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circuits first class circuits hackage package search browse what s new upload user accounts circuits first class circuits bsd3 control library propose tags report a vulnerability circuits provides a suite of tools that make coding with circuits first class skip to readme modules last documentation circuit circuit algebra circuit category circuit channel circuit dagger circuit discrete circuit ends circuit free circuit hyper circuit layer circuit loop circuit net circuit sym circuit tensor downloads circuits 0 2 0 0 tar gz browse cabal source package package description as included in the package maintainer s corner package maintainers tonyday567 for package maintainers and hackage trustees edit package information candidates no candidates versions rss 0 1 0 0 0 2 0 0 change log changelog md dependencies base 4 18 5 profunctors 5 0 6 stm 2 5 3 details tested with ghc 9 10 1 ghc 9 12 2 ghc 9 14 1 license bsd 3 clause copyright tony day c 2025 2026 author tony day maintainer tonyday567 gmail com uploaded by tonyday567 at 2026 07 20t08 01 25z category control home page https github com tonyday567 circuits readme bug tracker https github com tonyday567 circuits issues source repo head git clone https github com tonyday567 circuits distributions downloads 9 total 3 in the last 30 days rating no votes yet estimated by bayesian average your rating λ λ λ status docs not available build log all reported builds failed as of 2026 07 20 all 2 reports readme for circuits 0 2 0 0 back to package description circuits circuits is a toolkit for analysing circuits a circuit here is any computation that has direction sequence and flow data moves through arrows feeds back on itself and forks or joins along the way the library gives you small composable pieces for building those structures and reasoning about them solid arrows are enrichment dashed arrows are the laws a free construction draws on when it folds open full page graph lr category category channel channel strength strength traced traced tensor tensor action action free free sym sym net net loop loop category free strength loop traced loop action sym action net traced net category channel strength traced category tensor action free sym net loop net linkstyle 0 1 2 3 4 5 stroke c44e8a stroke width 2px linkstyle 6 7 8 9 10 stroke 4b7fbd stroke width 2px linkstyle 11 12 13 stroke 8fb83a stroke width 2px style category fill 1f7050 stroke 1f7050 color 1b1e23 style channel fill 4b7fbd stroke 4b7fbd color 1b1e23 style strength fill c44e8a stroke c44e8a color 1b1e23 style traced fill 3d3d7a stroke 3d3d7a color c8ccd4 style tensor fill d98a3a stroke d98a3a color 1b1e23 style action fill 4b9680 stroke 4b9680 color 1b1e23 style free fill 4b9680 stroke 4b9680 color 1b1e23 style sym fill 8fb83a stroke 8fb83a color 1b1e23 style net fill d98a3a stroke d98a3a color 1b1e23 style loop fill c44e8a stroke c44e8a color 1b1e23 the module view groups the classes into their source files and adds the satellites around the core open full page graph lr category circuit category subgraph channel circuit channel channelclass channel strength strength traced traced end subgraph tensor circuit tensor tensorclass tensor action action end free circuit free sym circuit sym net circuit net loop circuit loop hyper circuit hyper dagger circuit dagger ends circuit ends category channelclass strength traced category tensorclass action free sym net loop net loop hyper dagger net ends loop linkstyle 0 1 2 stroke 4b7fbd stroke width 2px linkstyle 3 4 stroke 4b9680 stroke width 2px linkstyle 5 6 stroke 8fb83a stroke width 2px linkstyle 7 8 stroke 9b6bc0 stroke width 2px linkstyle 9 stroke 4b96b0 stroke width 2px style channel fill transparent stroke 4b7fbd stroke width 2px stroke dasharray 5 5 style tensor fill transparent stroke d98a3a stroke width 2px stroke dasharray 5 5 style category fill 1f7050 stroke 1f7050 color 1b1e23 style channelclass fill 4b7fbd stroke 4b7fbd color 1b1e23 style strength fill c44e8a stroke c44e8a color 1b1e23 style traced fill 3d3d7a stroke 3d3d7a color c8ccd4 style tensorclass fill d98a3a stroke d98a3a color 1b1e23 style action fill 4b9680 stroke 4b9680 color 1b1e23 style free fill 4b9680 stroke 4b9680 color 1b1e23 style sym fill 8fb83a stroke 8fb83a color 1b1e23 style net fill d98a3a stroke d98a3a color 1b1e23 style loop fill c44e8a stroke c44e8a color 1b1e23 style hyper fill 6b4c8a stroke 6b4c8a color c8ccd4 style dagger fill e07a9e stroke e07a9e color 1b1e23 style ends fill 4b96b0 stroke 4b96b0 color 1b1e23 the shape of the library everything is built over a base arrow that you bring kleisli m matrices over a semiring the library does not pick a semantics it adds structure along two ladders a ladder of laws the type classes form chains out of category channel strength traced monoidal structure tensorial strength feedback via trace and tensor action the concrete and either machinery each rung is one more law a target category can satisfy these classes say nothing about syntax they are the contracts that folds have to meet a deck of languages the gadts form a parallel chain of free constructions each rung one enrichment of the last free lift compose sym free par swap net sym knot copy discard plus zero free is the free category sym the free symmetric monoidal category net the free traced prop with a bimonoid where every wire is a constructor you can inspect loop sits to the side of this chain rather than on it it is the free traced monoidal category in normal form its laws are performed by its instances so every value collapses to at most one knot over a base arrow net and loop are the two poles of the library wiring you can read backwards and wiring that has been melted into a single loop melt goes from one to the other between the ladders there is a family of folds each free construction can be evaluated into any target category that satisfies the right laws the gadt s constructors are forgotten one at a time layer captures this pattern uniformly and algebra provides the same deck à la carte from signature functors in many of the free objects we tag common computation patterns function application composition tracing and type tensoring this bootstraps a first class foundation for computational circuits direction sequence and flow without baking in a particular semantics too early applications and closures can be delayed for analysis and measurement or retried the feedback itself is visible as a wire not hidden in a closure potential uses the core stays small companion libraries apply it to specific domains library what it adds circuits ad reverse mode automatic differentiation pullbacks and star elimination circuits examples paste into ghci example cards circuits int int construction and polynomial functor sketches circuits io sockets queues servers and concrete io transports circuits llm small transformer style language model experiments circuits mat matrices over a semiring as a traced monoidal category circuits meter one line performance metering and stopwatch pipelines circuits parser parser combinators over a coinductive stream decomposition circuits pca principal component analysis as a residual ownership protocol circuits repl repl primitives commit emit dual turns channels sessions install add circuits to your build depends ghc 9 10 tested with 9 14 dependencies beyond base profunctors and stm examples the example cards live in the separate circuits examples repository each md file is a short paste into ghci walkthrough with yaml front matter name description tags cards are not a secondary dump for outdated material they are the development surface of the library stable cards document supported api experimental cards grow ideas that are not yet in the api when a card matures it gets promoted into src and the public api thanks built on launchbury krstic sauerwein 2013 and kidney wu 2026 the hyper type is theirs the normal form that makes it inspectable is ours llms and agents helped with category theory coding refactoring and documentation produced by hackage and cabal 3 16 1 0