Pattern Matching (F#)

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04/28/2015

Patterns are rules for transforming input data. They are used throughout the F# language to compare data with a logical structure or structures, decompose data into constituent parts, or extract information from data in various ways.

Remarks

Patterns are used in many language constructs, such as the match expression. They are used when you are processing arguments for functions in let bindings, lambda expressions, and in the exception handlers associated with the try...with expression. For more information, see Match Expressions (F#), let Bindings (F#), Lambda Expressions: The fun Keyword (F#), and Exceptions: The try...with Expression (F#).

For example, in the match expression, the pattern is what follows the pipe symbol.

match expression with

| pattern [ when condition ] -> result-expression

...

Each pattern acts as a rule for transforming input in some way. In the match expression, each pattern is examined in turn to see if the input data is compatible with the pattern. If a match is found, the result expression is executed. If a match is not found, the next pattern rule is tested. The optional when condition part is explained in Match Expressions (F#).

Supported patterns are shown in the following table. At run time, the input is tested against each of the following patterns in the order listed in the table, and patterns are applied recursively, from first to last as they appear in your code, and from left to right for the patterns on each line.

Name	Description	Example
Constant pattern	Any numeric, character, or string literal, an enumeration constant, or a defined literal identifier	1.0, "test", 30, Color.Red
Identifier pattern	A case value of a discriminated union, an exception label, or an active pattern case	Some(x) Failure(msg)
Variable pattern	identifier	a
as pattern	pattern as identifier	(a, b) as tuple1
OR pattern	pattern1 \| pattern2	([h] \| [h; _])
AND pattern	pattern1 & pattern2	(a, b) & (_, "test")
Cons pattern	identifier :: list-identifier	h :: t
List pattern	[ pattern_1; ... ; pattern_n ]	[ a; b; c ]
Array pattern	[\| pattern_1; ..; pattern_n ]	[\| a; b; c \|]
Parenthesized pattern	( pattern )	( a )
Tuple pattern	( pattern_1, ... , pattern_n )	( a, b )
Record pattern	{ identifier1 = pattern_1; ... ; identifier_n = pattern_n }	{ Name = name; }
Wildcard pattern	_	_
Pattern together with type annotation	pattern : type	a : int
Type test pattern	:? type [ as identifier ]	:? System.DateTime as dt
Null pattern	null	null

Constant Patterns

Constant patterns are numeric, character, and string literals, enumeration constants (with the enumeration type name included). A match expression that has only constant patterns can be compared to a case statement in other languages. The input is compared with the literal value and the pattern matches if the values are equal. The type of the literal must be compatible with the type of the input.

The following example demonstrates the use of literal patterns, and also uses a variable pattern and an OR pattern.

[<Literal>]
let Three = 3

let filter123 x =
    match x with 
    // The following line contains literal patterns combined with an OR pattern.
    | 1 | 2 | Three -> printfn "Found 1, 2, or 3!" 
    // The following line contains a variable pattern.
    | var1 -> printfn "%d" var1

for x in 1..10 do filter123 x

Another example of a literal pattern is a pattern based on enumeration constants. You must specify the enumeration type name when you use enumeration constants.

type Color =
    | Red = 0
    | Green = 1
    | Blue = 2

let printColorName (color:Color) =
    match color with
    | Color.Red -> printfn "Red"
    | Color.Green -> printfn "Green"
    | Color.Blue -> printfn "Blue"
    | _ -> ()

printColorName Color.Red
printColorName Color.Green
printColorName Color.Blue

Identifier Patterns

If the pattern is a string of characters that forms a valid identifier, the form of the identifier determines how the pattern is matched. If the identifier is longer than a single character and starts with an uppercase character, the compiler tries to make a match to the identifier pattern. The identifier for this pattern could be a value marked with the Literal attribute, a discriminated union case, an exception identifier, or an active pattern case. If no matching identifier is found, the match fails and the next pattern rule, the variable pattern, is compared to the input.

Discriminated union patterns can be simple named cases or they can have a value, or a tuple containing multiple values. If there is a value, you must specify an identifier for the value. In the case of a tuple, you must supply a tuple pattern with an identifier for each element of the tuple or an identifier with a field name for one or more named union fields. See the code examples in this section for examples.

