My interest in Type Theory

Posted on September 21, 2014 by Jack Fox

Through the Oregon Programming Languages Summer School videos I became interested in Type Theory over a year ago, and in what little so-called spare time I have these days it has become my primary recreational interest.

I have presented a couple of different talks on the subject over the past few months. A presentation on Homotopy Type Theory which is derived from a prior talk I gave at Tachyus on Type Theory and Practical Application.

A note of caution to anyone diving into Type Theory through anything I have written. I have presented on Type Theory and Hott in particular because there is a lot of interest by programmers in this topic. Preparing and giving both talks was a learning opportunity for me. A lot of questions followed from the perspective of category theory, and fortunately there was usually someone with a background in that area willing to take them. There’s flagrant overreaching in my presentations. Calling path induction “the fundamental theorem of type theory” is way too provocative for a neophyte to attempt, and in introducing the axiom of univalence I did not set up nearly enough introduction for it to make sense. Specifically the equivalence operator needs quite a bit of introduction.

Both my presentations evoked lively discussion and stretched out to two hours. It is really too much to cover in one presentation, even for an introduction. Ideally a follow-up presentation (or two) would be outlined as follows.

Cover the formation, introduction, elimination, and computation rules for the primary types…and perhaps some of the later specific types introduced in The Hott Book.¹
An in depth look at path induction.
What is equivalence?
Only then can function extensionality and univalence have the context necessary for introduction.
…and cover sets in type theory and mere propositions.

Notes

[1] The HoTT Book, §1.5. This is all math-speak. I will attempt to translate into programmer-speak.

Formation Rule: How one forms a type, the representation syntax.

Introduction Rule: The constructor(s) for forming elements of the type.

Elimination Rule: How to use an element of the type, the usage syntax.

Computation Rule: a.k.a. β-reduction to the theorists. Simply put, using the constructor in an expression.

Upcoming Events

Posted on September 21, 2014 by Jack Fox

Long time since last post. I’ve been having a great time, but very busy, working for Tachyus, the first Silicon Valley tech company devoted to the oil and gas industry. Working on technology solutions for the physical world is emotionally rewarding, and all the better that we code the software side almost exclusively in F#.

I’m participating in a lot of community activities in the next couple of months.

October 2 & 3 at the Progressive F# Tutorials NYC

I’m really excited about meeting old and new F# colleagues. Shout-out to jet.com for sponsoring. This is a great conference for anyone interested in F# at any level, with top notch beginners and advanced tracks. Fellow Tachyus engineer Will Smith (Twitter @tihan) is doing an advanced track presentation on his project for inlining C code in F#.

October 11 & 12 Silicon Valley Code Camp

The 9th annual edition of the world’s largest free software development conference. This year I helped put together an F# track of sessions on Saturday, as well as a Sunday session, Functional Programming for Production Quality Code, that I will present.

Big shout out to

Peter Kellner (Twitter: @pkellner) for being the guiding light of SVCC,

as well as

Mathias Brandewinder (Twitter: @brandewinder), (spiritual leader of the Bay Area F# community),

Will Smith (again),

Ryan Riley (Twitter: @panesofglass) (another Tachyon),

and Riccardo Terrell (Twitter: @TRikace)

for contributing talks to the F# track.

November 2 – 6 Microsoft MVP Global Summit

This event is not open to the public, but if you are an MVP or work for Microsoft, Ryan and I will be presenting the F# open source projects Tachyus uses and contributes to at the Sunday afternoon MVP Expo. We are also going to try to schedule an MVP to MVP talk on the subject.

Combining FsCheck Properties in a single Test

Posted on January 28, 2014 by Jack Fox

You may have a bunch of tests that are very similar, and you don’t want to repeat yourself so many times. In FsCheck you can “and” properties with the .&. operator and label failures with either of the @| or |@ operators. The only problem is the first failing property will trigger all the subsequent labels to write as well. Here’s a little work-around to that situation:

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[<Test>]
let ``returns expected length``() =
    Check.VerboseThrowOnFailure 
        ( (1 = 1) |@ sprintf "1 != 2" 
        .&. (2 = 3) |@ sprintf (if false then "" else "2 != 3")
        .&. (3 = 3) |@ sprintf (if (3 = 3) then "" else "3 != 4") 
        .&. (4 = 5) |@ sprintf (if false then "" else "4 != 5") )

Remember the code to the left of |@ is an FsCheck property, and the similar looking statement to the right is an F# expression returning a bool, so you have to keep these two pieces of code in sync. Other than that hassle, this works and will only print labels from failing properties in your combined test.

val ( returns expected length ) : unit -> unit

Full name: Snippet.( returns expected length )

type Check =
  static member All : config:Config -> unit
  static member All : config:Config * test:Type -> unit
  static member Method : config:Config * methodInfo:MethodInfo * ?target:obj -> unit
  static member One : config:Config * property:’Testable -> unit
  static member One : name:string * config:Config * property:’Testable -> unit
  static member Quick : property:’Testable -> unit
  static member Quick : name:string * property:’Testable -> unit
  static member QuickAll : unit -> unit
  static member QuickAll : test:Type -> unit
  static member QuickThrowOnFailure : property:’Testable -> unit
  …

Full name: FsCheck.Check

static member Check.VerboseThrowOnFailure : property:’Testable -> unit

val sprintf : format:Printf.StringFormat<‘T> -> ‘T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.sprintf

Transparent Heterogeneous Parallel Async with F#

Posted on January 8, 2014 by Jack Fox

Here’s a strikingly transparent solution to performing parallel Async returning heterogeneous types. Take a look for yourself.

