How to make immutable F# more performant? - f#

I'm wanting to write a big chunk of C# code using immutable F#. It's a device monitor, and the current implementation works by constantly getting data from a serial port and updating member variables based on new data. I'd like to transfer that to F# and get the benefits of immutable records, but my first shot at a proof-of-concept implementation is really slow.
open System
open System.Diagnostics
type DeviceStatus = { RPM : int;
Pressure : int;
Temperature : int }
// I'm assuming my actual implementation, using serial data, would be something like
// "let rec UpdateStatusWithSerialReadings (status:DeviceStatus) (serialInput:string[])".
// where serialInput is whatever the device streamed out since the previous check: something like
// ["RPM=90","Pres=50","Temp=85","RPM=40","Pres=23", etc.]
// The device streams out different parameters at different intervals, so I can't just wait for them all to arrive and aggregate them all at once.
// I'm just doing a POC here, so want to eliminate noise from parsing etc.
// So this just updates the status's RPM i times and returns the result.
let rec UpdateStatusITimes (status:DeviceStatus) (i:int) =
match i with
| 0 -> status
| _ -> UpdateStatusITimes {status with RPM = 90} (i - 1)
let initStatus = { RPM = 80 ; Pressure = 100 ; Temperature = 70 }
let stopwatch = new Stopwatch()
stopwatch.Start()
let endStatus = UpdateStatusITimes initStatus 100000000
stopwatch.Stop()
printfn "endStatus.RPM = %A" endStatus.RPM
printfn "stopwatch.ElapsedMilliseconds = %A" stopwatch.ElapsedMilliseconds
Console.ReadLine() |> ignore
This runs in about 1400 ms on my machine, whereas the equivalent C# code (with mutable member variables) runs in around 310 ms. Is there any way to speed this up without losing the immutability? I was hoping that the F# compiler would notice that initStatus and all the intermediate status variables were never reused, and thus simply mutate those records behind the scene, but I guess not.

In the F# community, imperative code and mutable data aren't frowned upon as long as they're not part of your public interface. I.e., using mutable data is fine as long as you encapsulate it and isolate it from the rest of your code. To that end, I suggest something like:
type DeviceStatus =
{ RPM : int
Pressure : int
Temperature : int }
// one of the rare scenarios in which I prefer explicit classes,
// to avoid writing out all the get/set properties for each field
[<Sealed>]
type private DeviceStatusFacade =
val mutable RPM : int
val mutable Pressure : int
val mutable Temperature : int
new(s) =
{ RPM = s.RPM; Pressure = s.Pressure; Temperature = s.Temperature }
member x.ToDeviceStatus () =
{ RPM = x.RPM; Pressure = x.Pressure; Temperature = x.Temperature }
let UpdateStatusITimes status i =
let facade = DeviceStatusFacade(status)
let rec impl i =
if i > 0 then
facade.RPM <- 90
impl (i - 1)
impl i
facade.ToDeviceStatus ()
let initStatus = { RPM = 80; Pressure = 100; Temperature = 70 }
let stopwatch = System.Diagnostics.Stopwatch.StartNew ()
let endStatus = UpdateStatusITimes initStatus 100000000
stopwatch.Stop ()
printfn "endStatus.RPM = %d" endStatus.RPM
printfn "stopwatch.ElapsedMilliseconds = %d" stopwatch.ElapsedMilliseconds
stdin.ReadLine () |> ignore
This way, the public interface is unaffected – UpdateStatusITimes still takes and returns an intrinsically immutable DeviceStatus – but internally UpdateStatusITimes uses a mutable class to eliminate allocation overhead.
EDIT: (In response to comment) This is the style of class I would normally prefer, using a primary constructor and lets + properties rather than vals:
[<Sealed>]
type private DeviceStatusFacade(status) =
let mutable rpm = status.RPM
let mutable pressure = status.Pressure
let mutable temp = status.Temperature
member x.RPM with get () = rpm and set n = rpm <- n
member x.Pressure with get () = pressure and set n = pressure <- n
member x.Temperature with get () = temp and set n = temp <- n
member x.ToDeviceStatus () =
{ RPM = rpm; Pressure = pressure; Temperature = temp }
But for simple facade classes where each property will be a blind getter/setter, I find this a bit tedious.
F# 3+ allows for the following instead, but I still don't find it to be an improvement, personally (unless one dogmatically avoids fields):
[<Sealed>]
type private DeviceStatusFacade(status) =
member val RPM = status.RPM with get, set
member val Pressure = status.Pressure with get, set
member val Temperature = status.Temperature with get, set
member x.ToDeviceStatus () =
{ RPM = x.RPM; Pressure = x.Pressure; Temperature = x.Temperature }

