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Sjoerd Visscher @sjoerdvisscher.w3future.com · 26/09/2026

If you have laws-as-code and you have code-as-diagrams, you get (you guessed it) laws-as-diagrams for free! github.com/sjoerdvissch...

The 6 laws of a traced monoidal category, rendered as diagrams.

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 14/09/2026

It's in, but I had to drop the ascii again.

New optics diagram, now including Glass.

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 07/09/2026

New optics just dropped! #haskell #category-theory

Optics diagram, showing:

-- > Iso <: Lens, MonoidalLens, Prism, Kaleidoscope
-- > Lens <: Getter, AffineTraversal
-- > MonoidalLens <: Getter, MonoidalTraversal
-- > Prism <: Review, AffineTraversal, MonoidalTraversal
-- > Kaleidoscope <: MonoidalTraversal, Grate
-- > Grate <: Setter
-- > Getter <: AffineFold
-- > AffineTraversal <: AffineFold, Traversal
-- > MonoidalTraversal <: Traversal
-- > AffineFold <: Fold
-- > Traversal <: Fold, Setter

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 06/08/2026

I never thought the proarrow library would grow this big. I expected to hit a major roadblock at some point but that just didn't happen. sjoerdvisscher.github.io/proarrow/ #haskell

The contents of the proarrow library listing its 137 modules.

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 23/06/2026

Is de hittekracht-schaal nu al weer toe aan een update? www.hittekracht.net/verwachting @knmi.nl @helgavanleur.bsky.social

Hittekracht verwachting voor de komende week, vandaag 8, dan 5 dagen 10 (!!) en maandag weer 7.

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 22/05/2026

Isn't it amazing that these are all different representations of the same thing, each useful in its own way?

(s -> a, s -> b -> t)
forall f. Functor f => (a -> f b) -> s -> f t
forall p. Strong p => p a b -> p s t
exist m. (s -> (m, a), (m, b) -> t)
forall y. (s, t -> y) -> (a, b -> y)

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 19/02/2026

trace @_ @(D '["A"]) @(D '["X"]) @(D '["Y"]) (node "f" == node @'["Z"] "g")

A dot diagram showing the trace of the composition of functions f : A x X -> Z and g : Z -> A x Y

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 19/02/2026

line || unitAdj @"L" @"R" == counitAdj @"L" @"R" || line

A dot diagram showing a zigzag composition of the unit and counit of an adjunction

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 19/02/2026

(comult @(D '["Y"]) == line || counit) || (comult @(D '["X"]) == mappend @(D '["X"])) || (comult @(D '["Z"]) == counit @(D '["Z"]) || line)

A dot diagram showing monoid and comonoid operations.

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 05/09/2025

Yay! (It's a live leaderboard, I don't have many more ideas so others will probably catch up) #IcfpContest2025 #haskell

Current leaderboard of the ICFP contest, I'm 4th at the moment!

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 13/08/2025

There's a perfectly valid instance for Generic1 ((->) a), given an instance for Generic a. Should this be included in base? Probably not. But would anything break? I don't know! #haskell gist.github.com/sjoerdvissch...

Rep1 ((->) Bool) = Par1 :*: Par1
Rep1 ((->) (a, b)) = Rec1 ((->) a) :.: Rec1 ((->) b)
Rep1 ((->) [a]) = Par1 :*: (Rec1 ((->) a) :.: Rec1 ((->) [a]))

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 14/07/2025

Smallcheck fun: Let's just check the (->) profunctor instance on functions on a tiny datatype, say data Three = A | B | C. Hmm, why is it taking so long?? Oh, there are 27 functions of type Three -> Three, and the composition test takes 5 of those, that's 27^5 :-)

Profunctor Laws
dimap id id = id: OK
27 tests completed
dimap composition: OK (62.03s)
14348907 tests completed

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 11/05/2025

Just got this one with the central force turned on!

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 23/02/2025

I love it when generalizations bring out more symmetry! #haskell #categorytheory sjoerdvisscher.github.io/proarrow/Pro... sjoerdvisscher.github.io/proarrow/Pro...

Code showing that Promonad (Writer w) needs Monoid w and Procomonad (Writer w) needs Comonoid w.

Code showing that Promonad (Reader r) needs Comonoid r and Procomonad (Reader r) needs Monoid r.

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 09/01/2025

Still loving the view from my home office window!

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 03/01/2025

This is the actual code. (Note that I don't draw vSplit and vCombine) The original proof is here: ncatlab.org/nlab/show/2-...

vId' l' ||| unit @f @g
=== ( vCombine
=== limitUniv @j
( vSplit
=== (limit @j === vSplit) ||| vId @f
=== vId @d ||| counit @f @g
)
)
||| vId @g

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 03/01/2025

The first success with squares in proarrow! I managed to implement preservation of limits by right adjoints using squares. I tried it before without but got bogged down with details. sjoerdvisscher.github.io/proarrow/Pro...

Some screenshots of the documentation, see the link!

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 10/12/2024

You can't read "A survey of graphical languages for monoidal categories" by Peter Selinger and then not post the impressive diagram at the end!

A large diagram showing 25 different graphical languages and their relationships.

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Sjoerd Visscher @sjoerdvisscher.w3future.com · 07/12/2024

I never used Control.Parellel.Strategies before, but I did today with #AdventOfCode. It's just adding `withStrategy (parTraversable rseq)` and each line is solved in parallel, all pure! #haskell

main :: IO ()
main = interact (show . sum . withStrategy (parTraversable rseq) . map (val . parse) . lines)

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