The Expression Problem and its solutions (2016)
eli.thegreenplace.net
eli.thegreenplace.net
If I have O operations (e.g. evaluate, stringify) and T types, then I need O•T implementations. If I fix O, I can add types until the cows come home by adding O implementations per new type. If I fix T, I can add new operations with T implementations per operation. If I want to let O and T vary, then the number of implementations I need to add per additional operation/type varies depending on what I’ve added before. No amount of programming language magic will change this basic count.
ISTM what’s really going on in the article is that the author is using the programming language as a registry of implementations. Those O•T implementations need to be stored somewhere so their callers can find them. In C++ this can be done when very verbose inheritance and virtual calls. In other languages, it’s less verbose. If multiple dispatch is built in, then one can use it directly. One can, of course, also build an actual table indexed on operation and type as a data structure in just about any language and use it, and in a language like C++ the result may well be quite a bit nicer than using a class hierarchy.
[1]: https://craftinginterpreters.com/representing-code.html#the-...
In practice, Multiple Dispatch shines when you have 1) more than one argument type (duh) 2) higher order `O` operation [1]
[1]: think of a numerical routine that calls eigen or something, and you want eigen to exploit the matrix's type, such as symmetry or upper-triangular, and this is encoded as a matrix type)
I don't understand what problem the author is trying to solve here - maybe it's language specific? More related to dynamic typing and efficient dispatch?
In any case, operator overloading, while it can make for cute-to-read code, isn't really a good idea for code readability and maintenance.
The expression problem only arises in statically typed programming languages, it does not exist in dynamically typed programming languages.
Operating overloading has nothing to do with the problem and can not be used to resolve it. Operators are nothing more than a one-off syntax so we can use familiar childhood notation like a + b, etc... they are not particularly meaningful. The ability to overload operators or functions in general is also irrelevant since such overloads are resolved statically at compile time.
Wadler's list of requirements for solving the expression problem include "with static checking that all cases are covered", so in one sense, yes, dynamic languages don't have this "problem". But in another sense, dynamic languages simply have no chance to solve the problem because they don't statically check anything.
It is true that it's much easier to do multiple dispatch and open-ended extension in dymamic languages. That's a nice benefit of them. But you do sacrifice all of the safety, code navigation, and performance of static types in order to get that.
The problem Wadler is trying to solve is "how can we have this sort of open-ended extension in both directions without giving up static safety?"
That's an interesting point in the design space where you get the flexibility of dynamic types (and multiple dispatch!) and good runtime speed. But you pay for it with slower startup times, less predictable performance, and much higher memory usage. You are also married to a JIT. Julia really is designed to be run interactively in a REPL from source. The language isn't well-suited to compiling a standalone executable ahead of time. That makes perfect sense for its use cases, but would make it a challenge to adopt in other use cases.
(For example, I work on Dart which is mostly used for building mobile apps. That means we care deeply about executable size, startup speed, and the ability to compile ahead-of-time to native executables.)
The "problem" exists for dynamically-typed languages as well. If you define a new class in Python, you still need to teach existing code how to operate on it (though you might be using inheritance to automatically derive some of those implementations, but inheritance obviously isn't limited to dynamic languages).
You've got T types (some new), and O operators (some new) and want to implement all operators for all types ... This is the exact definition of operator overloading.
There is no magic (other than inheritance or generics, if applicable) that will remove the need to individually implement all those O x T cases, and while that is obviously necessary, it is also all that you need to do.
If you are not talking about operator overloading - supporting the same operator for multiple different custom types, then what are you talking about ?!
so should we write `add_int_int(1,1)` and `add_int_double(1, 1.0)` and `add_double_double(1.0, 1.0)`?...
Applying arithmetic operators to non-arithmetic types starts to become a problem, even if some cases (set union/difference, string catenation) are natural...
The same goes for other operators... overloading '[]' indexing for maps as well as arrays seems natural, but would be highly confusing if you overloaded it for something unrelated to an index-like concept.
I think there are two alternate guidelines for use of operator overloading that would make sense.
1) Just don't overload operators at all for your own types! Leave that to the standard libraries and types that they define.
OR
2) Overload, but keep to the semantics of the operators as used by the language's built-in types (e.g. use arithmetic operators for arithmetic operations, comparison operators for ordering operations, etc). If your project was using a style guideline like this, then violations would be caught by code review (maybe automated by AI in the future?).
