There's more to learning a new language than the language itself. In order to be productive, you need to memorize a big chunk of the standard library and be aware of most of the rest of it. For example, if you know C#, you can pick up Javathelanguage quite quickly, but you won't really get up to speed until you are comfortable with the Java Class Library as well.
Similarly, you can't really be effective in F# until you have some familiarity with all the F# functions that work with collections.
In C# there are only a few LINQ methods you need to know^{1} (Select
, Where
, and so on).
But in F#, there are currently almost 100 functions in the List module (and similar counts in the Seq and Array modules). That's a lot!
^{1} Yes, there are more, but you can get by with just a few. In F# it's more important to know them all.
If you are coming to F# from C#, then, the large number of list functions can be overwhelming.
So I have written this post to help guide you to the one you want. And for fun, I've done it in a "Choose Your Own Adventure" style!
First, a table with information about the different kinds of standard collections. There are five "native" F# ones: list
, seq
, array
, map
and set
,
and ResizeArray
and IDictionary
are also often used.
Immutable?  Notes  

list  Yes 
Pros:

seq  Yes 
Alias for

array  No 
Same as BCL

map  Yes  Immutable dictionary. Requires keys to implement IComparable . 
set  Yes  Immutable set. Requires elements to implement IComparable . 
ResizeArray  No  Alias for BCL List . Pros and cons similar to array, but resizable. 
IDictionary  Yes 
For an alternate dictionary that does not requires elements to implement Note that mutation methods such as 
These are the main collection types that you will encounter in F#, and will be good enough for all common cases.
If you need other kinds of collections though, there are lots of choices:
All functions are available for list
, seq
and array
in F# v4 unless noted. The Map
and Set
modules have some of them as well, but I won't be discussing map
and set
here.
For the function signatures I will use list
as the standard collection type. The signatures for the seq
and array
versions will be similar.
Many of these functions are not yet documented on MSDN so I’m going to link directly to the source code on GitHub, which has the uptodate comments. Click on the function name for the link.
The availability of these functions may depend on which version of F# you use.
If you want to know what changed between F# v3 and F# v4, please see this chart (from here). The chart shows the new APIs in F# v4 (green), previouslyexisting APIs (blue), and intentional remaining gaps (white).
Some of the functions documented below are not in this chart  these are newer still! If you are using an older version of F#, you can simply reimplement them yourself using the code on GitHub.
With that disclaimer out of the way, you can start your adventure!
What kind of collection do you have?
So you want to create a new collection. How do you want to create it?
If you want to create a new empty or oneelement collection, use these functions:
empty : 'T list
.
Returns an empty list of the given type.singleton : value:'T > 'T list
.
Returns a list that contains one item only.If you know the size of the collection in advance, it is generally more efficient to use a different function. See section 4 below.
let list0 = List.empty
// list0 = []
let list1 = List.singleton "hello"
// list1 = ["hello"]
If you want to create a new collection of known size with each element having the same value, you want to use replicate
:
replicate : count:int > initial:'T > 'T list
.
Creates a collection by replicating the given initial value.create : count:int > value:'T > 'T[]
.
Creates an array whose elements are all initially the supplied value.zeroCreate : count:int > 'T[]
.
Creates an array where the entries are initially the default value.Array.create
is basically the same as replicate
(although with a subtly different implementation!) but replicate
was only implemented for Array
in F# v4.
let repl = List.replicate 3 "hello"
// val repl : string list = ["hello"; "hello"; "hello"]
let arrCreate = Array.create 3 "hello"
// val arrCreate : string [] = ["hello"; "hello"; "hello"]
let intArr0 : int[] = Array.zeroCreate 3
// val intArr0 : int [] = [0; 0; 0]
let stringArr0 : string[] = Array.zeroCreate 3
// val stringArr0 : string [] = [null; null; null]
Note that for zeroCreate
, the target type must be known to the compiler.
If you want to create a new collection of known size with each element having a potentially different value, you can choose one of three ways:
init : length:int > initializer:(int > 'T) > 'T list
.
Creates a collection by calling the given generator on each index.[1; 2; 3]
(lists) and [1; 2; 3]
(arrays).for .. in .. do .. yield
.// using list initializer
let listInit1 = List.init 5 (fun i> i*i)
// val listInit1 : int list = [0; 1; 4; 9; 16]
// using list comprehension
let listInit2 = [for i in [1..5] do yield i*i]
// val listInit2 : int list = [1; 4; 9; 16; 25]
// literal
let listInit3 = [1; 4; 9; 16; 25]
// val listInit3 : int list = [1; 4; 9; 16; 25]
let arrayInit3 = [1; 4; 9; 16; 25]
// val arrayInit3 : int [] = [1; 4; 9; 16; 25]
Literal syntax allows for an increment as well:
// literal with +2 increment
let listOdd= [1..2..10]
// val listOdd : int list = [1; 3; 5; 7; 9]
The comprehension syntax is even more flexible because you can yield
more than once:
// using list comprehension
let listFunny = [
for i in [2..3] do
yield i
yield i*i
yield i*i*i
]
// val listFunny : int list = [2; 4; 8; 3; 9; 27]
and it can also be used as a quick and dirty inline filter:
let primesUpTo n =
let rec sieve l =
match l with
 [] > []
 p::xs >
p :: sieve [for x in xs do if (x % p) > 0 then yield x]
[2..n] > sieve
primesUpTo 20
// [2; 3; 5; 7; 11; 13; 17; 19]
Two other tricks:
yield!
to return a list rather than a single valueHere is an example of both tricks being used to count up to 10 by twos:
let rec listCounter n = [
if n <= 10 then
yield n
yield! listCounter (n+2)
]
listCounter 3
// val it : int list = [3; 5; 7; 9]
listCounter 4
// val it : int list = [4; 6; 8; 10]
If you want an infinite list, you have to use a seq rather than a list or array.
initInfinite : initializer:(int > 'T) > seq<'T>
.
Generates a new sequence which, when iterated, will return successive elements by calling the given function.// generator version
let seqOfSquares = Seq.initInfinite (fun i > i*i)
let firstTenSquares = seqOfSquares > Seq.take 10
firstTenSquares > List.ofSeq // [0; 1; 4; 9; 16; 25; 36; 49; 64; 81]
// recursive version
let seqOfSquares_v2 =
let rec loop n = seq {
yield n * n
yield! loop (n+1)
}
loop 1
let firstTenSquares_v2 = seqOfSquares_v2 > Seq.take 10
Sometimes you don’t know how big the collection will be in advance. In this case you need a function that will keep adding elements until it gets a signal to stop.
unfold
is your friend here, and the "signal to stop" is whether you return a None
(stop) or a Some
(keep going).
unfold : generator:('State > ('T * 'State) option) > state:'State > 'T list
.
Returns a collection that contains the elements generated by the given computation.This example reads from the console in a loop until an empty line is entered:
let getInputFromConsole lineNo =
let text = System.Console.ReadLine()
if System.String.IsNullOrEmpty(text) then
None
else
// return value and new threaded state
// "text" will be in the generated sequence
Some (text,lineNo+1)
let listUnfold = List.unfold getInputFromConsole 1
unfold
requires that a state be threaded through the generator. You can ignore it (as in the ReadLine
example above), or you can
use it to keep track of what you have done so far. For example, you can create a Fibonacci series generator using unfold
:
let fibonacciUnfolder max (f1,f2) =
if f1 > max then
None
else
// return value and new threaded state
let fNext = f1 + f2
let newState = (f2,fNext)
// f1 will be in the generated sequence
Some (f1,newState)
let fibonacci max = List.unfold (fibonacciUnfolder max) (1,1)
fibonacci 100
// int list = [1; 1; 2; 3; 5; 8; 13; 21; 34; 55; 89]
If you are working with one list and...
