Dice.camp

HoldMyTypeExample: is is{{{5^5 } ^5 }^5 }^5 a natural number? It is not of the form 0 or Suc(0), or Suc(Suc(0)), ... We need to use induction to show that this is a natural number.

Sjoerd VisscherI believe proarrow equipments are a great setting to study optics in. You can see the expression for optics and the equivalent string diagram below.The string diagram even looks like it's just a schematic drawing of an optic, but it really contains all the required information! The arrow heads indicate that s, t, a and b are all tight arrows, but in the loose direction.If you specialize to the proarrow equipment of functors and profunctors and simplify, you get the final expression. And if you then make S and T constant functors, and A and B monoidal actions, you get back mixed optics.<a href="https://types.pl/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a> <a href="https://types.pl/tags/optics" class="mention hashtag" rel="nofollow noopener" target="_blank">#optics</a>

José A. AlonsoReadings shared July 4, 2025. <a href="https://jaalonso.github.io/vestigium/posts/2025/07/05-readings_shared_07-04-25" rel="nofollow noopener" translate="no" target="_blank">https://jaalonso.github.io/vestigium/posts/2025/07/05-readings_shared_07-04-25</a> <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a> <a href="https://mathstodon.xyz/tags/FunctionalProgramming" class="mention hashtag" rel="nofollow noopener" target="_blank">#FunctionalProgramming</a> <a href="https://mathstodon.xyz/tags/Haskell" class="mention hashtag" rel="nofollow noopener" target="_blank">#Haskell</a> <a href="https://mathstodon.xyz/tags/ITP" class="mention hashtag" rel="nofollow noopener" target="_blank">#ITP</a> <a href="https://mathstodon.xyz/tags/IsabelleHOL" class="mention hashtag" rel="nofollow noopener" target="_blank">#IsabelleHOL</a> <a href="https://mathstodon.xyz/tags/LLMs" class="mention hashtag" rel="nofollow noopener" target="_blank">#LLMs</a> <a href="https://mathstodon.xyz/tags/LeanProver" class="mention hashtag" rel="nofollow noopener" target="_blank">#LeanProver</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#Logic</a> <a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/Rust" class="mention hashtag" rel="nofollow noopener" target="_blank">#Rust</a> <a href="https://mathstodon.xyz/tags/TypeTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#TypeTheory</a>

Programming Languages Delft"2-Functoriality of Initial Semantics, and Applications" by Benedikt Ahrens, Ambroise Lafont, and Thomas Lamiaux was accepted at <a href="https://akademienl.social/tags/icfp" class="mention hashtag" rel="nofollow noopener" target="_blank">#icfp</a> "We provide tools to compare and relate the models obtained from a signature for different choices of monoidal category [..] we use our results to relate the models of the different implementation [..] and to provide a generalized recursion principle for simply-typed syntax."Read it on <a href="https://akademienl.social/tags/arXiv" class="mention hashtag" rel="nofollow noopener" target="_blank">#arXiv</a>: <a href="https://arxiv.org/abs/2503.10863" rel="nofollow noopener" translate="no" target="_blank">https://arxiv.org/abs/2503.10863</a><a href="https://akademienl.social/tags/TypeTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#TypeTheory</a> <a href="https://akademienl.social/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a>

Counting Is Hard<a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a>

Counting Is HardThanks to the work of <a href="https://mastodon.acm.org/@mspstrath" class="u-url mention" rel="nofollow noopener" target="_blank">@mspstrath</a> all the TYPES 2025 talks are available (including mine)<a href="https://www.youtube.com/watch?v=W-lYwG3E_x4&list=PLjPpkiIsfkBP2Iarv-Zvd7QS7WrGcDqem&index=80" rel="nofollow noopener" translate="no" target="_blank">https://www.youtube.com/watch?v=W-lYwG3E_x4&list=PLjPpkiIsfkBP2Iarv-Zvd7QS7WrGcDqem&index=80</a>Like comment and subscribe, ring the bell, all that stuff<a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a> <a href="https://mathstodon.xyz/tags/computability" class="mention hashtag" rel="nofollow noopener" target="_blank">#computability</a>