This won't answer your question, but it's probably worth stepping back and considering the big picture:
What do you perceive as the advantage of immutable data structures for this use case? F# supports mutable data structures, too.
You claim that the F# is "really slow" - but it's only 4.5 times slower than the C# code, and is making more than 70 million updates per second... Is this likely to be unacceptable performance for your actual application? Do you have a specific performance target in mind? Is there reason to believe that this type of code will be the bottleneck in your application?
Design is always about tradeoffs. You may find that for recording many changes in a short period of time, immutable data structures have an unacceptable performance penalty given your needs. On the other hand, if you have requirements such as keeping track of multiple older versions of a data structure at once, then the benefits of immutable data structures may make them attractive despite the performance penalty.

I suspect the performance problem you are seeing is due to the block memory zeroing involved when cloning the record (plus a negligible time for allocating it and subsequently garbage collecting it) in every iteration of the loop. You could rewrite your example using a struct:
[<Struct>]
type DeviceStatus =
val RPM : int
val Pressure : int
val Temperature : int
new(rpm:int, pres:int, temp:int) = { RPM = rpm; Pressure = pres; Temperature = temp }
let rec UpdateStatusITimes (status:DeviceStatus) (i:int) =
match i with
| 0 -> status
| _ -> UpdateStatusITimes (DeviceStatus(90, status.Pressure, status.Temperature)) (i - 1)
let initStatus = DeviceStatus(80, 100, 70)
The performance will now be close to that of using global mutable variables or by redefining UpdateStatusITimes status i as UpdateStatusITimes rpm pres temp i. This will only work if your struct is no more than 16 bytes long as otherwise it will get copied in the same sluggish manner as the record.
If, as you've hinted at in your comments, you intend to use this as part of a shared-memory multi-threaded design then you will need mutability at some point. Your choices are a) a shared mutable variable for each parameter b) one shared mutable variable containing a struct or c) a shared facade object containing mutable fields (like in ildjarn's answer). I would go for the last one since it is nicely encapsulated and scales beyond four int fields.

Using a tuple as follows is 15× faster than your original solution:
type DeviceStatus = int * int * int
let rec UpdateStatusITimes (rpm, pressure, temp) (i:int) =
match i with
| 0 -> rpm, pressure, temp
| _ -> UpdateStatusITimes (90,pressure,temp) (i - 1)
while true do
let initStatus = 80, 100, 70
let stopwatch = new Stopwatch()
stopwatch.Start()
let rpm,_,_ as endStatus = UpdateStatusITimes initStatus 100000000
stopwatch.Stop()
printfn "endStatus.RPM = %A" rpm
printfn "Took %fs" stopwatch.Elapsed.TotalSeconds
BTW, you should use stopwatch.Elapsed.TotalSeconds when timing.

Related

How do I make a mutable argument in a function through F#?

