Difference between #seq and seq in F# - f#

I was wondering what #seq means in the F# interactive shell.
I had a collect function with 2 parameters, a function and a sequence, where this function is applied to the sequence.
let rec collect f sq =
seq {
let a = Seq.item 0 sq
let sq1 = Seq.skip 1 sq
let ris = f a
yield! ris
yield! collect f sq1
}
When the shell evaluates the collect it gives back the following signature
val collect: f: ('a -> #seq<'c>) -> sq: seq<'a> -> seq<'c>
What does # mean before seq in this instance?

seq<'a> is the F# spelling for IEnumerable<T>
The # before a type is a flexible type annotation. This allows you to use any type that implements the indicated interface.

Related

F# -- The resulting type would be infinite error

Here is a simple code to generate all permutations, based on implementation found here: All permutations of a list
let concatElement element sequence =
seq {
yield element
yield! sequence
}
let rec permute (choices : 'a seq)=
seq {
if Seq.isEmpty choices then
yield Seq.empty
else
for choice in choices do
let remaining = choices |> Seq.where (fun el -> el <> choice)
yield concatElement choice (permute remaining)
}
I get a compile-time error "The resulting type would be infinite when unifying ''a' and 'seq<'a>'" on "yield concatElement choice (permute remaining)"
What is wrong here?
You're trying to yield an 'a seq as a single element of a sequence which has type 'a seq. For that to work, then 'a must be the same type as 'a seq, and so on, so the type is "infinite" - you'd have to have nested them infinitely for it to "work".
I see in your answer that you recognised you have to loop through the sequence elements somehow. You can, as you have, use the for .. in syntax to iterate through, or F# gives you the yield! operator which actually does this for you. In this spirit, your answer could be written as
let rec permute (choices : 'a seq) (permBuilder: 'a seq) : seq<seq<'a>>= seq {
if Seq.isEmpty choices then
yield permBuilder
else
for choice in choices do
let remaining = choices |> Seq.where (fun el -> el <> choice)
let newBuilder = concatElement choice permBuilder
yield! permute remaining newBuilder }
Or, alternatively, we can use the Seq.collect function to automatically gather a sequence of sequences (of sequences!) for us, and we're left with nice functional-style code with no explicit iterators:
let prepend element sequence = seq { yield element; yield! sequence }
let rec permute input =
if Seq.length input <= 1 then Seq.singleton input
else
let without element = Seq.where ((<>) element) input
let permutations element = permute (without element) |> Seq.map (prepend element)
Seq.collect permutations input
Something to consider, though: what happens if you have two elements which aren't distinct? For example, what happens if you try to get the permutations of [1; 1; 2]? Your current method can't handle this neatly - even if you improved the without closure, you'd get duplicate answers.
I think I got it
let concatElement element sequence =
seq {
yield element
yield! sequence
}
let rec permute (choices : 'a seq) (permBuilder: 'a seq) : seq<seq<'a>>=
seq {
if Seq.isEmpty choices then
yield permBuilder
else
for choice in choices do
let remaining = choices |> Seq.where (fun el -> el <> choice)
let newBuilder = concatElement choice permBuilder
for perm in permute remaining newBuilder do
yield perm
As Lee've has commented, I tried to concat seq<'a> with seq< seq<'a>>. My code lacked a loop over permutations.

How do I write a computation expression builder that accumulates a value and also allows standard language constructs?

I have a computation expression builder that builds up a value as you go, and has many custom operations. However, it does not allow for standard F# language constructs, and I'm having a lot of trouble figuring out how to add this support.
To give a stand-alone example, here's a dead-simple and fairly pointless computation expression that builds F# lists:
type Items<'a> = Items of 'a list
type ListBuilder() =
member x.Yield(()) = Items []
[<CustomOperation("add")>]
member x.Add(Items current, item:'a) =
Items [ yield! current; yield item ]
[<CustomOperation("addMany")>]
member x.AddMany(Items current, items: seq<'a>) =
Items [ yield! current; yield! items ]
let listBuilder = ListBuilder()
let build (Items items) = items
I can use this to build lists just fine:
let stuff =
listBuilder {
add 1
add 5
add 7
addMany [ 1..10 ]
add 42
}
|> build
However, this is a compiler error:
listBuilder {
let x = 5 * 39
add x
}
// This expression was expected to have type unit, but
// here has type int.
And so is this:
listBuilder {
for x = 1 to 50 do
add x
}
// This control construct may only be used if the computation expression builder
// defines a For method.
I've read all the documentation and examples I can find, but there's something I'm just not getting. Every .Bind() or .For() method signature I try just leads to more and more confusing compiler errors. Most of the examples I can find either build up a value as you go along, or allow for regular F# language constructs, but I haven't been able to find one that does both.
If someone could point me in the right direction by showing me how to take this example and add support in the builder for let bindings and for loops (at minimum - using, while and try/catch would be great, but I can probably figure those out if someone gets me started) then I'll be able to gratefully apply the lesson to my actual problem.
The best place to look is the spec. For example,
b {
let x = e
op x
}
gets translated to
T(let x = e in op x, [], fun v -> v, true)
=> T(op x, {x}, fun v -> let x = e in v, true)
=> [| op x, let x = e in b.Yield(x) |]{x}
=> b.Op(let x = e in in b.Yield(x), x)
So this shows where things have gone wrong, though it doesn't present an obvious solution. Clearly, Yield needs to be generalized since it needs to take arbitrary tuples (based on how many variables are in scope). Perhaps more subtly, it also shows that x is not in scope in the call to add (see that unbound x as the second argument to b.Op?). To allow your custom operators to use bound variables, their arguments need to have the [<ProjectionParameter>] attribute (and take functions from arbitrary variables as arguments), and you'll also need to set MaintainsVariableSpace to true if you want bound variables to be available to later operators. This will change the final translation to:
b.Op(let x = e in b.Yield(x), fun x -> x)
Building up from this, it seems that there's no way to avoid passing the set of bound values along to and from each operation (though I'd love to be proven wrong) - this will require you to add a Run method to strip those values back off at the end. Putting it all together, you'll get a builder which looks like this:
type ListBuilder() =
member x.Yield(vars) = Items [],vars
[<CustomOperation("add",MaintainsVariableSpace=true)>]
member x.Add((Items current,vars), [<ProjectionParameter>]f) =
Items (current # [f vars]),vars
[<CustomOperation("addMany",MaintainsVariableSpace=true)>]
member x.AddMany((Items current, vars), [<ProjectionParameter>]f) =
Items (current # f vars),vars
member x.Run(l,_) = l
The most complete examples I've seen are in §6.3.10 of the spec, especially this one:
/// Computations that can cooperatively yield by returning a continuation
type Eventually<'T> =
| Done of 'T
| NotYetDone of (unit -> Eventually<'T>)
[<CompilationRepresentation(CompilationRepresentationFlags.ModuleSuffix)>]
module Eventually =
/// The bind for the computations. Stitch 'k' on to the end of the computation.
