Brent A. Yorgey http://ozark.hendrix.edu/~yorgey/forest/index/ index /~yorgey/forest/index/ Brent Yorgey false http://ozark.hendrix.edu/~yorgey/forest/contact/ contact /~yorgey/forest/contact/ Contact information Office MC Reynolds 310; make an appointment Phone +1 501 450 1377 Email last name at hendrix.edu Github byorgey IRC byorgey on LiberaChat Mastodon https://mathstodon.xyz/@byorgey Brent A. Yorgey 2025 10 24 http://ozark.hendrix.edu/~yorgey/forest/0001/ 0001 /~yorgey/forest/0001/ About this site This site is a "forest" created using Forester. Click on headings to collapse or expand sections, or click on the alphanumeric ID next to a section heading to open the section in a new page. Type Ctrl+K to search the graph. 2025 10 24 http://ozark.hendrix.edu/~yorgey/forest/0005/ 0005 /~yorgey/forest/0005/ Links My biography How to pronounce my last name What I'm up to right now My weekly notes The list of productivity tools I use Want to ask me for a letter of reference? Read this guide first. Brent A. Yorgey 2026 3 7 http://ozark.hendrix.edu/~yorgey/forest/009L/ 009L /~yorgey/forest/009L/ Statement on LLMs I do not and will not use LLMs, in any form, for any purpose. Although LLMs are fascinating from a purely technical perspective, I refuse to participate in or contribute to such systems that are built on massive exploitation of human labor and make profligate use of scarce resources. I also don't think they are actually very good for a lot of the applications people seem excited about. Even in cases where LLMs are technically good at a task, that does not necessarily mean their use for that task contributes positively to human flourishing. A good way to describe myself is as a generative AI vegetarian. You can find a fuller explanation—and many, many links—at the above essay by Sean Boots, which I agree with almost 100%. On bad days, I find myself feeling more like Anthony Moser. 2025 10 25 http://ozark.hendrix.edu/~yorgey/forest/0007/ 0007 /~yorgey/forest/0007/ News and announcements 2025 9 25 http://ozark.hendrix.edu/~yorgey/forest/005Y/ 005Y /~yorgey/forest/005Y/ ZuriHac invited keynote on competitive programming I gave an invited keynote talk on competitive programming at ZuriHac 2025. 2025 1 23 http://ozark.hendrix.edu/~yorgey/forest/0008/ 0008 /~yorgey/forest/0008/ New JFP paper published My paper, You Could Have Invented Fenwick Trees (Functional Pearl), is now published in the Journal of Functional Programming! 2024 12 19 http://ozark.hendrix.edu/~yorgey/forest/0009/ 0009 /~yorgey/forest/0009/ Haskell Symposium keynote I gave a keynote presentation at the Haskell Symposium on The Joy of Building (Functional) Languages (invited keynote). 2023 8 24 http://ozark.hendrix.edu/~yorgey/forest/000A/ 000A /~yorgey/forest/000A/ New Disco paper published My paper, Disco: A Functional Programming Language for Discrete Mathematics, has been published in the proceedings of TFPIE '23: Trends in Functional Programming in Education. 2025 10 24 http://ozark.hendrix.edu/~yorgey/forest/0002/ 0002 /~yorgey/forest/0002/ Teaching I teach computer science and mathematics at Hendrix College. 2025 10 24 http://ozark.hendrix.edu/~yorgey/forest/0003/ 0003 /~yorgey/forest/0003/ Current courses (Spring 2026) This spring, I am teaching two courses and one lab section: MATH 240, Discrete Mathematics CSCI 365, Functional Programming I will also be facilitating one lab section for CSCI 150, Foundations of Computer Science. 2025 10 24 http://ozark.hendrix.edu/~yorgey/forest/0004/ 0004 /~yorgey/forest/0004/ Previous courses 2025 10 25 http://ozark.hendrix.edu/~yorgey/forest/000I/ 000I /~yorgey/forest/000I/ Previous courses taught at Hendrix College LBST 150J, The Engaged Citizen: The Art and Science of Creativity (co-taught with Melissa Gill, F '20) LBST 101, Explorations (F '18, F '20, F '22, F '24) CSCI 150, Foundations of Computer Science (F '15, S '16, S '17, S '18, F '18, S '19, F '19, S '20, S '21, F '22, S '23, F '23, S '24, S '25, F '25, S '26) CSCI 151, Data Structures (F '16, F '17, S '19) MATH 240, Discrete Mathematics (S '20, S '21, S '22, S '23, S '25, S '26) CSCI 322, Computing Systems Organization (S '22, S '24) CSCI 382, Algorithms (S '16, S '17, F '17, F '18, F '19, F '20, F '22, F '23, F '24, F '25) CSCI 360, Programming Languages (F '16, F '18, S '21, S '23, S '25) CSCI 365, Functional Programming (S '16, S '18, S '20, S '22, S '24, S '26) CSCI 410, Senior Seminar (F '16, F '17, F '19, F '20, F '22, F '24) 2025 10 25 http://ozark.hendrix.edu/~yorgey/forest/000J/ 000J /~yorgey/forest/000J/ Previous courses taught at Williams College CS 134, Digital Communication and Computation, an Introduction to Computer Science (co-taught with Bill Lenhart, F '14) CS 354, Functional Programming and the Art of Recursion (F '14) CS 136, Data Structures and Advanced Programming (S '15) 2025 10 25 http://ozark.hendrix.edu/~yorgey/forest/000K/ 