kmath/kmath-ast/README.md

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# Module kmath-ast
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Abstract syntax tree expression representation and related optimizations.
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- [expression-language](src/jvmMain/kotlin/space/kscience/kmath/ast/parser.kt) : Expression language and its parser
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- [mst](../kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/MST.kt) : MST (Mathematical Syntax Tree) as expression language's syntax intermediate representation
- [mst-building](../kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/MstAlgebra.kt) : MST building algebraic structure
- [mst-interpreter](../kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/MST.kt) : MST interpreter
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- [mst-jvm-codegen](src/jvmMain/kotlin/space/kscience/kmath/asm/asm.kt) : Dynamic MST to JVM bytecode compiler
- [mst-js-codegen](src/jsMain/kotlin/space/kscience/kmath/estree/estree.kt) : Dynamic MST to JS compiler
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## Artifact:
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The Maven coordinates of this project are `space.kscience:kmath-ast:0.3.0-dev-4`.
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**Gradle:**
```gradle
repositories {
maven { url 'https://repo.kotlin.link' }
maven { url 'https://dl.bintray.com/hotkeytlt/maven' }
maven { url "https://dl.bintray.com/kotlin/kotlin-eap" } // include for builds based on kotlin-eap
}
dependencies {
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implementation 'space.kscience:kmath-ast:0.3.0-dev-4'
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}
```
**Gradle Kotlin DSL:**
```kotlin
repositories {
maven("https://repo.kotlin.link")
maven("https://dl.bintray.com/kotlin/kotlin-eap") // include for builds based on kotlin-eap
maven("https://dl.bintray.com/hotkeytlt/maven") // required for a
}
dependencies {
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implementation("space.kscience:kmath-ast:0.3.0-dev-4")
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}
```
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## Dynamic expression code generation
### On JVM
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`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.
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For example, the following builder:
```kotlin
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DoubleField.mstInField { symbol("x") + 2 }.compile()
```
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… leads to generation of bytecode, which can be decompiled to the following Java class:
```java
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package space.kscience.kmath.asm.generated;
import java.util.Map;
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import kotlin.jvm.functions.Function2;
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import space.kscience.kmath.asm.internal.MapIntrinsics;
import space.kscience.kmath.expressions.Expression;
import space.kscience.kmath.expressions.Symbol;
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public final class AsmCompiledExpression_45045_0 implements Expression<Double> {
private final Object[] constants;
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public final Double invoke(Map<Symbol, ? extends Double> arguments) {
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return (Double)((Function2)this.constants[0]).invoke((Double)MapIntrinsics.getOrFail(arguments, "x"), 2);
}
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public AsmCompiledExpression_45045_0(Object[] constants) {
this.constants = constants;
}
}
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```
### Example Usage
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This API extends MST and MstExpression, so you may optimize as both of them:
```kotlin
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DoubleField.mstInField { symbol("x") + 2 }.compile()
DoubleField.expression("x+2".parseMath())
```
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#### Known issues
- The same classes may be generated and loaded twice, so it is recommended to cache compiled expressions to avoid
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class loading overhead.
- This API is not supported by non-dynamic JVM implementations (like TeaVM and GraalVM) because of using class loaders.
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### On JS
A similar feature is also available on JS.
```kotlin
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DoubleField.mstInField { symbol("x") + 2 }.compile()
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```
The code above returns expression implemented with such a JS function:
```js
var executable = function (constants, arguments) {
return constants[1](constants[0](arguments, "x"), 2);
};
```
#### Known issues
- This feature uses `eval` which can be unavailable in several environments.
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## Rendering expressions
kmath-ast also includes an extensible engine to display expressions in LaTeX or MathML syntax.
Example usage:
```kotlin
import space.kscience.kmath.ast.*
import space.kscience.kmath.ast.rendering.*
public fun main() {
val mst = "exp(sqrt(x))-asin(2*x)/(2e10+x^3)/(-12)".parseMath()
val syntax = FeaturedMathRendererWithPostProcess.Default.render(mst)
val latex = LatexSyntaxRenderer.renderWithStringBuilder(syntax)
println("LaTeX:")
println(latex)
println()
val mathML = MathMLSyntaxRenderer.renderWithStringBuilder(syntax)
println("MathML:")
println(mathML)
}
```
Result LaTeX:
![](http://chart.googleapis.com/chart?cht=tx&chl=e%5E%7B%5Csqrt%7Bx%7D%7D-%5Cfrac%7B%5Cfrac%7B%5Coperatorname%7Bsin%7D%5E%7B-1%7D%5C,%5Cleft(2%5C,x%5Cright)%7D%7B2%5Ctimes10%5E%7B10%7D%2Bx%5E%7B3%7D%7D%7D%7B-12%7D)
Result MathML (embedding MathML is not allowed by GitHub Markdown):
```html
<mrow><msup><mrow><mi>e</mi></mrow><mrow><msqrt><mi>x</mi></msqrt></mrow></msup><mo>-</mo><mfrac><mrow><mfrac><mrow><msup><mrow><mo>sin</mo></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mspace width="0.167em"></mspace><mfenced open="(" close=")" separators=""><mn>2</mn><mspace width="0.167em"></mspace><mi>x</mi></mfenced></mrow><mrow><mn>2</mn><mo>&times;</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>10</mn></mrow></msup><mo>+</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mfrac></mrow><mrow><mo>-</mo><mn>12</mn></mrow></mfrac></mrow>
```
It is also possible to create custom algorithms of render, and even add support of other markup languages
(see API reference).