Understanding F# applicatives and custom operators

[This post originally appeared on Jonathan’s personal blog -> https://blog.jonathanchannon.com/2020-07-17-understanding-fsharp-applicatives-custom-operators]

After discussing something with Ian Russell he suggested I take some time to read through another fine blog post he has written and understand F# applicatives and custom operators. I found myself in familiar territory when reading F# blog posts and it's something similar to the five stages of grief. Nod, Nod, I understand what's going on, Umm, WTF is going on. As Ian did in his Intro to F# series he sets out a simple domain problem and goes about how to address it. We want to return a ValidatedUser from a function but if the user fails validation we return a list of validation errors.

The code in the blog post was pretty self explanatory until, it wasn't, which I have pasted below:

As you can see, there is commented out code on the last line because he has lined up the 3 arguments that are required to call the create function but calling it as-is won't work because the function takes in string,string,DateTime and we have Result<string, ValidationFailure list>, Result<string, ValidationFailure list>,Result<DateTime, ValidationFailure list>. As we know from my previous blog post we can use the Result.map function to do this sort of thing.

I will skip to the solution to this and work backwards because this is where I started to scratch my head a lot! Luckily the F# Software Foundation slack channel helped a lot, in particular Paul Blasucci.

I then went back to the line of code after being informed that |< data-preserve-html-node="true" will always get called after |>. So what we have is create is passed in as the function to call in Result.map and the Result type is the validatedName variable. PARTIAL APPLICATION!!! Ok I get it now!

So once I could see what was happening it was time to understand what the apply function was doing. The first argument is a Result type whose generic args were a function and a list of validation failures, the second argument was a Result type whose generic args were a value and a list of validation failures. What apply does is match the two Result types together to check for (Ok, Ok) or (Ok, Error) etc and on success call the unwrapped function of the first arg with the unwrapped value of the second arg.

What confused me here was F# compiler magic. Now I knew about partial application but what I didn't understand was that when you assign a variable by calling a function using partial application the resulting type is not the result of the function being called. It's just a type of the function with one less argument to call, the compiler knows when to call the actual function once all arguments have been passed to it. What the function is doing is chaining argument calls to a partial application function. So we can see:

baz now is the final result of a call to execute the create function.

We can then remove the lets above and get to the final solution I mentioned previously:

If like me you were totally confused by this then please see Ian's blog post for a full explanation but here's my take away.

As we saw above the apply function takes an "elevated" function and "elevated" value and then calls the function with the value and returns an elevated result. So we know in long hand version we have: