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<td colspan="2"><em>(C) Copyright 2002, Julian Hyde</em></td>
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<td>Julian Hyde (<a href="mailto:julian.hyde@mail.com">julian.hyde@mail.com</a>)</td>
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<h1>Saffron overview</h1>
<p>Julian Hyde, November 5th, 2001.</p>
<h2>Overview</h2>
<p>Saffron is a seamless integration of SQL-like relational expressions into Java.
As we shall see, the tight integration means that relational expressions are
much more powerful than those offered by SQL.</p>
<h2>How is Saffron different from SQL?</h2>
<ol>
<li><b>You can use Saffron expressions directly from Java code</b>. For example,
an <code>exists </code>condition:<blockquote>
<pre>if (exists (select from emp where emp.salary > 50000)) {
...
}</pre>
</blockquote>
<p>An <code>in </code>condition:</p>
<blockquote>
<pre>if ("Fred" in (select emp.ename from emp where emp.salary > 50000)) {
...
}</pre>
</blockquote>
<p>A <code>for </code>loop:</p>
<blockquote>
<pre>for (emp in (select from emp order by emp.salary)) {
System.out.println(emp.ename + " earns " + emp.salary);
}</pre>
</blockquote>
<p>And an array initialized using a relational expression:</p>
<blockquote>
<pre>Emp[] programmers = (select from emp
where emp.title.equals("Programmer"));</pre>
</blockquote>
</li>
<li><b>Saffron</b><b> uses Java expression syntax</b>. You can call java methods,
construct objects and arrays, and access java objects just as you would in
regular java code. For example,<blockquote>
<pre>select emp.ename.substring(ename.indexOf(".")) from emp</pre>
</blockquote>
</li>
<li><b>Saffron</b><b> relational expressions use Java's type system</b>. Runtime type
conversions (of, say, a <code>DECIMAL(8,2)</code> column to a java <code>float
</code>variable) are inefficient, error-prone, and can lose information.
The names of tables and columns are checked at compile time, so your programs
are more maintainable.</li>
<li><b>Saffron</b><b> doesn't use 3-valued logic</b>. A condition in Saffron
always
evaluates to <code>true</code> or <code>false</code>, whereas in SQL a
condition can sometimes evaluates to NULL.</li>
<li><b>Saffron</b><b> expressions are evaluated efficiently</b>. If an expression
involves only Java objects (no tables), the Saffron compiler will generate Java
code which is almost as efficient as hand-written code.</li>
<li><b>Saffron</b><b> accesses heterogeneous data better</b>. Consider the following
query, which accesses data from an in-memory array (<code>manufacturers</code>), and tables from two
different relational databases (<code>orderDb </code>and <code>productDb</code>).<blockquote>
<pre>String[] manufacturers = new String[] {"Heinz", "Guinness"};
int[] customers = (
select order.customerId
from productDb.products as product
join orderDb.orders as order on order.productId == productId
where product.manufacturer in manufacturers);</pre>
</blockquote>
Should the query be executed on the orders database or the products database?
And how should the manufacturer list be sent over: as a hard-coded in-list, or
by restarting the query for each manufacturer in the list? It really
doesn't matter: the Saffron optimizer will decide for you.
</li>
</ol>
<h2>How does Saffron improve Java?</h2>
<p>We have already discussed how Saffron makes your life easier if you are
embedding SQL statements in Java using JDBC. But Saffron can help even if
you are not accessing data stored in a relational database. This is
because in-memory data is often relational, and the algorithms to deal with it
are often the familiar relational operations: sort, join, filter, union,
intersect, minus.</p>
<p>Suppose I have two lists of customers, and I want to create a list of both,
with duplicates eliminated. An experienced Java programmer would probably
write something like this:</p>
<blockquote>
<pre>Customer[] addCustomerLists(Customer[] list1, Customer[] list2) {
Hashtable hashtable = new Hashtable();
for (int i = 0; i < list1.length; i++) {
Customer c = list1[i];
hashtable.put(c, c);
}
for (int i = 0; i < list2.length; i++) {
Customer c = list2[i];
hashtable.put(c, c);
}
Customer[] list3 = new Customer[hashtable.size()];
hashtable.asList().copyInto(list3);
return list3;
}</pre>
</blockquote>
<p>They would test it, notice that the customers are now in arbitrary order, and
add</p>
<blockquote>
<pre> java.util.Arrays.sort(list3);</pre>
</blockquote>
<p>just before returning the result. In Saffron, a programmer would write</p>
<blockquote>
<pre>Customer[] list3 = select from (list1 union list2) c order by c;</pre>
</blockquote>
<p>They don't need to know Hashtable is the 'correct' data structure to use.