The option type is a discriminated union that has two cases, Some and None. One case (Some) has a value, but the other (None) is just a named case. Therefore, Some needs to have a variable for the value associated with the Some case, but None must appear by itself. In the following code, the variable var1 is given the value that is obtained by matching to the Some case.

let printOption (data : int option) =
    match data with
    | Some var1  -> printfn "%d" var1
    | None -> ()

In the following example, the PersonName discriminated union contains a mixture of strings and characters that represent possible forms of names. The cases of the discriminated union are FirstOnly, LastOnly, and FirstLast.

type PersonName =
    | FirstOnly of string
    | LastOnly of string
    | FirstLast of string * string

let constructQuery personName = 
    match personName with
    | FirstOnly(firstName) -> printf "May I call you %s?" firstName
    | LastOnly(lastName) -> printf "Are you Mr. or Ms. %s?" lastName
    | FirstLast(firstName, lastName) -> printf "Are you %s %s?" firstName lastName

For discriminated unions that have named fields, you use the equals sign (=) to extract the value of a named field. For example, consider a discriminated union with a declaration like the following.

type Shape =
| Rectangle of height : float * width : float
| Circle of radius : float

You can use the named fields in a pattern matching expression as follows.

let matchShape shape =
    match shape with
    | Rectangle(height = h) -> printfn "Rectangle with length %f" h
    | Circle(r) -> printfn "Circle with radius %f" r

The use of the named field is optional, so in the previous example, both Circle(r) and Circle(radius = r) have the same effect.

When you specify multiple fields, use the semicolon (;) as a separator.

match shape with
| Rectangle(height = h; width = w) -> printfn "Rectangle with height %f and width %f" h w
| _ -> ()

Active patterns enable you to define more complex custom pattern matching. For more information about active patterns, see Active Patterns (F#).

The case in which the identifier is an exception is used in pattern matching in the context of exception handlers. For information about pattern matching in exception handling, see Exceptions: The try...with Expression (F#).

Variable Patterns

The variable pattern assigns the value being matched to a variable name, which is then available for use in the execution expression to the right of the -> symbol. A variable pattern alone matches any input, but variable patterns often appear within other patterns, therefore enabling more complex structures such as tuples and arrays to be decomposed into variables.

The following example demonstrates a variable pattern within a tuple pattern.

let function1 x =
    match x with
    | (var1, var2) when var1 > var2 -> printfn "%d is greater than %d" var1 var2 
    | (var1, var2) when var1 < var2 -> printfn "%d is less than %d" var1 var2
    | (var1, var2) -> printfn "%d equals %d" var1 var2

function1 (1,2)
function1 (2, 1)
function1 (0, 0)

as Pattern

The as pattern is a pattern that has an as clause appended to it. The as clause binds the matched value to a name that can be used in the execution expression of a match expression, or, in the case where this pattern is used in a let binding, the name is added as a binding to the local scope.

The following example uses an as pattern.

let (var1, var2) as tuple1 = (1, 2)
printfn "%d %d %A" var1 var2 tuple1

OR Pattern

The OR pattern is used when input data can match multiple patterns, and you want to execute the same code as a result. The types of both sides of the OR pattern must be compatible.

The following example demonstrates the OR pattern.

let detectZeroOR point =
    match point with
    | (0, 0) | (0, _) | (_, 0) -> printfn "Zero found."
    | _ -> printfn "Both nonzero."
detectZeroOR (0, 0)
detectZeroOR (1, 0)
detectZeroOR (0, 10)
detectZeroOR (10, 15)

AND Pattern

The AND pattern requires that the input match two patterns. The types of both sides of the AND pattern must be compatible.

The following example is like detectZeroTuple shown in the Tuple Pattern section later in this topic, but here both var1 and var2 are obtained as values by using the AND pattern.

let detectZeroAND point =
    match point with
    | (0, 0) -> printfn "Both values zero."
    | (var1, var2) & (0, _) -> printfn "First value is 0 in (%d, %d)" var1 var2
    | (var1, var2)  & (_, 0) -> printfn "Second value is 0 in (%d, %d)" var1 var2
    | _ -> printfn "Both nonzero."
detectZeroAND (0, 0)
detectZeroAND (1, 0)
detectZeroAND (0, 10)
detectZeroAND (10, 15)

Cons Pattern

The cons pattern is used to decompose a list into the first element, the head, and a list that contains the remaining elements, the tail.

let list1 = [ 1; 2; 3; 4 ]

// This example uses a cons pattern and a list pattern. 
let rec printList l =
    match l with
    | head :: tail -> printf "%d " head; printList tail
    | [] -> printfn ""

printList list1

List Pattern

The list pattern enables lists to be decomposed into a number of elements. The list pattern itself can match only lists of a specific number of elements.

// This example uses a list pattern. 
let listLength list =
    match list with
    | [] -> 0
    | [ _ ] -> 1
    | [ _; _ ] -> 2
    | [ _; _; _ ] -> 3
    | _ -> List.length list

printfn "%d" (listLength [ 1 ])
printfn "%d" (listLength [ 1; 1 ])
printfn "%d" (listLength [ 1; 1; 1; ])
printfn "%d" (listLength [ ] )

Array Pattern

The array pattern resembles the list pattern and can be used to decompose arrays of a specific length.

