open FunctionRegistry_Core open FunctionRegistry_Helpers let nameSpace = "Danger" let requiresNamespace = true module NNumbersToNumber = { module One = { let make = (name, fn) => FnDefinition.make( ~name, ~inputs=[FRTypeNumber], ~run=(_, inputs, _, _) => { inputs ->getOrError(0) ->E.R.bind(Prepare.oneNumber) ->E.R2.fmap(fn) ->E.R2.fmap(Wrappers.evNumber) }, (), ) } module Two = { let make = (name, fn) => FnDefinition.make( ~name, ~inputs=[FRTypeNumber, FRTypeNumber], ~run=(_, inputs, _, _) => { inputs->Prepare.ToValueTuple.twoNumbers->E.R2.fmap(fn)->E.R2.fmap(Wrappers.evNumber) }, (), ) } module Three = { let make = (name, fn) => FnDefinition.make( ~name, ~inputs=[FRTypeNumber, FRTypeNumber, FRTypeNumber], ~run=(_, inputs, _, _) => { inputs->Prepare.ToValueTuple.threeNumbers->E.R2.fmap(fn)->E.R2.fmap(Wrappers.evNumber) }, (), ) } } module Internals = { // Probability functions let factorial = Stdlib.Math.factorial let choose = ((n, k)) => factorial(n) /. (factorial(n -. k) *. factorial(k)) let pow = (base, exp) => Js.Math.pow_float(~base, ~exp) let binomial = ((n, k, p)) => choose((n, k)) *. pow(p, k) *. pow(1.0 -. p, n -. k) // Integral helper functions let applyFunctionAtPoint = ( aLambda, internalNumber: internalExpressionValue, environment, reducer, ): result => { let result = Reducer_Expression_Lambda.doLambdaCall( aLambda, list{internalNumber}, environment, reducer, ) result } let castFloatToInternalNumber = x => ReducerInterface_InternalExpressionValue.IEvNumber(x) let castArrayOfFloatsToInternalArrayOfInternals = xs => ReducerInterface_InternalExpressionValue.IEvArray( Belt.Array.map(xs, x => castFloatToInternalNumber(x)), ) @dead let applyFunctionAtFloat = (aLambda, point, environment, reducer) => // reason for existence: might be an useful template to have for calculating diminishing marginal returns later on applyFunctionAtPoint(aLambda, castFloatToInternalNumber(point), environment, reducer) // integrate function itself let integrateFunctionBetweenWithNumIntegrationPoints = ( aLambda, min: float, max: float, numIntegrationPoints: float, // cast as int? environment, reducer, ) => { let applyFunctionAtFloatToFloatOption = (point: float) => { // Defined here so that it has access to environment, reducer let pointAsInternalExpression = castFloatToInternalNumber(point) let resultAsInternalExpression = Reducer_Expression_Lambda.doLambdaCall( aLambda, list{pointAsInternalExpression}, environment, reducer, ) let result = switch resultAsInternalExpression { | Ok(IEvNumber(x)) => Ok(x) | Error(_) => Error( "Error 1 in Danger.integrate. It's possible that your function doesn't return a number, try definining auxiliaryFunction(x) = mean(yourFunction(x)) and integrate auxiliaryFunction instead", ) | _ => Error("Error 2 in Danger.integrate") } result } // worked example in comments below, assuming min=0, max = 10 let numTotalPoints = Belt.Float.toInt(numIntegrationPoints) // superflous declaration, but useful to keep track that we are interpreting "numIntegrationPoints" as the total number on which we evaluate the function, not e.g., as the inner integration points. let numInnerPoints = numTotalPoints - 2 let numOuterPoints = 2 let totalWeight = max -. min let weightForAnInnerPoint = totalWeight /. E.I.toFloat(numTotalPoints - 1) let weightForAnOuterPoint = totalWeight /. E.I.toFloat(numTotalPoints - 1) /. 