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In this blog post we will explore the consequences of postulating 0 = 1 in an algebraic structure with two binary operations (S, +, 0) and (S, ⋅, 1). Such united monoids have a few interesting properties, which are not immediately obvious. For example, we will see that the axiom 0 = 1 is equivalent to a seemingly less extravagant axiom ab = ab + a, which will send us tumbling down the rabbit hole
Graph theory is my favourite topic in mathematics and computing science and in this blog post I’ll introduce an algebra of graphs that I’ve been working on for a while. The algebra has become my go-to tool for manipulating graphs and I hope you will find it useful too. The roots of this work can be traced back to my CONCUR’09 conference submission that was rightly rejected. I subsequently publishe
As part of my 6-month research secondment to Microsoft Research in Cambridge I am taking up the challenge of migrating the current GHC build system based on standard make into a new and (hopefully) better one based on Shake. If you are curious about the project you can find more details on the wiki page. During this week I’ve been trying to wrap my head around the current build system and so far I
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