Merged with staging

packages/squiggle-lang/README.md

@@ -13,6 +13,9 @@ Other:
 yarn start  # listens to files and recompiles at every mutation
 yarn test
 yarn test:watch  # keeps an active session and runs all tests at every mutation
+
+# where o := open in osx and o := xdg-open in linux,  
+yarn coverage; o _coverage/index.html  # produces coverage report and opens it in browser
 ```
 
 # TODO: clean up this README.md 

packages/squiggle-lang/__tests__/Distributions/DistributionOperation_test.res

@@ -18,6 +18,8 @@ let {
   triangularDist,
   exponentialDist,
 } = module(GenericDist_Fixtures)
+let mkNormal = (mean, stdev) => GenericDist_Types.Symbolic(#Normal({mean: mean, stdev: stdev}))
+
 let {toFloat, toDist, toString, toError} = module(DistributionOperation.Output)
 let {run} = module(DistributionOperation)
 let {fmap} = module(DistributionOperation.Output)
@@ -110,7 +112,7 @@ describe("toPointSet", () => {
       ->outputMap(FromDist(ToFloat(#Mean)))
       ->toFloat
       ->toExt
-    expect(result)->toBeCloseTo(5.09)
+    expect(result)->toBeSoCloseTo(5.0, ~digits=0)
   })
 
   test("on sample set distribution with under 4 points", () => {
@@ -121,7 +123,7 @@ describe("toPointSet", () => {
     expect(result)->toEqual(GenDistError(Other("Converting sampleSet to pointSet failed")))
   })
 
-  Skip.test("on sample set", () => {
+  test("on sample set", () => {
     let result =
       run(FromDist(ToDist(ToPointSet), normalDist5))
       ->outputMap(FromDist(ToDist(ToSampleSet(1000))))
@@ -129,6 +131,6 @@ describe("toPointSet", () => {
       ->outputMap(FromDist(ToFloat(#Mean)))
       ->toFloat
       ->toExt
-    expect(result)->toBeCloseTo(5.09)
+    expect(result)->toBeSoCloseTo(5.0, ~digits=-1)
   })
 })

packages/squiggle-lang/__tests__/Distributions/Mixture_test.res

@@ -0,0 +1,70 @@
+open Jest
+open Expect 
+open TestHelpers 
+
+// TODO: use Normal.make (etc.), but preferably after the new validation dispatch is in. 
+let mkNormal = (mean, stdev) => GenericDist_Types.Symbolic(#Normal({mean: mean, stdev: stdev}))
+let mkBeta = (alpha, beta) => GenericDist_Types.Symbolic(#Beta({alpha: alpha, beta: beta}))
+let mkExponential = rate => GenericDist_Types.Symbolic(#Exponential({rate: rate}))
+let mkUniform = (low, high) => GenericDist_Types.Symbolic(#Uniform({low: low, high: high})) 
+let mkCauchy = (local, scale) => GenericDist_Types.Symbolic(#Cauchy({local: local, scale: scale}))
+let mkLognormal = (mu, sigma) => GenericDist_Types.Symbolic(#Lognormal({mu: mu, sigma: sigma}))
+
+describe("mixture", () => {
+  testAll("fair mean of two normal distributions", list{(0.0, 1e2), (-1e1, -1e-4), (-1e1, 1e2), (-1e1, 1e1)}, tup => {  // should be property
+    let (mean1, mean2) = tup
+    let meanValue = {
+        run(Mixture([(mkNormal(mean1, 9e-1), 0.5), (mkNormal(mean2, 9e-1), 0.5)])) 
+        -> outputMap(FromDist(ToFloat(#Mean)))
+    }
+    meanValue -> unpackFloat -> expect -> toBeSoCloseTo((mean1 +. mean2) /. 2.0, ~digits=-1) 
+  })
+  testAll(
+      "weighted mean of a beta and an exponential",
+      // This would not survive property testing, it was easy for me to find cases that NaN'd out. 
