Alternative approach to avoid "Incomplete pattern match" warning - f#

I have written a function that takes an array as input and returns an array of equal size as output. For example:
myFunc [| "apple"; "orange"; "banana" |]
> val it : (string * string) [] =
[|("red", "sphere"); ("orange", "sphere"); ("yellow", "oblong")|]
Now I want to assign the results via a let binding. For example:
let [|
( appleColor, appleShape );
( orangeColor, orangeShape );
( bananaColor, bananaShape )
|] =
myFunc [| "apple"; "orange"; "banana" |]
Which works great...
> val orangeShape : string = "sphere"
> val orangeColor : string = "orange"
> val bananaShape : string = "oblong"
> val bananaColor : string = "yellow"
> val appleShape : string = "sphere"
> val appleColor : string = "red"
...except it produces a warning:
warning FS0025: Incomplete pattern matches on this expression. For example, the value '[|_; _; _; _|]' may indicate a case not covered by the pattern(s).
The source and reason for the warning has already been covered, I'm just looking for a succinct work-around. This function call occurs near the top of my function, and I don't like the idea of putting the entire function body inside a match:
let otherFunc =
match myFunc [| "apple"; "orange"; "banana" |] with
| [|
( appleColor, appleShape );
( orangeColor, orangeShape );
( bananaColor, bananaShape )
|] ->
// ... the rest of my function logic
| _ -> failwith "Something impossible just happened!"
That just smells bad. I don't like the idea of ignoring the warning either - goes against my better judgment. Are there any other options open to me, or do I just need to find a different approach entirely?


One possibility if you expect this kind of calling pattern to be frequent is to make wrappers that act on the sizes of tuples you expect, e.g.
myFunc3 (in1,in2,in3) =
match myFunc [|in1;in2;in3|] with
[|out1;out2;out3|] -> out1, out2, out3
_ -> failwith "Internal error"
etc. But all it does is move the ugly code to a standard place, and writing out the wrappers will be inconvenient.
I don't think there's any better option with this API, because there's no way to tell the compiler that myFunc always returns the same number of elements it is passed.
Another option might be to replace myFunc with an IDisposable class:
type MyClass() =
let expensiveResource = ...
member this.MyFunc(v) = ...calculate something with v using expensiveResource
interface IDisposable with
override this.Dispose() = // cleanup resource
and then use it in a block like
use myClass = new MyClass()
let appleColor, appleShape = myClass.MyFunc(apple)
...


Adapting #Ganesh's answer, here's a primitive way to approach the problem:
let Tuple2Map f (u, v)
= (f u, f v)
let Tuple3Map f (u, v, w)
= (f u, f v, f w)
let Tuple4Map f (u, v, w, x)
= (f u, f v, f w, f x)
Example:
let Square x = x * x
let (a,b) = Tuple2Map Square (4,6)
// Output:
// val b : int = 36
// val a : int = 16
But I guess something even more primitive would be this:
let Square x = x * x
let (a,b) = (Square 4, Square 6)
And if the function name is too long, e.g.
// Really wordy way to assign to (a,b)
let FunctionWithLotsOfInput w x y z = w * x * y * z
let (a,b) =
(FunctionWithLotsOfInput input1 input2 input3 input4A,
FunctionWithLotsOfInput input1 input2 input3 input4B)
We can define temporary function
let FunctionWithLotsOfInput w x y z = w * x * y * z
// Partially applied function, temporary function
let (a,b) =
let f = (FunctionWithLotsOfInput input1 input2 input3)
(f input4A, f input4B)

Related

How to implement the List Monad (computation expression) with a condition?

I'm trying to understand how to use F# computation expressions and it certainly puzzles me.
The following example makes some amount of sense to me.
type ListMonad() =
member o.Bind( (m:'a list), (f: 'a -> 'b list) ) = List.collect f m
member o.Return(x) = [x]
let list = ListMonad()
let test =
list {
let! x = [ 1 .. 10]
let! y = [2 .. 2 .. 20]
return (x,y)
}
My question is, how would you add a condition to this computation expression? Specifically, how would you alter it to return a list of elements only where the x value is strictly smaller than the y value? (Let's not filter it out afterward).

