Set up new expressionTree directory

This commit is contained in:
Ozzie Gooen 2020-07-02 18:12:03 +01:00
parent 19e9eaee83
commit 41eca03618
17 changed files with 467 additions and 505 deletions

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@ -383,9 +383,9 @@ describe("Shape", () => {
let numSamples = 10000;
open Distributions.Shape;
let normal: SymbolicTypes.symbolicDist = `Normal({mean, stdev});
let normalShape = TreeNode.toShape(numSamples, `Leaf(`SymbolicDist(normal)));
let normalShape = ExpressionTree.toShape(numSamples, `Leaf(`SymbolicDist(normal)));
let lognormal = SymbolicDist.Lognormal.fromMeanAndStdev(mean, stdev);
let lognormalShape = TreeNode.toShape(numSamples, `Leaf(`SymbolicDist(lognormal)));
let lognormalShape = ExpressionTree.toShape(numSamples, `Leaf(`SymbolicDist(lognormal)));
makeTestCloseEquality(
"Mean of a normal",

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@ -37,13 +37,13 @@ module DemoDist = {
let parsed1 = MathJsParser.fromString(guesstimatorString);
let shape =
switch (parsed1) {
| Ok(r) => Some(TreeNode.toShape(10000, r))
| Ok(r) => Some(ExpressionTree.toShape(10000, r))
| _ => None
};
let str =
switch (parsed1) {
| Ok(r) => TreeNode.toString(r)
| Ok(r) => ExpressionTree.toString(r)
| Error(e) => e
};

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@ -389,7 +389,7 @@ module Draw = {
let numSamples = 3000;
let normal: SymbolicTypes.symbolicDist = `Normal({mean, stdev});
let normalShape = TreeNode.toShape(numSamples, `Leaf(`SymbolicDist(normal)));
let normalShape = ExpressionTree.toShape(numSamples, `Leaf(`SymbolicDist(normal)));
let xyShape: Types.xyShape =
switch (normalShape) {
| Mixed(_) => {xs: [||], ys: [||]}

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@ -110,7 +110,7 @@ let toDiscretePointMassesFromTriangulars =
};
let combineShapesContinuousContinuous =
(op: SymbolicTypes.algebraicOperation, s1: DistTypes.xyShape, s2: DistTypes.xyShape)
(op: ExpressionTypes.algebraicOperation, s1: DistTypes.xyShape, s2: DistTypes.xyShape)
: DistTypes.xyShape => {
let t1n = s1 |> XYShape.T.length;
let t2n = s2 |> XYShape.T.length;

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@ -282,7 +282,7 @@ module Continuous = {
let combineAlgebraicallyWithDiscrete =
(
~downsample=false,
op: SymbolicTypes.algebraicOperation,
op: ExpressionTypes.algebraicOperation,
t1: t,
t2: DistTypes.discreteShape,
) => {
@ -291,7 +291,7 @@ module Continuous = {
let t1n = t1s |> XYShape.T.length;
let t2n = t2s |> XYShape.T.length;
let fn = SymbolicTypes.Algebraic.toFn(op);
let fn = Operation.Algebraic.toFn(op);
let outXYShapes: array(array((float, float))) =
Belt.Array.makeUninitializedUnsafe(t2n);
@ -333,7 +333,7 @@ module Continuous = {
};
let combineAlgebraically =
(~downsample=false, op: SymbolicTypes.algebraicOperation, t1: t, t2: t) => {
(~downsample=false, op: ExpressionTypes.algebraicOperation, t1: t, t2: t) => {
let s1 = t1 |> getShape;
let s2 = t2 |> getShape;
let t1n = s1 |> XYShape.T.length;
@ -413,7 +413,7 @@ module Discrete = {
/* This multiples all of the data points together and creates a new discrete distribution from the results.
Data points at the same xs get added together. It may be a good idea to downsample t1 and t2 before and/or the result after. */
let combineAlgebraically =
(op: SymbolicTypes.algebraicOperation, t1: t, t2: t) => {
(op: ExpressionTypes.algebraicOperation, t1: t, t2: t) => {
let t1s = t1 |> getShape;
let t2s = t2 |> getShape;
let t1n = t1s |> XYShape.T.length;
@ -426,7 +426,7 @@ module Discrete = {
t2.knownIntegralSum,
);
let fn = SymbolicTypes.Algebraic.toFn(op);
let fn = Operation.Algebraic.toFn(op);
let xToYMap = E.FloatFloatMap.empty();
for (i in 0 to t1n - 1) {
@ -840,7 +840,7 @@ module Mixed = {
});
let combineAlgebraically =
(~downsample=false, op: SymbolicTypes.algebraicOperation, t1: t, t2: t)
(~downsample=false, op: ExpressionTypes.algebraicOperation, t1: t, t2: t)
: t => {
// Discrete convolution can cause a huge increase in the number of samples,
// so we'll first downsample.
@ -914,7 +914,7 @@ module Shape = {
));
let combineAlgebraically =
(op: SymbolicTypes.algebraicOperation, t1: t, t2: t): t => {
(op: ExpressionTypes.algebraicOperation, t1: t, t2: t): t => {
switch (t1, t2) {
| (Continuous(m1), Continuous(m2)) =>
DistTypes.Continuous(
@ -1096,7 +1096,7 @@ module Shape = {
};
});
let operate = (distToFloatOp: SymbolicTypes.distToFloatOperation, s) =>
let operate = (distToFloatOp: ExpressionTypes.distToFloatOperation, s) =>
switch (distToFloatOp) {
| `Pdf(f) => pdf(f, s)
| `Inv(f) => inv(f, s)