/// Note combinators like this are usually written in the reverse way,
/// for example,
/// e |> bind k
let rec bind k e =
match e with
| Done x -> NotYetDone (fun () -> k x)
| NotYetDone work -> NotYetDone (fun () -> bind k (work()))
/// The return for the computations.
let result x = Done x
type OkOrException<'T> =
| Ok of 'T
| Exception of System.Exception
/// The catch for the computations. Stitch try/with throughout
/// the computation and return the overall result as an OkOrException.
let rec catch e =
match e with
| Done x -> result (Ok x)
| NotYetDone work ->
NotYetDone (fun () ->
let res = try Ok(work()) with | e -> Exception e
match res with
| Ok cont -> catch cont // note, a tailcall
| Exception e -> result (Exception e))
/// The delay operator.
let delay f = NotYetDone (fun () -> f())
/// The stepping action for the computations.
let step c =
match c with
| Done _ -> c
| NotYetDone f -> f ()
// The rest of the operations are boilerplate.
/// The tryFinally operator.
/// This is boilerplate in terms of "result", "catch" and "bind".
let tryFinally e compensation =
catch (e)
|> bind (fun res -> compensation();
match res with
| Ok v -> result v
| Exception e -> raise e)
/// The tryWith operator.
/// This is boilerplate in terms of "result", "catch" and "bind".
let tryWith e handler =
catch e
|> bind (function Ok v -> result v | Exception e -> handler e)
/// The whileLoop operator.
/// This is boilerplate in terms of "result" and "bind".
let rec whileLoop gd body =
if gd() then body |> bind (fun v -> whileLoop gd body)
else result ()
/// The sequential composition operator
/// This is boilerplate in terms of "result" and "bind".
let combine e1 e2 =
e1 |> bind (fun () -> e2)
/// The using operator.
let using (resource: #System.IDisposable) f =
tryFinally (f resource) (fun () -> resource.Dispose())
/// The forLoop operator.
/// This is boilerplate in terms of "catch", "result" and "bind".
let forLoop (e:seq<_>) f =
let ie = e.GetEnumerator()
tryFinally (whileLoop (fun () -> ie.MoveNext())
(delay (fun () -> let v = ie.Current in f v)))
(fun () -> ie.Dispose())
// Give the mapping for F# computation expressions.
type EventuallyBuilder() =
member x.Bind(e,k) = Eventually.bind k e
member x.Return(v) = Eventually.result v
member x.ReturnFrom(v) = v
member x.Combine(e1,e2) = Eventually.combine e1 e2
member x.Delay(f) = Eventually.delay f
member x.Zero() = Eventually.result ()
member x.TryWith(e,handler) = Eventually.tryWith e handler
member x.TryFinally(e,compensation) = Eventually.tryFinally e compensation
member x.For(e:seq<_>,f) = Eventually.forLoop e f
member x.Using(resource,e) = Eventually.using resource e
The tutorial at "F# for fun and profit" is first class in this regard.
http://fsharpforfunandprofit.com/posts/computation-expressions-intro/
Following a similar struggle to Joel's (and not finding §6.3.10 of the spec that helpful) my issue with getting the For construct to generate a list came down to getting types to line up properly (no special attributes required). In particular I was slow to realise that For would build a list of lists, and therefore need flattening, despite the best efforts of the compiler to put me right. Examples that I found on the web were always wrappers around seq{}, using the yield keyword, repeated use of which invokes a call to Combine, which does the flattening. In case a concrete example helps, the following excerpt uses for to build a list of integers - my ultimate aim being to create lists of components for rendering in a GUI (with some additional laziness thrown in). Also In depth talk on CE here which elaborates on kvb's points above.
module scratch
type Dispatcher = unit -> unit
type viewElement = int
type lazyViews = Lazy<list<viewElement>>
type ViewElementsBuilder() =
member x.Return(views: lazyViews) : list<viewElement> = views.Value
member x.Yield(v: viewElement) : list<viewElement> = [v]
member x.ReturnFrom(viewElements: list<viewElement>) = viewElements
member x.Zero() = list<viewElement>.Empty
member x.Combine(listA:list<viewElement>, listB: list<viewElement>) = List.concat [listA; listB]
member x.Delay(f) = f()
member x.For(coll:seq<'a>, forBody: 'a -> list<viewElement>) : list<viewElement> =
// seq {for v in coll do yield! f v} |> List.ofSeq
Seq.map forBody coll |> Seq.collect id |> List.ofSeq
let ve = new ViewElementsBuilder()
let makeComponent(m: int, dispatch: Dispatcher) : viewElement = m
let makeComponents() : list<viewElement> = [77; 33]
let makeViewElements() : list<viewElement> =
let model = {| Scores = [33;23;22;43;] |> Seq.ofList; Trainer = "John" |}
let d:Dispatcher = fun() -> () // Does nothing here, but will be used to raise messages from UI
ve {
for score in model.Scores do
yield makeComponent (score, d)
yield makeComponent (score * 100 / 50 , d)
if model.Trainer = "John" then
return lazy
[ makeComponent (12, d)
makeComponent (13, d)
]
else
return lazy
[ makeComponent (14, d)
makeComponent (15, d)
]
yield makeComponent (33, d)
return! makeComponents()
}

How to rewrite this function using the pipeline operator

These are the function definitions.
func1: 'a -> unit
func2: 'b -> 'a
func3: string -> 'b list
The current function
let f = Seq.iter((fun a -> func1(func2 a)) func3(s)
This is as far as I got
let f = func3(s)
|> ((fun a -> func2 a
|> func1)
|> Seq.iter)
I have the feeling it should be possible to loose the lambda and the parens'.
