9 Pattern Matching (original) (raw)

9 Pattern Matching🔗ℹ

Pattern Matching in The Racket Guide introduces pattern matching.

The match form and related forms support general pattern matching on Racket values. See also Regular Expressions for information on regular-expression matching on strings, bytes, and streams.

(match val-expr clause ...)
clause = [pat option=> option ... body ...+] option=> = | (=> id) option = #:when cond-expr	#:do [do-body ...]

Finds the first pat that matches the result ofval-expr, and evaluates the corresponding bodys with bindings introduced by pat (if any). Bindings introduced bypat are not available in other parts of pat. The last bodyin the matching clause is evaluated in tail position with respect to the match expression.

To find a match, the clauses are tried in order. If noclause matches, then the exn:misc:match? exception is raised.

An optional #:when cond-expr specifies that the pattern should only match if cond-expr produces a true value.cond-expr is in the scope of all of the variables bound inpat. cond-expr must not mutate the object being matched before calling the failure procedure, otherwise the behavior of matching is unpredictable. See also failure-cont, which is a lower-level mechanism achieving the same ends.

Examples:

> (define (m x) (match x [(list a b c) #:when (= 6 (+ a b c)) 'sum-is-six] [(list a b c) 'sum-is-not-six]))
> (m '(1 2 3))
'sum-is-six
> (m '(2 3 4))
'sum-is-not-six

An optional #:do [do-body ...] executes do-body forms. In particular, the forms may introduce definitions that are visible in the remaining options and the main clause body. Both #:when and #:do options may appear multiple times

Examples:

> (define (m x) (match x [(list a b c) #:do [(define sum (+ a b c))] #:when (> sum 6) (format "the sum, which is ~a, is greater than 6" sum)] [(list a b c) 'sum-is-not-greater-than-six]))
> (m '(1 2 3))
'sum-is-not-greater-than-six
> (m '(2 3 4))
"the sum, which is 9, is greater than 6"

An optional (=> id), which must appear immediately after pat, is bound to a failure procedure of zero arguments.id is visible in all clause options and the clause body. If this procedure is invoked, it escapes back to the pattern matching expression, and resumes the matching process as if the pattern had failed to match. The bodys must not mutate the object being matched before calling the failure procedure, otherwise the behavior of matching is unpredictable.

Examples:

> (m '(1 2 3))
'sum-is-six
> (m '(2 3 4))
'sum-is-not-six

The grammar of pat is as follows, where non-italicized identifiers are recognized symbolically (i.e., not by binding).

In more detail, patterns match as follows:

• id (excluding the reserved names _,..., ___,..k, and__k for non-negative integersk)

  Unlike in cond and case,else is not a keyword in match. Use the _ pattern for the “else” clause.
  or (var id)— matches anything, and binds id to the matching values. If an id is used multiple times within a pattern, the corresponding matches must be the same according to (match-equality-test), except that instances of an id in different or andnot sub-patterns are independent. The binding for id is not available in other parts of the same pattern.
  Examples:

  '(3 2 1)
  '(1 (x y z))
  > (match #f [else (cond [#f 'not-evaluated] [else 'also-not-evaluated])])

• _ — matches anything, without binding any identifiers.
  Example:
• #t, #f, string, bytes,number, char, or (quote datum) — matches an equal? constant.

Example:

> (match "yes" ["no" #f] ["yes" #t])
#t

• (list lvp ...) — matches a list of elements. In the case of (list pat ...), the pattern matches a list with as many elements aspats, and each element must match the correspondingpat. In the more general case, each lvpcorresponds to a “spliced” list of greedy matches.
  For spliced lists, ... and ___are aliases for zero or more matches. The..k and __kforms are also aliases, specifying k or more matches. Pattern variables that precede these splicing operators are bound to lists of matching forms.
  Examples:

  '(3 2 1)
  '(2 3)
  > (match '(1 2 3) [(list 1 a ..3) a] [_ 'else])
  'else
  > (match '(1 2 3 4) [(list 1 a ..3) a] [_ 'else])
  '(2 3 4)
  > (match '(1 2 3 4 5) [(list 1 a ..3 5) a] [_ 'else])
  '(2 3 4)
  > (match '(1 (2) (2) (2) 5) [(list 1 (list a) ..3 5) a] [_ 'else])
  '(2 2 2)

• (list-rest lvp ... pat) or (list* lvp ... pat) — similar to a list pattern, but the finalpat matches the “rest” of the list after the lastlvp. In fact, the matched value can be a non-list chain of pairs (i.e., an “improper list”) if pat matches non-list values.
  Examples:

  > (match '(1 2 3 . 4) [(list-rest a b c d) d])
  4
  > (match '(1 2 3 . 4) [(list-rest a ... d) (list a d)])
  '((1 2 3) 4)

• (list-no-order pat ...) —similar to a list pattern, but the elements to match each pat can appear in the list in any order.
  Example:

  > (match '(1 2 3) [(list-no-order 3 2 x) x])
  1

  Unlike other patterns, list-no-order doesn’t allow duplicate identifiers between subpatterns. For example the patterns (list-no-order x 1 x) and(list-no-order x 1 x ...) both produce syntax errors.

• (list-no-order pat ... lvp) —generalizes list-no-order to allow a pattern that matches multiple list elements that are interspersed in any order with matches for the other patterns.
  Example:

  > (match '(1 2 3 4 5 6) [(list-no-order 6 2 y ...) y])
  '(1 3 4 5)

• (vector lvp ...) — like alist pattern, but matching a vector.
  Example:

  > (match #(1 (2) (2) (2) 5) [(vector 1 (list a) ..3 5) a])
  '(2 2 2)

• (hash expr pat ... ... ht-opt) —matches against a hash table where expr matches a key and pat matches a corresponding value.
  Examples:

  '(2 1)
  > (match (hash "aa" 1 "b" 2) [(hash "b" _ "c" _) 'matched] [_ 'not-matched])
  'not-matched
  The key matchings use the key comparator of the matching hash table.
  Examples:
  The behavior of residue key-value entries in the hash table value depends on ht-opt.
  When ht-opt is not provided or when it is #:closed, all of the keys in the hash table value must be matched. I.e., the matching is closed to extension.
  Example:
  > (match (hash "a" 1 "b" 2) [(hash "b" _) 'matched] [_ 'not-matched])
  ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  'not-matched
  When ht-opt is #:open, there can be keys in the hash table value that are not specified in the pattern. I.e., the matching is open to extension.
  Example:
  > (match (hash "a" 1 "b" 2) [(hash "b" _ #:open) 'matched] [_ 'not-matched])
  -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  'matched
  When ht-opt is #:rest pat, pat is further matched against the residue hash table. If the matching hash table is immutable, this residue matching is efficient. Otherwise, the matching hash table will be copied, which could be expensive.
  Example:
  Many key exprs could evaluate to the same value.
  Example:
  > (match (hash "a" 1 "b" 2) [(hash "b" _ "b" 2 "a" _) 'matched] [_ 'not-matched])
  ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  'matched

• (hash* [expr pat kv-opt] ... ht-opt) —similar to hash, but with the following differences:
  • The key-value pattern must be grouped syntactically.
  • If ht-opt is not specified, it behaves like #:open(as opposed to #:closed).
  • If kv-opt is specified with #:default def-expr, and the key does not exist in the hash table value, then the default value from def-expr will be matched against the value pattern, instead of immediately failing to match.
    Examples:

    > (match (hash "a" 1 "b" 2) [(hash* ["b" b] ["a" a]) (list b a)])
    '(2 1)
    > (match (hash "a" 1 "b" 2) [(hash* ["b" b]) 'matched] [_ 'not-matched])
    'matched
    > (match (hash "a" 1 "b" 2) [(hash* ["a" a #:default 42] ["c" c #:default 100]) (list a c)] [_ #f])
    '(1 100)

• (hash-table (pat pat) ...) — This pattern is deprecated because it can be incorrect.However, many programs rely on the incorrect behavior, so we still provide this pattern for backward compatibility reasons.
  Similar to list-no-order, but matching against hash table’s key–value pairs.
  Example:

  > (match #hash(("a" . 1) ("b" . 2)) [(hash-table ("b" b) ("a" a)) (list b a)])
  '(2 1)

• (hash-table (pat pat) ...+ ooo) — This pattern is deprecated because it can be incorrect.However, many programs rely on the incorrect behavior, so we still provide this pattern for backward compatibility reasons.
  Generalizes hash-table to support a final repeating pattern.
  Example:

  > (match #hash(("a" . 1) ("b" . 2)) [(hash-table (key val) ...) key])
  '("b" "a")

• (cons pat1 pat2) — matches a pair value.
  Example:
• (mcons pat1 pat2) — matches a mutable pair value.
  Example:
• (box pat) — matches a boxed value.
  Example:

  > (match #&1 [(box a) a])
  1

• (struct-id pat ...) or(struct struct-id (pat ...)) —matches an instance of a structure type namedstruct-id, where each field in the instance matches the corresponding pat. See also struct*.
  Usually, struct-id is defined withstruct. More generally, struct-idmust be bound to expansion-time information for a structure type (see Structure Type Transformer Binding), where the information includes at least a predicate binding and field accessor bindings corresponding to the number of fieldpats. In particular, a module import or aunit import with a signature containing astruct declaration can provide the structure type information.
  Examples:

  (struct tree (val left right))
  > (match (tree 0 (tree 1 #f #f) #f) [(tree a (tree b _ _) _) (list a b)])
  '(0 1)

• (struct struct-id _) —matches any instance of struct-id, without regard to contents of the fields of the instance.
• (regexp rx-expr) — matches a string that matches the regexp pattern produced by rx-expr, where rx-expr can be either a regexp, a pregexp, a byte-regexp, a byte-pregexp, a string, or a byte string. A string and byte string value is converted to a pattern usingregexp and byte-regexp respectively. See Regular Expressions for more information about regexps.
  Examples:

  > (match "apple" [(regexp #rx"p+") 'yes] [_ 'no])
  'yes
  > (match "banana" [(regexp #px"(na){2}") 'yes] [_ 'no])
  'yes
  > (match "banana" [(regexp "(na){2}") 'yes] [_ 'no])
  'no
  > (match #"apple" [(regexp #rx#"p+") 'yes] [_ 'no])
  'yes
  > (match #"banana" [(regexp #px#"(na){2}") 'yes] [_ 'no])
  'yes
  > (match #"banana" [(regexp #"(na){2}") 'yes] [_ 'no])
  'no

• (regexp rx-expr pat) — extends the regexp form to further constrain the match where the result of regexp-match is matched againstpat.
  Examples:
• (pregexp rx-expr) or(pregexp rx-expr pat) — like theregexp patterns, but rx-expr must be either a pregexp, a byte-pregexp, a string, or a byte string. A string and byte string value is converted to a pattern usingpregexp and byte-pregexp respectively.
• (and pat ...) — matches if all of the pats match. This pattern is often used as(and id pat) to bind idto the entire value that matches pat. The pats are matched in the order that they appear.
  Example:
• (or pat ...) — matches if any of the pats match. Each pat must bind the same set of identifiers.
  Example:
• (not pat ...) — matches when none of the pats match, and binds no identifiers.
  Examples:
• (app expr pats ...) — appliesexpr to the value to be matched; each result of the application is matched against one of the pats, respectively.
  Examples:

  > (match '(1 2) [(app length 2) 'yes])
  'yes
  '(I got 3.14)
  'yes
  '(yes 1 2 3)

• (? expr pat ...) — appliesexpr to the value to be matched, and checks whether the result is a true value; the additional pats must also match; i.e., ? combines a predicate application and an and pattern. However,?, unlike and, guarantees thatexpr is matched before any of the pats.

