What I mean is that if you really want to understand something, the best way is to try and explain it to someone else. That forces you to sort it out in your mind. And the more slow and dim-witted your pupil, the more you have to break things down into more and more simple ideas. And that’s really the essence of programming. By the time you’ve sorted out a complicated idea into little steps that even a stupid machine can deal with, you’ve learned something about it yourself.

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I’m interested in all kinds of languages, so I’d read about multimethods and generic functions in Common Lisp, Clojure and Dylan. Even lesser-known languages like Cecil and Nice. But it wasn’t until I implemented them in my own language that I ran into a seemingly innocuous question: how are they scoped?

This question consumed a great number of showers and morning commutes. I implemented a bunch of different versions and watched them break. What I finally stumbled on is really simple, but… wrong-feeling. This post is an explanation of how multimethods are scoped in Magpie, but also sort of a rationalization since the answer turns out to be “globally”.

But I’m getting ahead of myself. First, let me rewind and set up some preliminaries. OK, maybe a lot of preliminaries. This is a corner of language design that I think few people wander into and previous explorers don’t seem have left a map so maybe there will be some value in this.

What Is Scope?

When you hear “scope” you probably think something like this:

{ int a = 1 ; { int a = 2 ; printf ( "%d" , a ); } printf ( "%d" , a ); }

The curly braces in C++ define block scopes. When you declare a local variable, it goes in the nearest enclosing scope. When the compiler sees a use of a variable (here a ), it looks in the surrounding scopes to figure out what it’s bound to.

Scopes can nest, like you see here. When a variable is defined in multiple scopes, the innermost one shadows the others and wins. So this program will print 2 followed by 1 .

Some languages like JavaScript (before ES6) and C (before C99) don’t have block scope like this. Instead they just have function scope. Each function body can have its own local variables, but there are no nested scopes inside that (unless you actually nest a function in JS). You still have variables outside of functions, so you still have to think about nesting, though.

Both of these kinds of scope have something in common: they use lexical scoping. It’s called that because you can tell what a variable name is bound to just be looking at the text (hence “lexical”) of the program. This is in contrast to dynamic scoping where you can only tell what a name is bound to at runtime. Lexical scoping was one of the big innovations of ALGOL, and almost every language works like it these days.

This is all well and good for scoping variables, but for the sake of this post, I’ll widen the term to talk about any kind of identifier that appears in a program. Variables aren’t the only place names appear in many languages. Consider this bit of JavaScript:

function ( who ) { alert ( who . favoriteColor ); }

Here we have two names in the program (ignoring alert ), who and favoriteColor . We need to figure out what they represent in order to run the code. who is easy, it’s just a lexically scoped variable and we can see that it’s bound to whatever you pass to the function.

What’s about favoriteColor ? Since it comes after a . , that means it’s a property accessor. Each object in JS carries a little bag of named properties around with it. When we do .favoriteColor here, it looks for a property named favoriteColor in that bag at runtime and returns its value. We’ll call this object scope.

Being a prototype-based language, JS is pretty simple here. It only has lexical scope and object scope. Class-based object-oriented languages often have a couple more scopes. Methods will be looked up on the class of the receiver, and there is usually a separate scope for “static” methods.

What Scopes Does Magpie Have?

OK, so we have block scope, object scope, method scope, static scope. There’s lexical scoping and dynamic scoping. Which of these does Magpie have?

Just one: lexical block scope.

Magpie is a class-based object-oriented language, and its syntax is designed to look (more or less) like one. It doesn’t use a dot to separate the “receiver” from the method or property, but it otherwise looks like it would have object, method, and static scope:

list add ( item )

When it’s compiling list add(item) , the variables list and item are looked up in lexical scope like you expect. But the method add is too. In Magpie, methods are not bound to classes. Instead, they are defined separately. If you know C’s model of “structs + functions”, you have roughly the right idea. If you know CLOS or Dylan, you have exactly the right idea.

When you see list add(item) it looks like you’re calling add “on” some list object, but what it really means is “call this add method, passing in list and item as arguments”. It’s the same as add(list, item) in other languages. Magpie just has a syntax that lets you stick the method name in the middle.

In addition, “property accessors” in Magpie are just methods too. So when you see person favoriteColor , that’s just favoriteColor(person) . To compile that, we just look up favoriteColor in lexical scope like you would a variable.

So how far up do these scopes go? In Magpie, each source file is a module and each module has its own top-level scope. There is no single global shared scope. Instead, each module is its own little island that only sees the names that it defines or explicitly imports.

What About Polymorphism?

“Polymorphism” in the object-oriented sense means that the same method can do different things at runtime given different kinds of objects. “Single-dispatch” OOP languages, which are probably what you’re familiar with, achieve this by treating the receiving object (i.e. this ) as a scope. By looking up the method on the receiver at runtime, you get behavior that varies based on that object. Magpie on the other hand, just looks up the method in lexical scope.

If methods aren’t looked up on the object (or on its class), how do we get polymorphism in Magpie? How can I make an add() method that does the right thing given a list, a set, or a map?