You can do without pipes, simply
Seq.iter (func1 << func2) << func3
(this is a function with some arguments [same than func3] and same output than Seq.iter).
You can test it
let func1 x = printfn "Number: %d" x
let func2 (a, b) = a + b
let func3 = Seq.map (fun n -> (n, 2 * n))
let f : (seq<_> -> unit) = Seq.iter (func1 << func2) << func3
f [1..5]
with output
Number: 3
Number: 6
Number: 9
Number: 12
Number: 15
val func1 : x:int -> unit
val func2 : a:int * b:int -> int
val func3 : (seq<int> -> seq<int * int>)
val f : (seq<int> -> unit)
val it : unit = ()
:)
You can use function composition operator >>:
func3() |> Seq.iter (func2 >> func1)
I think the question is, why do you want to use the pipeline operator?
I find your original code quite readable. You should not try to use pipeline operator (or function composition) just for the sake of using them. Now, in your code, the input s comes at the end, which is a bit unfortunate (you cannot quite see what is the main input for the code). I would probably rewrite it as (also, s is not really a descriptive name):
s |> func3
|> Seq.iter (fun a -> func1 (func2 a))
You can use function composition too - but I do not use it very often, because it does not (always) help with readability. But using it in the argument of Seq.iter is probably quite reasonable.
On a completely unrelated note, you could just use for loop and write:
for a in func3 s do
func1 (func2 a)
I actually find this more readable than any other version of the code here (if F# gives you a language feature for iterating over sequences that does exactly what you need, why not use it?)

Parallel pipelining

(fileNameToCharStream "bigfile"
|>> fuse [length;
splitBy (fun x -> x = ' ' || x = '\n') removeEmpty |>> length;
splitBy (fun x -> x = '\n') keepEmpty |>> length;
])
(*fuse "fuses" the three functions to run concurrently*)
|> run 2 (*forces to run in parallel on two threads*)
|> (fun [num_chars; num_words; num_lines] ->
printfn "%d %d %d"
num_chars num_words, num_lines))
I want to make this code work in the following way:
split the original stream into two exactly in the middle; then
for each half run a separate computation that
computes 3 things: the length (i.e. number of chars),
the number of words, the number of lines.
However, I do not want to have a problem if
I erroneously split over a word. This has to be
taken care of. The file should be read only once.
How should I program the functions specified and the operator |>>?
Is it possible?
It looks like your asking for quite a bit. I'll leave it up to you to figure out the string manipulation, but I'll show you how to define an operator which executes a series of operations in parallel.
Step 1: Write a fuse function
Your fuse function appears to map a single input using multiple functions, which is easy enough to write as follows:
//val fuse : seq<('a -> 'b)> -> 'a -> 'b list
let fuse functionList input = [ for f in functionList -> f input]
Note that all of your mapping functions need to have the same type.
Step 2: Define operator to execute functions in parallel
The standard parallel map function can be written as follows:
//val pmap : ('a -> 'b) -> seq<'a> -> 'b array
let pmap f l =
seq [for a in l -> async { return f a } ]
|> Async.Parallel
|> Async.RunSynchronously
To my knowledge, Async.Parallel will execute async operations in parallel, where the number of parallel tasks executing at any given time is equal to the number of cores on a machine (someone can correct me if I'm wrong). So on a dual core machine, we should have at most 2 threads running on my machine when this function is called. This is a good thing, since we don't expect any speedup by running more than one thread per core (in fact the extra context switching might slow things down).
We can define an operator |>> in terms of pmap and fuse:
//val ( |>> ) : seq<'a> -> seq<('a -> 'b)> -> 'b list array
let (|>>) input functionList = pmap (fuse functionList) input
So the |>> operator takes a bunch of inputs and maps them using lots of different outputs. So far, if we put all this together, we get the following (in fsi):
> let countOccurrences compareChar source =
source |> Seq.sumBy(fun c -> if c = compareChar then 1 else 0)
let length (s : string) = s.Length
let testData = "Juliet is awesome|Someone should give her a medal".Split('|')
let testOutput =
testData
|>> [length; countOccurrences 'J'; countOccurrences 'o'];;
val countOccurrences : 'a -> seq<'a> -> int
val length : string -> int
val testData : string [] =
[|"Juliet is awesome"; "Someone should give her a medal"|]
val testOutput : int list array = [|[17; 1; 1]; [31; 0; 3]|]
testOutput contains two elements, both of which were computed in parallel.
Step 3: Aggregate elements into a single output
Alright, so now we have partial results represented by each element in our array, and we want to merge our partial results into a single aggregate. I assume each element in the array should be merged the same function, since each element in the input has the same datatype.
Here's a really ugly function I wrote for the job:
> let reduceMany f input =
input
|> Seq.reduce (fun acc x -> [for (a, b) in Seq.zip acc x -> f a b ]);;
val reduceMany : ('a -> 'a -> 'a) -> seq<'a list> -> 'a list
> reduceMany (+) testOutput;;
val it : int list = [48; 1; 4]
reduceMany takes sequence of n-length sequences, and it returns an n-length array as an output. If you can think of a better way to write this function, be my guest :)
To decode the output above:
48 = sum of the lengths of my two input strings. Note the original string was 49 chars, but splitting it on the "|" ate up one char per "|".
1 = sum of all instances of 'J' in my input
4 = sum of all instances of 'O'.
Step 4: Put everything together
let pmap f l =
seq [for a in l -> async { return f a } ]
|> Async.Parallel
|> Async.RunSynchronously
let fuse functionList input = [ for f in functionList -> f input]
let (|>>) input functionList = pmap (fuse functionList) input
let reduceMany f input =
input
|> Seq.reduce (fun acc x -> [for (a, b) in Seq.zip acc x -> f a b ])
let countOccurrences compareChar source =
source |> Seq.sumBy(fun c -> if c = compareChar then 1 else 0)
let length (s : string) = s.Length
let testData = "Juliet is awesome|Someone should give her a medal".Split('|')
let testOutput =
testData
|>> [length; countOccurrences 'J'; countOccurrences 'o']
|> reduceMany (+)

Handy F# snippets [closed]

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Closed 10 years ago.
