what is 'and!' in the validation computation expression with FsToolkit.ErrorHandling, in F#

Question

when using FsToolkit.ErrorHandling and looking at this example:

testCase "Happy Path Result" <| fun () ->
        let actual : Validation<int, string> = validation {
            let! a = Ok 3
            and! b = Ok 2
            and! c = Ok 1
            return a + b - c
        }

what is the meaning of and!? it looks like let! gets mapped to Result.bind, but I don't see a different behavior between let! and and!

as far as I can see, it looks like replacing and! with let! keeps the same behavior.

I've just started dabbling in computation expressions and things are starting to make sense, although I don't really understand why we have different nomenclature between the F# keywords like let and the actual functions like bind so it's adding a layer of confusion. So the answer to this may be obvious :)

Answer 1

That's the new support for "applicative computation expressions" introduced in F# 5.0.

The difference between let! and and! is that let! allows a value to depend on a prior result, while and! does not. This is useful for cases where your computation is an applicative, but not a full monad, or when you want to perform independent steps in a computation in parallel.

For example, with let! you could write this:

let! a = Ok 3
let! b = Ok (2 * a)   // Allowed: value of b depends on a

But you can't write this:

let! a = Ok 3
and! b = Ok (2 * a)   // Not allowed: value of b depends on a