000K /~yorgey/forest/000K/ Previous courses taught at University of Pennsylvania The Art of Recursion (F '12) CIS 194, Introduction to Haskell (F '10, S '12, S '13) CIS 500, Software Foundations (TA; S '10, S '11) CIS 120, Programming Languages and Techniques I (TA; F '09) 2025 10 25 http://ozark.hendrix.edu/~yorgey/forest/000L/ 000L /~yorgey/forest/000L/ Other previously taught courses Woodrow Wilson Senior High School, Washington DC Introduction to Computer Science ('04-'05, '05-'06) AP Computer Science AB ('04-'05, '05-'06) Honors Precalculus ('05-'06) Correspondence course in precalculus with homeschool students ('08-'09) http://ozark.hendrix.edu/~yorgey/forest/000C/ 000C /~yorgey/forest/000C/ Projects http://ozark.hendrix.edu/~yorgey/forest/000N/ 000N /~yorgey/forest/000N/ Disco Disco is a functional teaching language for discrete mathematics, implemented in Haskell. Heinrich Apfelmus recently built a basic web UI for students to be able to use Disco in their browser, and I'm using it to teach MATH 240, Discrete Mathematics this semester. Related talks and papers Brent A. Yorgey 2023 8 14 http://ozark.hendrix.edu/~yorgey/forest/yorgey-disco-2023/ yorgey-disco-2023 /~yorgey/forest/yorgey-disco-2023/ Disco: A Functional Programming Language for Discrete Mathematics Reference TFPIE '23: Trends in Functional Programming in Education 10.4204/EPTCS.382.4 http://ozark.hendrix.edu/~yorgey/pub/disco-tfpie23.pdf https://github.com/disco-lang/disco http://ozark.hendrix.edu/~yorgey/pub/disco-tfpie23-talk.pdf Disco is a pure, strict, statically typed functional programming language designed to be used in the setting of a discrete mathematics course. The goals of the language are to introduce students to functional programming concepts early, and to enhance their learning of mathematics by providing a computational platform for them to play with. It features mathematically-inspired notation, property-based testing, equirecursive algebraic types, subtyping, built-in list, bag, and finite set types, a REPL, and student-focused documentation. Disco is implemented in Haskell, with source code available on GitHub, and interactive web-based REPL available through replit. 2025 10 26 http://ozark.hendrix.edu/~yorgey/forest/000O/ 000O /~yorgey/forest/000O/ Swarm In the fall of 2021 I started developing a game called Swarm and built a small open-source community around its development. So far we have made a few official alpha releases, and development continues to hum along. We finally merged a big import feature to the language. I'm now working on various smaller additions. I've also been writing up some notes about a planned redesign of the type system. 2025 10 26 http://ozark.hendrix.edu/~yorgey/forest/000P/ 000P /~yorgey/forest/000P/ Applicative inference While working on a mini-DSL as part of the Swarm project, I got an intuitive sense that the types of DSLs involving an applicative functor can be fully inferred from (suitably restricted) programs that just use regular applicative notation, whereas for monads this would be ambiguous. I have been working, intermittently, on a research project to formalize and prove this idea. 2025 10 26 Related talks and papers Brent A. Yorgey 2025 1 30 http://ozark.hendrix.edu/~yorgey/forest/idiomatic-inference-PLV/ idiomatic-inference-PLV /~yorgey/forest/idiomatic-inference-PLV/ Idiomatic Inference for DSLs Reference Portland State University PLV seminar http://ozark.hendrix.edu/~yorgey/pub/PLV-idiomatic-inference.pdf https://github.com/byorgey/infer-applicative McBride and Paterson's idioms, or applicative functors, are a well-known abstraction defining function application in some ambient effectful context. It would often be useful, especially in the context of designing domain-specific languages, to infer such "idiomatic'' application, allowing the programmer to use plain function application syntax—but only when doing so is unambiguous. I will present work in progress characterizing the conditions necessary for this to be possible. 2025 10 28 http://ozark.hendrix.edu/~yorgey/forest/000S/ 000S /~yorgey/forest/000S/ Diagrams Diagrams is an embedded domain-specific language in Haskell for creating vector graphics, which I and several other contributors developed starting in 2008. Development has more or less stopped at this point, but I still keep it updated to compile with the latest versions of GHC and its dependencies. 