There are already two questions about F#/functional snippets.
However what I'm looking for here are useful snippets, little 'helper' functions that are reusable. Or obscure but nifty patterns that you can never quite remember.
Something like:
open System.IO
let rec visitor dir filter=
seq { yield! Directory.GetFiles(dir, filter)
for subdir in Directory.GetDirectories(dir) do
yield! visitor subdir filter}
I'd like to make this a kind of handy reference page. As such there will be no right answer, but hopefully lots of good ones.
EDIT Tomas Petricek has created a site specifically for F# snippets http://fssnip.net/.
Perl style regex matching
let (=~) input pattern =
System.Text.RegularExpressions.Regex.IsMatch(input, pattern)
It lets you match text using let test = "monkey" =~ "monk.+" notation.
Infix Operator
I got this from http://sandersn.com/blog//index.php/2009/10/22/infix-function-trick-for-f go to that page for more details.
If you know Haskell, you might find yourself missing infix sugar in F#:
// standard Haskell call has function first, then args just like F#. So obviously
// here there is a function that takes two strings: string -> string -> string
startsWith "kevin" "k"
//Haskell infix operator via backQuotes. Sometimes makes a function read better.
"kevin" `startsWith` "K"
While F# doesn't have a true 'infix' operator, the same thing can be accomplished almost as elegantly via a pipeline and a 'backpipeline' (who knew of such a thing??)
// F# 'infix' trick via pipelines
"kevin" |> startsWith <| "K"
Multi-Line Strings
This is pretty trivial, but it seems to be a feature of F# strings that is not widely known.
let sql = "select a,b,c \
from table \
where a = 1"
This produces:
val sql : string = "select a,b,c from table where a = 1"
When the F# compiler sees a back-slash followed by a carriage return inside a string literal, it will remove everything from the back-slash to the first non-space character on the next line. This allows you to have multi-line string literals that line up, without using a bunch of string concatenation.
Generic memoization, courtesy of the man himself
let memoize f =
let cache = System.Collections.Generic.Dictionary<_,_>(HashIdentity.Structural)
fun x ->
let ok, res = cache.TryGetValue(x)
if ok then res
else let res = f x
cache.[x] <- res
res
Using this, you could do a cached reader like so:
let cachedReader = memoize reader
Simple read-write to text files
These are trivial, but make file access pipeable:
open System.IO
let fileread f = File.ReadAllText(f)
let filewrite f s = File.WriteAllText(f, s)
let filereadlines f = File.ReadAllLines(f)
let filewritelines f ar = File.WriteAllLines(f, ar)
So
let replace f (r:string) (s:string) = s.Replace(f, r)
"C:\\Test.txt" |>
fileread |>
replace "teh" "the" |>
filewrite "C:\\Test.txt"
And combining that with the visitor quoted in the question:
let filereplace find repl path =
path |> fileread |> replace find repl |> filewrite path
let recurseReplace root filter find repl =
visitor root filter |> Seq.iter (filereplace find repl)
Update Slight improvement if you want to be able to read 'locked' files (e.g. csv files which are already open in Excel...):
let safereadall f =
use fs = new FileStream(f, FileMode.Open, FileAccess.Read, FileShare.ReadWrite)
use sr = new StreamReader(fs, System.Text.Encoding.Default)
sr.ReadToEnd()
let split sep (s:string) = System.Text.RegularExpressions.Regex.Split(s, sep)
let fileread f = safereadall f
let filereadlines f = f |> safereadall |> split System.Environment.NewLine
For performance intensive stuff where you need to check for null
let inline isNull o = System.Object.ReferenceEquals(o, null)
if isNull o then ... else ...
Is about 20x faster then
if o = null then ... else ...
Active Patterns, aka "Banana Splits", are a very handy construct that let one match against multiple regular expression patterns. This is much like AWK, but without the high performance of DFA's because the patterns are matched in sequence until one succeeds.
#light
open System
open System.Text.RegularExpressions
let (|Test|_|) pat s =
if (new Regex(pat)).IsMatch(s)
then Some()
else None
let (|Match|_|) pat s =
let opt = RegexOptions.None
let re = new Regex(pat,opt)
let m = re.Match(s)
if m.Success
then Some(m.Groups)
else None
Some examples of use:
let HasIndefiniteArticle = function
| Test "(?: |^)(a|an)(?: |$)" _ -> true
| _ -> false
type Ast =
| IntVal of string * int
| StringVal of string * string
| LineNo of int
| Goto of int
let Parse = function
| Match "^LET\s+([A-Z])\s*=\s*(\d+)$" g ->
IntVal( g.[1].Value, Int32.Parse(g.[2].Value) )
| Match "^LET\s+([A-Z]\$)\s*=\s*(.*)$" g ->
StringVal( g.[1].Value, g.[2].Value )
| Match "^(\d+)\s*:$" g ->
LineNo( Int32.Parse(g.[1].Value) )
| Match "^GOTO \s*(\d+)$" g ->
Goto( Int32.Parse(g.[1].Value) )
| s -> failwithf "Unexpected statement: %s" s
Maybe monad
type maybeBuilder() =
member this.Bind(v, f) =
match v with
| None -> None
| Some(x) -> f x
member this.Delay(f) = f()
member this.Return(v) = Some v
let maybe = maybeBuilder()
Here's a brief intro to monads for the uninitiated.
Option-coalescing operators
I wanted a version of the defaultArg function that had a syntax closer to the C# null-coalescing operator, ??. This lets me get the value from an Option while providing a default value, using a very concise syntax.
/// Option-coalescing operator - this is like the C# ?? operator, but works with
/// the Option type.
/// Warning: Unlike the C# ?? operator, the second parameter will always be
/// evaluated.
/// Example: let foo = someOption |? default
let inline (|?) value defaultValue =
defaultArg value defaultValue
/// Option-coalescing operator with delayed evaluation. The other version of
/// this operator always evaluates the default value expression. If you only
/// want to create the default value when needed, use this operator and pass
/// in a function that creates the default.