This requires unsafe casting and thus doesn't actually solve the expression problem, which is about how to do this without compromising safety. Your approach is what the solution to the expression problem in Haskell effectively does at runtime though, via type classes and the dictionary-passing translation that they undergo during compilation, but it's all type safe.
No - in C++ you'd just define the operators (either as global functions, or member functions of the types/classes in question), and the language's overload resolution rules would select the right implementation for each usage.
You could use inheritence (and virtual overrides if needed), or templates/generics, if you wanted to - C++ certainly gives you a lot of ways to make things more complex and shoot yourself in the foot, but the normal/obvious way would just be to define the overloaded operators and be done with it.
Virtual methods overload the corresponding method in the parent class they are inheriting from. It could be a named method like "add()", or an operator like "+()".
The author of that comment is implicitly assuming that all types are derived via inheritance from a common base type that defines all the (virtual) methods/operators being overloaded.
Overuse of inheritance is one of the ways to shoot yourself in the foot with C++. If you want to overload (apply same operator to multiple types - related or not), then just overload - don't use inheritance.
Your own example, above (B defines new type, C defines new operator) doesn't appear to be about inheritance at all - you don't even say what language you are talking about, and elsewhere you say (contracticting the article author) that this "expression problem" only applies to dynamic languages ... you seem to be all over the map on this one!
The problem statement is: You have code (e.g. a library) that supports polymorphic operations on a range of types. It is called the “expression problem” because the prototypical example is to have a type representing an expression (like an arithmetic expression) that can have various forms (subtypes, not necessarily in the OOP sense), and there are operations like evaluating the expression or printing the expression, which of course need to be implemented for all those subtypes (you need to know how to print a constant, how to print a binary expression, and so on).
There is code that can take an arbitrary expression whose exact subtype will only be known at runtime, and which invokes one of the available operations on the expression object.
Now, you want to be able to write secondary libraries (or programs) that extend the first library by extending the set of subtypes and/or the set of operations, but without modifying the first library (and without duplicating code from the first library). With OOP inheritance, adding new subtypes is easy. With the visitor pattern (or equivalent runtime case-distinction mechanisms like pattern matching in functional languages), adding new operations is easy. But the combination of both is difficult, if not unsolvable.
Overloading doesn’t apply, because overloading would dispatch on the static type of the expression variable, but the use case is that this is an expression parsed from a textual representation at runtime (e.g. in the context of an interpreter or compiler, or maybe some data format parser), so the variable holding the expression object has a generic type and could be holding any expression.
If the problem statement is just how to add operators and types to a dynamically typed expression (in some arbitrary language), then in addition to implementing any new operator overloads, there is the question of how to dispatch, which would most obviously be done by mapping (operator, operand type) pairs to the registered type-specific operator implementation (aka overload). Again, not sure what the big deal is here.
You are likely mixing up the term overload with the term override.
Mechanism vs functionality.
Static (compile-time) guarantees are only applicable to languages with static binding rules, in which case there is no problem - the compiler will just report "cannot resolve overloaded function" or something similar.
This is of course one of the downsides to languages with dynamic types and dynamic binding ... that many errors can only be detected at runtime.
Object algebras: https://i.cs.hku.hk/~bruno/oa/
Tagless final: https://okmij.org/ftp/tagless-final/course/lecture.pdf
and Data types a’la carte: https://webspace.science.uu.nl/~swier004/publications/2008-j...
In languages that do not allow that (e.g. Java), one has to implement it by hand, using a Visitor pattern. Instead of relying on the language to do the dynamic dispatch, one has to explicitly add a visiting method for another data type.
To me, the turn towards interfaces / typeclasses / traits / protocols is one of the most notable bits of progress in the newer crop of programming languages (and, importantly, their standard libraries).
I really recommmend giving this a read: https://craftinginterpreters.com/representing-code.html#the-...
The problem as explained in what you linked:
> an object-oriented language wants you to orient your code along the rows of types. A functional language instead encourages you to lump each column’s worth of code together into a function.
The point was that the final protocol implementation in Clojure solves this. There is no more lumping. The whole thing is freeform. You can extend an existing record (say it's coming from a library or somewhere outside your control) and add interfaces. Or you can make a new record and implement all the existing interfaces
On the other hand, Rust / Haskell provide partial solutions with static typing — but run into annoying boilerplate related to the orphan rule.