+      list{((128.0, 1.0), 2.0), ((2e-1, 64.0), 16.0), ((1e0, 1e0), 64.0)}, 
+      tup => {
+        let ((alpha, beta), rate) = tup
+        let betaWeight = 0.25
+        let exponentialWeight = 0.75
+        let meanValue = {
+          run(Mixture(
+              [
+                (mkBeta(alpha, beta), betaWeight), 
+                (mkExponential(rate), exponentialWeight)
+              ]
+          )) -> outputMap(FromDist(ToFloat(#Mean)))
+        }
+        let betaMean = 1.0 /. (1.0 +. beta /. alpha)
+        let exponentialMean = 1.0 /. rate
+        meanValue 
+        -> unpackFloat 
+        -> expect 
+        -> toBeSoCloseTo(
+            betaWeight *. betaMean +. exponentialWeight *. exponentialMean, 
+            ~digits=-1
+        )
+      }
+  )
+  testAll(
+      "weighted mean of lognormal and uniform", 
+      // Would not survive property tests: very easy to find cases that NaN out. 
+      list{((-1e2,1e1), (2e0,1e0)), ((-1e-16,1e-16), (1e-8,1e0)), ((0.0,1e0), (1e0,1e-2))}, 
+      tup => {
+          let ((low, high), (mu, sigma)) = tup
+          let uniformWeight = 0.6
+          let lognormalWeight = 0.4
+          let meanValue = {
+              run(Mixture([(mkUniform(low, high), uniformWeight), (mkLognormal(mu, sigma), lognormalWeight)]))
+              -> outputMap(FromDist(ToFloat(#Mean)))
+          }
+          let uniformMean = (low +. high) /. 2.0
+          let lognormalMean = mu +. sigma ** 2.0 /. 2.0
+          meanValue
+          -> unpackFloat
+          -> expect
+          -> toBeSoCloseTo(uniformWeight *. uniformMean +. lognormalWeight *. lognormalMean, ~digits=-1)
+      }
+  )
+})
+

packages/squiggle-lang/__tests__/Distributions/Samples_test.res

@@ -0,0 +1,41 @@
+open Jest
+open TestHelpers
+
+describe("Continuous and discrete splits", () => {
+  makeTest(
+    "splits (1)",
+    SampleSet.Internals.T.splitContinuousAndDiscrete([1.432, 1.33455, 2.0]),
+    ([1.432, 1.33455, 2.0], E.FloatFloatMap.empty()),
+  )
+  makeTest(
+    "splits (2)",
+    SampleSet.Internals.T.splitContinuousAndDiscrete([
+      1.432,
+      1.33455,
+      2.0,
+      2.0,
+      2.0,
+      2.0,
+    ]) |> (((c, disc)) => (c, disc |> E.FloatFloatMap.toArray)),
+    ([1.432, 1.33455], [(2.0, 4.0)]),
+  )
+
+  let makeDuplicatedArray = count => {
+    let arr = Belt.Array.range(1, count) |> E.A.fmap(float_of_int)
+    let sorted = arr |> Belt.SortArray.stableSortBy(_, compare)
+    E.A.concatMany([sorted, sorted, sorted, sorted]) |> Belt.SortArray.stableSortBy(_, compare)
+  }
+
+  let (_, discrete1) = SampleSet.Internals.T.splitContinuousAndDiscrete(
+    makeDuplicatedArray(10),
+  )
+  let toArr1 = discrete1 |> E.FloatFloatMap.toArray
+  makeTest("splitMedium at count=10", toArr1 |> Belt.Array.length, 10)
+
+  let (_c, discrete2) = SampleSet.Internals.T.splitContinuousAndDiscrete(
+    makeDuplicatedArray(500),
+  )
+  let toArr2 = discrete2 |> E.FloatFloatMap.toArray
+  makeTest("splitMedium at count=500", toArr2 |> Belt.Array.length, 500)
+})
+

packages/squiggle-lang/__tests__/Distributions/Symbolic_test.res