The following functions get a element in the collection by position:
head : list:'T list > 'T
.
Returns the first element of the collection.last : list:'T list > 'T
.
Returns the last element of the collection.item : index:int > list:'T list > 'T
.
Indexes into the collection. The first element has index 0.nth
and item
for lists and sequences. They are not designed for random access, and so they will be slow in general.nth : list:'T list > index:int > 'T
.
The older version of item
. NOTE: Deprecated in v4  use item
instead.get : array:'T[] > index:int > 'T
.
Yet another version of item
.exactlyOne : list:'T list > 'T
.
Returns the only element of the collection.But what if the collection is empty? Then head
and last
will fail with an exception (ArgumentException).
And if the index is not found in the collection? Then another exception again (ArgumentException for lists, IndexOutOfRangeException for arrays).
I would therefore recommend that you avoid these functions in general and use the tryXXX
equivalents below:
tryHead : list:'T list > 'T option
.
Returns the first element of the collection, or None if the collection is empty.tryLast : list:'T list > 'T option
.
Returns the last element of the collection, or None if the collection is empty.tryItem : index:int > list:'T list > 'T option
.
Indexes into the collection, or None if the index is not valid.let head = [1;2;3] > List.head
// val head : int = 1
let badHead : int = [] > List.head
// System.ArgumentException: The input list was empty.
let goodHeadOpt =
[1;2;3] > List.tryHead
// val goodHeadOpt : int option = Some 1
let badHeadOpt : int option =
[] > List.tryHead
// val badHeadOpt : int option = None
let goodItemOpt =
[1;2;3] > List.tryItem 2
// val goodItemOpt : int option = Some 3
let badItemOpt =
[1;2;3] > List.tryItem 99
// val badItemOpt : int option = None
As noted, the item
function should be avoided for lists. For example, if you want to process each item in a list, and you come from an imperative background,
you might write a loop with something like this:
// Don't do this!
let helloBad =
let list = ["a";"b";"c"]
let listSize = List.length list
[ for i in [0..listSize1] do
let element = list > List.item i
yield "hello " + element
]
// val helloBad : string list = ["hello a"; "hello b"; "hello c"]
Don't do that! Use something like map
instead. It's both more concise and more efficient:
let helloGood =
let list = ["a";"b";"c"]
list > List.map (fun element > "hello " + element)
// val helloGood : string list = ["hello a"; "hello b"; "hello c"]
You can search for an element or its index using find
and findIndex
:
find : predicate:('T > bool) > list:'T list > 'T
.
Returns the first element for which the given function returns true.findIndex : predicate:('T > bool) > list:'T list > int
.
Returns the index of the first element for which the given function returns true.And you can also search backwards:
findBack : predicate:('T > bool) > list:'T list > 'T
.
Returns the last element for which the given function returns true.findIndexBack : predicate:('T > bool) > list:'T list > int
.
Returns the index of the last element for which the given function returns true.But what if the item cannot be found? Then these will fail with an exception (KeyNotFoundException
).
I would therefore recommend that, as with head
and item
, you avoid these functions in general and use the tryXXX
equivalents below:
tryFind : predicate:('T > bool) > list:'T list > 'T option
.
Returns the first element for which the given function returns true, or None if no such element exists.tryFindBack : predicate:('T > bool) > list:'T list > 'T option
.
Returns the last element for which the given function returns true, or None if no such element exists.tryFindIndex : predicate:('T > bool) > list:'T list > int option
.
Returns the index of the first element for which the given function returns true, or None if no such element exists.tryFindIndexBack : predicate:('T > bool) > list:'T list > int option
.
Returns the index of the last element for which the given function returns true, or None if no such element exists.If you are doing a map
before a find
you can often combine the two steps into a single one using pick
(or better, tryPick
). See below for a usage example.
pick : chooser:('T > 'U option) > list:'T list > 'U
.
Applies the given function to successive elements, returning the first result where the chooser function returns Some.tryPick : chooser:('T > 'U option) > list:'T list > 'U option
.
Applies the given function to successive elements, returning the first result where the chooser function returns Some, or None if no such element exists.let listOfTuples = [ (1,"a"); (2,"b"); (3,"b"); (4,"a"); ]
listOfTuples > List.find ( fun (x,y) > y = "b")
// (2, "b")
listOfTuples > List.findBack ( fun (x,y) > y = "b")
// (3, "b")
listOfTuples > List.findIndex ( fun (x,y) > y = "b")
// 1
listOfTuples > List.findIndexBack ( fun (x,y) > y = "b")
// 2
listOfTuples > List.find ( fun (x,y) > y = "c")
// KeyNotFoundException
With pick
, rather than returning a bool, you return an option:
listOfTuples > List.pick ( fun (x,y) > if y = "b" then Some (x,y) else None)
// (2, "b")
That 'pick' function might seem unnecessary, but it is useful when dealing with functions that return options.
For example, say that there is a function tryInt
that parses a string and returns Some int
if the string is a valid int, otherwise None
.
// string > int option
let tryInt str =
match System.Int32.TryParse(str) with
 true, i > Some i
 false, _ > None
And now say that we want to find the first valid int in a list. The crude way would be:
tryInt
Some
using find
Option.get
The code might look something like this:
let firstValidNumber =
["a";"2";"three"]
// map the input
> List.map tryInt
// find the first Some
> List.find (fun opt > opt.IsSome)
// get the data from the option
> Option.get
// val firstValidNumber : int = 2
But pick
will do all these steps at once! So the code becomes much simpler:
let firstValidNumber =
["a";"2";"three"]
> List.pick tryInt
If you want to return many elements in the same way as pick
, consider using choose
(see section 12).
The previous section was about getting one element. How can you get more than one element? Well you're in luck! There's lots of functions to choose from.
To extract elements from the front, use one of these:
take: count:int > list:'T list > 'T list
.
Returns the first N elements of the collection.takeWhile: predicate:('T > bool) > list:'T list > 'T list
.
Returns a collection that contains all elements of the original collection while the given predicate returns true, and then returns no further elements.truncate: count:int > list:'T list > 'T list
.
Returns at most N elements in a new collection.To extract elements from the rear, use one of these:
skip: count:int > list: 'T list > 'T list
.
Returns the collection after removing the first N elements.skipWhile: predicate:('T > bool) > list:'T list > 'T list
.
Bypasses elements in a collection while the given predicate returns true, and then returns the remaining elements of the collection.tail: list:'T list > 'T list
.
Returns the collection after removing the first element.To extract other subsets of elements, use one of these:
filter: predicate:('T > bool) > list:'T list > 'T list
.
Returns a new collection containing only the elements of the collection for which the given function returns true.except: itemsToExclude:seq<'T> > list:'T list > 'T list when 'T : equality
.
Returns a new collection with the distinct elements of the input collection which do not appear in the itemsToExclude sequence, using generic hash and equality comparisons to compare values.choose: chooser:('T > 'U option) > list:'T list > 'U list
.
Applies the given function to each element of the collection. Returns a collection comprised of the elements where the function returns Some.where: predicate:('T > bool) > list:'T list > 'T list
.
Returns a new collection containing only the elements of the collection for which the given predicate returns true.
NOTE: "where" is a synonym for "filter".sub : 'T [] > int > int > 'T []
.