// This example uses array patterns. 
let vectorLength vec =
    match vec with
    | [| var1 |] -> var1
    | [| var1; var2 |] -> sqrt (var1*var1 + var2*var2)
    | [| var1; var2; var3 |] -> sqrt (var1*var1 + var2*var2 + var3*var3)
    | _ -> failwith "vectorLength called with an unsupported array size of %d." (vec.Length)

printfn "%f" (vectorLength [| 1. |])
printfn "%f" (vectorLength [| 1.; 1. |])
printfn "%f" (vectorLength [| 1.; 1.; 1.; |])
printfn "%f" (vectorLength [| |] )

Parenthesized Pattern

Parentheses can be grouped around patterns to achieve the desired associativity. In the following example, parentheses are used to control associativity between an AND pattern and a cons pattern.

let countValues list value =
    let rec checkList list acc =
       match list with
       | (elem1 & head) :: tail when elem1 = value -> checkList tail (acc + 1)
       | head :: tail -> checkList tail acc
       | [] -> acc
    checkList list 0

let result = countValues [ for x in -10..10 -> x*x - 4 ] 0
printfn "%d" result

Tuple Pattern

The tuple pattern matches input in tuple form and enables the tuple to be decomposed into its constituent elements by using pattern matching variables for each position in the tuple.

The following example demonstrates the tuple pattern and also uses literal patterns, variable patterns, and the wildcard pattern.

let detectZeroTuple point =
    match point with
    | (0, 0) -> printfn "Both values zero."
    | (0, var2) -> printfn "First value is 0 in (0, %d)" var2
    | (var1, 0) -> printfn "Second value is 0 in (%d, 0)" var1
    | _ -> printfn "Both nonzero."
detectZeroTuple (0, 0)
detectZeroTuple (1, 0)
detectZeroTuple (0, 10)
detectZeroTuple (10, 15)

Record Pattern

The record pattern is used to decompose records to extract the values of fields. The pattern does not have to reference all fields of the record; any omitted fields just do not participate in matching and are not extracted.

// This example uses a record pattern. 

type MyRecord = { Name: string; ID: int }

let IsMatchByName record1 (name: string) =
    match record1 with
    | { MyRecord.Name = nameFound; MyRecord.ID = _; } when nameFound = name -> true
    | _ -> false 

let recordX = { Name = "Parker"; ID = 10 }
let isMatched1 = IsMatchByName recordX "Parker" 
let isMatched2 = IsMatchByName recordX "Hartono"

Wildcard Pattern

The wildcard pattern is represented by the underscore (_) character and matches any input, just like the variable pattern, except that the input is discarded instead of assigned to a variable. The wildcard pattern is often used within other patterns as a placeholder for values that are not needed in the expression to the right of the -> symbol. The wildcard pattern is also frequently used at the end of a list of patterns to match any unmatched input. The wildcard pattern is demonstrated in many code examples in this topic. See the preceding code for one example.

Patterns That Have Type Annotations

Patterns can have type annotations. These behave like other type annotations and guide inference like other type annotations. Parentheses are required around type annotations in patterns. The following code shows a pattern that has a type annotation.

let detect1 x =
    match x with
    | 1 -> printfn "Found a 1!"
    | (var1 : int) -> printfn "%d" var1
detect1 0
detect1 1

Type Test Pattern

The type test pattern is used to match the input against a type. If the input type is a match to (or a derived type of) the type specified in the pattern, the match succeeds.

The following example demonstrates the type test pattern.

open System.Windows.Forms

let RegisterControl(control:Control) =
    match control with
    | :? Button as button -> button.Text <- "Registered."
    | :? CheckBox as checkbox -> checkbox.Text <- "Registered."
    | _ -> ()

Null Pattern

The null pattern matches the null value that can appear when you are working with types that allow a null value. Null patterns are frequently used when interoperating with .NET Framework code. For example, the return value of a .NET API might be the input to a match expression. You can control program flow based on whether the return value is null, and also on other characteristics of the returned value. You can use the null pattern to prevent null values from propagating to the rest of your program.

The following example uses the null pattern and the variable pattern.

let ReadFromFile (reader : System.IO.StreamReader) =
    match reader.ReadLine() with
    | null -> printfn "\n"; false
    | line -> printfn "%s" line; true 

let fs = System.IO.File.Open("..\..\Program.fs", System.IO.FileMode.Open)
let sr = new System.IO.StreamReader(fs)
while ReadFromFile(sr) = true do ()
sr.Close()

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