@@ -0,0 +1,161 @@
+open Jest
+open Expect
+open TestHelpers
+
+// TODO: use Normal.make (but preferably after teh new validation dispatch is in)
+let mkNormal = (mean, stdev) => GenericDist_Types.Symbolic(#Normal({mean: mean, stdev: stdev}))
+
+describe("(Symbolic) normalize", () => {
+  testAll("has no impact on normal distributions", list{-1e8, -1e-2, 0.0, 1e-4, 1e16}, mean => {
+    let normalValue = mkNormal(mean, 2.0)
+    let normalizedValue = run(FromDist(ToDist(Normalize), normalValue))
+    normalizedValue 
+    -> unpackDist
+    -> expect
+    -> toEqual(normalValue)
+  })
+})
+
+describe("(Symbolic) mean", () => {
+  testAll("of normal distributions", list{-1e8, -16.0, -1e-2, 0.0, 1e-4, 32.0, 1e16}, mean => {
+    run(FromDist(ToFloat(#Mean), mkNormal(mean, 4.0))) 
+    -> unpackFloat 
+    -> expect 
+    -> toBeCloseTo(mean)
+  })
+
+  Skip.test("of normal(0, -1) (it NaNs out)", () => {
+    run(FromDist(ToFloat(#Mean), mkNormal(1e1, -1e0)))
+    -> unpackFloat
+    -> expect
+    -> ExpectJs.toBeFalsy
+  })
+
+  test("of normal(0, 1e-8) (it doesn't freak out at tiny stdev)", () => {
+    run(FromDist(ToFloat(#Mean), mkNormal(0.0, 1e-8)))
+    -> unpackFloat
+    -> expect
+    -> toBeCloseTo(0.0)
+  })
+
+  testAll("of exponential distributions", list{1e-7, 2.0, 10.0, 100.0}, rate => {
+    let meanValue = run(FromDist(ToFloat(#Mean), GenericDist_Types.Symbolic(#Exponential({rate: rate}))))
+    meanValue -> unpackFloat -> expect -> toBeCloseTo(1.0 /. rate)  // https://en.wikipedia.org/wiki/Exponential_distribution#Mean,_variance,_moments,_and_median
+  })
+
+  test("of a cauchy distribution", () => {
+    let meanValue = run(FromDist(ToFloat(#Mean), GenericDist_Types.Symbolic(#Cauchy({local: 1.0, scale: 1.0}))))
+    meanValue
+    -> unpackFloat
+    -> expect
+    -> toBeCloseTo(2.01868297874546)
+    //-> toBe(GenDistError(Other("Cauchy distributions may have no mean value.")))
+  })
+
+  testAll("of triangular distributions", list{(1.0,2.0,3.0), (-1e7,-1e-7,1e-7), (-1e-7,1e0,1e7), (-1e-16,0.0,1e-16)}, tup => {
+    let (low, medium, high) = tup
+    let meanValue = run(FromDist(
+      ToFloat(#Mean), 
+      GenericDist_Types.Symbolic(#Triangular({low: low, medium: medium, high: high}))
+    ))
+    meanValue 
+    -> unpackFloat 
+    -> expect 
+    -> toBeCloseTo((low +. medium +. high) /. 3.0)  // https://www.statology.org/triangular-distribution/
+  })
+
+  // TODO: nonpositive inputs are SUPPOSED to crash. 
+  testAll("of beta distributions", list{(1e-4, 6.4e1), (1.28e2, 1e0), (1e-16, 1e-16), (1e16, 1e16), (-1e4, 1e1), (1e1, -1e4)}, tup => {
+    let (alpha, beta) = tup
+    let meanValue = run(FromDist(
+      ToFloat(#Mean), 
+      GenericDist_Types.Symbolic(#Beta({alpha: alpha, beta: beta}))
+    ))
+    meanValue 
+    -> unpackFloat 
+    -> expect 
+    -> toBeCloseTo(1.0 /. (1.0 +. (beta /. alpha)))  // https://en.wikipedia.org/wiki/Beta_distribution#Mean
+  })
+
+  // TODO: When we have our theory of validators we won't want this to be NaN but to be an error.
