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