Recursively find all files from a sequence of directories

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open System.IO
let rec allFiles dirs =
    if Seq.isEmpty dirs then Seq.empty else
        seq { yield! dirs |> Seq.collect Directory.EnumerateFiles
              yield! dirs |> Seq.collect Directory.EnumerateDirectories |> allFiles }

namespace System

namespace System.IO

val allFiles : dirs:seq<string> -> seq<string>

Full name: Script.allFiles

val dirs : seq<string>

module Seq

from Microsoft.FSharp.Collections

val isEmpty : source:seq<'T> -> bool

Full name: Microsoft.FSharp.Collections.Seq.isEmpty

val empty<'T> : seq<'T>

Full name: Microsoft.FSharp.Collections.Seq.empty

Multiple items
val seq : sequence:seq<'T> -> seq<'T>

Full name: Microsoft.FSharp.Core.Operators.seq

--------------------
type seq<'T> = System.Collections.Generic.IEnumerable<'T>

Full name: Microsoft.FSharp.Collections.seq<_>

val collect : mapping:('T -> #seq<'U>) -> source:seq<'T> -> seq<'U>

Full name: Microsoft.FSharp.Collections.Seq.collect

type Directory =
  static member CreateDirectory : path:string -> DirectoryInfo + 1 overload
  static member Delete : path:string -> unit + 1 overload
  static member EnumerateDirectories : path:string -> IEnumerable<string> + 2 overloads
  static member EnumerateFileSystemEntries : path:string -> IEnumerable<string> + 2 overloads
  static member EnumerateFiles : path:string -> IEnumerable<string> + 2 overloads
  static member Exists : path:string -> bool
  static member GetAccessControl : path:string -> DirectorySecurity + 1 overload
  static member GetCreationTime : path:string -> DateTime
  static member GetCreationTimeUtc : path:string -> DateTime
  static member GetCurrentDirectory : unit -> string
  ...

Full name: System.IO.Directory

Directory.EnumerateFiles(path: string) : System.Collections.Generic.IEnumerable<string>
Directory.EnumerateFiles(path: string, searchPattern: string) : System.Collections.Generic.IEnumerable<string>
Directory.EnumerateFiles(path: string, searchPattern: string, searchOption: SearchOption) : System.Collections.Generic.IEnumerable<string>

Directory.EnumerateDirectories(path: string) : System.Collections.Generic.IEnumerable<string>
Directory.EnumerateDirectories(path: string, searchPattern: string) : System.Collections.Generic.IEnumerable<string>
Directory.EnumerateDirectories(path: string, searchPattern: string, searchOption: SearchOption) : System.Collections.Generic.IEnumerable<string>