They tell the system <i>what </i>they want, and the system figures <i>how </i>to
compute it efficiently.</p>
<p>This is a rather simple example. It gets better, because Saffron is a <i>
closed </i>language. This means that you can use a Saffron expression anywhere </p>
<h2>Grammar</h2>
<p><i>Definition</i>. A <dfn>set expression</dfn> is
an expression which returns more than one item; namely, a query, an array, an
iterator or collection, or a <code>Table</code>.</p>
<h3>Relational expressions</h3>
<blockquote>
<pre><code>select</code> [<code>{</code>[<i>expression</i> [<code>as </code><i>alias</i>]], ...<code>}</code> | <i>expression</i>]
[<code>from </code><i>from-expression</i>]
[<code>where </code><i>expression</i>]
[<code>order by </code>[<i>expression </i>[<code>asc </code>| <code>desc</code>]], ...]</pre>
<pre><i>expression </i><code>union </code><i>expression</i></pre>
<pre><i>expression </i><code>intersect </code><i>expression</i></pre>
<pre><i>expression </i><code>minus </code><i>expression</i></pre>
</blockquote>
<p>The syntax for the from list <i>from-expression</i> is as follows:</p>
<blockquote>
<pre><i>expression </i>[as alias]</pre>
<pre><i>from-expression </i>[<code>left</code> | <code>right</code> | <code>full</code> | ] <code>join</code><i>
</i> <i>from-expression </i>[<code>on</code> <i>condition</i>]</pre>
</blockquote>
<p>Notes:</p>
<ol>
<li>The select list can have 3 forms.<ol>
<li>An <i><dfn>empty select list</dfn> </i>means return everything from the from clause.
If the from clause has precisely one item, the result is the same type as that
item (for example, each row from <code>select from emp</code> has type <code>
Emp</code>); otherwise, the result is a record, with one field per from item
(for example, each row from <code>select from emp join dept</code> has type
<code>{Emp emp; Dept dept}</code>; each row
from <code>select</code> has type <code>{}</code>).</li>
<li>A <dfn>single-item select list</dfn> means
return rows without boxing them into records. So, for example, each row from
<code>select three from new int[] {1, 2, 3} as three</code> is an <code>int</code>. </li>
<li>A <dfn>boxed select list</dfn> (enclosed in
<code>{</code> ... <code>}</code>) means create a record for each row. The
optimizer will create a synthetic class to describe the type of the row. Two
rows with the same types and aliases, in the same order, will have the same
synthetic class (and are therefore union-compatible). For example, each
row from <code>select {three} from new int[] {1, 2, 3} as three</code> is
<code>class Synthetic$124 { int three; }</code>; the type of <code>select {emp.empno,
emp.ename as name} from emp</code> is <code>class Synthetic$527 { int empno;
String name; }</code>.</li>
</ol>
</li>
<li>Aliases of items in from and select lists default to variable, field, and
method names. The aliases of the fields in <code>Emp emp; select emp,
dept.deptno, dept.dname.substring(3) from dept</code> are <code>emp</code>,
<code>deptno</code>, and <code>substring</code>, respectively. Other
kinds of expression have no default alias, and therefore an alias must be
specified. Whether implied or explicit, the aliases in a select or from
list must be distinct.</li>
<li>If the from clause is missing, the input to the select statement is a
table with one row and no columns.</li>
<li>Expressions in the from list must be set expressions.
Any kind of expression is allowed in the select list; queries are returned as
arrays.</li>
<li>If <code>on</code><i> condition </i>is omitted from a <i>from-expression</i>
it defaults to <code>true</code> (hence, a cartesian product). The keywords
<code>left</code>, <code>right</code> and <code>full</code> indicate that an
outer join is to be performed.</li>
<li>No plans to do <i>aggregation</i>.</li>
</ol>
<h3>Boolean expressions</h3>
<p>We add the following boolean expressions to Java:</p>
<blockquote>
<pre><i>expression</i> <code>in </code><i>expression</i></pre>
<pre><code>exists </code>(<i>expression</i>)</pre>
</blockquote>
<p>The right-hand expressions must be set expressions.</p>
<p>These expressions can, of course, occur inside relational expressions. The
sub-query so created is said to be <dfn>correlated</dfn> if it refers to rows
from the outer query. For example, the following query
is correlated on <code>dept.deptno</code>:</p>
<blockquote>
<pre><code>select
from </code>depts <code>as </code>dept
<code>where exists </code>(
<code>select from </code>emps <code>as </code>emp
<code> where </code>emp.deptno == dept.deptno &&
emp.gender.equals("F"))</pre>
</blockquote>
<p>We do not provide a <code>not</code> operator to negate these. Use the
regular Java <code>!</code> operator, for example, <code>!("apple" in fruit)</code>
or <code>!exists (select from fruit where fruit.equals("apple")</code>.</p>
<h3>Statements</h3>
<blockquote>
<pre><code>for </code>([<i>type</i>]<i> variable</i> <code>in </code><i>expression</i>) {
<i>statement list
</i>}</pre>
</blockquote>
<h3>Aggregation</h3>
<p>Simple example:</p>
<blockquote>
<pre><code>select</code> emp.deptno, sum(emp.sal)<code> as</code> sumSal<code>
group by</code> emp.deptno<code>
from </code>emps <code>as </code>emp</pre>
</blockquote>
<p>Unlike SQL, the <code>group by</code> clause comes before the <code>from</code>
clause, and is mandatory if you want to aggregate. The equivalent of the SQL <code>select
sum(emp.sal) from emp</code> has an empty <code>group by</code> clause in Saffron: <code>select sum(emp.sal)
group by from emp</code>.</p>
<p>In Saffron, the <code>where</code> clause is applied <i>after</i> aggregation
has been performed, more like a SQL <code>having</code> clause than a <code>
where</code> clause. Expressions in the <code>where</code> clause can only
reference aggregations and grouping expressions, not ungrouped expressions. If
you want to filter the rows going into the aggregation, use a subquery in the
from list:</p>
<blockquote>
<pre><code>select</code> femp.deptno, sum(femp.sal)<code> as</code> sumSal<code>
group by</code> femp.deptno<code>
from </code>(
<code>select</code>
<code>from</code> emps <code>as</code> emp
<code>where</code> emp.gender.equals("F")) <code>as </code>femp
<code>where </code>avg(femp.sal) > 50000</pre>
</blockquote>
<p>There are 3 kinds of aggregation function:</p>
<ol>
<li>Builtin aggregation functions (such as <code>count</code>) are treated
specially by the system, and generate optimized code.</li>
<li>A regular java function which takes a set (array, collection, or iterator)
will be called if its argument matches the element type in the actual usage.
