# Dependencies in path operation decorators

In some cases you don't really need the return value of a dependency inside your *path operation function*.

Or the dependency doesn't return a value.

But you still need it to be executed/solved.

For those cases, instead of declaring a *path operation function* parameter with `Depends`, you can add a `list` of `dependencies` to the *path operation decorator*.

    EquivalenceTester.of(Equivalence.equals().onResultOf(Functions.toStringFunction()))
        .addEquivalenceGroup(new IntValue(1), new IntValue(1))
        .addEquivalenceGroup(new IntValue(2))
        .test();
  }

  public void testOnResultOf_equals() {
    new EqualsTester()
        .addEqualityGroup(
            Equivalence.identity().onResultOf(Functions.toStringFunction()),

   * exception (typically, but not necessarily, {@link IllegalArgumentException}).
   *
   * <p>The returned converter is serializable if both provided functions are.
   *
   * @since 17.0
   */
  public static <A, B> Converter<A, B> from(
      Function<? super A, ? extends B> forwardFunction,
      Function<? super B, ? extends A> backwardFunction) {

```

////

But then we get a `dict` in the parameter `commons` of the *path operation function*.

And we know that editors can't provide a lot of support (like completion) for `dict`s, because they can't know their keys and value types.

We can do better...

## What makes a dependency

Up to now you have seen dependencies declared as functions.

    }
    return nodeConnections.buildOrThrow();
  }

  @SuppressWarnings("unchecked")
  private static <N> GraphConnections<N, Presence> connectionsOf(Graph<N> graph, N node) {
    Function<N, Presence> edgeValueFn =
        (Function<N, Presence>) Functions.constant(Presence.EDGE_EXISTS);
    return graph.isDirected()
        ? DirectedGraphConnections.ofImmutable(node, graph.incidentEdges(node), edgeValueFn)

//     grad_outputs[1]->Ref();
//     return OkStatus();
//   }
//   ~AddGradientFunction() override {}
// };
//
// GradientFunction* AddRegisterer(const ForwardOperation& op) {
//   // More complex gradient functions can use inputs/attrs etc. from the
//   // forward `op`.
//   return new AddGradientFunction;
// }
//
// Status RegisterGradients(GradientRegistry* registry) {
//   return registry->Register("Add", AddRegisterer);

	var _C_zero *C.mpz_t

and then replacing all instances of C.zero with (*_C_zero).

Cgo's most interesting translation is for functions.  If xxx is a C
function, then cgo rewrites C.xxx into a new function _C_xxx that
calls the C xxx in a standard pthread.  The new function translates
its arguments, calls xxx, and translates the return value.

Translation of parameters and the return value follows the type

  }

  /**
   * A function from an input to a result.
   *
   * @param <T> the type of the input to the function
   * @param <U> the type of the result of the function
   */
  public interface ClosingFunction<T extends @Nullable Object, U extends @Nullable Object> {

    /**
     * Applies this function to an input, or throws an exception if unable to do so.
     *

          V,
          I extends Table<R, C, V>>
      Collector<T, ?, I> toTable(
          java.util.function.Function<? super T, ? extends R> rowFunction,
          java.util.function.Function<? super T, ? extends C> columnFunction,
          java.util.function.Function<? super T, ? extends V> valueFunction,
          java.util.function.Supplier<I> tableSupplier) {
    return TableCollectors.<T, R, C, V, I>toTable(

import com.google.common.annotations.GwtCompatible;
import com.google.common.annotations.GwtIncompatible;
import com.google.common.annotations.J2ktIncompatible;
import com.google.common.base.Function;
import com.google.common.base.Functions;
import com.google.common.collect.Table.Cell;
import com.google.common.collect.testing.CollectionTestSuiteBuilder;
import com.google.common.collect.testing.MapInterfaceTest;