Creates an array that contains the supplied subrange, which is specified by starting index and length.myArray.[2..5]
. See below for examples.To reduce the list to distinct elements, use one of these:
distinct: list:'T list > 'T list when 'T : equality
.
Returns a collection that contains no duplicate entries according to generic hash and equality comparisons on the entries.distinctBy: projection:('T > 'Key) > list:'T list > 'T list when 'Key : equality
.
Returns a collection that contains no duplicate entries according to the generic hash and equality comparisons on the keys returned by the given keygenerating function.Taking elements from the front:
[1..10] > List.take 3
// [1; 2; 3]
[1..10] > List.takeWhile (fun i > i < 3)
// [1; 2]
[1..10] > List.truncate 4
// [1; 2; 3; 4]
[1..2] > List.take 3
// System.InvalidOperationException: The input sequence has an insufficient number of elements.
[1..2] > List.takeWhile (fun i > i < 3)
// [1; 2]
[1..2] > List.truncate 4
// [1; 2] // no error!
Taking elements from the rear:
[1..10] > List.skip 3
// [4; 5; 6; 7; 8; 9; 10]
[1..10] > List.skipWhile (fun i > i < 3)
// [3; 4; 5; 6; 7; 8; 9; 10]
[1..10] > List.tail
// [2; 3; 4; 5; 6; 7; 8; 9; 10]
[1..2] > List.skip 3
// System.ArgumentException: The index is outside the legal range.
[1..2] > List.skipWhile (fun i > i < 3)
// []
[1] > List.tail > List.tail
// System.ArgumentException: The input list was empty.
To extract other subsets of elements:
[1..10] > List.filter (fun i > i%2 = 0) // even
// [2; 4; 6; 8; 10]
[1..10] > List.where (fun i > i%2 = 0) // even
// [2; 4; 6; 8; 10]
[1..10] > List.except [3;4;5]
// [1; 2; 6; 7; 8; 9; 10]
To extract a slice:
Array.sub [1..10] 3 5
// [4; 5; 6; 7; 8]
[1..10].[3..5]
// [4; 5; 6]
[1..10].[3..]
// [4; 5; 6; 7; 8; 9; 10]
[1..10].[..5]
// [1; 2; 3; 4; 5; 6]
Note that slicing on lists can be slow, because they are not random access. Slicing on arrays is fast however.
To extract the distinct elements:
[1;1;1;2;3;3] > List.distinct
// [1; 2; 3]
[ (1,"a"); (1,"b"); (1,"c"); (2,"d")] > List.distinctBy fst
// [(1, "a"); (2, "d")]
As with pick
, the choose
function might seem awkward, but it is useful when dealing with functions that return options.
In fact, choose
is to filter
as pick
is to find
, Rather than using a boolean filter, the signal is Some
vs. None
.
As before, say that there is a function tryInt
that parses a string and returns Some int
if the string is a valid int, otherwise None
.
// string > int option
let tryInt str =
match System.Int32.TryParse(str) with
 true, i > Some i
 false, _ > None
And now say that we want to find all the valid ints in a list. The crude way would be:
tryInt
Some
Option.get
The code might look something like this:
let allValidNumbers =
["a";"2";"three"; "4"]
// map the input
> List.map tryInt
// include only the "Some"
> List.filter (fun opt > opt.IsSome)
// get the data from each option
> List.map Option.get
// val allValidNumbers : int list = [2; 4]
But choose
will do all these steps at once! So the code becomes much simpler:
let allValidNumbers =
["a";"2";"three"; "4"]
> List.choose tryInt
If you already have a list of options, you can filter and return the "Some" in one step by passing id
into choose
:
let reduceOptions =
[None; Some 1; None; Some 2]
> List.choose id
// val reduceOptions : int list = [1; 2]
If you want to return the first element in the same way as choose
, consider using pick
(see section 11).
If you want to do a similar action as choose
but for other wrapper types (such as a Success/Failure result), there is a discussion here.
There are lots of different ways to split a collection! Have a look at the usage examples to see the differences:
chunkBySize: chunkSize:int > list:'T list > 'T list list
.
Divides the input collection into chunks of size at most chunkSize
.groupBy : projection:('T > 'Key) > list:'T list > ('Key * 'T list) list when 'Key : equality
.
Applies a keygenerating function to each element of a collection and yields a list of unique keys. Each unique key contains a list of all elements that match to this key.pairwise: list:'T list > ('T * 'T) list
.
Returns a collection of each element in the input collection and its predecessor, with the exception of the first element which is only returned as the predecessor of the second element.partition: predicate:('T > bool) > list:'T list > ('T list * 'T list)
.
Splits the collection into two collections, containing the elements for which the given predicate returns true and false respectively.splitAt: index:int > list:'T list > ('T list * 'T list)
.
Splits a collection into two collections at the given index.splitInto: count:int > list:'T list > 'T list list
.
Splits the input collection into at most count chunks.windowed : windowSize:int > list:'T list > 'T list list
.
Returns a list of sliding windows containing elements drawn from the input collection. Each window is returned as a fresh collection. Unlike pairwise
the windows are collections,
not tuples.[1..10] > List.chunkBySize 3
// [[1; 2; 3]; [4; 5; 6]; [7; 8; 9]; [10]]
// note that the last chunk has one element
[1..10] > List.splitInto 3
// [[1; 2; 3; 4]; [5; 6; 7]; [8; 9; 10]]
// note that the first chunk has four elements
['a'..'i'] > List.splitAt 3
// (['a'; 'b'; 'c'], ['d'; 'e'; 'f'; 'g'; 'h'; 'i'])
['a'..'e'] > List.pairwise
// [('a', 'b'); ('b', 'c'); ('c', 'd'); ('d', 'e')]
['a'..'e'] > List.windowed 3
// [['a'; 'b'; 'c']; ['b'; 'c'; 'd']; ['c'; 'd'; 'e']]
let isEven i = (i%2 = 0)
[1..10] > List.partition isEven
// ([2; 4; 6; 8; 10], [1; 3; 5; 7; 9])
let firstLetter (str:string) = str.[0]
["apple"; "alice"; "bob"; "carrot"] > List.groupBy firstLetter
// [('a', ["apple"; "alice"]); ('b', ["bob"]); ('c', ["carrot"])]
All the functions other than splitAt
and pairwise
handle edge cases gracefully:
[1] > List.chunkBySize 3
// [[1]]
[1] > List.splitInto 3
// [[1]]
['a'; 'b'] > List.splitAt 3
// InvalidOperationException: The input sequence has an insufficient number of elements.
['a'] > List.pairwise
// InvalidOperationException: The input sequence has an insufficient number of elements.
['a'] > List.windowed 3
// []
[1] > List.partition isEven
// ([], [1])
[] > List.groupBy firstLetter
// []
The most generic way to aggregate the elements in a collection is to use reduce
:
reduce : reduction:('T > 'T > 'T) > list:'T list > 'T
.
Apply a function to each element of the collection, threading an accumulator argument through the computation.reduceBack : reduction:('T > 'T > 'T) > list:'T list > 'T
.
Applies a function to each element of the collection, starting from the end, threading an accumulator argument through the computation.and there are specific versions of reduce
for frequently used aggregations:
max : list:'T list > 'T when 'T : comparison
.
Return the greatest of all elements of the collection, compared via Operators.max.maxBy : projection:('T > 'U) > list:'T list > 'T when 'U : comparison
.
Returns the greatest of all elements of the collection, compared via Operators.max on the function result.min : list:'T list > 'T when 'T : comparison
.