Sorry for my question but I did not understand the answers that was related to this question so I hope someone can enlighten me further.
I am a new data science student and we are going to learn how to program in the functional language F#. We are learning about algorithms and I wanted to write the algorithms as F# functions to check if my calculations on paper were correct.
I get the following error saying:
"This value is not mutable. Consider using the mutable keyword let mutable n = expression"
My code looks like this:
let loop5( n ) =
let mutable x = 0
while n > 0 do
x <- x + 1
n <- n + 1
printfn "loop5(): x=%i for n=%i" x n
loop5(4)
I'm trying to write a function looking like this (pseudocode):
loop5(n)
x = 0
while n > 0
x = x + 1
n = n + 1
return x
Hope I made a clear question and someone can help me out here :-) Have a nice weekend
You're trying to mutate the loop's parameter n. The parameter is not mutable, so the compiler doesn't let you. That's exactly what the error tells you.
Now, normally, to make the error go away, you'd make the variable mutable. However, you can't make a function parameter mutable, so that's not an option.
Here you want to think what the meaning of your program should be. Does the loop function need to pass the updated value of n back to its caller, or is the whole mutation its internal business? If it's the former, please see #AnyMoose's answer, but from your example and explanation, I suspect it's the latter. If that is the case, simply make a mutable copy of the parameter and work with it:
let loop n' =
let mutable x = 0
let mutable n = n'
...
Separately, I want to point out that your program, as written, would actually loop indefinitely (or until it wraps around the max int value anyway), because instead of decreasing n at each step you're increasing it. If you want your program to actually finish before the next Ice Age, you need to make n decrease with each iteration:
n <- n - 1
Ref cells
Ref cells get around some of the limitations of mutables. In fact, ref cells are very simple datatypes which wrap up a mutable field in a record type. Ref cells are defined by F# as follows:
type 'a ref = { mutable contents : 'a }
The F# library contains several built-in functions and operators for working with ref cells:
let ref v = { contents = v } (* val ref : 'a -> 'a ref *)
let (!) r = r.contents (* val (!) : 'a ref -> 'a *)
let (:=) r v = r.contents <- v (* val (:=) : 'a ref -> 'a -> unit *)
The ref function is used to create a ref cell, the ! operator is used to read the contents of a ref cell, and the := operator is used to assign a ref cell a new value. Here is a sample in fsi:
let x = ref "hello";;
val x : string ref
x;; (* returns ref instance *)
val it : string ref = {contents = "hello";}
!x;; (* returns x.contents *)
val it : string = "hello"
x := "world";; (* updates x.contents with a new value *)
val it : unit = ()
!x;; (* returns x.contents *)
val it : string = "world"
Since ref cells are allocated on the heap, they can be shared across multiple functions:
open System
let withSideEffects x =
x := "assigned from withSideEffects function"
let refTest() =
let msg = ref "hello"
printfn "%s" !msg
let setMsg() =
msg := "world"
setMsg()
printfn "%s" !msg
withSideEffects msg
printfn "%s" !msg
let main() =
refTest()
Console.ReadKey(true) |> ignore
main()
The withSideEffects function has the type val withSideEffects : string ref -> unit.
This program outputs the following:
hello
world
Assigned from withSideEffects function
The withSideEffects function is named as such because it has a side-effect, meaning it can change the state of a variable in other functions. Ref Cells should be treated like fire. Use it cautiously when it is absolutely necessary but avoid it in general. If you find yourself using Ref Cells while translating code from C/C++, then ignore efficiency for a while and see if you can get away without Ref Cells or at worst using mutable. You would often stumble upon a more elegant and more maintanable algorithm
Aliasing Ref Cells
Note: While imperative programming uses aliasing extensively, this practice has a number of problems. In particular it makes programs hard to follow since the state of any variable can be modified at any point elsewhere in an application. Additionally, multithreaded applications sharing mutable state are difficult to reason about since one thread can potentially change the state of a variable in another thread, which can result in a number of subtle errors related to race conditions and dead locks.
A ref cell is very similar to a C or C++ pointer. Its possible to point to two or more ref cells to the same memory address; changes at that memory address will change the state of all ref cells pointing to it. Conceptually, this process looks like this:
Let's say we have 3 ref cells looking at the same address in memory:
Three references to an integer with value 7
cell1, cell2, and cell3 are all pointing to the same address in memory. The .contents property of each cell is 7. Let's say, at some point in our program, we execute the code cell1 := 10, this changes the value in memory to the following:
Three references to an integer with value 10
By assigning cell1.contents a new value, the variables cell2 and cell3 were changed as well. This can be demonstrated using fsi as follows:
let cell1 = ref 7;;
val cell1 : int ref
let cell2 = cell1;;
val cell2 : int ref
let cell3 = cell2;;
val cell3 : int ref
!cell1;;
val it : int = 7
!cell2;;
val it : int = 7
!cell3;;
val it : int = 7
cell1 := 10;;
val it : unit = ()
!cell1;;
val it : int = 10
!cell2;;
val it : int = 10
!cell3;;
val it : int = 10

Dealing with .NET generic dictionaries in F#?