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@ -0,0 +1,22 @@
open ExpressionTypes.ExpressionTree;
let toShape = (sampleCount: int, node: node) => {
let renderResult =
ExpressionTreeEvaluator.toLeaf(`Operation(`Render(node)), sampleCount);
switch (renderResult) {
| Ok(`Leaf(`RenderedDist(rs))) =>
let continuous = Distributions.Shape.T.toContinuous(rs);
let discrete = Distributions.Shape.T.toDiscrete(rs);
let shape = MixedShapeBuilder.buildSimple(~continuous, ~discrete);
shape |> E.O.toExt("Could not build final shape.");
| Ok(_) => E.O.toExn("Rendering failed.", None)
| Error(message) => E.O.toExn("No shape found, error: " ++ message, None)
};
};
let rec toString =
fun
| `Leaf(`SymbolicDist(d)) => SymbolicDist.T.toString(d)
| `Leaf(`RenderedDist(_)) => "[shape]"
| `Operation(op) => Operation.T.toString(toString, op);

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@ -0,0 +1,294 @@
/* This module represents a tree node. */
open ExpressionTypes;
open ExpressionTypes.ExpressionTree;
type t = node;
type tResult = node => result(node, string);
/* Given two random variables A and B, this returns the distribution
of a new variable that is the result of the operation on A and B.
For instance, normal(0, 1) + normal(1, 1) -> normal(1, 2).
In general, this is implemented via convolution. */
module AlgebraicCombination = {
let toTreeNode = (op, t1, t2) =>
`Operation(`AlgebraicCombination((op, t1, t2)));
let tryAnalyticalSolution =
fun
| `Operation(
`AlgebraicCombination(
operation,
`Leaf(`SymbolicDist(d1)),
`Leaf(`SymbolicDist(d2)),
),
) as t =>
switch (SymbolicDist.T.attemptAnalyticalOperation(d1, d2, operation)) {
| `AnalyticalSolution(symbolicDist) =>
Ok(`Leaf(`SymbolicDist(symbolicDist)))
| `Error(er) => Error(er)
| `NoSolution => Ok(t)
}
| t => Ok(t);
// todo: I don't like the name evaluateNumerically that much, if this renders and does it algebraically. It's tricky.
let evaluateNumerically = (algebraicOp, operationToLeaf, t1, t2) => {
// force rendering into shapes
let renderShape = r => operationToLeaf(`Render(r));
switch (renderShape(t1), renderShape(t2)) {
| (Ok(`Leaf(`RenderedDist(s1))), Ok(`Leaf(`RenderedDist(s2)))) =>
Ok(
`Leaf(
`RenderedDist(
Distributions.Shape.combineAlgebraically(algebraicOp, s1, s2),
),
),
)
| (Error(e1), _) => Error(e1)
| (_, Error(e2)) => Error(e2)
| _ => Error("Could not render shapes.")
};
};
let toLeaf =
(
operationToLeaf,
algebraicOp: ExpressionTypes.algebraicOperation,
t1: t,
t2: t,
)
: result(node, string) =>
toTreeNode(algebraicOp, t1, t2)
|> tryAnalyticalSolution
|> E.R.bind(
_,
fun
| `Leaf(d) => Ok(`Leaf(d)) // the analytical simplifaction worked, nice!
| `Operation(_) =>
// if not, run the convolution
evaluateNumerically(algebraicOp, operationToLeaf, t1, t2),
);
};
module VerticalScaling = {
let toLeaf = (operationToLeaf, scaleOp, t, scaleBy) => {
// scaleBy has to be a single float, otherwise we'll return an error.
let fn = Operation.Scale.toFn(scaleOp);
let knownIntegralSumFn = Operation.Scale.toKnownIntegralSumFn(scaleOp);
let renderedShape = operationToLeaf(`Render(t));
switch (renderedShape, scaleBy) {
| (Ok(`Leaf(`RenderedDist(rs))), `Leaf(`SymbolicDist(`Float(sm)))) =>
Ok(
`Leaf(
`RenderedDist(
Distributions.Shape.T.mapY(
~knownIntegralSumFn=knownIntegralSumFn(sm),
fn(sm),
rs,
),
),
),
)
| (Error(e1), _) => Error(e1)
| (_, _) => Error("Can only scale by float values.")
};
};
};
module PointwiseCombination = {
let pointwiseAdd = (operationToLeaf, t1, t2) => {
let renderedShape1 = operationToLeaf(`Render(t1));
let renderedShape2 = operationToLeaf(`Render(t2));
switch (renderedShape1, renderedShape2) {
| (Ok(`Leaf(`RenderedDist(rs1))), Ok(`Leaf(`RenderedDist(rs2)))) =>
Ok(
`Leaf(
`RenderedDist(
Distributions.Shape.combinePointwise(
~knownIntegralSumsFn=(a, b) => Some(a +. b),
(+.),
rs1,
rs2,
),
),
),
)
| (Error(e1), _) => Error(e1)
| (_, Error(e2)) => Error(e2)
| _ => Error("Could not perform pointwise addition.")
};
};
let pointwiseMultiply = (operationToLeaf, t1, t2) => {
// TODO: construct a function that we can easily sample from, to construct
// a RenderedDist. Use the xMin and xMax of the rendered shapes to tell the sampling function where to look.
Error(
"Pointwise multiplication not yet supported.",
);
};
let toLeaf = (operationToLeaf, pointwiseOp, t1, t2) => {
switch (pointwiseOp) {
| `Add => pointwiseAdd(operationToLeaf, t1, t2)
| `Multiply => pointwiseMultiply(operationToLeaf, t1, t2)
};
};
};
module Truncate = {
module Simplify = {
let tryTruncatingNothing: tResult =
fun
| `Operation(`Truncate(None, None, `Leaf(d))) => Ok(`Leaf(d))
| t => Ok(t);
let tryTruncatingUniform: tResult =
fun
