Commit: 6a8366ee56760ce851c638da2089f149632957bc - cammy (git)

A categorical programming language

Commit MetaInfo

• Révision: 6a8366ee56760ce851c638da2089f149632957bc (tree)
• l'heure: 2023-04-03 15:18:56
• Auteur: Corbin <cds@corb...>
• Commiter: Corbin

Message de Log

Print basic descriptions of arrows.

Change Summary

• modified: hive.json
• modified: movelist/cammy-repl.scm
• modified: todo.txt

Modification

--- a/hive.json
+++ b/hive.json
@@ -1 +1 @@
-{"jets":{"dup":["pair","id","id"],"app":["uncurry","id"],"n-pred-maybe":["pr","right",["comp",["case","succ","zero"],"left"]],"n-add":["uncurry",["pr",["curry","snd"],["curry",["comp","app","succ"]]]],"n-mul":["uncurry",["pr",["curry",["comp","ignore","zero"]],["curry",["comp",["pair","app","snd"],"n-add"]]]],"n-double":["pr","zero",["comp","succ","succ"]]},"symbols":{"tree/singleton":[1480,""],"array/split":[1470,""],"tree/tip":[1452,""],"bool/conj":[1451,""],"conal/delta":[1440,""],"conal/derivative":[1414,""],"conal/nullable":[1410,""],"f/0.05":[1409,""],"f/1.75":[1407,""],"hv2rgb":[85,"\n\nConvert a hue/value pair to a red/green/blue triple. The components are based\non the hue, then scaled by the value.\n"],"zoom-out":[107,""],"in-ellipse?":[122,""],"fstsnd":[28,""],"3b1b-newton-poly":[140,""],"sndfst":[25,""],"subset-range":[182,""],"hailstone":[234,""],"nat-mul3":[229,""],"int-fractal-maybe":[253,"\n\nLike fractal-maybe, but internal.\n"],"snoc":[255,""],"app":[63,""],"mogensen-eval":[260,""],"f-succ":[262,""],"erdos-primitive-sequence":[326,""],"stay-zoomed-out":[329,"\n"],"either-cyan-or-black":[333,""],"repeating-circles":[341,""],"f-double":[343,""],"sndsnd":[29,""],"shift-by-4":[98,"\n"],"burning-ship-detail":[381,"\n\nA nice closeup of a self-similar instance of the Burning Ship fractal along\nthe main line.\n"],"h2rgb":[75,"\n\nConvert a hue to its red, green, and blue components.\n"],"fstfst":[24,""],"fib-dyn":[382,"\n\nThe dynamics of the Fibonacci sequence.\n"],"continued-logarithm":[393,""],"odd-numbers":[394,""],"step-comp":[401,"\n\n([Y x N, Z x N + N] x [X x N, Y x N + N]) x (X x N) -> Z x N + N\n\n[Y x N, Z x N + N] x [X x N, Y x N + N] -> [X x N, Z x N + N]\n"],"triang":[404,""],"setup-step-fractal":[411,"\n\nConvert an iterative fractal to count steps until it diverges.\n"],"advance-lentz-coeffs":[429,""],"list-choose":[437,""],"enclosing":[454,"\n\nThe smallest AABB enclosing two AABBs.\n"],"morton-spread":[458,""],"bool-sum":[204,""],"nat-div2":[210,""],"3b1b-horner":[483,""],"sdf2d":[490,"\n"],"f-halve":[492,""],"app-pair-at-point":[494,""],"int/succ":[499,"\n\nThe successor of an integer.\n"],"int/abs":[500,"\n\nThe absolute value of an integer.\n"],"int/neg":[501,"\n\nThe negation of an integer.\n"],"int/zero":[502,"\n\nThe integer zero. For no particular reason, we choose positive zero.\n"],"int/zero?":[503,"\n\nWhether an integer is zero.\n"],"monoids/mul/add":[228,""],"monoids/mul/zero":[344,""],"monoids/endo/add":[507,"\n\nAddition in an endomorphism monoid.\n"],"monoids/endo/zero":[57,"\n\nThe zero of an endomorphism monoid.\n"],"monoids/add/add":[224,""],"monoids/add/zero":[141,""],"sdf3/sphere":[516,""],"nat/20":[352,""],"nat/256":[525,"\n"],"nat/pred-maybe":[160,"\n\nThe predecessor of a natural number, or a distinguished point for zero.\n"],"nat/mul":[228,"\n"],"nat/odd?":[526,"\n\nWhether a natural number is odd.\n"],"nat/3":[215,"\n"],"nat/sum":[527,"\n\nThe sum of a list of natural numbers.\n"],"nat/sum-of-sqr":[533,"\n\nThe sum of squares of natural numbers up to (but not including) the input.\n"],"nat/add":[224,"\n\nAddition of two natural numbers.\n"],"nat/exp":[524,"\n"],"nat/monus":[537,"\n"],"nat/1":[344,""],"nat/to-f":[313,"\n\nConvert a unary natural number to a floating-point number. The conversion uses\nbinary as an intermediate step to allow construction of large numbers.\n"],"nat/pred":[162,"\n\nThe predecessor of a natural number. Zero is mapped to itself.\n"],"nat/5":[348,"\n"],"nat/double-alt":[351,"\n\nDouble a natural number by counting every successor operation twice.\n"],"nat/64":[540,"\n"],"nat/fact":[546,"\n\nThe factorial function on natural numbers.\n"],"nat/7":[359,"\n"],"nat/leonardo":[548,""],"nat/lt-eq?":[557,"\n\nThe less-than-or-equal relation on natural numbers.\n"],"nat/eq?":[168,"\n\nEquality on natural numbers is decidable.\n"],"nat/4":[361,"\n"],"nat/2":[214,"\n"],"nat/fib":[548,""],"nat/double":[349,"\n\nDouble a natural number by adding it to itself.\n"],"nat/100":[369,""],"nat/horner":[567,"\n\nEvaluate a polynomial in the natural numbers with Horner's rule.\n"],"nat/9":[569,"\n"],"nat/32":[539,"\n"],"nat/cube":[573,"\n\nThe cube of a natural number.\n"],"nat/16":[538,"\n"],"nat/sqr":[368,"\n\n\n"],"nat/zero?":[153,"\n\nWhether a natural number is zero.\n"],"nat/sqr-of-sum":[575,"\n\nThe square of the sum of the natural numbers up to (but not including) the\ninput.\n"],"nat/rem":[585,""],"nat/rshift":[595,"\n\nShift all of the bits in a natural number towards the least-significant bit.\nThe least-significant bit itself is also returned.\n"],"nat/10":[350,"\n"],"nat/81":[597,"\n\n\n"],"nat/pot":[600,"\n\nThe powers of two.\n"],"nat/8":[517,"\n"],"nat/sylvester":[604,""],"nat/even?":[184,"\n\nWhether a natural number is even. Zero is even.\n"],"magma/square":[608,"\n\nA magma can be squared to produce an endomorphism.\n"],"magma/braid":[612,"\n\nBraid a magma, obtaining its opposite magma.\n"],"poly/deriv":[624,"\n\nThe derivative of a polynomial, which itself is a polynomial.\n"],"poly/nice-deriv":[626,""],"poly/zero":[127,"\n\nThe zero polynomial.\n"],"poly/order":[629,"\n\nThe largest exponent in a polynomial. \n"],"poly/const":[430,"\n\nA constant polynomial which always evaluating to the given natural number.\n"],"combinators/k":[630,""],"combinators/s":[635,""],"combinators/w":[639,""],"fun/distribr":[198,"\n\nDistribute to the right.\n"],"fun/int-comp":[507,"\n\nAn internalized version of composition.\n"],"fun/app":[63,"\n\nApply a function to a value.\n\nIn categorical jargon, this is the [evaluation\nmap](https://ncatlab.org/nlab/show/evaluation%20map).\n"],"fun/int-flip":[643,"\n"],"fun/factorr":[645,"\n\nFactor out a product from a sum.\n"],"fun/factorl":[649,"\n\nFactor out a product from a sum.\n"],"fun/distribl":[193,"\n\nDistribute to the left.\n"],"double/to-pair":[651,"\n\nConvert a double value to a pair containing a Boolean tag indicating which\nside of the double the value occupies.\n"],"double/merge":[500,"\n\nEither side of a double.\n"],"double/from-pair":[658,"\n\nConvert a pair into a double, where the first component of the pair is the\nelement to embed and the second component is a Boolean tag indicating which\nside of the sum to occupy.\n"],"baire/omega":[1,"\n\nAs a non-standard natural number, $\\omega$ is the smallest natural number\ngreater than all standard natural numbers.\n"],"baire/add":[660,"\n\nAddition of non-standard natural numbers in Baire space.\n"],"list/every-other":[676,""],"list/reverse-onto":[297,"\n\nReverse a list onto an input suffix.\n"],"list/zip":[699,"\n\nZip two lists together.\n"],"list/nil?":[700,"\n\nWhether a list is nil.\n"],"list/head":[701,"\n\nThe most exterior constructed value in a list, if it exists.\n"],"list/repeat":[708,"\n"],"list/flatten":[709,"\n\nFlatten a list of lists into a single list.\n"],"list/append":[435," \n\nConcatenate two lists into a single list.\n"],"list/evens":[715,"\n\n\n"],"list/reverse":[298,"\n\nReverse a list in linear time.\n"],"list/gauss":[716,"\n"],"list/flatmap":[709,""],"list/uncons":[686,"\n\nTry to decompose a list at its extremal cell.\n"],"list/cat_maybes":[719,"\n\nSelect the left-hand elements of a list of sums.\n"],"list/drop":[725,""],"list/double":[728,"\n\nRepeat each value in a list twice.\n"],"list/singleton":[430,"\n\nA list with only one value.\n"],"list/tail":[720,"\n\nThe tail of a list. The tail of the empty list is the empty list.\n"],"list/len":[628,"\n"],"list/tails":[737,""],"list/pair":[742,"\n\nZip a single value into a list.\n"],"list/range":[147,"\n"],"bool/pick":[252,"\n"],"bool/all?":[743,"\n\nWhether every element in a list is true.\n"],"bool/popcount":[748,"\n\nThe number of set bits in a list of bits.\n"],"bool/parity":[749,"\n\nThe parity of a list of bits.\n"],"bool/half-adder":[270,"\n\nAdd two bits, returning a pair of the result and carry bit.\n"],"bool/any?":[750,"\n\nWhether any element in a list is true.\n"],"bool/xor":[269,"\n\nThe exclusive-or operation, also known as the parity operation.\n"],"sdf2/circle":[752,"\n\n\n"],"draw/complex-fun":[765,"\n\nMap a complex number to a color. The magnitude is mapped to luminance and the\nangle is mapped to hue.\n"],"mat2/mul":[777,"\n\nMultiply two matrices.\n"],"mat2/vec":[772,"\n\nApply a matrix to a column vector.\n"],"mat2/trans":[767,"\n\nTranspose a matrix.\n"],"mat2/rotate":[783,""],"mat2/id":[785,"\n\nAn identity matrix.\n"],"square/to-pair":[788,"\n\nConvert a square to a pair.\n"],"square/from-pair":[790,"\n\nConvert a pair to a square.\n"],"extnat/succ":[791,"\n\nThe successor of an extended natural number is also an extended natural\nnumber.\n"],"extnat/pred":[806,"\n\nThe predecessor of an extended natural number. The extra point signals when\nthe input is zero.\n"],"nonempty/unfold":[817,"\n"],"nonempty/to-list":[129,"\n\nA nonempty list is a list.\n"],"fps/add":[822,"\n\nThe sum of two formal power series.\n"],"fps/diff":[826,"\n\nThe formal derivative of a formal power series.\n"],"fps/extract":[827,"\n\nExtract a coefficient from a formal power series.\n"],"fps/zero":[829,"\n\nThe zero formal power series.\n"],"weekend/image1":[833,"\n\nCode for Image 1. The viewport is from (0,0) to (1,1), but flipped\nupside-down.\n\nWhen rendering this image, flip the viewport like:\n\n    0.0 1.0 1.0 0.0\n"],"weekend/finish-quadratic2":[849,"\n\nCompute the quadratic formula, replacing $b$ with $h$ where $b = 2h$.\n"],"weekend/image2":[893,""],"weekend/image4":[933,"\n"],"weekend/discriminant":[938,"\n\nCompute the discriminant for the quadratic formula.\n"],"weekend/aim-ray":[855,""],"weekend/ray_color4":[932,"\n\n\n"],"weekend/ray_color3":[956,"\n\n\n"],"weekend/ray_color":[892,"\n"],"weekend/ray_at":[917,"\n\nAdvance a ray in time. The ray is given as a pair of origin and direction.\n"],"weekend/make-normal":[919,""],"weekend/ray_color2":[970,"\n\n\n"],"weekend/image3":[971,"\n"],"weekend/sphere_center":[894,""],"weekend/finish-quadratic":[953,"\n\nCompute the quadratic formula.\n"],"weekend/origin":[331,""],"weekend/sky":[879,"\n"],"weekend/discriminant2":[838,"\n\nCompute the discriminant for the quadratic formula. Note that $b$ is replaced\nwith $h$, where $b = 2h$.\n"],"comonads/store/duplicate":[973,""],"comonads/store/counit":[63,"\n"],"comonads/product/duplicate":[974,"\n"],"comonads/product/counit":[12,"\n"],"demo/burning-ship-color":[1008,"\n\nDraw membership for the [Burning Ship\nfractal](https://en.wikipedia.org/wiki/Burning_Ship_fractal), a relative of\nthe Mandelbrot set.\n"],"demo/metaball":[1036,"\n\n\n"],"demo/red-ellipse":[1039,"\n\n\n"],"demo/burning-ship-fast":[1080,"\n\nDraw membership for the [Burning Ship\nfractal](https://en.wikipedia.org/wiki/Burning_Ship_fractal), a relative of\nthe Mandelbrot set.\n"],"demo/mandelbrot":[1100,"\n\nDraw membership in the [Mandelbrot\nset](https://en.wikipedia.org/wiki/Mandelbrot_set).\n"],"demo/burning-ship":[1113,"\n\nDraw membership for the [Burning Ship\nfractal](https://en.wikipedia.org/wiki/Burning_Ship_fractal), a relative of\nthe Mandelbrot set.\n"],"demo/deco-circles":[1114,""],"demo/anim/red-ellipse":[1118,""],"demo/anim/hue":[1119,""],"demo/anim/ellipse-color":[1128,"\n\n\n"],"demo/anim/max-headroom":[1138,"\n"],"demo/anim/deco-circles":[1141,"\n"],"demo/anim/jupiter-storm":[1153,"\n\nA variation on the classic \"Jupiter Storm\" demo effect.\n"],"v2/polar":[1154,"\n\nConvert from rectangular coordinates to polar coordinates on the Cartesian\nplane.\n"],"v2/mandelbrot":[1086,"\n\nPerform a Mandelbrot iteration. The Mandelbrot set is composed of points\nwhich do not diverge under iteration.\n"],"v2/burning-ship":[987,"\n\nAn iteration of the Burning Ship fractal, a relative of the Mandelbrot set.\n"],"v2/scale-by":[105,""],"v2/rotate-by":[1117,""],"v2/complex/mag-2?":[242,"\n\nWhether a complex number's magnitude is less than 2.