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matchable

This extension implements Andrew Wright's pattern matching macros.

Overview

Pattern matching allows complicated control decisions based on data structure to be expressed in a concise manner. Pattern matching is found in several modern languages, notably Standard ML, Haskell and Miranda.

This wiki page is based on Andrew Wright's paper Pattern Matching for Scheme.

Interface

[syntax] (match exp (pat body …) …)

The basic form of pattern matching expression, where exp is an expression, pat is a pattern, and body is one or more expressions (like the body of a lambda-expression). The match form matches its first subexpression against a sequence of patterns, and branches to the body corresponding to the first pattern successfully matched.

For example, the following code defines the usual map function:

(define map
  (lambda (f l)
    (match l
      [() '()]
      [(x . y) (cons (f x) (map f y))] )))

The first pattern () matches the empty list. The second pattern (x . y) matches a pair, binding x to the first component of the pair and y to the second component of the pair.

[syntax] (match-lambda (pat body …) …)
[syntax] (match-lambda* (pat body …) …)

The match-lambda and match-lambda* forms are convenient combinations of match and lambda, and can be explained as follows:

(match-lambda  (pat body …) …)
  --> (lambda (x) (match x (pat body …) …))

(match-lambda* (pat body …) …)
  --> (lambda x   (match x (pat body) …))

where x is a unique variable.

The match-lambda form is convenient when defining a single argument function that immediately destructures its argument. The match-lambda* form constructs a function that accepts any number of arguments; the patterns of match-lambda* should be lists.

For example, the map procedure can be written as:

(define map
  (match-lambda*
    [(_ ()) '()]
    [(f (x . y)) (cons (f x) (map f y))] ))
[syntax] (match-let [var] ((pat exp) …) body …)
[syntax] (match-let* ((pat exp) …) body …)
[syntax] (match-letrec ((pat exp) …) body …)

The match-let, match-let* and match-letrec forms generalize Scheme's let, let*, letrec, and define expressions to allow patterns in the binding position rather than just variables. For example, the following expression:

(match-let (((x y z) (list 1 2 3)))
            ((a b c) (list 4 5 6)))
  body …)

binds x to 1, y to 2, z to 3, a to 4, b to 5, and c to 6 in body …. These forms are convenient for destructuring the result of a function that returns multiple values as a list or vector. As usual for letrec, pattern variables bound by match-letrec should not be used in computing the bound value.

Analogously to named let, match-let accepts an optional loop variable var before the binding list, turning match-let into a general looping construct.

Pattern Matching Expressions

The complete syntax of the pattern matching expressions follows:

exp ::= (match exp clause …)
     |  (match-lambda clause …)
     |  (match-lambda* clause …)
     |  (match-let ([pat exp] …) body)
     |  (match-let* ([pat exp] …) body)
     |  (match-letrec ([pat exp] …) body)
     |  (match-let var ([pat exp] …) body)

clause ::= [pat body]
     |  [pat (=> identifier) body]

pat ::= identifier           matches anything, and binds identifier as a variable
     |  _                    anything
     |  ()                   itself (the empty list)
     |  #t                   itself
     |  #f                   itself
     |  string               an `equal?' string
     |  number               an `equal?' number
     |  character            an `equal?' character
     |  's-expression        an `equal?' s-expression
     |  (pat-1 … pat-n)    a proper list of n elements
     |  (pat-1 … pat-n . pat-n+1)  
                             a list of n or more elements
     |  (pat-1 … pat-n pat-n+1 ...)  
                             a proper list of n+k or more elements [1]
     |  #(pat-1 … pat-n)   a vector of n elements
     |  #(pat-1 … pat-n pat-n+1 ...)  
                             a vector of n+k or more elements
     |  ($ struct pat-1 … pat-n)  
                             a structure
     |  (= field pat)        a field of a structure
     |  (and pat-1 … pat-n)  
                             if all of pat-1 through pat-n match
     |  (or pat-1 … pat-n) 
                             if any of pat-1 through pat-n match
     |  (not pat-1 … pat-n)
                             if none of pat-1 through pat-n match
     |  (? predicate pat-1 … pat-n)  
                             if predicate true and pat-1 through pat-n all match
     |  (set! identifier)    anything, and binds identifier as a setter
     |  (get! identifier)    anything, and binds identifier as a getter
     |  (pat-1 *** pat-2)    a tree pattern
     |  `qp                  a quasipattern

qp ::= ()                    itself (the empty list)
    |  #t                    itself
    |  #f                    itself
    |  string                an `equal?' string
    |  number                an `equal?' number
    |  character             an `equal?' character
    |  symbol                an `equal?' symbol
    |  (qp-1 … qp-n)       a proper list of n elements
    |  (qp-1 … qp-n . qp-n+1)  
                             a list of n or more elements
    |  (qp-1 … qp-n qp-n+1 ...)  
                             a proper list of n+k or more elements
    |  #(qp-1 … qp-n)      a vector of n elements
    |  #(qp-1 … qp-n qp-n+1 ...)  
                             a vector of n+k or more elements
    |  ,pat                  a pattern
    |  ,@pat                 a pattern, spliced