Since computation expressions can be parameterized, you might first think to try something like this:
let filterAndCollect (pred : 'a -> 'b -> bool) (f : 'a -> 'b list) (m : 'a list) =
let f' a = [ for b in f a do if pred a b then yield b ]
List.collect f' m
type FilteringListMonad(pred) =
member o.Bind( (m:'a list), (f: 'a -> 'b list) ) = filterAndCollect pred f m
member o.Return(x) = [x]
let filteredList = FilteringListMonad(fun x y -> x < y)
let test2 =
filteredList {
let! x = [1 .. 10]
let! y = [2 .. 2 .. 20]
return (x,y)
}
However, that fails with a type error on the (x,y) tuple:
This expression was expected to have type 'int' but here has type ''a * 'b'
There are also two compiler warnings: on the y of the x < y expression in the FilteringListMonad constructor, there's a warning:
This construct causes code to be less generic than indicated by the type annotations. The type variable 'a has been constrained to be type ''b'.
And on the number 1 in the let! x = [1 .. 10] expression, there's a warning:
This construct causes code to be less generic than indicated by the type annotations. The type variable 'b has been constrained to be type 'int'.
So between these two constraints, the return type of the computation expression (a 'b list) has been constrained to be int list, but your expression is returning a int * int list instead. After some thinking about the type constraints, you might conclude that there's no way this can work. But there's a way to make it work. The key is to realize that the 'b type that will be the output of your computation expression is, in this example, actually the tuple int * int, so you rewrite the predicate function to actually just take that 'b type, and then everything works:
let filterAndCollect (pred : 'b -> bool) (f : 'a -> 'b list) (m : 'a list) =
let f' a = [ for b in f a do if pred b then yield b ]
List.collect f' m
type FilteringListMonad(pred) =
member o.Bind( (m:'a list), (f: 'a -> 'b list) ) = filterAndCollect pred f m
member o.Return(x) = [x]
let filteredList = FilteringListMonad(fun (x:int,y:int) -> x < y)
let test2 =
filteredList {
let! x = [ 1 .. 10]
let! y = [2 .. 2 .. 20]
return (x,y)
}
Note that I also had to specify the types of the predicate function's inputs. Without that, F# was generalizing them to be "any type that implements System.IComparable, but I was passing in ints, which are value types and thus don't implement any interfaces. This led to the error
This expression was expected to have type 'System.IComparable' but here has type 'int'.
However, declaring both parameters to the predicate as int did the trick.

OP already accepted an answer, I will just provide a different approach which might be useful to help understand computation expressions in F#
One can extend computation expression with the useful ReturnFrom and Zero like so:
type ListMonad() =
member o.Bind (m, f) = List.collect f m
member o.Return x = [x]
member o.ReturnFrom l = l : _ list
member o.Zero () = []
let listM = ListMonad()
ReturnFrom allows us to return empty lists using return! [] as a result which enables filtering. Zero is a short-hand for this in that if the else branch isn't defined Zero is used.
This allows us to filter like so:
let test =
listM {
let! x = [ 1 .. 10]
let! y = [2 .. 2 .. 20]
if x % y = 0 then
return (x,y)
// By defining .Zero F# implicitly adds else branch if not defined
// else
// return! []
}
F# will expand the computation into something roughly like this:
let testEq =
[ 1 .. 10]
|> List.collect
(fun x ->
[2 .. 2 .. 20]
|> List.collect (fun y -> if x % y = 0 then [x,y] else [])
)

How to make a lazy computational workflow?

I'm trying to write a computational workflow which would allow a computation which can produce side effects like log or sleep and a return value
A usage example would be something like this
let add x y =
compute {
do! log (sprintf "add: x = %d, y= %d" x y)
do! sleep 1000
let r = x + y
do! log (sprintf "add: result= %d" r)
return r
}
...
let result = run (add 100 1000)
and I would like the side effects to be produced when executeComputation is called.
My attempt is
type Effect =
| Log of string
| Sleep of int
type Computation<'t> = Computation of Lazy<'t * Effect list>
let private bind (u : 'u, effs : Effect list)
(f : 'u -> 'v * Effect list)
: ('v * Effect list) =
let v, newEffs = f u
let allEffects = List.append effs newEffs
v, allEffects
type ComputeBuilder() =
member this.Zero() = lazy ((), [])
member this.Return(x) = x, []
member this.ReturnFrom(Computation f) = f.Force()
member this.Bind(x, f) = bind x f
member this.Delay(funcToDelay) = funcToDelay
member this.Run(funcToRun) = Computation (lazy funcToRun())
let compute = new ComputeBuilder()
let log msg = (), [Log msg]
let sleep ms = (), [Sleep ms]
let run (Computation x) = x.Force()
...but the compiler complains about the let! lines in the following code:
let x =
compute {
let! a = add 10 20
let! b = add 11 2000
return a + b
}
Error FS0001: This expression was expected to have type
'a * Effect list
but here has type
Computation<'b> (FS0001)
Any suggestions?

