Slices
This article explains how to take slices from existing F# types and how to define your own slices.
In F#, a slice is a subset of any data type. Slices are similar to indexers, but instead of yielding a single value from the underlying data structure, they yield multiple ones. Slices use the .. operator syntax to select the range of specified indices in a data type. For more information, see the looping expression reference article.
F# currently has intrinsic support for slicing strings, lists, arrays, and multidimensional (2D, 3D, 4D) arrays. Slicing is most commonly used with F# arrays and lists. You can add slicing to your custom data types by using the GetSlice method in your type definition or in an in-scope type extension.
Slicing F# lists and arrays
The most common data types that are sliced are F# lists and arrays. The following example demonstrates how to slice lists:
// Generate a list of 100 integers
let fullList = [ 1 .. 100 ]
// Create a slice from indices 1-5 (inclusive)
let smallSlice = fullList[1..5]
printfn $"Small slice: {smallSlice}"
// Create a slice from the beginning to index 5 (inclusive)
let unboundedBeginning = fullList[..5]
printfn $"Unbounded beginning slice: {unboundedBeginning}"
// Create a slice from an index to the end of the list
let unboundedEnd = fullList[94..]
printfn $"Unbounded end slice: {unboundedEnd}"
Slicing arrays is just like slicing lists:
// Generate an array of 100 integers
let fullArray = [| 1 .. 100 |]
// Create a slice from indices 1-5 (inclusive)
let smallSlice = fullArray[1..5]
printfn $"Small slice: {smallSlice}"
// Create a slice from the beginning to index 5 (inclusive)
let unboundedBeginning = fullArray[..5]
printfn $"Unbounded beginning slice: {unboundedBeginning}"
// Create a slice from an index to the end of the list
let unboundedEnd = fullArray[94..]
printfn $"Unbounded end slice: {unboundedEnd}"
Prior to F# 6, slicing used the syntax expr.[start..finish] with the extra .. If you choose, you can still use this syntax. For more information, see RFC FS-1110.
Slicing multidimensional arrays
F# supports multidimensional arrays in the F# core library. As with one-dimensional arrays, slices of multidimensional arrays can also be useful. However, the introduction of additional dimensions mandates a slightly different syntax so that you can take slices of specific rows and columns.
The following examples demonstrate how to slice a 2D array:
// Generate a 3x3 2D matrix
let A = array2D [[1;2;3];[4;5;6];[7;8;9]]
printfn $"Full matrix:\n {A}"
// Take the first row
let row0 = A[0,*]
printfn $"{row0}"
// Take the first column
let col0 = A[*,0]
printfn $"{col0}"
// Take all rows but only two columns
let subA = A[*,0..1]
printfn $"{subA}"
// Take two rows and all columns
let subA' = A[0..1,*]
printfn $"{subA}"
// Slice a 2x2 matrix out of the full 3x3 matrix
let twoByTwo = A[0..1,0..1]
printfn $"{twoByTwo}"
Defining slices for other data structures
The F# core library defines slices for a limited set of types. If you wish to define slices for more data types, you can do so either in the type definition itself or in a type extension.
For example, here's how you might define slices for the ArraySegment<T> class to allow for convenient data manipulation:
open System
type ArraySegment<'TItem> with
member segment.GetSlice(start, finish) =
let start = defaultArg start 0
let finish = defaultArg finish segment.Count
ArraySegment(segment.Array, segment.Offset + start, finish - start)
let arr = ArraySegment [| 1 .. 10 |]
let slice = arr[2..5] //[ 3; 4; 5]
Another example using the Span<T> and ReadOnlySpan<T> types:
open System
type ReadOnlySpan<'T> with
member sp.GetSlice(startIdx, endIdx) =
let s = defaultArg startIdx 0
let e = defaultArg endIdx sp.Length
sp.Slice(s, e - s)
type Span<'T> with
member sp.GetSlice(startIdx, endIdx) =
let s = defaultArg startIdx 0
let e = defaultArg endIdx sp.Length
sp.Slice(s, e - s)
let printSpan (sp: Span<int>) =
let arr = sp.ToArray()
printfn $"{arr}"
let sp = [| 1; 2; 3; 4; 5 |].AsSpan()
printSpan sp[0..] // [|1; 2; 3; 4; 5|]
printSpan sp[..5] // [|1; 2; 3; 4; 5|]
printSpan sp[0..3] // [|1; 2; 3|]
printSpan sp[1..3] // |2; 3|]
Built-in F# slices are end-inclusive
All intrinsic slices in F# are end-inclusive; that is, the upper bound is included in the slice. For a given slice with starting index x and ending index y, the resulting slice will include the yth value.
// Define a new list
let xs = [1 .. 10]
printfn $"{xs[2..5]}" // Includes the 5th index
Built-in F# empty slices
F# lists, arrays, sequences, strings, multidimensional (2D, 3D, 4D) arrays will all produce an empty slice if the syntax could produce a slice that doesn't exist.
Consider the following example:
let l = [ 1..10 ]
let a = [| 1..10 |]
let s = "hello!"
let emptyList = l[-2..(-1)]
let emptyArray = a[-2..(-1)]
let emptyString = s[-2..(-1)]
Important
C# developers may expect these to throw an exception rather than produce an empty slice. This is a design decision rooted in the fact that empty collections compose in F#. An empty F# list can be composed with another F# list, an empty string can be added to an existing string, and so on. It can be common to take slices based on values passed in as parameters, and being tolerant of out-of-bounds > by producing an empty collection fits with the compositional nature of F# code.
Fixed-index slices for 3D and 4D arrays
For F# 3D and 4D arrays, you can "fix" a particular index and slice other dimensions with that index fixed.
To illustrate this, consider the following 3D array:
z = 0
| x\y | 0 | 1 |
|---|---|---|
| 0 | 0 | 1 |
| 1 | 2 | 3 |
z = 1
| x\y | 0 | 1 |
|---|---|---|
| 0 | 4 | 5 |
| 1 | 6 | 7 |
If you want to extract the slice [| 4; 5 |] from the array, use a fixed-index slice.
let dim = 2
let m = Array3D.zeroCreate<int> dim dim dim
let mutable count = 0
for z in 0..dim-1 do
for y in 0..dim-1 do
for x in 0..dim-1 do
m[x,y,z] <- count
count <- count + 1
// Now let's get the [4;5] slice!
m[*, 0, 1]
The last line fixes the y and z indices of the 3D array and takes the rest of the x values that correspond to the matrix.