| `Operation(`Truncate(lc, rc, `Leaf(`SymbolicDist(`Uniform(u))))) => {
// just create a new Uniform distribution
let newLow = max(E.O.default(neg_infinity, lc), u.low);
let newHigh = min(E.O.default(infinity, rc), u.high);
Ok(`Leaf(`SymbolicDist(`Uniform({low: newLow, high: newHigh}))));
}
| t => Ok(t);
let attempt = (leftCutoff, rightCutoff, t): result(node, string) => {
let originalTreeNode =
`Operation(`Truncate((leftCutoff, rightCutoff, t)));
originalTreeNode
|> tryTruncatingNothing
|> E.R.bind(_, tryTruncatingUniform);
};
};
let evaluateNumerically = (leftCutoff, rightCutoff, operationToLeaf, t) => {
// TODO: use named args in renderToShape; if we're lucky we can at least get the tail
// of a distribution we otherwise wouldn't get at all
let renderedShape = operationToLeaf(`Render(t));
switch (renderedShape) {
| Ok(`Leaf(`RenderedDist(rs))) =>
let truncatedShape =
rs |> Distributions.Shape.T.truncate(leftCutoff, rightCutoff);
Ok(`Leaf(`RenderedDist(rs)));
| Error(e1) => Error(e1)
| _ => Error("Could not truncate distribution.")
};
};
let toLeaf =
(
operationToLeaf,
leftCutoff: option(float),
rightCutoff: option(float),
t: node,
)
: result(node, string) => {
t
|> Simplify.attempt(leftCutoff, rightCutoff)
|> E.R.bind(
_,
fun
| `Leaf(d) => Ok(`Leaf(d)) // the analytical simplifaction worked, nice!
| `Operation(_) =>
evaluateNumerically(leftCutoff, rightCutoff, operationToLeaf, t),
); // if not, run the convolution
};
};
module Normalize = {
let rec toLeaf = (operationToLeaf, t: node): result(node, string) => {
switch (t) {
| `Leaf(`RenderedDist(s)) =>
Ok(`Leaf(`RenderedDist(Distributions.Shape.T.normalize(s))))
| `Leaf(`SymbolicDist(_)) => Ok(t)
| `Operation(op) =>
operationToLeaf(op) |> E.R.bind(_, toLeaf(operationToLeaf))
};
};
};
module FloatFromDist = {
let symbolicToLeaf = (distToFloatOp: distToFloatOperation, s) => {
SymbolicDist.T.operate(distToFloatOp, s)
|> E.R.bind(_, v => Ok(`Leaf(`SymbolicDist(`Float(v)))));
};
let renderedToLeaf =
(distToFloatOp: distToFloatOperation, rs: DistTypes.shape)
: result(node, string) => {
Distributions.Shape.operate(distToFloatOp, rs)
|> (v => Ok(`Leaf(`SymbolicDist(`Float(v)))));
};
let rec toLeaf =
(operationToLeaf, distToFloatOp: distToFloatOperation, t: node)
: result(node, string) => {
switch (t) {
| `Leaf(`SymbolicDist(s)) => symbolicToLeaf(distToFloatOp, s) // we want to evaluate the distToFloatOp on the symbolic dist
| `Leaf(`RenderedDist(rs)) => renderedToLeaf(distToFloatOp, rs)
| `Operation(op) =>
E.R.bind(operationToLeaf(op), toLeaf(operationToLeaf, distToFloatOp))
};
};
};
module Render = {
let rec toLeaf =
(
operationToLeaf: operation => result(t, string),
sampleCount: int,
t: node,
)
: result(t, string) => {
switch (t) {
| `Leaf(`SymbolicDist(d)) =>
Ok(`Leaf(`RenderedDist(SymbolicDist.T.toShape(sampleCount, d))))
| `Leaf(`RenderedDist(_)) as t => Ok(t) // already a rendered shape, we're done here
| `Operation(op) =>
E.R.bind(operationToLeaf(op), toLeaf(operationToLeaf, sampleCount))
};
};
};
let rec operationToLeaf =
(sampleCount: int, op: operation): result(t, string) => {
// the functions that convert the Operation nodes to Leaf nodes need to
// have a way to call this function on their children, if their children are themselves Operation nodes.
switch (op) {
| `AlgebraicCombination(algebraicOp, t1, t2) =>
AlgebraicCombination.toLeaf(
operationToLeaf(sampleCount),
algebraicOp,
t1,
t2 // we want to give it the option to render or simply leave it as is
)
| `PointwiseCombination(pointwiseOp, t1, t2) =>
PointwiseCombination.toLeaf(
operationToLeaf(sampleCount),
pointwiseOp,
t1,
t2,
)
| `VerticalScaling(scaleOp, t, scaleBy) =>
VerticalScaling.toLeaf(operationToLeaf(sampleCount), scaleOp, t, scaleBy)
| `Truncate(leftCutoff, rightCutoff, t) =>
Truncate.toLeaf(operationToLeaf(sampleCount), leftCutoff, rightCutoff, t)
| `FloatFromDist(distToFloatOp, t) =>
FloatFromDist.toLeaf(operationToLeaf(sampleCount), distToFloatOp, t)
| `Normalize(t) => Normalize.toLeaf(operationToLeaf(sampleCount), t)
| `Render(t) => Render.toLeaf(operationToLeaf(sampleCount), sampleCount, t)
};
};
/* This function recursively goes through the nodes of the parse tree,
replacing each Operation node and its subtree with a Data node.
Whenever possible, the replacement produces a new Symbolic Data node,
but most often it will produce a RenderedDist.
This function is used mainly to turn a parse tree into a single RenderedDist
that can then be displayed to the user. */
let toLeaf = (node: t, sampleCount: int): result(t, string) => {
switch (node) {
| `Leaf(d) => Ok(`Leaf(d))
| `Operation(op) => operationToLeaf(sampleCount, op)
};
};