The main thing that is not right with your definition is that some of the members of the computation builder use your Computation<'T> type and some of the other members use directly a pair of value and list of effects.
To make it type check, you need to be consistent. The following version uses Computation<'T> everywhere - have a look at the type signature of Bind, for example:
let private bind (Computation c) f : Computation<_> =
Computation(Lazy.Create(fun () ->
let u, effs = c.Value
let (Computation(c2)) = f u
let v, newEffs = c2.Value
let allEffects = List.append effs newEffs
v, allEffects))
type ComputeBuilder() =
member this.Zero() = Computation(lazy ((), []))
member this.Return(x) = Computation(lazy (x, []))
member this.ReturnFrom(c) = c
member this.Bind(x, f) = bind x f
member this.Delay(funcToDelay:_ -> Computation<_>) =
Computation(Lazy.Create(fun () ->
let (Computation(r)) = funcToDelay()
r.Value))

Parsing values from string array

I am trying to create a save/load function for 2d objects that has been drawn into a form.
type circle = { X : int; Y : int; Diameter : int; Brush : Brush}
type Square = { X : int; Y : int; Length : int; Height: int; Brush : Brush}
When i create the object i put them into 2 lists 1 for each type.
My initial thought was to read and write these objects to a textfile, see below:
saveFile.Click.Add(fun _ ->
for c in listOfCircles do
myfile.WriteLine("Circle," + c.X.ToString() + "," + c.Y.ToString() + "," + c.Diameter.ToString() + "," + c.Brush.ToString())
for s in listOfSquares do
myfile.WriteLine("Square," + s.X.ToString() + "," + s.Y.ToString() + "," + s.Height.ToString() + "," + s.Length.ToString() + "," + s.Brush.ToString())
myfile.Close() // close the file
And in the textfile it looks like this
Circle,200,200,50,System.Drawing.SolidBrush
Square,50,55,45,55,System.Drawing.SolidBrush
From here i want to read these values and then be able to parse them and recreate the objects by adding the objects the lists and redraw them.
let readCircle =
System.IO.File.ReadAllLines path
|> Array.choose (fun s ->
match s.Split ',' with
| [|x; y ; z ; b ; _|] when x = "Circle" -> Some (y, z, b)
| _ -> None )
let readSquare =
System.IO.File.ReadAllLines path
|> Array.choose (fun s ->
match s.Split ',' with
| [|x; y ; z ; b ; a ; _|] when x = "Square" -> Some (y, z, b, a)
| _ -> None )
These functions gives me
val readCircle : (string * string * string) [] = [|("200", "200", "50")|]
val readSquare : (string * string * string * string) [] = [|("50", "55", "45", "55")|]
The problem i have now is im not sure how to obtain the values from the array. Beneath is example with multiple circles.
val readCircle : (string * string * string) [] = [|("200", "200", "50"); ("200", "200","50")|]
Any ideas or comments about how to go from here/how to resolve this issue is very appreciated! Question summary: how could i get the values from the array and put them in for example my already created add functions, see below:
listOfCircles.Add({ X = 200; Y = 200; Diameter = 50; Brush = Brushes.Black})