\n"],"v2/complex/norm":[240,"\n\nThe norm of a complex number.\n"],"v2/complex/mul":[474,"\n"],"v2/complex/sqrt":[1172,"\n\nThe principal square root of a complex number.\n"],"v2/complex/add":[32,""],"v2/complex/exp":[1180,"\n\nThe exponential function in the complex plane.\n"],"v2/complex/i":[784,"\n\nThe imaginary unit $i$. By convention, multiplication by $i$ corresponds to a\nquarter turn counterclockwise on the Cartesian plane.\n"],"v2/complex/one":[123,""],"v2/complex/conjugate":[314,""],"v2/complex/horner":[482,""],"v2/complex/zero":[124,""],"v2/complex/sqr":[983,"\n\n\n"],"v2/dual/mul":[1183,"\n\nMultiplication in the dual numbers.\n"],"v2/dual/e":[784,"\n\nThe epsilon unit.\n"],"v3/dot":[511,"\n\nDot product of two vectors.\n"],"v3/norm":[513,"\n\nThe length of a vector.\n"],"v3/mul":[84,"\n"],"v3/add":[34,"\n"],"v3/int-scale":[861,"\n\nScale a vector by a varying amount.\n"],"v3/sub":[898,"\n"],"v3/div":[1188,"\n"],"v3/normalise":[862,"\n\nA unit vector which points in the same direction as the input vector.\n"],"v3/centre":[1196,"\n\nThe center of an AABB.\n"],"v3/length_squared":[512,"\n\nThe positive square of the length of a vector.\n"],"v3/cross":[1223,"\n\nThe cross product of two vectors.\n"],"v3/rgb/black":[331,"\n\nThe least saturated color possible.\n"],"v3/rgb/cyan":[330,""],"v3/rgb/green":[1224,""],"v3/rgb/blue":[1225,""],"v3/rgb/red":[961,""],"v3/rgb/white":[884,"\n\nThe most saturated color which can reliably be displayed.\n"],"f/3":[10,"\n\nThree.\n"],"f/radians-to-turns":[759,"\n\nConvert radians to turns.\n"],"f/sum":[1226,"\n\nAn uncompensated sum of a list of floating-point numbers.\n"],"f/sub3":[1233,"\n\nSubtraction of two three-dimensional vectors.\n"],"f/product":[1234,""],"f/ln":[322,""],"f/abs":[64,"\n\nThe absolute value of a floating-point number.\n"],"f/sub":[315,"\n\nSubtraction of floating-point numbers.\n"],"f/5":[1144,""],"f/min":[439,"\n\nThe minimum of two floating-point numbers.\n"],"f/add2":[32,"\n\nAddition of two-dimensional vectors.\n"],"f/max":[447,"\n"],"f/e":[1235,"\n\nEuler's constant.\n"],"f/div":[17,"\n\nDivide two floating-point numbers. Division by zero yields:\n\n* $\\infty$ for positive dividends\n* $-\\infty$ for negative dividends\n* $\\pm 0$ for zero dividends\n\nSigns are respected; the result is negative when exactly one input is\nnegative, and positive otherwise.\n"],"f/euclidean3":[1236,"\n\nThe Euclidean distance between two three-dimensional vectors.\n"],"f/2pi":[756,"\n\nThe constant $2\\pi$, sometimes called $\\tau$.\n"],"f/invert-interval":[869,""],"f/eq?":[1240,""],"f/-1":[125,""],"f/4":[109,"\n\nFour.\n"],"f/mad":[423,""],"f/2":[8,"\n\nTwo.\n"],"f/add3":[34,"\n\nAddition of three-dimensional vectors.\n"],"f/negate3":[1230,"\n\nNegate a three-dimensional vector.\n"],"f/9":[91,"\n\nNine.\n"],"f/ln2":[1241,""],"f/dot2":[235,"\n\nThe dot product of two two-dimensional vectors.\n"],"f/cube":[1243,"\n\nThe cube of a floating-point number.\n"],"f/sqrt-pos":[239,"\n\nThe square root of a floating-point number, clamped to zero for negative\ninputs.\n"],"f/sqr":[90,"\n\nThe square of a floating-point number.\n"],"f/fract":[44,"\n\nThe fractional component of a floating-point number.\n"],"f/inf":[319,"\n"],"f/10":[1245,"\n\nTen.\n"],"f/half":[337,"\n\nOne half.\n"],"f/0.7":[876,"\n"],"f/disc-to-interval":[866,""],"f/1000":[1246,"\n\nOne thousand.\n"],"f/dot3":[511,"\n\nThe dot product of two three-dimensional vectors.\n"],"monads/maybe/int-bind":[1248,"\n\nAn internal version of bind for the maybe monad.\n"],"monads/maybe/unit":[158,"\n\nThe unit of the maybe monad.\n"],"monads/maybe/int-comp":[1252,"\n\nAn internalized version of composition in the Kleisli category for the maybe\nmonad.\n"],"monads/maybe/join":[1253,"\n\nThe join operation for the maybe monad.\n"],"monads/maybe/int-cps":[1257,"\n\nConvert the maybe monad to continuation-passing style. Explained at\n[n-Category\nCafé](https://golem.ph.utexas.edu/category/2012/09/where_do_monads_come_from.html#c042100).\n"],"monads/state/unit":[972,"\n"],"monads/state/join":[1259,""],"monads/list/int-bind":[1265,"\n\nInternal bind in the list monad.\n"],"monads/list/unit":[430,"\n"],"monads/list/add":[435,"\n\nAddition in the list monad.\n"],"monads/list/join":[709,"\n\nThe join operation in the list monad.\n"],"monads/list/zero":[127,"\n\nThe zero of the list monad.\n"],"monads/cost/unit":[1266,"\n"],"monads/cost/join":[1061,"\n"],"monads/cost/strength":[275,"\n\nStrength in the cost monad.\n"],"monads/cost/enrich":[1268,"\n\nEnrichment for the cost monad.\n"],"monads/logic/unit":[1271,"\n"],"monads/either/unit":[156,"\n"],"monads/either/join":[1272,"\n"],"monads/searchable/unit":[630,"\n"],"monads/reader/unit":[630,"\n"],"monads/reader/join":[1274,"\n"],"monads/step/int-bind":[1065,"\n\nAn internal version of binding in the step monad.\n"],"monads/step/unit":[1049,"\n\nThe unit of the step monad.\n"],"monads/step/from-maybe":[1275,"\n\nLift from the maybe monad to the step monad.\n"],"monads/step/increment":[1278,"\n\nTake a step if the action is successful, otherwise do nothing.\n"],"monads/writer/write":[257,""],"monads/subset/guard":[1280,""],"monads/subset/add":[179,""],"monads/subset/join":[639,""],"monads/subset/zero":[151,""],"monads/cont/unit":[1281,"\n"],"monads/cont/join":[1285,"\n\nCollapse two layers of continuations into one.\n"],"monads/cont/bind":[1290,"\n\nChain continuations together.\n"],"monads/cont/run":[1287,"\n\nRun a computation with continuations.\n"],"subobj/empty":[149,"\n\nAn empty subobject.\n"],"subobj/disj":[1292,"\n\nThe union of two subobjects.\n"],"subobj/full":[206,"\n\nA subobject that is just the original object.\n"],"subobj/conj":[1294,"\n\nThe intersection of two subobjects.\n"],"subobj/complement":[1296,"\n\nThe complement of a subobject.\n"],"pe/6":[1300,"\n\nA complete solution to [Project Euler Problem\n6](https://projecteuler.net/problem=6).\n"],"bits/succ":[288,"\n\nThe successor of a natural number is also a natural number.\n"],"bits/left-shift":[1302,""],"bits/to-f":[312,"\n\nConvert a binary natural number to a floating-point number.\n"],"bits/morton-fst":[1303,""],"bits/from-nat":[289,"\n\nConvert a natural number from unary to binary.\n"],"bits/zero":[127,"\n"],"bits/to-nat":[1308,"\n\nConvert a natural number from binary to unary.\n"],"cats/cost/f-cos":[1309,"\n"],"cats/cost/f-sin":[1310,"\n"],"cats/cost/snd":[1311,"\n"],"cats/cost/succ":[1312,"\n"],"cats/cost/f-pi":[1313,"\n"],"cats/cost/f-floor":[1314,"\n"],"cats/cost/f-lt":[1315,"\n"],"cats/cost/disj":[1316,"\n"],"cats/cost/f-negate":[1317,"\n"],"cats/cost/f-mul":[1318,"\n"],"cats/cost/n-add":[1320,"\n"],"cats/cost/fst":[1321,"\n"],"cats/cost/not":[1322,"\n"],"cats/cost/f-add":[1323,"\n"],"cats/cost/f-one":[1324,"\n"],"cats/cost/left":[407,"\n"],"cats/cost/f-sqrt":[1325,"\n"],"cats/cost/conj":[1326,"\n"],"cats/cost/f-zero":[1327,"\n"],"cats/cost/f-recip":[1328,"\n"],"cats/cost/right":[1329,"\n"],"cats/cost/f-atan2":[1330,"\n"],"cats/cost/cons":[1331,"\n"],"cats/cost/zero":[1332,"\n"],"cats/cost/n-pred-maybe":[1334,"\n"],"cats/cost/id":[1266,"\n"],"cats/cost/f-sign":[1335,"\n"],"cats/cost/t":[1336,"\n"],"cats/cost/f-exp":[1337,"\n"],"cats/cost/nil":[1338,"\n"],"cats/cost/either":[1339,"\n"],"cats/cost/ignore":[1340,"\n"],"cats/cost/f":[1341,"\n"],"lens/pair/fst":[1345,""],"fifo/empty?":[1349,"\n\nWhether a queue is empty.\n"],"fifo/refill":[1357,"\n\nPrepare a queue for a pop by refilling the pop stack.\n"],"fifo/push":[1359,"\n\nPush a value onto a queue.\n"],"fifo/pop":[1364,"\n\nPop an item from a queue, returning it in the left-hand component. The\nright-hand component is used to signal an empty queue.\n"],"fifo/nil":[1365,"\n\nAn empty queue.\n"],"scott/bool/true":[630,"\n"],"scott/bool/false":[534,"\n"],"pair/rotl":[665,""],"pair/assr":[275,"\n\nReassociate to the right.\n"],"pair/assl":[265,"\n\nReassociate to the left.\n"],"pair/dup":[2,"\n\nThe [diagonal map](https://ncatlab.org/nlab/show/diagonal+morphism).\n"],"pair/swap":[189,"\n\nSwap the first and second components of a pair.\n\nSwapping twice in a row is equivalent to the identity arrow.\n\nThis expression is the smallest with its type signature.\n"],"sum/left?":[1366,"\n"],"sum/assr":[797,"\n\nReassociate a triple sum to the right.\n"],"sum/assl":[803,"\n\nReassociate a triple sum to the left.\n"],"sum/swap":[501,"\n\nSwap the two cases of a sum.\n"],"mat3/mul":[1399,"\n"],"mat3/vec":[1391,"\n"],"mat3/trans":[1380,"\n\nTranspose a 3x3 matrix.\n"],"mat3/id":[1401,"\n\nA 3x3 identity 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Given a maximum number of\nsteps, we iterate the IFS for a fractal in the complex plane until its\nabsolute value exceeds 2, and return a value in [0,1] indicating how many\nsteps were taken before divergence.\n"],"monad-choose":[["fold",0,["comp",["pair",["comp","fst",1],"snd"],2]],""],"l":[["comp",["pair",0,1],"cons"],""],"fractal-maybe":[["comp",["comp",0,["pair",["comp",["pair",["comp",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]],"f-add"]],["comp","f-sqrt",["case","id","f-zero"]]],["comp","ignore",["comp",["pair","f-one","f-one"],"f-add"]]],"f-lt"],["pair","left",["comp","ignore","right"]]]],["comp",["pair",["comp","fst",["comp","either",["case",["curry",["comp","snd","fst"]],["curry",["comp","snd","snd"]]]]],"snd"],["uncurry","id"]]],"\n\nTake a step in an IFS, failing if the step has magnitude 2 or greater.\n"],"pick-const":[["comp","either",["case",0,1]],""],"iter-fractal-fast":[["comp",["pair","ignore","id"],["uncurry",["comp",["pair",0,["comp",["pair",["comp","ignore",["curry",["comp","snd",["curry",["comp",["comp",["uncurry","id"],["comp",["pair",["comp",["pair",["comp",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]],"f-add"]],["comp","f-sqrt",["case","id","f-zero"]]],["comp","ignore",["comp",["pair","f-one","f-one"],"f-add"]]],"f-lt"],["pair","left",["comp","ignore","right"]]],["comp",["pair",["comp","fst",["comp","either",["case",["curry",["comp","snd","fst"]],["curry",["comp","snd","snd"]]]]],"snd"],["uncurry","id"]]]],["case",["pair","left",["comp","ignore",["comp","zero","succ"]]],["pair","right",["comp","ignore","zero"]]]]]]]],["comp",["comp","f-zero",["pair","id","id"]],1]],["uncurry","id"]]],["uncurry",["pr",["curry",["comp","fst",["curry",["comp","snd",["pair","left",["comp","ignore","zero"]]]]]],["curry",["comp",["pair","snd",["uncurry","id"]],["curry",["comp",["pair",["comp",["pair",["comp","fst","snd"],"snd"],["uncurry","id"]],["comp","fst","fst"]],["comp",["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["uncurry",["case",["curry","left"],["curry","right"]]]],["case",["comp",["pair",["comp",["pair",["comp","snd","snd"],"fst"],["uncurry","id"]],["comp","snd","fst"]],["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry",["pr",["curry",["comp","snd","id"]],["curry",["comp",["uncurry","id"],"succ"]]]]]]]],["pair",["comp","ignore","right"],["comp","snd","fst"]]]]]]]]]]]]],"\n\nGiven a maximum number of steps, iterate the given fractal.\n"],"graph-fun":[["comp",0,["pair","id",["pair","id",["comp","ignore","f-one"]]]],"\n\nGraph a real function on the plane. 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fractal-membership, but just returning the length so that we can\nfalse-color it.\n"],"dynamics":[["pair",["comp","fst",["comp",["pair",["curry",["comp","snd",0]],"id"],["curry",["comp",["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry","id"]]]],["uncurry","id"]]]]],"snd"],"\n\nThe dynamics of a deterministic automaton. The second component of the pair is\nleft free, but usually is a status value, like a Boolean.\n"],"setup-viewport":[["comp",["comp",["pair","id",["comp","ignore",1]],["pair",["comp",["pair",["comp","fst","fst"],"snd"],"f-mul"],["comp",["pair",["comp","fst","snd"],"snd"],"f-mul"]]],["comp",["pair","id",["comp","ignore",0]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]]]]],"\n\nSet up a preferred viewport for 2D rendering. 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an [IFS](https://en.wikipedia.org/wiki/Iterated_function_system) for a\ngiven number of steps.