I am not a functional programmer.
I am learning F#.
I got a problem here.
Let me start from following piece of code:
type XmlNode(tagName, innerValue) =
member this.TagName = tagName
member this.InnerValue = innerValue
member this.Atts = Dictionary<string, obj>()
I don't use F# dict because (as I know) that one is readonly, however I obviously need to modify my attributes.
So I am really struggling to make it pure functional way:
type XmlNode with member this.WriteTo (output:StringBuilder) =
output.Append("<" + this.TagName) |> ignore
//let writeAtts =
// List.map2 (fun key value -> " " + key + "=" + value.ToString())
(List.ofSeq this.Atts.Keys) (List.ofSeq this.Atts.Values)
// |> List.reduce (fun acc str -> acc + " " + str)
//output.Append((writeAtts)) |> ignore
output.Append(">" + this.InnerValue + "</" + this.TagName + ">") |> ignore
output
The code I commented out was my (probably stupid) attemp to use mapping and reduction to concat all the atts in the single correctly formatted string. And that compiles OK.
But when I try to access my Atts property:
[<EntryPoint>]
let main argv =
let root = new XmlNode("root", "test")
root.Atts.Add("att", "val") // trying to add a new KVP
let output = new StringBuilder()
printfn "%O" (root.WriteTo(output))
Console.ReadLine()|>ignore
0 // return an integer exit code
...new attribute does not appear inside the Atts property, i.e. it remains empty.
So:
1) help me to make my code more functional.
2) and to understand how to deal with modificable dictionaries in F#.
Thank you.
First, your immediate problem: the way you defined the Atts property, it's not one value that is "stored" somewhere and is accessible via property. Instead, your definition means "every time somebody reads this property, create a new dictionary and return it". This is why your new attribute doesn't appear in the dictionary: it's a different dictionary every time you read root.Atts.
To create a property with a backing field and initial value, use member val:
type XmlNode(...) =
...
member val Atts = Dictionary<string,object>()
Now, answers to some implied questions.
First order of business: "modify the attributes" and "purely functional" are contradictory ideas. Functional programming implies immutable data. Nothing changes ever. The way to advance your computation is to create a new datum at every step, without overwriting the previous one. This basic idea turns out to be immensely valuable in practice: safer threading, trivial "undo" scenarios, trivial parallelization, trivial distribution to other machines, and even reduced memory consumption via persistent data structures.
Immutability is a very important point, and I urge you not to glance over it. Accepting it requires a mental shift. From my own (and other people I know) experience, it is very hard coming from imperative programming, but it is well worth it.
Second: do not use classes and properties. Technically speaking, object-oriented programming (in the sense of message passing) is not contradictory to functional, but the Enterprise flavor that is used in practice and implemented in C++, Java, C# et al., is contradictory, because it emphasizes this idea that "methods are operations that change an object's state", which is not functional (see above). So it's better to avoid object-oriented constructs, at least while you're learning. And especially since F# provides much better ways to encode data:
type XmlNode = { TagName: string; InnerValue: string; Atts: (string*string) list }
(notice how my Atts is not a dictionary; we'll come to this in a bit)
Similarly, to represent operations on your data, use functions, not methods:
let printNode (node: XmlNode) = (* we'll come to the implementation later *)
Third: why do you say that you "obviously" need to modify the attributes? The code you've shown does not call for this. For example, using my definition of XmlNode above, I can rewrite your code this way:
[<EntryPoint>]
let main argv =
let root = { TagName = "root"; InnerValue = "test"; Atts = ["att", "val"] }
printfn "%s" (printNode root)
...
But even if that was a real need, you shouldn't do it "in place". As I've described above while talking about immutability, you should not mutate the existing node, but rather create a new node that differs from the original one in whatever way you wanted to "modify":
let addAttr node name value = { node with Atts = (name, value) :: node.Atts }
In this implementation, I take a node and name/value of an attribute, and produce a new node whose Atts list consists of whatever was in the original node's Atts with the new attribute prepended.
The original Atts list stays intact, unmodified. But this does not mean twice the memory consumption: because we know that the original list never changes, we can reuse it: we create the new list by only allocating memory for the new item and including a reference to the old list as "other items". If the old list was subject to change, we couldn't do that, we would have to create a full copy (see "Defensive Copy"). This strategy is known as "Persistent Data Structure". It is one of the pillars of functional programming.
Finally, for string formatting, I recommend using sprintf instead of StringBuilder. It offers similar performance benefits, but in addition provides type safety. For example, code sprintf "%s" 5 will not compile, complaining that the format expects a string, but the final argument 5 is a number. With this, we can implement the printNode function:
let printNode (node: XmlNode) =
let atts = seq { for n, v in node.Atts -> sprintf " %s=\"%s\"" n v } |> String.concat ""
sprintf "<%s%s>%s</%s>" node.TagName atts node.InnerValue node.TagName
For reference, here's your complete program, rewritten in functional style:
type XmlNode = { TagName: string; InnerValue: string; Atts: (string*string) list }
let printNode (node: XmlNode) =
let atts = seq { for n, v in node.Atts -> sprintf " %s=\"%s\"" n v } |> String.concat ""
sprintf "<%s%s>%s</%s>" node.TagName atts node.InnerValue node.TagName
[<EntryPoint>]
let main argv =
let root = { TagName = "root"; InnerValue = "test"; Atts = ["att", "val"] }
printfn "%s" (printNode root)
Console.ReadLine() |> ignore
0