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@ -0,0 +1,24 @@
type algebraicOperation = [ | `Add | `Multiply | `Subtract | `Divide];
type pointwiseOperation = [ | `Add | `Multiply];
type scaleOperation = [ | `Multiply | `Exponentiate | `Log];
type distToFloatOperation = [ | `Pdf(float) | `Inv(float) | `Mean | `Sample];
type abstractOperation('a) = [
| `AlgebraicCombination(algebraicOperation, 'a, 'a)
| `PointwiseCombination(pointwiseOperation, 'a, 'a)
| `VerticalScaling(scaleOperation, 'a, 'a)
| `Render('a)
| `Truncate(option(float), option(float), 'a)
| `Normalize('a)
| `FloatFromDist(distToFloatOperation, 'a)
];
module ExpressionTree = {
type leaf = [
| `SymbolicDist(SymbolicTypes.symbolicDist)
| `RenderedDist(DistTypes.shape)
];
type node = [ | `Leaf(leaf) | `Operation(operation)]
and operation = abstractOperation(node);
};

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@ -86,13 +86,13 @@ module MathAdtToDistDst = {
);
};
let normal: array(arg) => result(TreeNode.treeNode, string) =
let normal: array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(mean), Value(stdev)|] =>
Ok(`Leaf(`SymbolicDist(`Normal({mean, stdev}))))
| _ => Error("Wrong number of variables in normal distribution");
let lognormal: array(arg) => result(TreeNode.treeNode, string) =
let lognormal: array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(mu), Value(sigma)|] =>
Ok(`Leaf(`SymbolicDist(`Lognormal({mu, sigma}))))
@ -114,7 +114,7 @@ module MathAdtToDistDst = {
}
| _ => Error("Wrong number of variables in lognormal distribution");
let to_: array(arg) => result(TreeNode.treeNode, string) =
let to_: array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(low), Value(high)|] when low <= 0.0 && low < high => {
Ok(
@ -134,31 +134,31 @@ module MathAdtToDistDst = {
Error("Low value must be less than high value.")
| _ => Error("Wrong number of variables in lognormal distribution");
let uniform: array(arg) => result(TreeNode.treeNode, string) =
let uniform: array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(low), Value(high)|] =>
Ok(`Leaf(`SymbolicDist(`Uniform({low, high}))))
| _ => Error("Wrong number of variables in lognormal distribution");
let beta: array(arg) => result(TreeNode.treeNode, string) =
let beta: array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(alpha), Value(beta)|] =>
Ok(`Leaf(`SymbolicDist(`Beta({alpha, beta}))))
| _ => Error("Wrong number of variables in lognormal distribution");
let exponential: array(arg) => result(TreeNode.treeNode, string) =
let exponential: array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(rate)|] =>
Ok(`Leaf(`SymbolicDist(`Exponential({rate: rate}))))
| _ => Error("Wrong number of variables in Exponential distribution");
let cauchy: array(arg) => result(TreeNode.treeNode, string) =
let cauchy: array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(local), Value(scale)|] =>
Ok(`Leaf(`SymbolicDist(`Cauchy({local, scale}))))
| _ => Error("Wrong number of variables in cauchy distribution");
let triangular: array(arg) => result(TreeNode.treeNode, string) =
let triangular: array(arg) => result(ExpressionTypes.ExpressionTree.node, string) =
fun
| [|Value(low), Value(medium), Value(high)|] =>
Ok(`Leaf(`SymbolicDist(`Triangular({low, medium, high}))))
@ -166,7 +166,7 @@ module MathAdtToDistDst = {
let multiModal =
(
args: array(result(TreeNode.treeNode, string)),
args: array(result(ExpressionTypes.ExpressionTree.node, string)),
weights: option(array(float)),
) => {
let weights = weights |> E.O.default([||]);
@ -215,7 +215,7 @@ module MathAdtToDistDst = {
};
};
let arrayParser = (args: array(arg)): result(TreeNode.treeNode, string) => {
let arrayParser = (args: array(arg)): result(ExpressionTypes.ExpressionTree.node, string) => {
let samples =
args
|> E.A.fmap(
@ -241,7 +241,7 @@ module MathAdtToDistDst = {
};
let operationParser =
(name: string, args: array(result(TreeNode.treeNode, string))) => {
(name: string, args: array(result(ExpressionTypes.ExpressionTree.node, string))) => {
let toOkAlgebraic = r => Ok(`Operation(`AlgebraicCombination(r)));
let toOkTrunctate = r => Ok(`Operation(`Truncate(r)));
switch (name, args) {
@ -347,7 +347,7 @@ module MathAdtToDistDst = {
| Symbol(_) => Error("Symbol not valid as top level")
| Object(_) => Error("Object not valid as top level");
let run = (r): result(TreeNode.treeNode, string) =>
let run = (r): result(ExpressionTypes.ExpressionTree.node, string) =>
r |> MathAdtCleaner.run |> topLevel;
};

