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# Category Archives: math

## Generating plane tilings with diagrams

I’ve finally set up a diagrams-contrib package to serve as a home for user contributions to the diagrams project—generation of specialized diagrams, fun or instructive examples, half-baked ideas, stuff which is not sufficiently polished or general to go in the … Continue reading

## Themes on Streams, Part II

In a previous post I claimed that comonad structures on R -> a are in one-to-one correspondence with monoid structures on R. In this post and the next I’ll justify that claim. Characterizing comonads on R -> a Suppose we … Continue reading

Posted in haskell, math
Tagged comonad, free theorem, functor, parametricity, representable
2 Comments

## Themes on Streams

> {-# LANGUAGE DeriveFunctor, FlexibleInstances #-} Recall that a stream is a countably infinite sequence of values: > data Stream a = a :> Stream a > deriving (Functor, Show) > > sHead (a :> _) = a > sTail … Continue reading

## Math.OEIS needs a new maintainer

Summary: the OEIS has switched servers and the oeis package needs updating to match, so I’m looking for someone to take over development. All the rest is padding in the form of entertaining stories. Recently, Michael Snoyman’s wonderful packdeps tool … Continue reading

## Things I have learned about vector spaces

Work on the diagrams library is coming along rather nicely. I’ll have more to say about it soon, but for now here are two things I have learned recently: Normals transform as the inverse transpose (see Subject 5.27). Be very … Continue reading

## Species and Functors and Types, Oh My!

My paper on combinatorial species and the species library (an improved version of my previous ICFP submission) has been accepted to the 2010 Haskell Symposium! I look forward to seeing people in Baltimore in September, and in the meantime the … Continue reading

Posted in combinatorics, haskell, math, writing
Tagged 2010, combinatorics, haskell, paper, species, symposium
2 Comments

## Math.Combinatorics.Multiset and Sawada’s algorithm

I’ve uploaded a new version of my Math.Combinatorics.Multiset library (see the previous announcement here). I’ve added a few more fairly simple algorithms (splitting a multiset into two pieces in all possible ways; finding all size-k submultisets of a multiset), and … Continue reading