latex source for papers that I am working on Updated - 10 May 2021
I build using: LATEX => PS => PDF I need to go via postscript because I use the pstricks packages.
I have the habit of naming the top-level file in each folder as `paper.tex'.
I include files from folder SharedMacros. If you check out this "Theory" repository then all should be well and the pdfs should build ok. Currently I use MiKTeX 2.9.
Worthy:
- GAT of Contextual Categories - the generalised algebraic theory of contextual categories. aka C-systems
- Generalised Algebraic Meta Theory - the generalised algebraic theory of generalised algebraic theories. aka B-systems?
- Instance of Generalised Algebraic Theories - another look at the tie up of generalised algebraic theories and contextual categories.
- Relational Data Design Part One - The approach described here is followed up in the Mathematical Theory Of Data.
- Preparation for a Mathematical Theory of Data - What can we say about presentations of categories as data specifications?
- Mathematical Theory Of Data - This started life as Relational Data Design Part Two but actually is bigger than that.
- Dependency Categories - Under this new name this paper is intended to correct my 1986 description of network categories. Dependency categories are to be a variation on the notion of contextual category in that the category of dependency categories, as defined here, is to be shown equivalent to the category of (?cancellative?) contextual categories. As in 1986 the motivation has been to formalise and foreground the network structure of type dependencies so as to provide a theoretical foundation for the use of networks of composition relationships in entity modelling as applied both conceptually and, for the most practical of purposes, in systems development. This work, therefore, is part of the mathematical theory of data.
- Congruence Structures - written as a stepping stone toward the construction of depdendecy categories from contextual categories the development of which has since stalled.
- Soundness of Ellipsis within Generalised Algebraic Theories - part solution to a problem from 1978.
- Regarding cwfs - a look at Peter Dybjer's definition of categories with families. Categories with families that are contextual are pretty much the same thing as contextual categories.
Private:
-
Contextual Category et al Literature Review
-
Database Literature Review
-
Project on Definitions of Contextual Categories - a project that hasn't got very far.
-
Notation - About the latex macros used in these papers.
-
Unification in the presence of sequence variables - documentation of unification algorithm intended to be suitable for rewriting theory of contextual categories. The method is sound but it doesn't solve the problem I wanted it to in that I couldn't achieve a church-rosser style rewrite system for contextual categories.
-
Introduction To Types That Vary - an attempt at a general purpose introduction.
-
Updated definitions - other ramblings