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@ -0,0 +1,93 @@
open ExpressionTypes;
module Algebraic = {
type t = algebraicOperation;
let toFn: (t, float, float) => float =
fun
| `Add => (+.)
| `Subtract => (-.)
| `Multiply => ( *. )
| `Divide => (/.);
let applyFn = (t, f1, f2) => {
switch (t, f1, f2) {
| (`Divide, _, 0.) => Error("Cannot divide $v1 by zero.")
| _ => Ok(toFn(t, f1, f2))
};
};
let toString =
fun
| `Add => "+"
| `Subtract => "-"
| `Multiply => "*"
| `Divide => "/";
let format = (a, b, c) => b ++ " " ++ toString(a) ++ " " ++ c;
};
module Pointwise = {
type t = pointwiseOperation;
let toString =
fun
| `Add => "+"
| `Multiply => "*";
let format = (a, b, c) => b ++ " " ++ toString(a) ++ " " ++ c;
};
module DistToFloat = {
type t = distToFloatOperation;
let format = (operation, value) =>
switch (operation) {
| `Pdf(f) => {j|pdf(x=$f,$value)|j}
| `Inv(f) => {j|inv(x=$f,$value)|j}
| `Sample => "sample($value)"
| `Mean => "mean($value)"
};
};
module Scale = {
type t = scaleOperation;
let toFn =
fun
| `Multiply => ( *. )
| `Exponentiate => ( ** )
| `Log => ((a, b) => log(a) /. log(b));
let format = (operation: t, value, scaleBy) =>
switch (operation) {
| `Multiply => {j|scaleMultiply($value, $scaleBy) |j}
| `Exponentiate => {j|ScaleExponentiate($value, $scaleBy) |j}
| `Log => {j|ScaleLog($value, $scaleBy) |j}
};
let toKnownIntegralSumFn =
fun
| `Multiply => ((a, b) => Some(a *. b))
| `Exponentiate => ((_, _) => None)
| `Log => ((_, _) => None);
};
module T = {
let truncateToString =
(left: option(float), right: option(float), nodeToString) => {
let left = left |> E.O.dimap(Js.Float.toString, () => "-inf");
let right = right |> E.O.dimap(Js.Float.toString, () => "inf");
{j|truncate($nodeToString, $left, $right)|j};
};
let toString = nodeToString =>
fun
| `AlgebraicCombination(op, t1, t2) =>
Algebraic.format(op, nodeToString(t1), nodeToString(t2))
| `PointwiseCombination(op, t1, t2) =>
Pointwise.format(op, nodeToString(t1), nodeToString(t2))
| `VerticalScaling(scaleOp, t, scaleBy) =>
Scale.format(scaleOp, nodeToString(t), nodeToString(scaleBy))
| `Normalize(t) => "normalize(" ++ nodeToString(t) ++ ")"
| `FloatFromDist(floatFromDistOp, t) =>
DistToFloat.format(floatFromDistOp, nodeToString(t))
| `Truncate(lc, rc, t) => truncateToString(lc, rc, nodeToString(t))
| `Render(t) => nodeToString(t);
};

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@ -43,7 +43,7 @@ module ShapeRenderer = {
module Symbolic = {
type inputs = {length: int};
type outputs = {
graph: TreeNode.treeNode,
graph: ExpressionTypes.ExpressionTree.node,
shape: DistTypes.shape,
};
let make = (graph, shape) => {graph, shape};

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@ -21,7 +21,7 @@ let runSymbolic = (guesstimatorString, length) => {
|> E.R.fmap(g =>
RenderTypes.ShapeRenderer.Symbolic.make(
g,
TreeNode.toShape(length, g),
ExpressionTree.toShape(length, g),
)
);
};

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@ -1,8 +0,0 @@
const math = require("mathjs");
function parseMath(f){ return JSON.parse(JSON.stringify(math.parse(f))) };
module.exports = {
parseMath,
};

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@ -76,7 +76,7 @@ module Normal = {
`Normal({mean, stdev});
};
let operate = (operation: SymbolicTypes.Algebraic.t, n1: t, n2: t) =>
let operate = (operation: Operation.Algebraic.t, n1: t, n2: t) =>
switch (operation) {
| `Add => Some(add(n1, n2))
| `Subtract => Some(subtract(n1, n2))
@ -130,7 +130,7 @@ module Lognormal = {
let sigma = l1.sigma +. l2.sigma;
`Lognormal({mu, sigma});
};
let operate = (operation: SymbolicTypes.Algebraic.t, n1: t, n2: t) =>
let operate = (operation: Operation.Algebraic.t, n1: t, n2: t) =>
switch (operation) {
| `Multiply => Some(multiply(n1, n2))
| `Divide => Some(divide(n1, n2))
@ -246,7 +246,7 @@ module T = {
| `Uniform(n) => Uniform.mean(n)
| `Float(n) => Float.mean(n);
let operate = (distToFloatOp: distToFloatOperation, s) =>
let operate = (distToFloatOp: ExpressionTypes.distToFloatOperation, s) =>
switch (distToFloatOp) {
| `Pdf(f) => Ok(pdf(f, s))
| `Inv(f) => Ok(inv(f, s))
@ -283,12 +283,12 @@ module T = {
(
d1: symbolicDist,
d2: symbolicDist,
op: SymbolicTypes.algebraicOperation,
op: ExpressionTypes.algebraicOperation,
)
: analyticalSolutionAttempt =>
switch (d1, d2) {
| (`Float(v1), `Float(v2)) =>
switch (SymbolicTypes.Algebraic.applyFn(op, v1, v2)) {
switch (Operation.Algebraic.applyFn(op, v1, v2)) {
| Ok(r) => `AnalyticalSolution(`Float(r))
| Error(n) => `Error(n)
}