(The solution presented here is based on a gist sent to me by Anton Tayanovskyy, Twitter: @t0yv0.)

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let myInt, myChar, myBool, myString =
    Parallel.Pure (fun w x y z -> (w, x, y, z))
    <*> async { return 1 }
    <*> async { return 'b' }
    <*> async { return true }
    <*> async { return "abc" }
    |> Parallel.Run
    |> Async.RunSynchronously

The custom infix operator clearly maps the parallel operations to the elements of the resulting tuple. That’s it. Done.

The use case I was struggling with involved multiple queries using SqlCommandProvider that the host application could perform in parallel, except SqlCommandProvider returns sequences of records typed to the result of each query, and the Parallel member in Async<'T> requires a consistently typed 'T. Requiring heterogeneously typed responses that the app can perform in parallel is such a common use case I expected a literature search to turn up an appealing solution, but it seemed like authors were ignoring this important case.

You still have to tune it

The project I was working on required 9 asynchronous calls to the SQL Server.¹ Sequentially calling out the queries to the server took 438ms, and this is within an online app, so parallelization is clearly desirable. Packaging-up all 9 queries into the heterogeneous parallelizer resulted in…1,816ms!! Not exactly the result I was looking for. What happened?

The application host workstation had a quad-core processor running @3.60 GHz, but SQL Server was running on an old dual-core server running @2.33 GHz. It seems overloading the maximum number of simultaneous processes, four, on the SQL Server results in a bottleneck that is four times as slow as sequentially processing the 9 queries. A little experimenting with different configurations resulted in these timings:

Configuration	Time
Parallel 9	1,816 ms
Parallel 6-3	751 ms
Sequential 9	438 ms
Parallel 3-3-3	357 ms
Parallel 4-4-1	278 ms
Parallel 4-5	258 ms

For this hardware configuration the sweet spot appears to be matching or overloading by no more than one the number of processes available on the server ² and sequentially executing twice. The moral of the story is to tune the number of parallel Asyncs according to the run environment.

Conceivably if you make calls to different hosts there would be no practical upper bound to the number of Asyncs you could parallelize, but this is not true. Parallel<'T> is using the local host’s thread pool, for which there is some overhead for each additional thread. Also you also might do some local housekeeping within each Async<'T>. In my case that would be instantiating the record sequences from SqlCommandProvider into lists or arrays. As you cross over from IO-bound to CPU-bound tasks, you will have to tune to meet the thread pool constraints on the application host.

Under the hood

It’s important to note Parallel is a helper type and the <*> operator provides a facade over the F# standard library implementation of Async.Parallel, which is where the real work of parallel scheduling is taking place.

Let’s take a look at the full implementation of this clever solution.

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type Parallel<'T> =
    private {
        Compute : Async<obj>[]
        Unpack : obj [] -> int -> 'T
    }

    static member ( <*> ) (f: Parallel<'A -> 'B>, x: Parallel<'A>) : Parallel<'B> =
        {
            Compute = Array.append f.Compute x.Compute
            Unpack = fun xs pos ->
                let fv = f.Unpack xs pos
                let xv = x.Unpack xs (pos + f.Compute.Length)
                fv xv
        }

    static member ( <*> ) (f: Parallel<'A ->' B>, x: Async<'A>) : Parallel<'B> =
        f <*> Parallel.Await(x)

and Parallel =

    static member Run<'T> (p: Parallel<'T>) : Async<'T> =
        async {
            let! results =
                match p.Compute.Length with
                | 0 -> async.Return [|box ()|]
                | 1 -> async { let! r = p.Compute.[0] 
                               return [| r |] }
                | _ -> Async.Parallel p.Compute
            return p.Unpack results 0
        }

    static member Await<'T> (x: Async<'T>) : Parallel<'T> =
        {
            Compute =
                [|
                    async {
                        let! v = x
                        return box v
                    }
                |]
            Unpack = fun xs pos -> unbox xs.[pos]
        }

    static member Pure<'T>(x: 'T) : Parallel<'T> =
        {
            Compute = [||]
            Unpack = fun _ _ -> x
        }

Given the signature of Async.Parallel<'T>, seq<Async<'T>> -> Async<'T []>, the only practical way to execute over heterogeneous types is to box them. The innovation of the Parallel type is to make this easy and flexible. Walking through the code execution, the Pure member takes a fully generic function returning a tuple and returns a Parallel typed by that function. Each subsequent useage of the <*> operator and AsyncBuilder returns a new Parallel with the return type of the builder partially applied to the previous function type until strong types have been fully applied and the resulting Parallel is of type the return required strongly typed tuple.

The following illustrates this process (interspersed comments show the state of the let binding if it had ended there):

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let test1 () =
    Parallel.Pure (fun x y z -> (x, y, z))
        // unit -> Parallel<('a -> 'b -> 'c -> 'a * 'b * 'c)>

    <*> async { return 1 }
        // unit -> Parallel<('b -> 'c -> int * 'b * 'c)>

    <*> async { return 'b' }
        // unit -> Parallel<('c -> int * char * 'c)>

    <*> async { return true }
        // unit -> Parallel<int * char * bool>

    |> Parallel.Run
        // unit -> Async<int * char * bool>

    |> Async.RunSynchronously
        // unit -> int * char * bool

As you can tell, there is more complexity involved in eventually returning strongly-typed tuple. I suggest stepping through the debugger for a deeper understanding.

Check out the code in F# Snippets and try running it in Tsunami Cloud by clicking "tsunami.io" from the snippet.

Footnotes

[1] I picked a time of minimal network activity for my testing, resulting in very little variance in my test results. In some cases the average actually coincided with the median. Where they differ I split the difference and report that number. I repeated each test 10 times. The workstation acting as app host and SQL Server are on the same sub-net. Of course repeated calls to the same queries resulted in caching on the server.

[2] This was actually the staging environment of a production system. What a dilemma this presents! Tune for the production system with a 24 core server, resulting in terrible responsiveness in the staging environment ("trust me, QA, this will be fast in production"), or add complexity to the code by implementing different tunings for different environments. I did not test with the production server, but my guess is it would be most efficient to perform all 9 queries in parallel.

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel

——————–
type Parallel<'T> =
  private {Compute: Async<obj> [];
           Unpack: obj [] -> int -> 'T;}
  static member ( <*> ) : f:Parallel<('A -> 'B)> * x:Parallel<'A> -> Parallel<'B>
  static member ( <*> ) : f:Parallel<('A -> 'B)> * x:Async<'A> -> Parallel<'B>

Full name: Snippet.Parallel.Parallel<_>

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

——————–
type Async
static member AsBeginEnd : computation:('Arg -> Async<'T>) -> ('Arg * AsyncCallback * obj -> IAsyncResult) * (IAsyncResult -> 'T) * (IAsyncResult -> unit)
static member AwaitEvent : event:IEvent<'Del,'T> * ?cancelAction:(unit -> unit) -> Async<'T> (requires delegate and 'Del :> Delegate)
static member AwaitIAsyncResult : iar:IAsyncResult * ?millisecondsTimeout:int -> Async<bool>
static member AwaitTask : task:Task<'T> -> Async<'T>
static member AwaitWaitHandle : waitHandle:WaitHandle * ?millisecondsTimeout:int -> Async<bool>
static member CancelDefaultToken : unit -> unit
static member Catch : computation:Async<'T> -> Async<Choice<'T,exn>>
static member FromBeginEnd : beginAction:(AsyncCallback * obj -> IAsyncResult) * endAction:(IAsyncResult -> 'T) * ?cancelAction:(unit -> unit) -> Async<'T>
static member FromBeginEnd : arg:'Arg1 * beginAction:('Arg1 * AsyncCallback * obj -> IAsyncResult) * endAction:(IAsyncResult -> 'T) * ?cancelAction:(unit -> unit) -> Async<'T>
static member FromBeginEnd : arg1:'Arg1 * arg2:'Arg2 * beginAction:('Arg1 * 'Arg2 * AsyncCallback * obj -> IAsyncResult) * endAction:(IAsyncResult -> 'T) * ?cancelAction:(unit -> unit) -> Async<'T>
static member FromBeginEnd : arg1:'Arg1 * arg2:'Arg2 * arg3:'Arg3 * beginAction:('Arg1 * 'Arg2 * 'Arg3 * AsyncCallback * obj -> IAsyncResult) * endAction:(IAsyncResult -> 'T) * ?cancelAction:(unit -> unit) -> Async<'T>
static member FromContinuations : callback:(('T -> unit) * (exn -> unit) * (OperationCanceledException -> unit) -> unit) -> Async<'T>
static member Ignore : computation:Async<'T> -> Async<unit>
static member OnCancel : interruption:(unit -> unit) -> Async<IDisposable>
static member Parallel : computations:seq<Async<'T>> -> Async<'T []>
static member RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:CancellationToken -> 'T
static member Sleep : millisecondsDueTime:int -> Async<unit>
static member Start : computation:Async<unit> * ?cancellationToken:CancellationToken -> unit
static member StartAsTask : computation:Async<'T> * ?taskCreationOptions:TaskCreationOptions * ?cancellationToken:CancellationToken -> Task<'T>
static member StartChild : computation:Async<'T> * ?millisecondsTimeout:int -> Async<Async<'T>>
static member StartChildAsTask : computation:Async<'T> * ?taskCreationOptions:TaskCreationOptions -> Async<Task<'T>>
static member StartImmediate : computation:Async<unit> * ?cancellationToken:CancellationToken -> unit
static member StartWithContinuations : computation:Async<'T> * continuation:('T -> unit) * exceptionContinuation:(exn -> unit) * cancellationContinuation:(OperationCanceledException -> unit) * ?cancellationToken:CancellationToken -> unit
static member SwitchToContext : syncContext:SynchronizationContext -> Async<unit>
static member SwitchToNewThread : unit -> Async<unit>
static member SwitchToThreadPool : unit -> Async<unit>
static member TryCancelled : computation:Async<'T> * compensation:(OperationCanceledException -> unit) -> Async<'T>
static member CancellationToken : Async<CancellationToken>
static member DefaultCancellationToken : CancellationToken

