kmath-ast

Extensions to MST API: transformations, dynamic compilation and visualization.

  • src/commonMain/kotlin/space/kscience/kmath/ast/parser.kt : Expression language and its parser

  • src/jvmMain/kotlin/space/kscience/kmath/asm/asm.kt : Dynamic MST to JVM bytecode compiler

  • src/jsMain/kotlin/space/kscience/kmath/estree/estree.kt : Dynamic MST to JS compiler

  • src/commonMain/kotlin/space/kscience/kmath/ast/rendering/MathRenderer.kt : Extendable MST rendering

Artifact:

The Maven coordinates of this project are space.kscience:kmath-ast:0.3.0.

Gradle Groovy:

repositories {
maven { url 'https://repo.kotlin.link' }
mavenCentral()
}

dependencies {
implementation 'space.kscience:kmath-ast:0.3.0'
}

Gradle Kotlin DSL:

repositories {
maven("https://repo.kotlin.link")
mavenCentral()
}

dependencies {
implementation("space.kscience:kmath-ast:0.3.0")
}

Parsing expressions

In this module there is a parser from human-readable strings like "x^3-x+3" (in the more specific reference/ArithmeticsEvaluator.g4) to MST instances.

Supported literals:

  1. Constants and variables (consist of latin letters, digits and underscores, can't start with digit): x, _Abc2.

  2. Numbers: 123, 1.02, 1e10, 1e-10, 1.0e+3—all parsed either as kotlin.Long or kotlin.Double.

Supported binary operators (from the highest precedence to the lowest one):

  1. ^

  2. *, /

  3. +, -

Supported unary operator:

  1. -, e. g. -x

Arbitrary unary and binary functions are also supported: names consist of latin letters, digits and underscores, can't start with digit. Examples:

  1. sin(x)

  2. add(x, y)

Dynamic expression code generation

On JVM

kmath-ast JVM module supports runtime code generation to eliminate overhead of tree traversal. Code generator builds a special implementation of Expression<T> with implemented invoke function.

For example, the following code:

import space.kscience.kmath.asm.compileToExpression
import space.kscience.kmath.operations.DoubleField

"x^3-x+3".parseMath().compileToExpression(DoubleField)

… leads to generation of bytecode, which can be decompiled to the following Java class:

import java.util.*;
import kotlin.jvm.functions.*;
import space.kscience.kmath.asm.internal.*;
import space.kscience.kmath.complex.*;
import space.kscience.kmath.expressions.*;

public final class CompiledExpression_45045_0 implements Expression<Complex> {
private final Object[] constants;

public Complex invoke(Map<Symbol, ? extends Complex> arguments) {
Complex var2 = (Complex)MapIntrinsics.getOrFail(arguments, "x");
return (Complex)((Function2)this.constants[0]).invoke(var2, (Complex)this.constants[1]);
}
}

For LongRing, IntRing, and DoubleField specialization is supported for better performance:

import java.util.*;
import space.kscience.kmath.asm.internal.*;
import space.kscience.kmath.expressions.*;

public final class CompiledExpression_-386104628_0 implements DoubleExpression {
private final SymbolIndexer indexer;

public SymbolIndexer getIndexer() {
return this.indexer;
}

public double invoke(double[] arguments) {
double var2 = arguments[0];
return Math.pow(var2, 3.0D) - var2 + 3.0D;
}

public final Double invoke(Map<Symbol, ? extends Double> arguments) {
double var2 = ((Double)MapIntrinsics.getOrFail(arguments, "x")).doubleValue();
return Math.pow(var2, 3.0D) - var2 + 3.0D;
}
}

Setting JVM system property space.kscience.kmath.ast.dump.generated.classes to 1 makes the translator dump class files to program's working directory, so they can be reviewed manually.

Limitations

  • The same classes may be generated and loaded twice, so it is recommended to cache compiled expressions to avoid class loading overhead.

  • This API is not supported by non-dynamic JVM implementations like TeaVM or GraalVM Native Image because they may not support class loaders.

