Tag Archives: natural

Subtracting natural numbers: types and usability

Posted on February 7, 2023 by Brent

For several years now I have been working on a functional teaching language for discrete mathematics, called Disco. It has a strong static type system, subtyping, equirecursive algebraic types, built-in property-based testing, and mathematically-inspired syntax. If you want to know … Continue reading →

Posted in projects, teaching | Tagged , , , , | 3 Comments

Signed sets and ballots and naturality

Posted on February 27, 2017 by Brent

This is blog post #3 in a series on signed sets and ballots (the previous posts are here and here). Naturality, isomorphism, and equipotence When are two species isomorphic? Since species are, by definition, functors , the obvious answer is … Continue reading →

Posted in combinatorics, math, species | Tagged , , , , , , , | 2 Comments

Signed sets and ballots, part 2

Posted on February 24, 2017 by Brent

Recall, from my previous post, that our goal is to find a combinatorial proof showing the correspondence between signed sets and signed ballots, where a signed set is just a set of elements, considered positive or negative according to the … Continue reading →

Posted in combinatorics, math, species | Tagged , , , , , , , | 1 Comment

Species subtraction made simple

Posted on November 24, 2010 by Brent

> {-# OPTIONS_GHC -fno-warn-missing-methods #-} > module Virtual where > > import Control.Applicative > import Test.QuickCheck Yesterday on #haskell, augur asked me to explain how subtraction works for combinatorial species. (For an introduction to species, see my paper from the … Continue reading →

Posted in combinatorics, haskell | Tagged , , , , , , , | 15 Comments