2025 10 28 Diagrams-related talks and papers Ryan Yates Brent A. Yorgey 2015 8 30 http://ozark.hendrix.edu/~yorgey/forest/yates-yorgey-2015/ yates-yorgey-2015 /~yorgey/forest/yates-yorgey-2015/ Diagrams: A Functional EDSL for Vector Graphics Reference FARM '15: International Workshop on Functional Art, Music, Modelling and Design 10.1145/2808083.2808085 http://ozark.hendrix.edu/~yorgey/pub/diagrams-FARM.pdf https://www.youtube.com/watch?v=oAz8AEf7WDA Diagrams is a domain-specific language for creating vector graphics. We will give a short diagrams tutorial/demo, particularly highlighting the power of a functional, embedded domain-specific language. Brent A. Yorgey 2013 11 20 http://ozark.hendrix.edu/~yorgey/forest/yorgey-diagrams-NYHUG-2013/ yorgey-diagrams-NYHUG-2013 /~yorgey/forest/yorgey-diagrams-NYHUG-2013/ Diagrams: Declarative Vector Graphics in Haskell Reference New York Haskell Users' Group https://vimeo.com/84104226 https://vimeo.com/84249042 http://ozark.hendrix.edu/~yorgey/pub/13-11-25-nyhaskell-diagrams.pdf Over the past ten years, I have solved over 1700 competitive programming problems in Haskell, just for fun (as well as a few that were not fun). I will give a brief introduction to competitive programming and show off some examples demonstrating the unique benefits of Haskell in this context. We will then have a miniature programming contest, open to all—only Haskell allowed! Andy Gill Brent A. Yorgey 2013 9 28 http://ozark.hendrix.edu/~yorgey/forest/yorgey-active-2013/ yorgey-active-2013 /~yorgey/forest/yorgey-active-2013/ Functional Active Animation Reference FARM '13: International Workshop on Functional Art, Music, Modelling and Design http://www.youtube.com/watch?v=fb2K3h7t8fo Brent A. Yorgey 2012 9 13 http://ozark.hendrix.edu/~yorgey/forest/yorgey-monoids-2012/ yorgey-monoids-2012 /~yorgey/forest/yorgey-monoids-2012/ Monoids: Theme and Variations (Functional Pearl) Reference Haskell '12: Haskell Symposium 10.1145/2430532.2364520 http://ozark.hendrix.edu/~yorgey/pub/monoid-pearl.pdf http://ozark.hendrix.edu/~yorgey/pub/12-09-13-monoid-pearl-HS.pdf http://www.youtube.com/watch?v=X-8NCkD2vOw The monoid is a humble algebraic structure, at first glance even downright boring. However, there's much more to monoids than meets the eye. Using examples taken from the diagrams vector graphics framework as a case study, I demonstrate the power and beauty of monoids for library design. The paper begins with an extremely simple model of diagrams and proceeds through a series of incremental variations, all related somehow to the central theme of monoids. Along the way, I illustrate the power of compositional semantics; why you should also pay attention to the monoid's even humbler cousin, the semigroup; monoid homomorphisms; and monoid actions. Brent A. Yorgey 2012 4 13 http://ozark.hendrix.edu/~yorgey/forest/yorgey-compositional-drawing-2012/ yorgey-compositional-drawing-2012 /~yorgey/forest/yorgey-compositional-drawing-2012/ Embedded, functional, compositional drawing Reference Williams College 2025 10 28 http://ozark.hendrix.edu/~yorgey/forest/000R/ 000R /~yorgey/forest/000R/ Blog In this forest you'll find short musings and notes; I occasionally post longer-form articles at blog :: Brent -> [String]. 2025 10 25 http://ozark.hendrix.edu/~yorgey/forest/000F/ 000F /~yorgey/forest/000F/ Competitive programming I enjoy recreational competitive programming, especially in Haskell. I have solved about 2700 problems on Open Kattis, over 2000 of them in Haskell. I've written a series of blog posts about competitive programming in Haskell. I am the coach of the Hendrix College competitive programming team. 2025 10 25 Presentations on competitive programming Brent A. Yorgey 2025 6 9 http://ozark.hendrix.edu/~yorgey/forest/yorgey-zurihac-2025/ yorgey-zurihac-2025 /~yorgey/forest/yorgey-zurihac-2025/ Haskell for Competitive Programming (invited keynote) Reference ZuriHac 2025 https://www.youtube.com/watch?v=Bp_mQ62c_74 Over the past ten years, I have solved over 1700 competitive programming problems in Haskell, just for fun (as well as a few that were not fun). I will give a brief introduction to competitive programming and show off some examples demonstrating the unique benefits of Haskell in this context. We will then have a miniature programming contest, open to all—only Haskell allowed! Brent A. Yorgey 2021 9 10 http://ozark.hendrix.edu/~yorgey/forest/comprog-haskell-love/ comprog-haskell-love /~yorgey/forest/comprog-haskell-love/ Competitive Programming in Haskell Reference Haskell Love https://www.youtube.com/watch?v=pyHdHZyyYGg https://github.com/byorgey/HaskellLove21 Competitive programming is an exciting mind sport where competitors race to solve difficult programming tasks as quickly as possible, either individually or as part of a team. It requires sharp problem-solving skills, broad knowledge of algorithms and data structures, and (often) developing a good library of reusable code components ahead of time. Most serious competitive programmers use C++, but this is an arena where Haskell can shine: Haskell's strong type system helps prevent stupid mistakes made in the heat of the moment, and its capability for abstraction allows us to develop versatile libraries and solve problems using a minimum of boilerplate. In this talk, I will livecode a solution