The answer is that all methods in Magpie are multimethods. The docs have the full story, but here’s the TL;DR: You can define multiple methods with the same name but different argument patterns, like so:

def ( list is List ) add ( item ) // add stuff to list... end def ( set is Set ) add ( item ) // add stuff to set... end def ( map is Map ) add ( item ) // add stuff to map... end

In C, this would just be an error because the names collide. In Magpie, it’s A-OK. What this does is a create a single add() multimethod that contains those three methods. When you call add() , it looks at the types of the arguments at runtime and picks the right method to call. Instead of using scoping for polymorphism, it essentially uses pattern matching.

Time For a Snack Break

That probably all sounds a bit hand-wavey. Let’s walk through a concrete example and see how all of the moving parts mesh together. First, let’s make a module that defines a class and some methods for it.

// sandwich.mag defclass Sandwich val meat val condiment end def ( sandwich is Sandwich ) isVegetarian sandwich meat == "tofu" end def ( sandwich is Sandwich ) toString "A tasty " + meat + " and " + condiment + " sandwich" end

So we have a class Sandwich . This will also automatically give us getter methods for meat and condiment that will return the appropriate fields given a Sandwich instance on the left. In addition, we add another method isVegetarian . It takes a sandwich and returns true if it doesn’t have any meat in it. Finally, we give it a toString method so you can print it and stuff.

Now let’s make another module that uses this one:

// main.mag import sandwich val sandwich = Sandwich new ( meat : "ham" , condiment : "mayo" ) print ( "veggie? " + sandwich isVegetarian ) print ( sandwich )

Seems pretty simple, right? It turns out that not binding methods to classes leads to a couple of subtle but deep problems. (At least they were subtle to me. I didn’t realize them until I’d implemented the intepreter and ran straight into them.)

These problems all turn out to be related exactly to the original question of this post, how methods are scoped, and solving them is what led to Magpie’s current (and perhaps surprising) answer.

The First Problem: “Overriding” Methods

So what happens when we run this example? Let’s say for now that methods are scoped just like variables, which is how Magpie used to work. We’ll walk through it a line at a time.

import sandwich

This takes all of the top-level variables and methods in sandwich.mag and binds them to the same names in main.mag . After that Sandwich , meat , condiment , isVegetarian , and toString are all available for use.

val sandwich = Sandwich new ( meat : "ham" , condiment : "mayo" )

This creates a new Sandwich instance and stores it in a variable sandwich .

print ( "veggie? " + sandwich isVegetarian )

This calls isVegetarian . We’ve imported that method, so there’s no problem here. Now consider the last line:

print ( sandwich )

print() is a built-in method that takes an object, converts it to a string by calling toString on it, and then displays it. “Built-in” just means it’s defined in another core module and is automatically imported, so we do indeed have access to it from main.mag . So we call it and pass in the sandwich. What happens next?

What doesn’t happen is that it doesn’t call the toString that we actually defined for Sandwich . That method is scoped to sandwich.mag . We imported it into main.mag so we could call it there. But we aren’t calling toString in main.mag . It’s being called from print , which is in core . It has no idea there’s this other toString method specialized for sandwiches because the toString multimethod core knows about is unrelated to the one sandwich.mag and main.mag have.

Ouch. Our intent in sandwich.mag is that defining toString would work like overriding in other OOP languages. Any place that is calling toString should see that new specialization even if it hasn’t directly imported the module that contains it.

The First Solution: Shared Multimethod Objects

My fix for this was to change what it means to import a multimethod. In our little example, the import graph is like:

core ^ |\ | \ | sandwich | ^ | / |/ main

main.mag imports sandwich.mag and they both also (implicitly) import core . Core itself contains a toString method with specializations for the atomic types like numbers and strings.

The first fix was that when you import a method, you import the exact same multimethod object. So sandwich.mag imports the toString multimethod from core . When it then defines a new (sandwich is Sandwich) toString specialization, that goes into the exact same multimethod that core is using. There is basically a single toString object in memory that all of those modules have a reference to.

This works because core is the first module that created it, and our other two modules are both importing it. So every place that’s using toString has a path of imports that ultimately traces back to the root in core .

The Second Problem: Colliding Imports

Problem solved, right? Well, not so fast. After I did this, I ran into the next issue. Here’s another example. We’ve got these two modules:

// pal.mag defclass Pal val name end // pet.mag defclass Pet val name end

They both define classes that have name fields. That means they both implicitly create name methods. Then we use them:

// main.mag import Pal import Pet def greet ( who ) print ( "Hi, " + who name + "!" ) end greet ( Pal new ( name : "Fred" )) greet ( Pet new ( name : "Rex" ))

The intent here is clear: greet() should be able to print anything that has a name getter. What happens if we run this with our current semantics? It turns out we don’t get very far.

The import Pal line works fine. It brings Pal and name into main.mag . Then the second import comes along. It defines Pet fine, but there’s already a name multimethod defined now. We have a name collision.

We didn’t have a name collision in the first example. Even though toString got imported into main.mag both from core and sandwich.mag , they were the exact same object, so we could just safely ignore it. Here, though, that isn’t the case. The import graph is like:

pal pet ^ ^ \ / \/ main

There is no root module where a single name multimethod is being created. Instead, pal.mag and pet.mag both create their own unrelated name multimethods. When main.mag tries to import them both, they aren’t the same object, so they collide.