How to memoize the result of a property of a Discriminated Union in F#

I have a Discriminated Union ("DU") type and a property OR method which computes something based on the DU instance. I am trying to achieve a pattern where the instance property performs the calculation the first time it is requested and then remembers the result - akin to a Singleton Pattern in Object Oriented Terms.
I am finding this challenging without the aid of a local instance variable to store the state of things...
I have tried simple memoization of a method but I then run into the problem of not having anywhere (in the instance) to store the memoized result.
Note: there will be many instances of this DU type in my application.
Code
// Terrible mutable variable needed alongside the DU to achieve a singleton-like pattern
let mutable result: int option = None
type DU =
| Good of int
| Bad of int
with
// behaves like a Singleton
member this.GetSomething =
match result with
| None ->
printfn "Big bad side-effect to let us know it's a first time"
// big bad calculation that we only want to do once
let x = 1 + 1
// "memoize" it
result <- Some x
x
| Some y -> y
let instance = Good 1
let f1 = instance.GetSomething // first time
let f2 = instance.GetSomething // second call - no side effect1
You can't memoize inside of an immutable value, because memoization involves changing and maintaining state.
Obviously, you can do it outside of an immutable value:
let smth = getSomething "foo"
As long as you reuse smth instead of calling getSomething "foo" again, you've essentially memoized the result. This is safe if getSomething is referentially transparent; otherwise, it's not.
From the sample code posted in the OP, it looks more like you're looking for lazy initialization, which you can get from the Lazy<T> class. You'll still need an object in which to store the Lazy<T> instance, though.
open System
type MyObject() =
let result =
lazy
printfn "Big bad side-effect to let us know it's a first time"
// big bad calculation that we only want to do once
1 + 1
member this.GetSomething = result.Value
As you can see, in F# you can also use lazy expressions for this.
> let mo = MyObject ();;
val mo : MyObject
> let smth1 = mo.GetSomething;;
Big bad side-effect to let us know it's a first time
val smth1 : int = 2
> let smth2 = mo.GetSomething;;
val smth2 : int = 2
The MyObject class may look immutable, but that's only because state is being kept inside of the lazy expression.
This way it is possible to have a lazy inside a DU.
Because the type is Lazy.
type DU =
| Good of Lazy<int> // Lazy not lazy
| Bad of Lazy<int>
type MyObject() =
let result =
lazy(
printfn "Big bad side-effect to let us know it's a first time"
// big bad calculation that we only want to do once
1 + 1) |> Good
member this.GetSomething = result
let mo = MyObject()
let f() =
match mo.GetSomething with
| Good x -> x.Value
| Bad y -> y.Value
f()
f()
Output
Big bad side-effect to let us know it's a first time
val it : int = 2
>
val it : int = 2

