Tag Archives: combinatorics

A (work in progress) translation of Joyal’s original paper on species

Posted on February 13, 2018 by Brent

tl;dr: I’m working on an English translation, with additional commentary, of Joyal’s 1981 paper introducing the concept of combinatorial species. Collaboration and feedback welcome! Back when I was writing my PhD thesis on combinatorial species, I was aware that André … Continue reading →

Posted in combinatorics, projects, species, writing | Tagged , , , , , , | 6 Comments

Pan-Galactic Division in Haskell

Posted on May 12, 2015 by Brent

Summary: given an injective function , it is possible to constructively “divide by ” to obtain an injection , as shown recently by Peter Doyle and Cecil Qiu and expounded by Richard Schwartz. Their algorithm is nontrivial to come up … Continue reading →

Posted in haskell, math, species | Tagged , , , , , , , , , | 6 Comments

Counting linear lambda terms

Posted on January 26, 2011 by Brent

Just a little something with which I’ve been idly occupying spare brain cycles lately… read on for an interesting puzzle. Warm up: counting lambda terms Consider a stripped-down version of Haskell’s type system with only natural numbers, polymorphism, functions, and … Continue reading →

Posted in combinatorics | Tagged , , , , , | 10 Comments

Species and Functors and Types, Oh My!

Posted on August 1, 2010 by Brent

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 , , , , , | 2 Comments

Species operations: differentiation

Posted on August 5, 2009 by Brent

Continuing my series describing my new combinatorial species library, today we’ll take a look at the operation of differentiation. You may remember that the Species type class has an Algebra.Differential constraint, which, as I previously explained, transitively implies an Algebra.Ring … Continue reading →

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

Primitive species and species operations, part II

Posted on July 31, 2009 by Brent

In my previous post, I began describing the primitive species and species operations supported by my combinatorial species library; we looked at the ring structure on species, that is, the primitive species and , and the operations of species sum … Continue reading →

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

Primitive species and species operations

Posted on July 30, 2009 by Brent

In this second post about my new combinatorial species library, I plan to begin writing about the species DSL itself: what are the primitive combinatorial species and the primitive operations on species? (The first post described the concept of combinatorial … Continue reading →

Posted in combinatorics, haskell, math | Tagged , , , | 3 Comments

Introducing Math.Combinatorics.Species!

Posted on July 24, 2009 by Brent

I have just uploaded to Hackage version 0.1 of the species package, a Haskell library for computing with combinatorial species. Much like David Amos’s great series of posts introducing his Haskell for Maths library, I plan to write a series … Continue reading →

Posted in combinatorics, haskell, math, projects | Tagged , | 14 Comments

Monad.Reader article (Multiset partitions)

Posted on September 28, 2007 by Brent

I imagine that most who read this blog have already seen it, but for those who haven’t, my article Generating Multiset Partitions has been published in Issue #8 of The Monad.Reader.  In it, I discuss the problem of generating multiset … Continue reading →

Posted in haskell, math, writing | Tagged , , , , | 2 Comments