\n"],"nat/do-if-not-zero":[["comp",["comp",["pair","id",["pr","t",["comp","ignore","f"]]],"swap"],["uncurry",["comp","either",["case",["curry",["comp","snd",["comp","ignore","right"]]],["curry",["comp","snd",["comp",0,"left"]]]]]]],"\n"],"nat/kata":[["pr",0,1],""],"nat/para":[["comp",["pr",["pair","zero",0],["pair",["comp","fst","succ"],1]],"snd"],""],"poly/horner":[["comp",["pair",["comp","fst",["comp",["pair","id",["comp","ignore","nil"]],["uncurry",["fold",["curry",["comp","snd","id"]],["curry",["comp",["pair",["comp","fst","snd"],["comp",["pair",["comp","fst","fst"],"snd"],"cons"]],["uncurry","id"]]]]]]],"snd"],["uncurry",["fold",["curry",["comp","snd",["comp","ignore",0]]],["curry",["comp",["pair",["pair",["comp","fst","fst"],["comp",["pair",["comp","fst","snd"],"snd"],["uncurry","id"]]],"snd"],["comp",["pair",["comp",["pair",["comp","fst","snd"],"snd"],2],["comp","fst","fst"]],1]]]]]],"\n\nEvaluate a polynomial at an input coordinate using Horner's rule, given:\n\n* A 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The dependent sum is merely postcomposition.\n"],"fun/hom-const":[["curry",["comp","fst",0]],"\n\nTake and discard an additional argument by creating a hom.\n"],"fun/unname":[["comp",["pair","ignore","id"],["uncurry",0]],"\n\nReference an arrow by name.\n"],"fun/apppair":[["comp",["pair",0,1],["uncurry","id"]],"\n\nApply the output of one arrow onto the output of another.\n"],"fun/name":[["curry",["comp","snd",0]],"\n\nThe name of an arrow.\n"],"fun/graph":[["pair","id",0],"\n"],"fun/iter-maybe":[["pr",["curry",["comp","snd","left"]],["comp",["pair","id",["comp","ignore",["curry",["comp","snd",0]]]],["curry",["comp",["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry","id"]]]],["comp",["comp",["comp",["pair","snd","fst"],["uncurry",["case",["curry","left"],["curry","right"]]]],["case",["comp",["pair","snd","fst"],"left"],["comp",["pair","snd","fst"],"right"]]],["case",["uncurry","id"],["comp","ignore","right"]]]]]]],"\n\nIterate a given arrow up to zero or more times.\n"],"fun/precomp":[["curry",["comp",["pair","fst",["comp","snd",0]],["uncurry","id"]]],"\n\nPrecompose a function type with an arrow. This is like the inverse-image\nfunctor for an arbitrary classifier. It is also like one version of the Yoneda\nembedding for the given arrow.\n"],"fun/observe":[["curry",["comp",["pair","snd","fst"],["uncurry",["comp",["pair",["comp","ignore",["curry",["comp","snd",0]]],["pr",["curry",["comp","snd","id"]],["comp",["pair","id",["comp","ignore",["curry",["comp","snd",1]]]],["curry",["comp",["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry","id"]]]],["uncurry","id"]]]]]],["curry",["comp",["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry","id"]]]],["uncurry","id"]]]]]]],"\n\nObserve the value of an endomorphism after a specified number of iterations.\n"],"fun/flip":[["curry",["comp",["pair","snd","fst"],["uncurry",0]]],"\n\nSwap the order in which arguments are applied onto a curried arrow.\n"],"fun/postcomp":[["curry",["comp",["uncurry","id"],0]],"\n\nPostcompose a function type with an arrow. This is like one version of the\nYoneda embedding for the given arrow.\n"],"fun/const":[["comp","ignore",0],"\n"],"list/map":[["fold","nil",["comp",["pair",["comp","fst",0],"snd"],"cons"]],"\n"],"list/conspair":[["comp",["pair",0,1],"cons"],"\n\nBuild a list whose head is the output of one arrow and whose tail is the\noutput of another arrow.\n"],"list/kata":[["fold",0,1],""],"list/eq?":[["comp",["pair",["comp",["pair",["comp","fst",["fold","zero",["comp","snd","succ"]]],["comp","snd",["fold","zero",["comp","snd","succ"]]]],["uncurry",["pr",["curry",["comp","snd",["pr","t",["comp","ignore","f"]]]],["curry",["comp",["pair","fst",["comp","snd",["comp",["pr","right",["comp",["case","succ","zero"],"left"]],["case","id","zero"]]]],["uncurry","id"]]]]]],["comp",["uncurry",["fold",["curry",["comp","snd",["comp","ignore","nil"]]],["curry",["comp",["pair","fst",["comp","snd",["fold","right",["comp",["pair","fst",["comp","snd",["comp",["case","cons","nil"],"left"]]],["comp",["comp",["comp",["pair","snd","fst"],["uncurry",["case",["curry","left"],["curry","right"]]]],["case",["comp",["pair","snd","fst"],"left"],["comp",["pair","snd","fst"],"right"]]],["case","left",["comp","ignore","right"]]]]]]],["comp",["comp",["comp",["pair","snd","fst"],["uncurry",["case",["curry","left"],["curry","right"]]]],["case",["comp",["pair","snd","fst"],"left"],["comp",["pair","snd","fst"],"right"]]],["case",["comp",["pair",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["uncurry","id"]]],"cons"],["comp",["pair",["comp","fst","snd"],["comp","ignore","nil"]],["uncurry","id"]]]]]]]],["comp",["fold","nil",["comp",["pair",["comp","fst",0],"snd"],"cons"]],["fold","t","conj"]]]],"conj"],"\n\nEquality on lists is decidable, provided that equality of elements is\ndecidable.\n"],"list/para":[["comp",["fold",["pair","nil",0],["pair",["comp",["pair","fst",["comp","snd","fst"]],"cons"],1]],"snd"],""],"list/filter":[["fold","nil",["comp",["pair",["comp","fst",0],["pair","cons","snd"]],["comp",["pair",["comp","fst",["comp","either",["case",["curry",["comp","snd","fst"]],["curry",["comp","snd","snd"]]]]],"snd"],["uncurry","id"]]]],"\n\nApply a predicate to every element of a list, and retain the elements which\nthe predicate admits.\n"],"list/scan":[["comp",["fold",["pair",0,"nil"],["comp",["comp",["pair",["pair","fst",["comp","snd","fst"]],["comp","snd","snd"]],["pair",1,"snd"]],["pair","fst","cons"]]],"snd"],"\n\n\n"],"bool/ternary":[["comp",["comp",["pair","id",0],["pair","fst",["comp","snd","either"]]],["comp",["comp",["comp",["pair","snd","fst"],["uncurry",["case",["curry","left"],["curry","right"]]]],["case",["comp",["pair","snd","fst"],"left"],["comp",["pair","snd","fst"],"right"]]],["case",["comp","fst",1],["comp","fst",2]]]],""],"bool/both":[["comp",["pair",0,1],"conj"],"\n\nWhether two predicates both hold.\n"],"bool/if":[["comp","either",["case",["curry",["comp","snd",0]],["curry",["comp","snd",1]]]],"\n\nAs close as we can get to an if-expression.\n"],"bool/either":[["comp",["pair",0,1],"disj"],"\n\nWhether either predicate holds.\n"],"sdf2/extrude":[["comp",["pair",1,["comp",["comp","ignore",0],"f-negate"]],"f-add"],"\n"],"sdf2/scale":[["comp",["pair",["comp",["comp",["pair","id",["comp","ignore",["pair",0,0]]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-recip"]],"f-mul"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-recip"]],"f-mul"]]]],1],["comp","ignore",0]],"f-mul"],"\n"],"sdf2/union":[["comp",["pair",0,1],["comp",["pair","f-lt","id"],["comp",["pair",["comp","fst",["comp","either",["case",["curry",["comp","snd","fst"]],["curry",["comp","snd","snd"]]]]],"snd"],["uncurry","id"]]]],"\n"],"sdf2/translate":[["comp",["comp",["pair","id",["comp","ignore",0]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]]]],1],"\n"],"sdf2/metaballs":[["comp",["pair",["comp",["pair",["comp",1,["fold",["curry",["comp","snd",["comp","ignore","f-zero"]]],["curry",["comp",["pair",["comp",["pair",["comp",["comp","fst","fst"],"snd"],["comp",["comp",["pair",["comp",["comp","fst","fst"],"fst"],"snd"],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]]]],["comp",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]],"f-add"]],["comp","f-sqrt",["case","id","f-zero"]]]]],["comp",["pair","fst",["comp","snd","f-recip"]],"f-mul"]],["comp",["pair",["comp","fst","snd"],"snd"],["uncurry","id"]]],"f-add"]]]],"id"],["uncurry","id"]],["comp",["comp","ignore",0],"f-negate"]],"f-add"],"\n\n\n"],"mat2/vecpair":[["comp",["pair",0,1],["pair",["comp",["pair",["comp","fst","fst"],"snd"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]],"f-add"]],["comp",["pair",["comp","fst","snd"],"snd"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]],"f-add"]]]],"\n"],"weekend/hit_sphere3?":[["comp",["comp",["pair",["comp","fst",["comp",["pair","id",["comp","ignore",0]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]]]]]]],"snd"],["pair",["comp","snd",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["pair",["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]],["comp",["pair",["comp","fst",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["comp",["comp",["comp","ignore",1],["comp",["pair","id","id"],"f-mul"]],"f-negate"]],"f-add"]]]],["comp",["comp",["pair",["pair","fst",["comp","snd","fst"]],["comp",["comp",["pair",["comp",["comp","snd","fst"],["comp",["pair","id","id"],"f-mul"]],["comp",["comp",["pair","fst",["comp","snd","snd"]],"f-mul"],"f-negate"]],"f-add"],"f-sqrt"]],["comp",["comp",["pair","snd","fst"],["uncurry",["case",["curry","left"],["curry","right"]]]],["case",["comp",["pair","snd","fst"],"left"],["comp",["pair","snd","fst"],"right"]]]],["case",["comp",["comp",["pair",["comp",["pair",["comp",["comp","fst","snd"],"f-negate"],["comp","snd","f-negate"]],"f-add"],["comp","fst","fst"]],["comp",["pair","fst",["comp","snd","f-recip"]],"f-mul"]],"left"],["comp","ignore","right"]]]],"\n\nBasically the same as hit_sphere2?, but now the quadratic formula is rewritten\nin terms of $h$, where $b = 2h$.\n"],"weekend/hit_sphere":[["comp",["pair",["comp","fst",["comp",["pair","id",["comp","ignore",0]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]]]]]]],"snd"],["pair",["comp","snd",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["pair",["comp",["pair",["comp","ignore",["comp",["pair","f-one","f-one"],"f-add"]],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]],"f-mul"],["comp",["pair",["comp","fst",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["comp",["comp",["comp","ignore",1],["comp",["pair","id","id"],"f-mul"]],"f-negate"]],"f-add"]]]],"\n\nTest whether a ray hits a sphere, generating coefficients for the quadratic\nformula.\n"],"weekend/hit_sphere2":[["comp",["pair",["comp","fst",["comp",["pair","id",["comp","ignore",0]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]]]]]]],"snd"],["pair",["comp","snd",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["pair",["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]],["comp",["pair",["comp","fst",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["comp",["comp",["comp","ignore",1],["comp",["pair","id","id"],"f-mul"]],"f-negate"]],"f-add"]]]],"\n\nTest whether a ray hits a sphere, generating coefficients for the quadratic\nformula. The coefficients are not $a$, $b$, and $c$, but $a$, $h$, and $c$,\nwhere $b = 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The absolute tolerance is one millionth.\n"],"f/error":[["comp",["pair",["comp","fst",0],["comp","snd","f-negate"]],"f-add"],"\n\nThe error between the output value of the given arrow at the input value and\nthe expected input value.\n"],"f/dot2pair":[["comp",["pair",0,1],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]],"f-add"]],"\n\nApply the dot product to a pair of arrows.\n"],"f/minpair":[["comp",["pair",0,1],["comp",["pair","f-lt","id"],["comp",["pair",["comp","fst",["comp","either",["case",["curry",["comp","snd","fst"]],["curry",["comp","snd","snd"]]]]],"snd"],["uncurry","id"]]]],"\n\nThe minimum of two arrows at an input value.\n"],"monads/iter":[["pr",["curry",["comp","snd",0]],["comp",["pair","id",["comp","ignore",["curry",["comp","snd",2]]]],["curry",["comp",["pair",["comp",["pair",["comp","fst","snd"],"snd"],["uncurry","id"]],["comp","fst","fst"]],1]]]],"\n\nGiven a unit and internal bind in some monad, iterate an endomorphism in that\nmonad.\n\nFor example, to iterate in the maybe monad:\n\n    (monads/iter monads/maybe/unit monads/maybe/int-bind @0)\n\nIteration can terminate early in short-circuiting monads.\n"],"monads/guard":[["comp",["pair",2,"id"],["uncurry",["comp","either",["case",["curry",["comp","snd",["comp","ignore",1]]],["curry",["comp","snd",0]]]]]],"\n\nGiven the unit and zero of some monad, and some filtering predicate, test a\nvalue in that monad.\n"],"monads/int-comp":[["curry",["comp",["pair",["comp",["pair",["comp","fst","snd"],"snd"],["uncurry","id"]],["comp","fst","fst"]],0]],"\n\nInternal composition in any monad, built from the internal bind.\n"],"monads/int-iter":[["uncurry",["pr",["curry",["comp","fst",["curry",["comp","snd",0]]]],["curry",["comp",["pair","snd",["uncurry","id"]],["curry",["comp",["pair",["comp",["pair",["comp","fst","snd"],"snd"],["uncurry","id"]],["comp","fst","fst"]],1]]]]]],"\n\nInstead of just N, we're 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two arrows in parallel, acting on pairs of values.\n\nIn categorical jargon, the [tensor\nproduct](https://ncatlab.org/nlab/show/tensor+product) is a functor from pairs\nof arrows to arrows:\n\n$$\n\\bigotimes : C \\times C \\to C\n$$\n"],"pair/mapfst":[["pair",["comp","fst",0],"snd"],"\n\nMap over the first component of a pair.\n"],"pair/mapsnd":[["pair","fst",["comp","snd",0]],"\n\nMap over the second component of a pair.\n"],"pair/bimap":[["pair",["comp","fst",0],["comp","snd",0]],"\n\nMap uniformly over both components of a pair.\n"],"pair/of":[["comp",["pair",1,2],0],"\n\nCall an arrow of two arguments by building both arguments from a single input.\n"],"yoneda/embed":[["curry",["comp",["uncurry","id"],0]],"\n\nThe Yoneda embedding of an arrow.\n"],"yoneda/lift":[["comp",["pair","ignore","id"],["uncurry",["comp",["comp","ignore",["curry",["comp","snd","id"]]],0]]],"\n\nUndo the Yoneda embedding.\n"],"sum/mapright":[["case","left",["comp",0,"right"]],"\n\nMap over the right-hand 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\ No newline at end of file