Lazy.. but eager data loader in F#

Does anyone know of 'prior art' regarding the following subject :
I have data that take some decent time to load. they are historical level for various stocks.
I would like to preload them somehow, to avoid the latency when using my app
However, preloading them in one chunk at start makes my app unresponsive first which is not user friendly
So I would like to not load my data.... unless the user is not requesting any and playing with what he already has, in which case I would like to get little by little. So it is neither 'lazy' nor 'eager', more 'lazy when you need' and 'eager when you can', hence the acronym LWYNEWYC.
I have made the following which seems to work, but I just wonder if there is a recognized and blessed approach for such thing ?
let r = LoggingFakeRepo () :> IQuoteRepository
r.getHisto "1" |> ignore //prints Getting histo for 1 when called
let rc = RepoCached (r) :> IQuoteRepository
rc.getHisto "1" |> ignore //prints Getting histo for 1 the first time only
let rcc = RepoCachedEager (r) :> IQuoteRepository
rcc.getHisto "100" |> ignore //prints Getting histo 1..100 by itself BUT
//prints Getting histo 100 immediately when called
And the classes
type IQuoteRepository =
abstract getUnderlyings : string seq
abstract getHisto : string -> string
type LoggingFakeRepo () =
interface IQuoteRepository with
member x.getUnderlyings = printfn "getting underlyings"
[1 .. 100] |> List.map string :> _
member x.getHisto udl = printfn "getting histo for %A" udl
"I am a historical dataset in a disguised party"
type RepoCached (rep : IQuoteRepository) =
let memoize f =
let cache = new System.Collections.Generic.Dictionary<_, _>()
fun x ->
if cache.ContainsKey(x) then cache.[x]
else let res = f x
cache.[x] <- res
res
let udls = lazy (rep.getUnderlyings )
let gethistom = memoize rep.getHisto
interface IQuoteRepository with
member x.getUnderlyings = udls.Force()
member x.getHisto udl = gethistom udl
type Message = string * AsyncReplyChannel<UnderlyingWrap>
type RepoCachedEager (rep : IQuoteRepository) =
let udls = rep.getUnderlyings
let agent = MailboxProcessor<Message>.Start(fun inbox ->
let repocached = RepoCached (rep) :> IQuoteRepository
let rec loop l =
async { try
let timeout = if l|> List.isEmpty then -1 else 50
let! (udl, replyChannel) = inbox.Receive(timeout)
replyChannel.Reply(repocached.getHisto udl)
do! loop l
with
| :? System.TimeoutException ->
let udl::xs = l
repocached.getHisto udl |> ignore
do! loop xs
}
loop (udls |> Seq.toList))
interface IQuoteRepository with
member x.getUnderlyings = udls
member x.getHisto udl = agent.PostAndReply(fun reply -> udl, reply)
I like your solution. I think using agent to implement some background loading with a timeout is a great way to go - agents can nicely encapsulate mutable state, so it is clearly safe and you can encode the behaviour you want quite easily.
I think asynchronous sequences might be another useful abstraction (if I'm correct, they are available in FSharpX these days). An asynchronous sequence represents a computation that asynchronously produces more values, so they might be a good way to separate the data loader from the rest of the code.
I think you'll still need an agent to synchronize at some point, but you can nicely separate different concerns using async sequences.
The code to load the data might look something like this:
let loadStockPrices repo = asyncSeq {
// TODO: Not sure how you detect that the repository has no more data...
while true do
// Get next item from the repository, preferably asynchronously!
let! data = repo.AsyncGetNextHistoricalValue()
// Return the value to the caller...
yield data }
This code represents the data loader, and it separates it from the code that uses it. From the agent that consumes the data source, you can use AsyncSeq.iterAsync to consume the values and do something with them.
With iterAsync, the function that you specify as a consumer is asynchronous. It may block (i.e. using Sleep) and when it blocks, the source - that is.your loader - is also blocked. This is quite nice implicit way to control the loader from the code that consumes the data.
A feature that is not in the library yet (but would be useful) is an partially eager evaluator that takes AsyncSeq<'T> and returns a new AsyncSeq<'T> but obtains a certain number of elements from the source as soon as possible and caches them (so that the consumer does not have to wait when it asks for a value, as long as the source can produce values fast enough).