to a representative challenge, showing off techniques and libraries along the way. I will also highlight some areas needing work. In some cases, in order to fit within the time limit imposed by the creators of a problem, it is necessary to write code that runs within a small constant multiple of the time taken by a C++ solution. This is possible but difficult; the name of the game is to create libraries of algorithms and data structures that are highly optimized internally but present a flexible and idiomatic interface suitable for use in a contest. I hope that Haskellers of all skill levels will be able to take away something new, and that some will be convinced to take up a new hobby, or contribute some code! Brent A. Yorgey http://ozark.hendrix.edu/~yorgey/forest/000D/ 000D /~yorgey/forest/000D/ Publications Brent A. Yorgey Published papers Brent A. Yorgey 2025 1 17 http://ozark.hendrix.edu/~yorgey/forest/yorgey-fenwick-2025/ yorgey-fenwick-2025 /~yorgey/forest/yorgey-fenwick-2025/ You Could Have Invented Fenwick Trees (Functional Pearl) Reference Journal of Functional Programming ICFP '25: International Conference on Functional Programming 10.1017/S0956796824000169 http://ozark.hendrix.edu/~yorgey/pub/Fenwick-ext.pdf https://github.com/byorgey/fenwick http://ozark.hendrix.edu/~yorgey/pub/fenwick-ICFP.pdf https://youtu.be/jG2u1z_9_fg Fenwick trees, also known as binary indexed trees, are a clever solution to the problem of maintaining a sequence of values while allowing both updates and range queries in sublinear time. Their implementation is concise and efficient—but also somewhat baffling, consisting largely of nonobvious bitwise operations on indices. We begin with segment trees, a much more straightforward, easy-to-verify, purely functional solution to the problem, and use equational reasoning to explain the implementation of Fenwick trees as an optimized variant, making use of a Haskell EDSL for operations on infinite two's complement binary numbers. See also this blog post summary. Published as part of a special issue on program calculation. Brent A. Yorgey 2023 8 14 http://ozark.hendrix.edu/~yorgey/forest/yorgey-disco-2023/ yorgey-disco-2023 /~yorgey/forest/yorgey-disco-2023/ Disco: A Functional Programming Language for Discrete Mathematics Reference TFPIE '23: Trends in Functional Programming in Education 10.4204/EPTCS.382.4 http://ozark.hendrix.edu/~yorgey/pub/disco-tfpie23.pdf https://github.com/disco-lang/disco http://ozark.hendrix.edu/~yorgey/pub/disco-tfpie23-talk.pdf Disco is a pure, strict, statically typed functional programming language designed to be used in the setting of a discrete mathematics course. The goals of the language are to introduce students to functional programming concepts early, and to enhance their learning of mathematics by providing a computational platform for them to play with. It features mathematically-inspired notation, property-based testing, equirecursive algebraic types, subtyping, built-in list, bag, and finite set types, a REPL, and student-focused documentation. Disco is implemented in Haskell, with source code available on GitHub, and interactive web-based REPL available through replit. Brent A. Yorgey Kenny Foner 2018 7 30 http://ozark.hendrix.edu/~yorgey/forest/yorgey-foner-2018/ yorgey-foner-2018 /~yorgey/forest/yorgey-foner-2018/ What's the Difference? A Functional Pearl on Subtracting Bijections Reference ICFP '18: International Conference on Functional Programming 10.1145/3236796 http://ozark.hendrix.edu/~yorgey/pub/GCBP-author-version.pdf https://github.com/kwf/GCBP http://ozark.hendrix.edu/~yorgey/pub/GCBP-ICFP-18-slides.pdf https://www.youtube.com/watch?v=hq9gAe-pmzM It is a straightforward exercise to write a program to "add" two bijections—resulting in a bijection between two sum types, which runs the first bijection on elements from the left summand and the second bijection on the right. It is much less obvious how to "subtract" one bijection from another. This problem has been studied in the context of combinatorics, with several computational principles known for producing the "difference" of two bijections. We consider the problem from a computational and algebraic perspective, showing how to construct such bijections at a high level, avoiding pointwise reasoning or being forced to construct the forward and backward directions separately—without sacrificing performance. Satvik Chauhan Piyush P. Kurur Brent A. Yorgey 2016 9 8 http://ozark.hendrix.edu/~yorgey/forest/chauhan-kurur-yorgey-2016/ chauhan-kurur-yorgey-2016 /~yorgey/forest/chauhan-kurur-yorgey-2016/ How to Twist Pointers without Breaking Them Reference Haskell '16: Haskell Symposium 10.1145/2976002.2976004 http://ozark.hendrix.edu/~yorgey/pub/twisted.pdf Using the theory of monoids and monoid actions, we give a unified framework that handles three common pointer manipulation