Optional "=>" failure procedure syntax

The match, match-lambda, and match-lambda* forms allow the optional syntax (=> identifier) between the pattern and the body of a clause. When the pattern match for such a clause succeeds, the identifier is bound to a failure procedure of zero arguments within the body. If this procedure is invoked, it jumps back to the pattern matching expression, and resumes the matching process as if the pattern had failed to match. The body must not mutate the object being matched, otherwise unpredictable behavior may result.

Patterns
identifier
matches anything, and binds a variable of this name to the matching value in the body. Excludes the reserved names ? , = _ ... and or not set! get!.
_
matches anything, without binding any variables.
(), #t, #f, string, number, character, 's-expression
These constant patterns match themselves, i.e., the corresponding value must be equal? to the pattern.
(pat-1 … pat-n)
matches a proper list of n elements that match pat-1 through pat-n.
(pat-1 … pat-n . pat-n+1)
matches a (possibly improper) list of at least n elements that ends in something matching pat-n+1.
(pat-1 … pat-n pat-n+1 ...)
matches a proper list of n or more elements, where each element of the tail matches pat-n+1. Each pattern variable in pat-n+1 is bound to a list of the matching values. For example, the expression:
(match '(let ([x 1][y 2]) z)
  [('let ((binding values) ...) exp)  body ...])

binds binding to the list '(x y), values to the list '(1 2), and exp to 'z in the body of the match-expression. For the special case where pat-n+1 is a pattern variable, the list bound to that variable may share with the matched value.

(pat-1 … pat-n pat-n+1 ___)
This pattern means the same thing as the previous pattern.
#(pat-1 … pat-n)
matches a vector of length n, whose elements match pat-1 through pat-n.
#(pat-1 … pat-n pat-n+1 ...)
matches a vector of length n or more, where each element beyond n matches pat-n+1.
($ struct pat-1 … pat-n)
matches a structure declared with define-record or define-record-type.
(= field pat)
is intended for selecting a field from a structure. field may be any expression; it is applied to the value being matched, and the result of this application is matched against pat.
(and pat-1 … pat-n)
matches if all of the subpatterns match. At least one subpattern must be present. This pattern is often used as (and x pat) to bind x to to the entire value that matches pat (cf. as-patterns in ML or Haskell).
(or pat-1 … pat-n)
matches if any of the subpatterns match. At least one subpattern must be present. All subpatterns must bind the same set of pattern variables.
(not pat-1 … pat-n)
matches if none of the subpatterns match. At least one subpattern must be present. The subpatterns may not bind any pattern variables.
(? predicate pat-1 … pat-n)
In this pattern, predicate must be an expression evaluating to a single argument function. This pattern matches if predicate applied to the corresponding value is true, and the subpatterns pat-1 ... pat-n all match. The predicate should not have side effects, as the code generated by the pattern matcher may invoke predicates repeatedly in any order. The predicate expression is bound in the same scope as the match expression, i.e., free variables in predicate are not bound by pattern variables.
(set! identifier)
matches anything, and binds identifier to a procedure of one argument that mutates the corresponding field of the matching value. This pattern must be nested within a pair, vector, box, or structure pattern. For example, the expression:
(define x (list 1 (list 2 3)))
(match x [(_ (_ (set! setit)))  (setit 4)])

mutates the cadadr of x to 4, so that x is '(1 (2 4)).

(get! identifier)
matches anything, and binds identifier to a procedure of zero arguments that accesses the corresponding field of the matching value. This pattern is the complement to set!. As with set!, this pattern must be nested within a pair, vector, box, or structure pattern.
`qp
Quasiquote introduces a quasipattern, in which identifiers are considered to be symbolic constants. Like Scheme's quasiquote for data, unquote (,) and unquote-splicing (,@) escape back to normal patterns.

Record Structures Pattern

The $ pattern handles native record structures and SRFI-9 records transparently.

Tree Pattern

Here we allow patterns of the form

 (x *** y)

to represent the pattern y located somewhere in a tree where the path from the current object to y can be seen as a list of the form (X …). Y can immediately match the current object in which case the path is the empty list. In a sense it's a 2-dimensional version of the ... pattern.

As a common case the pattern (_ *** y) can be used to search for Y anywhere in a tree, regardless of the path used.

Examples

You can find examples in:

About this extension

Author

Alex Shinn

License

Public domain

History
1.0
initial release for CHICKEN 5, based on version 2.7 from CHICKEN 4