ThomasRobert Rosen's approach of grounding formalization in science in the ultimate formalization, math, is as self-similar as thinking about thought.His use of "category theory" provides a mathematical analogy to analogies.I must confess that I need a lot of time to understand his writings - I keep learning new things every time I read it again.<a href="https://mas.to/tags/RobertRosen" class="mention hashtag" rel="nofollow noopener" target="_blank">#RobertRosen</a> <a href="https://mas.to/tags/Formalization" class="mention hashtag" rel="nofollow noopener" target="_blank">#Formalization</a> <a href="https://mas.to/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a>

Counting Is HardToo late to add this meme to my talk for types<a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a> <a href="https://mathstodon.xyz/tags/memes" class="mention hashtag" rel="nofollow noopener" target="_blank">#memes</a>

José A. AlonsoReadings shared June 9, 2025. <a href="https://jaalonso.github.io/vestigium/posts/2025/06/09-readings_shared_06-09-25" rel="nofollow noopener" translate="no" target="_blank">https://jaalonso.github.io/vestigium/posts/2025/06/09-readings_shared_06-09-25</a> <a href="https://mathstodon.xyz/tags/AI" class="mention hashtag" rel="nofollow noopener" target="_blank">#AI</a> <a href="https://mathstodon.xyz/tags/AIforMath" class="mention hashtag" rel="nofollow noopener" target="_blank">#AIforMath</a> <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a> <a href="https://mathstodon.xyz/tags/FunctionalProgramming" class="mention hashtag" rel="nofollow noopener" target="_blank">#FunctionalProgramming</a> <a href="https://mathstodon.xyz/tags/Haskell" class="mention hashtag" rel="nofollow noopener" target="_blank">#Haskell</a> <a href="https://mathstodon.xyz/tags/ITP" class="mention hashtag" rel="nofollow noopener" target="_blank">#ITP</a> <a href="https://mathstodon.xyz/tags/IsabelleHOL" class="mention hashtag" rel="nofollow noopener" target="_blank">#IsabelleHOL</a> <a href="https://mathstodon.xyz/tags/LLMs" class="mention hashtag" rel="nofollow noopener" target="_blank">#LLMs</a> <a href="https://mathstodon.xyz/tags/LeanProver" class="mention hashtag" rel="nofollow noopener" target="_blank">#LeanProver</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicProgramming" class="mention hashtag" rel="nofollow noopener" target="_blank">#LogicProgramming</a> <a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/Prolog" class="mention hashtag" rel="nofollow noopener" target="_blank">#Prolog</a> <a href="https://mathstodon.xyz/tags/Rust" class="mention hashtag" rel="nofollow noopener" target="_blank">#Rust</a>

Counting Is HardAs promised. Here is the sequel to my Weihrauch reductions are Containers post, this time relating strong reductions to dependent adaptors. Enjoy!<a href="https://www.countingishard.org/blog/strong-reducibility-as-an-adaptor" rel="nofollow noopener" translate="no" target="_blank">https://www.countingishard.org/blog/strong-reducibility-as-an-adaptor</a><a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a> <a href="https://mathstodon.xyz/tags/computability" class="mention hashtag" rel="nofollow noopener" target="_blank">#computability</a>

Ramin Honary<a class="u-url mention" href="https://chaos.social/@das_g" rel="nofollow noopener" target="_blank">@das_g</a> True. It is certainly magical that there is a programming language which defines a state monad called “IO” (or sometimes “Effect”) which carries around with it a symbol of the entire Real World in order to model the idea that any evaluation of a function of that type of monad may (or may not) create a change somewhere out in the real world, as opposed to “pure” functions which can only ever manipulate the stack.<a class="hashtag" href="https://fe.disroot.org/tag/tech" rel="nofollow noopener" target="_blank">#tech</a> <a class="hashtag" href="https://fe.disroot.org/tag/software" rel="nofollow noopener" target="_blank">#software</a> <a class="hashtag" href="https://fe.disroot.org/tag/haskell" rel="nofollow noopener" target="_blank">#Haskell</a> <a class="hashtag" href="https://fe.disroot.org/tag/programminglanguage" rel="nofollow noopener" target="_blank">#ProgrammingLanguage</a> <a class="hashtag" href="https://fe.disroot.org/tag/typetheory" rel="nofollow noopener" target="_blank">#TypeTheory</a> <a class="hashtag" href="https://fe.disroot.org/tag/categorytheory" rel="nofollow noopener" target="_blank">#CategoryTheory</a>