On JS

A similar feature is also available on JS.

import space.kscience.kmath.expressions.Symbol.Companion.x
import space.kscience.kmath.expressions.*
import space.kscience.kmath.operations.*
import space.kscience.kmath.estree.*

MstField { x + 2 }.compileToExpression(DoubleField)

The code above returns expression implemented with such a JS function:

var executable = function (constants, arguments) {
return constants[1](constants[0](arguments, "x"), 2);
};

JS also supports experimental expression optimization with WebAssembly IR generation. Currently, only expressions inside DoubleField and IntRing are supported.

import space.kscience.kmath.expressions.Symbol.Companion.x
import space.kscience.kmath.expressions.*
import space.kscience.kmath.operations.*
import space.kscience.kmath.wasm.*

MstField { x + 2 }.compileToExpression(DoubleField)

An example of emitted Wasm IR in the form of WAT:

(func \$executable (param \$0 f64) (result f64)
(f64.add
(local.get \$0)
(f64.const 2)
)
)

Limitations

  • ESTree expression compilation uses eval which can be unavailable in several environments.

  • WebAssembly isn't supported by old versions of browsers (see https://webassembly.org/roadmap/).

Rendering expressions

kmath-ast also includes an extensible engine to display expressions in LaTeX or MathML syntax.

Example usage:

import space.kscience.kmath.ast.*
import space.kscience.kmath.ast.rendering.*
import space.kscience.kmath.misc.*

Extensions to MST API: transformations, dynamic compilation and visualization.

  • src/commonMain/kotlin/space/kscience/kmath/ast/parser.kt : Expression language and its parser

  • src/jvmMain/kotlin/space/kscience/kmath/asm/asm.kt : Dynamic MST to JVM bytecode compiler

  • src/jsMain/kotlin/space/kscience/kmath/estree/estree.kt : Dynamic MST to JS compiler

  • src/commonMain/kotlin/space/kscience/kmath/ast/rendering/MathRenderer.kt : Extendable MST rendering

Artifact:

The Maven coordinates of this project are space.kscience:kmath-ast:0.3.0.

Gradle Groovy:

repositories {
maven { url 'https://repo.kotlin.link' }
mavenCentral()
}

dependencies {
implementation 'space.kscience:kmath-ast:0.3.0'
}

Gradle Kotlin DSL:

repositories {
maven("https://repo.kotlin.link")
mavenCentral()
}

dependencies {
implementation("space.kscience:kmath-ast:0.3.0")
}

Parsing expressions

In this module there is a parser from human-readable strings like "x^3-x+3" (in the more specific reference/ArithmeticsEvaluator.g4) to MST instances.

Supported literals:

  1. Constants and variables (consist of latin letters, digits and underscores, can't start with digit): x, _Abc2.

  2. Numbers: 123, 1.02, 1e10, 1e-10, 1.0e+3—all parsed either as kotlin.Long or kotlin.Double.

Supported binary operators (from the highest precedence to the lowest one):

  1. ^

  2. *, /

  3. +, -

Supported unary operator:

  1. -, e. g. -x

Arbitrary unary and binary functions are also supported: names consist of latin letters, digits and underscores, can't start with digit. Examples:

  1. sin(x)

  2. add(x, y)

Dynamic expression code generation

On JVM

kmath-ast JVM module supports runtime code generation to eliminate overhead of tree traversal. Code generator builds a special implementation of Expression<T> with implemented invoke function.

For example, the following code:

import space.kscience.kmath.asm.compileToExpression
import space.kscience.kmath.operations.DoubleField

"x^3-x+3".parseMath().compileToExpression(DoubleField)

… leads to generation of bytecode, which can be decompiled to the following Java class:

import java.util.*;
import kotlin.jvm.functions.*;
import space.kscience.kmath.asm.internal.*;
import space.kscience.kmath.complex.*;
import space.kscience.kmath.expressions.*;

public final class CompiledExpression_45045_0 implements Expression<Complex> {
private final Object[] constants;

public Complex invoke(Map<Symbol, ? extends Complex> arguments) {
Complex var2 = (Complex)MapIntrinsics.getOrFail(arguments, "x");
return (Complex)((Function2)this.constants[0]).invoke(var2, (Complex)this.constants[1]);
}
}