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The components are based\non the hue, then scaled by the value.\n"],"zoom-out":[107,""],"in-ellipse?":[122,""],"fstsnd":[28,""],"3b1b-newton-poly":[140,""],"sndfst":[25,""],"subset-range":[182,""],"hailstone":[234,""],"nat-mul3":[229,""],"int-fractal-maybe":[253,"\n\nLike fractal-maybe, but internal.\n"],"snoc":[255,""],"app":[63,""],"mogensen-eval":[260,""],"f-succ":[262,""],"erdos-primitive-sequence":[326,""],"stay-zoomed-out":[329,"\n"],"either-cyan-or-black":[333,""],"repeating-circles":[341,""],"f-double":[343,""],"sndsnd":[29,""],"shift-by-4":[98,"\n"],"burning-ship-detail":[381,"\n\nA nice closeup of a self-similar instance of the Burning Ship fractal along\nthe main line.\n"],"h2rgb":[75,"\n\nConvert a hue to its red, green, and blue components.\n"],"fstfst":[24,""],"fib-dyn":[382,"\n\nThe dynamics of the Fibonacci sequence.\n"],"continued-logarithm":[393,""],"odd-numbers":[394,""],"step-comp":[401,"\n\n([Y x N, Z x N + N] x [X x N, Y x N + N]) x (X x N) -> Z x N + N\n\n[Y x N, Z x N + N] x [X x N, Y x N + N] -> [X x N, Z x N + N]\n"],"triang":[404,""],"setup-step-fractal":[411,"\n\nConvert an iterative fractal to count steps until it diverges.\n"],"advance-lentz-coeffs":[429,""],"list-choose":[437,""],"enclosing":[454,"\n\nThe smallest AABB enclosing two AABBs.\n"],"morton-spread":[458,""],"bool-sum":[204,""],"nat-div2":[210,""],"3b1b-horner":[483,""],"sdf2d":[490,"\n"],"f-halve":[492,""],"app-pair-at-point":[494,""],"int/succ":[499,"\n\nThe successor of an integer.\n"],"int/abs":[500,"\n\nThe absolute value of an integer.\n"],"int/neg":[501,"\n\nThe negation of an integer.\n"],"int/zero":[502,"\n\nThe integer zero. For no particular reason, we choose positive zero.\n"],"int/zero?":[503,"\n\nWhether an integer is zero.\n"],"monoids/mul/add":[228,""],"monoids/mul/zero":[344,""],"monoids/endo/add":[507,"\n\nAddition in an endomorphism monoid.\n"],"monoids/endo/zero":[57,"\n\nThe zero of an endomorphism monoid.\n"],"monoids/add/add":[224,""],"monoids/add/zero":[141,""],"sdf3/sphere":[516,""],"nat/20":[352,""],"nat/256":[525,"\n"],"nat/pred-maybe":[160,"\n\nThe predecessor of a natural number, or a distinguished point for zero.\n"],"nat/mul":[228,"\n"],"nat/odd?":[526,"\n\nWhether a natural number is odd.\n"],"nat/3":[215,"\n"],"nat/sum":[527,"\n\nThe sum of a list of natural numbers.\n"],"nat/sum-of-sqr":[533,"\n\nThe sum of squares of natural numbers up to (but not including) the input.\n"],"nat/add":[224,"\n\nAddition of two natural numbers.\n"],"nat/exp":[524,"\n"],"nat/monus":[537,"\n"],"nat/1":[344,""],"nat/to-f":[313,"\n\nConvert a unary natural number to a floating-point number. The conversion uses\nbinary as an intermediate step to allow construction of large numbers.\n"],"nat/pred":[162,"\n\nThe predecessor of a natural number. Zero is mapped to itself.\n"],"nat/5":[348,"\n"],"nat/double-alt":[351,"\n\nDouble a natural number by counting every successor operation twice.\n"],"nat/64":[540,"\n"],"nat/fact":[546,"\n\nThe factorial function on natural numbers.\n"],"nat/7":[359,"\n"],"nat/leonardo":[548,""],"nat/lt-eq?":[557,"\n\nThe less-than-or-equal relation on natural numbers.\n"],"nat/eq?":[168,"\n\nEquality on natural numbers is decidable.\n"],"nat/4":[361,"\n"],"nat/2":[214,"\n"],"nat/fib":[548,""],"nat/double":[349,"\n\nDouble a natural number by adding it to itself.\n"],"nat/100":[369,""],"nat/horner":[567,"\n\nEvaluate a polynomial in the natural numbers with Horner's rule.\n"],"nat/9":[569,"\n"],"nat/32":[539,"\n"],"nat/cube":[573,"\n\nThe cube of a natural number.\n"],"nat/16":[538,"\n"],"nat/sqr":[368,"\n\n\n"],"nat/zero?":[153,"\n\nWhether a natural number is zero.\n"],"nat/sqr-of-sum":[575,"\n\nThe square of the sum of the natural numbers up to (but not including) the\ninput.\n"],"nat/rem":[585,""],"nat/rshift":[595,"\n\nShift all of the bits in a natural number towards the least-significant bit.\nThe least-significant bit itself is also returned.\n"],"nat/10":[350,"\n"],"nat/81":[597,"\n\n\n"],"nat/pot":[600,"\n\nThe powers of two.\n"],"nat/8":[517,"\n"],"nat/sylvester":[604,""],"nat/even?":[184,"\n\nWhether a natural number is even. Zero is even.\n"],"magma/square":[608,"\n\nA magma can be squared to produce an endomorphism.\n"],"magma/braid":[612,"\n\nBraid a magma, obtaining its opposite magma.\n"],"poly/deriv":[624,"\n\nThe derivative of a polynomial, which itself is a polynomial.\n"],"poly/nice-deriv":[626,""],"poly/zero":[127,"\n\nThe zero polynomial.\n"],"poly/order":[629,"\n\nThe largest exponent in a polynomial. \n"],"poly/const":[430,"\n\nA constant polynomial which always evaluating to the given natural number.\n"],"combinators/k":[630,""],"combinators/s":[635,""],"combinators/w":[639,""],"fun/distribr":[198,"\n\nDistribute to the right.\n"],"fun/int-comp":[507,"\n\nAn internalized version of composition.\n"],"fun/app":[63,"\n\nApply a function to a value.\n\nIn categorical jargon, this is the [evaluation\nmap](https://ncatlab.org/nlab/show/evaluation%20map).\n"],"fun/int-flip":[643,"\n"],"fun/factorr":[645,"\n\nFactor out a product from a sum.\n"],"fun/factorl":[649,"\n\nFactor out a product from a sum.\n"],"fun/distribl":[193,"\n\nDistribute to the left.\n"],"double/to-pair":[651,"\n\nConvert a double value to a pair containing a Boolean tag indicating which\nside of the double the value occupies.\n"],"double/merge":[500,"\n\nEither side of a double.\n"],"double/from-pair":[658,"\n\nConvert a pair into a double, where the first component of the pair is the\nelement to embed and the second component is a Boolean tag indicating which\nside of the sum to occupy.\n"],"baire/omega":[1,"\n\nAs a non-standard natural number, $\\omega$ is the smallest natural number\ngreater than all standard natural numbers.\n"],"baire/add":[660,"\n\nAddition of non-standard natural numbers in Baire space.\n"],"list/every-other":[676,""],"list/reverse-onto":[297,"\n\nReverse a list onto an input suffix.\n"],"list/zip":[699,"\n\nZip two lists together.\n"],"list/nil?":[700,"\n\nWhether a list is nil.\n"],"list/head":[701,"\n\nThe most exterior constructed value in a list, if it exists.\n"],"list/repeat":[708,"\n"],"list/flatten":[709,"\n\nFlatten a list of lists into a single list.\n"],"list/append":[435," \n\nConcatenate two lists into a single list.\n"],"list/evens":[715,"\n\n\n"],"list/reverse":[298,"\n\nReverse a list in linear time.\n"],"list/gauss":[716,"\n"],"list/flatmap":[709,""],"list/uncons":[686,"\n\nTry to decompose a list at its extremal cell.\n"],"list/cat_maybes":[719,"\n\nSelect the left-hand elements of a list of sums.\n"],"list/drop":[725,""],"list/double":[728,"\n\nRepeat each value in a list twice.\n"],"list/singleton":[430,"\n\nA list with only one value.\n"],"list/tail":[720,"\n\nThe tail of a list. The tail of the empty list is the empty list.\n"],"list/len":[628,"\n"],"list/tails":[737,""],"list/pair":[742,"\n\nZip a single value into a list.\n"],"list/range":[147,"\n"],"bool/pick":[252,"\n"],"bool/all?":[743,"\n\nWhether every element in a list is true.\n"],"bool/popcount":[748,"\n\nThe number of set bits in a list of bits.\n"],"bool/parity":[749,"\n\nThe parity of a list of bits.\n"],"bool/half-adder":[270,"\n\nAdd two bits, returning a pair of the result and carry bit.\n"],"bool/any?":[750,"\n\nWhether any element in a list is true.\n"],"bool/xor":[269,"\n\nThe exclusive-or operation, also known as the parity operation.\n"],"sdf2/circle":[752,"\n\n\n"],"draw/complex-fun":[765,"\n\nMap a complex number to a color. The magnitude is mapped to luminance and the\nangle is mapped to hue.\n"],"mat2/mul":[777,"\n\nMultiply two matrices.\n"],"mat2/vec":[772,"\n\nApply a matrix to a column vector.\n"],"mat2/trans":[767,"\n\nTranspose a matrix.\n"],"mat2/rotate":[783,""],"mat2/id":[785,"\n\nAn identity matrix.\n"],"square/to-pair":[788,"\n\nConvert a square to a pair.\n"],"square/from-pair":[790,"\n\nConvert a pair to a square.\n"],"extnat/succ":[791,"\n\nThe successor of an extended natural number is also an extended natural\nnumber.\n"],"extnat/pred":[806,"\n\nThe predecessor of an extended natural number. The extra point signals when\nthe input is zero.\n"],"nonempty/unfold":[817,"\n"],"nonempty/to-list":[129,"\n\nA nonempty list is a list.\n"],"fps/add":[822,"\n\nThe sum of two formal power series.\n"],"fps/diff":[826,"\n\nThe formal derivative of a formal power series.\n"],"fps/extract":[827,"\n\nExtract a coefficient from a formal power series.\n"],"fps/zero":[829,"\n\nThe zero formal power series.\n"],"weekend/image1":[833,"\n\nCode for Image 1. The viewport is from (0,0) to (1,1), but flipped\nupside-down.\n\nWhen rendering this image, flip the viewport like:\n\n    0.0 1.0 1.0 0.0\n"],"weekend/finish-quadratic2":[849,"\n\nCompute the quadratic formula, replacing $b$ with $h$ where $b = 2h$.\n"],"weekend/image2":[893,""],"weekend/image4":[933,"\n"],"weekend/discriminant":[938,"\n\nCompute the discriminant for the quadratic formula.\n"],"weekend/aim-ray":[855,""],"weekend/ray_color4":[932,"\n\n\n"],"weekend/ray_color3":[956,"\n\n\n"],"weekend/ray_color":[892,"\n"],"weekend/ray_at":[917,"\n\nAdvance a ray in time. The ray is given as a pair of origin and direction.\n"],"weekend/make-normal":[919,""],"weekend/ray_color2":[970,"\n\n\n"],"weekend/image3":[971,"\n"],"weekend/sphere_center":[894,""],"weekend/finish-quadratic":[953,"\n\nCompute the quadratic formula.\n"],"weekend/origin":[331,""],"weekend/sky":[879,"\n"],"weekend/discriminant2":[838,"\n\nCompute the discriminant for the quadratic formula. Note that $b$ is replaced\nwith $h$, where $b = 2h$.\n"],"comonads/store/duplicate":[973,""],"comonads/store/counit":[63,"\n"],"comonads/product/duplicate":[974,"\n"],"comonads/product/counit":[12,"\n"],"demo/burning-ship-color":[1008,"\n\nDraw membership for the [Burning Ship\nfractal](https://en.wikipedia.org/wiki/Burning_Ship_fractal), a relative of\nthe Mandelbrot set.\n"],"demo/metaball":[1036,"\n\n\n"],"demo/red-ellipse":[1039,"\n\n\n"],"demo/burning-ship-fast":[1080,"\n\nDraw membership for the [Burning Ship\nfractal](https://en.wikipedia.org/wiki/Burning_Ship_fractal), a relative of\nthe Mandelbrot set.\n"],"demo/mandelbrot":[1100,"\n\nDraw membership in the [Mandelbrot\nset](https://en.wikipedia.org/wiki/Mandelbrot_set).\n"],"demo/burning-ship":[1113,"\n\nDraw membership for the [Burning Ship\nfractal](https://en.wikipedia.org/wiki/Burning_Ship_fractal), a relative of\nthe Mandelbrot set.\n"],"demo/deco-circles":[1114,""],"demo/anim/red-ellipse":[1118,""],"demo/anim/hue":[1119,""],"demo/anim/ellipse-color":[1128,"\n\n\n"],"demo/anim/max-headroom":[1138,"\n"],"demo/anim/deco-circles":[1141,"\n"],"demo/anim/jupiter-storm":[1153,"\n\nA variation on the classic \"Jupiter Storm\" demo effect.\n"],"v2/polar":[1154,"\n\nConvert from rectangular coordinates to polar coordinates on the Cartesian\nplane.\n"],"v2/mandelbrot":[1086,"\n\nPerform a Mandelbrot iteration. The Mandelbrot set is composed of points\nwhich do not diverge under iteration.\n"],"v2/burning-ship":[987,"\n\nAn iteration of the Burning Ship fractal, a relative of the Mandelbrot set.\n"],"v2/scale-by":[105,""],"v2/rotate-by":[1117,""],"v2/complex/mag-2?":[242,"\n\nWhether a complex number's magnitude is less than 2.\n"],"v2/complex/norm":[240,"\n\nThe norm of a complex number.