For example, if <code>emp.sal</code> is of type <code>double</code>, then
<code>double sum(double[] a)</code> would match. Likewise, <code>int
count(Iterator iter)</code> would match <code>select count(emp) from emps as
emp</code>, because Emp can be up-cast to Object, the element type of Iterator.</li>
<li>User-defined aggregations.</li>
</ol>
<pA user-defined aggregation is a class which implements <code>interface {@link
saffron.AggregationExtender}</code>. If you invoke the {@link
saffron.AggregationExtender#aggregate} pseudo-method, the system generates the
right code to calculate the aggregation.</p>
<p>Now let's see how the Saffron system invokes a user-defined aggregation
while evaluating a query. Suppose we have written <code>class MySum</code>,
which can total both <code> int</code> and <code>double</code> values, and
evaluate the query</p>
<blockquote>
<pre><code>select</code> MySum(i)
<code>from new int</code>[] {2, 3, 4} <code>as</code> i</pre>
</blockquote>
<p>The Saffron system makes following calls. Note how the <code>resolve</code>
method deals with operator overloading. Note how <code>int</code>s are wrapped
as <code>Integer</code>s then in arrays to be passed to <code>addOne</code>, and returned from
<code>result</code>.</p>
<blockquote>
<pre>AggregatorClass sum = new MySum();
AggregationExtender intSum = sum.resolve(new Class[] {Integer.TYPE});
Object total = intSum.start(null);
intSum.addOne(total, new Object[] {new Integer(2)});
intSum.addOne(total, new Object[] {new Integer(4)});
Object total2 = intSum.start(null);
intSum.addOne(total2, new Object[] {new Integer(3)});
intSum.merge(total, total2);
System.out.println("Result is " +
((Integer) intSum.result(total)).intValue());</pre>
</blockquote>
<p>Examples of more complex aggregations:</p>
<ul>
<li>The <code>median</code> aggregation ({@link saffron.ext.Median}) requires a
variable-size workspace. A typical implementation would use an {@link java.util.ArrayList} to collect the values, sort them, then return the middle one.</li>
<li>The <code>nth</code> aggregation {@link saffron.ext.Nth}) returns the <i>n</i>th item of a set. <i>n</i>
is passed to the <code>start</code> method, so must be independent of any
particular row. Example:<blockquote>
<pre><code>select</code> new Nth(3).aggregate(name) <code>from</code> (<code>select from</code> emps <code>order by</code> salary)</pre>
</blockquote>
</li>
<li>The <code>closest</code> aggregation computes the nearest of a set of
points to a given point. Its <code>start</code> method receives the latitude
and longitude of the initial point (as <code>new Object[] {new Double(42), new
Double(129)}</code>), and the <code>addOne</code> method receives the latitude
and longitude of each subsequent point.<blockquote>
<pre><code>select</code> closest(42, -129, office.latitude, office.longitude)
<code>from</code> offices <code>as</code> office</pre>
</blockquote>
</li>
</ul>
<p>Notes & issues:</p>
<ol>
<li>Arguments are zero or more primitive types or objects. Primitives are
passed wrapped as objects.</li>
<li>A robust aggregation of median (not possible without invoking custom
code-generation) would internally expand it to<blockquote>
<pre><code>select </code>nth(count() / 2, sorted)
<code>from</code> (<code>select from new int</code>[] {2, 3, 4} <code>as</code> i <code>order by</code> i) <code>as </code>sorted</pre>
</blockquote>
</li>
<li>Distinct aggregations. Syntax? Implementation?</li>
<li>Could we use aggregations as rolling averages? (I guess the <code>{@link saffron.AggregationExtender}.result()</code> method would have to be non-destructive.)</li>
</ol>
<h2>Type-checking</h2>
<p>One of Java's most important features is its strong type system. To
take advantage of this, every relational expression is always has a result which
is an array type.</p>
<p>This doesn't mean that the array is actually created. If you use the
<code>for (... in ...)</code> construct, for example, the system will implement the loop
using an iterator, and is unlikely to construct the result as an array.
