type Age = Age of int
type Email = Email of string
type Person = { Age: Age; Email: Email }

let age : Age = Age 13
let email : Email = Email "jo@gmail.com"
let me : Person = {Age = age; Email = email }

me

13

jo@gmail.com

type MyBasicResult = Ok | Error

let a : MyBasicResult = Ok
let b : MyBasicResult = Error
(a,b)

type MyResult = Ok of int | Error of string

let a = Ok 13
let b = Error "an error"
(a,b)

13

an error

type Result<'a,'b> = Ok of 'a | Error of 'b

let ok : Result<int,string> = Ok 13
let nok : Result<int,string> = Error "a problem!"
(ok, nok)

13

a problem!

let ok : Result<string,int> = Ok "an okay string value"
let nok : Result<string,int> = Error 666
(ok,nok)

an okay string value

666

type Validation<'a> = Result<'a, string list>

let ok : Validation<int> = Ok 13
let nok : Validation<bool> = Error ["We have a problem!"]
(ok,nok)

13

We have a problem!

<null>

<null>

The input list was empty.

<null>

<null>

FSharp.Core

-2146233079

   at Microsoft.FSharp.Collections.FSharpList`1.get_Head() in D:\a\_work\1\s\src\FSharp.Core\prim-types.fs:line 4141
   at lambda_method316(Closure, FSharpList`1)
   at Microsoft.DotNet.Interactive.Formatting.MemberAccessor`1.GetValueOrException(T instance) in D:\a\_work\1\s\src\Microsoft.DotNet.Interactive.Formatting\MemberAccessor{T}.cs:line 58

let foo a = a + 1

let foo (a : int)   : int = a + 1
(*       |a is an int  | it returns an int *)

let foo : int -> int = 
(*         | takes an int
                  | returns an int
*)
    fun a -> a + 1

let mkPerson (a: Age) (e: Email) : Person = { Age = a; Email = e }
mkPerson (Age 99) (Email "me@old.com")

99

me@old.com

//map :: (a->b)->E(a)->E(b)
let map (f: 'a -> 'b) (a: Validation<'a>) : Validation<'b> =
    match a with
    | Ok v -> Ok(f v)
    | Error e -> Error e

let haveBirthDay (Age a) : Age = Age (a + 1)

haveBirthDay (Age 35)

36

let ok : Validation<Age> = Ok (Age 35)
map haveBirthDay ok

36

let nok : Validation<Age> = Error ["not a valid age"]
map haveBirthDay nok

not a valid age

<null>

<null>

get_Head

100663764

True

False

False

<null>

<null>

Ok (Age 23)
|> map haveBirthDay
|> map haveBirthDay
|> map haveBirthDay

26

nok
|> map haveBirthDay
|> map haveBirthDay
|> map haveBirthDay

not a valid age

<null>

<null>

get_Head

100663764

True

False

False

<null>

<null>

//map::(a->b)->E(a)->E(b)

//apply::E(a->b)->E(a)->E(b)

let apply (f: Validation<'a -> 'b>) (a: Validation<'a>) : Validation<'b> =
    match f, a with
    | Ok f, Ok v -> Ok(f v)
    | Error e1, Error e2 -> Error(e1 @ e2)
    | Error e, _ -> Error e
    | _, Error e -> Error e

let parseAge (text: string) : Validation<Age> =
    match System.Int32.TryParse text with
    | false, _ -> Error [ sprintf "<%s> is not a valid age" text ]
    | true, parsed -> Ok(Age parsed)

let parseEmail (text: string) : Validation<Email> =
    if text.Contains("@") then
        Ok(Email text)
    else
        Error [ sprintf "<%s> is not a valid email" text ]

let okAge = parseAge "12"
let nokAge = parseAge "jo@gmail.com"
let okEmail = parseEmail "jo@gmail.com"
let nokEmail = parseEmail "13"
(okAge,nokAge,okEmail, nokEmail)

12

<jo@gmail.com> is not a valid age

<null>

<null>

The input list was empty.