Returns the lowest of all elements of the collection, compared via Operators.min.minBy : projection:('T > 'U) > list:'T list > 'T when 'U : comparison
.
Returns the lowest of all elements of the collection, compared via Operators.min on the function result.sum : list:'T list > 'T when 'T has static members (+) and Zero
.
Returns the sum of the elements in the collection.sumBy : projection:('T > 'U) > list:'T list > 'U when 'U has static members (+) and Zero
.
Returns the sum of the results generated by applying the function to each element of the collection.average : list:'T list > 'T when 'T has static members (+) and Zero and DivideByInt
.
Returns the average of the elements in the collection.
Note that a list of ints cannot be averaged  they must be cast to floats or decimals.averageBy : projection:('T > 'U) > list:'T list > 'U when 'U has static members (+) and Zero and DivideByInt
.
Returns the average of the results generated by applying the function to each element of the collection.Finally there are some counting functions:
length: list:'T list > int
.
Returns the length of the collection.countBy : projection:('T > 'Key) > list:'T list > ('Key * int) list when 'Key : equality
.
Applies a keygenerating function to each element and returns a collection yielding unique keys and their number of occurrences in the original collection.reduce
is a variant of fold
without an initial state  see section 19 for more on fold
. One way to think of it is just inserting a operator between
each element.
["a";"b";"c"] > List.reduce (+)
// "abc"
is the same as
"a" + "b" + "c"
Here's another example:
[2;3;4] > List.reduce (*)
// is same as
2 * 3 * 4
// Result is 24
Some ways of combining elements depend on the order of combining, and so there are two variants of "reduce":
reduce
moves forward through the list.reduceBack
, not surprisingly, moves backwards through the list.Here's a demonstration of the difference. First reduce
:
[1;2;3;4] > List.reduce (fun state x > (state)*10 + x)
// built up from // state at each step
1 // 1
(1)*10 + 2 // 12
((1)*10 + 2)*10 + 3 // 123
(((1)*10 + 2)*10 + 3)*10 + 4 // 1234
// Final result is 1234
Using the same combining function with reduceBack
produces a different result! It looks like this:
[1;2;3;4] > List.reduceBack (fun x state > x + 10*(state))
// built up from // state at each step
4 // 4
3 + 10*(4) // 43
2 + 10*(3 + 10*(4)) // 432
1 + 10*(2 + 10*(3 + 10*(4))) // 4321
// Final result is 4321
Again, see section 19 for a more detailed discussion of the related functions fold
and foldBack
.
The other aggregation functions are much more straightforward.
type Suit = Club  Diamond  Spade  Heart
type Rank = Two  Three  King  Ace
let cards = [ (Club,King); (Diamond,Ace); (Spade,Two); (Heart,Three); ]
cards > List.max // (Heart, Three)
cards > List.maxBy snd // (Diamond, Ace)
cards > List.min // (Club, King)
cards > List.minBy snd // (Spade, Two)
[1..10] > List.sum
// 55
[ (1,"a"); (2,"b") ] > List.sumBy fst
// 3
[1..10] > List.average
// The type 'int' does not support the operator 'DivideByInt'
[1..10] > List.averageBy float
// 5.5
[ (1,"a"); (2,"b") ] > List.averageBy (fst >> float)
// 1.5
[1..10] > List.length
// 10
[ ("a","A"); ("b","B"); ("a","C") ] > List.countBy fst
// [("a", 2); ("b", 1)]
[ ("a","A"); ("b","B"); ("a","C") ] > List.countBy snd
// [("A", 1); ("B", 1); ("C", 1)]
Most of the aggregation functions do not like empty lists! You might consider using one of the fold
functions to be safe  see section 19.
let emptyListOfInts : int list = []
emptyListOfInts > List.reduce (+)
// ArgumentException: The input list was empty.
emptyListOfInts > List.max
// ArgumentException: The input sequence was empty.
emptyListOfInts > List.min
// ArgumentException: The input sequence was empty.
emptyListOfInts > List.sum
// 0
emptyListOfInts > List.averageBy float
// ArgumentException: The input sequence was empty.
let emptyListOfTuples : (int*int) list = []
emptyListOfTuples > List.countBy fst
// (int * int) list = []
You can change the order of the elements using reversing, sorting and permuting. All of the following return new collections:
rev: list:'T list > 'T list
.
Returns a new collection with the elements in reverse order.sort: list:'T list > 'T list when 'T : comparison
.
Sorts the given collection using Operators.compare.sortDescending: list:'T list > 'T list when 'T : comparison
.
Sorts the given collection in descending order using Operators.compare.sortBy: projection:('T > 'Key) > list:'T list > 'T list when 'Key : comparison
.
Sorts the given collection using keys given by the given projection. Keys are compared using Operators.compare.sortByDescending: projection:('T > 'Key) > list:'T list > 'T list when 'Key : comparison
.
Sorts the given collection in descending order using keys given by the given projection. Keys are compared using Operators.compare.sortWith: comparer:('T > 'T > int) > list:'T list > 'T list
.
Sorts the given collection using the given comparison function.permute : indexMap:(int > int) > list:'T list > 'T list
.
Returns a collection with all elements permuted according to the specified permutation.And there are also some arrayonly functions that sort in place:
sortInPlace: array:'T[] > unit when 'T : comparison
.
Sorts the elements of an array by mutating the array inplace. Elements are compared using Operators.compare.sortInPlaceBy: projection:('T > 'Key) > array:'T[] > unit when 'Key : comparison
.
Sorts the elements of an array by mutating the array inplace, using the given projection for the keys. Keys are compared using Operators.compare.sortInPlaceWith: comparer:('T > 'T > int) > array:'T[] > unit
.
Sorts the elements of an array by mutating the array inplace, using the given comparison function as the order.[1..5] > List.rev
// [5; 4; 3; 2; 1]
[2;4;1;3;5] > List.sort
// [1; 2; 3; 4; 5]
[2;4;1;3;5] > List.sortDescending
// [5; 4; 3; 2; 1]
[ ("b","2"); ("a","3"); ("c","1") ] > List.sortBy fst
// [("a", "3"); ("b", "2"); ("c", "1")]
[ ("b","2"); ("a","3"); ("c","1") ] > List.sortBy snd
// [("c", "1"); ("b", "2"); ("a", "3")]
// example of a comparer
let tupleComparer tuple1 tuple2 =
if tuple1 < tuple2 then
1
elif tuple1 > tuple2 then
1
else
0
[ ("b","2"); ("a","3"); ("c","1") ] > List.sortWith tupleComparer
// [("a", "3"); ("b", "2"); ("c", "1")]
[1..10] > List.permute (fun i > (i + 3) % 10)
// [8; 9; 10; 1; 2; 3; 4; 5; 6; 7]
[1..10] > List.permute (fun i > 9  i)
// [10; 9; 8; 7; 6; 5; 4; 3; 2; 1]
These set of functions all return true or false.
contains: value:'T > source:'T list > bool when 'T : equality
.
Tests if the collection contains the specified element.exists: predicate:('T > bool) > list:'T list > bool
.
Tests if any element of the collection satisfies the given predicate.forall: predicate:('T > bool) > list:'T list > bool
.
Tests if all elements of the collection satisfy the given predicate.isEmpty: list:'T list > bool
.