\n"],"v2/complex/mul":[474,"\n"],"v2/complex/sqrt":[1172,"\n\nThe principal square root of a complex number.\n"],"v2/complex/add":[32,""],"v2/complex/exp":[1180,"\n\nThe exponential function in the complex plane.\n"],"v2/complex/i":[784,"\n\nThe imaginary unit $i$. By convention, multiplication by $i$ corresponds to a\nquarter turn counterclockwise on the Cartesian plane.\n"],"v2/complex/one":[123,""],"v2/complex/conjugate":[314,""],"v2/complex/horner":[482,""],"v2/complex/zero":[124,""],"v2/complex/sqr":[983,"\n\n\n"],"v2/dual/mul":[1183,"\n\nMultiplication in the dual numbers.\n"],"v2/dual/e":[784,"\n\nThe epsilon unit.\n"],"v3/dot":[511,"\n\nDot product of two vectors.\n"],"v3/norm":[513,"\n\nThe length of a vector.\n"],"v3/mul":[84,"\n"],"v3/add":[34,"\n"],"v3/int-scale":[861,"\n\nScale a vector by a varying amount.\n"],"v3/sub":[898,"\n"],"v3/div":[1188,"\n"],"v3/normalise":[862,"\n\nA unit vector which points in the same direction as the input vector.\n"],"v3/centre":[1196,"\n\nThe center of an AABB.\n"],"v3/length_squared":[512,"\n\nThe positive square of the length of a vector.\n"],"v3/cross":[1223,"\n\nThe cross product of two vectors.\n"],"v3/rgb/black":[331,"\n\nThe least saturated color possible.\n"],"v3/rgb/cyan":[330,""],"v3/rgb/green":[1224,""],"v3/rgb/blue":[1225,""],"v3/rgb/red":[961,""],"v3/rgb/white":[884,"\n\nThe most saturated color which can reliably be displayed.\n"],"f/3":[10,"\n\nThree.\n"],"f/radians-to-turns":[759,"\n\nConvert radians to turns.\n"],"f/sum":[1226,"\n\nAn uncompensated sum of a list of floating-point numbers.\n"],"f/sub3":[1233,"\n\nSubtraction of two three-dimensional vectors.\n"],"f/product":[1234,""],"f/ln":[322,""],"f/abs":[64,"\n\nThe absolute value of a floating-point number.\n"],"f/sub":[315,"\n\nSubtraction of floating-point numbers.\n"],"f/5":[1144,""],"f/min":[439,"\n\nThe minimum of two floating-point numbers.\n"],"f/add2":[32,"\n\nAddition of two-dimensional vectors.\n"],"f/max":[447,"\n"],"f/e":[1235,"\n\nEuler's constant.\n"],"f/div":[17,"\n\nDivide two floating-point numbers. Division by zero yields:\n\n* $\\infty$ for positive dividends\n* $-\\infty$ for negative dividends\n* $\\pm 0$ for zero dividends\n\nSigns are respected; the result is negative when exactly one input is\nnegative, and positive otherwise.\n"],"f/euclidean3":[1236,"\n\nThe Euclidean distance between two three-dimensional vectors.\n"],"f/2pi":[756,"\n\nThe constant $2\\pi$, sometimes called $\\tau$.\n"],"f/invert-interval":[869,""],"f/eq?":[1240,""],"f/-1":[125,""],"f/4":[109,"\n\nFour.\n"],"f/mad":[423,""],"f/2":[8,"\n\nTwo.\n"],"f/add3":[34,"\n\nAddition of three-dimensional vectors.\n"],"f/negate3":[1230,"\n\nNegate a three-dimensional vector.\n"],"f/9":[91,"\n\nNine.\n"],"f/ln2":[1241,""],"f/dot2":[235,"\n\nThe dot product of two two-dimensional vectors.\n"],"f/cube":[1243,"\n\nThe cube of a floating-point number.\n"],"f/sqrt-pos":[239,"\n\nThe square root of a floating-point number, clamped to zero for negative\ninputs.\n"],"f/sqr":[90,"\n\nThe square of a floating-point number.\n"],"f/fract":[44,"\n\nThe fractional component of a floating-point number.\n"],"f/inf":[319,"\n"],"f/10":[1245,"\n\nTen.\n"],"f/half":[337,"\n\nOne half.\n"],"f/0.7":[876,"\n"],"f/disc-to-interval":[866,""],"f/1000":[1246,"\n\nOne thousand.\n"],"f/dot3":[511,"\n\nThe dot product of two three-dimensional vectors.\n"],"monads/maybe/int-bind":[1248,"\n\nAn internal version of bind for the maybe monad.\n"],"monads/maybe/unit":[158,"\n\nThe unit of the maybe monad.\n"],"monads/maybe/int-comp":[1252,"\n\nAn internalized version of composition in the Kleisli category for the maybe\nmonad.\n"],"monads/maybe/join":[1253,"\n\nThe join operation for the maybe monad.\n"],"monads/maybe/int-cps":[1257,"\n\nConvert the maybe monad to continuation-passing style. Explained at\n[n-Category\nCafé](https://golem.ph.utexas.edu/category/2012/09/where_do_monads_come_from.html#c042100).\n"],"monads/state/unit":[972,"\n"],"monads/state/join":[1259,""],"monads/list/int-bind":[1265,"\n\nInternal bind in the list monad.\n"],"monads/list/unit":[430,"\n"],"monads/list/add":[435,"\n\nAddition in the list monad.\n"],"monads/list/join":[709,"\n\nThe join operation in the list monad.\n"],"monads/list/zero":[127,"\n\nThe zero of the list monad.\n"],"monads/cost/unit":[1266,"\n"],"monads/cost/join":[1061,"\n"],"monads/cost/strength":[275,"\n\nStrength in the cost monad.\n"],"monads/cost/enrich":[1268,"\n\nEnrichment for the cost monad.\n"],"monads/logic/unit":[1271,"\n"],"monads/either/unit":[156,"\n"],"monads/either/join":[1272,"\n"],"monads/searchable/unit":[630,"\n"],"monads/reader/unit":[630,"\n"],"monads/reader/join":[1274,"\n"],"monads/step/int-bind":[1065,"\n\nAn internal version of binding in the step monad.\n"],"monads/step/unit":[1049,"\n\nThe unit of the step monad.\n"],"monads/step/from-maybe":[1275,"\n\nLift from the maybe monad to the step monad.\n"],"monads/step/increment":[1278,"\n\nTake a step if the action is successful, otherwise do nothing.\n"],"monads/writer/write":[257,""],"monads/subset/guard":[1280,""],"monads/subset/add":[179,""],"monads/subset/join":[639,""],"monads/subset/zero":[151,""],"monads/cont/unit":[1281,"\n"],"monads/cont/join":[1285,"\n\nCollapse two layers of continuations into one.\n"],"monads/cont/bind":[1290,"\n\nChain continuations together.\n"],"monads/cont/run":[1287,"\n\nRun a computation with continuations.\n"],"subobj/empty":[149,"\n\nAn empty subobject.\n"],"subobj/disj":[1292,"\n\nThe union of two subobjects.\n"],"subobj/full":[206,"\n\nA subobject that is just the original object.\n"],"subobj/conj":[1294,"\n\nThe intersection of two subobjects.\n"],"subobj/complement":[1296,"\n\nThe complement of a subobject.\n"],"pe/6":[1300,"\n\nA complete solution to [Project Euler Problem\n6](https://projecteuler.net/problem=6).\n"],"bits/succ":[288,"\n\nThe successor of a natural number is also a natural number.\n"],"bits/left-shift":[1302,""],"bits/to-f":[312,"\n\nConvert a binary natural number to a floating-point number.\n"],"bits/morton-fst":[1303,""],"bits/from-nat":[289,"\n\nConvert a natural number from unary to binary.\n"],"bits/zero":[127,"\n"],"bits/to-nat":[1308,"\n\nConvert a natural number from binary to unary.\n"],"cats/cost/f-cos":[1309,"\n"],"cats/cost/f-sin":[1310,"\n"],"cats/cost/snd":[1311,"\n"],"cats/cost/succ":[1312,"\n"],"cats/cost/f-pi":[1313,"\n"],"cats/cost/f-floor":[1314,"\n"],"cats/cost/f-lt":[1315,"\n"],"cats/cost/disj":[1316,"\n"],"cats/cost/f-negate":[1317,"\n"],"cats/cost/f-mul":[1318,"\n"],"cats/cost/n-add":[1320,"\n"],"cats/cost/fst":[1321,"\n"],"cats/cost/not":[1322,"\n"],"cats/cost/f-add":[1323,"\n"],"cats/cost/f-one":[1324,"\n"],"cats/cost/left":[407,"\n"],"cats/cost/f-sqrt":[1325,"\n"],"cats/cost/conj":[1326,"\n"],"cats/cost/f-zero":[1327,"\n"],"cats/cost/f-recip":[1328,"\n"],"cats/cost/right":[1329,"\n"],"cats/cost/f-atan2":[1330,"\n"],"cats/cost/cons":[1331,"\n"],"cats/cost/zero":[1332,"\n"],"cats/cost/n-pred-maybe":[1334,"\n"],"cats/cost/id":[1266,"\n"],"cats/cost/f-sign":[1335,"\n"],"cats/cost/t":[1336,"\n"],"cats/cost/f-exp":[1337,"\n"],"cats/cost/nil":[1338,"\n"],"cats/cost/either":[1339,"\n"],"cats/cost/ignore":[1340,"\n"],"cats/cost/f":[1341,"\n"],"lens/pair/fst":[1345,""],"fifo/empty?":[1349,"\n\nWhether a queue is empty.\n"],"fifo/refill":[1357,"\n\nPrepare a queue for a pop by refilling the pop stack.\n"],"fifo/push":[1359,"\n\nPush a value onto a queue.\n"],"fifo/pop":[1364,"\n\nPop an item from a queue, returning it in the left-hand component. The\nright-hand component is used to signal an empty queue.\n"],"fifo/nil":[1365,"\n\nAn empty queue.\n"],"scott/bool/true":[630,"\n"],"scott/bool/false":[534,"\n"],"pair/rotl":[665,""],"pair/assr":[275,"\n\nReassociate to the right.\n"],"pair/assl":[265,"\n\nReassociate to the left.\n"],"pair/dup":[2,"\n\nThe [diagonal map](https://ncatlab.org/nlab/show/diagonal+morphism).\n"],"pair/swap":[189,"\n\nSwap the first and second components of a pair.\n\nSwapping twice in a row is equivalent to the identity arrow.\n\nThis expression is the smallest with its type signature.\n"],"sum/left?":[1366,"\n"],"sum/assr":[797,"\n\nReassociate a triple sum to the right.\n"],"sum/assl":[803,"\n\nReassociate a triple sum to the left.\n"],"sum/swap":[501,"\n\nSwap the two cases of a sum.\n"],"mat3/mul":[1399,"\n"],"mat3/vec":[1391,"\n"],"mat3/trans":[1380,"\n\nTranspose a 3x3 matrix.\n"],"mat3/id":[1401,"\n\nA 3x3 identity 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Given a maximum number of\nsteps, we iterate the IFS for a fractal in the complex plane until its\nabsolute value exceeds 2, and return a value in [0,1] indicating how many\nsteps were taken before divergence.\n"],"monad-choose":[["fold",0,["comp",["pair",["comp","fst",1],"snd"],2]],""],"l":[["comp",["pair",0,1],"cons"],""],"fractal-maybe":[["comp",["comp",0,["pair",["comp",["pair",["comp",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]],"f-add"]],["comp","f-sqrt",["case","id","f-zero"]]],["comp","ignore",["comp",["pair","f-one","f-one"],"f-add"]]],"f-lt"],["pair","left",["comp","ignore","right"]]]],["comp",["pair",["comp","fst",["comp","either",["case",["curry",["comp","snd","fst"]],["curry",["comp","snd","snd"]]]]],"snd"],["uncurry","id"]]],"\n\nTake a step in an IFS, failing if the step has magnitude 2 or greater.\n"],"pick-const":[["comp","either",["case",0,1]],""],"iter-fractal-fast":[["comp",["pair","ignore","id"],["uncurry",["comp",["pair",0,["comp",["pair",["comp","ignore",["curry",["comp","snd",["curry",["comp",["comp",["uncurry","id"],["comp",["pair",["comp",["pair",["comp",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]],"f-add"]],["comp","f-sqrt",["case","id","f-zero"]]],["comp","ignore",["comp",["pair","f-one","f-one"],"f-add"]]],"f-lt"],["pair","left",["comp","ignore","right"]]],["comp",["pair",["comp","fst",["comp","either",["case",["curry",["comp","snd","fst"]],["curry",["comp","snd","snd"]]]]],"snd"],["uncurry","id"]]]],["case",["pair","left",["comp","ignore",["comp","zero","succ"]]],["pair","right",["comp","ignore","zero"]]]]]]]],["comp",["comp","f-zero",["pair","id","id"]],1]],["uncurry","id"]]],["uncurry",["pr",["curry",["comp","fst",["curry",["comp","snd",["pair","left",["comp","ignore","zero"]]]]]],["curry",["comp",["pair","snd",["uncurry","id"]],["curry",["comp",["pair",["comp",["pair",["comp","fst","snd"],"snd"],["uncurry","id"]],["comp","fst","fst"]],["comp",["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["uncurry",["case",["curry","left"],["curry","right"]]]],["case",["comp",["pair",["comp",["pair",["comp","snd","snd"],"fst"],["uncurry","id"]],["comp","snd","fst"]],["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry",["pr",["curry",["comp","snd","id"]],["curry",["comp",["uncurry","id"],"succ"]]]]]]]],["pair",["comp","ignore","right"],["comp","snd","fst"]]]]]]]]]]]]],"\n\nGiven a maximum number of steps, iterate the given fractal.\n"],"graph-fun":[["comp",0,["pair","id",["pair","id",["comp","ignore","f-one"]]]],"\n\nGraph a real function on the plane. 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fractal-membership, but just returning the length so that we can\nfalse-color it.\n"],"dynamics":[["pair",["comp","fst",["comp",["pair",["curry",["comp","snd",0]],"id"],["curry",["comp",["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry","id"]]]],["uncurry","id"]]]]],"snd"],"\n\nThe dynamics of a deterministic automaton. The second component of the pair is\nleft free, but usually is a status value, like a Boolean.\n"],"setup-viewport":[["comp",["comp",["pair","id",["comp","ignore",1]],["pair",["comp",["pair",["comp","fst","fst"],"snd"],"f-mul"],["comp",["pair",["comp","fst","snd"],"snd"],"f-mul"]]],["comp",["pair","id",["comp","ignore",0]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]]]]],"\n\nSet up a preferred viewport for 2D rendering. 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steps.