I’m not sure if there’s a true solution, given the level of thinking which has gone into these two forks in the road.
> run into annoying boilerplate related to the orphan rule
I always forget this, but it's not an orphan if you put the instance in the same module as the class definition (as opposed to bundling it with a newtype elsewhere). Class definitions and instances would go in Evaluatable and Stringable.
In Clojure, if in your application you extend a record (say from some library) and implement a new protocol, you've effectively implicitly created a new extended record type. In Clojure that happens transparently b/c its dynamic. In the static typing scenario you have to explicitly create this "extended type" that has the parent type and also implements the new protocol. You'd then explicitly use ExtendedRecordA. It can still be used where the parent was expected.
That's more verbose but maybe manageable.. Now if you have multiple libraries extending one record with different protocols .. and then you have a library/application where you included all these libraries. You want to use all these protocols from that one record.. how do you not do that? you'd need some aggregation step to make ExtendedRecordA and ExtendedRecordB and ExtendedRecordC all come together under some new super-type that has all the protocols. It's not impossible but it's just messier
The Expression Problem and its solutions - https://news.ycombinator.com/item?id=11683379 - May 2016 (49 comments)
I think Antlr 4 does similar, I just haven't used it in as much anger because its runtime always jammed me up https://github.com/antlr/antlr4/blob/4.13.2/doc/listeners.md...
I thought that IntelliJ did similarly but I am misremembering since they generate recursive descent style https://github.com/JetBrains/Grammar-Kit/blob/v2023.3/HOWTO....
This is in contrast to if you had used an enum (sum type) instead, wherein adding a new operation is easy and can be done in a single place. But then in exchange, adding new variants requires going around and updating every existing pattern match to support the new variant.
I know inheritance has its own severe problems, but adding a generic abstract method at the base class could create reusable code that can be accessed by any new class that inherits from it.
P.S. ah ok, it's mentioned in the article at the Visitor section.
As I understand the Expression problem, the limitation of programming languages is that they force you to modify the previous existing types even if the new behavior is a generic method that works the same for all types, so it should be enough to define it once for all classes. A virtual method in the base class should be able to do that.
This does not solve the issue at its core, I think.
That seems like a pretty ok 90% solution, and in a lot of ways cleaner and more well defined a way to grow your types anyhow.
We use this pretty effectively in our iOS app to model and implement Effect types in a functional core / imperative shell architecture.
It's refreshing to see this very clear problem statement, which feels like an ideal anti-thesis that reveals the hidden glory of Rust's traits/impls:
> It turns out that adding new operations isn't as easy as adding new types. We'd have to change the Expr interface, and consequently change every existing expression type to support the new method(s). If we don't control the original code or it's hard to change it for other reasons, we're in trouble.
> In other words, we'd have to violate the venerable open-closed principle, one of the main principles of object-oriented design, defined as:
> software entities (classes, modules, functions, etc.) should be open for extension, but closed for modification
Apologies for the self link, but this came up very recently in a sub thread about Rust & I'm so glad to close the loop & find a name for this. I said there & I'll say again, I think this is one of Rust's Greta superpowers, that we are not trapped by the design parameters of the libraries we consume, that Rust allows us to layer in more and more to our types, as we please. An amazing superpower of Rust that imo gets way too little attention, where-as the borrow-checking tends to soak all the attention/fixation for the language. https://news.ycombinator.com/item?id=45041286#45045202
There's a whole chapter of the Rust book on Rust & OOP, btw, which provides a side-ways look at how Rust & OOP and the Expression Problem relate. https://doc.rust-lang.org/book/ch18-00-oop.html
C# and others have extension methods, where you can add operations. But most of the language & it's use is pretty conventional OOP; it's a feature not the core. Mentioned in the thread above, there's a claim that Standard ML functors have similarities to rust: I haven't investigated yet but that'a piqued my interest & I'm eager to find out at some point!
The expression problem is about being able to extend both data types (new cases) and operations (new functions) without modifying existing code while preserving static type safety.
C#'s extension methods can't be virtual, so you can't use them to actually add any new operations which can be dispatched on. They're just syntactic sugar for adding static methods which in non-OOP languages can be accomplished by declaring a free function.
Rust traits let you add new types (just impl the Trait), but it doesn't let you add new functions, so it doesn't do anything to solve the problem.
Each data type is a `struct`. Each operation is a trait. You `impl` each trait on each struct.
