kmath-commons/src/main/kotlin/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt

@@ -26,6 +26,9 @@ public class DerivativeStructureField(
     public inner class DerivativeStructureSymbol(symbol: Symbol, value: Double) :
         DerivativeStructure(bindings.size, order, bindings.keys.indexOf(symbol), value), Symbol {
         override val identity: String = symbol.identity
+        override fun toString(): String = identity
+        override fun equals(other: Any?): Boolean = this.identity == (other as? Symbol)?.identity
+        override fun hashCode(): Int = identity.hashCode()
     }
 
     /**

kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/DifferentiableExpression.kt

@@ -0,0 +1,21 @@
+package kscience.kmath.expressions
+
+/**
+ * And object that could be differentiated
+ */
+public interface Differentiable<T> {
+    public fun derivative(orders: Map<Symbol, Int>): T
+}
+
+public interface DifferentiableExpression<T> : Differentiable<Expression<T>>, Expression<T>
+
+public fun <T> DifferentiableExpression<T>.derivative(vararg orders: Pair<Symbol, Int>): Expression<T> =
+    derivative(mapOf(*orders))
+
+public fun <T> DifferentiableExpression<T>.derivative(symbol: Symbol): Expression<T> = derivative(symbol to 1)
+
+public fun <T> DifferentiableExpression<T>.derivative(name: String): Expression<T> = derivative(StringSymbol(name) to 1)
+
+//public interface DifferentiableExpressionBuilder<T, E, A : ExpressionAlgebra<T, E>>: ExpressionBuilder<T,E,A> {
+//    public override fun expression(block: A.() -> E): DifferentiableExpression<T>
+//}

kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/Expression.kt

@@ -56,21 +56,6 @@ public operator fun <T> Expression<T>.invoke(vararg pairs: Pair<Symbol, T>): T =
 public operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T =
     invoke(mapOf(*pairs).mapKeys { StringSymbol(it.key) })
 
-/**
- * And object that could be differentiated
- */
-public interface Differentiable<T> {
-    public fun derivative(orders: Map<Symbol, Int>): T
-}
-
-public interface DifferentiableExpression<T> : Differentiable<Expression<T>>, Expression<T>
-
-public fun <T> DifferentiableExpression<T>.derivative(vararg orders: Pair<Symbol, Int>): Expression<T> =
-    derivative(mapOf(*orders))
-
-public fun <T> DifferentiableExpression<T>.derivative(symbol: Symbol): Expression<T> = derivative(symbol to 1)
-
-public fun <T> DifferentiableExpression<T>.derivative(name: String): Expression<T> = derivative(StringSymbol(name) to 1)
 
 /**
  * A context for expression construction
@@ -96,6 +81,10 @@ public interface ExpressionAlgebra<in T, E> : Algebra<E> {
     public fun const(value: T): E
 }
 
+//public interface ExpressionBuilder<T, E, A : ExpressionAlgebra<T, E>> {
+//    public fun expression(block: A.() -> E): Expression<T>
+//}
+
 /**
  * Bind a given [Symbol] to this context variable and produce context-specific object.
  */

kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/FunctionalExpressionAlgebra.kt

@@ -7,8 +7,9 @@ import kscience.kmath.operations.*
  *
  * @param algebra The algebra to provide for Expressions built.
  */
-public abstract class FunctionalExpressionAlgebra<T, A : Algebra<T>>(public val algebra: A) :
-    ExpressionAlgebra<T, Expression<T>> {
+public abstract class FunctionalExpressionAlgebra<T, A : Algebra<T>>(
+    public val algebra: A,
+) : ExpressionAlgebra<T, Expression<T>> {
     /**
      * Builds an Expression of constant expression which does not depend on arguments.
      */

kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/SimpleAutoDiff.kt

@@ -15,11 +15,11 @@ import kotlin.contracts.contract
 public open class AutoDiffValue<out T>(public val value: T)
 
 /**
- * Represents result of [withAutoDiff] call.
+ * Represents result of [simpleAutoDiff] call.
  *
  * @param T the non-nullable type of value.
  * @param value the value of result.
- * @property withAutoDiff The mapping of differentiated variables to their derivatives.
+ * @property simpleAutoDiff The mapping of differentiated variables to their derivatives.
  * @property context The field over [T].
  */
 public class DerivationResult<T : Any>(
@@ -62,7 +62,7 @@ public fun <T : Any> DerivationResult<T>.grad(vararg variables: Symbol): Point<T
  * @param body the action in [AutoDiffField] context returning [AutoDiffVariable] to differentiate with respect to.
  * @return the result of differentiation.
  */
-public fun <T : Any, F : Field<T>> F.withAutoDiff(
+public fun <T : Any, F : Field<T>> F.simpleAutoDiff(
     bindings: Map<Symbol, T>,
     body: AutoDiffField<T, F>.() -> AutoDiffValue<T>,
 ): DerivationResult<T> {
@@ -71,10 +71,10 @@ public fun <T : Any, F : Field<T>> F.withAutoDiff(
     return AutoDiffContext(this, bindings).derivate(body)
 }
 