/// Example: let foo = someOption |?! (fun () -> new Default())
let inline (|?!) value f =
match value with Some x -> x | None -> f()
'Unitize' a function which doesn't handle units
Using the FloatWithMeasure function http://msdn.microsoft.com/en-us/library/ee806527(VS.100).aspx.
let unitize (f:float -> float) (v:float<'u>) =
LanguagePrimitives.FloatWithMeasure<'u> (f (float v))
Example:
[<Measure>] type m
[<Measure>] type kg
let unitize (f:float -> float) (v:float<'u>) =
LanguagePrimitives.FloatWithMeasure<'u> (f (float v))
//this function doesn't take units
let badinc a = a + 1.
//this one does!
let goodinc v = unitize badinc v
goodinc 3.<m>
goodinc 3.<kg>
OLD version:
let unitize (f:float -> float) (v:float<'u>) =
let unit = box 1. :?> float<'u>
unit * (f (v/unit))
Kudos to kvb
Scale/Ratio function builder
Again, trivial, but handy.
//returns a function which will convert from a1-a2 range to b1-b2 range
let scale (a1:float<'u>, a2:float<'u>) (b1:float<'v>,b2:float<'v>) =
let m = (b2 - b1)/(a2 - a1) //gradient of line (evaluated once only..)
(fun a -> b1 + m * (a - a1))
Example:
[<Measure>] type m
[<Measure>] type px
let screenSize = (0.<px>, 300.<px>)
let displayRange = (100.<m>, 200.<m>)
let scaleToScreen = scale displayRange screenSize
scaleToScreen 120.<m> //-> 60.<px>
Transposing a list (seen on Jomo Fisher's blog)
///Given list of 'rows', returns list of 'columns'
let rec transpose lst =
match lst with
| (_::_)::_ -> List.map List.head lst :: transpose (List.map List.tail lst)
| _ -> []
transpose [[1;2;3];[4;5;6];[7;8;9]] // returns [[1;4;7];[2;5;8];[3;6;9]]
And here is a tail-recursive version which (from my sketchy profiling) is mildly slower, but has the advantage of not throwing a stack overflow when the inner lists are longer than 10000 elements (on my machine):
let transposeTR lst =
let rec inner acc lst =
match lst with
| (_::_)::_ -> inner (List.map List.head lst :: acc) (List.map List.tail lst)
| _ -> List.rev acc
inner [] lst
If I was clever, I'd try and parallelise it with async...
F# Map <-> C# Dictionary
(I know, I know, System.Collections.Generic.Dictionary isn't really a 'C#' dictionary)
C# to F#
(dic :> seq<_>) //cast to seq of KeyValuePair
|> Seq.map (|KeyValue|) //convert KeyValuePairs to tuples
|> Map.ofSeq //convert to Map
(From Brian, here, with improvement proposed by Mauricio in comment below. (|KeyValue|) is an active pattern for matching KeyValuePair - from FSharp.Core - equivalent to (fun kvp -> kvp.Key, kvp.Value))
Interesting alternative
To get all of the immutable goodness, but with the O(1) lookup speed of Dictionary, you can use the dict operator, which returns an immutable IDictionary (see this question).
I currently can't see a way to directly convert a Dictionary using this method, other than
(dic :> seq<_>) //cast to seq of KeyValuePair
|> (fun kvp -> kvp.Key, kvp.Value) //convert KeyValuePairs to tuples
|> dict //convert to immutable IDictionary
F# to C#
let dic = Dictionary()
map |> Map.iter (fun k t -> dic.Add(k, t))
dic
What is weird here is that FSI will report the type as (for example):
val it : Dictionary<string,int> = dict [("a",1);("b",2)]
but if you feed dict [("a",1);("b",2)] back in, FSI reports
IDictionary<string,int> = seq[[a,1] {Key = "a"; Value = 1; } ...
Tree-sort / Flatten a tree into a list
I have the following binary tree:
___ 77 _
/ \
______ 47 __ 99
/ \
21 _ 54
\ / \
43 53 74
/
39
/
32
Which is represented as follows:
type 'a tree =
| Node of 'a tree * 'a * 'a tree
| Nil
let myTree =
Node
(Node
(Node (Nil,21,Node (Node (Node (Nil,32,Nil),39,Nil),43,Nil)),47,
Node (Node (Nil,53,Nil),54,Node (Nil,74,Nil))),77,Node (Nil,99,Nil))
A straightforward method to flatten the tree is:
let rec flatten = function
| Nil -> []
| Node(l, a, r) -> flatten l # a::flatten r
This isn't tail-recursive, and I believe the # operator causes it to be O(n log n) or O(n^2) with unbalanced binary trees. With a little tweaking, I came up with this tail-recursive O(n) version:
let flatten2 t =
let rec loop acc c = function
| Nil -> c acc
| Node(l, a, r) ->
loop acc (fun acc' -> loop (a::acc') c l) r
loop [] (fun x -> x) t
Here's the output in fsi:
> flatten2 myTree;;
val it : int list = [21; 32; 39; 43; 47; 53; 54; 74; 77; 99]
LINQ-to-XML helpers
namespace System.Xml.Linq
// hide warning about op_Explicit
#nowarn "77"
[<AutoOpen>]
module XmlUtils =
/// Converts a string to an XName.
let xn = XName.op_Implicit
/// Converts a string to an XNamespace.
let xmlns = XNamespace.op_Implicit
/// Gets the string value of any XObject subclass that has a Value property.
let inline xstr (x : ^a when ^a :> XObject) =
(^a : (member get_Value : unit -> string) x)
/// Gets a strongly-typed value from any XObject subclass, provided that
/// an explicit conversion to the output type has been defined.
/// (Many explicit conversions are defined on XElement and XAttribute)
/// Example: let value:int = xval foo
let inline xval (x : ^a when ^a :> XObject) : ^b =
((^a or ^b) : (static member op_Explicit : ^a -> ^b) x)
/// Dynamic lookup operator for getting an attribute value from an XElement.
/// Returns a string option, set to None if the attribute was not present.