  The expr procedure may be called more than once on identical input (although this happens only rarely), and the order in which calls to expr are made should not be relied upon.
  Example:

• (quasiquote qp) — introduces a quasipattern, in which identifiers match symbols. Like thequasiquote expression form, unquoteand unquote-splicing escape back to normal patterns.
  Example:

  > (match '(1 2 3) [`(1 ,a ,(? odd? b)) (list a b)])
  '(2 3)

• derived-pattern — matches a pattern defined by a macro extension via define-match-expander.

Note that the matching process may destructure the input multiple times, and may evaluate expressions embedded in patterns such as (app expr pat) in arbitrary order, or multiple times. Therefore, such expressions must be safe to call multiple times, or in an order other than they appear in the original program.

Changed in version 8.9.0.5 of package base: Added a support for #:do.
Changed in version 8.11.1.10: Added the hash andhash* patterns.

9.1 Additional Matching Forms🔗ℹ

(match* (val-expr ...+) clause* ...)
clause* = [(pat ...+) option=> option ... body ...+]

Matches a sequence of values against each clause in order, matching only when all patterns in a clause match. Each clause must have the same number of patterns as the number of val-exprs.

Examples:

(match/values expr clause* clause* ...)

If expr evaluates to n values, then match all nvalues against the patterns in clause* .... Each clause must contain exactly n patterns. At least one clause is required to determine how many values to expect from expr.

Example:

(define/match (head args) match*-clause ...)
head = id | (head args) args = arg ...	arg ... . rest-id arg = arg-id	[arg-id default-expr]	keyword arg-id	keyword [arg-id default-expr] match*-clause = [(pat ...+) option=> option ... body ...+]

Binds id to a procedure that is defined by pattern matching clauses using match*. Each clause takes a sequence of patterns that correspond to the arguments in the function header. The arguments are ordered as they appear in the function header for matching purposes.

Examples:

(define/match (fact n) [(0) 1] [(n) (* n (fact (sub1 n)))])
> (fact 5)
120

The function header may also contain optional or keyword arguments, may have curried arguments, and may also contain a rest argument.

Examples:

(define/match ((f x) #:y [y '(1 2 3)]) [((regexp #rx"p+") `(,a 2 3)) a] [(_ _) #f])
> ((f "ape") #:y '(5 2 3))
5
> ((f "dog"))
#f
(define/match (g x y . rst) [(0 0 '()) #t] [(5 5 '(5 5)) #t] [(_ _ _) #f])
> (g 0 0)
#t
> (g 5 5 5 5)
#t
> (g 1 2)
#f

(match-lambda clause ...)
(match-λ clause ...)

Equivalent to (lambda (id) (match id clause ...)).

Changed in version 8.13.0.5 of package base: Added match-λ.

(match-lambda* clause ...)
(match-λ* clause ...)

Equivalent to (lambda lst (match lst clause ...)).

Changed in version 8.13.0.5 of package base: Added match-λ*.

(match-lambda** clause* ...)
(match-λ** clause ...)

Equivalent to (lambda (args ...) (match* (args ...) clause* ...)), where the number of args ... is computed from the number of patterns appearing in each of the clause*.

Changed in version 8.13.0.5 of package base: Added match-λ**.

(match-let ([pat expr] ...) body ...+)

Generalizes let to support pattern bindings. Eachexpr is matched against its corresponding pat (the match must succeed), and the bindings that pat introduces are visible in the bodys.

Example:

(match-let* ([pat expr] ...) body ...+)

Like match-let, but generalizes let*, so that the bindings of each pat are available in each subsequentexpr.

Example:

(match-let-values ([(pat ...) expr] ...) body ...+)

(match-let*-values ([(pat ...) expr] ...) body ...+)

(match-letrec ([pat expr] ...) body ...+)

Like match-let, but generalizes letrec.

(match-letrec-values ([(pat ...) expr] ...) body ...+)

Added in version 6.1.1.8 of package base.

Defines the names bound by pat to the values produced by matching against the result of expr.

Examples:

> (match-define (list a b) '(1 2))
> b
2

(match-define-values (pat pats ...) expr)

Like match-define but for when expr produces multiple values. Like match/values, it requires at least one pattern to determine the number of values to expect.

