Ah ha! You're totally right. I totally forgot about using inheritance to deal with overlapping patterns even though I use it all the time in Java (you could do the same overlap with open unions, but there's other ergonomic reasons you don't want to do that if you have exhaustiveness checking.)
> In an OO language, the reason you'd prefer the Visitor pattern to downcasting is that it allows extending behavior by simply declaring new subtypes, instead of having to edit the central evaluator. This is why I keep insisting that the Visitor pattern is about double virtual dispatch, not about discriminated unions.
I don't think that's true. If you give up statically checked combinations I don't think you need double dispatch at all.
Here's a version that does everything with downcasting (and the accompanying error). One class has disappeared altogether because we don't need them anymore (ComplexExpression) and we don't need any classes for the evaluators (other than a container to hold them as a sort of utility class with a bunch of static methods). And we don't have visitors at all.
And it represents Addition(Multiplication(1, 2), 3) just fine.
Am I missing something here?
// ------ BEGIN : In some external library
interface Expression { // This could be empty
}
record Literal(int n) : Expression {}
record Addition(Expression x, Expression y) : Expression {}
// Your evaluator doesn't even need to be a true class anymore and can just be
// a bag of static methods
// You could if you wanted to, but there's isn't a lot of value
class BuiltInEvaluators {
public static string StringEvaluator(Expression expression) {
switch(expression) {
case Literal literal: return literal.n.ToString();
case Addition addition: return $"{StringEvaluator(addition.x)} + {StringEvaluator(addition.y)}";
// You could remove this boilerplate if you wanted by wrapping this in a true class
// and then throwing the exception in a wrapper method
default: throw new ArgumentException("Expression incompatible with evaluator!");
}
}
public static int ExecutionEvaluator(Expression expression) {
switch(expression) {
case Literal literal: return literal.n;
case Addition addition: return ExecutionEvaluator(addition.x) + ExecutionEvaluator(addition.y);
default: throw new ArgumentException("Expression incompatible with evaluator!");
}
}
}
// ------- END : No longer in some external library
// ------- BEGIN : My own code
record Multiply(Expression x, Expression y) : Expression {}
class MyOwnEvaluators {
public static string ExtendedStringEvaluator(Expression expression) {
switch(expression) {
case Multiply multiply: return $"{ExtendedStringEvaluator(multiply.x)} * {ExtendedStringEvaluator(multiply.y)}";
case Expression x: return BuiltInEvaluators.StringEvaluator(x);
default: throw new ArgumentException("Expression incompatible with evaluator!");
}
}
public static int ExtendedExecutionEvaluator(Expression expression) {
switch(expression) {
case Multiply multiply: return ExtendedExecutionEvaluator(multiply.x) * BuiltInEvaluators.ExecutionEvaluator(multiply.y);
case Expression x: return BuiltInEvaluators.ExecutionEvaluator(x);
default: throw new ArgumentException("Expression incompatible with evaluator!");
}
}
public static string HexadecimalEvaluator(Expression expression) {
switch(expression) {
// Our only interesting case
case Literal l: return l.n.ToString("x");
case Expression x: return ExtendedStringEvaluator(x);
default: throw new ArgumentException("Expression incompatible with evaluator!");
}
}
}
// ------- END : My own code
Well, one thing that this solution misses is virtual dispatch - HexadecimalEvaluator won't work for Addition(Literal(1),Literal(2)) for example, because ExtendedStringEvaluator doesn't know to call HexadecimalEvaluator back.
Still, this is easily fixable by transforming the static functions into virtual methods on a class:
//keeping all of the definitions so far the same
class ExtendedStringEvaluator : BuiltInEvaluators.StringEvaluator {
public override string visit(Expression expression) {
switch(expression) {
case Multiply multiply: return $"{ExtendedStringEvaluator(multiply.x)} * {ExtendedStringEvaluator(multiply.y)}";
default : return super(expression);
}
}
}
class HexadecimalEvaluator : ExtendedStringEvaluator {
public override string visit(Expression expression) {
switch(expression) {
case Literal literal: return return l.n.ToString("x");
default : return super(expression);
}
}
}
Still, this switch on the class type is essentially exactly a virtual call on the type of Expression, just controlled by someone other than the original class. That is, the Expression doesn't "know" any more that it is being visited, so you couldn't create a LoggingExpression let's say. On the other hand, the Visitor now has more control over the way it interprets expression subtypes. So even here we are doing double dispatch: we are dispatching manually based on the runtime type of `expression`, and then allowing the language to dispatch based on the runtime type of `this`.
> Well, one thing that this solution misses is virtual dispatch - HexadecimalEvaluator won't work for Addition(Literal(1),Literal(2)) for example, because ExtendedStringEvaluator doesn't know to call HexadecimalEvaluator back.
Ah of course, I accidentally switched back into closed recursion rather than open recursion (that was ExpressionOpen). This indeed is exactly analogous to early binding vs late binding. You can't exactly write the same form of open recursion I wrote earlier because C# doesn't have higher-kinded generics (so for example you can't write
), but that's a language-specific thing. If you had higher-kinded generics you could exactly model virtual dispatch with open recursion because they're the same thing.
> That is, the Expression doesn't "know" any more that it is being visited, so you couldn't create a LoggingExpression let's say. On the other hand, the Visitor now has more control over the way it interprets expression subtypes. So even here we are doing double dispatch: we are dispatching manually based on the runtime type of `expression`, and then allowing the language to dispatch based on the runtime type of `this`.
You can call it visitor, but at this point it really is the same as discriminated unions (indeed this is exactly analogous to the first iteration of code just without the last bit to ensure that combinations matched up). And you can exactly replicate `LoggingExpression` in the evaluator, there is no difference in expressivity.
This shouldn't be surprising; after all the whole thing that kicked off all of this is that there is an isomorphism between discriminated unions and the visitor pattern. It should not be a surprise that it is possible to interpret one in the other.
My point at the beginning of all this was to object to the statement that this was not an isomorphism. Anything you can do with the visitor pattern you can do with discriminated unions and vice versa. The only differences are in ancillary language support (e.g. virtual dispatch and higher-kinded generics). Hence in a very real real sense the visitor pattern is just discriminated unions and vice versa.
The only preference for one or the two comes down to issues of code size and maintenance.
Ah ha! You're totally right. I totally forgot about using inheritance to deal with overlapping patterns even though I use it all the time in Java (you could do the same overlap with open unions, but there's other ergonomic reasons you don't want to do that if you have exhaustiveness checking.)
> In an OO language, the reason you'd prefer the Visitor pattern to downcasting is that it allows extending behavior by simply declaring new subtypes, instead of having to edit the central evaluator. This is why I keep insisting that the Visitor pattern is about double virtual dispatch, not about discriminated unions.
I don't think that's true. If you give up statically checked combinations I don't think you need double dispatch at all.
Here's a version that does everything with downcasting (and the accompanying error). One class has disappeared altogether because we don't need them anymore (ComplexExpression) and we don't need any classes for the evaluators (other than a container to hold them as a sort of utility class with a bunch of static methods). And we don't have visitors at all.
And it represents Addition(Multiplication(1, 2), 3) just fine.
Am I missing something here?