Name this operation by Mark Seemann

A type of operation seems to be repeatedly appearing in my code, but I can't figure out what to call it; can you help me?

Across various code bases that I work with, it seems like operations (methods or functions) like these keep appearing:

public IDictionary<string, string> Foo(
    IDictionary<string, string> bar, 
    Baz baz)

In order to keep the example general, I've renamed the method to Foo, and the arguments to bar and baz; in this article throughout, I'll make heavy use of metasyntactic variables. The types involved aren't particularly important; in this example they are IDictionary<string, string> and Baz, but they could be anything. The crux of the matter is that the output type is the same as one of the inputs (in this case, IDictionary<string, string> is both input and output).

Another C# example could be:

public int Qux(int corge, string grault)

Notice that the types involved don't have to be interfaces or complex types. The only recurring motif seems to be that the type of one of the arguments is identical to the return type.

Although the return value shares its type with one of the input arguments, the implementation doesn't have to echo the value as output. In fact, this is often not the case.

At this point, there's also no implicit assumption that the operation is referentially transparent. Thus, we may have implementation where some database is queried. Another possibility is that the operation is a closure over additional values. Here's an F# example:

let sign calculateSignature issuer (expiry : DateTimeOffset) claims =
    claims |> List.append [
        { Type = "signature"; Value = calculateSignature claims }
        { Type = "issuer"; Value = issuer }
        { Type = "expiry"; Value = expiry.ToString "o" }]

You could imagine that the purpose of this function is to sign a set of security claims, by calculating a signature and add this and other issuer claims to the input list of claims. The signature of this particular function is (Claim list -> string) -> string -> DateTimeOffset -> Claim list -> Claim list. However, the leftmost arguments aren't going to vary much, so it would make sense to partially apply the function. Imagine that you have a correctly implemented signature function called calculateHMacSha, and that the name of the issuer should be "Ploeh":

let sign' = sign calculateHMacSha "Ploeh"

The type of the sign' function is DateTimeOffset -> Claim list -> Claim list, which is equivalent to the above Foo and Qux methods.

The question is: What should we call such an operation?

Why care?

In its general form, such an operation would have the shape

public interface IGrault<T1, T2>
{
    T1 Garply(T1 waldo, T2 fred);
}

in C# syntax, or 'a -> 'b -> 'b type in F# syntax.

Why should you care about operations like these?

It turns out that they are rather composable. For instance, it's trivial to implement the Null Object pattern, because you can always simply return the matching argument. Often, it also makes sense to make Composites out of them, or chain them in various ways.

In Functional Programming, you may just do this by composing functions together (while not particularly considering the terminology of what you're doing), but in Object-Oriented languages like C#, we have to name the abstraction before we can use it (because we have to define the type).

If T2 or 'a is a predicate, the operation might be a filter, but as illustrated with the above sign' function, the operation may also enrich the input. In some cases, it may even replace the original input and return a completely different value (of the same type). Thus, such an operation could be a 'filter', an 'expansion', or a 'replacement'; those are quite vague properties, so any name for such operations are likely to be vague or broad as well.

My question to you is: what do we call this type of operation?

While I do have a short-list of candidate names, I encounter these constructs so often that I'd be surprised if such operations don't already have a conceptual name. If so, what is it? If not, what should we call them?

(I'd hoped that this type of operation was already a 'thing' in functional programming, so I asked on Twitter, but the context is often lost on Twitter, so therefore this blog post.)

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