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.Parallel.myInt

val myChar : char

Full name: Snippet.Parallel.myChar

val myBool : bool

Full name: Snippet.Parallel.myBool

val myString : string

Full name: Snippet.Parallel.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel

Full name: Snippet.Parallel.Parallel<_>

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.Parallel.myInt

val myChar : char

Full name: Snippet.Parallel.myChar

val myBool : bool

Full name: Snippet.Parallel.myBool

val myString : string

Full name: Snippet.Parallel.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel

Full name: Snippet.Parallel.Parallel<_>

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.Parallel.myInt

val myChar : char

Full name: Snippet.Parallel.myChar

val myBool : bool

Full name: Snippet.Parallel.myBool

val myString : string

Full name: Snippet.Parallel.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel

Full name: Snippet.Parallel.Parallel<_>

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.Parallel.myInt

val myChar : char

Full name: Snippet.Parallel.myChar

val myBool : bool

Full name: Snippet.Parallel.myBool

val myString : string

Full name: Snippet.Parallel.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel

Full name: Snippet.Parallel.Parallel<_>

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.Parallel.myInt

val myChar : char

Full name: Snippet.Parallel.myChar

val myBool : bool

Full name: Snippet.Parallel.myBool

val myString : string

Full name: Snippet.Parallel.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel

Full name: Snippet.Parallel.Parallel<_>

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.Parallel.myInt

val myChar : char

Full name: Snippet.Parallel.myChar

val myBool : bool

Full name: Snippet.Parallel.myBool

val myString : string

Full name: Snippet.Parallel.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel

Full name: Snippet.Parallel.Parallel<_>

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.Parallel.myInt

val myChar : char

Full name: Snippet.Parallel.myChar

val myBool : bool

Full name: Snippet.Parallel.myBool

val myString : string

Full name: Snippet.Parallel.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel

Full name: Snippet.Parallel.Parallel<_>

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.Parallel.myInt

val myChar : char

Full name: Snippet.Parallel.myChar

val myBool : bool

Full name: Snippet.Parallel.myBool

val myString : string

Full name: Snippet.Parallel.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel

Full name: Snippet.Parallel.Parallel<_>

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.Parallel.myInt

val myChar : char

Full name: Snippet.Parallel.myChar

val myBool : bool

Full name: Snippet.Parallel.myBool

val myString : string

Full name: Snippet.Parallel.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel

Full name: Snippet.Parallel.Parallel<_>

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.Parallel.myInt

val myChar : char

Full name: Snippet.Parallel.myChar

val myBool : bool

Full name: Snippet.Parallel.myBool

val myString : string

Full name: Snippet.Parallel.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel

Full name: Snippet.Parallel.Parallel<_>

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.Parallel.myInt

val myChar : char

Full name: Snippet.Parallel.myChar

val myBool : bool

Full name: Snippet.Parallel.myBool

val myString : string

Full name: Snippet.Parallel.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel

Full name: Snippet.Parallel.Parallel<_>

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.Parallel.myInt

val myChar : char

Full name: Snippet.Parallel.myChar

val myBool : bool

Full name: Snippet.Parallel.myBool

val myString : string

Full name: Snippet.Parallel.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel

Full name: Snippet.Parallel.Parallel<_>

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.Parallel.myInt

val myChar : char

Full name: Snippet.Parallel.myChar

val myBool : bool

Full name: Snippet.Parallel.myBool

val myString : string

Full name: Snippet.Parallel.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel

Full name: Snippet.Parallel.Parallel<_>

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.Parallel.myInt

val myChar : char

Full name: Snippet.Parallel.myChar

val myBool : bool

Full name: Snippet.Parallel.myBool

val myString : string

Full name: Snippet.Parallel.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel

Full name: Snippet.Parallel<_>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.myInt

val myChar : char

Full name: Snippet.myChar

val myBool : bool

Full name: Snippet.myBool

val myString : string

Full name: Snippet.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

Parallel.Compute: Async<obj> []

Multiple items
type Async<'T>

Full name: Microsoft.FSharp.Control.Async<_>

Full name: Microsoft.FSharp.Control.Async

type obj = System.Object

Full name: Microsoft.FSharp.Core.obj

Parallel.Unpack: obj [] -> int -> 'T

Multiple items
val int : value:'T -> int (requires member op_Explicit)

