kmath/kmath-ast/README.md

# Module kmath-ast

Abstract syntax tree expression representation and related optimizations.

 - [expression-language](src/jvmMain/kotlin/space/kscience/kmath/ast/parser.kt) : Expression language and its parser
 - [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
 - [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


## Artifact:

The Maven coordinates of this project are `space.kscience:kmath-ast:0.3.0-dev-4`.

**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 {
    implementation 'space.kscience:kmath-ast:0.3.0-dev-4'
}
```
**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 {
    implementation("space.kscience:kmath-ast:0.3.0-dev-4")
}
```

## 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 builder:

```kotlin
DoubleField.mstInField { symbol("x") + 2 }.compile()
``` 

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

```java
package space.kscience.kmath.asm.generated;

import java.util.Map;
import kotlin.jvm.functions.Function2;
import space.kscience.kmath.asm.internal.MapIntrinsics;
import space.kscience.kmath.expressions.Expression;
import space.kscience.kmath.expressions.Symbol;

public final class AsmCompiledExpression_45045_0 implements Expression<Double> {
    private final Object[] constants;

    public final Double invoke(Map<Symbol, ? extends Double> arguments) {
        return (Double)((Function2)this.constants[0]).invoke((Double)MapIntrinsics.getOrFail(arguments, "x"), 2);
    }

    public AsmCompiledExpression_45045_0(Object[] constants) {
        this.constants = constants;
    }
}

```

### Example Usage

This API extends MST and MstExpression, so you may optimize as both of them:

```kotlin
DoubleField.mstInField { symbol("x") + 2 }.compile()
DoubleField.expression("x+2".parseMath())
```

#### Known issues

- 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 and GraalVM) because of using class loaders.

### On JS

A similar feature is also available on JS.

```kotlin
DoubleField.mstInField { symbol("x") + 2 }.compile()
``` 

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.

## 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).