HoldMyTypeWhat is negation? hint- there s more to it than meet the eye

DarthViI've been reading "Category Theory Illustrated" by Jencel Panic (more about it here <a href="https://abuseofnotation.github.io/category-theory-illustrated/" rel="nofollow noopener" translate="no" target="_blank">https://abuseofnotation.github.io/category-theory-illustrated/</a>).I am reading about functors, but I wanted to share some screenshots about the Curry-Howard Isomorphism.<a href="https://hachyderm.io/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a> <a href="https://hachyderm.io/tags/CurryHowardIsomorphism" class="mention hashtag" rel="nofollow noopener" target="_blank">#CurryHowardIsomorphism</a>

José A. AlonsoIntroducing category theory (Version 26 Apr 2025). ~ Peter Smith. <a href="https://www.logicmatters.net/resources/pdfs/SmithCat.pdf" rel="nofollow noopener" translate="no" target="_blank">https://www.logicmatters.net/resources/pdfs/SmithCat.pdf</a> <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a>

Jencel PanicA <a href="https://mathstodon.xyz/tags/monad" class="mention hashtag" rel="nofollow noopener" target="_blank">#monad</a> is when you know how to convert $M (M a)$ to $M a$, but not $M a$ to $a$.<a href="https://mathstodon.xyz/tags/haskell" class="mention hashtag" rel="nofollow noopener" target="_blank">#haskell</a> <a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a> <a href="https://mathstodon.xyz/tags/functionalprogramming" class="mention hashtag" rel="nofollow noopener" target="_blank">#functionalprogramming</a>

2somethingThe set of all sets that are not big enough to trigger Russell's Paradox. Okay that sounds like a joke, but I have a clear memory of my algebra professor in undergrad saying "If you have a large category, you can always shrink it to a small category that includes all the objects you care about." Unless you're a foundations creature, in which case the objects you care about might include sets or categories which are big enough to cause trouble. <a href="https://transfem.social/tags/SetTheory" rel="nofollow noopener" target="_blank">#SetTheory</a> <a href="https://transfem.social/tags/CategoryTheory" rel="nofollow noopener" target="_blank">#CategoryTheory</a> <a href="https://transfem.social/tags/Math" rel="nofollow noopener" target="_blank">#Math</a>

2somethingThe GNU project claims their software is "free," but I have never seen a proof that GNU Sed is a free object in the category of software. <a href="https://transfem.social/tags/CategoryTheory" rel="nofollow noopener" target="_blank">#CategoryTheory</a> <a href="https://transfem.social/tags/GNU" rel="nofollow noopener" target="_blank">#GNU</a>

Programming Languages DelftMaster thesis by Niyousha Najmaei: "The Internal Language of Comprehension Categories""[..] we propose a candidate type theory for the internal language of comprehension categories by extracting a type theory from the semantics given by a general comprehension category which is not full and split. We also give an interpretation of this type theory in every comprehension category."<a href="https://repository.tudelft.nl/record/uuid:39e79d29-122c-4b54-827f-fd9908495e17" rel="nofollow noopener" translate="no" target="_blank">https://repository.tudelft.nl/record/uuid:39e79d29-122c-4b54-827f-fd9908495e17</a><a href="https://akademienl.social/tags/TypeTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#TypeTheory</a> <a href="https://akademienl.social/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a> <a href="https://akademienl.social/tags/MLTT" class="mention hashtag" rel="nofollow noopener" target="_blank">#MLTT</a> <a href="https://akademienl.social/tags/thesis" class="mention hashtag" rel="nofollow noopener" target="_blank">#thesis</a>

Tom de JongMany thanks to everyone who attended and made this an amazing day of <a href="https://mathstodon.xyz/tags/logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#logic</a>, <a href="https://mathstodon.xyz/tags/computabilitytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#computabilitytheory</a> and <a href="https://mathstodon.xyz/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#categorytheory</a>!Recordings and slides will be available on the website sometime next week (hopefully)!

amen zwa, esq.I have a quick question, <a href="https://mathstodon.xyz/@Joshua" class="u-url mention" rel="nofollow noopener" target="_blank">@Joshua</a>. Are you guys teaching <a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a> alongside Computability and Complexity to the undergrad <a href="https://mathstodon.xyz/tags/CS" class="mention hashtag" rel="nofollow noopener" target="_blank">#CS</a> these days?In my days, Categories were taught only as beginning grad subject. But kids these days are scary smart, so....

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