And the optimizer tries hard not to convert intermediate sets, such as that
created by an <code>in </code>operator, into arrays.</p>
<p>Regular java expressions can also be used as relational expressions:</p>
<ul>
<li>arrays</li>
<li>collections (<code>Collection</code>, including <code>Vector</code>)</li>
<li>iterators (<code>Enumeration</code>, <code>Iterator</code>)</li>
</ul>
<p>The problem with collections and iterators (until generics arrive in Java
1.4) is that we don't know what type of objects they contain. We allow the
programmer to specify that type information using by a dummy cast to an array
type. For example:</p>
<blockquote>
<pre>Vector fruit = new Vector();
fruit.addElement("apple");
fruit.addElement("banana");
fruit.addElement("orange");
fruit.addElement("mango");
String[] tropicalFruit = (select fruit
from (String[]) fruit
where fruit.indexOf("n") >= 0);</pre>
</blockquote>
<p>You can cast a collection or iterator to an array of primitive types,
provided that the collection does not contain null values.</p>
<h3>Casting input datasets</h3>
<p>Some data sources, such as vectors, iterators and external data sources such
as JDBC tables, contain very little type information, and this makes it
difficult to write concise queries. For example,</p>
<blockquote>
<pre>Vector emps = new Vector();
emps.addElement(fred);
emps.addElement(barney);
for (emp in select from emps as emp where ((Emp) emp).deptno == 20) {
print(((Emp) emp).name);
}</pre>
</blockquote>
<p>Better to tell the system just once that <code>emps </code>is a collection of
<code>Emp </code>objects:</p>
<blockquote>
<pre>for (emp in select from (Emp[]) emps as emp where emp.deptno == 20) {
print(emp.name);
}</pre>
</blockquote>
<p>The cast does not necessarily cause the vector to be converted to an array:
we are simply providing the Saffron compiler with more type information, and
allowing it to choose the most efficient plan.</p>
<h3>Determining the output type</h3>
<p>By default, a relational expression returns an array. You can produce results
in a different format by using a dummy cast, like this:</p>
<blockquote>
<pre>Iterator emps;
Iterator femaleEmps = (Iterator)
(select from (Emp[]) emps as emp
where emp.gender.equals("F"));</pre>
</blockquote>
<p>This is particularly useful where the output is large (even infinite!) and
you to iterate over the first few rows without computing the whole result.</p>
<p>The available types are {@link java.util.Iterator}, {@link
java.util.Enumeration}, {@link java.util.Collection}, {@link java.util.Vector},
and <code>type[]</code>. In future, we may add {@link java.sql.ResultSet}.</p>
<h3><a name="Tables_and_Schemas">Tables and Schemas</a></h3>
<p>The interfaces Table, Schema and Connection allow you to access data sources
which have arbitrary access methods. A table (<code>interface {@link
saffron.Table}</code>) represents a set of relational data, and it provides
methods to describe the data source, discover its access methods, and so
forth. Schemas (<code>interface {@link saffron.Schema}</code>) make it easy to
expose a set of tables and the information necessary to compile programs which
use them. If you can to access data in a JDBC database, derive a class from
<code>class {@link saffron.ext.ReflectSchema}</code> and create a member of
type {@link saffron.ext.JdbcTable} for each table your wish to access
(<code>class {@link sales.Sales}</code> is an example of this.)</p>
<p>Let's look at what happens when you compile a program which uses a
schema.</p>
<ol>
<li>The compiler notices a piece of code (<code>sales.emps</code>) which
accesses a member or method of an object (<code>sales</code>) which implements <code>
interface {@link saffron.Connection}</code>.</li>
<li>The compiler calls the static method <code>getSchema</code> on that
object. (Why call a static method, not a method in the interface?
Well, remember that this is happening at compile time. The real object
does not exist yet.)</li>
<li>The compiler invokes the schema's <code>getMemberTable</code> or <code>
getMethodTable</code> method, to retrieve a <code>Table</code>. If there is no
such table, these methods may throw <code>openjava.mop.NoSuchMemberException</code>,
which will be reported as a compilation error.</li>
<li>The compiler invokes the table's <code>toRel</code> method, passing the
piece of parse tree which represents the expression which will yields the
schema. (The <i>real </i>schema object only gets created at run time,
remember.)</li>
<li>The compiler calls schema's getTable method with the parse object
be for example, class Sales.</li>
</ol>
<p>In particular, we provide <code>abstract class {@link saffron.ext.JdbcTable}
implements {@link saffron.Table}</code> to make it easy to access tables via
JDBC. We recommend that you group tables into a schema class, which extends
<code>class {@link saffron.ext.ReflectSchema}</code>. For
example,</p><blockquote>
<pre>class SalesConnection
extends saffron.ext.JdbcConnection
implements saffron.Connection
{
public SalesConnection(String connect) {
super(connect);
}
// required for saffron.Connection
public static saffron.Schema getSchema() {
return new SalesSchema();
}
};
class SalesSchema
extends saffron.ext.ReflectSchema
implements saffron.Schema
{
public static class Emp {
public int empno;
public String name;
public int deptno;
};
public static class Dept {
public int deptno;
public String name;
};
public saffron.Table emp = new saffron.ext.JdbcTable(
this, "EMP", Emp.class);
public saffron.Table depts = new saffron.ext.JdbcTable(
this, "DEPT", Dept.class);
};
SalesConnection sales = new SalesConnection("jdbc:odbc:MyDatabase");
for (emp in sales.emps) {
<i>some code</i>
}</pre>
</blockquote>
<p>The Saffron compiler creates an instance of the schema, and interrogates it
regarding the objects it contains. When it sees the expression <code>sales.emps</code>,
it invokes <code>SalesConnection.getSchema().getTableForMember("emps")</code> to
get a {@link saffron.Table} which describes <code>emps</code> and, in particular,
that it returns rows of type <code>Emp</code>. The translator then calls
the table's <code>toRel()</code> method to create a relational expression node;
in this case a {@link saffron.rel.TableAccess}. (The translator actually converts <code>
sales.emp</code> into a brief intermediate expression <code>(Emp[])
sales.contentsAsArray("emps")</code>. The <code>contentsAsArray</code> function
is a placeholder which has special meaning to the translator. Note how an array
cast is used to provide type information.)</p>
<p>As well as type information, the schema could in future provide information
about volumetrics, indexes, and even custom rules for optimizing the query.</p>
<p><i>todo</i>: Expose <code>Map</code>s (including <code>Hashtable</code>s) as
relations with 2 columns.</p>
<h3>Non-relational schemas</h3>
<p>A schema could be used to present non-relational data in a relational format.