This works even if you're using a library that has declared `struct A` and `struct B` and `trait F` and `trait G`, and you want to add both a `struct C` and a `trait H`, and fill out the whole 3x3 grid without modifying the library.
The library says:
struct A { ... }
struct B { ... }
trait F { ... }
impl F for A { ... }
impl F for B { ... }
trait G { ... }
impl G for A { ... }
impl G for B { ... }
fn some_function<T: F + G>(data: T) { ... }
use library::{A, B, F, G};
struct C { ... }
impl F for C { ... }
impl G for C { ... }
trait H { ... }
impl H for A { ... }
impl H for B { ... }
impl H for C { ... }
fn another_function<T: F + G + H>(data: T);
What you've done is different, you've simply added a new trait entirely. That's not unique to Rust, you can add new interfaces in any language...
Supposing we started off with a trait for expression nodes:
pub trait ExprNode { fn eval(&self, ctx: &Context) -> Value; }
pub trait CanValidate { fn validate(&self) -> Result<(), ValidationError>; }
pub struct Expr<N> { root: N, ctx: Context }
impl<N: ExprNode> Expr<N> {
pub fn eval(&self) -> Value { self.root.eval(&self.ctx) }
}
impl<N: CanValidate + ExprNode> Expr<N> {
pub fn validate(&self) -> Result<(), ValidationError> { self.root.validate() }
}
To me it looks like this is exactly the expression problem. The expression problem is not about adding methods to a trait, it's about adding an operation to a set of types. In this case every operation is defined by a single trait.
The idea behind the expression problem is to be able to define either a new operation or a new type in such a way that the code is nicely together. Rust trait system accomplish this beautifully.
> That's not unique to Rust, you can add new interfaces in any language...
Many languages have interfaces, but most of them don't allow you to implement them for an arbitrary type that you have not defined. For example, in Java, if you create an interface called `PrettyPrintable`, but you can't implement it for the `ArrayList` type from the standard library. In Rust you can do this kind of things.
Rust does let you impl traits for types or traits that are inside of your crate, so your example strictly speaking works, but it does not let you impl traits if both the type and the trait are not inside of your crate. This is known as the orphan rule:
https://doc.rust-lang.org/reference/items/implementations.ht...
As the article points out, the expression problem itself is pretty simple to solve for code that you control, it's when writing modular software that can vary independently that gives rise to issues.
The orphan rule only disallow impls if both the trait and the type are defined outside the crate.
But in this example if you are adding a new type (struct) or a new operation (trait), well this new item should be in your crate, so all the impls that follow are allowed.
The goal isn't to allow a new type to work for an existing implementation of a function nor is it to take an existing type and write a new function that works with it. In the proposed solution you have `some_function` and the author claims that this solves the expression problem because you can take a new type C and pass it into some_function. Pretty much every language has a way to define new types and pass them into existing functions.
The goal is to allow for that new type, C, to have its own implementation of `some_function` that is particular to C, as well as the ability to write new functions that can be specialized for existing types. In particular we want calls to `some_function` through an interface to call C's specific implementation when the runtime type of an object resolves to C, and calls whatever other implementations exist when called through another interface.
The author's solution doesn't do that, it literally does nothing that you can't do in pretty much any other language.
struct Constant { value: i32 }
struct BinaryPlus { lhs: i32, rhs: i32 }
trait Evaluate {
fn evaluate(&self) -> i32;
}
impl Evaluate for Constant {
fn evaluate(&self) -> i32 { self.value }
}
impl Evaluate for BinaryPlus {
fn evaluate(&self) -> i32 { self.lhs + self.rhs }
}
// Adding a new operation is easy. Let's add stringify:
trait Stringify {
fn stringify(&self) -> String;
}
impl Stringify for Constant {
fn stringify(&self) -> String { format!("{}", self.value) }
}
impl Stringify for BinaryPlus {
fn stringify(&self) -> String { format!("{} + {}", self.lhs, self.rhs) }
}
// How about adding new types? Suppose we want to add FunctionCall
struct FunctionCall { name: String, arguments: Vec<i32> }
impl Evaluate for FunctionCall {
fn evaluate(&self) -> i32 { todo!() }
}
impl Stringify for FunctionCall {
fn stringify(&self) -> String { todo!() }
}Assuming the whole Stringify section goes into a new file (likewise with FunctionCall) then I agree that this solves the expression problem.