For LongRing, IntRing, and DoubleField specialization is supported for better performance:

import java.util.*;
import space.kscience.kmath.asm.internal.*;
import space.kscience.kmath.expressions.*;

public final class CompiledExpression_-386104628_0 implements DoubleExpression {
private final SymbolIndexer indexer;

public SymbolIndexer getIndexer() {
return this.indexer;
}

public double invoke(double[] arguments) {
double var2 = arguments[0];
return Math.pow(var2, 3.0D) - var2 + 3.0D;
}

public final Double invoke(Map<Symbol, ? extends Double> arguments) {
double var2 = ((Double)MapIntrinsics.getOrFail(arguments, "x")).doubleValue();
return Math.pow(var2, 3.0D) - var2 + 3.0D;
}
}

Setting JVM system property space.kscience.kmath.ast.dump.generated.classes to 1 makes the translator dump class files to program's working directory, so they can be reviewed manually.

Limitations

  • The same classes may be generated and loaded twice, so it is recommended to cache compiled expressions to avoid class loading overhead.

  • This API is not supported by non-dynamic JVM implementations like TeaVM or GraalVM Native Image because they may not support class loaders.

On JS

A similar feature is also available on JS.

import space.kscience.kmath.expressions.Symbol.Companion.x
import space.kscience.kmath.expressions.*
import space.kscience.kmath.operations.*
import space.kscience.kmath.estree.*

MstField { x + 2 }.compileToExpression(DoubleField)

The code above returns expression implemented with such a JS function:

var executable = function (constants, arguments) {
return constants[1](constants[0](arguments, "x"), 2);
};

JS also supports experimental expression optimization with WebAssembly IR generation. Currently, only expressions inside DoubleField and IntRing are supported.

import space.kscience.kmath.expressions.Symbol.Companion.x
import space.kscience.kmath.expressions.*
import space.kscience.kmath.operations.*
import space.kscience.kmath.wasm.*

MstField { x + 2 }.compileToExpression(DoubleField)

An example of emitted Wasm IR in the form of WAT:

(func \$executable (param \$0 f64) (result f64)
(f64.add
(local.get \$0)
(f64.const 2)
)
)

Limitations

  • ESTree expression compilation uses eval which can be unavailable in several environments.

  • WebAssembly isn't supported by old versions of browsers (see https://webassembly.org/roadmap/).

Rendering expressions

kmath-ast also includes an extensible engine to display expressions in LaTeX or MathML syntax.

Example usage:

import space.kscience.kmath.ast.*
import space.kscience.kmath.ast.rendering.*
import space.kscience.kmath.misc.*

Extensions to MST API: transformations, dynamic compilation and visualization.

  • src/commonMain/kotlin/space/kscience/kmath/ast/parser.kt : Expression language and its parser

  • src/jvmMain/kotlin/space/kscience/kmath/asm/asm.kt : Dynamic MST to JVM bytecode compiler

  • src/jsMain/kotlin/space/kscience/kmath/estree/estree.kt : Dynamic MST to JS compiler

  • src/commonMain/kotlin/space/kscience/kmath/ast/rendering/MathRenderer.kt : Extendable MST rendering

Artifact:

The Maven coordinates of this project are space.kscience:kmath-ast:0.3.0.

Gradle Groovy:

repositories {
maven { url 'https://repo.kotlin.link' }
mavenCentral()
}

dependencies {
implementation 'space.kscience:kmath-ast:0.3.0'
}

Gradle Kotlin DSL:

repositories {
maven("https://repo.kotlin.link")
mavenCentral()
}

dependencies {
implementation("space.kscience:kmath-ast:0.3.0")
}

Parsing expressions

In this module there is a parser from human-readable strings like "x^3-x+3" (in the more specific reference/ArithmeticsEvaluator.g4) to MST instances.

