FSharpx: Validating with applicative functors

I've been recently interested in Functors, applicatives and monads, especially in context of complex validation. FSharpx has a validation module (among many other wonderful features). I've played with it a bit:

	open FSharpx.Choice
	open FSharpx.Validation
	open FSharpx.Collections
	open System
	// generic validator which returns Success if given predicate succeeds, otherwise Failure of NonEmptyList of errors
	let validator pred error value =
	if pred value then Choice1Of2 value
	else Choice2Of2 (NonEmptyList.singleton error)
	// some simple validators
	let notEqual x = validator ((<>) x) <| sprintf "should not equal to %d" x
	let evenNumber = validator (fun x -> x % 2 = 0) "should be even"
	// a more complex validator made by combining a couple of simpler ones
	let validateNumber n =
	returnM n
	<* evenNumber n
	<* notEqual 3 n
	let printRes res =
	match res with
	| Success n -> printfn "%A" n
	| Failure errors -> errors |> String.concat ", " |> printfn "%s"
	// test
	[-5..5] |> List.iter (fun x -> (x, validateNumber x) ||> print)
	results:
	-5 | should be even
	-4 | -4
	-3 | should be even
	-2 | -2
	-1 | should be even
	0 | 0
	1 | should be even
	2 | 2
	3 | should be even, should not equal to 3
	4 | 4
	5 | should be even

view raw applicative validation.fs hosted with ❤ by GitHub

Applicatives can be combined using several operators and functions, for example all following functions are equivalent:

	let validateNumber n =
	returnM n
	<* evenNumber n
	<* notEqual 3 n
	let validateNumber' n =
	returnM (fun _ _ -> n)
	<*> evenNumber n
	<*> notEqual 3 n
	let validateNumber'' n =
	returnM (konst2 n)
	<*> evenNumber n
	<*> notEqual 3 n
	let validateNumber''' n =
	konst2 n
	<!> evenNumber n
	<*> notEqual 3 n
	let validateNumber'''' n =
	returnM (konst2 n)
	|> ap (evenNumber n)
	|> ap (notEqual 3 n)
	let validateNumber''''' n =
	konst n
	<!> (evenNumber >=> notEqual 3) n
	let validateNumber'''''' n =
	returnM n <* sequence [evenNumber n; notEqual 3 n]

view raw combine applicatives.fs hosted with ❤ by GitHub