gistfile1.java

import java.io.IOException;
import java.sql.SQLException;

public class Test {

    public static String a(String x) throws IOException {
        return x;
    }

    public static String b(String x) throws SQLException {
        return x;
    }

    public static <X, Y, Z, T1 extends Throwable, T2 extends Throwable> FuncThrowingTwoExceptions<X, Z, T1, T2> compose(
            FuncThrowingOneException<X, Y, T1> a, FuncThrowingOneException<Y, Z, T2> b) {
        return t -> b.apply(a.apply(t));
    }

    public static String c(String x) throws IOException, SQLException {
        return compose(Test::a, Test::b).apply(x);
    }
}

interface FuncThrowingOneException<X, Y, T extends Throwable> {
    Y apply(X x) throws T;
}

interface FuncThrowingTwoExceptions<X, Y, T1 extends Throwable, T2 extends Throwable> {
    Y apply(X x) throws T1, T2;
}