It would know that 'getDept(40)' was the same as 'select from dept where deptno
= 40' and 'dept.getEmployees()' is the same as 'select from emp where emp.deptno
== dept.deptno'. We would need a mechanism to construct an <dfn>
extent</dfn> (the set of all instances of a given
entity). The schema could declare an explicit method to find the instances of an
entity; another way is to use mandatory relationships (for example, since every
employee must work in a department, given all departments, we can find all
employees by traversing the 'works in' relationship). It helps if the
relationship is many- (or one-) to-one, since we don't need to eliminate
duplicates. There could be more than one access path to an entity.</p>
<p>How to represent such mappings? Views: dept.getEmployees() is equivalent to
select from emp where emp.deptno == dept.deptno. Better, parameterized views.
Example {@link sales.Reflect} presents Java's type system ({@link
java.lang.Class}, {@java.lang.reflect.Field}, <i>et cetera</i>) as
relations.</p>
<p><i>todo: </i>Could allow a type (e.g. <code>boolean</code>,
<code>int</code>) to serve as a relation. Could implement by iterating over all
possible values of that type (rarely practical) or joining to an attribute of a
more finite relation. Example: <code>select from int as i where i in (select
emp.deptno from emp)</code>.</p>
<h2>Null semantics</h2>
<p>Saffron uses Java, not SQL, null semantics. <code>null</code>
is always the Java null value. Every boolean expression evaluates to
either <code>true </code>or <code>false</code>. And yes, <code>null ==
null</code> evaluates to <code>true</code>.</p>
<h2>Comparison semantics</h2>
<p>In Saffron, as in Java, the <code>==</code> operator
compares addresses, not content. The expression <code>"abc" == "a"
+ "bc"</code> may, on some Java systems, evaluate to false, so you should
write <code>"abc".equals("a" + "bc")</code> instead.</p>
<p>The <code>in </code>operator expands to expressions which use the <code>
equals()</code> and <code>hashCode()</code> methods, so you should only uses it
on classes for which these methods are well-behaved. And the expression</p>
<blockquote>
<pre>null in new String[] {"apple", "orange"}</pre>
</blockquote>
<p>will give a <code>NullPointerException</code>.</p>
<p>The <code>order by</code> operator requires that objects implement the <code>
interface java.lang.Comparable</code>. (<i>todo: Compile- or run-time error if
not?</i>)</p>
<p>Primitive types are compared using the primitive operators <code>==</code>,
<code><</code> etc.</p>
<p>Two instances of a synthetic classes are equal if and only if each of their
components are equal. Synthetic classes are compared lexicographically.
Example:</p>
<blockquote>
<pre>select
from (select from twos join threes) as i
join (select from twos join threes) as j
where i < j</pre>
</blockquote>
<h2>Primitive values</h2>
<p>Saffron accepts primitive values, such as <code>int</code>, <code>char</code>,
<code>double</code>, in most places that it accepts objects. A couple of
exceptions:</p>
<ol>
<li>Outer joins need to produce null values. For example,<pre>select {twos, threes}
from new int[] {2, 4, 6, 8} as twos
left join new int[] {3, 6, 9} as threes
on twos == threes</pre>
would produce<pre>2, 0
4, 0
6, 6
8, 0 </pre>
</li>
<li>Saffron uses Java collections to implement certain algorithms. For example,
in the following expression, it uses a Hashtable to detect values which have
already been emitted.
<pre>select from new int[] {2, 4, 6, 8} as twos
minus
select from new int[] {3, 6, 9} as threes</pre>
It automatically boxes and unboxes primitive values.</li>
</ol>
<h2>Planning and evaluation</h2>
<p>The Saffron system runs in static and dynamic mode.</p>
<p>In static mode, relational expressions are embedded into Java programs. A
pre-processor checks that the relational expressions are valid, and converts
them into regular java. There are many ways to evaluate a relational expression, </p>
<p>A query optimizer chooses an evaluation plan.</p>
<h2>Evaluation model</h2>
<h2>Implementation issues</h2>
<h3>Composite rows</h3>
<p>If a relational expression has more than one expression in its <code>select
</code>clause, it produces rows which are not atomic. For example,</p>
<blockquote>
<pre>int[] twos = new int[] {2,4,6,8};
int[] threes = new int[] {3,6,9};
for (i in (select twos, threes twos cross join threes)) {
...
}</pre>
</blockquote>
<p>creates rows which are pairs of <code>int</code>s. It is translated to</p>
<blockquote>
<pre>int[] twos = new int[] {2,4,6,8};
int[] threes = new int[] {3,6,9};
for (int x = 0; x < twos.length; x++) {
for (int y = 0; y < threes.length; y++) {
Synth1 i = new Synth1(twos[x], threes[y]);
...
