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*This is my semi active blog, each article is a by-product of me attempting to understand some mathematics. Most articles, hence, are just rehashes of existing literature and most original contributions are either through mistakes which I apologise for in advance, or through non-traditional reordering of topics to suit my taste. It can however provide a starting point to some of the content, or an alternate perspective if you're already familiar with the material.*

March 16, 2021 (foundations)

We define the signature of a first-order language as a collection of symbols for functions, predicates and *constants*. Does removing any of them make the language less expressive? Here we look at an example that shows constant-symbols (or some equivalent) are necessary to express certain properties.

October 5, 2020 (foundations)

Alonzo Churchâ€™s Lambda Calculus is what makes type-free functional programming work. A powerful model of computation, at its heart is a very simple abstract rewrite systemâ€“ a directed graph. This short article touches upon why Lambda-calculus might be a natural thing to think about, and presents an elegant proof of the Church-Rosser theorem.