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

——————–
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

——————–
type int = int32

Full name: Microsoft.FSharp.Core.int

val f : Parallel<('A -> 'B)>

Multiple items
type Parallel =
  static member Await : x:Async<'T> -> Parallel<'T>
  static member Pure : x:'T -> Parallel<'T>
  static member Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel

Full name: Snippet.Parallel<_>

val x : Parallel<'A>

module Array

from Microsoft.FSharp.Collections

val append : array1:'T [] -> array2:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.append

val xs : obj []

val pos : int

val fv : ('A -> 'B)

Parallel.Unpack: obj [] -> int -> 'A -> 'B

val xv : 'A

Parallel.Unpack: obj [] -> int -> 'A

property System.Array.Length: int

val x : Async<'A>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

Full name: Snippet.Parallel.Run

val p : Parallel<'T>

val async : AsyncBuilder

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.async

val results : obj []

member AsyncBuilder.Return : value:'T -> Async<'T>

val box : value:'T -> obj

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

val r : obj

static member Async.Parallel : computations:seq<Async<'T>> -> Async<'T []>

static member Parallel.Await : x:Async<'T> -> Parallel<'T>

Full name: Snippet.Parallel.Await

val x : Async<'T>

val v : 'T

val unbox : value:obj -> 'T

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

static member Parallel.Pure : x:'T -> Parallel<'T>

Full name: Snippet.Parallel.Pure

val x : 'T

val myInt : int

Full name: Snippet.myInt

val myChar : char

Full name: Snippet.myChar

val myBool : bool

Full name: Snippet.myBool

val myString : string

Full name: Snippet.myString

static member Parallel.Pure : x:'T -> Parallel<'T>

val w : int

val x : char

val y : bool

val z : string

static member Parallel.Run : p:Parallel<'T> -> Async<'T>

static member Async.RunSynchronously : computation:Async<'T> * ?timeout:int * ?cancellationToken:System.Threading.CancellationToken -> 'T

val test1 : unit -> int * char * bool

Full name: Snippet.test1

val x : int

val y : char

val z : bool

Great Ideas Made Real in F#

Posted on November 23, 2013 by Jack Fox

I’m honored to have been chosen by Microsoft as a Most Valuable Professional for F#, and the recent 5 days I spent at the annual MVP Summit were thrilling, stimulating, and eye-opening. While I can’t talk about much of what I learned and participated in, I want to pass on some great things that are completely out in the open, yet little known. They are on the cutting edge of philosophical accomplishment, both changing the world, really. And Microsoft Research is implementing these two great ideas with my favourite programming language.

Quantum Computing

The idea of a quantum computer gestated throughout the 1980’s, most famously in a 1981 proposal by Richard Feynman. The early 1990’s saw the discovery of the first quantum computing algorithm (one that could provably do something much faster than any classical algorithm) and by the middle of the decade Shor’s Algorithm became the first quantum algorithm that could do something really interesting (and spawned a whole genre of misinterpretation of quantum computing capabilities in popular journalism).

MSR is at the forefront of quantum computing research with LIQUi|> (pronounced “liquid”), the most advanced platform for quantum computing simulation in the world. There are no universal quantum computers in the world, yet. Until there are, LIQUi|> plays an important role in evaluating quantum computing capabilities, for instance in physical processes (the real intention of Feynman’s original work), and in providing a platform to evaluate academic work in the field. And it is poised to be the world’s first quantum computing development environment as soon as enough qubits can be entangled to build the worlds first quantum computer.

You can learn more about LIQUi|> in this video and accompanying slides.

The Computational Science Trinity

Here’s another idea, the Trinity of Computational Science. Frequently expounded upon by Robert Harper of Carnegie Mellon’s CS department, this is the unity of Type Theory, Proof Theory, and Category Theory. Taking it down a level towards the practical, think of it as Type Systems (strong typing), proving program correctness, and Functional Programming. The Oregon Programming Languages Summer School (sponsored in part by MSR) is dedicated to teaching these foundations to advance research and practical software engineering.

This is another area of leadership by MSR. This time with a derivative language of F# called F* (F Star). This language and others, like Idris, implement dependent types, an extension of type theory beyond the familiar strong typing of F#, where types can depend on functions, but F* takes it to another level. By interfacing to MSR’s Z3 theorem prover, F* effectively unifies the Computational Science Trinity. Functions and types become manifestations of the same thing and directly connect to correctness proof.

You can download F* and/or work through the interactive tutorial and experiment with it online.

FSharpTest: F# VS Test Project Template

Posted on October 16, 2013 by Jack Fox

Update Nov. 30, 2013: v1.2 adds VS 2013 support.

Update Nov. 10, 2013: v1.1 adds links to documentation (and just realized I forgot link to NUnit docs) and more samples of FsUnit and FsCheck, including stateful testing.

I finally did something about scratching an itch I’ve had for some time, that is to create an F# test project template, and I have released it upon the world as FSharpTest. No more fumbling around installing all the NuGet packages and opening another of my projects to see how to implement model test cases when I want to add a test project to a Visual Studio solution .