Returns true if the collection contains no elements, false otherwise.[1..10] > List.contains 5
// true
[1..10] > List.contains 42
// false
[1..10] > List.exists (fun i > i > 3 && i < 5)
// true
[1..10] > List.exists (fun i > i > 5 && i < 3)
// false
[1..10] > List.forall (fun i > i > 0)
// true
[1..10] > List.forall (fun i > i > 5)
// false
[1..10] > List.isEmpty
// false
I sometimes like to think of functional programming as "transformationoriented programming", and map
(aka Select
in LINQ) is one of the most fundamental ingredients for this approach.
In fact, I have devoted a whole series to it here.
map: mapping:('T > 'U) > list:'T list > 'U list
.
Builds a new collection whose elements are the results of applying the given function to each of the elements of the collection.Sometimes each element maps to a list, and you want to flatten out all the lists. For this case, use collect
(aka SelectMany
in LINQ).
collect: mapping:('T > 'U list) > list:'T list > 'U list
.
For each element of the list, applies the given function. Concatenates all the results and return the combined list.Other transformation functions include:
choose
in section 12 is a map and option filter combined.cast: source:IEnumerable > seq<'T>
.
Wraps a looselytyped System.Collections
sequence as a typed sequence.Here are some examples of using map
in the conventional way, as a function that accepts a list and a mapping function and returns a new transformed list:
let add1 x = x + 1
// map as a list transformer
[1..5] > List.map add1
// [2; 3; 4; 5; 6]
// the list being mapped over can contain anything!
let times2 x = x * 2
[ add1; times2] > List.map (fun f > f 5)
// [6; 10]
You can also think of map
as a function transformer. It turns an elementtoelement function into a listtolist function.
let add1ToEachElement = List.map add1
// "add1ToEachElement" transforms lists to lists rather than ints to ints
// val add1ToEachElement : (int list > int list)
// now use it
[1..5] > add1ToEachElement
// [2; 3; 4; 5; 6]
collect
works to flatten lists. If you already have a list of lists, you can use collect
with id
to flatten them.
[2..5] > List.collect (fun x > [x; x*x; x*x*x] )
// [2; 4; 8; 3; 9; 27; 4; 16; 64; 5; 25; 125]
// using "id" with collect
let list1 = [1..3]
let list2 = [4..6]
[list1; list2] > List.collect id
// [1; 2; 3; 4; 5; 6]
Finally, Seq.cast
is useful when working with older parts of the BCL that have specialized collection classes rather than generics.
For example, the Regex library has this problem, and so the code below won't compile because MatchCollection
is not an IEnumerable<T>
open System.Text.RegularExpressions
let matches =
let pattern = "\d\d\d"
let matchCollection = Regex.Matches("123 456 789",pattern)
matchCollection
> Seq.map (fun m > m.Value) // ERROR
// ERROR: The type 'MatchCollection' is not compatible with the type 'seq<'a>'
> Seq.toList
The fix is to cast MatchCollection
to a Seq<Match>
and then the code will work nicely:
let matches =
let pattern = "\d\d\d"
let matchCollection = Regex.Matches("123 456 789",pattern)
matchCollection
> Seq.cast<Match>
> Seq.map (fun m > m.Value)
> Seq.toList
// output = ["123"; "456"; "789"]
Normally, when processing a collection, we transform each element to a new value using map
. But occasionally we need to process all the elements with a function which doesn't
produce a useful value (a "unit function").
iter: action:('T > unit) > list:'T list > unit
.
Applies the given function to each element of the collection.unit
.The most common examples of unit functions are all about sideeffects: printing to the console, updating a database, putting a message on a queue, etc.
For the examples below, I will just use printfn
as my unit function.
[1..3] > List.iter (fun i > printfn "i is %i" i)
(*
i is 1
i is 2
i is 3
*)
// or using partial application
[1..3] > List.iter (printfn "i is %i")
// or using a for loop
for i = 1 to 3 do
printfn "i is %i" i
// or using a forin loop
for i in [1..3] do
printfn "i is %i" i
As noted above, the expression inside an iter
or forloop must return unit. In the following examples, we try to add 1 to the element, and get a compiler error:
[1..3] > List.iter (fun i > i + 1)
// ~~~
// ERROR error FS0001: The type 'unit' does not match the type 'int'
// a forloop expression *must* return unit
for i in [1..3] do
i + 1 // ERROR
// This expression should have type 'unit',
// but has type 'int'. Use 'ignore' ...
If you are sure that this is not a logic bug in your code, and you want to get rid of this error, you can pipe the results into ignore
:
[1..3] > List.iter (fun i > i + 1 > ignore)
for i in [1..3] do
i + 1 > ignore
The fold
function is the most basic and powerful function in the collection arsenal. All other functions (other than generators like unfold
) can be written in terms of it. See the examples below.
fold<'T,'State> : folder:('State > 'T > 'State) > state:'State > list:'T list > 'State
.
Applies a function to each element of the collection, threading an accumulator argument through the computation.foldBack<'T,'State> : folder:('T > 'State > 'State) > list:'T list > state:'State > 'State
.
Applies a function to each element of the collection, starting from the end, threading an accumulator argument through the computation.
WARNING: Watch out for using Seq.foldBack
on infinite lists! The runtime will laugh at you ha ha ha and then go very quiet.The fold
function is often called "fold left" and foldBack
is often called "fold right".
The scan
function is like fold
but returns the intermediate results and thus can be used to trace or monitor the iteration.
scan<'T,'State> : folder:('State > 'T > 'State) > state:'State > list:'T list > 'State list
.
Like fold
, but returns both the intermediary and final results.scanBack<'T,'State> : folder:('T > 'State > 'State) > list:'T list > state:'State > 'State list
.
Like foldBack
, but returns both the intermediary and final results.Just like the fold twins, scan
is often called "scan left" and scanBack
is often called "scan right".
Finally, mapFold
combines map
and fold
into one awesome superpower. More complicated than using map
and fold
separately but also more efficient.
mapFold<'T,'State,'Result> : mapping:('State > 'T > 'Result * 'State) > state:'State > list:'T list > 'Result list * 'State
.
Combines map and fold. Builds a new collection whose elements are the results of applying the given function to each of the elements of the input collection. The function is also used to accumulate a final value.mapFoldBack<'T,'State,'Result> : mapping:('T > 'State > 'Result * 'State) > list:'T list > state:'State > 'Result list * 'State
.
Combines map and foldBack. Builds a new collection whose elements are the results of applying the given function to each of the elements of the input collection. The function is also used to accumulate a final value.fold
examplesOne way of thinking about fold
is that it is like reduce
but with an extra parameter for the initial state:
["a";"b";"c"] > List.fold (+) "hello: "
// "hello: abc"
// "hello: " + "a" + "b" + "c"
[1;2;3] > List.fold (+) 10
// 16
// 10 + 1 + 2 + 3
As with reduce
, fold
and foldBack
can give very different answers.
[1;2;3;4] > List.fold (fun state x > (state)*10 + x) 0
// state at each step
1 // 1
(1)*10 + 2 // 12
((1)*10 + 2)*10 + 3 // 123
(((1)*10 + 2)*10 + 3)*10 + 4 // 1234
// Final result is 1234
And here's the foldBack
version:
List.foldBack (fun x state > x + 10*(state)) [1;2;3;4] 0
// state at each step
4 // 4
3 + 10*(4) // 43
2 + 10*(3 + 10*(4)) // 432
1 + 10*(2 + 10*(3 + 10*(4))) // 4321
// Final result is 4321
Note that foldBack
has a different parameter order to fold
: the list is second last, and the initial state is last, which means that piping is not as convenient.
It's easy to get confused between fold
vs. foldBack
. I find it helpful to think of fold
as being about iteration while foldBack
is about recursion.