/// Example: let value = foo?href
/// Example with default: let value = defaultArg foo?Name "<Unknown>"
let (?) (el:XElement) (name:string) =
match el.Attribute(xn name) with
| null -> None
| att -> Some(att.Value)
/// Dynamic operator for setting an attribute on an XElement.
/// Example: foo?href <- "http://www.foo.com/"
let (?<-) (el:XElement) (name:string) (value:obj) =
el.SetAttributeValue(xn name, value)
OK, this has nothing to do with snippets, but I keep forgetting this:
If you are in the interactive window, you hit F7 to jump back to the code window (without deselecting the code which you just ran...)
Going from code window to F# window (and also to open the F# window) is Ctrl Alt F
(unless CodeRush has stolen your bindings...)
Weighted sum of arrays
Calculating a weighted [n-array] sum of a [k-array of n-arrays] of numbers, based on a [k-array] of weights
(Copied from this question, and kvb's answer)
Given these arrays
let weights = [|0.6;0.3;0.1|]
let arrs = [| [|0.0453;0.065345;0.07566;1.562;356.6|] ;
[|0.0873;0.075565;0.07666;1.562222;3.66|] ;
[|0.06753;0.075675;0.04566;1.452;3.4556|] |]
We want a weighted sum (by column), given that both dimensions of the arrays can be variable.
Array.map2 (fun w -> Array.map ((*) w)) weights arrs
|> Array.reduce (Array.map2 (+))
First line: Partial application of the first Array.map2 function to weights yields a new function (Array.map ((*) weight) which is applied (for each weight) to each array in arr.
Second line: Array.reduce is like fold, except it starts on the second value and uses the first as the initial 'state'. In this case each value is a 'line' of our array of arrays. So applying an Array.map2 (+) on the first two lines means that we sum the first two arrays, which leaves us with a new array, which we then (Array.reduce) sum again onto the next (in this case last) array.
Result:
[|0.060123; 0.069444; 0.07296; 1.5510666; 215.40356|]
Performance testing
(Found here and updated for latest release of F#)
open System
open System.Diagnostics
module PerformanceTesting =
let Time func =
let stopwatch = new Stopwatch()
stopwatch.Start()
func()
stopwatch.Stop()
stopwatch.Elapsed.TotalMilliseconds
let GetAverageTime timesToRun func =
Seq.initInfinite (fun _ -> (Time func))
|> Seq.take timesToRun
|> Seq.average
let TimeOperation timesToRun =
GC.Collect()
GetAverageTime timesToRun
let TimeOperations funcsWithName =
let randomizer = new Random(int DateTime.Now.Ticks)
funcsWithName
|> Seq.sortBy (fun _ -> randomizer.Next())
|> Seq.map (fun (name, func) -> name, (TimeOperation 100000 func))
let TimeOperationsAFewTimes funcsWithName =
Seq.initInfinite (fun _ -> (TimeOperations funcsWithName))
|> Seq.take 50
|> Seq.concat
|> Seq.groupBy fst
|> Seq.map (fun (name, individualResults) -> name, (individualResults |> Seq.map snd |> Seq.average))
DataSetExtensions for F#, DataReaders
System.Data.DataSetExtensions.dll adds the ability to treat a DataTable as an IEnumerable<DataRow> as well as unboxing the values of individual cells in a way that gracefully handles DBNull by supporting System.Nullable. For example, in C# we can get the value of an integer column that contains nulls, and specify that DBNull should default to zero with a very concise syntax:
var total = myDataTable.AsEnumerable()
.Select(row => row.Field<int?>("MyColumn") ?? 0)
.Sum();
There are two areas where DataSetExtensions are lacking, however. First, it doesn't support IDataReader and second, it doesn't support the F# option type. The following code does both - it allows an IDataReader to be treated as a seq<IDataRecord>, and it can unbox values from either a reader or a dataset, with support for F# options or System.Nullable. Combined with the option-coalescing operator in another answer, this allows for code such as the following when working with a DataReader:
let total =
myReader.AsSeq
|> Seq.map (fun row -> row.Field<int option>("MyColumn") |? 0)
|> Seq.sum
Perhaps a more idiomatic F# way of ignoring database nulls would be...
let total =
myReader.AsSeq
|> Seq.choose (fun row -> row.Field<int option>("MyColumn"))
|> Seq.sum
Further, the extension methods defined below are usable from both F# and from C#/VB.
open System
open System.Data
open System.Reflection
open System.Runtime.CompilerServices
open Microsoft.FSharp.Collections
/// Ported from System.Data.DatasetExtensions.dll to add support for the Option type.
[<AbstractClass; Sealed>]
type private UnboxT<'a> private () =
// This class generates a converter function based on the desired output type,
// and then re-uses the converter function forever. Because the class itself is generic,
// different output types get different cached converter functions.
static let referenceField (value:obj) =
if value = null || DBNull.Value.Equals(value) then
Unchecked.defaultof<'a>
else
unbox value
static let valueField (value:obj) =
if value = null || DBNull.Value.Equals(value) then
raise <| InvalidCastException("Null cannot be converted to " + typeof<'a>.Name)
else
unbox value
static let makeConverter (target:Type) methodName =
Delegate.CreateDelegate(typeof<Converter<obj,'a>>,
typeof<UnboxT<'a>>
.GetMethod(methodName, BindingFlags.NonPublic ||| BindingFlags.Static)
.MakeGenericMethod([| target.GetGenericArguments().[0] |]))
|> unbox<Converter<obj,'a>>
|> FSharpFunc.FromConverter
static let unboxFn =
let theType = typeof<'a>
if theType.IsGenericType && not theType.IsGenericTypeDefinition then
let genericType = theType.GetGenericTypeDefinition()
if typedefof<Nullable<_>> = genericType then
makeConverter theType "NullableField"
elif typedefof<option<_>> = genericType then
makeConverter theType "OptionField"
else
invalidOp "The only generic types supported are Option<T> and Nullable<T>."
elif theType.IsValueType then
valueField
else
referenceField
static member private NullableField<'b when 'b : struct and 'b :> ValueType and 'b:(new:unit -> 'b)> (value:obj) =
if value = null || DBNull.Value.Equals(value) then
Nullable<_>()
else
Nullable<_>(unbox<'b> value)
static member private OptionField<'b> (value:obj) =
if value = null || DBNull.Value.Equals(value) then
None
else
Some(unbox<'b> value)
static member inline Unbox =
unboxFn
/// F# data-related extension methods.