}
}</pre>
</blockquote>
<p>This illustrates two issues with composite rows. First, these rows need
a type. The Saffron compiler solves this issue by generating a synthetic
class (in this case, <code>class Synth1</code>). We don't know what this
class will be called, so we use <code>for (<i>variable</i> in ...)</code>
syntax, which lets the system infer the type for us.</p>
<p>Second, the system creates a new object for every row, which might be
expensive. In this case, they are emitted from the query, so we can't avoid
creating them. If the composite rows are not emitted, the Saffron optimizer will
do its best to avoid creating them.</p>
<h2>How the optimizer works</h2>
<p>The job of the optimizer is to convert a parse tree containing Saffron expressions into a regular parse tree. Its input and output, therefore, are both
parse trees.</p>
<p>In between times, it searches for Saffron expressions, and converts them to
tree of intermediate relational expressions (<code>class {@link saffron.rel.Rel}</code>).</p>
<p>These relational expressions still contain fragments of regular Java
expressions for select expressions, method calls, and so forth. The Java
expressions are translated into internal form. Except for references to
variables outside the Saffron expression, variables tend to disappear, to be
replaced by mysterious-looking expressions. For example, in the expression</p>
<blockquote>
<pre>select
from location
join (select
from emp
join dept on emp.deptno == dept.deptno)
on location.state.equals(dept.state) </pre>
</blockquote>
<p>the join condition <code>location.state.equals(dept.state)</code> becomes <code>$input0.state.equals($input1.$f1.state)</code>.
Here, <code>$input0</code> and <code>$input1</code> represent the 2
inputs to the join node (which is the context for this Java fragment); <code>$f1</code>
is the first field of the composite row produced by the inner query. That
field's type is Dept, and therefore it has a <code>state</code> field.</p>
<p>The optimizer uses a dynamic programming approach based upon that used by the
Volcano optimizer. Starting with the initial expression, it applies
transformation rules to convert it, and its sub-expressions, into semantically
equivalent expressions. It estimates the cost of each expression, and
cultivates variants of expressions until it finds cheap implementations of them.</p>
<p>An expression can be implemented using several <dfn>calling
conventions</dfn>. Calling conventions include array,
vector, iterator. The most important (and efficient) calling convention is
inline. Inline means that a piece of code will be executed for every row
in the expression; no collection of objects is created, just <i>stuff happens</i>.
An inline implementation of</p>
<blockquote>
<pre>for (o in (select from emp join dept on emp.deptno == dept.deptno)) {
System.out.println(o.emp.ename + " works in " + o.dept.dname);
}</pre>
</blockquote>
<p>would be</p>
<blockquote>
<pre>for (int i = 0; i < emp.length; i++) {
for (int j = 0; j < dept.length; j++) {
if (emp[i].deptno == dept[j].deptno) {
Synth1 o = new Synth1(emp[i], dept[j]);
System.out.println(o.emp.ename + " works in " + o.dept.dname);
}
}
}</pre>
</blockquote>
<p>This is rather tricky to implement, because the stuff in the middle of the
for loop corresponds to stuff at the top of Rel tree. Each Rel node's
implement method has to handle a callback from a child saying 'I have placed a
row in variable <i>xyz</i>; please generate code to do something with it.'</p>
<p>If two expressions have the same meaning but different calling conventions,
they are not immediately interchangeable. It may be cheaper to evaluate a
particular expression as an array, but another algorithm may find it more
convenient if that expression is a vector. For this reason, there are
special kinds of rule called <dfn>conversion rules</dfn>.
They can convert from one convention to another, but they have a non-zero cost.
The optimizer may decide that it is cheaper to build a vector in the first
place, rather than paying the cost of converting it to a vector later.</p>
<p>There is a special kind of node called a <dfn>Terminator</dfn>
(<code>class {@link saffron.rel.java.Terminator}</code>).
