/schreiben nutzen. | ||
| \item \textbf{Entitäten} (\textit{Entity} / \textit{Entities}): Ein Typ $E$, der eine Wertemenge (beispielswiese \texttt{uint32\_t}) zur Identifikation von zusammengehörigen Komponenten ermöglicht. | ||
| Eine Entität definiert sich über die Menge der ihr zugeordneten Komponenten und lässt sich über den Entitätswert identifizieren:\footnote{ | ||
| Der Entitätsidentifikator beschreibt die Daten und damit das repräsentierte Domänenobjekt. ``A truly component bsed object is nothing more but the sum of its parts.``~\ref[S. 85]{Fab18} |
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| \begin{alignat}{3} | ||
| \text{Sparse}_i &: E \rightharpoonup \mathcal{D}_i \\ | ||
| \text{Dense}_i &: \mathcal{D}_i \rightarrow K_i, \mathcal{D}_i \subseteq \mathbb{N}_0 | ||
| \end{alignat} |
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| \nt{component\_term} | ||
| &\Coloneqq& | ||
| k\ label |
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| Des Weiteren haben wir Nichtterminale $entity_type, mutation:type, entity term und componentterm$ eingeführt, die als Metavariablen zu verstehen sind: Von dem darunterliegenden Programm, dass Core ECS implenentiert, sind dies entsprechend konkrete Werte der repräsentierten Typen, bzw. der zu verwendenden Werte.\\ | ||
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| Außerdem soll ncoh auf eine sematische bedingung hingewiesen werdne, dass nämlich, für jede Produktion, die $label$ enthält, dieses Label für jedes Vorkommen gleich sein muss. Als gedankliches Modell kann man sich hier vorstellen, dass die entsprechenden Produktionen an den Komponententyp - vertreten durch das Label in der Grammatik - gebunden sind.\\ | ||
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| Farblich hervorgehobene Einträge in den Produktionen bezeichnen keinen Teil der GRammatik, sondern durch das unterliegende Programma usgedrückte Typsystem. |
| \bigskip | ||
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| \begin{proof} | ||
| Seien beliebige $x = (e_m, k_{i}) \in P_{e_m}, y = (e_n, k_j) \in P_{e_n}, k_i \in K_i, j \in K_j, i, j \in I$ gegeben.\\ |
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| \[ | ||
| \begin{alignat}{3} | ||
| x = y &\Leftrightarrow (e_m, k_i) = (e_n, k_j) \\ | ||
| &\Leftrightarrow e_m = e_n \land k_i = k_j | ||
| \end{alignat} | ||
| \] |
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