6. Pattern Matching
Pattern matching is a key feature of most modern functional programming languages since it allows clean and secure code to be written. Internally, "pattern-matching forms" should be translated (compiled) into cascades of "elementary tests" where code is made as efficient as possible, avoiding redundant tests; STklos "pattern matching compiler" provides this :footnote[The "pattern matching compiler" has been written by Jean-Marie Geffroy and is part of the Manuel Serrano’s Bigloo compiler since several years [Bigloo]. The code (and documentation) included in STklos has been stolen from the Bigloo package v2.4 (the only difference between both package is the pattern matching of structures which is absent in STklos.
The technique used is described in details in C. Queinnec and J-M. Geffroy paper [QuG92], and the code generated can be considered optimal
The "pattern language" allows the expression of a wide variety of patterns, including:
-
Non-linear patterns: pattern variables can appear more than once, allowing comparison of subparts of the datum (through
eq?) -
Recursive patterns on lists: for example, checking that the datum is a list of zero or more
as followed by zero or more`bs. -
Pattern matching on lists as well as on vectors.
6.1. The Pattern Language
The syntax for <pattern> is:
[:small]
| <pattern> | Matches: |
|---|---|
<atom> |
the <atom>. |
(kwote <atom>) |
any expression eq? to <atom>. |
(and <pat1> … <patn>) |
if all of <pati> match. |
(or <pat1> … …<patn>) |
if any of <pat1> through <patn> matches. |
(not <pat>) |
if <pat> doesn’t match. |
(? <predicate>) |
if <predicate> is true. |
(<pat1> … <patn>) |
a list of n elements. Here, … is a meta-character denoting a finite repetition of patterns. |
<pat> … |
a (possibly empty) repetition of <pat> in a list. |
#(<pat> … <patn>) |
a vector of n elements. |
?<id> |
anything, and binds id as a variable. |
?- |
anything. |
??- |
any (possibly empty) repetition of anything in a list. |
???- |
any end of list. |
Remark: and, or, not and kwote must be quoted in order to be treated
as literals. This is the only justification for having the kwote pattern
since, by convention, any atom which is not a keyword is quoted.
Explanations Through Examples
-
?-matches any s-expr. -
amatches the atom'a. -
?amatches any expression, and binds the variableato this expression. -
(? integer?)matches any integer. -
(a (a b))matches the only list'(a (a b)). -
???-can only appear at the end of a list, and always succeeds. For instance,(a ???-)is equivalent to(a . ?-). -
when occurring in a list,
??-matches any sequence of anything:(a ??- b)matches any list whosecarisaand lastcarisb. -
(a …)matches any list of `a’s, possibly empty. -
(?x ?x)matches any list of length 2 whosecaris eq to itscadr. -
((and (not a) ?x) ?x)matches any list of length 2 whosecaris not eq to'abut is eq to itscadr. -
#(?- ?- ???-)matches any vector whose length is at least 2.
??- and … patterns can not appear inside a vector, where you
should use ???-For example, #(a ??- b) or #(a…) are invalid
patterns, whereas #(a ???-) is valid and matches any vector whose first
element is the atom a.
|
6.2. STklos Pattern Matching Facilities
Only two special forms are provided for this in STklos: match-case and
match-lambda.
STklos syntax
The argument key may be any expression and each clause has the form
(<pattern> <expression> ...)
A match-case expression is evaluated as follows: <key> is evaluated
and the result is compared with each successive pattern. If the <pattern>
in some clause yields a match, then the <expression>s in that clause are
evaluated from left to right in an environment where the pattern variables
are bound to the corresponding subparts of <key>, and the result of the
last expression in that clause is returned as the result of the
match-case expression. If no pattern in any clause matches the <key>,
then, if there is an else clause, its expressions are evaluated and
the result of the last is the result of the whole match-case
expression; otherwise the result of the match-case expression
is unspecified.
The equality predicate used for tests is eq?.
(match-case '(a b a)
((?x ?x) 'foo)
((?x ?- ?x) 'bar)) => bar
(match-case '(a (b c) d)
((?x ?y) (list 'length=2 y x))
((?x ?y ?z) (list 'length=3 z y x)))
=> (length=3 d (b c) a)
STklos syntax
match-lambda expands into a lambda-expression expecting an argument
which, once applied to an expression, behaves exactly like a
match-case expression.
((match-lambda
((?x ?x) 'foo)
((?x ?- ?x) 'bar))
'(a b a)) => bar