[<AutoOpen>]
module FsDataEx =
type System.Data.IDataReader with
/// Exposes a reader's current result set as seq<IDataRecord>.
/// Reader is closed when sequence is fully enumerated.
member this.AsSeq =
seq { use reader = this
while reader.Read() do yield reader :> IDataRecord }
/// Exposes all result sets in a reader as seq<seq<IDataRecord>>.
/// Reader is closed when sequence is fully enumerated.
member this.AsMultiSeq =
let rowSeq (reader:IDataReader) =
seq { while reader.Read() do yield reader :> IDataRecord }
seq {
use reader = this
yield rowSeq reader
while reader.NextResult() do
yield rowSeq reader
}
/// Populates a new DataSet with the contents of the reader. Closes the reader after completion.
member this.ToDataSet () =
use reader = this
let dataSet = new DataSet(RemotingFormat=SerializationFormat.Binary, EnforceConstraints=false)
dataSet.Load(reader, LoadOption.OverwriteChanges, [| "" |])
dataSet
type System.Data.IDataRecord with
/// Gets a value from the record by name.
/// DBNull and null are returned as the default value for the type.
/// Supports both nullable and option types.
member this.Field<'a> (fieldName:string) =
this.[fieldName] |> UnboxT<'a>.Unbox
/// Gets a value from the record by column index.
/// DBNull and null are returned as the default value for the type.
/// Supports both nullable and option types.
member this.Field<'a> (ordinal:int) =
this.GetValue(ordinal) |> UnboxT<'a>.Unbox
type System.Data.DataRow with
/// Identical to the Field method from DatasetExtensions, but supports the F# Option type.
member this.Field2<'a> (columnName:string) =
this.[columnName] |> UnboxT<'a>.Unbox
/// Identical to the Field method from DatasetExtensions, but supports the F# Option type.
member this.Field2<'a> (columnIndex:int) =
this.[columnIndex] |> UnboxT<'a>.Unbox
/// Identical to the Field method from DatasetExtensions, but supports the F# Option type.
member this.Field2<'a> (column:DataColumn) =
this.[column] |> UnboxT<'a>.Unbox
/// Identical to the Field method from DatasetExtensions, but supports the F# Option type.
member this.Field2<'a> (columnName:string, version:DataRowVersion) =
this.[columnName, version] |> UnboxT<'a>.Unbox
/// Identical to the Field method from DatasetExtensions, but supports the F# Option type.
member this.Field2<'a> (columnIndex:int, version:DataRowVersion) =
this.[columnIndex, version] |> UnboxT<'a>.Unbox
/// Identical to the Field method from DatasetExtensions, but supports the F# Option type.
member this.Field2<'a> (column:DataColumn, version:DataRowVersion) =
this.[column, version] |> UnboxT<'a>.Unbox
/// C# data-related extension methods.
[<Extension; AbstractClass; Sealed>]
type CsDataEx private () =
/// Populates a new DataSet with the contents of the reader. Closes the reader after completion.
[<Extension>]
static member ToDataSet(this:IDataReader) =
this.ToDataSet()
/// Exposes a reader's current result set as IEnumerable{IDataRecord}.
/// Reader is closed when sequence is fully enumerated.
[<Extension>]
static member AsEnumerable(this:IDataReader) =
this.AsSeq
/// Exposes all result sets in a reader as IEnumerable{IEnumerable{IDataRecord}}.
/// Reader is closed when sequence is fully enumerated.
[<Extension>]
static member AsMultipleEnumerable(this:IDataReader) =
this.AsMultiSeq
/// Gets a value from the record by name.
/// DBNull and null are returned as the default value for the type.
/// Supports both nullable and option types.
[<Extension>]
static member Field<'T> (this:IDataRecord, fieldName:string) =
this.Field<'T>(fieldName)
/// Gets a value from the record by column index.
/// DBNull and null are returned as the default value for the type.
/// Supports both nullable and option types.
[<Extension>]
static member Field<'T> (this:IDataRecord, ordinal:int) =
this.Field<'T>(ordinal)
Handling arguments in a command line application:
//We assume that the actual meat is already defined in function
// DoStuff (string -> string -> string -> unit)
let defaultOutOption = "N"
let defaultUsageOption = "Y"
let usage =
"Scans a folder for and outputs results.\n" +
"Usage:\n\t MyApplication.exe FolderPath [IncludeSubfolders (Y/N) : default=" +
defaultUsageOption + "] [OutputToFile (Y/N): default=" + defaultOutOption + "]"
let HandlArgs arr =
match arr with
| [|d;u;o|] -> DoStuff d u o
| [|d;u|] -> DoStuff d u defaultOutOption
| [|d|] -> DoStuff d defaultUsageOption defaultOutOption
| _ ->
printf "%s" usage
Console.ReadLine() |> ignore
[<EntryPoint>]
let main (args : string array) =
args |> HandlArgs
0
(I had a vague memory of this technique being inspired by Robert Pickering, but can't find a reference now)
A handy cache function that keeps up to max (key,reader(key)) in a dictionary and use a SortedList to track the MRU keys
let Cache (reader: 'key -> 'value) max =
let cache = new Dictionary<'key,LinkedListNode<'key * 'value>>()
let keys = new LinkedList<'key * 'value>()
fun (key : 'key) -> (
let found, value = cache.TryGetValue key
match found with
|true ->
keys.Remove value
keys.AddFirst value |> ignore
(snd value.Value)
|false ->
let newValue = key,reader key
let node = keys.AddFirst newValue
cache.[key] <- node
if (keys.Count > max) then
let lastNode = keys.Last
cache.Remove (fst lastNode.Value) |> ignore
keys.RemoveLast() |> ignore
(snd newValue))
Creating XElements
Nothing amazing, but I keep getting caught out by the implicit conversion of XNames:
#r "System.Xml.Linq.dll"
open System.Xml.Linq
//No! ("type string not compatible with XName")
//let el = new XElement("MyElement", "text")
//better
let xn s = XName.op_Implicit s
let el = new XElement(xn "MyElement", "text")
//or even
let xEl s o = new XElement(xn s, o)
let el = xEl "MyElement" "text"
Pairwise and pairs
I always expect Seq.pairwise to give me [(1,2);(3;4)] and not [(1,2);(2,3);(3,4)]. Given that neither exist in List, and that I needed both, here's the code for future reference. I think they're tail recursive.