The Components

NUnit is my “go to” test framework and FsUnit lets me write test assertions in a more fluent composeable style. FsCheck and Unquote round-out the template with failing test case examples.

This is a first release to get community feedback, so let me know what you think. It occurred to me I don’t have a sample test case of FsUnit at work, and I should have added links to all the included test tool docs in the code comments, something for the next release. I also want to add more FsCheck technique examples including Stateful Testing and include TickSpec, as soon as I become familiar with that tool.

The available F# testing tools are really first class and I hope this makes it easier and faster for people to bring up tests.

Under the Covers

If you want to create your own distributable VS extension you will need to install the Visual Studio SDK. Here is the article on how to create project templates and you will find the template parameters reference helpful as well.

A template is a handy thing, but if you want to share it you need to wrap it in an
installable project template extension by using the VSIX project template. The steps in this article are pretty complete, but I never did find the “Content” section it talks about, and it doesn’t explicitly explain you have to add the template zip file to the project through the “Assets” tab.

Hackit Yurself

You can actually hack-up a VSIX file by changing its file type to “zip” and editing the contents. In fact that’s mostly how I crafted the entire template. Once you create the original template zip just edit the files and add NuGet packages in the root.

Now that you know that secret you can modify this extension to your own liking, but do let me know how you customize it so I can benefit too and consider putting the changes in future releases.

F# for Functional Enthusiasts Bibliography

Posted on October 2, 2013 by Jack Fox

Bibliograhy and slides for my talk to the Bay Area Clojure User Group .

Type Providers

F# Type Providers

F# R Provider

Visualize World Bank data in R with F# Type Providers

Types, Constraints, and Generics

Engineering Random Bits: F# Generics

The “Designing with types” series

Active patterns and member constraint

Type hackery

Help build optional type systems for Clojure and Clojurescript.

Type system as expressing intent 16:00

Eager Rose Tree, Vector, Parsing, Computational Expressions

Eager Rose Tree

Vector

CrockSolution

TestSandbox

{m}brace demos

Community-Driven Development

The F# Software Foundation

FAKE – F# Make

F# Formatting: Documentation tools

FunScript : F# to JavaScript with type providers

Charting World Bank data with F#

Develop CUDA applications

F# quotations to OpenCL translation

Web client to #websharper channel

Development Alternatives

Tsunami IDE

Missile Command playable in tsunami.io

Configuring Sublime Text 2 To Work With FSharp

Create iOS, Android, Mac and Windows apps

Using Sublime Text 2 as F# REPL

IKVM

IKVM.NET Home Page

Building a Java VM on the .NET Framework

Learning F#

F# Programming

A Course of F# Study

A directory of useful pages

F# Cheatsheet

Visual F#

Coming in F# 3.1

The Great New York F# Expedition of 2013

Posted on September 22, 2013 by Jack Fox

Halfway through the first day of our walking tour of New York, Paul tweets me while Sue and I are riding the Statten Island Ferry, can I extend my lightning talk to the N.Y. F# meetup on Tuesday evening? OK, it ended up making for a much better presentation. I spent the evening cutting down my Lambda Jam presentation to its essence, which I pretentiously titled “Semantically Coherent Functional Linear Data Structures”. The video is here This is the latest incarnation of the thoughts I’ve been trying to express since this blog post about the unity of linear purely functional data structures providing alternate composeable linear views and their capabilities.

I was followed by Rachel Reese’s excellent presentation on F# Agents.

NY Progressive F# Tutorials

Wendy and the Skills Matter crew put on a really nice conference For the NY Progressive F# Tutorials. This was my first experience with a Skills Matter conference, and it won’t be my last. Their reputation preceeds them, and now I can vouch they put on no-nonsense hands-on learning conferences for real practitioners. It helps that they get the best speakers. Don Syme’s keynote is captured on video, and the rest of the sessions on audio.

	Keynote: F# in the Open Source World Don Syme : 18th Sep 2013
	Calling and extending the F# compiler Don Syme and Tomas Petricek : 18th Sep 2013
	FCell: Numerical Development in Excel Tomas Petricek and Adam Mlocek : 18th Sep 2013
	Try F# from Zero to Data Science Rachel Reese and Phil Trelford : 18th Sep 2013
	F# Koans: An Interactive Way to Learn Chris Marinos : 18th Sep 2013
	Keynote: F# Beyond Windows Miguel de Icaza : 18th Sep 2013
	Graph Man Contest Richard Minerich and Paulmichael Blasucci : 18th Sep 2013
	Machine Learning with F# Phil Trelford and Mathias Brandewinder : 18th Sep 2013
	Code Quotations: Code-as-Data for F# Dmitry Mozorov and Jack Pappas : 18th Sep 2013
	Pac-Man Kata Phil Trelford and Mathias Brandewinder : 18th Sep 2013

The finale of the conference was Tyler Smith mopping the floor with me in the Pac Man AI programming competition, a group photo,

NYC Progressive F# Tutorials 2013 group

and dinner.

NYC Progressive F# Tutorials 2013 dinner

The F# conversations lasted until late in the night, I met some more of the international F# set, and once again the F# community was friendly, inclusive, and interested in progressing everyone’s skills and the state of the art.