Let's say we want to calculate the sum of a list. The iterative way would be to use a forloop. You start with a (mutable) accumulator and thread it through each iteration, updating it as you go.
let iterativeSum list =
let mutable total = 0
for e in list do
total < total + e
total // return sum
On the other hand, the recursive approach says that if the list has a head and tail, calculate the sum of the tail (a smaller list) first, and then add the head to it.
Each time the tail gets smaller and smaller until it is empty, at which point you're done.
let rec recursiveSum list =
match list with
 [] >
0
 head::tail >
head + (recursiveSum tail)
Which approach is better?
For aggregation, the iterative way is (fold
) often easiest to understand.
But for things like constructing new lists, the recursive way is (foldBack
) is easier to understand.
For example, if we were going to going to create a function from scratch that turned each element into the corresponding string, we might write something like this:
let rec mapToString list =
match list with
 [] >
[]
 head::tail >
head.ToString() :: (mapToString tail)
[1..3] > mapToString
// ["1"; "2"; "3"]
Using foldBack
we can transfer that same logic "as is":
[]
head.ToString() :: state
Here is the resulting function:
let foldToString list =
let folder head state =
head.ToString() :: state
List.foldBack folder list []
[1..3] > foldToString
// ["1"; "2"; "3"]
On the other hand, a big advantage of fold
is that it is easier to use "inline" because it plays better with piping.
Luckily, you can use fold
(for list construction at least) just like foldBack
as long as you reverse the list at the end.
// inline version of "foldToString"
[1..3]
> List.fold (fun state head > head.ToString() :: state) []
> List.rev
// ["1"; "2"; "3"]
fold
to implement other functionsAs I mentioned above, fold
is the core function for operating on lists and can emulate most other functions,
although perhaps not as efficiently as a custom implementation.
For example, here is map
implemented using fold
:
/// map a function "f" over all elements
let myMap f list =
// helper function
let folder state head =
f head :: state
// main flow
list
> List.fold folder []
> List.rev
[1..3] > myMap (fun x > x + 2)
// [3; 4; 5]
And here is filter
implemented using fold
:
/// return a new list of elements for which "pred" is true
let myFilter pred list =
// helper function
let folder state head =
if pred head then
head :: state
else
state
// main flow
list
> List.fold folder []
> List.rev
let isOdd n = (n%2=1)
[1..5] > myFilter isOdd
// [1; 3; 5]
And of course, you can emulate the other functions in a similar way.
scan
examplesEarlier, I showed an example of the intermediate steps of fold
:
[1;2;3;4] > List.fold (fun state x > (state)*10 + x) 0
// state at each step
1 // 1
(1)*10 + 2 // 12
((1)*10 + 2)*10 + 3 // 123
(((1)*10 + 2)*10 + 3)*10 + 4 // 1234
// Final result is 1234
For that example, I had to manually calculate the intermediate states,
Well, if I had used scan
, I would have got those intermediate states for free!
[1;2;3;4] > List.scan (fun state x > (state)*10 + x) 0
// accumulates from left ===> [0; 1; 12; 123; 1234]
scanBack
works the same way, but backwards of course:
List.scanBack (fun x state > (state)*10 + x) [1;2;3;4] 0
// [4321; 432; 43; 4; 0] <=== accumulates from right
Just as with foldBack
the parameter order for "scan right" is inverted compared with "scan left".
scan
Here's an example where scan
is useful. Say that you have a news site, and you need to make sure headlines fit into 50 chars.
You could just truncate the string at 50, but that would look ugly. Instead you want to have the truncation end at a word boundary.
Here's one way of doing it using scan
:
scan
to concat the words back together, generating a list of fragments, each with an extra word added.// start by splitting the text into words
let text = "Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor."
let words = text.Split(' ')
// ["Lorem"; "ipsum"; "dolor"; "sit"; ... ]
// accumulate a series of fragments
let fragments = words > Seq.scan (fun frag word > frag + " " + word) ""
(*
" Lorem"
" Lorem ipsum"
" Lorem ipsum dolor"
" Lorem ipsum dolor sit"
" Lorem ipsum dolor sit amet,"
etc
*)
// get the longest fragment under 50
let longestFragUnder50 =
fragments
> Seq.takeWhile (fun s > s.Length <= 50)
> Seq.last
// trim off the first blank
let longestFragUnder50Trimmed =
longestFragUnder50 > (fun s > s.[1..])
// The result is:
// "Lorem ipsum dolor sit amet, consectetur"
Note that I'm using Seq.scan
rather than Array.scan
. This does a lazy scan and avoids having to create fragments that are not needed.
Finally, here is the complete logic as a utility function:
// the whole thing as a function
let truncText max (text:string) =
if text.Length <= max then
text
else
text.Split(' ')
> Seq.scan (fun frag word > frag + " " + word) ""
> Seq.takeWhile (fun s > s.Length <= max3)
> Seq.last
> (fun s > s.[1..] + "...")
"a small headline" > truncText 50
// "a small headline"
text > truncText 50
// "Lorem ipsum dolor sit amet, consectetur..."
Yes, I know that there is a more efficient implementation than this, but I hope that this little example shows off the power of scan
.
mapFold
examplesThe mapFold
function can do a map and a fold in one step, which can be convenient on occasion.
Here's an example of combining an addition and a sum in one step using mapFold
:
let add1 x = x + 1
// add1 using map
[1..5] > List.map (add1)
// Result => [2; 3; 4; 5; 6]
// sum using fold
[1..5] > List.fold (fun state x > state + x) 0
// Result => 15
// map and sum using mapFold
[1..5] > List.mapFold (fun state x > add1 x, (state + x)) 0
// Result => ([2; 3; 4; 5; 6], 15)
Often, you need the index of the element as you do an iteration. You could use a mutable counter, but why not sit back and let the library do the work for you?
mapi: mapping:(int > 'T > 'U) > list:'T list > 'U list
.
Like map
, but with the integer index passed to the function as well. See section 17 for more on map
.iteri: action:(int > 'T > unit) > list:'T list > unit
.
Like iter
, but with the integer index passed to the function as well. See section 18 for more on iter
.indexed: list:'T list > (int * 'T) list
.
Returns a new list whose elements are the corresponding elements of the input list paired with the index (from 0) of each element.['a'..'c'] > List.mapi (fun index ch > sprintf "the %ith element is '%c'" index ch)
// ["the 0th element is 'a'"; "the 1th element is 'b'"; "the 2th element is 'c'"]
// with partial application
['a'..'c'] > List.mapi (sprintf "the %ith element is '%c'")
// ["the 0th element is 'a'"; "the 1th element is 'b'"; "the 2th element is 'c'"]
['a'..'c'] > List.iteri (printfn "the %ith element is '%c'")
(*
the 0th element is 'a'
the 1th element is 'b'
the 2th element is 'c'
*)
indexed
generates a tuple with the index  a shortcut for a specific use of mapi
:
['a'..'c'] > List.mapi (fun index ch > (index, ch) )
// [(0, 'a'); (1, 'b'); (2, 'c')]
// "indexed" is a shorter version of above
['a'..'c'] > List.indexed
// [(0, 'a'); (1, 'b'); (2, 'c')]
You often need to convert from one kind of collection to another. These functions do this.
The ofXXX
functions are used to convert from XXX
to the module type. For example, List.ofArray
will turn an array into a list.
ofArray : array:'T[] > 'T list
.
Builds a new collection from the given array.ofSeq: source:seq<'T> > 'T list
.
