Understanding F# applicatives and custom operators

type UnvalidatedUser = {
    Name : string
    Email : string
    DateOfBirth : string
}

type ValidatedUser = {   
    Name : string
    Email : string
    DateOfBirth : DateTime
}

type ValidationFailure =
    | NameIsInvalidFailure
    | EmailIsInvalidFailure
    | DateOfBirthIsInvalidFailure

let (|ParseRegex|_|) regex str =
   let m = Regex(regex).Match(str)
   if m.Success then Some (List.tail [ for x in m.Groups -> x.Value ])
   else None

let (|IsValidName|_|) input =
    if input <> String.Empty then Some () else None

let (|IsValidEmail|_|) input =
    match input with
    | ParseRegex ".*?@(.*)" [ _ ] -> Some input
    | _ -> None

let (|IsValidDate|_|) (input:string) =
    let (success, value) = DateTime.TryParse(input)
    if success then Some value else None

let validateName input = // string -> Result
    match input with
    | IsValidName -> Ok input
    | _ -> Error [ NameIsInvalidFailure ]

let validateEmail input = // string -> Result
    match input with
    | IsValidEmail email -> Ok email
    | _ -> Error [ EmailIsInvalidFailure ]

let validateDateOfBirth input = // string -> Result
    match input with
    | IsValidDate dob -> Ok dob //Add logic for DOB
    | _ -> Error [ DateOfBirthIsInvalidFailure ]

let apply fResult xResult = // Result<('a -> 'b), 'c list> -> Result<'a,'c list> -> Result<'b,'c list>
    match fResult,xResult with
    | Ok f, Ok x -> Ok (f x)
    | Error ex, Ok _ -> Error ex
    | Ok _, Error ex -> Error ex
    | Error ex1, Error ex2 -> Error (List.concat [ex1; ex2])

let () = Result.map
let (<*>) = apply

let create name email dateOfBirth =
    { Name = name; Email = email; DateOfBirth = dateOfBirth }

let validate (input:UnvalidatedUser) : Result =
    let validatedName = input.Name |> validateName
    let validatedEmail = input.Email |> validateEmail
    let validatedDateOfBirth = input.DateOfBirth |> validateDateOfBirth
    // create validatedName validatedEmail validatedDateOfBirth

create
    |> Result.map <| validatedName
    |> apply <| validatedEmail
    |> apply <| validatedDateOfBirth

From the last blog post I showed how to call functions in a chain of functions where Result types needed to be unwrapped and their values passed to the next function. So my first thought looking at this was validatedName is a value not a function so how is Result.map working? I also didn't quite understand the precedence of |> and |< data-preserve-html-node="true" how that worked. As part of my investigation, or some may say my learning and understanding, I was told Don Syme regretted making the back pipe and that using forward and back pipes together can make code unreadable. The take away there is to be careful about it's usage. The good thing here is that we only have one usage of it but it still didn't make sense to me. So I tried to split it up:

let foo = create |> Result.map <| validatedName

I still didn't quite get it, foo is a type of Result<(string -> DateTime -> ValidatedUser), ValidationFailure list> which means it's taken the name argument and now wants the email and date of birth passed to it. I understood partial application but still it didn't click. I went back to the previous blog post and looked at what the function signature of Result.map is. It takes in a function and a Result<'a,'b>. If the Result is OK it calls the passed in function with the unwrapped Result of 'a and returns a Result type of Ok(fn a) otherwise it returns Error e Here's the code for it:

let map mapping result = match result with Error e -> Error e | Ok x -> Ok (mapping x)

let foo = create |> Result.map <| validatedName // Result.map create validatedName
let bar = foo |> apply <| validatedEmail // apply foo validatedEmail
let baz = bar |> apply <| validatedDateOfBirth // apply bar validatedDateOfBirth

create
    |> Result.map <| validatedName
    |> apply <| validatedEmail
    |> apply <| validatedDateOfBirth

As mentioned above it's advised not to use back pipes and so what we could end up with is:

create  validatedName <*> validatedEmail <*> validatedDateOfBirth

apply (apply (Result.map create validatedName) validatedEmail) validatedDateOfBirth

We can also use operators to replace function names to tidy things up so we end up with:

let () = Result.map
let (<*>) = apply

And we can make the above look like:

(<*>) ((<*>) (() create validatedName) validatedEmail) validatedDateOfBirth

This hopefully all makes sense, but now a slight lesson in math notation which blew my mind. We know the signature 1 + 1 = 2. However, + is actually a function that takes two numbers, so in that regard what you have known since you were aged three should look like + 1 1 if we were to apply common programming signatures. Interestingly, you could also call the + function like 1 1 +. Where the + sits in the signature is called notation. Typically programming languages will use "prefix notation" function arg1 arg2 and some may use "postfix notation" arg1 arg2 function and arithmetic generally uses "infix notation" arg1 function arg2. However, in F# you can use "infix notation" which looks like the typical 1 + 1 signature which is let add x y = x + y. If we replace x + y knowing that the + is the function we can go from "prefix notation" (<!>) create validatedName to "infix notation" create <!> validatedName and apply it to our functions above. As we apply the calls to our infixed functions what we end up with is:

create  validatedName <*> validatedEmail <*> validatedDateOfBirth

This looks much neater than apply (apply (Result.map create validatedName) validatedEmail) validatedDateOfBirth but it does take a bit of learning and re-thinking to work out how the final solution create <!> validatedName <*> validatedEmail <*> validatedDateOfBirth actually works. I know this has been quite a learning curve for me but thankfully there are resources, people in the F# community and colleagues (thanks Ian!) that are keen to help and I thank them very much for this!