tasks, namely, data serialisation, deserialisation, and memory allocation. Our main theoretical contribution is the formulation of the notion of a twisted functor, a generalisation of the semi-direct product construction for monoids. We show that semi-direct products and twisted functors are particularly well suited as an abstraction for many pointer manipulation tasks. We describe the implementation of these abstractions in the context of a cryptographic library for Haskell. Twisted functors allow us to abstract all pointer arithmetic and size calculations into a few lines of code, significantly reducing the opportunities for buffer overflows. Dan Piponi Brent A. Yorgey 2015 1 1 http://ozark.hendrix.edu/~yorgey/forest/piponi-yorgey-2015/ piponi-yorgey-2015 /~yorgey/forest/piponi-yorgey-2015/ Polynomial Functors Constrained by Regular Expressions Reference MPC '15: International Conference on Mathematics of Program Construction 10.1007/978-3-319-19797-5_6 http://ozark.hendrix.edu/~yorgey/pub/type-matrices.pdf http://ozark.hendrix.edu/~yorgey/pub/type-matrices-mpc-15.pdf We show that every regular language, via some DFA which accepts it, gives rise to a homomorphism from the semiring of polynomial functors to the semiring of matrices over polynomial functors. Given some polynomial functor and a regular language, this homomorphism can be used to automatically derive a functor whose values have the same shape as those of the original functor, but whose sequences of leaf types correspond to strings in the language. The primary interest of this result lies in the fact that certain regular languages correspond to previously studied derivative-like operations on polynomial functors, which have proven useful in program construction. For example, the regular language yields the derivative of a polynomial functor, and its dissection. Using our framework, we are able to unify and lend new perspective on this previous work. For example, it turns out that dissection of polynomial functors corresponds to taking divided differences of real or complex functions, and, guided by this parallel, we show how to generalize binary dissection to -ary dissection. Brent A. Yorgey 2012 9 13 http://ozark.hendrix.edu/~yorgey/forest/yorgey-monoids-2012/ yorgey-monoids-2012 /~yorgey/forest/yorgey-monoids-2012/ Monoids: Theme and Variations (Functional Pearl) Reference Haskell '12: Haskell Symposium 10.1145/2430532.2364520 http://ozark.hendrix.edu/~yorgey/pub/monoid-pearl.pdf http://ozark.hendrix.edu/~yorgey/pub/12-09-13-monoid-pearl-HS.pdf http://www.youtube.com/watch?v=X-8NCkD2vOw The monoid is a humble algebraic structure, at first glance even downright boring. However, there's much more to monoids than meets the eye. Using examples taken from the diagrams vector graphics framework as a case study, I demonstrate the power and beauty of monoids for library design. The paper begins with an extremely simple model of diagrams and proceeds through a series of incremental variations, all related somehow to the central theme of monoids. Along the way, I illustrate the power of compositional semantics; why you should also pay attention to the monoid's even humbler cousin, the semigroup; monoid homomorphisms; and monoid actions. Brent A. Yorgey Stephanie Weirich Julien Cretin Simon Petyon Jones Dimitrios Vytiniotis José Pedro Magalhães 2012 1 28 http://ozark.hendrix.edu/~yorgey/forest/yorgey-promotion-2012/ yorgey-promotion-2012 /~yorgey/forest/yorgey-promotion-2012/ Giving Haskell a Promotion Reference TLDI '12: Workshop on Types in Language Design and Implementation 10.1145/2103786.2103795 http://ozark.hendrix.edu/~yorgey/pub/promotion.pdf Static type systems strive to be richly expressive while still being simple enough for programmers to use. We describe an experiment that enriches Haskell's kind system with two features promoted from its type system: data types and polymorphism. The new system has a very good power-to-weight ratio: it offers a significant improvement in expressiveness, but, by re-using concepts that programmers are already familiar with, the system is easy to understand and implement. Stephanie Weirich Brent A. Yorgey Tim Sheard 2011 9 19 http://ozark.hendrix.edu/~yorgey/forest/weirich-yorgey-sheard-2011/ weirich-yorgey-sheard-2011 /~yorgey/forest/weirich-yorgey-sheard-2011/ Binders Unbound Reference ICFP '11: International Conference on Functional Programming 10.1145/2034773.2034818 http://ozark.hendrix.edu/~yorgey/pub/unbound.pdf https://dl.acm.org/doi/suppl/10.1145/2034574.2034818/suppl_file/_talk6.mp4 Implementors of compilers, program refactorers, theorem provers, proof checkers, and other systems that manipulate syntax know that dealing with name binding is difficult to do well. Operations such as α-equivalence and capture-avoiding substitution seem simple, yet subtle bugs often go undetected. Furthermore, their implementations are tedious, requiring "boilerplate" code that must be updated whenever the object language definition changes. Many researchers have therefore sought to specify binding syntax declaratively, so that tools can correctly handle the details behind the scenes. This idea has been the inspiration for many new systems (such as Beluga, Delphin, FreshML, FreshOCaml, Cαml, FreshLib, and Ott) but there is still room for improvement in expressivity, simplicity and convenience. In this paper, we present a new domain-specific language, Unbound, for specifying binding structure. Our language is particularly expressive - it supports multiple atom types, pattern binders, type annotations, recursive binders, and nested binding (necessary for telescopes, a feature found in dependently-typed languages). However, our specification language is also simple, consisting of just five basic combinators. We provide a formal semantics for this language derived from a locally nameless representation and prove that it satisfies a number of desirable properties. We also present an implementation of our binding specification language as a GHC Haskell library implementing an embedded domain specific language (EDSL). By using Haskell type constructors to represent binding combinators, we implement the EDSL succinctly using datatype-generic programming. Our implementation supports a number of features necessary for practical programming, including flexibility in the treatment of user-defined types, best-effort name preservation (for error messages), and integration with Haskell's monad transformer library. Brent A. Yorgey 2010 9 30 http://ozark.hendrix.edu/~yorgey/forest/yorgey-species-2010/ yorgey-species-2010 /~yorgey/forest/yorgey-species-2010/ Species and Functors and Types, Oh My! (Functional Pearl) Reference Haskell '10: Haskell Symposium 10.1145/1863523.186354 http://ozark.hendrix.edu/~yorgey/pub/species-pearl.pdf http://vimeo.com/16753644 The theory of combinatorial species, although invented as a purely mathematical formalism to unify much of combinatorics, can also serve as a powerful and expressive language for talking about data types. With potential applications to automatic test generation, generic programming, and language design, the theory deserves to be much better known in the functional programming community. This paper aims to teach the basic theory of combinatorial species using motivation and examples from the world of functional programming. It also introduces the species library, available on Hackage, which is used to illustrate the concepts introduced and can serve as a platform for continued study and research. Brent A. Yorgey Dissertation Brent A. Yorgey 2014 10 14 http://ozark.hendrix.edu/~yorgey/forest/yorgey-species-2015/ yorgey-species-2015 /~yorgey/forest/yorgey-species-2015/ Combinatorial Species and Labelled Structures Reference Doctoral dissertation, University of Pennsylvania http://ozark.hendrix.edu/~yorgey/pub/thesis.pdf http://ozark.hendrix.edu/~yorgey/pub/yorgey-defense-slides.pdf The theory of combinatorial species was developed in the 1980s as part of the mathematical subfield of enumerative combinatorics, unifying and putting on a firmer theoretical basis a collection of techniques centered around generating functions. The theory of algebraic data types was developed, around the same time, in functional programming languages such as Hope and Miranda, and is still used today in languages such as Haskell, the ML family, and Scala. Despite their disparate origins, the two theories have striking similarities. In particular, both constitute algebraic frameworks in which to construct structures of interest. Though the similarity has not gone unnoticed, a link between combinatorial species and algebraic data types has never been systematically explored. This dissertation lays the theoretical groundwork for a precise—and, hopefully, useful—bridge bewteen the two theories. One of the key contributions is to port the theory of species from a classical, untyped set theory to a constructive type theory. This porting process is nontrivial, and involves fundamental issues related to equality and finiteness; the recently developed homotopy type theory is put to good use formalizing these issues in a satisfactory way. In conjunction with this port, species as general functor categories are considered, systematically analyzing the categorical properties necessary to define each standard species operation. Another key contribution is to clarify the role of species as labelled shapes, not containing any data, and to use the theory of analytic functors to model labelled data structures, which have both labelled shapes and data associated to the labels. Finally, some novel species variants are considered, which may prove to be of use in explicitly modelling the memory layout used to store labelled data