2.0 let innerPointIncrement = (max -. min) /. E.I.toFloat(numTotalPoints - 1) let innerXs = Belt.Array.makeBy(numInnerPoints, i => min +. Belt_Float.fromInt(i + 1) *. innerPointIncrement ) // Gotcha: makeBy goes from 0 to (n-1): let ysOptions = Belt.Array.map(innerXs, x => applyFunctionAtFloatToFloatOption(x)) let okYs = E.A.R.filterOk(ysOptions) /* Logging, with a worked example. */ // Useful for understanding what is happening. // assuming min = 0, max = 10, numTotalPoints=10, results below: let verbose = false if verbose { Js.Console.log2("numTotalPoints", numTotalPoints) // 5 Js.Console.log2("numInnerPoints", numInnerPoints) // 3 Js.Console.log2("numOuterPoints", numOuterPoints) // always 2 Js.Console.log2("totalWeight", totalWeight) // 10 - 0 = 10 Js.Console.log2("weightForAnInnerPoint", weightForAnInnerPoint) // 10/4 = 2.5 Js.Console.log2("weightForAnOuterPoint", weightForAnOuterPoint) // 10/4/2 = 1.25 Js.Console.log2( "weightForAnInnerPoint * numInnerPoints + weightForAnOuterPoint * numOuterPoints", weightForAnInnerPoint *. E.I.toFloat(numInnerPoints) +. weightForAnOuterPoint *. E.I.toFloat(numOuterPoints), ) // should be 10 Js.Console.log2( "sum of weights == totalWeight", weightForAnInnerPoint *. E.I.toFloat(numInnerPoints) +. weightForAnOuterPoint *. E.I.toFloat(numOuterPoints) == totalWeight, ) // true Js.Console.log2("innerPointIncrement", innerPointIncrement) // (10-0)/4 = 2.5 Js.Console.log2("innerXs", innerXs) // 2.5, 5, 7.5 Js.Console.log2("ysOptions", ysOptions) Js.Console.log2("okYs", okYs) } let result = switch E.A.length(ysOptions) == E.A.length(okYs) { | true => { let innerPointsSum = okYs->E.A.reduce(0.0, (a, b) => a +. b) let resultWithOuterPoints = switch ( applyFunctionAtFloatToFloatOption(min), applyFunctionAtFloatToFloatOption(max), ) { | (Ok(yMin), Ok(yMax)) => { let result = (yMin +. yMax) *. weightForAnOuterPoint +. innerPointsSum *. weightForAnInnerPoint let wrappedResult = result->ReducerInterface_InternalExpressionValue.IEvNumber->Ok wrappedResult } | (Error(b), _) => Error(b) | (_, Error(b)) => Error(b) } resultWithOuterPoints } | false => Error( "Integration error 3 in Danger.integrate. It's possible that your function doesn't return a number, try definining auxiliaryFunction(x) = mean(yourFunction(x)) and integrate auxiliaryFunction instead", ) } result } type diminishingReturnsAccumulatorInner = { optimalAllocations: array, currentMarginalReturns: result, string>, } let findBiggestElementIndex = xs => E.A.reducei(xs, 0, (acc, newElement, index) => { switch newElement > xs[acc] { | true => index | false => acc } }) type diminishingReturnsAccumulator = result let diminishingMarginalReturnsForTwoFunctions = ( lambda1, lambda2, funds, approximateIncrement, environment, reducer, ) => { /* Two possible algorithms (n=funds/increment, m=num lambdas) 1. O(n): Iterate through value on next n dollars. At each step, only compute the new marginal return of the function which is spent 2. O(n*m): Iterate through all possible spending combinations. Fun is, it doesn't assume that the returns of marginal spending are diminishing. */ let applyFunctionAtFloatToFloatOption = (lambda, point: float) => { // Defined here so that it has access to environment, reducer let pointAsInternalExpression = castFloatToInternalNumber(point) let resultAsInternalExpression = Reducer_Expression_Lambda.doLambdaCall( lambda, list{pointAsInternalExpression}, environment, reducer, ) let result = switch resultAsInternalExpression { | Ok(IEvNumber(x)) => Ok(x) | Error(_) => Error( "Integration error 1 in Danger.diminishingMarginalReturnsForTwoFunctions. It's possible that your function doesn't return a number, try definining auxiliaryFunction(x) = mean(yourFunction(x)) and integrate auxiliaryFunction instead", ) | _ => Error("Integration error 2 in Danger.diminishingMarginalReturnsForTwoFunctions") } result } let numDivisions = Js.Math.round(funds /. approximateIncrement) let numDivisionsInt = Belt.Float.toInt(numDivisions) let increment = funds /. numDivisions let arrayOfIncrements = Belt.Array.makeBy(numDivisionsInt, _ => increment) let initAccumulator: diminishingReturnsAccumulator = Ok({ optimalAllocations: [0.0, 0.0], currentMarginalReturns: E.A.R.firstErrorOrOpen([ applyFunctionAtFloatToFloatOption(lambda1, 0.0), applyFunctionAtFloatToFloatOption(lambda2, 0.0), ]), }) let optimalAllocationEndAccumulator = E.A.reduce(arrayOfIncrements, initAccumulator, ( acc, newIncrement, ) => { switch acc { | Ok(accInner) => { let oldMarginalReturnsWrapped = accInner.currentMarginalReturns let newAccWrapped = switch oldMarginalReturnsWrapped { | Ok(oldMarginalReturns) => { let indexOfBiggestDMR = findBiggestElementIndex(oldMarginalReturns) let newOptimalAllocations = Belt.Array.copy(accInner.optimalAllocations) let newOptimalAllocationsi = newOptimalAllocations[indexOfBiggestDMR] +. newIncrement newOptimalAllocations[indexOfBiggestDMR] = newOptimalAllocationsi let lambdai = indexOfBiggestDMR == 0 ? lambda1 : lambda2 // to do: generalize let newMarginalResultsLambdai = applyFunctionAtFloatToFloatOption( lambdai, newOptimalAllocationsi, ) let newCurrentMarginalReturns = switch newMarginalResultsLambdai { | Ok(value) => { let result = Belt.Array.copy(oldMarginalReturns) result[indexOfBiggestDMR] = value Ok(result) } | Error(b) => Error(b) } let newAcc: diminishingReturnsAccumulatorInner = { optimalAllocations: newOptimalAllocations, currentMarginalReturns: newCurrentMarginalReturns, } Ok(newAcc) } | Error(b) => Error(b) } newAccWrapped } | Error(b) => Error(b) } /* let findSmaller = (_) => 0 let smallerDMR = acc */ }) let optimalAllocationResult = switch optimalAllocationEndAccumulator { | Ok(inner) => Ok(castArrayOfFloatsToInternalArrayOfInternals(inner.optimalAllocations)) | Error(b) => Error(b) } optimalAllocationResult } let diminishingMarginalReturnsForManyFunctionsSkeleton = ( lambdas, funds, approximateIncrement, environment, reducer, ) => { let result = [0.0, 0.0]->castArrayOfFloatsToInternalArrayOfInternals->Ok result } /* let diminishingMarginalReturnsForManyFunctions = ( lambdas, funds, approximateIncrement, environment, reducer, ) => { /* Two possible algorithms (n=funds/increment, m=num lambdas) 1. O(n): Iterate through value on next n dollars. At each step, only compute the new marginal return of the function which is spent 2. O(n*m): Iterate through all possible spending combinations. Fun is, it doesn't assume that the returns of marginal spending are diminishing. */ let applyFunctionAtFloatToFloatOption = (lambda, point: float) => { // Defined here so