+  test("of beta(0, 0)", () => {
+    let meanValue = run(FromDist(
+      ToFloat(#Mean), 
+      GenericDist_Types.Symbolic(#Beta({alpha: 0.0, beta: 0.0}))
+    ))
+    meanValue
+    -> unpackFloat
+    -> expect
+    -> ExpectJs.toBeFalsy
+  })
+
+  testAll("of lognormal distributions", list{(2.0, 4.0), (1e-7, 1e-2), (-1e6, 10.0), (1e3, -1e2), (-1e8, -1e4), (1e2, 1e-5)}, tup => { 
+    let (mu, sigma) = tup
+    let meanValue = run(FromDist(
+      ToFloat(#Mean), 
+      GenericDist_Types.Symbolic(#Lognormal({mu: mu, sigma: sigma}))
+    ))
+    meanValue 
+    -> unpackFloat 
+    -> expect 
+    -> toBeCloseTo(Js.Math.exp(mu +. sigma ** 2.0 /. 2.0 ))  // https://brilliant.org/wiki/log-normal-distribution/
+  })
+
+  testAll("of uniform distributions", list{(1e-5, 12.345), (-1e4, 1e4), (-1e16, -1e2), (5.3e3, 9e9)}, tup => {
+    let (low, high) = tup
+    let meanValue = run(FromDist(
+      ToFloat(#Mean), 
+      GenericDist_Types.Symbolic(#Uniform({low: low, high: high}))
+    ))
+    meanValue 
+    -> unpackFloat 
+    -> expect 
+    -> toBeCloseTo((low +. high) /. 2.0)  // https://en.wikipedia.org/wiki/Continuous_uniform_distribution#Moments
+  })
+
+  test("of a float", () => {
+    let meanValue = run(FromDist(
+      ToFloat(#Mean), 
+      GenericDist_Types.Symbolic(#Float(7.7))
+    ))
+    meanValue -> unpackFloat -> expect -> toBeCloseTo(7.7)
+  })
+})
+
+describe("Normal distribution with sparklines", () => {
+
+  let parameterWiseAdditionPdf = (n1: SymbolicDistTypes.normal, n2: SymbolicDistTypes.normal) => {
+    let normalDistAtSumMeanConstr = SymbolicDist.Normal.add(n1, n2)
+    let normalDistAtSumMean: SymbolicDistTypes.normal = switch normalDistAtSumMeanConstr {
+      | #Normal(params) => params
+    }
+    x => SymbolicDist.Normal.pdf(x, normalDistAtSumMean)
+  }
+
+  let normalDistAtMean5: SymbolicDistTypes.normal = {mean: 5.0, stdev: 2.0}
+  let normalDistAtMean10: SymbolicDistTypes.normal = {mean: 10.0, stdev: 2.0}
+  let range20Float = E.A.Floats.range(0.0, 20.0, 20) // [0.0,1.0,2.0,3.0,4.0,...19.0,]
+
+  test("mean=5 pdf", () => {
+    let pdfNormalDistAtMean5 = x => SymbolicDist.Normal.pdf(x, normalDistAtMean5)
+    let sparklineMean5 = fnImage(pdfNormalDistAtMean5, range20Float) 
+    Sparklines.create(sparklineMean5, ()) 
+    -> expect 
+    -> toEqual(`▁▂▃▆██▇▅▂▁▁▁▁▁▁▁▁▁▁▁`)
+  })
+  
+  test("parameter-wise addition of two normal distributions", () => {  
+    let sparklineMean15 = normalDistAtMean5 -> parameterWiseAdditionPdf(normalDistAtMean10) -> fnImage(range20Float)
+    Sparklines.create(sparklineMean15, ())
+    -> expect
+    -> toEqual(`▁▁▁▁▁▁▁▁▁▂▃▄▆███▇▅▄▂`)
+  })
+
+  test("mean=10 cdf", () => {
+    let cdfNormalDistAtMean10 = x => SymbolicDist.Normal.cdf(x, normalDistAtMean10)
+    let sparklineMean10 = fnImage(cdfNormalDistAtMean10, range20Float)
+    Sparklines.create(sparklineMean10, ())
+    -> expect
+    -> toEqual(`▁▁▁▁▁▁▁▁▂▄▅▇████████`)
+  })
+})

packages/squiggle-lang/__tests__/Samples__test.res

@@ -1,47 +0,0 @@
-open Jest
-open Expect
-
-let makeTest = (~only=false, str, item1, item2) =>
-  only
-    ? Only.test(str, () => expect(item1) -> toEqual(item2))
-    : test(str, () => expect(item1) -> toEqual(item2))
-
-describe("Lodash", () =>
-  describe("Lodash", () => {
-    makeTest(
-      "split",
-      SampleSet.Internals.T.splitContinuousAndDiscrete([1.432, 1.33455, 2.0]),
-      ([1.432, 1.33455, 2.0], E.FloatFloatMap.empty()),
-    )
-    makeTest(
-      "split",
-      SampleSet.Internals.T.splitContinuousAndDiscrete([