//converts to 'windowed tuples' ([1;2;3;4;5] -> [(1,2);(2,3);(3,4);(4,5)])
let pairwise lst =
let rec loop prev rem acc =
match rem with
| hd::tl -> loop hd tl ((prev,hd)::acc)
| _ -> List.rev acc
loop (List.head lst) (List.tail lst) []
//converts to 'paged tuples' ([1;2;3;4;5;6] -> [(1,2);(3,4);(5,6)])
let pairs lst =
let rec loop rem acc =
match rem with
| l::r::tl -> loop tl ((l,r)::acc)
| l::[] -> failwith "odd-numbered list"
| _ -> List.rev acc
loop lst []
Naive CSV reader (i.e., won't handle anything nasty)
(Using filereadlines and List.transpose from other answers here)
///Given a file path, returns a List of row lists
let ReadCSV =
filereadlines
>> Array.map ( fun line -> line.Split([|',';';'|]) |> List.ofArray )
>> Array.toList
///takes list of col ids and list of rows,
/// returns array of columns (in requested order)
let GetColumns cols rows =
//Create filter
let pick cols (row:list<'a>) = List.map (fun i -> row.[i]) cols
rows
|> transpose //change list of rows to list of columns
|> pick cols //pick out the columns we want
|> Array.ofList //an array output is easier to index for user
Example
"C:\MySampleCSV"
|> ReadCSV
|> List.tail //skip header line
|> GetColumns [0;3;1] //reorder columns as well, if needs be.
Date Range
simple but useful list of dates between fromDate and toDate
let getDateRange fromDate toDate =
let rec dates (fromDate:System.DateTime) (toDate:System.DateTime) =
seq {
if fromDate <= toDate then
yield fromDate
yield! dates (fromDate.AddDays(1.0)) toDate
}
dates fromDate toDate
|> List.ofSeq
toggle code to sql
More trivial than most on this list, but handy nonetheless:
I'm always taking sql in and out of code to move it to a sql environment during development. Example:
let sql = "select a,b,c "
+ "from table "
+ "where a = 1"
needs to be 'stripped' to:
select a,b,c
from table
where a = 1
keeping the formatting. It's a pain to strip out the code symbols for the sql editor, then put them back again by hand when I've got the sql worked out. These two functions toggle the sql back and forth from code to stripped:
// reads the file with the code quoted sql, strips code symbols, dumps to FSI
let stripForSql fileName =
File.ReadAllText(fileName)
|> (fun s -> Regex.Replace(s, "\+(\s*)\"", ""))
|> (fun s -> s.Replace("\"", ""))
|> (fun s -> Regex.Replace(s, ";$", "")) // end of line semicolons
|> (fun s -> Regex.Replace(s, "//.+", "")) // get rid of any comments
|> (fun s -> printfn "%s" s)
then when you are ready to put it back into your code source file:
let prepFromSql fileName =
File.ReadAllText(fileName)
|> (fun s -> Regex.Replace(s, #"\r\n", " \"\r\n+\"")) // matches newline
|> (fun s -> Regex.Replace(s, #"\A", " \""))
|> (fun s -> Regex.Replace(s, #"\z", " \""))
|> (fun s -> printfn "%s" s)
I'd love to get rid of the input file but can't even begin to grok how to make that happen. anyone?
edit:
I figured out how to eliminate the requirement of a file for these functions by adding a windows forms dialog input/output. Too much code to show, but for those who would like to do such a thing, that's how I solved it.
Pascal's Triangle (hey, someone might find it useful)
So we want to create a something like this:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
Easy enough:
let rec next = function
| [] -> []
| x::y::xs -> (x + y)::next (y::xs)
| x::xs -> x::next xs
let pascal n =
seq { 1 .. n }
|> List.scan (fun acc _ -> next (0::acc) ) [1]
The next function returns a new list where each item[i] = item[i] + item[i + 1].
Here's the output in fsi:
> pascal 10 |> Seq.iter (printfn "%A");;
[1]
[1; 1]
[1; 2; 1]
[1; 3; 3; 1]
[1; 4; 6; 4; 1]
[1; 5; 10; 10; 5; 1]
[1; 6; 15; 20; 15; 6; 1]
[1; 7; 21; 35; 35; 21; 7; 1]
[1; 8; 28; 56; 70; 56; 28; 8; 1]
[1; 9; 36; 84; 126; 126; 84; 36; 9; 1]
[1; 10; 45; 120; 210; 252; 210; 120; 45; 10; 1]
For the adventurous, here's a tail-recursive version:
let rec next2 cont = function
| [] -> cont []
| x::y::xs -> next2 (fun l -> cont <| (x + y)::l ) <| y::xs
| x::xs -> next2 (fun l -> cont <| x::l ) <| xs
let pascal2 n =
set { 1 .. n }
|> Seq.scan (fun acc _ -> next2 id <| 0::acc)) [1]
Flatten a List
if you have something like this:
let listList = [[1;2;3;];[4;5;6]]
and want to 'flatten' it down to a singe list so the result is like this:
[1;2;3;4;5;6]
it can be done thusly:
let flatten (l: 'a list list) =
seq {
yield List.head (List.head l)
for a in l do yield! (Seq.skip 1 a)
}
|> List.ofSeq
List comprehensions for float
This [23.0 .. 1.0 .. 40.0] was marked as deprecated a few versions backed.
But apparently, this works:
let dl = 9.5 / 11.
let min = 21.5 + dl
let max = 40.5 - dl
let a = [ for z in min .. dl .. max -> z ]
let b = a.Length
(BTW, there's a floating point gotcha in there. Discovered at fssnip - the other place for F# snippets)
Parallel map
let pmap f s =
seq { for a in s -> async { return f s } }
|> Async.Parallel
|> Async.Run

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