View File

@ -46,80 +46,4 @@ type symbolicDist = [
| `Triangular(triangular)
| `ContinuousShape(continuousShape)
| `Float(float) // Dirac delta at x. Practically useful only in the context of multimodals.
];
// todo: These operations are really applicable for all dists
type algebraicOperation = [ | `Add | `Multiply | `Subtract | `Divide];
type pointwiseOperation = [ | `Add | `Multiply];
type scaleOperation = [ | `Multiply | `Exponentiate | `Log];
type distToFloatOperation = [ | `Pdf(float) | `Inv(float) | `Mean | `Sample];
module Algebraic = {
type t = algebraicOperation;
let toFn: (t, float, float) => float =
fun
| `Add => (+.)
| `Subtract => (-.)
| `Multiply => ( *. )
| `Divide => (/.);
let applyFn = (t, f1, f2) => {
switch (t, f1, f2) {
| (`Divide, _, 0.) => Error("Cannot divide $v1 by zero.")
| _ => Ok(toFn(t, f1, f2))
};
};
let toString =
fun
| `Add => "+"
| `Subtract => "-"
| `Multiply => "*"
| `Divide => "/";
let format = (a, b, c) => b ++ " " ++ toString(a) ++ " " ++ c;
};
module Pointwise = {
type t = pointwiseOperation;
let toString =
fun
| `Add => "+"
| `Multiply => "*";
let format = (a, b, c) => b ++ " " ++ toString(a) ++ " " ++ c;
};
module DistToFloat = {
type t = distToFloatOperation;
let format = (operation, value) =>
switch (operation) {
| `Pdf(f) => {j|pdf(x=$f,$value)|j}
| `Inv(f) => {j|inv(x=$f,$value)|j}
| `Sample => "sample($value)"
| `Mean => "mean($value)"
};
};
module Scale = {
type t = scaleOperation;
let toFn =
fun
| `Multiply => ( *. )
| `Exponentiate => ( ** )
| `Log => ((a, b) => log(a) /. log(b));
let format = (operation:t, value, scaleBy) =>
switch (operation) {
| `Multiply => {j|scaleMultiply($value, $scaleBy) |j}
| `Exponentiate => {j|ScaleExponentiate($value, $scaleBy) |j}
| `Log => {j|ScaleLog($value, $scaleBy) |j}
};
let toKnownIntegralSumFn =
fun
| `Multiply => ((a, b) => Some(a *. b))
| `Exponentiate => ((_, _) => None)
| `Log => ((_, _) => None);
};
];