After a tree has been optimized, a Terminator is placed on the root to drive
code-generation. It behaves somewhat like a Rel node (in that it has
inputs, and can be called-back to generate code), but it does not actually
produce any result. (<i>todo</i>: Maybe Terminator should be a calling
convention?)</p>
<h1>Appendix 1: Design notes</h1>
<h2>Syntax of <code>group by</code></h2>
<p>There are several problems with a SQL-like aggregation:</p>
<ol>
<li>If a <code>select</code> statement contains a <code>group by</code> clause,
the validation rules for expressions within that statement are altered: only
expressions which are in the <code>group by</code> can be used outside of an
aggregate function.</li>
<li>Even if there is no <code>group by</code> clause present, aggregation
implicitly occurs if an aggregate function occurs anywhere in the <code>select</code>
statement. For example, every expression in<blockquote>
<pre>select emp.gender.toLowerCase(), emp.name
from emp
where emp.name.startsWith("P")</pre>
</blockquote>
<p>becomes illegal if an aggregation is added:</p>
<blockquote>
<pre>select emp.gender.toLowerCase(), emp.name
from emp
where emp.name.startsWith("P") && min(emp.salary) > 50000</pre>
</blockquote>
<p>This syntax problem could be fixed fairly easily, by requiring an empty <code>
group by</code> clause in such cases.</p>
</li>
<li>If we allow functions on sets to be used as aggregation functions, then
certain statements are ambiguous. Consider the following:<blockquote>
<pre>int count(Object[] a) {
int n = 0;
for (int i = 0; i < a.length; i++) {
if (a[i] != null) {
n++;
}
}
return n;
}
class Emp {
String name;
Person[] dependents;
};
select count(emp.dependents) from emp;</pre>
</blockquote>
<p>It is not clear whether Saffron should return a row for each employee with
the number of the dependents that employee has, or a single number, the number
of employees whose <code>dependents</code> field is not null.</li>
</ol>
<p>The underlying problem is that SQL aggregation makes a scalar expression
behave like a set, and this undermines the usual rules of expression validation
and type-checking. We can make the set explicit, but the resulting expression</p>
<blockquote>
<pre>select deptno,
sum(select emp.sal from emps as emp
where emp.deptno == deptno) as sumSal,
min(select emp.sal from emps as emp
where emp.deptno == deptno) as minSal
from (select distinct deptno from emps) as deptno</pre>
</blockquote>
<p>is more verbose -- the underlying set, <code>emps</code>, is referenced three
times -- and perhaps less efficient.</p>
<p>We need to make grouping an aggregation explicit.</p>
<p>QUEL aggregations are more like scalar sub-queries. They are more verbose. They are also more powerful: note how we can sum only female employees'
salaries. In this syntax, the set of values to be aggregated over (in this case,
<code>select ... from emp</code>) is formed for each aggregate expression; the
optimizer recognizes common expressions and evaluates them only once. Example:</p>
<blockquote>
<pre><code>select distinct </code>emp.deptno,
min(<code>select</code> emp.sal <code>from </code>emps <code>as </code>emp2
<code>where </code>emp2.deptno == emp.deptno) <code>as </code>minSal
sum(<code>select</code> emp.sal <code>from </code>emps <code>as </code>emp2
<code>where </code>emp2.deptno == emp.deptno &&
gender.equals("F")) <code>as </code>sumFemaleSal
<code>from </code>emps <code>as </code>emp</pre>
</blockquote>
<h2>Aggregation types</h2>
<p>Jim Gray et al. [<a href="#GBLP96">GBLP96</a>] classify aggregation operators into 3
categories, in increasing order of complexity:</p>
<ul>
<li><dfn>Distributive</dfn> aggregations requires fixed storage, and two totals can
be merged. Example: <code>sum</code>, <code>count</code>, <code>min</code>,
<code>max</code>. To merge two partial sums, take <code>sum(S1 u S2) =
sum({sum(S1), sum(S2)})</code>. (Here, <code>S1</code> and <code>S2</code> are
the sets of values which formed the partial sums, and <code>S1 u S2</code> is
their union, the set of all values.) <code>min</code> and <code>max</code>
work the same. <code>count</code> is different, in that it cannot be used to
merge two sums; instead, you use <code>+</code>: <code>count(S1 u S2) =
count(S1) + count(S2)</code>.</li>
<li><dfn>Algebraic</dfn> aggregations also require
fixed storage, but two totals cannot be merged. Example: <code>avg</code>,
<code>stddev</code>.</li>
<li><dfn>Holistic</dfn> aggregations require
variable storage. Example: <code>median</code>, <code>countDistinct</code>.</li>
</ul>
<p>Some algebraic aggregates can be decomposed into distributive aggregates, as
follows: avg(S) = sum(S) / count(S). We could provide better
support for these; maybe a new method <code>Expression {@link saffron.rel.Aggregation}.preExpand()</code>, which is called before the parse tree is
converted into a {@link saffron.rel.Aggregate} relational operator.</p>
<p>It is hard to implement holistic aggregations efficiently. For example, <code>
median</code> can be translated into an efficient relational expressions by
hand:</p>
<blockquote>
<pre>select {nth(countEmp / 2, salary) as medianSalary}
group by {emp.deptno}
from (select from emp order by emp.deptno) empSorted
join (select {emp.deptno, count() as empCount}
group by {emp.deptno} from emp) empCounted
on empSorted.deptno == empCounted.deptno</pre>
</blockquote>
<p>Similarly distinct <code>count</code>:</p>
<blockquote>
<pre>select {
empGrouped.deptno,
count(empGrouped.gender) as countDistinctGender}
group by {empGrouped.deptno}
from (
select distinct {emp.deptno, emp.gender}
from emps as emp) as empGrouped</pre>
</blockquote>
<p>We should supply an extender which can transform either the parse tree or the
relational operator tree in such a way.</p>
<h2>Start parameters for aggregations</h2>
<p>Aggregations can take parameters per query, per group, and per row. Examples:</p>
<ul>
<li>Conventional aggregations take parameters only per row.</li>
<li>The nth(count, value), count is per-group, and value is per-row.</li>
<li>In min(collator, value), collator is per-query, and value is per-row.</li>
</ul>
<p>One way to provide per-group parameters is for aggregations to have two sets
of parameters: the first passed at start time, the other passed per row.</p>
<p>But custom aggregations can also do the job. They are a little less efficient,
and the syntax is a little more verbose, but what's going on is clearer.