-        1.432,
-        1.33455,
-        2.0,
-        2.0,
-        2.0,
-        2.0,
-      ]) |> (((c, disc)) => (c, disc |> E.FloatFloatMap.toArray)),
-      ([1.432, 1.33455], [(2.0, 4.0)]),
-    )
-
-    let makeDuplicatedArray = count => {
-      let arr = Belt.Array.range(1, count) |> E.A.fmap(float_of_int)
-      let sorted = arr |> Belt.SortArray.stableSortBy(_, compare)
-      E.A.concatMany([sorted, sorted, sorted, sorted]) |> Belt.SortArray.stableSortBy(_, compare)
-    }
-
-    let (_, discrete) = SampleSet.Internals.T.splitContinuousAndDiscrete(
-      makeDuplicatedArray(10),
-    )
-    let toArr = discrete |> E.FloatFloatMap.toArray
-    makeTest("splitMedium", toArr |> Belt.Array.length, 10)
-
-    let (_c, discrete) = SampleSet.Internals.T.splitContinuousAndDiscrete(
-      makeDuplicatedArray(500),
-    )
-    let toArr = discrete |> E.FloatFloatMap.toArray
-    makeTest("splitMedium", toArr |> Belt.Array.length, 500)
-  })
-)

packages/squiggle-lang/__tests__/Symbolic_test.res

@@ -1,33 +0,0 @@
-open Jest
-open Expect
-open Js.Array
-open SymbolicDist
-
-let makeTest = (~only=false, str, item1, item2) =>
-  only
-    ? Only.test(str, () => expect(item1) -> toEqual(item2))
-    : test(str, () => expect(item1) -> toEqual(item2))
-
-let pdfImage = (thePdf, inps) => map(thePdf, inps)
-
-let parameterWiseAdditionHelper = (n1: SymbolicDistTypes.normal, n2: SymbolicDistTypes.normal) => {
-  let normalDistAtSumMeanConstr = Normal.add(n1, n2)
-  let normalDistAtSumMean: SymbolicDistTypes.normal = switch normalDistAtSumMeanConstr {
-    | #Normal(params) => params
-  }
-  x => Normal.pdf(x, normalDistAtSumMean)
-}
-
-describe("Normal distribution with sparklines", () => {
-
-  let normalDistAtMean5: SymbolicDistTypes.normal = {mean: 5.0, stdev: 2.0}
-  let normalDistAtMean10: SymbolicDistTypes.normal = {mean: 10.0, stdev: 2.0}
-  let range20Float = E.A.Floats.range(0.0, 20.0, 20) // [0.0,1.0,2.0,3.0,4.0,...19.0,]
-
-  let pdfNormalDistAtMean5 = x => Normal.pdf(x, normalDistAtMean5)
-  let sparklineMean5 = pdfImage(pdfNormalDistAtMean5, range20Float)
-  makeTest("mean=5", Sparklines.create(sparklineMean5, ()), `▁▂▃▆██▇▅▂▁▁▁▁▁▁▁▁▁▁▁`)
-
-  let sparklineMean15 = normalDistAtMean5 -> parameterWiseAdditionHelper(normalDistAtMean10) -> pdfImage(range20Float)
-  makeTest("parameter-wise addition of two normal distributions", Sparklines.create(sparklineMean15, ()), `▁▁▁▁▁▁▁▁▁▂▃▄▆███▇▅▄▂`)
-})

packages/squiggle-lang/__tests__/TestHelpers.res

@@ -0,0 +1,26 @@
+open Jest
+open Expect
+
+let makeTest = (~only=false, str, item1, item2) =>
+  only
+    ? Only.test(str, () => expect(item1) -> toEqual(item2))
+    : test(str, () => expect(item1) -> toEqual(item2))
+
+
+let {toFloat, toDist, toString, toError, fmap} = module(DistributionOperation.Output)
+
+let fnImage = (theFn, inps) => Js.Array.map(theFn, inps)
+
+let env: DistributionOperation.env = {
+  sampleCount: 100,
+  xyPointLength: 100,
+}
+
+let run = DistributionOperation.run(~env)
+let outputMap = fmap(~env)
+let unreachableInTestFileMessage = "Should be impossible to reach (This error is in test file)"
+let toExtFloat: option<float> => float = E.O.toExt(unreachableInTestFileMessage)
+let toExtDist: option<GenericDist_Types.genericDist> => GenericDist_Types.genericDist = E.O.toExt(unreachableInTestFileMessage)
+// let toExt: option<'a> => 'a = E.O.toExt(unreachableInTestFileMessage)
+let unpackFloat = x => x -> toFloat -> toExtFloat
+let unpackDist = y => y -> toDist -> toExtDist

packages/squiggle-lang/bsconfig.json

