Category Archives: Uncategorized

Upwards and downwards accumulations

Continuing my work in regress, this post revisits—with the benefit of much hindsight—what I was working on for my DPhil thesis (which was summarized in a paper at MPC 1992) and in subsequent papers at MPC 1998 and in SCP … Continue reading

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Distributivity in Horner’s Rule

This is a continuation of my previous post on Horner’s Rule, and in particular, of the discussion there about distributivity in the datatype-generic version of the Maximum Segment Sum problem: the essential property behind Horner’s Rule is one of distributivity. … Continue reading

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Horner’s Rule

This post is about my all-time favourite calculation, of a linear-time algorithm for the maximum segment sum problem, based on Horner’s Rule. The problem was popularized in Jon Bentley’s Programming Pearls series in CACM (and in the subsequent book), but … Continue reading

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Morality and temptation

Inspired by Bob Harper’s recent postings, I too have a confession to make. I know what is morally right; but sometimes the temptation is too great, and my resolve is weak, and I lapse. Fast and loose reasoning may excuse … Continue reading

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Extreme solutions

Not all problem statements are amenable to translation via Galois connections or adjunctions. A reasonable characterization of those that are suitable is the optimization problems—finding the least or greatest solution satisfying a given collection of constraints, according to some ordering. … Continue reading

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Adjunctions

Universal properties are a generalization of the notion of a Galois connection between two orderings. Or perhaps I should say: universal properties arise from adjunctions, and it is adjunctions that are a generalization of Galois connections. Adjunctions capture in an … Continue reading

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Universal properties and Galois connections

One recurring theme throughout this series will be that of a universal property—an identity that captures an indirect means of solving a problem, by transforming that problem into a different (and hopefully simpler) domain, while still preserving all its essential … Continue reading

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Lenses are the coalgebras for the costate comonad

I took part in the Dagstuhl Seminar on Bidirectional Transformations “BX” earlier this month. It was a meeting of people from four communities—databases, graph transformations, programming languages, and software engineering—discussing their various perspectives—namely the view–update problem in databases, triple graph … Continue reading

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The stream monad

I read quite a nice problem on Nick Wu’s blog, which will serve as a fine warm-up exercise. It’s about the fact that streams (infinite lists) form a monad, in a different way from lists. Nick shows the “right” and … Continue reading

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Design patterns as higher-order datatype-generic programs

Well, I got side-tracked from working directly on the book. One of the sidetracks was working on my paper Design Patterns as Higher-Order Datatype-Generic Programs from the Workshop on Generic Programming in 2006, revising and extending it for a journal; I’ve … Continue reading

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