Builds a new collection from the given enumerable object.ofList: source:'T list > seq<'T>
.
Builds a new collection from the given list.The toXXX
are used to convert from the module type to the type XXX
. For example, List.toArray
will turn an list into an array.
toArray: list:'T list > 'T[]
.
Builds an array from the given collection.toSeq: list:'T list > seq<'T>
.
Views the given collection as a sequence.toList: source:seq<'T> > 'T list
.
Builds a list from the given collection.[1..5] > List.toArray // [1; 2; 3; 4; 5]
[1..5] > Array.ofList // [1; 2; 3; 4; 5]
// etc
One important use of these conversion functions is to convert a lazy enumeration (seq
) to a fully evaluated collection such as list
. This is particularly
important when there is a disposable resource involved, such as file handle or database connection. If the sequence is not converted into a list
you may encounter errors accessing the elements. See section 28 for more.
There are some special functions (for Seq only) that change the behavior of the collection as a whole.
cache: source:seq<'T> > seq<'T>
.
Returns a sequence that corresponds to a cached version of the input sequence. This result sequence will have the same elements as the input sequence. The result
can be enumerated multiple times. The input sequence will be enumerated at most once and only as far as is necessary.readonly : source:seq<'T> > seq<'T>
.
Builds a new sequence object that delegates to the given sequence object. This ensures the original sequence cannot be rediscovered and mutated by a type cast.delay : generator:(unit > seq<'T>) > seq<'T>
.
Returns a sequence that is built from the given delayed specification of a sequence.cache
exampleHere's an example of cache
in use:
let uncachedSeq = seq {
for i = 1 to 3 do
printfn "Calculating %i" i
yield i
}
// iterate twice
uncachedSeq > Seq.iter ignore
uncachedSeq > Seq.iter ignore
The result of iterating over the sequence twice is as you would expect:
Calculating 1
Calculating 2
Calculating 3
Calculating 1
Calculating 2
Calculating 3
But if we cache the sequence...
let cachedSeq = uncachedSeq > Seq.cache
// iterate twice
cachedSeq > Seq.iter ignore
cachedSeq > Seq.iter ignore
... then each item is only printed once:
Calculating 1
Calculating 2
Calculating 3
readonly
exampleHere's an example of readonly
being used to hide the underlying type of the sequence:
// print the underlying type of the sequence
let printUnderlyingType (s:seq<_>) =
let typeName = s.GetType().Name
printfn "%s" typeName
[1;2;3] > printUnderlyingType
// Int32[]
[1;2;3] > Seq.readonly > printUnderlyingType
// mkSeq@589 // a temporary type
delay
exampleHere's an example of delay
.
let makeNumbers max =
[ for i = 1 to max do
printfn "Evaluating %d." i
yield i ]
let eagerList =
printfn "Started creating eagerList"
let list = makeNumbers 5
printfn "Finished creating eagerList"
list
let delayedSeq =
printfn "Started creating delayedSeq"
let list = Seq.delay (fun () > makeNumbers 5 > Seq.ofList)
printfn "Finished creating delayedSeq"
list
If we run the code above, we find that just by creating eagerList
, we print all the "Evaluating" messages. But creating delayedSeq
does not trigger the list iteration.
Started creating eagerList
Evaluating 1.
Evaluating 2.
Evaluating 3.
Evaluating 4.
Evaluating 5.
Finished creating eagerList
Started creating delayedSeq
Finished creating delayedSeq
Only when the sequence is iterated over does the list creation happen:
eagerList > Seq.take 3 // list already created
delayedSeq > Seq.take 3 // list creation triggered
An alternative to using delay is just to embed the list in a seq
like this:
let embeddedList = seq {
printfn "Started creating embeddedList"
yield! makeNumbers 5
printfn "Finished creating embeddedList"
}
As with delayedSeq
, the makeNumbers
function will not be called until the sequence is iterated over.
If you have two lists, there are analogues of most of the common functions like map and fold.
map2: mapping:('T1 > 'T2 > 'U) > list1:'T1 list > list2:'T2 list > 'U list
.
Builds a new collection whose elements are the results of applying the given function to the corresponding elements of the two collections pairwise.mapi2: mapping:(int > 'T1 > 'T2 > 'U) > list1:'T1 list > list2:'T2 list > 'U list
.
Like mapi
, but mapping corresponding elements from two lists of equal length.iter2: action:('T1 > 'T2 > unit) > list1:'T1 list > list2:'T2 list > unit
.
Applies the given function to two collections simultaneously. The collections must have identical size.iteri2: action:(int > 'T1 > 'T2 > unit) > list1:'T1 list > list2:'T2 list > unit
.
Like iteri
, but mapping corresponding elements from two lists of equal length.forall2: predicate:('T1 > 'T2 > bool) > list1:'T1 list > list2:'T2 list > bool
.
The predicate is applied to matching elements in the two collections up to the lesser of the two lengths of the collections. If any application returns false then the overall result is false, else true.exists2: predicate:('T1 > 'T2 > bool) > list1:'T1 list > list2:'T2 list > bool
.
The predicate is applied to matching elements in the two collections up to the lesser of the two lengths of the collections. If any application returns true then the overall result is true, else false.fold2<'T1,'T2,'State> : folder:('State > 'T1 > 'T2 > 'State) > state:'State > list1:'T1 list > list2:'T2 list > 'State
.
Applies a function to corresponding elements of two collections, threading an accumulator argument through the computation.foldBack2<'T1,'T2,'State> : folder:('T1 > 'T2 > 'State > 'State) > list1:'T1 list > list2:'T2 list > state:'State > 'State
.
Applies a function to corresponding elements of two collections, threading an accumulator argument through the computation.compareWith: comparer:('T > 'T > int) > list1:'T list > list2:'T list > int
.
Compares two collections using the given comparison function, element by element. Returns the first nonzero result from the comparison function. If the end of a collection
is reached it returns a 1 if the first collection is shorter and a 1 if the second collection is shorter.append
, concat
, and zip
in section 26: combining and uncombining collections.These functions are straightforward to use:
let intList1 = [2;3;4]
let intList2 = [5;6;7]
List.map2 (fun i1 i2 > i1 + i2) intList1 intList2
// [7; 9; 11]
// TIP use the > operator to pipe a tuple as two arguments
(intList1,intList2) > List.map2 (fun i1 i2 > i1 + i2)
// [7; 9; 11]
(intList1,intList2) > List.mapi2 (fun index i1 i2 > index,i1 + i2)
// [(0, 7); (1, 9); (2, 11)]
(intList1,intList2) > List.iter2 (printf "i1=%i i2=%i; ")
// i1=2 i2=5; i1=3 i2=6; i1=4 i2=7;
(intList1,intList2) > List.iteri2 (printf "index=%i i1=%i i2=%i; ")
// index=0 i1=2 i2=5; index=1 i1=3 i2=6; index=2 i1=4 i2=7;
(intList1,intList2) > List.forall2 (fun i1 i2 > i1 < i2)
// true
(intList1,intList2) > List.exists2 (fun i1 i2 > i1+10 > i2)
// true
(intList1,intList2) > List.fold2 (fun state i1 i2 > (10*state) + i1 + i2) 0
// 801 = 234 + 567
List.foldBack2 (fun i1 i2 state > i1 + i2 + (10*state)) intList1 intList2 0
// 1197 = 432 + 765
(intList1,intList2) > List.compareWith (fun i1 i2 > i1.CompareTo(i2))
// 1
(intList1,intList2) > List.append
// [2; 3; 4; 5; 6; 7]
[intList1;intList2] > List.concat
// [2; 3; 4; 5; 6; 7]
(intList1,intList2) > List.zip
// [(2, 5); (3, 6); (4, 7)]
By using fold2
and foldBack2
you can easily create your own functions. For example, some filter2
functions can be defined like this:
/// Apply a function to each element in a pair
/// If either result passes, include that pair in the result
let filterOr2 filterPredicate list1 list2 =
let pass e = filterPredicate e
let folder e1 e2 state =
if (pass e1)  (pass e2) then
(e1,e2)::state
else
state
List.foldBack2 folder list1 list2 ([])
/// Apply a function to each element in a pair
/// Only if both results pass, include that pair in the result
let filterAnd2 filterPredicate list1 list2 =
let pass e = filterPredicate e
let folder e1 e2 state =
if (pass e1) && (pass e2) then
(e1,e2)::state
else
state
List.foldBack2 folder list1 list2 []
// test it
let startsWithA (s:string) = (s.[0] = 'A')
let strList1 = ["A1"; "A3"]
let strList2 = ["A2"; "B1"]
(strList1, strList2) > filterOr2 startsWithA
// [("A1", "A2"); ("A3", "B1")]
(strList1, strList2) > filterAnd2 startsWithA
// [("A1", "A2")]
See also section 25.
