Category Archives: combinatorics

Counting linear lambda terms: Mersenne numbers

In a previous post I posed the challenge of coming up with polymorphic types admitting certain numbers of linear inhabitants. (If you didn’t see the previous post and want to puzzle over an interesting lambda-calculus based problem, stop reading now … Continue reading

Posted in combinatorics | 18 Comments

Counting linear lambda terms

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 subtraction made simple

> {-# 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 , , , , , , , | 14 Comments

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 , , , , , | 2 Comments

Functional pearl on combinatorial species

I’ve just submitted a Functional Pearl to ICFP explaining combinatorial species in a way that is (hopefully) accessible and interesting to functional programmers. You can read the draft here — as always, comments, suggestions, etc. are welcome (although it’s too … Continue reading

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

How to solve this differential equation?

How would you solve the differential equation with the initial condition ? I know what the answer is supposed to be, but I don’t know how to directly solve it. In case you’re wondering, is the exponential generating function for … Continue reading

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

Species operations: differentiation

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 , , | 1 Comment