structures. Brent A. Yorgey Books Benjamin C. Pierce Arthur Azevedo de Amorim Chris Casinghino Marco Gaboardi Michael Greenberg Cătălin Hriţcu Vilhelm Sjöberg Brent A. Yorgey http://ozark.hendrix.edu/~yorgey/forest/sf1/ sf1 /~yorgey/forest/sf1/ Software Foundations, Volume 1: Logical Foundations Reference https://softwarefoundations.cis.upenn.edu/lf-current/index.html Benjamin C. Pierce Arthur Azevedo de Amorim Chris Casinghino Marco Gaboardi Michael Greenberg Cătălin Hriţcu Vilhelm Sjöberg Andrew Tolmach Brent A. Yorgey http://ozark.hendrix.edu/~yorgey/forest/sf2/ sf2 /~yorgey/forest/sf2/ Software Foundations, Volume 2: Programming Language Foundations Reference https://softwarefoundations.cis.upenn.edu/plf-current/index.html Brent A. Yorgey Presentations Brent A. Yorgey 2025 6 9 http://ozark.hendrix.edu/~yorgey/forest/yorgey-zurihac-2025/ yorgey-zurihac-2025 /~yorgey/forest/yorgey-zurihac-2025/ Haskell for Competitive Programming (invited keynote) Reference ZuriHac 2025 https://www.youtube.com/watch?v=Bp_mQ62c_74 Over the past ten years, I have solved over 1700 competitive programming problems in Haskell, just for fun (as well as a few that were not fun). I will give a brief introduction to competitive programming and show off some examples demonstrating the unique benefits of Haskell in this context. We will then have a miniature programming contest, open to all—only Haskell allowed! Brent A. Yorgey 2025 1 30 http://ozark.hendrix.edu/~yorgey/forest/idiomatic-inference-PLV/ idiomatic-inference-PLV /~yorgey/forest/idiomatic-inference-PLV/ Idiomatic Inference for DSLs Reference Portland State University PLV seminar http://ozark.hendrix.edu/~yorgey/pub/PLV-idiomatic-inference.pdf https://github.com/byorgey/infer-applicative McBride and Paterson's idioms, or applicative functors, are a well-known abstraction defining function application in some ambient effectful context. It would often be useful, especially in the context of designing domain-specific languages, to infer such "idiomatic'' application, allowing the programmer to use plain function application syntax—but only when doing so is unambiguous. I will present work in progress characterizing the conditions necessary for this to be possible. Brent A. Yorgey 2024 9 6 http://ozark.hendrix.edu/~yorgey/forest/joy-functional-haskell/ joy-functional-haskell /~yorgey/forest/joy-functional-haskell/ The Joy of Building (Functional) Languages (invited keynote) Reference Haskell '24: Haskell Symposium http://ozark.hendrix.edu/~yorgey/pub/HS24-keynote.pdf https://github.com/byorgey/HS24-keynote https://www.youtube.com/watch?v=C8PcRqIToCM For almost as long as I can remember, all my best projects—the ones that I’m proudest of, the ones that have been the most fruitful and brought me the most joy—have all centered around building some kind of language. Perhaps I am just weird, but I think there is something uniquely joyful about not just expressing oneself, but creating a whole new means of expression for oneself and others. I will take you on a tour of some of my most interesting and joyful language-building projects (some of which you have probably heard of, some of which you definitely haven’t), and then we will build a language together! Brent A. Yorgey 2021 9 10 http://ozark.hendrix.edu/~yorgey/forest/comprog-haskell-love/ comprog-haskell-love /~yorgey/forest/comprog-haskell-love/ Competitive Programming in Haskell Reference Haskell Love https://www.youtube.com/watch?v=pyHdHZyyYGg https://github.com/byorgey/HaskellLove21 Competitive programming is an exciting mind sport where competitors race to solve difficult programming tasks as quickly as possible, either individually or as part of a team. It requires sharp problem-solving skills, broad knowledge of algorithms and data structures, and (often) developing a good library of reusable code components ahead of time. Most serious competitive programmers use C++, but this is an arena where Haskell can shine: Haskell's strong type system helps prevent stupid mistakes made in the heat of the moment, and its capability for abstraction allows us to develop versatile libraries and solve problems using a minimum of boilerplate. In this talk, I will livecode a solution to a representative challenge, showing off techniques and libraries along the way. I will also highlight some areas needing work. In some cases, in order to fit within the time limit imposed by the creators of a problem, it is necessary to write code that runs within a small constant multiple of the time taken by a C++ solution. This is possible but difficult; the name of the game is to create libraries of algorithms and data structures that are highly optimized internally but present a flexible and idiomatic interface suitable for use in a contest. I hope that Haskellers of all skill levels will be able to take away something new, and that some will be convinced