Java Method Handles: propagate unbound arguments across functions

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I would like to create a method handle that allows me to pass as argument a value that will be bound to a placeholder way down the method handle tree.

Figure, something like this: f(x) = plus( minus( x, 2), 3) where x is passed at invoke, and 2 and 3 are some constants MethodHandles that return always 2 or 3.

I'm running in a problem that I don't understand:

import java.lang.invoke.MethodHandle;
import java.lang.invoke.MethodHandles;
import java.lang.invoke.MethodType;

public class TTest {

    public static double plus( double a, double b) { return a + b; }
    public static double minus(double a, double b) { return a - b; }

    public static void main(String[] args) throws Throwable {


        MethodHandle mh_minus = MethodHandles.lookup().findStatic(TTest.class, "minus", MethodType.methodType(double.class, double.class, double.class));
        MethodHandle mh_plus =  MethodHandles.lookup().findStatic(TTest.class, "plus",  MethodType.methodType(double.class, double.class, double.class));


        // f(x) = plus( minus( x, 2), 3)
        MethodHandle doubleInvoker = MethodHandles.exactInvoker(MethodType.methodType(double.class));

        // mh_minus takes 2 doubles as input. The second one needs to take a MethodHandle that returns a constant:
        MethodHandle minus_2 = MethodHandles.filterArguments(mh_minus, 1, doubleInvoker);
        minus_2 = MethodHandles.insertArguments(minus_2, 1, MethodHandles.constant(double.class, 2));

        // mh_plus takes 2 doubles as input. The second one needs to take a MethodHandle that returns a constant:
        MethodHandle plus_3 = MethodHandles.filterArguments(mh_plus, 1, doubleInvoker);
        plus_3 = MethodHandles.insertArguments(plus_3, 1, MethodHandles.constant(double.class, 3));

        // the first arg of plus_3 is minus_2, but minus_2 is a MethodHandle that takes a double and returns a double, so we need to filter the first arg of plus_3 by an exact invoker

        // EXCEPTION HERE:
        plus_3 = MethodHandles.filterArguments(plus_3, 0, MethodHandles.exactInvoker(MethodType.methodType(double.class, double.class)));
        MethodHandle comp = plus_3.bindTo(minus_2);
        double res = (double)comp.invokeExact(3.0); // performs (3 - 2) + 3
    }
}

This returns an exception when trying to filter plus_3:

Exception in thread "main" java.lang.IllegalArgumentException: target and filter types do not match: (double)double, (MethodHandle,double)double
    at java.lang.invoke.MethodHandleStatics.newIllegalArgumentException(MethodHandleStatics.java:145)
    at java.lang.invoke.MethodHandles.filterArgumentChecks(MethodHandles.java:2631)
    at java.lang.invoke.MethodHandles.filterArgument(MethodHandles.java:2608)
    at java.lang.invoke.MethodHandles.filterArguments(MethodHandles.java:2601)
    at TTest.main(TTest.java:31)

What I don't understand, is how I can compose plus with minus, where minus has one argument that is not yet fullfilled.

Can you help me?

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For those interested, the trick here is : MethodHandles::collectArguments.

The code looks like this now:

   public static void withCollectArguments() throws Throwable {

        MethodHandle mh_minus      = MethodHandles.lookup().findStatic(
                TTest.class,
                "minus",
                MethodType.methodType(
                        double.class, // output
                        double.class, // arg1
                        double.class  // arg2
                )
        );

        MethodHandle mh_plus       =  MethodHandles.lookup().findStatic(
                TTest.class,
                "plus",
                MethodType.methodType(
                        double.class,
                        double.class,
                        double.class
                )
        );

        // this guys here is used in filters to do a MethodHandle.invoke() -> double conversion
        MethodHandle doubleInvoker = MethodHandles.exactInvoker(
                MethodType.methodType(
                        double.class
                )
        );

        // I want: f(x) = plus( minus( x, 2.0), 3.0) === (x - 2.0 ) + 3.0

        // mh_minus takes 2 doubles as input. The second one needs to
        // take a MethodHandle that returns a constant, so we filter
        MethodHandle x_minus_2 = MethodHandles.filterArguments(
                mh_minus,
                1,
                doubleInvoker
        );

        x_minus_2 = MethodHandles.insertArguments(
                x_minus_2,
                1,
                MethodHandles.constant(double.class, 2)
        );

        // this here is the magic: we collect arguments of mh_plus (double, double),
        // starting at argument index 0,and the collector is minus_2 ( double ) :
        // we will "eat" the first arg of mh_plus and replace it with minus_2
        MethodHandle x_minus_2_plus_y = MethodHandles.collectArguments(
                mh_plus,
                0,
                x_minus_2
        );

        // we then curry x_minus_2_plus_y with a constant as 2nd argument: y => 3
        MethodHandle x_minus_2_plus_3 = MethodHandles.filterArguments(
                x_minus_2_plus_y,
                1,
                doubleInvoker
        );

        // "( x - 2 ) + y" becomes "( x - 2 ) + 3"
        x_minus_2_plus_3 = MethodHandles.insertArguments(
                x_minus_2_plus_3,
                1,
                MethodHandles.constant(
                        double.class,
                        3
                )
        );

        // we now have a method handle that takes 1 argument and dispatches it to minus
        double res = (double)x_minus_2_plus_3.invokeExact(1.0); // performs ( x=1.0 - 2.0) + 3.0
        Assert.assertEquals(res, 2.0);

        res = (double)x_minus_2_plus_3.invokeExact(5.0); // performs ( x=5.0 -2.0 ) + 3.0
        Assert.assertEquals(res, 6.0);
    }