that it has access to environment, reducer let pointAsInternalExpression = castFloatToInternalNumber(point) let resultAsInternalExpression = Reducer_Expression_Lambda.doLambdaCall( lambda, list{pointAsInternalExpression}, environment, reducer, ) let result = switch resultAsInternalExpression { | Ok(IEvNumber(x)) => Ok(x) | Error(_) => Error( "Error 1 in Danger.diminishingMarginalReturnsForManyFunctions. It's possible that your function doesn't return a number, try definining auxiliaryFunction(x) = mean(yourFunction(x)) and integrate auxiliaryFunction instead", ) | _ => Error("Error 2 in Danger.diminishingMarginalReturnsForManyFunctions") } result } let numDivisions = Js.Math.round(funds /. approximateIncrement) let numDivisionsInt = Belt.Float.toInt(numDivisions) let increment = funds /. numDivisions let arrayOfIncrements = Belt.Array.makeBy(numDivisionsInt, _ => increment) let numLambdas = E.A.length(lambdas) let initAccumulator: diminishingReturnsAccumulator = Ok({ optimalAllocations: Belt.Array.makeBy(numLambdas, _ => 0.0), currentMarginalReturns: E.A.fmap( lambda => applyFunctionAtFloatToFloatOption(lambda, 0.0), lambdas, )->E.A.R.firstErrorOrOpen, }) let optimalAllocationEndAccumulator = E.A.reduce(arrayOfIncrements, initAccumulator, ( acc, newIncrement, ) => { switch acc { | Ok(accInner) => { let oldMarginalReturnsWrapped = accInner.currentMarginalReturns let newAccWrapped = switch oldMarginalReturnsWrapped { | Ok(oldMarginalReturns) => { let indexOfBiggestDMR = findBiggestElementIndex(oldMarginalReturns) let newOptimalAllocations = Belt.Array.copy(accInner.optimalAllocations) let newOptimalAllocationsi = newOptimalAllocations[indexOfBiggestDMR] +. newIncrement newOptimalAllocations[indexOfBiggestDMR] = newOptimalAllocationsi let lambdai = lambdas[indexOfBiggestDMR] let newMarginalResultsLambdai = applyFunctionAtFloatToFloatOption( lambdai, newOptimalAllocationsi, ) let newCurrentMarginalReturns = switch newMarginalResultsLambdai { | Ok(value) => { let result = Belt.Array.copy(oldMarginalReturns) result[indexOfBiggestDMR] = value Ok(result) } | Error(b) => Error(b) } let newAcc: diminishingReturnsAccumulatorInner = { optimalAllocations: newOptimalAllocations, currentMarginalReturns: newCurrentMarginalReturns, } Ok(newAcc) } | Error(b) => Error(b) } newAccWrapped } | Error(b) => Error(b) } }) let optimalAllocationResult = switch optimalAllocationEndAccumulator { | Ok(inner) => Ok(castArrayOfFloatsToInternalArrayOfInternals(inner.optimalAllocations)) | Error(b) => Error(b) } optimalAllocationResult //let result = [0.0, 0.0]->castArrayOfFloatsToInternalArrayOfInternals->Ok // result }*/ } let library = [ Function.make( ~name="laplace", ~nameSpace, ~requiresNamespace, ~output=EvtNumber, ~examples=[`Danger.laplace(1, 20)`], ~definitions=[ NNumbersToNumber.Two.make("laplace", ((successes, trials)) => (successes +. 1.0) /. (trials +. 