\n"],"nat/do-if-not-zero":[["comp",["comp",["pair","id",["pr","t",["comp","ignore","f"]]],"swap"],["uncurry",["comp","either",["case",["curry",["comp","snd",["comp","ignore","right"]]],["curry",["comp","snd",["comp",0,"left"]]]]]]],"\n"],"nat/kata":[["pr",0,1],""],"nat/para":[["comp",["pr",["pair","zero",0],["pair",["comp","fst","succ"],1]],"snd"],""],"poly/horner":[["comp",["pair",["comp","fst",["comp",["pair","id",["comp","ignore","nil"]],["uncurry",["fold",["curry",["comp","snd","id"]],["curry",["comp",["pair",["comp","fst","snd"],["comp",["pair",["comp","fst","fst"],"snd"],"cons"]],["uncurry","id"]]]]]]],"snd"],["uncurry",["fold",["curry",["comp","snd",["comp","ignore",0]]],["curry",["comp",["pair",["pair",["comp","fst","fst"],["comp",["pair",["comp","fst","snd"],"snd"],["uncurry","id"]]],"snd"],["comp",["pair",["comp",["pair",["comp","fst","snd"],"snd"],2],["comp","fst","fst"]],1]]]]]],"\n\nEvaluate a polynomial at an input coordinate using Horner's rule, given:\n\n* A 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The dependent sum is merely postcomposition.\n"],"fun/hom-const":[["curry",["comp","fst",0]],"\n\nTake and discard an additional argument by creating a hom.\n"],"fun/unname":[["comp",["pair","ignore","id"],["uncurry",0]],"\n\nReference an arrow by name.\n"],"fun/apppair":[["comp",["pair",0,1],["uncurry","id"]],"\n\nApply the output of one arrow onto the output of another.\n"],"fun/name":[["curry",["comp","snd",0]],"\n\nThe name of an arrow.\n"],"fun/graph":[["pair","id",0],"\n"],"fun/iter-maybe":[["pr",["curry",["comp","snd","left"]],["comp",["pair","id",["comp","ignore",["curry",["comp","snd",0]]]],["curry",["comp",["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry","id"]]]],["comp",["comp",["comp",["pair","snd","fst"],["uncurry",["case",["curry","left"],["curry","right"]]]],["case",["comp",["pair","snd","fst"],"left"],["comp",["pair","snd","fst"],"right"]]],["case",["uncurry","id"],["comp","ignore","right"]]]]]]],"\n\nIterate a given arrow up to zero or more times.\n"],"fun/precomp":[["curry",["comp",["pair","fst",["comp","snd",0]],["uncurry","id"]]],"\n\nPrecompose a function type with an arrow. This is like the inverse-image\nfunctor for an arbitrary classifier. It is also like one version of the Yoneda\nembedding for the given arrow.\n"],"fun/observe":[["curry",["comp",["pair","snd","fst"],["uncurry",["comp",["pair",["comp","ignore",["curry",["comp","snd",0]]],["pr",["curry",["comp","snd","id"]],["comp",["pair","id",["comp","ignore",["curry",["comp","snd",1]]]],["curry",["comp",["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry","id"]]]],["uncurry","id"]]]]]],["curry",["comp",["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry","id"]]]],["uncurry","id"]]]]]]],"\n\nObserve the value of an endomorphism after a specified number of iterations.\n"],"fun/flip":[["curry",["comp",["pair","snd","fst"],["uncurry",0]]],"\n\nSwap the order in which arguments are applied onto a curried arrow.\n"],"fun/postcomp":[["curry",["comp",["uncurry","id"],0]],"\n\nPostcompose a function type with an arrow. This is like one version of the\nYoneda embedding for the given arrow.\n"],"fun/const":[["comp","ignore",0],"\n"],"list/map":[["fold","nil",["comp",["pair",["comp","fst",0],"snd"],"cons"]],"\n"],"list/conspair":[["comp",["pair",0,1],"cons"],"\n\nBuild a list whose head is the output of one arrow and whose tail is the\noutput of another arrow.\n"],"list/kata":[["fold",0,1],""],"list/eq?":[["comp",["pair",["comp",["pair",["comp","fst",["fold","zero",["comp","snd","succ"]]],["comp","snd",["fold","zero",["comp","snd","succ"]]]],["uncurry",["pr",["curry",["comp","snd",["pr","t",["comp","ignore","f"]]]],["curry",["comp",["pair","fst",["comp","snd",["comp",["pr","right",["comp",["case","succ","zero"],"left"]],["case","id","zero"]]]],["uncurry","id"]]]]]],["comp",["uncurry",["fold",["curry",["comp","snd",["comp","ignore","nil"]]],["curry",["comp",["pair","fst",["comp","snd",["fold","right",["comp",["pair","fst",["comp","snd",["comp",["case","cons","nil"],"left"]]],["comp",["comp",["comp",["pair","snd","fst"],["uncurry",["case",["curry","left"],["curry","right"]]]],["case",["comp",["pair","snd","fst"],"left"],["comp",["pair","snd","fst"],"right"]]],["case","left",["comp","ignore","right"]]]]]]],["comp",["comp",["comp",["pair","snd","fst"],["uncurry",["case",["curry","left"],["curry","right"]]]],["case",["comp",["pair","snd","fst"],"left"],["comp",["pair","snd","fst"],"right"]]],["case",["comp",["pair",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["uncurry","id"]]],"cons"],["comp",["pair",["comp","fst","snd"],["comp","ignore","nil"]],["uncurry","id"]]]]]]]],["comp",["fold","nil",["comp",["pair",["comp","fst",0],"snd"],"cons"]],["fold","t","conj"]]]],"conj"],"\n\nEquality on lists is decidable, provided that equality of elements is\ndecidable.\n"],"list/para":[["comp",["fold",["pair","nil",0],["pair",["comp",["pair","fst",["comp","snd","fst"]],"cons"],1]],"snd"],""],"list/filter":[["fold","nil",["comp",["pair",["comp","fst",0],["pair","cons","snd"]],["comp",["pair",["comp","fst",["comp","either",["case",["curry",["comp","snd","fst"]],["curry",["comp","snd","snd"]]]]],"snd"],["uncurry","id"]]]],"\n\nApply a predicate to every element of a list, and retain the elements which\nthe predicate admits.\n"],"list/scan":[["comp",["fold",["pair",0,"nil"],["comp",["comp",["pair",["pair","fst",["comp","snd","fst"]],["comp","snd","snd"]],["pair",1,"snd"]],["pair","fst","cons"]]],"snd"],"\n\n\n"],"bool/ternary":[["comp",["comp",["pair","id",0],["pair","fst",["comp","snd","either"]]],["comp",["comp",["comp",["pair","snd","fst"],["uncurry",["case",["curry","left"],["curry","right"]]]],["case",["comp",["pair","snd","fst"],"left"],["comp",["pair","snd","fst"],"right"]]],["case",["comp","fst",1],["comp","fst",2]]]],""],"bool/both":[["comp",["pair",0,1],"conj"],"\n\nWhether two predicates both hold.\n"],"bool/if":[["comp","either",["case",["curry",["comp","snd",0]],["curry",["comp","snd",1]]]],"\n\nAs close as we can get to an if-expression.\n"],"bool/either":[["comp",["pair",0,1],"disj"],"\n\nWhether either predicate holds.\n"],"sdf2/extrude":[["comp",["pair",1,["comp",["comp","ignore",0],"f-negate"]],"f-add"],"\n"],"sdf2/scale":[["comp",["pair",["comp",["comp",["pair","id",["comp","ignore",["pair",0,0]]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-recip"]],"f-mul"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-recip"]],"f-mul"]]]],1],["comp","ignore",0]],"f-mul"],"\n"],"sdf2/union":[["comp",["pair",0,1],["comp",["pair","f-lt","id"],["comp",["pair",["comp","fst",["comp","either",["case",["curry",["comp","snd","fst"]],["curry",["comp","snd","snd"]]]]],"snd"],["uncurry","id"]]]],"\n"],"sdf2/translate":[["comp",["comp",["pair","id",["comp","ignore",0]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]]]],1],"\n"],"sdf2/metaballs":[["comp",["pair",["comp",["pair",["comp",1,["fold",["curry",["comp","snd",["comp","ignore","f-zero"]]],["curry",["comp",["pair",["comp",["pair",["comp",["comp","fst","fst"],"snd"],["comp",["comp",["pair",["comp",["comp","fst","fst"],"fst"],"snd"],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]]]],["comp",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]],"f-add"]],["comp","f-sqrt",["case","id","f-zero"]]]]],["comp",["pair","fst",["comp","snd","f-recip"]],"f-mul"]],["comp",["pair",["comp","fst","snd"],"snd"],["uncurry","id"]]],"f-add"]]]],"id"],["uncurry","id"]],["comp",["comp","ignore",0],"f-negate"]],"f-add"],"\n\n\n"],"mat2/vecpair":[["comp",["pair",0,1],["pair",["comp",["pair",["comp","fst","fst"],"snd"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]],"f-add"]],["comp",["pair",["comp","fst","snd"],"snd"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]],"f-add"]]]],"\n"],"weekend/hit_sphere3?":[["comp",["comp",["pair",["comp","fst",["comp",["pair","id",["comp","ignore",0]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]]]]]]],"snd"],["pair",["comp","snd",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["pair",["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]],["comp",["pair",["comp","fst",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["comp",["comp",["comp","ignore",1],["comp",["pair","id","id"],"f-mul"]],"f-negate"]],"f-add"]]]],["comp",["comp",["pair",["pair","fst",["comp","snd","fst"]],["comp",["comp",["pair",["comp",["comp","snd","fst"],["comp",["pair","id","id"],"f-mul"]],["comp",["comp",["pair","fst",["comp","snd","snd"]],"f-mul"],"f-negate"]],"f-add"],"f-sqrt"]],["comp",["comp",["pair","snd","fst"],["uncurry",["case",["curry","left"],["curry","right"]]]],["case",["comp",["pair","snd","fst"],"left"],["comp",["pair","snd","fst"],"right"]]]],["case",["comp",["comp",["pair",["comp",["pair",["comp",["comp","fst","snd"],"f-negate"],["comp","snd","f-negate"]],"f-add"],["comp","fst","fst"]],["comp",["pair","fst",["comp","snd","f-recip"]],"f-mul"]],"left"],["comp","ignore","right"]]]],"\n\nBasically the same as hit_sphere2?, but now the quadratic formula is rewritten\nin terms of $h$, where $b = 2h$.\n"],"weekend/hit_sphere":[["comp",["pair",["comp","fst",["comp",["pair","id",["comp","ignore",0]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]]]]]]],"snd"],["pair",["comp","snd",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["pair",["comp",["pair",["comp","ignore",["comp",["pair","f-one","f-one"],"f-add"]],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]],"f-mul"],["comp",["pair",["comp","fst",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["comp",["comp",["comp","ignore",1],["comp",["pair","id","id"],"f-mul"]],"f-negate"]],"f-add"]]]],"\n\nTest whether a ray hits a sphere, generating coefficients for the quadratic\nformula.\n"],"weekend/hit_sphere2":[["comp",["pair",["comp","fst",["comp",["pair","id",["comp","ignore",0]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]]]]]]],"snd"],["pair",["comp","snd",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["pair",["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]],["comp",["pair",["comp","fst",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["comp",["comp",["comp","ignore",1],["comp",["pair","id","id"],"f-mul"]],"f-negate"]],"f-add"]]]],"\n\nTest whether a ray hits a sphere, generating coefficients for the quadratic\nformula. The coefficients are not $a$, $b$, and $c$, but $a$, $h$, and $c$,\nwhere $b = 2h$.\n"],"weekend/hit_sphere?":[["comp",["pair",["comp","ignore","f-zero"],["comp",["comp",["pair",["comp","fst",["comp",["pair","id",["comp","ignore",0]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]]]]]]],"snd"],["pair",["comp","snd",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["pair",["comp",["pair",["comp","ignore",["comp",["pair","f-one","f-one"],"f-add"]],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]],"f-mul"],["comp",["pair",["comp","fst",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["comp",["comp",["comp","ignore",1],["comp",["pair","id","id"],"f-mul"]],"f-negate"]],"f-add"]]]],["comp",["pair",["comp",["comp","snd","fst"],["comp",["pair","id","id"],"f-mul"]],["comp",["comp",["pair",["comp","ignore",["comp",["pair",["comp",["pair","f-one","f-one"],"f-add"],["comp",["pair","f-one","f-one"],"f-add"]],"f-add"]],["comp",["pair","fst",["comp","snd","snd"]],"f-mul"]],"f-mul"],"f-negate"]],"f-add"]]],"f-lt"],"\n\n\n"],"weekend/hit_sphere2?":[["comp",["comp",["pair",["comp","fst",["comp",["pair","id",["comp","ignore",0]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["comp",["pair","fst",["comp","snd","f-negate"]],"f-add"]]]]]]],"snd"],["pair",["comp","snd",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["pair",["comp",["pair",["comp","ignore",["comp",["pair","f-one","f-one"],"f-add"]],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]],"f-mul"],["comp",["pair",["comp","fst",["comp",["pair","id","id"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]],["comp",["comp",["comp","ignore",1],["comp",["pair","id","id"],"f-mul"]],"f-negate"]],"f-add"]]]],["comp",["comp",["pair",["pair","fst",["comp","snd","fst"]],["comp",["comp",["pair",["comp",["comp","snd","fst"],["comp",["pair","id","id"],"f-mul"]],["comp",["comp",["pair",["comp","ignore",["comp",["pair",["comp",["pair","f-one","f-one"],"f-add"],["comp",["pair","f-one","f-one"],"f-add"]],"f-add"]],["comp",["pair","fst",["comp","snd","snd"]],"f-mul"]],"f-mul"],"f-negate"]],"f-add"],"f-sqrt"]],["comp",["comp",["pair","snd","fst"],["uncurry",["case",["curry","left"],["curry","right"]]]],["case",["comp",["pair","snd","fst"],"left"],["comp",["pair","snd","fst"],"right"]]]],["case",["comp",["comp",["pair",["comp",["pair",["comp",["comp","fst","snd"],"f-negate"],["comp","snd","f-negate"]],"f-add"],["comp",["pair",["comp","fst","fst"],["comp","ignore",["comp",["pair","f-one","f-one"],"f-add"]]],"f-mul"]],["comp",["pair","fst",["comp","snd","f-recip"]],"f-mul"]],"left"],["comp","ignore","right"]]]],"\n\n\n"],"comonads/reader/duplicate":[["curry",["curry",["comp",["pair","snd",["comp","fst",0]],"fun/app"]]],""],"comonads/reader/counit":[["comp",["pair","id",["comp","ignore",0]],"fun/app"],""],"comonads/product/bind":[["pair","fst",0],""],"v2/dist-fun":[["comp",["comp",["comp",["pair",["comp","fst",0],["comp","snd","f-negate"]],"f-add"],["comp",["pair",["comp",["comp","f-sign","either"],["case",["curry",["comp","snd","id"]],["curry",["comp","snd","f-negate"]]]],"id"],["uncurry","id"]]],["comp",["comp","f-sqrt",["case","id","f-zero"]],["comp","f-sqrt",["case","id","f-zero"]]]],"\n"],"v2/map2":[["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],0],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],0]],"\n\n\nLift a binary operation to a vector space.