The problem is that you can't add new methods to an existing class.
In C++ classes, you have to be able to modify a class definition to extend it with new methods (or a new ancestor to multiply inherit from).
If your answer doesn't start with an "m" and end with a "ethod", then you may need to re-read the Rust book found here:
If you add a method to a trait, every implementation of that trait has to be modified in the original source code. The point of the expression problem is that you want to be able to add new operations in a way that is type safe and checked for completeness, even if you don't have access to the original source code.
Rust can probably do this, because its traits are equivalent to Haskell type classes and those have a solution to the expression problem, but it's not trivial. See the link in the article.
The problem you describe makes no sense. It sounds like, for example, wanting to add a new variant to an enum while also not wanting to modify match statements which now fail exhaustive testing. That’s a direct contradiction.
The only sensible charitable interpretation I can come up with is that you want to add new methods to a type without having to update any existing type definitions. This is what traits do.
No, that's not sufficient if done naively as I think you're describing. You seem to be missing the context of this discussion as described by the article. Other code already depends on the current compiled abstraction, and you want to extend it in various ways, safely, so that existing code continues to work without recompilation, but you can extend the abstraction that code is already safely handling with new types and new operations without modifying the original source code.
If you want to add a new node type to an AST, with algebraic data types you would have to modify the original source code of the original functions that match on those types, so types are closed to extension. You can leave the type open to extension via traits, but now the operations are closed to extension without modifying the original source code.
> It sounds like, for example, wanting to add a new variant to an enum while also not wanting to modify match statements which now fail exhaustive testing. That’s a direct contradiction.
No it's not, if enums and match statements were safely open to extension rather than closed. That's exactly what would solve the expression problem. This can and has been done [1] as the article described, via multimethods or via lifting data constructors to the type class level. It's obtuse and awkward, but in theory it doesn't have to be.
The ultimate goal is that the new type and/or pattern matching cases have to be provided together to cover all of missing combinations, but importantly "together" means by the time the final program is assembled and not in the source code that defined the original types or operations.
[1] open pattern matching and open algebraic data types have also been done in research languages
That is exactly what a new trait would accomplish. I remain confused as to the distinction you are making.
https://eli.thegreenplace.net/2018/more-thoughts-on-the-expr...
data Constant = Constant Double deriving (Show)
And there's typeclasses. Show is a typeclass. You can think of them as interfaces, so `instance Sqlite DB where open dsn = ...` is a bit like saying Sqlite is an implementation (instance) of the DB interface (typeclass). The typeclass itself could be defined like `class DB where open :: String -> IO ()` meaning the interface requires a function taking a string and having IO access (and of course you can require more than one function in your interface/typeclass).
The article also uses typeclasses with parameters. Parameters (and functions and variables) are written lowercase, while classes and constructors and such are capitalized, so
class (Expr e) => Stringify e where
stringify :: e -> String
instance Stringify Constant where
stringify (Constant x) = show x
I’m not trying to prove that rust is better or something. People who do that are annoying. It’s just weird to me that this is being presented as a fundamental and largely unsolved challenge when there is a simple solution at the heart of a widely deployed and well known language, which in turn stole it from elsewhere.
[1] https://doc.rust-lang.org/reference/items/traits.html#dyn-co...
------------
Say, you want to write a simple language interpreter.
You have an `Expr` enum (sum type), with say, a `Constant(f64)` and a `BinaryPlus(Expression, Expression)`.
You can easily add a new function expecting an `Expr` indeed, but if you were to add a new variant to the `Expr` enum, you would have to go through the code and change every use site.
You can solve the issue by simply making a `struct Constant` and a `struct BinaryPlus`. Now you can just define a new trait for both of them, and you can use that `dyn trait` in your code -- you can add new functions and also new types without code change at use site!
So what's the issue?
In Haskell, a logic like
```
func example(runtime_val: f64) -> Expr {
if (runtime_val is someRuntimeCheck())
return Constant(..)
else
return BinaryPlus(.., ..)```
can't compile in itself as `Expr` is a type class (=trait). Basically, in this mode Haskell awaits a concrete implementation (we actually get the exact same behavior with `impl Expr` in Rust), but here is my confusion: this can be circumvented in Rust with dyn traits..
Here is my (very ugly due to just hacking something together while pleasing the borrow checker) code showing it in Rust: https://play.rust-lang.org/?version=stable&mode=debug&editio...