@@ -47,7 +47,7 @@
     [
       "../../node_modules/bisect_ppx/ppx", 
       "--exclude-files", 
-      ".*_Test\\.res$$"
+      ".*_test\\.res$$"
     ]
   ]
 }

packages/squiggle-lang/jest.config.js

@@ -6,4 +6,7 @@ module.exports = {
   setupFilesAfterEnv: [
     "<rootdir>/../../node_modules/bisect_ppx/src/runtime/js/jest.bs.js"
   ],
+  testPathIgnorePatterns: [
+    "__tests__/TestHelpers.bs.js"
+  ], 
 };

packages/squiggle-lang/package.json

@@ -10,7 +10,7 @@
     "test:reducer": "jest --testPathPattern '.*__tests__/Reducer.*'",
     "test": "jest",
     "test:watch": "jest --watchAll",
-    "coverage": "rm -f *.coverage; yarn clean; BISECT_ENABLE=yes yarn build; yarn test; ./node_modules/.bin/bisect-ppx-report html", 
+    "coverage": "rm -f *.coverage; yarn clean; BISECT_ENABLE=yes yarn build; yarn test; bisect-ppx-report html", 
     "all": "yarn build && yarn bundle && yarn test"
   },
   "keywords": [

packages/squiggle-lang/src/rescript/Distributions/DistributionOperation/DistributionOperation.res

@@ -10,10 +10,10 @@ type env = {
 }
 
 type outputType =
-  | Dist(GenericDist_Types.genericDist)
+  | Dist(genericDist)
   | Float(float)
   | String(string)
-  | GenDistError(GenericDist_Types.error)
+  | GenDistError(error)
 
 /*
 We're going to add another function to this module later, so first define a

packages/squiggle-lang/src/rescript/Distributions/GenericDist/GenericDist_Types.res

@@ -1,6 +1,6 @@
 type genericDist =
   | PointSet(PointSetTypes.pointSetDist)
-  | SampleSet(array<float>)
+  | SampleSet(SampleSet.t)
   | Symbolic(SymbolicDistTypes.symbolicDist)
 
 type error =

packages/squiggle-lang/src/rescript/Distributions/SampleSetDist/SampleSet.res

@@ -1,3 +1,5 @@
+type t = array<float>
+
 // TODO: Refactor to raise correct error when not enough samples
 
 module Internals = {

packages/squiggle-lang/src/rescript/Distributions/SymbolicDist/SymbolicDist.res

@@ -55,7 +55,7 @@ module Exponential = {
             rate: rate,
           }),
         )
-      : Error("Exponential distributions mean must be larger than 0")
+      : Error("Exponential distributions rate must be larger than 0.")
   let pdf = (x, t: t) => Jstat.Exponential.pdf(x, t.rate)
   let cdf = (x, t: t) => Jstat.Exponential.cdf(x, t.rate)
   let inv = (p, t: t) => Jstat.Exponential.inv(p, t.rate)
@@ -71,7 +71,7 @@ module Cauchy = {
   let cdf = (x, t: t) => Jstat.Cauchy.cdf(x, t.local, t.scale)
   let inv = (p, t: t) => Jstat.Cauchy.inv(p, t.local, t.scale)
   let sample = (t: t) => Jstat.Cauchy.sample(t.local, t.scale)
-  let mean = (_: t) => Error("Cauchy distributions have no mean value.")
+  let mean = (_: t) => Error("Cauchy distributions may have no mean value.")
   let toString = ({local, scale}: t) => j`Cauchy($local, $scale)`
 }
 
@@ -80,8 +80,8 @@ module Triangular = {
   let make = (low, medium, high): result<symbolicDist, string> =>
     low < medium && medium < high
       ? Ok(#Triangular({low: low, medium: medium, high: high}))
-      : Error("Triangular values must be increasing order")
+      : Error("Triangular values must be increasing order.")
-  let pdf = (x, t: t) => Jstat.Triangular.pdf(x, t.low, t.high, t.medium)
+  let pdf = (x, t: t) => Jstat.Triangular.pdf(x, t.low, t.high, t.medium) // not obvious in jstat docs that high comes before medium? 
   let cdf = (x, t: t) => Jstat.Triangular.cdf(x, t.low, t.high, t.medium)
   let inv = (p, t: t) => Jstat.Triangular.inv(p, t.low, t.high, t.medium)
   let sample = (t: t) => Jstat.Triangular.sample(t.low, t.high, t.medium)