\n"],"v2/scale":[["comp",["pair",["comp",["comp",["pair","id",["comp","ignore",1]],["comp",["pair","fst",["comp","snd","f-recip"]],"f-mul"]],0],["comp","ignore",2]],"f-mul"],"\n\nScale a vector.\n"],"v2/map":[["pair",["comp","fst",0],["comp","snd",0]],"\n\nMap over both dimensions of a vector simultaneously.\n"],"v2/translate":[["comp",["pair",["comp",["comp",["pair","id",["comp",["comp","ignore",1],"f-negate"]],"f-add"],0],["comp","ignore",2]],"f-add"],"\n\nTranslate a vector.\n"],"v2/const":[["comp","ignore",["comp",0,["pair","id","id"]]],"\n\n\n"],"v3/map2":[["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],0],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],0],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],0]]]],"\n"],"v3/scale":[["comp",["pair",["pair",["comp","ignore",0],["pair",["comp","ignore",0],["comp","ignore",0]]],"id"],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]]],"\n\nScale a vector by a fixed amount.\n"],"v3/broadcast":[["pair",0,["pair",0,0]],"\n"],"v3/map":[["pair",["comp","fst",0],["pair",["comp",["comp","snd","fst"],0],["comp",["comp","snd","snd"],0]]],"\n\n"],"v3/fold":[["comp",["pair","fst",["comp","snd",0]],0],"\n"],"v3/lerp":[["comp",["comp",["pair",["comp",["pair",["comp","ignore","f-one"],["comp","id","f-negate"]],"f-add"],"id"],["pair",["comp","fst",["comp",["pair","id",["comp","ignore",0]],["comp",["pair",["comp","fst",["pair","id",["pair","id","id"]]],"snd"],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]]]]],["comp","snd",["comp",["pair","id",["comp","ignore",1]],["comp",["pair",["comp","fst",["pair","id",["pair","id","id"]]],"snd"],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]]]]]]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-add"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-add"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-add"]]]]],""],"v3/triple":[["pair",0,["pair",1,2]],"\n"],"f/mulpair":[["comp",["pair",0,1],"f-mul"],"\n\nApply multiplication to a pair of arrows.\n"],"f/dot3pair":[["comp",["pair",0,1],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]],"\n\nApply a dot product to a pair of arrows.\n"],"f/addpair":[["comp",["pair",0,1],"f-add"],"\n\nApply addition to a pair of arrows.\n"],"f/subpair":[["comp",["pair",0,["comp",1,"f-negate"]],"f-add"],"\n\nApply subtraction to a pair of arrows.\n"],"f/divpair":[["comp",["pair",0,1],["comp",["pair","fst",["comp","snd","f-recip"]],"f-mul"]],"\n\nApply division to a pair of arrows.\n"],"f/ltpair":[["comp",["pair",0,1],"f-lt"],"\n\nWhether one arrow is less than another at an input value.\n"],"f/approx":[["comp",["comp",["comp",["pair",["comp","fst",0],["comp","snd","f-negate"]],"f-add"],["comp",["pair","id","id"],"f-mul"]],["comp",["pair","id",["comp","ignore",["comp",["comp",["comp",["pair","f-one",["comp",["comp",["pair","f-one",["comp",["pair","f-one","f-one"],"f-add"]],"f-add"],["comp",["pair","id","id"],"f-mul"]]],"f-add"],["comp",["pair","id",["comp",["pair","id","id"],"f-mul"]],"f-mul"]],"f-recip"]]],"f-lt"]],"\n\nWhether the given functor is approximately equal to the input floating-point\nvalue at the input parameter. The absolute tolerance is one millionth.\n"],"f/error":[["comp",["pair",["comp","fst",0],["comp","snd","f-negate"]],"f-add"],"\n\nThe error between the output value of the given arrow at the input value and\nthe expected input value.\n"],"f/dot2pair":[["comp",["pair",0,1],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]],"f-add"]],"\n\nApply the dot product to a pair of arrows.\n"],"f/minpair":[["comp",["pair",0,1],["comp",["pair","f-lt","id"],["comp",["pair",["comp","fst",["comp","either",["case",["curry",["comp","snd","fst"]],["curry",["comp","snd","snd"]]]]],"snd"],["uncurry","id"]]]],"\n\nThe minimum of two arrows at an input value.\n"],"monads/iter":[["pr",["curry",["comp","snd",0]],["comp",["pair","id",["comp","ignore",["curry",["comp","snd",2]]]],["curry",["comp",["pair",["comp",["pair",["comp","fst","snd"],"snd"],["uncurry","id"]],["comp","fst","fst"]],1]]]],"\n\nGiven a unit and internal bind in some monad, iterate an endomorphism in that\nmonad.\n\nFor example, to iterate in the maybe monad:\n\n    (monads/iter monads/maybe/unit monads/maybe/int-bind @0)\n\nIteration can terminate early in short-circuiting monads.\n"],"monads/guard":[["comp",["pair",2,"id"],["uncurry",["comp","either",["case",["curry",["comp","snd",["comp","ignore",1]]],["curry",["comp","snd",0]]]]]],"\n\nGiven the unit and zero of some monad, and some filtering predicate, test a\nvalue in that monad.\n"],"monads/int-comp":[["curry",["comp",["pair",["comp",["pair",["comp","fst","snd"],"snd"],["uncurry","id"]],["comp","fst","fst"]],0]],"\n\nInternal composition in any monad, built from the internal bind.\n"],"monads/int-iter":[["uncurry",["pr",["curry",["comp","fst",["curry",["comp","snd",0]]]],["curry",["comp",["pair","snd",["uncurry","id"]],["curry",["comp",["pair",["comp",["pair",["comp","fst","snd"],"snd"],["uncurry","id"]],["comp","fst","fst"]],1]]]]]],"\n\nInstead of just N, we're going to have a pair N x @2\n\nThe zero case doesn't need the RHS\n\n\n(pr\n  (fun/name @0)\n  (comp (pair id (fun/const (fun/name @2))) (monads/int-comp @1)))\n\nGiven a unit and internal bind in some monad, iterate an endomorphism in that\nmonad.\n\nFor example, to iterate in the maybe monad:\n\n    (monads/iter monads/maybe/unit monads/maybe/int-bind @0)\n\nIteration can terminate early in short-circuiting monads.\n\n"],"monads/int-lift":[["curry",["comp",["uncurry","id"],0]],"\n\nLift an internal hom to a monad, given the unit of the monad.\n"],"monads/maybe/guard":[["comp",["pair",0,["pair","left",["comp","ignore","right"]]],["comp",["pair",["comp","fst",["comp","either",["case",["curry",["comp","snd","fst"]],["curry",["comp","snd","snd"]]]]],"snd"],["uncurry","id"]]],"\n\nDo nothing if a value passes a filter, otherwise fail.\n"],"monads/maybe/bind":[["comp",0,["case",1,"right"]],"\n\nBind for the maybe monad.\n"],"monads/maybe/lift":[["comp",0,"left"],"\n\nLift an arrow to the Kleisli category of the maybe monad.\n"],"monads/cost/map":[["pair",["comp","fst",0],"snd"],"\n"],"monads/cost/comp":[["comp",["comp",0,["pair",["comp","fst",1],"snd"]],["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry",["pr",["curry",["comp","snd","id"]],["curry",["comp",["uncurry","id"],"succ"]]]]]]]],"\n\n"],"monads/cost/lift":[["pair",0,["comp","ignore",["comp","zero","succ"]]],"\n"],"monads/writer/unit":[["pair","id",["comp","ignore",0]],""],"monads/writer/join":[["pair",["comp","fst","fst"],["comp",["pair",["comp","fst","snd"],"snd"],0]],""],"monads/writer/map":[["pair",["comp","fst",0],"snd"],""],"monads/subset/unit":[["curry",0],""],"monads/cont/lift":[["curry",["comp",["pair","snd",["comp","fst",0]],["uncurry","id"]]],"\n"],"bits/repeat-endo":[["comp",["comp",["pair","id",["comp","ignore","nil"]],["uncurry",["fold",["curry",["comp","snd","id"]],["curry",["comp",["pair",["comp","fst","snd"],["comp",["pair",["comp","fst","fst"],"snd"],"cons"]],["uncurry","id"]]]]]],["fold",["curry",["comp","snd","id"]],["comp",["pair","fst",["comp","snd",["comp",["pair","id","id"],["curry",["comp",["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry","id"]]]],["uncurry","id"]]]]]],["uncurry",["comp","either",["case",["curry",["comp","snd",["curry",["comp",["uncurry","id"],0]]]],["curry",["comp","snd","id"]]]]]]]],"\n\nRepeatedly apply an endomorphism.\n"],"bits/exp-sqr":[["comp",["comp",["pair","id",["comp","ignore","nil"]],["uncurry",["fold",["curry",["comp","snd","id"]],["curry",["comp",["pair",["comp","fst","snd"],["comp",["pair",["comp","fst","fst"],"snd"],"cons"]],["uncurry","id"]]]]]],["fold",0,["comp",["pair","fst",["comp","snd",2]],["uncurry",["comp","either",["case",["curry",["comp","snd",1]],["curry",["comp","snd","id"]]]]]]]],"\n\nGiven a zero, an increment, and a doubling operation, [exponentiate by\nsquaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring).\n"],"cats/cost/curry":[["pair",["curry",["comp",0,"fst"]],["comp","ignore","zero"]],"\n\nWrong, but close enough for now.\n"],"cats/cost/uncurry":[["comp",["pair",["comp","fst",0],"snd"],["pair",["comp",["pair",["comp","fst","fst"],"snd"],["uncurry","id"]],["comp","fst","snd"]]],"\n"],"cats/cost/pr":[["pr",0,["comp",["pair",["comp","fst",1],"snd"],["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry",["pr",["curry",["comp","snd","id"]],["curry",["comp",["uncurry","id"],"succ"]]]]]]]]],"\n"],"cats/cost/comp":[["comp",["comp",0,["pair",["comp","fst",1],"snd"]],["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry",["pr",["curry",["comp","snd","id"]],["curry",["comp",["uncurry","id"],"succ"]]]]]]]],"\n"],"cats/cost/fold":[["fold",0,["comp",["comp",["pair",["pair","fst",["comp","snd","fst"]],["comp","snd","snd"]],["pair",["comp","fst",1],"snd"]],["comp",["pair",["comp","fst","fst"],["pair",["comp","fst","snd"],"snd"]],["pair","fst",["comp","snd",["uncurry",["pr",["curry",["comp","snd","id"]],["curry",["comp",["uncurry","id"],"succ"]]]]]]]]],"\n"],"cats/cost/case":[["case",0,1],"\n"],"cats/cost/lift":[["pair",0,["comp","ignore",["comp","zero","succ"]]],"\n"],"cats/cost/pair":[["comp",["pair",0,1],["pair",["pair",["comp","fst","fst"],["comp","snd","fst"]],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["uncurry",["pr",["curry",["comp","snd","id"]],["curry",["comp",["uncurry","id"],"succ"]]]]]]],"\n"],"pair/tensor":[["pair",["comp","fst",0],["comp","snd",1]],"\n\nCompose two arrows in parallel, acting on pairs of values.\n\nIn categorical jargon, the [tensor\nproduct](https://ncatlab.org/nlab/show/tensor+product) is a functor from pairs\nof arrows to arrows:\n\n$$\n\\bigotimes : C \\times C \\to C\n$$\n"],"pair/mapfst":[["pair",["comp","fst",0],"snd"],"\n\nMap over the first component of a pair.\n"],"pair/mapsnd":[["pair","fst",["comp","snd",0]],"\n\nMap over the second component of a pair.\n"],"pair/bimap":[["pair",["comp","fst",0],["comp","snd",0]],"\n\nMap uniformly over both components of a pair.\n"],"pair/of":[["comp",["pair",1,2],0],"\n\nCall an arrow of two arguments by building both arguments from a single input.\n"],"yoneda/embed":[["curry",["comp",["uncurry","id"],0]],"\n\nThe Yoneda embedding of an arrow.\n"],"yoneda/lift":[["comp",["pair","ignore","id"],["uncurry",["comp",["comp","ignore",["curry",["comp","snd","id"]]],0]]],"\n\nUndo the Yoneda embedding.\n"],"sum/mapright":[["case","left",["comp",0,"right"]],"\n\nMap over the right-hand case of a sum.\n\n"],"sum/mapleft":[["case",["comp",0,"left"],"right"],"\n\nMap over the left-hand case of a sum.\n"],"sum/par":[["case",["comp",0,"left"],["comp",1,"right"]],""],"mat3/vecpair":[["comp",["pair",0,1],["pair",["comp",["pair",["comp","fst","fst"],"snd"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]],["pair",["comp",["pair",["comp",["comp","fst","snd"],"fst"],"snd"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]],["comp",["pair",["comp",["comp","fst","snd"],"snd"],"snd"],["comp",["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],["pair",["comp",["pair",["comp","fst","fst"],["comp","snd","fst"]],"f-mul"],["comp",["pair",["comp","fst","snd"],["comp","snd","snd"]],"f-mul"]]]],["comp",["pair","fst",["comp","snd","f-add"]],"f-add"]]]]]],"\n"]}}
\ No newline at end of file

