This Scheme library provides users with macros for pattern matching against non-free data types. This pattern-matching facility is originally proposed in this paper and implemented in the Egison programming language.
We have tested this library on Gauche 0.9.6.
Non-free data types are data types whose data have no standard forms. For example, multisets are non-free data types because the multiset {a,b,b} has two other equivalent but literally different forms {b,a,b} and {b,b,a}. This library provides users with a pattern-matching facility for these non-free data types.
For example, the following program pattern-matches a list (1 2 3 2 1) as a multiset.
This pattern matches if the target collection contains pairs of elements in sequnece.
A non-linear pattern is effectively used for expressing the pattern.
(match-all '(1 2 5 9 4) (Multiset Integer) [`(cons x (cons (val ,(lambda (x) (+ x 1))) _)) x])
; (1 4)
For more examples, please see test.scm and the following samples for now.
We do not use the eval function in this implementation.
It enables us to apply the method developed in this implementation to implementation of Haskell and OCaml extensions.
Matchers are defined as a function that takes a pattern and target, and returns next matching atoms.
For example, Multiset is defined as follows.
(Multiset is a function that takes and returns a matcher.)
(define Multiset
(lambda (M)
(lambda (p t)
(match p
(('cons px py)
(map (lambda (xy) `((,px ,M ,(car xy)) (,py ,(Multiset M) ,(cadr xy))))
(match-all t (List M)
['(join hs (cons x ts)) `(,x ,(append hs ts))])))
(pvar
`(((,pvar Something ,t))))
))))
Something is the only built-in matcher.
processMState has a branch for Something.
(define Something 'Something)
Match-all is transformed into an application of map whose arguments uses extract-pattern-variables and pattern-match as follows.
It allows us to implement match-all without using eval.
(match-all t m [p e])
->
`(map (lambda ,(extract-pattern-variables p) ,e) ,(pattern-match p m t))
extract-pattern-variables takes a pattern and returns a list of pattern variables that appear in the pattern.
The order of the pattern variables corresponds with the order they appeared in the pattern.
pattern-match returns a list of pattern-matching results.
The pattern-matching results consist of values that are going to bound to the pattern variables returned by extract-pattern-variables.
The order of the values in the pattern-matching results must correspond with the order of pattern variables returned by extract-pattern-variables.
(match-all '(1 2 3 2 1) (List Integer)
[`(join _ (cons x (join _ (cons (val ,(lambda (x) x)) _))))
x])
; (1 2)
We would like describe non-linear patterns as follows,
(match-all '(1 2 3 2 1) (List Integer)
[`(join _ (cons x (join _ (cons ,x _))))
x])
; (1 2)
instead of as follows.
(match-all '(1 2 3 2 1) (List Integer)
[`(join _ (cons x (join _ (cons (val ,(lambda (x) x)) _))))
x])
; (1 2)
If we implement the lazy match-all, we can support pattern matching with infinitely many results.
(take (match-all primes (List Integer)
[`(join _ (cons x (join _ (cons (val ,(lambda (p) (+ p 2))) _))))
`(,p ,(+ p 2))])
5)
; ((3 5) (5 7) (11 13) (17 19) (29 31))
We can implement these patterns using the same method in the Egison interpreter.
We can apply the method for implementing this macro for the other languages. However, additional work is required for implementing this pattern-matching facility for languages with a static type system such as Haskell and OCaml. For these languages, the translated programs need to have types. The most difficult part for making being typed is a stack of matching atoms. This is because the target type of each matching atom is different, therefore we cannot type a stack of matching atoms as a list of matching atoms simply.