-public fun <T : Any, F : Field<T>> F.withAutoDiff(
+public fun <T : Any, F : Field<T>> F.simpleAutoDiff(
     vararg bindings: Pair<Symbol, T>,
     body: AutoDiffField<T, F>.() -> AutoDiffValue<T>,
-): DerivationResult<T> = withAutoDiff(bindings.toMap(), body)
+): DerivationResult<T> = simpleAutoDiff(bindings.toMap(), body)
 
 /**
  * Represents field in context of which functions can be derived.
@@ -136,7 +136,7 @@ private class AutoDiffContext<T : Any, F : Field<T>>(
     override val one: AutoDiffValue<T> get() = const(context.one)
 
     /**
-     * Differentiable variable with value and derivative of differentiation ([withAutoDiff]) result
+     * Differentiable variable with value and derivative of differentiation ([simpleAutoDiff]) result
      * with respect to this variable.
      *
      * @param T the non-nullable type of value.
@@ -148,6 +148,8 @@ private class AutoDiffContext<T : Any, F : Field<T>>(
         var d: T,
     ) : AutoDiffValue<T>(value), Symbol{
         override fun toString(): String = identity
+        override fun equals(other: Any?): Boolean = this.identity == (other as? Symbol)?.identity
+        override fun hashCode(): Int = identity.hashCode()
     }
 
     private val bindings: Map<String, AutoDiffVariableWithDeriv<T>> = bindings.entries.associate {

kmath-core/src/commonTest/kotlin/kscience/kmath/expressions/SimpleAutoDiffTest.kt

@@ -10,21 +10,17 @@ import kotlin.test.assertEquals
 import kotlin.test.assertTrue
 
 class SimpleAutoDiffTest {
-    fun d(
-        vararg bindings: Pair<Symbol, Double>,
-        body: AutoDiffField<Double, RealField>.() -> AutoDiffValue<Double>,
-    ): DerivationResult<Double> = RealField.withAutoDiff(bindings = bindings, body)
 
     fun dx(
         xBinding: Pair<Symbol, Double>,
         body: AutoDiffField<Double, RealField>.(x: AutoDiffValue<Double>) -> AutoDiffValue<Double>,
-    ): DerivationResult<Double> = RealField.withAutoDiff(xBinding) { body(bind(xBinding.first)) }
+    ): DerivationResult<Double> = RealField.simpleAutoDiff(xBinding) { body(bind(xBinding.first)) }
 
     fun dxy(
         xBinding: Pair<Symbol, Double>,
         yBinding: Pair<Symbol, Double>,
         body: AutoDiffField<Double, RealField>.(x: AutoDiffValue<Double>, y: AutoDiffValue<Double>) -> AutoDiffValue<Double>,
-    ): DerivationResult<Double> = RealField.withAutoDiff(xBinding, yBinding) {
+    ): DerivationResult<Double> = RealField.simpleAutoDiff(xBinding, yBinding) {
         body(bind(xBinding.first), bind(yBinding.first))
     }
 
@@ -38,7 +34,7 @@ class SimpleAutoDiffTest {
 
     @Test
     fun testPlusX2() {
-        val y = d(x to 3.0) {
+        val y = RealField.simpleAutoDiff(x to 3.0) {
             // diff w.r.t this x at 3
             val x = bind(x)
             x + x
@@ -47,10 +43,21 @@ class SimpleAutoDiffTest {
         assertEquals(2.0, y.derivative(x)) // dy/dx = 2
     }
 
+    @Test
+    fun testPlusX2Expr() {
+        val expr = diff{
+            val x = bind(x)
+            x + x
+        }
+        assertEquals(6.0, expr(x to 3.0)) //    y  = x + x = 6
+        assertEquals(2.0, expr.derivative(x)(x to 3.0)) // dy/dx = 2
+    }
+
+
     @Test
     fun testPlus() {
         // two variables
-        val z = d(x to 2.0, y to 3.0) {
+        val z = RealField.simpleAutoDiff(x to 2.0, y to 3.0) {
             val x = bind(x)
             val y = bind(y)
             x + y
@@ -63,7 +70,7 @@ class SimpleAutoDiffTest {
     @Test
     fun testMinus() {
         // two variables
-        val z = d(x to 7.0, y to 3.0) {
+        val z = RealField.simpleAutoDiff(x to 7.0, y to 3.0) {
             val x = bind(x)
             val y = bind(y)