Cyclic lists in F#

Is it just me, or does F# not cater for cyclic lists?
I looked at the FSharpList<T> class via reflector, and noticed, that neither the 'structural equals' or the length methods check for cycles. I can only guess if 2 such primitive functions does not check, that most list functions would not do this either.
If cyclic lists are not supported, why is that?
Thanks
PS: Am I even looking at the right list class?
There are many different lists/collection types in F#.
F# list type. As Chris said, you cannot initialize a recursive value of this type, because the type is not lazy and not mutable (Immutability means that you have to create it at once and the fact that it's not lazy means that you can't use F# recursive values using let rec). As ssp said, you could use Reflection to hack it, but that's probably a case that we don't want to discuss.
Another type is seq (which is actually IEnumerable) or the LazyList type from PowerPack. These are lazy, so you can use let rec to create a cyclic value. However, (as far as I know) none of the functions working with them take cyclic lists into account - if you create a cyclic list, it simply means that you're creating an infinite list, so the result of (e.g.) map will be a potentially infinite list.
Here is an example for LazyList type:
#r "FSharp.PowerPack.dll"
// Valid use of value recursion
let rec ones = LazyList.consDelayed 1 (fun () -> ones)
Seq.take 5 l // Gives [1; 1; 1; 1; 1]
The question is what data types can you define yourself. Chris shows a mutable list and if you write operations that modify it, they will affect the entire list (if you interpret it as an infinite data structure).
You can also define a lazy (potentionally cyclic) data type and implement operations that handle cycles, so when you create a cyclic list and project it into another list, it will create cyclic list as a result (and not a potentionally infinite data structure).
The type declaration may look like this (I'm using object type, so that we can use reference equality when checking for cycles):
type CyclicListValue<'a> =
Nil | Cons of 'a * Lazy<CyclicList<'a>>
and CyclicList<'a>(value:CyclicListValue<'a>) =
member x.Value = value
The following map function handles cycles - if you give it a cyclic list, it will return a newly created list with the same cyclic structure:
let map f (cl:CyclicList<_>) =
// 'start' is the first element of the list (used for cycle checking)
// 'l' is the list we're processing
// 'lazyRes' is a function that returns the first cell of the resulting list
// (which is not available on the first call, but can be accessed
// later, because the list is constructed lazily)
let rec mapAux start (l:CyclicList<_>) lazyRes =
match l.Value with
| Nil -> new CyclicList<_>(Nil)
| Cons(v, rest) when rest.Value = start -> lazyRes()
| Cons(v, rest) ->
let value = Cons(f v, lazy mapAux start rest.Value lazyRes)
new CyclicList<_>(value)
let rec res = mapAux cl cl (fun () -> res)
res
The F# list type is essentially a linked list, where each node has a 'next'. This in theory would allow you to create cycles. However, F# lists are immutable. So you could never 'make' this cycle by mutation, you would have to do it at construction time. (Since you couldn't update the last node to loop around to the front.)
You could write this to do it, however the compiler specifically prevents it:
let rec x = 1 :: 2 :: 3 :: x;;
let rec x = 1 :: 2 :: 3 :: x;;
------------------------^^
stdin(1,25): error FS0260: Recursive values cannot appear directly as a construction of the type 'List`1' within a recursive binding. This feature has been removed from the F# language. Consider using a record instead.
If you do want to create a cycle, you could do the following:
> type CustomListNode = { Value : int; mutable Next : CustomListNode option };;
type CustomListNode =
{Value: int;
mutable Next: CustomListNode option;}
> let head = { Value = 1; Next = None };;
val head : CustomListNode = {Value = 1;
Next = null;}
> let head2 = { Value = 2; Next = Some(head) } ;;
val head2 : CustomListNode = {Value = 2;
Next = Some {Value = 1;
Next = null;};}
> head.Next <- Some(head2);;
val it : unit = ()
> head;;
val it : CustomListNode = {Value = 1;
Next = Some {Value = 2;
Next = Some ...;};}
The answer is same for all languages with tail-call optimization support and first-class functions (function types) support: it's so easy to emulate cyclic structures.
let rec x = seq { yield 1; yield! x};;
It's simplest way to emulate that structure by using laziness of seq.
Of course you can hack list representation as described here.
As was said before, your problem here is that the list type is immutable, and for a list to be cyclic you'd have to have it stick itself into its last element, so that doesn't work. You can use sequences, of course.
If you have an existing list and want to create an infinite sequence on top of it that cycles through the list's elements, here's how you could do it:
let round_robin lst =
let rec inner_rr l =
seq {
match l with
| [] ->
yield! inner_rr lst
| h::t ->
yield h
yield! inner_rr t
}
if lst.IsEmpty then Seq.empty else inner_rr []
let listcycler_sequence = round_robin [1;2;3;4;5;6]

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