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; Bigloo's ``pattern matching compiler'' provides this. The technique used is described in details in [QueinnecGeffroy92], and the code generated can be considered optimal In the cases of pattern matching in lists and vectors, not in structures for the moment. due to the way this ``pattern compiler'' was obtained.

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 and structures,
record types, and classes.

Bigloo pattern matching facilities

Only two special forms are provided for this in Bigloo: match-case and match-lambda.

match-case key clause...bigloo syntax

The argument key may be any expression and each clause has the form

(pattern s-expression...)

Semantics: 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 expressions in that clause are evaluated from left to right in an environment where the pattern variables are bound to the corresponding subparts of the datum, 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 datum, 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 is eq?.

(match-case '(a b a)
   ((?x ?x) 'foo)
   ((?x ?- ?x) 'bar))
   ⇒ bar

The following syntax is also available:

match-lambda clause...bigloo syntax

It 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

The pattern language

The syntax for <pattern> is:

<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.
| #{<struct> <pat> ... }    a structure.
| (isa <class> (<id> <pat>) ...) a class instance.
| ?<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, check 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.

• ?- matches any s-expr
• a matches the atom 'a.
• ?a matches any expression, and binds the variable a to
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 whose car is a and last car is b.
• (a ...) matches any list of a's, possibly empty.
• (?x ?x) matches any list of length 2 whose car is
eq to its cadr
• ((and (not a) ?x) ?x) matches any list of length 2 whose
car is not eq to 'a but is eq to its cadr
• #(?- ?- ???-) matches any vector whose length is at least 2.
• #{foo (?- . ?-) (? integer?)} matches any structure or
record foo whose first and second fields are respectively a pair and an integer. You can provide only the fields you want to test. The order is not relevant.

Remark: ??- 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.

Class Patterns

The isa pattern matches instances of Bigloo classes. The syntax is:

(isa <class-name> (<field-name> <pattern>) ...)

Each (<field-name> <pattern>) pair matches the named field against the given pattern. Fields not mentioned are ignored, allowing partial matching. If no fields are specified, only the type is checked.

The type check uses isa?, so a pattern (isa point ...) will match instances of point and any subclass of point.

(define-class point (x (default 0)) (y (default 0)))
(define-class point3d::point (z (default 0)))

;; Basic field binding
(match-case (instantiate::point (x 3) (y 4))
   ((isa point (x ?x) (y ?y)) (list x y)))
   ⇒ (3 4)

;; Partial matching (only check some fields)
(match-case (instantiate::point3d (x 1) (y 2) (z 3))
   ((isa point3d (z ?z)) z))
   ⇒ 3

;; Type-only check (no fields)
(match-case (instantiate::point (x 1) (y 2))
   ((isa point) 'yes)
   (else 'no))
   ⇒ yes

;; Literal values in fields
(match-case (instantiate::point (x 0) (y 5))
   ((isa point (x 0) (y ?y)) y)
   (else 'fail))
   ⇒ 5

;; Subclass matching via inheritance
(match-case (instantiate::point3d (x 1) (y 2) (z 3))
   ((isa point (x ?x) (y ?y)) (list x y)))
   ⇒ (1 2)

Class patterns compose freely with other pattern combinators:

;; or: match multiple class types
(match-case obj
   ((or (isa point3d (z ?v)) (isa point (x ?v))) v))

;; and: bind the whole object and destructure
(match-case obj
   ((and ?whole (isa point (x ?x) (y ?y)))
    (list whole x y)))

;; not: match non-instances
(match-case obj
   ((not (isa point)) 'not-a-point)
   (else 'is-a-point))

;; Predicates inside fields
(match-case obj
   ((isa point (x (and ?x (? positive?)))) x))

;; Nested class patterns
(define-class segment
   (start (default #unspecified))
   (end (default #unspecified)))

(match-case seg
   ((isa segment (start (isa point (x ?x1) (y ?y1)))
                 (end (isa point (x ?x2) (y ?y2))))
    (list x1 y1 x2 y2)))

;; Repeated variables (equality constraint across fields)
(define-class rect (width (default 0)) (height (default 0)))

(match-case (instantiate::rect (width 5) (height 5))
   ((isa rect (width ?s) (height ?s)) s)
   (else 'not-square))
   ⇒ 5