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Category Archives: combinatorics
Readers wanted!
tl;dr: Read a draft of my thesis and send me your feedback by September 9! Over the past year I’ve had several people say things along the lines of, “let me know if you want me to read through your … Continue reading
Posted in category theory, combinatorics, diagrams, grad school, math, species, writing
Tagged dissertation, feedback, readers, species, thesis
15 Comments
Random binary trees with a sizelimited critical Boltzmann sampler
Today I’d like to talk about generating random trees. First, some imports and such (this post is literate Haskell). > {# LANGUAGE GeneralizedNewtypeDeriving #} > > module BoltzmannTrees where > > import Control.Applicative > import Control.Arrow ((&&&)) > import Control.Lens … Continue reading
Posted in combinatorics, haskell, math, species
Tagged Boltzmann, generation, QuickCheck, random, sampler, tree
7 Comments
And now, back to your regularly scheduled combinatorial species
I’ve already mentioned this to people here and there, but haven’t yet announced it publically, so here it is: Stephanie Weirich and I have been awarded a grant from the NSF to study the intersection of combinatorial species and (functional) … Continue reading
Unordered tuples and type algebra
At Hac Phi a few weekends ago (which, by the way, was awesome), Dan Doel told me about a certain curiosity in type algebra, and we ended up working out a bunch more details together with Gershom Bazerman, Scott Walck, … Continue reading
Counting linear lambda terms: choice and correspondence
In my last post, I showed how to write down polymorphic types with numbers of linear inhabitants given by products of factorials and Mersenne numbers, but left open the question of types with five linear inhabitants in particular, and whether … Continue reading
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 lambdacalculus 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 strippeddown version of Haskell’s type system with only natural numbers, polymorphism, functions, and … Continue reading
Posted in combinatorics
Tagged combinatorics, lambda, linear, polymorphism, System F, terms
10 Comments