Supported literals:

  1. Constants and variables (consist of latin letters, digits and underscores, can't start with digit): x, _Abc2.

  2. Numbers: 123, 1.02, 1e10, 1e-10, 1.0e+3—all parsed either as kotlin.Long or kotlin.Double.

Supported binary operators (from the highest precedence to the lowest one):

  1. ^

  2. *, /

  3. +, -

Supported unary operator:

  1. -, e. g. -x

Arbitrary unary and binary functions are also supported: names consist of latin letters, digits and underscores, can't start with digit. Examples:

  1. sin(x)

  2. add(x, y)

Dynamic expression code generation

On JVM

kmath-ast JVM module supports runtime code generation to eliminate overhead of tree traversal. Code generator builds a special implementation of Expression<T> with implemented invoke function.

For example, the following code:

import space.kscience.kmath.asm.compileToExpression
import space.kscience.kmath.operations.DoubleField

"x^3-x+3".parseMath().compileToExpression(DoubleField)

… leads to generation of bytecode, which can be decompiled to the following Java class:

import java.util.*;
import kotlin.jvm.functions.*;
import space.kscience.kmath.asm.internal.*;
import space.kscience.kmath.complex.*;
import space.kscience.kmath.expressions.*;

public final class CompiledExpression_45045_0 implements Expression<Complex> {
private final Object[] constants;

public Complex invoke(Map<Symbol, ? extends Complex> arguments) {
Complex var2 = (Complex)MapIntrinsics.getOrFail(arguments, "x");
return (Complex)((Function2)this.constants[0]).invoke(var2, (Complex)this.constants[1]);
}
}

For LongRing, IntRing, and DoubleField specialization is supported for better performance:

import java.util.*;
import space.kscience.kmath.asm.internal.*;
import space.kscience.kmath.expressions.*;

public final class CompiledExpression_-386104628_0 implements DoubleExpression {
private final SymbolIndexer indexer;

public SymbolIndexer getIndexer() {
return this.indexer;
}

public double invoke(double[] arguments) {
double var2 = arguments[0];
return Math.pow(var2, 3.0D) - var2 + 3.0D;
}

public final Double invoke(Map<Symbol, ? extends Double> arguments) {
double var2 = ((Double)MapIntrinsics.getOrFail(arguments, "x")).doubleValue();
return Math.pow(var2, 3.0D) - var2 + 3.0D;
}
}

Setting JVM system property space.kscience.kmath.ast.dump.generated.classes to 1 makes the translator dump class files to program's working directory, so they can be reviewed manually.

Limitations

  • The same classes may be generated and loaded twice, so it is recommended to cache compiled expressions to avoid class loading overhead.

  • This API is not supported by non-dynamic JVM implementations like TeaVM or GraalVM Native Image because they may not support class loaders.

On JS

A similar feature is also available on JS.

import space.kscience.kmath.expressions.Symbol.Companion.x
import space.kscience.kmath.expressions.*
import space.kscience.kmath.operations.*
import space.kscience.kmath.estree.*

MstField { x + 2 }.compileToExpression(DoubleField)

The code above returns expression implemented with such a JS function:

var executable = function (constants, arguments) {
return constants[1](constants[0](arguments, "x"), 2);
};

JS also supports experimental expression optimization with WebAssembly IR generation. Currently, only expressions inside DoubleField and IntRing are supported.

import space.kscience.kmath.expressions.Symbol.Companion.x
import space.kscience.kmath.expressions.*
import space.kscience.kmath.operations.*
import space.kscience.kmath.wasm.*

MstField { x + 2 }.compileToExpression(DoubleField)

An example of emitted Wasm IR in the form of WAT:

(func \$executable (param \$0 f64) (result f64)
(f64.add
(local.get \$0)
(f64.const 2)
)
)

Limitations

  • ESTree expression compilation uses eval which can be unavailable in several environments.

  • WebAssembly isn't supported by old versions of browsers (see https://webassembly.org/roadmap/).

Rendering expressions

kmath-ast also includes an extensible engine to display expressions in LaTeX or MathML syntax.

Example usage:

import space.kscience.kmath.ast.*
import space.kscience.kmath.ast.rendering.*
import space.kscience.kmath.misc.*

Packages

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common
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common
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js
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js