如何使用 Java 1.8 实现教会数字

Question

我正在尝试在 Java 1.8 中实施教会数字。我的第一次尝试是：

import java.util.function.UnaryOperator;

@FunctionalInterface
public interface ChurchNumeral {
  public static ChurchNumeral valueOf(int n) {
    if (n < 0) {
      throw new IllegalArgumentException("Argument n must be non-negative.");
    }
    if (n == 0) {
      return (f, arg) -> arg;
    }
    return (f, arg) -> f(valueOf(n-1).apply(f, arg));
  }

  <T> T apply(UnaryOperator<T> f, T arg);
}

这失败了，因为函数方法有一个类型参数。（具体来说，带有 lambda 表达式的行给出错误："Illegal lambda expression: Method apply of type ChurchNumeral is generic"。）

根据对函数式接口使用泛型相关问题的回答，我尝试参数化 class:

import java.util.function.UnaryOperator;

@FunctionalInterface
public interface ChurchNumeral<T> {                // This line changed.
  public static ChurchNumeral<?> valueOf(int n) {  // This line changed.
    if (n < 0) {
      throw new IllegalArgumentException("Argument n must be non-negative.");
    }
    if (n == 0) {
      return (f, arg) -> arg;
    }
    return (f, arg) -> f(valueOf(n-1).apply(f, arg));
  }

  T apply(UnaryOperator<T> f, T arg);              // This line changed.
}

现在可以编译第一个 lambda 表达式，但第二个表达式失败并出现此错误：

The method apply(UnaryOperator, capture#1-of ?) in the type ChurchNumeral is not applicable for the arguments (UnaryOperator, Object)

此外，我不想为每种可能的 function/argument 类型设置不同版本的 ChurchNumeral.ZERO。

有什么建议吗？

Answer 1

Is there a way to do it so I don't need to create a ChurchNumeral for every possible type? I'd like to be able to apply ZERO (for example) to any UnaryOperator and argument of type T

我假设你的意思是你想做这样的事情：

ChurchNumeral five = ChurchNumeral.valueOf(5);
five.apply(s -> s + s, "s");
five.apply(Math::sqrt, Double.MAX_VALUE);

这意味着您第一个示例中的方法签名：

<T> T apply(UnaryOperator<T> f, T arg);

就是需要的那个。

然而，you can't use a lambda expression for a functional interface, if the method in the functional interface has type parameters.

解决方法是创建一个与 lambda 兼容的子接口，并将对 apply 的调用委托给它的方法，如下所示。

public static void main(String[]a){
    ChurchNumeral five = ChurchNumeral.valueOf(5);
    System.out.println(five.apply(s -> s + s, "s"));
    System.out.println(five.apply(Math::sqrt, Double.MAX_VALUE));
}
@FunctionalInterface
private interface ChurchNumeralT<T> extends ChurchNumeral {
    @SuppressWarnings({ "rawtypes", "unchecked" })
    @Override
    default<U> U apply(UnaryOperator<U> f, U arg){
        return (U)((ChurchNumeralT)this).tapply(f, arg);
    }
    T tapply(UnaryOperator<T> f, T arg);
}
public interface ChurchNumeral {

    <T> T apply(UnaryOperator<T> f, T arg);

    static ChurchNumeral valueOf(int n) {
        if (n < 0) {
            throw new IllegalArgumentException("Argument n must be non-negative.");
        }
        if (n == 0) {
            return (ChurchNumeralT<?>)(f, arg) -> arg;
        }
        return (ChurchNumeralT<?>)(f, arg) -> f.apply(valueOf(n - 1).apply(f, arg));
    }
}

Answer 2

static interface Church<T> extends UnaryOperator<UnaryOperator<T>> {

    static <T> Church<T> of(int n) {
        if (n < 0) {
            throw new IllegalArgumentException();
        } else if (n == 0) {
            return f -> (t -> t);
        } else {
            return sum(f -> f, Church.of(n-1));
        }
    }

    static <T> Church<T> sum(Church<T> a, Church<T> b) {
        return f -> b.apply(f).andThen(a.apply(f))::apply;
    }
}

public static void main(String[] args) {
    Church<Integer> five = Church.of(5);
    Church<Integer> three = Church.of(3);
    Church<Integer> eight = Church.sum(five, three);

    assert 3 == three.apply(x -> x + 1).apply(0);
    assert 5 == five.apply(x -> x + 1).apply(0);
    assert 8 == eight.apply(x -> x + 1).apply(0);
}

编辑： 如果您想要 apply(UnaryOperator<T> f, T arg) 就在教会界面中，这样您就可以调用 .apply(x->x+1,0) 而不是 .apply(x->x+1).apply(0)，您可以将这样的默认方法添加到上面的 Church 界面：

default T apply(UnaryOperator<T> f, T t) {
    return this.apply(f).apply(t);
}

编辑 2： 这是更新后的 class，可以在不同类型之间进行转换。我还添加了一个 mul 方法来乘法只是为了看看它是如何工作的：

static interface Church<T> extends UnaryOperator<UnaryOperator<T>> {

    static <T> Church<T> of(int n) {
        if (n < 0) {
            throw new IllegalArgumentException();
        } else if (n == 0) {
            return zero();
        } else {
            return sum(one(), Church.of(n - 1));
        }
    }

    static <T> Church<T> zero() {
        return f -> (t -> t);
    }

    static <T> Church<T> one() {
        return f -> f;
    }

    static <T> Church<T> sum(Church<T> a, Church<T> b) {
        return f -> b.apply(f).andThen(a.apply(f))::apply;
    }

    static <T> Church<T> mul(Church<T> a, Church<T> b) {
        return f -> a.apply(b.apply(f))::apply;
    }

    default <U> Church<U> convert() {
        return (Church<U>) this;
    }
}

public static void main(String[] args) {
    Church<Integer> zero = Church.zero();
    Church<Integer> five = Church.of(5);
    Church<Integer> three = Church.of(3);
    Church<Integer> eight = Church.sum(five, three);
    Church<Integer> fifteen = Church.mul(three, five);

    assert 0 == zero.apply(x -> x + 1).apply(0);
    assert 3 == three.apply(x -> x + 1).apply(0);
    assert 5 == five.apply(x -> x + 1).apply(0);
    assert 8 == eight.apply(x -> x + 1).apply(0);
    assert 15 == fifteen.apply(x -> x + 1).apply(0);

    Church<String> strOne = Church.one();     
    Church<String> strThree = three.convert();  // make Church<String>
                                                // from a Church<Integer>

    assert "foo:bar".equals(strOne.apply("foo:"::concat).apply("bar"));
    assert "foo:foo:foo:bar".equals(strThree.apply("foo:"::concat).apply("bar"));

}

如何使用 Java 1.8 实现教会数字

How to implement Church Numerals using Java 1.8

java

generics

lambda

church-encoding

java-8