ref: 2b105a52129a3124f1d75273f7b4e01b25ab25df
dir: /tests/ast/match.lsp/
; -*- scheme -*-
; tree regular expression pattern matching
; by Jeff Bezanson
(define (unique lst)
(if (null? lst)
()
(cons (car lst)
(filter (lambda (x) (not (eq x (car lst))))
(unique (cdr lst))))))
; list of special pattern symbols that cannot be variable names
(define metasymbols '(_ ...))
; expression tree pattern matching
; matches expr against pattern p and returns an assoc list ((var . expr) (var . expr) ...)
; mapping variables to captured subexpressions, or #f if no match.
; when a match succeeds, __ is always bound to the whole matched expression.
;
; p is an expression in the following pattern language:
;
; _ match anything, not captured
; <func> any scheme function; matches if (func expr) returns #t
; <var> match anything and capture as <var>. future occurrences of <var> in the pattern
; must match the same thing.
; (head <p1> <p2> etc) match an s-expr with 'head' matched literally, and the rest of the
; subpatterns matched recursively.
; (-/ <ex>) match <ex> literally
; (-^ <p>) complement of pattern <p>
; (-- <var> <p>) match <p> and capture as <var> if match succeeds
;
; regular match constructs:
; ... match any number of anything
; (-$ <p1> <p2> etc) match any of subpatterns <p1>, <p2>, etc
; (-* <p>) match any number of <p>
; (-? <p>) match 0 or 1 of <p>
; (-+ <p>) match at least 1 of <p>
; all of these can be wrapped in (-- var ) for capturing purposes
; This is NP-complete. Be careful.
;
(define (match- p expr state)
(cond ((symbol? p)
(cond ((eq p '_) state)
(#t
(let ((capt (assq p state)))
(if capt
(and (equal? expr (cdr capt)) state)
(cons (cons p expr) state))))))
((procedure? p)
(and (p expr) state))
((pair? p)
(cond ((eq (car p) '-/) (and (equal? (cadr p) expr) state))
((eq (car p) '-^) (and (not (match- (cadr p) expr state)) state))
((eq (car p) '--)
(and (match- (caddr p) expr state)
(cons (cons (cadr p) expr) state)))
((eq (car p) '-$) ; greedy alternation for toplevel pattern
(match-alt (cdr p) () (list expr) state #f 1))
(#t
(and (pair? expr)
(equal? (car p) (car expr))
(match-seq (cdr p) (cdr expr) state (length (cdr expr)))))))
(#t
(and (equal? p expr) state))))
; match an alternation
(define (match-alt alt prest expr state var L)
(if (null? alt) #f ; no alternatives left
(let ((subma (match- (car alt) (car expr) state)))
(or (and subma
(match-seq prest (cdr expr)
(if var
(cons (cons var (car expr))
subma)
subma)
(- L 1)))
(match-alt (cdr alt) prest expr state var L)))))
; match generalized kleene star (try consuming min to max)
(define (match-star- p prest expr state var min max L sofar)
(cond ; case 0: impossible to match
((> min max) #f)
; case 1: only allowed to match 0 subexpressions
((= max 0) (match-seq prest expr
(if var (cons (cons var (reverse sofar)) state)
state)
L))
; case 2: must match at least 1
((> min 0)
(and (match- p (car expr) state)
(match-star- p prest (cdr expr) state var (- min 1) (- max 1) (- L 1)
(cons (car expr) sofar))))
; otherwise, must match either 0 or between 1 and max subexpressions
(#t
(or (match-star- p prest expr state var 0 0 L sofar)
(match-star- p prest expr state var 1 max L sofar)))))
(define (match-star p prest expr state var min max L)
(match-star- p prest expr state var min max L ()))
; match sequences of expressions
(define (match-seq p expr state L)
(cond ((not state) #f)
((null? p) (if (null? expr) state #f))
(#t
(let ((subp (car p))
(var #f))
(if (and (pair? subp)
(eq (car subp) '--))
(begin (set! var (cadr subp))
(set! subp (caddr subp)))
#f)
(let ((head (if (pair? subp) (car subp) ())))
(cond ((eq subp '...)
(match-star '_ (cdr p) expr state var 0 L L))
((eq head '-*)
(match-star (cadr subp) (cdr p) expr state var 0 L L))
((eq head '-+)
(match-star (cadr subp) (cdr p) expr state var 1 L L))
((eq head '-?)
(match-star (cadr subp) (cdr p) expr state var 0 1 L))
((eq head '-$)
(match-alt (cdr subp) (cdr p) expr state var L))
(#t
(and (pair? expr)
(match-seq (cdr p) (cdr expr)
(match- (car p) (car expr) state)
(- L 1))))))))))
(define (match p expr) (match- p expr (list (cons '__ expr))))
; given a pattern p, return the list of capturing variables it uses
(define (patargs- p)
(cond ((and (symbol? p)
(not (member p metasymbols)))
(list p))
((pair? p)
(if (eq (car p) '-/)
()
(unique (apply append (map patargs- (cdr p))))))
(#t ())))
(define (patargs p)
(cons '__ (patargs- p)))
; try to transform expr using a pattern-lambda from plist
; returns the new expression, or expr if no matches
(define (apply-patterns plist expr)
(if (null? plist) expr
(if (procedure? plist)
(let ((enew (plist expr)))
(if (not enew)
expr
enew))
(let ((enew ((car plist) expr)))
(if (not enew)
(apply-patterns (cdr plist) expr)
enew)))))
; top-down fixed-point macroexpansion. this is a typical algorithm,
; but it may leave some structure that matches a pattern unexpanded.
; the advantage is that non-terminating cases cannot arise as a result
; of expression composition. in other words, if the outer loop terminates
; on all inputs for a given set of patterns, then the whole algorithm
; terminates. pattern sets that violate this should be easier to detect,
; for example
; (pattern-lambda (/ 2 3) '(/ 3 2)), (pattern-lambda (/ 3 2) '(/ 2 3))
; TODO: ignore quoted expressions
(define (pattern-expand plist expr)
(if (not (pair? expr))
expr
(let ((enew (apply-patterns plist expr)))
(if (eq enew expr)
; expr didn't change; move to subexpressions
(cons (car expr)
(map (lambda (subex) (pattern-expand plist subex)) (cdr expr)))
; expr changed; iterate
(pattern-expand plist enew)))))