<null>

<null>

FSharp.Core

-2146233079

   at Microsoft.FSharp.Collections.FSharpList`1.get_Head() in D:\a\_work\1\s\src\FSharp.Core\prim-types.fs:line 4141
   at lambda_method316(Closure, FSharpList`1)
   at Microsoft.DotNet.Interactive.Formatting.MemberAccessor`1.GetValueOrException(T instance) in D:\a\_work\1\s\src\Microsoft.DotNet.Interactive.Formatting\MemberAccessor{T}.cs:line 58

let f = Ok mkPerson
let age = parseAge "13"
let email = parseEmail "jo@gmail.com"
apply (apply f age) email

13

jo@gmail.com

//A function with 2 input arguments
//add::int->int->int
let add one other = one + other
add 2 3

5

//addThree::int->int
let addThree = add 3

addThree 2

5

let (<*>) = apply

(Ok mkPerson) <*> (parseAge "13") <*> (parseEmail "jo@gmail.com")

13

jo@gmail.com

(Ok mkPerson) <*> (parseAge "invalid age") <*> (parseEmail "invalid email")

<invalid age> is not a valid age

<invalid email> is not a valid email

<null>

<null>

The input list was empty.

<null>

<null>

FSharp.Core

-2146233079

   at Microsoft.FSharp.Collections.FSharpList`1.get_Head() in D:\a\_work\1\s\src\FSharp.Core\prim-types.fs:line 4141
   at lambda_method316(Closure, FSharpList`1)
   at Microsoft.DotNet.Interactive.Formatting.MemberAccessor`1.GetValueOrException(T instance) in D:\a\_work\1\s\src\Microsoft.DotNet.Interactive.Formatting\MemberAccessor{T}.cs:line 58

//Plain old function application
    mkPerson          (Age 36)          (Email "jo@gmail.com")

36

jo@gmail.com

//With baked-in validation, thanks to our apply
(Ok mkPerson) <*> (Ok (Age 36)) <*> (Ok (Email "jo@gmail.com"))

36

jo@gmail.com

//map::(a->b)->E(a)->E(b)

//map::(a->E(b))->E(a)->E(E(b))

let nested = [[1];[2;3];[4]]
let flatten = List.concat

flatten nested

1

2

3

4

0

<null>

<null>

<null>

<null>

<null>

//map:: (a->b)   ->E(a)->E(b)
//map:: (a->E(b))->E(a)->E(E(b))
//bind::(a->E(b))->E(a)->E(b)

//bind::(a->E(b))->E(a)->E(b)
let bind (f: ('a -> Validation<'b>)) (a: Validation<'a>) : Validation<'b> =
    match a with
    | Ok v -> f v
    | Error e -> Error e

bind (fun age -> bind (fun email -> Ok(mkPerson age email)) (parseEmail "jo@gmail.com")) (parseAge "13")

13

jo@gmail.com

parseAge "13"
|> bind (fun age ->
    parseEmail "jo@gmail.com"
    |> bind (fun email ->
        Ok(mkPerson age email)))

13

jo@gmail.com

//For F# "do syntax", we need some magic dust
type ValidatedResultBuilder() =
    member _.Return(x) = Ok x
    member _.Bind(m, f) = bind f m

let valid = new ValidatedResultBuilder()

valid {
    let! age = parseAge "13"
    let! email = parseEmail "jo@gmail.com"
    return mkPerson age email
}

13

jo@gmail.com

valid {
    let! age = parseAge "invalid"
    let! email = parseEmail "jo@gmail.com"
    return mkPerson age email
}

<invalid> is not a valid age

<null>

<null>

get_Head

100663764

True

False

False

<null>

<null>

FP - the scary parts¶

Prerequisites: types and functions¶

Types¶

Functors¶

Sidebar: elevated worlds¶

Applicative Functor¶

Sidebar: currying and partial function application¶

Back to Applicative¶

Monad¶

A small detour: applicative vs. monadic style¶

Conclusion¶

Further reading¶