If you have three lists, you only have one builtin function available. But see section 25 for an example of how you can build your own threelist functions.
map3: mapping:('T1 > 'T2 > 'T3 > 'U) > list1:'T1 list > list2:'T2 list > list3:'T3 list > 'U list
.
Builds a new collection whose elements are the results of applying the given function to the corresponding elements of the three collections simultaneously.append
, concat
, and zip3
in section 26: combining and uncombining collections.If you are working with more than three lists, there are no built in functions for you.
If this happens infrequently, then you could just collapse the lists into a single tuple using zip2
and/or zip3
in succession, and then process that tuple using map
.
Alternatively you can "lift" your function to the world of "zip lists" using applicatives.
let (<*>) fList xList =
List.map2 (fun f x > f x) fList xList
let (<!>) = List.map
let addFourParams x y z w =
x + y + z + w
// lift "addFourParams" to List world and pass lists as parameters rather than ints
addFourParams <!> [1;2;3] <*> [1;2;3] <*> [1;2;3] <*> [1;2;3]
// Result = [4; 8; 12]
If that seems like magic, see this series for a explanation of what this code is doing.
Finally, there are a number of functions that combine and uncombine collections.
append: list1:'T list > list2:'T list > 'T list
.
Returns a new collection that contains the elements of the first collection followed by elements of the second.@
is an infix version of append
for lists.concat: lists:seq<'T list> > 'T list
.
Builds a new collection whose elements are the results of applying the given function to the corresponding elements of the collections simultaneously.zip: list1:'T1 list > list2:'T2 list > ('T1 * 'T2) list
.
Combines two collections into a list of pairs. The two collections must have equal lengths.zip3: list1:'T1 list > list2:'T2 list > list3:'T3 list > ('T1 * 'T2 * 'T3) list
.
Combines three collections into a list of triples. The collections must have equal lengths.unzip: list:('T1 * 'T2) list > ('T1 list * 'T2 list)
.
Splits a collection of pairs into two collections.unzip3: list:('T1 * 'T2 * 'T3) list > ('T1 list * 'T2 list * 'T3 list)
.
Splits a collection of triples into three collections.These functions are straightforward to use:
List.append [1;2;3] [4;5;6]
// [1; 2; 3; 4; 5; 6]
[1;2;3] @ [4;5;6]
// [1; 2; 3; 4; 5; 6]
List.concat [ [1]; [2;3]; [4;5;6] ]
// [1; 2; 3; 4; 5; 6]
List.zip [1;2] [10;20]
// [(1, 10); (2, 20)]
List.zip3 [1;2] [10;20] [100;200]
// [(1, 10, 100); (2, 20, 200)]
List.unzip [(1, 10); (2, 20)]
// ([1; 2], [10; 20])
List.unzip3 [(1, 10, 100); (2, 20, 200)]
// ([1; 2], [10; 20], [100; 200])
Note that the zip
functions require the lengths to be the same.
List.zip [1;2] [10]
// ArgumentException: The lists had different lengths.
Arrays are mutable, and therefore have some functions that are not applicable to lists and sequences.
Array.blit: source:'T[] > sourceIndex:int > target:'T[] > targetIndex:int > count:int > unit
.
Reads a range of elements from the first array and write them into the second.Array.copy: array:'T[] > 'T[]
.
Builds a new array that contains the elements of the given array.Array.fill: target:'T[] > targetIndex:int > count:int > value:'T > unit
.
Fills a range of elements of the array with the given value.Array.set: array:'T[] > index:int > value:'T > unit
.
Sets an element of an array.I won't give examples. See the MSDN documentation.
One important use of conversion functions like List.ofSeq
is to convert a lazy enumeration (seq
) to a fully evaluated collection such as list
. This is particularly
important when there is a disposable resource involved such as file handle or database connection. If the sequence is not converted into a list
while the resource is available you may encounter errors accessing the elements later, after the resource has been disposed.
This will be an extended example, so let's start with some helper functions that emulate a database and a UI:
// a disposable database connection
let DbConnection() =
printfn "Opening connection"
{ new System.IDisposable with
member this.Dispose() =
printfn "Disposing connection" }
// read some records from the database
let readNCustomersFromDb dbConnection n =
let makeCustomer i =
sprintf "Customer %i" i
seq {
for i = 1 to n do
let customer = makeCustomer i
printfn "Loading %s from db" customer
yield customer
}
// show some records on the screen
let showCustomersinUI customers =
customers > Seq.iter (printfn "Showing %s in UI")
A naive implementation will cause the sequence to be evaluated after the connection is closed:
let readCustomersFromDb() =
use dbConnection = DbConnection()
let results = readNCustomersFromDb dbConnection 2
results
let customers = readCustomersFromDb()
customers > showCustomersinUI
The output is below. You can see that the connection is closed and only then is the sequence evaluated.
Opening connection
Disposing connection
Loading Customer 1 from db // error! connection closed!
Showing Customer 1 in UI
Loading Customer 2 from db
Showing Customer 2 in UI
A better implementation will convert the sequence to a list while the connection is open, causing the sequence to be evaluated immediately:
let readCustomersFromDb() =
use dbConnection = DbConnection()
let results = readNCustomersFromDb dbConnection 2
results > List.ofSeq
// Convert to list while connection is open
let customers = readCustomersFromDb()
customers > showCustomersinUI
The result is much better. All the records are loaded before the connection is disposed:
Opening connection
Loading Customer 1 from db
Loading Customer 2 from db
Disposing connection
Showing Customer 1 in UI
Showing Customer 2 in UI
A third alternative is to embed the disposable in the sequence itself:
let readCustomersFromDb() =
seq {
// put disposable inside the sequence
use dbConnection = DbConnection()
yield! readNCustomersFromDb dbConnection 2
}
let customers = readCustomersFromDb()
customers > showCustomersinUI
The output shows that now the UI display is also done while the connection is open:
Opening connection
Loading Customer 1 from db
Showing Customer 1 in UI
Loading Customer 2 from db
Showing Customer 2 in UI
Disposing connection
This may be a bad thing (longer time for the connection to stay open) or a good thing (minimal memory use), depending on the context.
You made it to the end  well done! Not really much of an adventure, though, was it? No dragons or anything. Nevertheless, I hope it was helpful.