The Second (Failed) Solution: Just Deal With It

My first stab at “fixing” this was to just declare those semantics are How It Should Be. If you have colliding method names, you just rename on import, like:

// main.mag import Pal with name as pal . name end import Pet with name as pet . name end

That works, but it’s really ugly. I found in practice that method collisions were surprisingly common, almost always coming from fields with simple names like name . Having to qualify those at every use site sucks:

greet(who) print("Hi, " + who pal.name + "!") end

Worse, it breaks duck typing. Using this scheme, there’s no way to create a single greet() method that works on both pets and pals since there isn’t a single name method it can call on both.

The Third (Failed) Solution: Do Something Really Complex

At first, I tried to fix this by doing some hairy method merging when you imported. If you had a method name collision on import, it would create a new local multimethod object that contained all of the specializations of both of the ones you’re importing. That fixes the above problem. main.mag will end up with one name method that can accept both pals and pets.

But it unfixes the first problem. If you import a multimethod (like toString in the first example) and then add a new specialization, you need to push that specialization back up to the modules that you imported.

So to get that working, I made it track where you had all of the modules you had imported a multimethod from. When you defined a new specialization, that would get pushed back up to those modules too.

This did sort of work, but it was complex, felt brittle, and was hard to reason about.

The Fourth Solution: Go Global

I spent a lot of time thinking about it and finally asked if there was a radically simpler answer that would work. One came to mind: make methods globally scoped.

Any time you define a method, in any module, it would just go into a single global pool of multimethods that all modules share. Overriding works, because you’re always overriding: there is only a single multimethod with a given name across the entire program. Duck typing works for the exact same reason.

But global scope is bad, right? I felt like I was committing some cardinal sin by even contemplating this. After much gnashing of teeth, I concocted a rationalization for why this might not be so bad. Here goes…

Consider your favorite conventional OOP language. We’ll do Ruby because it looks nice here:

class Cow def speak () puts "moo" end end class Dog def speak () puts "woof" end end

We have two classes that both define speak methods. We don’t think of speak as being “global” here because you get to the speak methods through an instance of Cow or Dog . Once you do, the method will correctly be associated with the right type and do the right thing. You can’t call Dog ‘s speak on an instance of Cow or some other unrelated type. Likewise, if you don’t have a dog or a cow, you can’t get to speak at all.

Now consider the Magpie equivalent, and assume that multimethods are globally scoped:

defclass Cow end def ( is Cow ) speak print ( "moo" ) end defclass Dog end def ( is Dog ) speak print ( "woof" ) end

How does it compare? Like the Ruby solution, you can’t call Cow ’s speak method using a Dog or some other type. If you don’t have a dog or a cow, you can’t get to speak at all.

What this means is that the multimethod is globally scoped. But actual specializations, the stuff you care about, functionally aren’t. Since they are specialized to types, if you don’t have an object of that type, you can’t get to the method. The multimethod is sitting there in global scope where anyone can get to it, but unless you have the key (an object of the right class), you can’t crack it open and get at the methods.

In other words, globally scoped multimethods in Magpie are isomorphic to methods in a single dispatch language. Actually, that’s only half true. Single-dispatch languages only support a subset of what multimethods let you do. Magpie can also express a bunch of stuff that single-dispatch languages can’t.

Better than Monkey-Patching

Multimethods match on all of their arguments, not just the “receiver” on the left-hand side. Let’s go back to our Ruby example. Say we need to serialize Dogs and Cows to a stream. Since classes in Ruby are open for extension, we can do:

class Dog def serialize ( stream ) stream write ( "dog" ) end end class Cow def serialize ( stream ) stream write ( "cow" ) end end

Swell. But then someone else on our team gets tasked with making dogs and cows support serializing to XML. If they aren’t aware of our monkey-patch and add:

class Dog def serialize ( xmlWriter ) xmlWriter write ( "<dog></dog>" ) end end class Cow def serialize ( xmlWriter ) xmlWriter write ( "<cow></cow>" ) end end

Then those serialize methods will obliterate the ones for writing to a stream. Or maybe the other way around. It depends on whose code gets to run last. Nasty.

Meanwhile, in Magpie:

def ( dog is Dog ) write ( stream is Stream ) stream write ( "dog" ) end def ( cow is Cow ) write ( stream is Stream ) stream write ( "cow" ) end def ( dog is Dog ) write ( writer is XmlWriter ) writer write ( "<dog></dog>" ) end def ( cow is Cow ) write ( writer is XmlWriter ) writer write ( "<cow></cow>" ) end

Here, there is no collision at all. When you call write , it will look at both the left-hand argument (a Cow or a Dog ) and the right-hand side (a Stream or an XmlWriter ) and pick the one perfect method for those types.

This means you can effectively “monkey-patch” with much finer-grained control and less chance of collision. The entire argument signature forms a key that’s used to select the right method. If you don’t want people to accidentally hit your specific method, just ensure that it requires an argument of a type that’s hard to get a hold of.