2.0) ), ], (), ), Function.make( ~name="factorial", ~nameSpace, ~requiresNamespace, ~output=EvtNumber, ~examples=[`Danger.factorial(20)`], ~definitions=[NNumbersToNumber.One.make("factorial", Internals.factorial)], (), ), Function.make( ~name="choose", ~nameSpace, ~requiresNamespace, ~output=EvtNumber, ~examples=[`Danger.choose(1, 20)`], ~definitions=[NNumbersToNumber.Two.make("choose", Internals.choose)], (), ), Function.make( ~name="binomial", ~nameSpace, ~requiresNamespace, ~output=EvtNumber, ~examples=[`Danger.binomial(1, 20, 0.5)`], ~definitions=[NNumbersToNumber.Three.make("binomial", Internals.binomial)], (), ), // Helper functions building up to the integral Function.make( ~name="applyFunctionAtZero", ~nameSpace, ~output=EvtNumber, ~requiresNamespace=false, ~examples=[`Danger.applyFunctionAtZero({|x| x+1})`], ~definitions=[ FnDefinition.make( ~name="applyFunctionAtZero", ~inputs=[FRTypeLambda], ~run=(inputs, _, environment, reducer) => { let result = switch inputs { | [IEvLambda(aLambda)] => Internals.applyFunctionAtPoint( aLambda, Internals.castFloatToInternalNumber(0.0), environment, reducer, )->E.R2.errMap(_ => "Error!") | _ => Error(impossibleError) } result }, (), ), ], (), ), Function.make( ~name="applyFunctionAtPoint", ~nameSpace, ~output=EvtNumber, ~requiresNamespace=false, ~examples=[`Danger.applyFunctionAtPoint({|x| x+1}, 1)`], ~definitions=[ FnDefinition.make( ~name="applyFunctionAtPoint", ~inputs=[FRTypeLambda, FRTypeNumber], ~run=(inputs, _, env, reducer) => switch inputs { | [IEvLambda(aLambda), point] => Internals.applyFunctionAtPoint(aLambda, point, env, reducer)->E.R2.errMap(_ => "Error!") | _ => Error(impossibleError) }, (), ), ], (), ), // Integral in terms of function, min, max, num points // Note that execution time will be more predictable, because it // will only depend on num points and the complexity of the function Function.make( ~name="integrateFunctionBetweenWithNumIntegrationPoints", ~nameSpace, ~output=EvtNumber, ~requiresNamespace=false, ~examples=[`Danger.integrateFunctionBetweenWithNumIntegrationPoints({|x| x+1}, 1, 10, 10)`], // should be [x^2/2 + x]1_10 = (100/2 + 10) - (1/2 + 1) = 60 - 1.5 = 58.5 // https://www.wolframalpha.com/input?i=integrate+x%2B1+from+1+to+10 ~definitions=[ FnDefinition.make( ~name="integrateFunctionBetweenWithNumIntegrationPoints", ~inputs=[FRTypeLambda, FRTypeNumber, FRTypeNumber, FRTypeNumber], ~run=(inputs, _, env, reducer) => { let result = switch inputs { | [_, _, _, IEvNumber(0.0)] => Error("Integration error 4 in Danger.integrate: Increment can't be 0.") | [IEvLambda(aLambda), IEvNumber(min), IEvNumber(max), IEvNumber(numIntegrationPoints)] => Internals.integrateFunctionBetweenWithNumIntegrationPoints( aLambda, min, max, numIntegrationPoints, env, reducer, ) | _ => Error( "Integration error 5 in Danger.integrate. Remember that inputs are (function, number (min), number (max), number(increment))", ) } result }, (), ), ], (), ), // Integral in terms of function, min, max, epsilon (distance between points) // Note that execution time will be less predictable, because it // will depend on min, max and epsilon together, // as well and the complexity of the function Function.make( ~name="integrateFunctionBetweenWithEpsilon", ~nameSpace, ~output=EvtNumber, ~requiresNamespace=false, ~examples=[`Danger.integrateFunctionBetweenWithEpsilon({|x| x+1}, 1, 10, 0.1)`], ~definitions=[ FnDefinition.make( ~name="integrateFunctionBetweenWithEpsilon", ~inputs=[FRTypeLambda, FRTypeNumber, FRTypeNumber, FRTypeNumber], ~run=(inputs, _, env, reducer) => { let result = switch inputs { | [_, _, _, IEvNumber(0.0)] => Error("Integration error in Danger.integrate: Increment can't be 