After the F#

I was kindly invited to see the keynote of the next day’s conference, “Agile Testing & BDD Exchange”, by Gojko Adzic. If you have any interest at all in testing or user experience, I highly recommend this keynote.

Then I was off to the simultaneous Global GameCraft event in the Dumbo Spot annex to Dumbo Loft hosted by Andrea and Phil, where Phil Trelford gave me a personal tutorial on TickSpec, and I could take the time to work up a draft of this article.

Great Lakes Functional Programming Conference and more

I want to give a plug for the upcoming Great Lakes Functional Programming Conference in Detroit, MI on November 9. If you don’t already know, there is a vibrant functional programming community in Detroit, and kudos to Onorio Catenacci for organizing this.

My next talk is coming up on October 3 in San Francisco to the Bay Area Clojure User Group, “F# for Functional Enthusiasts”. Check it out if you are in the area.

Finally, I just have to pass on this little gem which spilled out of this year’s Strange Loop (darn! missed it again this year).

Gaining FsCheck Fluency through Transparency

Posted on August 11, 2013 by Jack Fox

You know the most important quality of a good unit test? It has to be incredibly easy to run.
–Onorio Catenacci

Transparency is a close second. It should be obvious what the unit test tests, how it tests it, and when it fails, how it failed and how to reproduce the failure.

FsCheck is the F# implementation of the well known Haskell QuickCheck test combinator library (also available for many other languages). This article demonstrates some of the tools and techniques available in FsCheck not only to make your tests transparent, but also to make FsCheck itself transparent.

(The rest of this article assumes some familiarity with FsCheck. If it is new to you, or you need to brush up on it, FsCheck – Breaking Your Code in New and Exciting Ways is an excellent place to start, and don’t forget the FsCheck documentation )

Choose your Check

The examples in this article come from tests of new functions in FSharpx.Collections.Vector to support Vector<Vector<‘T>>. Let’s look at one test implementing familiar property-based test techniques.

[<Test>]
let WindowedTest() =
    let testWindowed = 
        gen { let! windowLength = Gen.choose(1,5)
              let! source = Arb.generate<List<int>>
              return ((windowSeq windowLength source), (windowLength, source))
        }

    Check.QuickThrowOnFailure   (Prop.forAll  (Arb.fromGen testWindowed)

        (fun (vOfV, (windowLength, source)) -> 
            let outerLength =
                if source.Length = 0 then 1
                else int (Math.Ceiling((float)source.Length/(float)windowLength))
            (outerLength = vOfV.Length &&
                flatten vOfV |> List.ofSeq = source)
            |> Prop.classify (source.Length > 0 && outerLength > 0) "windowLength, outerLength"
            |> Prop.classify (source.Length = 0) "empty"
            |> Prop.collect (windowLength, outerLength)
        )
)

My go to form of FsCheck checking is usually a derivative of Check.Quick, which will check a single property with a default check config. Using the NUnit external runner on a compiled test project, as I usually do, calls for using the Check.QuickThrowOnFailure method, otherwise the runner will leave your test green lit, even though it reports as falsifiable in the Text Output tab

Check a falsification

Let's look at what FsCheck returns upon falsification by slipping a falsification into the property under test:

(outerLength = vOfV.Length && true = false &&

which has the desired result of displaying the generated data that failed:

*** VectorTest.WindowedTest
Falsifiable, after 1 test (0 shrinks) (StdGen (1338874294,295749962)):
(seq [seq [1]], (3, [1]))

This test data came from the return of the gen {...} GenBuilder above. It helps to understand the function under test.

Returns a vector of vectors of given length from the seq. Result may be a jagged vector.
windowSeq : int  -> seq<'T> -> Vector<Vector<'T>>

The first member of the outer tuple of test data is a Vector<Vector<'T>> produced from the parameter data in the second member, a tuple of window length and a source list. (FsCheck does not know about Vector<Vector<'T>>, so it prints it as seq [seq []].)

Classify your input

Once satisfied how FsCheck reports generated data, let's display more information about the range of generated data. Otherwise upon success FsCheck only provides the happy, but otherwise unsatisfying report

*** VectorTest.WindowedTest
Ok, passed 100 tests.

This is where classify and collect come in, allowing us to categorize the input and satisfy ourselves its range is reasonable.

*** VectorTest.WindowedTest
Ok, passed 100 tests.

6% (5, 2), windowLength, outerLength.
6% (5, 1), windowLength, outerLength.
5% (5, 4), windowLength, outerLength.
5% (3, 1), windowLength, outerLength.
4% (5, 1), empty.
4% (4, 1), windowLength, outerLength.
...
1% (1, 11), windowLength, outerLength.
1% (1, 1), windowLength, outerLength.
1% (1, 1), empty.

Verbosely putting it all together

Digging further we can get FsCheck to report the data of every generated test case using Check.Verbose.