View File

@ -1,387 +0,0 @@
/* This module represents a tree node. */
open SymbolicTypes;
type leaf = [
| `SymbolicDist(SymbolicTypes.symbolicDist)
| `RenderedDist(DistTypes.shape)
];
/* TreeNodes are either Data (i.e. symbolic or rendered distributions) or Operations. Operations always refer to two child nodes.*/
type treeNode = [ | `Leaf(leaf) | `Operation(operation)]
and operation = [
| `AlgebraicCombination(algebraicOperation, treeNode, treeNode)
| `PointwiseCombination(pointwiseOperation, treeNode, treeNode)
| `VerticalScaling(scaleOperation, treeNode, treeNode)
| `Render(treeNode)
| `Truncate(option(float), option(float), treeNode)
| `Normalize(treeNode)
| `FloatFromDist(distToFloatOperation, treeNode)
];
module Operation = {
type t = operation;
let truncateToString =
(left: option(float), right: option(float), nodeToString) => {
let left = left |> E.O.dimap(Js.Float.toString, () => "-inf");
let right = right |> E.O.dimap(Js.Float.toString, () => "inf");
{j|truncate($nodeToString, $left, $right)|j};
};
let toString = nodeToString =>
fun
| `AlgebraicCombination(op, t1, t2) =>
SymbolicTypes.Algebraic.format(op, nodeToString(t1), nodeToString(t2))
| `PointwiseCombination(op, t1, t2) =>
SymbolicTypes.Pointwise.format(op, nodeToString(t1), nodeToString(t2))
| `VerticalScaling(scaleOp, t, scaleBy) =>
SymbolicTypes.Scale.format(
scaleOp,
nodeToString(t),
nodeToString(scaleBy),
)
| `Normalize(t) => "normalize(" ++ nodeToString(t) ++ ")"
| `FloatFromDist(floatFromDistOp, t) =>
SymbolicTypes.DistToFloat.format(floatFromDistOp, nodeToString(t))
| `Truncate(lc, rc, t) => truncateToString(lc, rc, nodeToString(t))
| `Render(t) => nodeToString(t);
};
module TreeNode = {
type t = treeNode;
type tResult = treeNode => result(treeNode, string);
let rec toString =
fun
| `Leaf(`SymbolicDist(d)) => SymbolicDist.T.toString(d)
| `Leaf(`RenderedDist(_)) => "[shape]"
| `Operation(op) => Operation.toString(toString, op);
/* The following modules encapsulate everything we can do with
* different kinds of operations. */
/* Given two random variables A and B, this returns the distribution
of a new variable that is the result of the operation on A and B.
For instance, normal(0, 1) + normal(1, 1) -> normal(1, 2).
In general, this is implemented via convolution. */
module AlgebraicCombination = {
let toTreeNode = (op, t1, t2) =>
`Operation(`AlgebraicCombination((op, t1, t2)));
let tryAnalyticalSolution =
fun
| `Operation(
`AlgebraicCombination(
operation,
`Leaf(`SymbolicDist(d1)),
`Leaf(`SymbolicDist(d2)),
),
) as t =>
switch (SymbolicDist.T.attemptAnalyticalOperation(d1, d2, operation)) {
| `AnalyticalSolution(symbolicDist) =>
Ok(`Leaf(`SymbolicDist(symbolicDist)))
| `Error(er) => Error(er)
| `NoSolution => Ok(t)
}
| t => Ok(t);
// todo: I don't like the name evaluateNumerically that much, if this renders and does it algebraically. It's tricky.
let evaluateNumerically = (algebraicOp, operationToLeaf, t1, t2) => {
// force rendering into shapes
let renderShape = r => operationToLeaf(`Render(r));
switch (renderShape(t1), renderShape(t2)) {
| (Ok(`Leaf(`RenderedDist(s1))), Ok(`Leaf(`RenderedDist(s2)))) =>
Ok(
`Leaf(
`RenderedDist(
Distributions.Shape.combineAlgebraically(algebraicOp, s1, s2),
),
),
)
| (Error(e1), _) => Error(e1)
| (_, Error(e2)) => Error(e2)
| _ => Error("Could not render shapes.")
};
};
let toLeaf =
(
operationToLeaf,
algebraicOp: SymbolicTypes.algebraicOperation,
t1: t,
t2: t,
)
: result(treeNode, string) =>
toTreeNode(algebraicOp, t1, t2)
|> tryAnalyticalSolution
|> E.R.bind(
_,
fun
| `Leaf(d) => Ok(`Leaf(d)) // the analytical simplifaction worked, nice!
| `Operation(_) =>
// if not, run the convolution
evaluateNumerically(algebraicOp, operationToLeaf, t1, t2),
);
};
module VerticalScaling = {
let toLeaf = (operationToLeaf, scaleOp, t, scaleBy) => {
// scaleBy has to be a single float, otherwise we'll return an error.
let fn = SymbolicTypes.Scale.toFn(scaleOp);
let knownIntegralSumFn =
SymbolicTypes.Scale.toKnownIntegralSumFn(scaleOp);
let renderedShape = operationToLeaf(`Render(t));
switch (renderedShape, scaleBy) {
| (Ok(`Leaf(`RenderedDist(rs))), `Leaf(`SymbolicDist(`Float(sm)))) =>
Ok(
`Leaf(
`RenderedDist(
Distributions.Shape.T.mapY(
~knownIntegralSumFn=knownIntegralSumFn(sm),
fn(sm),
rs,
),
),
),
)
| (Error(e1), _) => Error(e1)
| (_, _) => Error("Can only scale by float values.")
};
};
};
module PointwiseCombination = {
let pointwiseAdd = (operationToLeaf, t1, t2) => {
let renderedShape1 = operationToLeaf(`Render(t1));
let renderedShape2 = operationToLeaf(`Render(t2));
switch (renderedShape1, renderedShape2) {
| (Ok(`Leaf(`RenderedDist(rs1))), Ok(`Leaf(`RenderedDist(rs2)))) =>
Ok(
`Leaf(
`RenderedDist(
Distributions.Shape.combinePointwise(
~knownIntegralSumsFn=(a, b) => Some(a +. b),
(+.),
rs1,
rs2,
),
),
),
)
| (Error(e1), _) => Error(e1)
| (_, Error(e2)) => Error(e2)
| _ => Error("Could not perform pointwise addition.")
};
};
let pointwiseMultiply = (operationToLeaf, t1, t2) => {
// TODO: construct a function that we can easily sample from, to construct
// a RenderedDist. Use the xMin and xMax of the rendered shapes to tell the sampling function where to look.
Error(
"Pointwise multiplication not yet supported.",
);
};
let toLeaf = (operationToLeaf, pointwiseOp, t1, t2) => {
switch (pointwiseOp) {
| `Add => pointwiseAdd(operationToLeaf, t1, t2)
| `Multiply => pointwiseMultiply(operationToLeaf, t1, t2)
};
};
};
module Truncate = {
module Simplify = {
