Why LINQ (well, C#) is Broken

24 October, 2016

LINQ is a system that provides a flexible query interface for .NET languages. It allows a user to write queries over arbitrary data using an in-built SQL-like syntax. This syntactic sugar is mapped to method calls at compile time, so any data structure that implements the correct methods can be used with LINQ.

The essential methods for enabling LINQ support are Select and SelectMany, implemented as extension methods. They have the following types:

SomeData<B> Select<A,B>(this SomeData<A> a, Func<A,B> f)
SomeData<B> SelectMany<A,B>(this SomeData<A> a, Func<A,SomeData<B>> f)
SomeData<C> SelectMany<A,B,C>(this SomeData<A> a, Func<A,SomeData<B>> f, Func<A,B,C> g) // Overloaded to reduce levels of nesting

With implementations of these three methods, it is possible to write a query expression such as:

SomeData<A> myA = ...;
SomeData<B> myB = ...;
Func<A,B,C> f = ...;
SomeData<C> myC = from a in myA
                  from b in myB
                  select f(a,b);

which will be compiled to something like: SomeData<C> output = justWord.SelectMany(a => myB, (a, b) => f(a, b));

Readers who are familiar with Haskell or similar functional languages will notice that Select is fmap, SelectMany is >>= and the from .. in .. select syntax is equivalent to Monad comprehensions. The above code would be written in Haskell as follows:

myA = ...
myB = ...
f a b = ...
myC = do
  a <- myA
  b <- myB
  return $ f a b

LINQ was designed to bring Monad comprehensions to C#. And it does. Almost.

Consider our query from earlier:

SomeData<C> myC = from a in myA
                  from b in myB
                  select f(a,b);

This seems like a common pattern. We don’t want to write this code over and over, so we abstract myA, myB and f and make the query into a method.

SomeData<C> CombineWith<A,B,C>(SomeData<A> myA, SomeData<B> myB, Func<A,B,C> f)
    return from a in myA from b in myB select f(a,b);

Now say we define a new data type to use with LINQ, call it OtherData<A>, and implement Select and SelectMany appropriately. We also want to implement CombineWith because from .. in .. from .. in .. select .. is still a common pattern that we want to avoid writing:

OtherData<C> CombineWith<A,B,C>(OtherData<A> myA, OtherData<B> myB, Func<A,B,C> f)
    return from a in myA from b in myB select f(a,b);

There is a pattern emerging. For every data type that we want to use with LINQ, one must reimplement all LINQ-specific methods specifically for that type.

This is an issue because it grossly violates DRY (don’t repeat yourself). A well-written program should not have duplicated code - it makes maintenance more laborious and increases the chance of bugs.

So in an effort to save ourselves time, we should abstract over this common pattern. We require a function that specifies

for all generic classes F<???> implementing Select and SelectMany, given an instance of F containing As, another instance of F containing Bs, and a Func<A,B,C, return an F containing Cs

It turns out that it’s actually impossible to write this method in C#. I’d like to write something like F<C> CombineWith<F<?>,A,B,C>(F<A> myA, F<B> myB, Func<A,B,C> f), but C# only allows abstraction over non-generic types.

To add a little more weight to this revelation, let’s imagine if we could not abstract over the contents of a list ie. the method List<A> Sort<A>(List <A> input) cannot be expressed in this language. Due to this limitation, we would have to create a new list class every time we needed a different element type inside the list, then reimplement Sort for each new class.

ListOfInt.Sort ListOfBool.Sort ListOfSomeData.Sort

This is again a terrible violation of the “don’t repeat yourself” principle. You write n implementations of Sort, where n is the number of sortable classes. Imagine that each implementation used the proven incorrect version of TimSort. If you wanted to implement the correct version, you would have to update n methods.

Also consider the implementation of List<B> Map<A,B>(List<A> input, Func<A,B> f) in a generic-less language. You would have to write a different method for each inhabitant of A and B

ListOfInt.MapToListOfInt ListOfInt.MapToListOfBool ListOfInt.MapToListOfSomeData ListOfBool.MapToListOfBool

You write n^2 Map methods where n is the number of of mappable classes.

More generally, in this generic-less language, you write O(n^m) where m is the sum of should-be-generic inputs and should-be-generic outputs, and n is the number of should-be-generic classes.

This exponential growth of redundant nonsense also applies to our CombineWith issue. For every LINQ-able class, you have to write a separate implementation of CombineWith, even though it’s exactly the same code!

Haskell (and other sane functional languages) uses a concept called “Higher Kinded Types” to address this problem. Every type has a “kind” (denoted *). In C#, every type must have kind *. Higher-kinded types are functions from kinds to kinds. Given data declaration that has a single type variable, say Maybe a = Just a | Nothing, we say that Maybe has kind * -> *, which means that it is a higher-kinded type that takes a type of kind * and returns a type of kind *. In C#, every type must have kind * ie. if you have a defined the class List<A> then you get a compile error if you refer to List without the type argument.

Let’s take another look the Haskell implementation of CombineWith:

combineWith :: Monad m => m a -> m b -> (a -> b -> c) -> m c
combineWith myA myB f = do
  a <- myA
  b <- myB
  return $ f a b

In this function, and the definition of the Monad typeclass (read: interface)m implicitly has kind * -> *. This function will work for any type that is an instance of Monad (read: implements the Monad interface). In Haskell, this code only needs to be written once. The cost of implementation and maintenance of a group of functions has gone from O(n^m) to O(1).

Now you might say, “Well, I don’t use LINQ like that. I only use it for IEnumerable things”. This is akin to a user of our imaginary generic-less language saying “Well, I don’t use Sort like that. I only sort lists of integers”. It is agreed that a language without generics is counter to productivity. It follows that a language without higher-kinded types is also counter to productivity.