Examples:

A predicate for the exception raised in the case of a match failure.

Continues matching as if the current pattern failed. Note that unlike use of the => form, this does not escape the current context, and thus should only be used in tail position with respect to the match form.

9.2 Extending match🔗ℹ

(define-match-expander id proc-expr)
(define-match-expander id proc-expr proc-expr)

Binds id to a match expander.

The first proc-expr sub-expression must evaluate to a transformer that produces a pat for match. Whenever id appears as the beginning of a pattern, this transformer is given, at expansion time, a syntax object corresponding to the entire pattern (including id). The pattern is replaced with the result of the transformer.

A transformer produced by a second proc-expr sub-expression is used when id is used in an expression context. Using the second proc-expr, id can be given meaning both inside and outside patterns.

Match expanders are not invoked unless id appears in the first position in a sequence. Instead, identifiers bound by define-match-expanderare used as binding identifiers (like any other identifier) when they appear anywhere except the first position in a sequence.

For example, to extend the pattern matcher and destructure syntax lists,

And here is an example showing howdefine-match-expander-bound identifiers arenot treated specially unless they appear in the first position of pattern sequence. Consider this (incorrect) definition of a length function:

(define-match-expander nil
(λ (stx) #''())
(λ (stx) #''()))
(define (len l)
(match l
[nil 0]
[(cons hd tl) (+ 1 (len tl))]))

Because there are no parenthesis around nil,match treats the first case as an identifier (which matches everything) instead of a use of the match expander and len always returns 0.

> (len nil)
0
> (len (cons 1 nil))
0
> (len (cons 1 (cons 2 nil)))
0

Match expanders accept any syntax pair whose first element is anidentifier? bound to the expander. The following example shows a match expander which can be called with an improper syntax list of the form (expander a b . rest).

Changed in version 7.7.0.2 of package base: Match expanders now allowed any syntax pair whose first element is anidentifier? bound to the expander. The example above did not work with previous versions.

The property value must be an exact non-negative integer or a procedure of one or two arguments. In the former case, the integer designates a field within the structure that should contain a procedure; the integer must be between 0 (inclusive) and the number of non-automatic fields in the structure type (exclusive, not counting supertype fields), and the designated field must also be specified as immutable.

If the property value is a procedure of one argument, then the procedure serves as the transformer for match expansion. If the property value is a procedure of two arguments, then the first argument is the structure whose type hasprop:match-expander property, and the second argument is a syntax object as for a match expander..

If the property value is a assignment transformer, then the wrapped procedure is extracted withset!-transformer-procedure before it is called.

This binding is provided for-syntax.

Like prop:match-expander, but for the legacy match syntax.

This binding is provided for-syntax.

Predicates for values which implement the appropriate match expander properties.

Changed in version 6.90.0.29 of package base: Made equivalent to syntax-local-introduce.

A parameter that determines the comparison procedure used to check whether multiple uses of an identifier match the “same” value. The default is equal?.

(match/derived val-expr original-datum clause ...)
(match*/derived (val-expr ...) original-datum clause* ...)

Like match and match* respectively, but includes a sub-expression to be used as the source for all syntax errors within the form. For example, match-lambda expands to match/derived so that errors in the body of the form are reported in terms of match-lambdainstead of match.

9.3 Library Extensions🔗ℹ

(== val comparator)
(== val)

A match expanderwhich checks if the matched value is the same as val when compared by comparator. If comparator is not provided, it defaults to equal?.

Examples:

(struct* struct-id ([field pat] ...))

A match pattern form that matches an instance of a structure type named struct-id, where the field field in the instance matches the corresponding pat. The fields do not include those from super types.

Any field of struct-id may be omitted, and such fields can occur in any order.

Examples:

> (match (tree 0 (tree 1 #f #f) #f) [(struct* tree ([val a] [left (struct* tree ([right #f] [val b]))])) (list a b)])
'(0 1)
> (match (tree* 0 #f #f 42) [(and (struct* tree* ([val a])) (struct* tree ([val b]))) (list a b)])
'(42 0)