/*
This is the most basic file in our invariants family of tests. 

Validate that the addition of means equals the mean of the addition, similar for subtraction and multiplication. 

Details in https://develop--squiggle-documentation.netlify.app/docs/internal/invariants/

Note: epsilon of 1e3 means the invariants are, in general, not being satisfied. 
*/

open Jest
open Expect
open TestHelpers

module Internals = {
  let epsilon = 5e1

  let mean = DistributionTypes.Constructors.UsingDists.mean

  let expectImpossiblePath: string => assertion = algebraicOp =>
    `${algebraicOp} has`->expect->toEqual("failed")

  let distributions = list{
    normalMake(4e0, 1e0),
    betaMake(2e0, 4e0),
    exponentialMake(1.234e0),
    uniformMake(7e0, 1e1),
    // cauchyMake(1e0, 1e0),
    lognormalMake(2e0, 1e0),
    triangularMake(1e0, 1e1, 5e1),
    Ok(floatMake(1e1)),
  }
  let pairsOfDifferentDistributions = E.L.combinations2(distributions)

  let runMean: DistributionTypes.genericDist => float = dist => {
    dist->mean->run->toFloat->E.O2.toExn("Shouldn't see this because we trust testcase input")
  }

  let testOperationMean = (
    distOp: (
      DistributionTypes.genericDist,
      DistributionTypes.genericDist,
    ) => result<DistributionTypes.genericDist, DistributionTypes.error>,
    description: string,
    floatOp: (float, float) => float,
    dist1': SymbolicDistTypes.symbolicDist,
    dist2': SymbolicDistTypes.symbolicDist,
    ~epsilon: float,
  ) => {
    let dist1 = dist1'->DistributionTypes.Symbolic
    let dist2 = dist2'->DistributionTypes.Symbolic
    let received =
      distOp(dist1, dist2)->E.R2.fmap(mean)->E.R2.fmap(run)->E.R2.fmap(toFloat)->E.R.toExn("Expected float", _)
    let expected = floatOp(runMean(dist1), runMean(dist2))
    switch received {
    | None => expectImpossiblePath(description)
    | Some(x) => expectErrorToBeBounded(x, expected, ~epsilon)
    }
  }
}

let {
  algebraicAdd,
  algebraicMultiply,
  algebraicDivide,
  algebraicSubtract,
  algebraicLogarithm,
  algebraicPower,
} = module(DistributionOperation.Constructors)

let algebraicAdd = algebraicAdd(~env)
let algebraicMultiply = algebraicMultiply(~env)
let algebraicDivide = algebraicDivide(~env)
let algebraicSubtract = algebraicSubtract(~env)
let algebraicLogarithm = algebraicLogarithm(~env)
let algebraicPower = algebraicPower(~env)

let {testOperationMean, distributions, pairsOfDifferentDistributions, epsilon} = module(Internals)

describe("Means are invariant", () => {
  describe("for addition", () => {
    let testAdditionMean = testOperationMean(algebraicAdd, "algebraicAdd", \"+.", ~epsilon)

    testAll("with two of the same distribution", distributions, dist => {
      E.R.liftM2(testAdditionMean, dist, dist)->E.R.toExn("Means were not invariant", _)
    })

    testAll("with two different distributions", pairsOfDifferentDistributions, dists => {
      let (dist1, dist2) = dists
      E.R.liftM2(testAdditionMean, dist1, dist2)->E.R.toExn("Means were not invariant", _)
    })

    testAll(
      "with two different distributions in swapped order",
      pairsOfDifferentDistributions,
      dists => {
        let (dist1, dist2) = dists
        E.R.liftM2(testAdditionMean, dist2, dist1)->E.R.toExn("Means were not invariant", _)
      },
    )
  })

  describe("for subtraction", () => {
    let testSubtractionMean = testOperationMean(
      algebraicSubtract,
      "algebraicSubtract",
      \"-.",
      ~epsilon,
    )

    testAll("with two of the same distribution", distributions, dist => {
      E.R.liftM2(testSubtractionMean, dist, dist)->E.R.toExn("Means were not invariant", _)
    })

    testAll("with two different distributions", pairsOfDifferentDistributions, dists => {
      let (dist1, dist2) = dists
      E.R.liftM2(testSubtractionMean, dist1, dist2)->E.R.toExn("Means were not invariant", _)
    })

    testAll(
      "with two different distributions in swapped order",
      pairsOfDifferentDistributions,
      dists => {
        let (dist1, dist2) = dists
        E.R.liftM2(testSubtractionMean, dist2, dist1)->E.R.toExn("Means were not invariant", _)
      },
    )
  })

  describe("for multiplication", () => {
    let testMultiplicationMean = testOperationMean(
      algebraicMultiply,
      "algebraicMultiply",
      \"*.",
      ~epsilon,
    )

    testAll("with two of the same distribution", distributions, dist => {
      E.R.liftM2(testMultiplicationMean, dist, dist)->E.R.toExn("Means were not invariant", _)
    })

    testAll("with two different distributions", pairsOfDifferentDistributions, dists => {
      let (dist1, dist2) = dists
      E.R.liftM2(testMultiplicationMean, dist1, dist2)->E.R.toExn("Means were not invariant", _)
    })

    testAll(
      "with two different distributions in swapped order",
      pairsOfDifferentDistributions,
      dists => {
        let (dist1, dist2) = dists
        E.R.liftM2(testMultiplicationMean, dist2, dist1)->E.R.toExn("Means were not invariant", _)
      },
    )
  })
})