to take up a new hobby, or contribute some code! Brent A. Yorgey 2018 4 6 http://ozark.hendrix.edu/~yorgey/forest/yorgey-graph-coloring-SAT-CCSC/ yorgey-graph-coloring-SAT-CCSC /~yorgey/forest/yorgey-graph-coloring-SAT-CCSC/ Graph Coloring with a SAT Solver Reference CCSC Mid-South http://ozark.hendrix.edu/~yorgey/pub/CCSC-nifty-SAT.pdf Brent A. Yorgey Richard Eisenberg Harley Eades 2018 1 13 http://ozark.hendrix.edu/~yorgey/forest/yorgey-eisenberg-eades-errors-OBT/ yorgey-eisenberg-eades-errors-OBT /~yorgey/forest/yorgey-eisenberg-eades-errors-OBT/ Explaining Type Errors Reference OBT '18: Off The Beaten Track http://ozark.hendrix.edu/~yorgey/pub/explaining-errors.pdf http://ozark.hendrix.edu/~yorgey/pub/explaining-errors-slides.pdf Every beginning student of programming—that is, every student with the ill fortune of having a language with a static type system foisted upon them by a well-intentioned yet sadistic instructor—is well-acquainted with the Dreaded Type Error Message. Why do type error messages have to be so terrifying? Can’t we do a better job explaining type errors to programmers? We propose two interrelated theses: We ought to move away from static error “messages” and towards interactive error explanations. We ought to consider the problem of generating error explanations in a more systematic, disciplined, and formal way. Explaining errors to users shouldn’t just be relegated to the status of an “engineering issue”, but ought to have all the tools of programming language theory and practice applied to it. Ryan Yates Brent A. Yorgey 2015 8 30 http://ozark.hendrix.edu/~yorgey/forest/yates-yorgey-2015/ yates-yorgey-2015 /~yorgey/forest/yates-yorgey-2015/ Diagrams: A Functional EDSL for Vector Graphics Reference FARM '15: International Workshop on Functional Art, Music, Modelling and Design 10.1145/2808083.2808085 http://ozark.hendrix.edu/~yorgey/pub/diagrams-FARM.pdf https://www.youtube.com/watch?v=oAz8AEf7WDA Diagrams is a domain-specific language for creating vector graphics. We will give a short diagrams tutorial/demo, particularly highlighting the power of a functional, embedded domain-specific language. Brent A. Yorgey 2013 11 20 http://ozark.hendrix.edu/~yorgey/forest/yorgey-diagrams-NYHUG-2013/ yorgey-diagrams-NYHUG-2013 /~yorgey/forest/yorgey-diagrams-NYHUG-2013/ Diagrams: Declarative Vector Graphics in Haskell Reference New York Haskell Users' Group https://vimeo.com/84104226 https://vimeo.com/84249042 http://ozark.hendrix.edu/~yorgey/pub/13-11-25-nyhaskell-diagrams.pdf Over the past ten years, I have solved over 1700 competitive programming problems in Haskell, just for fun (as well as a few that were not fun). I will give a brief introduction to competitive programming and show off some examples demonstrating the unique benefits of Haskell in this context. We will then have a miniature programming contest, open to all—only Haskell allowed! Brent A. Yorgey 2013 10 29 http://ozark.hendrix.edu/~yorgey/forest/yorgey-trees-semirings/ yorgey-trees-semirings /~yorgey/forest/yorgey-trees-semirings/ Trees and Things (with Semirings!) Reference Houghton College Andy Gill Brent A. Yorgey 2013 9 28 http://ozark.hendrix.edu/~yorgey/forest/yorgey-active-2013/ yorgey-active-2013 /~yorgey/forest/yorgey-active-2013/ Functional Active Animation Reference FARM '13: International Workshop on Functional Art, Music, Modelling and Design http://www.youtube.com/watch?v=fb2K3h7t8fo Brent A. Yorgey 2012 4 13 http://ozark.hendrix.edu/~yorgey/forest/yorgey-compositional-drawing-2012/ yorgey-compositional-drawing-2012 /~yorgey/forest/yorgey-compositional-drawing-2012/ Embedded, functional, compositional drawing Reference Williams College Brent A. Yorgey 2010 10 1 http://ozark.hendrix.edu/~yorgey/forest/yorgey-type-level-HIW-2010/ yorgey-type-level-HIW-2010 /~yorgey/forest/yorgey-type-level-HIW-2010/ Typed type-level programming with GHC Reference HIW '10: Haskell Implementors' Workshop http://www.vimeo.com/15480577 http://ozark.hendrix.edu/~yorgey/pub/typetype-HIW-20101001.pdf Brent A. Yorgey 2009 11 24 http://ozark.hendrix.edu/~yorgey/forest/yorgey-species-2009/ yorgey-species-2009 /~yorgey/forest/yorgey-species-2009/ Random testing—and beyond! with combinatorial species Reference University of Kansas http://ozark.hendrix.edu/~yorgey/pub/combtesting-ku-20091124.pdf Brent A. Yorgey 2008 6 8 http://ozark.hendrix.edu/~yorgey/forest/yorgey-mathematics-haskell/ yorgey-mathematics-haskell /~yorgey/forest/yorgey-mathematics-haskell/ Executable Mathematics: a Whirlwind Introduction to Haskell Reference Williams College Brent A. Yorgey 2008 3 22 http://ozark.hendrix.edu/~yorgey/forest/yorgey-xmonad-FringeDC/ yorgey-xmonad-FringeDC /~yorgey/forest/yorgey-xmonad-FringeDC/ xmonad: a Haskell Success Story Reference FringeDC http://ozark.hendrix.edu/~yorgey/pub/xmonad.pdf References Context Backlinks Related Contributions