Row types refer to row polymorphism. It's a kind of polymorphism that lets you write code that's generic over different records with different fields without using subtyping.

Lets say you want to write a function that takes anything with a .length field:

    maxByLen a b = if a.length > b.length then a else b

How would you come up with the types for this? In a Java-like system of nominative sub-typing, you would make an interface Length and require types to declare it explicitly. However, this is messy, completely unnecessary and messes up type inference, so it's not a good idea.

You could also use structural sub-typing. You could declare the function to have a type like

    byLength : { length : Int } -> { length : Int } -> { length : Int }

where any record with a field length of type Int has the type { length : Int }. In other words, the type { length : Int, name : String } is a subtype of { length : Int } without needing to declare an interface explicitly. This is a definite improvement over the nominative Java case.

There are a couple of problems with this, however. A major one is that it "throws away" type information. In particular, all you know about either argument is that they have length fields. They might otherwise be of different types, with all their other fields completely different. You could compare a Foo and a Bar, as long as they both have lengths. Also, if you return something of the argument type, all you will know about it after that is that it has a length field; you've lost its actual type statically. To cast back up would require a potentially failing runtime check.

Consider that if we have two type Foo { length : Int, name : String} and Bar { length : Int, height : Int }, we can pass one of each into the function. Then which one it returns depends on runtime data: it might be a Foo and it might be a Bar. This means we cannot know the specific return type; all we know now is that it has to have a length field.

This is very different from normal parametric polymorphism which has type variables. While you don't know anything about the variable inside the function, it doesn't throw out type information when its used. For example, imagine this code instead:

    maxBy : (a -> Int) -> a -> a -> a
    maxBy pred a b = if pred a > pred b then a else b

This one can be used the same way by passing in a length function. However, since it doesn't use subtyping, both arguments have to have the same type! This means we can't use it to compare a foo and a bar. But when we do use it on Foos, for example, we know we will get a Foo out because that's what the a variable will be unified to:

    (a -> Int) -> a -> a -> a
    (Foo -> Int) -> Foo -> Foo -> Foo

When we use the function on a Foo, a gets instantiated to Foo giving us the second type.

Row types are just a way to bring this second style of polymorphism to records with different fields. Basically, it allows you to put a type variable representing the "rest" of the record:

    maxByLen : { length : Int | r } -> { length : Int | r } -> { length : Int | r }

Now, when we use this on a Foo, r gets instantiated to { name : String }; when we use it on a Bar, it gets instantiated to { height : Int }. This means we can't mix Foos and Bars and we don't lose type inference.

It also lets us do some other nice things. For example, we could add a field, polymorphically:

    annotate : { length : Int | r } -> { length : Int, lenStr : String | r }

It's also nice to note that we don't lose anything: we can get something very similar to the old behavior by throwing information away explicitly:

    maxBy : { length : Int | a} -> { length : Int | b } -> { length : Int }
    maxBy a b = if a.length > b.length then { length = a.length }
                                       else { length = b.length }

We can get almost exactly the sub-typing behavior by using existential types:

    maxBy : (exists a. { length | a }) -> (exists b. { length | b }) -> 
               (exists c. { length | c })
    maxBy a b = if a.length > b.length then a else b

I'm not sure why we would want this though! (I also don't know if any languages support this sort of syntax exactly, so you might have to jump through some additional hoops to simulate "exists".)

As a final note, I haven't used row polymorphism or existential types very much, so there might be some mistakes above.

It's also worth noting that Ermine has a slightly more general form of row polymorphism, but I'm not sure what the specific differences are.