You could convert the arrays of string tuples you have using Array.map, e.g.
[|("200", "200", "50"); ("200", "200","50")|]
|> Array.map (fun (x,y,d) -> {X = int32 x; Y = int32 y; Diameter = int32 d; Brush = Brushes.Black})
It might be a bit clearer if you converted to circle or square as you parsed the file, then you would have an array of circle or an array of square that you can add directly to your lists.
let readCircle =
System.IO.File.ReadAllLines path
|> Array.choose (fun s ->
match s.Split ',' with
| [|t; x; y; d; _|] when t = "Circle" ->
Some {X = int32 x; Y = int32 y; Diameter = int32 d; Brush = Brushes.Red}
| _ -> None )
But... if you wanted to make larger changes, you could use discriminated unions to represent your shapes, they would then share a common type of Shape and you could parse circles and squares in the same function.
type Shape =
| Circle of X : int * Y : int * Diameter : int * Brush : Brush
| Square of X : int * Y : int * Length : int * Height: int * Brush : Brush
let readShapes (data: string array) =
data
|> Array.choose (fun s ->
match s.Split ',' with
| [|t; x; y; d; _|] when t = "Circle" ->
Some (Circle(X = int32 x, Y = int32 y, Diameter = int32 d, Brush = Brushes.Red))
| [|t; x; y; l; h; _|] when t = "Square" ->
Some (Square(X = int32 x, Y = int32 y, Length = int32 l, Height = int32 h, Brush = Brushes.Red))
| _ -> None )
let listOfShapes = ResizeArray<_>()
let testInput = """
Circle,200,200,50,System.Drawing.SolidBrush
Square,50,55,45,55,System.Drawing.SolidBrush"""
testInput.Split('\n') // System.IO.File.ReadAllLines path
|> readShapes
|> Array.iter (listOfShapes.Add)
Which would result in
val it : System.Collections.Generic.List<Shape> =
seq
[Circle (200,200,50,System.Drawing.SolidBrush {Color = Color [Red];});
Square (50,55,45,55,System.Drawing.SolidBrush {Color = Color [Red];})]
You could then use pattern matching to draw each type of shape
let drawShape shape =
match shape with
| Circle(x,y,d,b) ->
printfn "Pretend I just drew a circle at %d,%d with diameter %d." x y d
| Square(x,y,l,h,b) ->
printfn "Pretend I just drew a rectangle at %d,%d that was %d long and %d high." x y l h
listOfShapes |> Seq.iter drawShape
Giving
Pretend I just drew a circle at 200,200 with diameter 50.
Pretend I just drew a rectangle at 50,55 that was 45 long and 55 high.

If I understand your goal, this is how I would go about it. I've only implemented Circle; you'll need to modify it to handle Square.
open System
open System.Collections.Generic
open System.Drawing
open System.IO
let memoize f =
let cache = Dictionary()
fun key ->
match cache.TryGetValue(key) with
| true, value -> value
| _ ->
let value = f key
cache.Add(key, value)
value
let getBrush =
memoize (fun name -> typeof<Brushes>.GetProperty(name).GetValue(null) :?> SolidBrush)
type Circle =
{ X : int
Y : int
Diameter : int
Brush : SolidBrush } with
override this.ToString() =
sprintf "Circle,%d,%d,%d,%s" this.X this.Y this.Diameter this.Brush.Color.Name
static member Parse(s: string) =
match s.Split(',') with
| [|"Circle";x;y;diameter;brushName|] -> {X=int x; Y=int y; Diameter=int diameter; Brush=getBrush brushName}
| _ -> invalidArg "s" "Cannot parse string"
let writeShapesToFile fileName shapes =
File.WriteAllLines(fileName, Seq.map (sprintf "%O") shapes)
let readShapesFromFile fileName =
File.ReadAllLines(fileName) |> Array.map Circle.Parse
Also, you might consider using a class hierarchy instead of records since much of the structure and behavior of Circle and Square are shared.

This is fun - I approached it in a totally different way than Daniel (but I agree with him that you classes might be a better approach for your shapes). Instead, I took advantage of discriminated unions (and there are better ways to do this - more later):
First, I define a type for a list of parameters for making a shape:
type Parameter =
| Label of string
| Number of int
Now let's convert a string to a parameter:
let toParameter s =
match Int32.TryParse(s) with
| (true, i) -> Number(i)
| (_, _) -> Label(s)
Now to convert a list of strings to a list of Parameter:
let stringListToParameterList stringlist = stringlist |> List.map(function s -> toParameter s)
Now to convert a comma-separated string to a list of string:
let commastringToList (s:string) = s.Split(',') |> Array.toList
OK - great - let's define your records and a master Shape:
type circlerec = { X : int; Y : int; Diameter : int; Brush : Brush}
type squarerec = { X : int; Y : int; Length : int; Height: int; Brush : Brush}
type Shape =
| Circle of circlerec
| Square of squarerec
With this we need a way to make a Shape from a parameter list. This is brute force, but it reads well enough:
let toShape list =
match list with
| Label("Circle") :: Number(x) :: Number(y) :: Number(diam) :: Label(colorName) :: [] ->
Circle({X = x; Y = y; Diameter = diam; Brush = new SolidBrush(Color.FromName(colorName)); })
| Label("Circle") :: rest -> raise <| new ArgumentException("parse error:expected Circle num num num color but got " + list.ToString())
| Label("Square") :: Number(x) :: Number(y) :: Number(length) :: Number(height) :: Label(colorName) :: [] ->
Square({X = x; Y = y; Length = length; Height = height; Brush = new SolidBrush(Color.FromName(colorName)); })
| Label("Square") :: rest -> raise <| new ArgumentException("parse error:expected Square num num num num color but got " + list.ToString())
| _ -> raise <| new ArgumentException("parse error: unknown shape: " + list.ToString())
It's dense, but I'm using F#'s pattern matching to spot the various parameters for each shape. Note that you could now do things like have Square,x,y,size,colorName in your file and make a Square where Length and Height are equal to size by just adding in the pattern.
Finally comes the piece de resistance, converting your file into shapes:
let toShapes path =
System.IO.File.ReadAllLines path |> Array.toList |>
List.map(function s -> s |> commastringToList |>
stringListToParameterList |> toShape)
which maps every line in the file to a list of string which then maps each line to a shape, but piping the comma string to the list converter and then through the parameter list and then to a shape.
Now where this is bad is that the error checking is pretty horrid and that the Parameter type should really include Pigment of Color, which would allow you to look at the string that comes in and if it's valid Color name, map it to a Pigment else a Label.