--- a/movelist/cammy-repl.scm
+++ b/movelist/cammy-repl.scm
@@ -136,8 +136,8 @@
 
 (define format-ty
   (match-lambda
-    [`(pair ,x ,y) (string-append (format-ty x) " × " (format-ty y))]
-    [`(sum ,x ,y) (string-append (format-ty x) " + " (format-ty y))]
+    [`(pair ,x ,y) (string-append "(" (format-ty x) " × " (format-ty y) ")")]
+    [`(sum ,x ,y) (string-append "(" (format-ty x) " + " (format-ty y) ")")]
     [`(hom ,x ,y) (string-append "[" (format-ty x) ", " (format-ty y) "]")]
     [`(list ,x) (string-append "[" (format-ty x) "]")]
     [`(tree ,x) (string-append "Tree(" (format-ty x) ")")]
@@ -145,6 +145,21 @@
     ; XXX WTF?
     [(? number? n) (number->string n)]))
 
+(define (describe-ty° s t ps)
+  (conde
+    ((== s '1) (== ps `("element of" ,t)))
+    ((== s '2) (== ps `("pair of" ,t)))
+    ((== s 'N) (== ps `("sequence of" ,t)))
+    ((== t '2) (== ps `("predicate/subset of" ,s)))))
+
+(define str-or-ty
+  (match-lambda [(? string? s) s] [ty (format-ty ty)]))
+
+(define (describe-ty s t)
+  (map
+    (lambda (ps) (string-intersperse (map str-or-ty ps) " "))
+    (run 3 (q) (describe-ty° s t q))))
+
 (define (format-type-arrow st)
   (string-append (format-ty (car st)) " → " (format-ty (cdr st))))
 
@@ -159,6 +174,13 @@
             (string-intersperse (map format-type-arrow ctx) ", ")
             ")")))]))
 
+(define format-type-description
+  (match-lambda
+    [`(ty ,s ,t ,_)
+      (string-append "Interpretations: "
+                     (string-intersperse (describe-ty s t) ", ")
+                     "…")]))
+
 (define build-holes
   (match-lambda
     [(? number? n) (build-num n)]
@@ -187,6 +209,7 @@
       ; (display fancy-expr)
       (display expr)
       (display (format-type-judgement ty)) (newline)
+      (display (format-type-description ty)) (newline)
       (set! most-recent-expr expr)
       (cammy-eval-timed expr ty))))
 

--- a/todo.txt
+++ b/todo.txt
@@ -75,19 +75,6 @@
         * 8 -> 2 is the type of octets
         * 1024 × 768 -> F is like a type of greyscale pixel buffers
         * Note the obvious issue: which sizes are efficient on hardware?
-  * The case for trees
-    * data Tree a = Leaf | Branch a (Tree a) (Tree a)
-    * well-founded whenever lists are well-founded
-    * Can be used to implement several nice collections
-      * Classic binary search trees
-        * Okasaki-style red-black trees?
-      * Skew heaps for priority queues https://themonadreader.files.wordpress.com/2010/05/issue16.pdf
-      * Efficient maps keyed by N
-    * Attempted to implement them, but ran into a problem: tree traversals on
-      CAM are not obvious
-      * Defunctionalization might work: can the tree traversal be linearized?
-        * Can be linearized on a second stack...
-      * Figured it out; the trick is to use GOTO, CALL, and RET
   * Deferreds
     * Monad API
       * Given x : 1 -> X, (seed x) : 1 -> DX
@@ -96,6 +83,8 @@
     * With trampoline monad, all of this should be possible
 * Ways of interpreting existing types
   * Building maths from N
+    * Ints
+      * int/sub
     * Rational numbers Q
       * Using binary quote notation?
       * Continued fractions?
@@ -117,6 +106,25 @@
       * Taxicab
       * Maximum
       * Lp
+  * Efficient difference lists
+    * Core type: [X] -> [X]
+      * Given a list of X, prepend a prefix
+  * The case for trees
+    * Classic binary search trees
+      * Okasaki-style red-black trees?
+    * Skew heaps for priority queues https://themonadreader.files.wordpress.com/2010/05/issue16.pdf
+    * Efficient maps keyed by N
+  * Universal approach to abstraction
+    * https://www.cs.tufts.edu/~nr/cs257/archive/john-hughes/lists.pdf
+    * To represent type T with representing type R, need:
+      * abs : R -> T
+      * rep : T -> R
+      * (comp rep abs) = id : T -> T
+      * For any arrow f : T -> T, it is implemented by g : R -> R when:
+        * (comp abs f) = (comp g abs)
+      * Examples
+        * [2] represents N
+        * [[X,X],[X,X]] is equivalent to N
   * CPS for particular monads, using codensity
     * maybe monad: X -> (X -> R) -> R -> R
     * list monad: X -> (X -> R -> R) -> R -> R
@@ -198,8 +206,6 @@
       * All of the pieces should be available
   * Non-empty lists form a comonad
   * Moore machines form a comonad?
-  * Ints
-    * int/sub
   * Run-length encoding
     * encoder : [2] -> [N]
       * could be generalized to any equality