let tryTruncatingNothing: tResult =
fun
| `Operation(`Truncate(None, None, `Leaf(d))) => Ok(`Leaf(d))
| t => Ok(t);
let tryTruncatingUniform: tResult =
fun
| `Operation(`Truncate(lc, rc, `Leaf(`SymbolicDist(`Uniform(u))))) => {
// just create a new Uniform distribution
let newLow = max(E.O.default(neg_infinity, lc), u.low);
let newHigh = min(E.O.default(infinity, rc), u.high);
Ok(
`Leaf(`SymbolicDist(`Uniform({low: newLow, high: newHigh}))),
);
}
| t => Ok(t);
let attempt = (leftCutoff, rightCutoff, t): result(treeNode, string) => {
let originalTreeNode =
`Operation(`Truncate((leftCutoff, rightCutoff, t)));
originalTreeNode
|> tryTruncatingNothing
|> E.R.bind(_, tryTruncatingUniform);
};
};
let evaluateNumerically = (leftCutoff, rightCutoff, operationToLeaf, t) => {
// TODO: use named args in renderToShape; if we're lucky we can at least get the tail
// of a distribution we otherwise wouldn't get at all
let renderedShape = operationToLeaf(`Render(t));
switch (renderedShape) {
| Ok(`Leaf(`RenderedDist(rs))) =>
let truncatedShape =
rs |> Distributions.Shape.T.truncate(leftCutoff, rightCutoff);
Ok(`Leaf(`RenderedDist(rs)));
| Error(e1) => Error(e1)
| _ => Error("Could not truncate distribution.")
};
};
let toLeaf =
(
operationToLeaf,
leftCutoff: option(float),
rightCutoff: option(float),
t: treeNode,
)
: result(treeNode, string) => {
t
|> Simplify.attempt(leftCutoff, rightCutoff)
|> E.R.bind(
_,
fun
| `Leaf(d) => Ok(`Leaf(d)) // the analytical simplifaction worked, nice!
| `Operation(_) =>
evaluateNumerically(leftCutoff, rightCutoff, operationToLeaf, t),
); // if not, run the convolution
};
};
module Normalize = {
let rec toLeaf = (operationToLeaf, t: treeNode): result(treeNode, string) => {
switch (t) {
| `Leaf(`RenderedDist(s)) =>
Ok(`Leaf(`RenderedDist(Distributions.Shape.T.normalize(s))))
| `Leaf(`SymbolicDist(_)) => Ok(t)
| `Operation(op) =>
operationToLeaf(op) |> E.R.bind(_, toLeaf(operationToLeaf))
};
};
};
module FloatFromDist = {
let symbolicToLeaf = (distToFloatOp: distToFloatOperation, s) => {
SymbolicDist.T.operate(distToFloatOp, s)
|> E.R.bind(_, v => Ok(`Leaf(`SymbolicDist(`Float(v)))));
};
let renderedToLeaf =
(distToFloatOp: distToFloatOperation, rs: DistTypes.shape)
: result(treeNode, string) => {
Distributions.Shape.operate(distToFloatOp, rs)
|> (v => Ok(`Leaf(`SymbolicDist(`Float(v)))));
};
let rec toLeaf =
(
operationToLeaf,
distToFloatOp: distToFloatOperation,
t: treeNode,
)
: result(treeNode, string) => {
switch (t) {
| `Leaf(`SymbolicDist(s)) => symbolicToLeaf(distToFloatOp, s) // we want to evaluate the distToFloatOp on the symbolic dist
| `Leaf(`RenderedDist(rs)) => renderedToLeaf(distToFloatOp, rs)
| `Operation(op) =>
E.R.bind(
operationToLeaf(op),
toLeaf(operationToLeaf, distToFloatOp),
)
};
};
};
module Render = {
let rec toLeaf =
(
operationToLeaf: operation => result(t, string),
sampleCount: int,
t: treeNode,
)
: result(t, string) => {
switch (t) {
| `Leaf(`SymbolicDist(d)) =>
Ok(`Leaf(`RenderedDist(SymbolicDist.T.toShape(sampleCount, d))))
| `Leaf(`RenderedDist(_)) as t => Ok(t) // already a rendered shape, we're done here
| `Operation(op) =>
E.R.bind(operationToLeaf(op), toLeaf(operationToLeaf, sampleCount))
};
};
};
let rec operationToLeaf =
(sampleCount: int, op: operation): result(t, string) => {
// the functions that convert the Operation nodes to Leaf nodes need to
// have a way to call this function on their children, if their children are themselves Operation nodes.
switch (op) {
| `AlgebraicCombination(algebraicOp, t1, t2) =>
AlgebraicCombination.toLeaf(
operationToLeaf(sampleCount),
algebraicOp,
t1,
t2 // we want to give it the option to render or simply leave it as is
)
| `PointwiseCombination(pointwiseOp, t1, t2) =>
PointwiseCombination.toLeaf(
operationToLeaf(sampleCount),
pointwiseOp,
t1,
t2,
)
| `VerticalScaling(scaleOp, t, scaleBy) =>
VerticalScaling.toLeaf(
operationToLeaf(sampleCount),
scaleOp,
t,
scaleBy,
)
| `Truncate(leftCutoff, rightCutoff, t) =>
Truncate.toLeaf(
operationToLeaf(sampleCount),
leftCutoff,
rightCutoff,
t,
)
| `FloatFromDist(distToFloatOp, t) =>
FloatFromDist.toLeaf(operationToLeaf(sampleCount), distToFloatOp, t)
| `Normalize(t) => Normalize.toLeaf(operationToLeaf(sampleCount), t)
| `Render(t) =>
Render.toLeaf(operationToLeaf(sampleCount), sampleCount, t)
};
};
/* This function recursively goes through the nodes of the parse tree,
replacing each Operation node and its subtree with a Data node.
Whenever possible, the replacement produces a new Symbolic Data node,
but most often it will produce a RenderedDist.
This function is used mainly to turn a parse tree into a single RenderedDist
that can then be displayed to the user. */
let toLeaf = (treeNode: t, sampleCount: int): result(t, string) => {
switch (treeNode) {
| `Leaf(d) => Ok(`Leaf(d))
| `Operation(op) => operationToLeaf(sampleCount, op)
};
};
};
let toShape = (sampleCount: int, treeNode: treeNode) => {
let renderResult =
TreeNode.toLeaf(`Operation(`Render(treeNode)), sampleCount);
switch (renderResult) {
| Ok(`Leaf(`RenderedDist(rs))) =>
let continuous = Distributions.Shape.T.toContinuous(rs);
let discrete = Distributions.Shape.T.toDiscrete(rs);
let shape = MixedShapeBuilder.buildSimple(~continuous, ~discrete);
shape |> E.O.toExt("Could not build final shape.");
| Ok(_) => E.O.toExn("Rendering failed.", None)
| Error(message) => E.O.toExn("No shape found, error: " ++ message, None)
};
};
let toString = (treeNode: treeNode) => TreeNode.toString(treeNode);