*** VectorTest.WindowedTest
0:
(seq [seq []], (4, []))

1:
(seq [seq [-1]; seq [2]; seq [2]; seq [-2]], (1, [-1; 2; 2; -2]))

2:
(seq [seq [1; -3]; seq [-3]], (2, [1; -3; -3]))

3:
(seq [seq []], (5, []))
...

99:
(seq
   [seq [-33; 8; 48]; seq [-77; -31; 10]; seq [50; -75; -29]; seq [12; 58; -69];
    ...],
 (3,
  [-33; 8; 48; -77; -31; 10; 50; -75; -29; 12; 58; -69; -27; 14; 60; -67; -32;
   31; 4; -10; -27; 60; -21; -54; 39; 9; -68; -9; -11; 83; 11; 0; -43; 60; 39;
   80; -41; -1; 41; 82; -39; 1; 43; -83; -37; 4; 44; -81; -35; 6; 46; -79; -33;
   8; 48; -77; -31; 10; -37; -64; -22; 24; 65; -62; -20; 26; 67; -54; -18; 28;
   69; -52; -12; 30; 71; -50; -10; 32; 73; -48; -7; 34; 75; -46]))

Ok, passed 100 tests.

8% (3, 1), windowLength, outerLength.
...

Model-based checking by Command

You now have full command of property-based tests. There is another testing paradigm available within FsCheck, and that is by progressing the object under test from one state to another by means of "commands" and checking the state against an expected model. Kurt Schelfthout shows us how to use this technique at the end of the FSharpx.Collections.Deque tests

I'm not going to fully explain how this technique works, you can read about it here and study the Deque and Vector test examples. Instead I want to focus on transparency in stateful testing.

Out of the box a successful test gives us output like this:

*** VectorTest.Grow Vector<Vector<'T>>, check by flatten
Ok, passed 100 tests.

73% long sequnecs (>6 commands).
20% short sequences (between 1-6 commands).
1% trivial.

FsCheck.Commands.asProperty already provides statistics on the range of our generated tests, but the range is over something generated like this:

let ``Grow, check by flatten`` = 
    [conjInner1Elem(checkFlatten); conjInnerEmpty(checkFlatten); appendInnerMulti(checkFlatten)]

[<Test>]
let ``Grow Vector&lt;Vector&lt;'T>>, check by flatten``() =
    Check.QuickThrowOnFailure (asProperty (specVofV ``Grow, check by flatten``))

The sequences referred to in the output are sequences of generated commands, each potentially altering the previous state of an object under test. This opens the possibilities of

1) using commands as primitives in generating objects under test, and

2) testing multiple features in a single test.

I took advantage of both these possibilities to test the remaining new functions for Vector<Vector<'T>>.

Commands verbosely

So what do generated tests look like? For that, let's turn again to Check.Verbose

*** VectorTest.Grow Vector<Vector<'T>>, check by flatten
0:
[conjInner1Elem: elem = 2; conjInner1Elem: elem = -1]

1:
[conjInner1Elem: elem = 1; conjInnerEmpty; conjInnerEmpty]

2:
[conjInnerEmpty]

3:
[]

4:
[conjInnerEmpty; conjInner1Elem: elem = 0;
 appendInnerMulti: elems = [-6; -2; 5; 6; -3; -2; 5];
 appendInnerMulti: elems = [-2; 5; 6]; appendInnerMulti: elems = [-6; 1; -5];
 conjInnerEmpty]
 ...
Ok, passed 100 tests.

75% long sequnecs (>6 commands).
16% short sequences (between 1-6 commands).
4% trivial.

It is necessary to override ToString() in the commands you write to provide as much information as necessary, otherwise the record of test generations will be considerably less informative:

*** VectorTest.Grow Vector>, check by flatten
0:
[conjInner1Elem; conjInner1Elem]
1:
[conjInner1Elem; conjInnerEmpty]

2:
[conjInnerEmpty]

3:
[]

4:
[conjInnerEmpty; conjInner1Elem; appendInnerMulti;
 appendInnerMult; appendInnerMult; conjInnerEmpty]
 ...

Falsified command

So what output will a falsified command return? For this we will plant a little time-bomb, in order to make it interesting. The Pre member will prevent execution of this command until the other commands have generated an object of sufficient length. Then changing the Post member, where the check is performed to not will cause falsification.

let conjInnerEmpty check = 
    Gen.constant <|
        { new ICommand<Vector2Actual,VectorModel>() with
            member x.RunActual c = c |> conj empty
            member x.RunModel m = m
            member x.Pre m = (length m) > 0
            member x.Post (c,m) = not (check (c,m))
            override x.ToString() = sprintf "conjInnerEmpty"}

Resulting in this falsification output:

VectorTest.Grow Vector<Vector<'T>>, check by flatten:
System.Exception : Falsifiable, after 6 tests (2 shrinks) (StdGen (1351373830,295750028)):
[appendInnerMulti: elems = [0; -4; 0; -3]; conjInnerEmpty]

Conclusion

All-in-all, FsCheck is a powerful tool for unit test generation that provides full visibility into generation, execution, and repeatability. All of the practices I've outlined, verbose checking, classifying and collecting, and intentional falsification, are good exercises to run through every time you write a new test.