0.") | [IEvLambda(aLambda), IEvNumber(min), IEvNumber(max), IEvNumber(epsilon)] => Internals.integrateFunctionBetweenWithNumIntegrationPoints( aLambda, min, max, (max -. min) /. epsilon, env, reducer, )->E.R2.errMap(_ => "Integration error 7 in Danger.integrate. Something went wrong along the way" ) | _ => Error( "Integration error 8 in Danger.integrate. Remember that inputs are (function, number (min), number (max), number(increment))", ) } result }, (), ), ], (), ), Function.make( ~name="diminishingMarginalReturnsForTwoFunctions", ~nameSpace, ~output=EvtArray, ~requiresNamespace=false, ~examples=[`Danger.diminishingMarginalReturnsForTwoFunctions({|x| x+1}, {|y| 10}, 100, 0.01)`], ~definitions=[ FnDefinition.make( ~name="diminishingMarginalReturnsForTwoFunctions", ~inputs=[FRTypeLambda, FRTypeLambda, FRTypeNumber, FRTypeNumber], ~run=(inputs, _, env, reducer) => switch inputs { | [ IEvLambda(lambda1), IEvLambda(lambda2), IEvNumber(funds), IEvNumber(approximateIncrement), ] => Internals.diminishingMarginalReturnsForTwoFunctions( lambda1, lambda2, funds, approximateIncrement, env, reducer, ) | _ => Error("Error in Danger.diminishingMarginalReturnsForTwoFunctions") }, (), ), ], (), ), Function.make( ~name="diminishingMarginalReturnsForFunctions3", ~nameSpace, ~output=EvtArray, ~requiresNamespace=false, ~examples=[ `Danger.diminishingMarginalReturnsForFunctions3({|x| x+1}, {|y| 10}, {|z| 20-2x}, 100, 0.01)`, ], ~definitions=[ FnDefinition.make( ~name="diminishingMarginalReturnsForFunctions3", ~inputs=[FRTypeLambda, FRTypeLambda, FRTypeLambda, FRTypeNumber, FRTypeNumber], ~run=(inputs, _, env, reducer) => switch inputs { | [ IEvLambda(lambda1), IEvLambda(lambda2), IEvLambda(lambda3), IEvNumber(funds), IEvNumber(approximateIncrement), ] => Internals.diminishingMarginalReturnsForManyFunctionsSkeleton( [lambda1, lambda2, lambda3], funds, approximateIncrement, env, reducer, ) | _ => Error("Error in Danger.diminishingMarginalReturnsForFunctions3") }, (), ), ], (), ), /* The following will compile, but not work, because of this bug: Instead, I am creating different functions for different numbers of inputs Function.make( ~name="diminishingMarginalReturnsForManyFunctions", ~nameSpace, ~output=EvtArray, ~requiresNamespace=false, ~examples=[ `Danger.diminishingMarginalReturnsForManyFunctions([{|x| x+1}, {|y| 10}], 100, 0.01)`, ], ~definitions=[ FnDefinition.make( ~name="diminishingMarginalReturnsForManyFunctions", ~inputs=[FRTypeArray(FRTypeLambda), FRTypeNumber, FRTypeNumber], ~run=(inputs, _, environment, reducer) => switch inputs { | [IEvArray(innerlambdas), IEvNumber(funds), IEvNumber(approximateIncrement)] => { let individuallyWrappedLambdas = E.A.fmap(innerLambda => { switch innerLambda { | ReducerInterface_InternalExpressionValue.IEvLambda(lambda) => Ok(lambda) | _ => Error( "Error in Danger.diminishingMarginalReturnsForManyFunctions. A member of the array wasn't a function", ) } }, innerlambdas) let wrappedLambdas = E.A.R.firstErrorOrOpen(individuallyWrappedLambdas) let result = switch wrappedLambdas { | Ok(lambdas) => { let result = Internals.diminishingMarginalReturnsForManyFunctions( lambdas, funds, approximateIncrement, environment, reducer, ) result } | Error(b) => Error(b) } result //Error("wtf man") } | _ => Error("Error in Danger.diminishingMarginalReturnsForTwoFunctions") }, (), ), ], (), ), */ ]