</p>
<p>Custom aggregation to do locale-specific min:</p>
<blockquote>
<pre>select {emp.dept.deptno,
new LocaleMin(emp.dept.locale).apply(name) minName}
group by {emp.dept}
from emps as emp</pre>
</blockquote>
<h2>Problems with iterators</h2>
<p><i>The ideas in this section are not implemented. So, if your iterator is
infinite, the optimizer may generate a plan which never finishes. And it may
generate a plan which requires iterators to be restarted.</i></p>
<p>Iterators (and enumerations) present peculiarities that finite data sources such as JDBC tables, arrays,
and collections don't present.</p>
<p><b>Restarting an iterator</b></p>
<p>First, they need to be restarted. Suppose the optimizer implemented</p>
<blockquote>
<pre>Iterator nouns, verbs;
for (i in (String[]) verbs intersect (String[]) nouns) {
print(verb + " is both a noun and a verb");
}</pre>
</blockquote>
<p>as a nested loops join,</p>
<blockquote>
<pre>while (nouns.hasNext()) {
String noun = (String) nouns.next();
while (verbs.hasNext()) {
String verb = (String) verbs.next();
if (verb.equals(noun)) {
print(verb " is both a noun and a verb");
}
}
}</pre>
</blockquote>
<p>This doesn't work. The problem is, the second time around the outer loop,
<code>verbs.hasNext()</code> has already returned <code>false</code>.</p>
<p>If possible, you should use a class which implements {@link java.util.Collection}
or {@link saffron.runtime.Iterable}; the optimizer calls the <code>iterate()</code>
method each time it needs to start an iteration.</p>
<p>If you supply an {@link java.util.Iterator}, the optimizer wraps it in a {@link
saffron.runtime.BufferedIterator}.</p>
<p><i>Enhancement</i>: If the plan never requires that the iterator is
restarted, the optimizer should leave the iterator unwrapped.</p>
<p><b>Infinite iterators</b></p>
<p>The second problem with iterators is that they can be infinite. This is a bad
idea if you're copying the results to an array, but you can achieve spectacular
results if you're prepared to go with the whole <i>streaming thing</i>. Here's
an example:</p>
<blockquote>
<pre>class MultiplesOf implements Iterator {
int i, n;
MultiplesOf(int n) {
this.n = n;
this.i = 0;
}
public boolean hasNext() {
return true;
}
public Object next() {
return i += n;
}
public void remove() {
throw new UnsupportedOperationException();
}
}
Iterator twos = new MultiplesOf(2);
Iterator tens = (Iterator) (select from twos where twos % 5 == 0);</pre>
</blockquote>
<p>We have created one infinite iterator from another!</p>
<p>The problem is that the optimizer might be tempted to do stupid things, like
storing the results in an intermediate array. We tell it not to by implementing
an empty interface, {@link saffron.runtime.Infinite}.</p>
<p><i>We have not implemented support for infinite iterators. Expressions
involving infinite iterators might just go on for ever.</i></p>
<h1>Appendix 2: Futures</h1>
<p>List:</p>
<ol>
<li>Aggregation<ol>
<li>Allow built-in aggregations in regular java (that is, outside <code>
select</code> statements with a <code>group by</code> clause). Example #1:
<code>select {deptno, count(select from emps as e2 where e2.deptno ==
e1.deptno) as countEmp} from emps as e1</code>. Example #2: <code>if (count(select from
emps as e2 where e2.deptno == e1.deptno</code>.</li>
</ol>
</li>
<li>Schema on top of persistence layer -- JDO say. Or JAXB. Talk to Castor
folks about it.</li>
<li>Refactoring.<ol>
<li>search for obsolete & deprecated</li>
</ol>
</li>
<li>Demos<ol>
<li>Swing application where you can enter expressions or statements, and
execute them. Can create a set of named connections.</li>
</ol>
</li>
<li>Environment<ol>
<li>log</li>
<li>hsqldb</li>
</ol>
</li>
<li>OpenJava<ol>
<li>Obsolete MSJavaCompiler maybe</li>
<li>Drive compiler from system properties</li>
<li>Drive parser from system properties (or only have one parser, and turn off
saffron features programmatically).</li>
</ol>
</li>
</ol>
<h1>Appendix 3: References</h1>
<dl>
<dt><a name="GBLP96">GBLP96</a></dt>
<dd>J. Gray, A. Bosworth, A. Layman, and H. Pirahesh. Data cube: A relational
aggregation operator generalizing group-by, cross-tab, and sub-totals. In <em>
IEEE 12th International Conference on Data Engineering</em>, pages 152—159,
1996 (<a href="http://research.microsoft.com/~gray/DataCube.doc">doc</a>).</dd>
</dl>
<table border="1" width="100%" class="clsStd">
<tr>
<td>End <i>$Id: //guest/julian_hyde/saffron/doc/overview.html#5 $</i></td>
</tr>
</table>
</html>
</body> | # | Change | User | Description | Committed | |
|---|---|---|---|---|---|
| #5 | 1748 | Julian Hyde |
saffron: convert unit tests to JUnit; add CallingConvention.ITERABLE; lots of other stuff; release 0.1. |
||
| #4 | 1485 | Julian Hyde | Saffron/Mondrian: John Sichi's feedback. | ||
| #3 | 1474 | Julian Hyde |
saffron: Aggregations are working. Renamed 'aggregator' to 'aggregation'. |
||
| #2 | 1467 | Julian Hyde |
saffron: First saffron check-in; incorporate my changes to openjava. |
||
| #1 | 1461 | Julian Hyde |
saffron: First check in. Just documents, and the unmodified OpenJava 20001010 source files. |