F# Checked Arithmetics Scope

F# allows to use checked arithmetics by opening Checked module, which redefines standard operators to be checked operators, for example:
open Checked
let x = 1 + System.Int32.MaxValue // overflow
will result arithmetic overflow exception.
But what if I want to use checked arithmetics in some small scope, like C# allows with keyword checked:
int x = 1 + int.MaxValue; // ok
int y = checked { 1 + int.MaxValue }; // overflow
How can I control the scope of operators redefinition by opening Checked module or make it smaller as possible?

You can always define a separate operator, or use shadowing, or use parens to create an inner scope for temporary shadowing:
let f() =
// define a separate operator
let (+.) x y = Checked.(+) x y
try
let x = 1 +. System.Int32.MaxValue
printfn "ran ok"
with e ->
printfn "exception"
try
let x = 1 + System.Int32.MaxValue
printfn "ran ok"
with e ->
printfn "exception"
// shadow (+)
let (+) x y = Checked.(+) x y
try
let x = 1 + System.Int32.MaxValue
printfn "ran ok"
with e ->
printfn "exception"
// shadow it back again
let (+) x y = Operators.(+) x y
try
let x = 1 + System.Int32.MaxValue
printfn "ran ok"
with e ->
printfn "exception"
// use parens to create a scope
(
// shadow inside
let (+) x y = Checked.(+) x y
try
let x = 1 + System.Int32.MaxValue
printfn "ran ok"
with e ->
printfn "exception"
)
// shadowing scope expires
try
let x = 1 + System.Int32.MaxValue
printfn "ran ok"
with e ->
printfn "exception"
f()
// output:
// exception
// ran ok
// exception
// ran ok
// exception
// ran ok
Finally, see also the --checked+ compiler option:
http://msdn.microsoft.com/en-us/library/dd233171(VS.100).aspx

Here is a complicated (but maybe interesting) alternative. If you're writing something serious then you should probably use one of the Brians suggestions, but just out of curiosity, I was wondering if it was possible to write F# computation expression to do this. You can declare a type that represents int which should be used only with checked operations:
type CheckedInt = Ch of int with
static member (+) (Ch a, Ch b) = Checked.(+) a b
static member (*) (Ch a, Ch b) = Checked.(*) a b
static member (+) (Ch a, b) = Checked.(+) a b
static member (*) (Ch a, b) = Checked.(*) a b
Then you can define a computation expression builder (this isn't really a monad at all, because the types of operations are completely non-standard):
type CheckedBuilder() =
member x.Bind(v, f) = f (Ch v)
member x.Return(Ch v) = v
let checked = new CheckedBuilder()
When you call 'bind' it will automatically wrap the given integer value into an integer that should be used with checked operations, so the rest of the code will use checked + and * operators declared as members. You end up with something like this:
checked { let! a = 10000
let! b = a * 10000
let! c = b * 21
let! d = c + 47483648 // !
return d }
This throws an exception because it overflows on the marked line. If you change the number, it will return an int value (because the Return member unwraps the numeric value from the Checked type). This is a bit crazy technique :-) but I thought it may be interesting!
(Note checked is a keyword reserved for future use, so you may prefer choosing another name)

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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