I recently wrote a little library, chez-docs, to make accessing documentation easier while learning Chez Scheme (blog post). The main procedure, doc, in chez-docs only returns results for exact matches with proc [1]. To aid in discovery, I've added a procedure, find-proc, that provides exact and approximate matching of search strings.

Levenshtein Distance

My initial thought was that I should approach this problem with approximate string matching. After a little searching, I learned that Levenshtein distance was one of the simplest approaches to calculate the distance between two strings. This excellent blog post included a few MATLAB implementations of Levenshtein distance algorithms [2] that were relatively easy for me to follow because of my experience with MATLAB and R.

I first implemented the recursive algorithm [3] thinking that it would be most natural in Scheme, but it was unacceptably slow. I then implemented the iterative two-row algorithm and found the performance to be sufficiently snappy for my needs.

(define (lev s t)
  (let* ([s (list->vector (string->list s))]
         [t (list->vector (string->list t))]
         [m (vector-length s)]
         [n (vector-length t)]
         [x (list->vector (iota (add1 n)))]
         [y (list->vector (make-list (add1 n) 0))])
    (do ((i 0 (add1 i)))
        ((= i m))
      (vector-set! y 0 i)
      (do ((j 0 (add1 j)))
          ((= j n))
        (let ([c (if (char=? (vector-ref s i) (vector-ref t j)) 0 1)])
          (vector-set! y (add1 j) (min (add1 (vector-ref y j))
                                       (add1 (vector-ref x (add1 j)))
                                       (+ c  (vector-ref x j))))))
      ;; swap x and y
      (let ([tmp x])
        (set! x y)
        (set! y tmp)))
    (vector-ref x n)))

This is the first time that I've used do loops in Scheme. In the example below, the looping index i is initialized to zero and incremented by one on each pass through the loop. The loop is exited when (= i 10). The equivalent code in R is for (i in 0:9) cat(paste0(i, " ")).

> (do ((i 0 (add1 i)))
      ((= i 10))
    (display (string-append (number->string i) " ")))
0 1 2 3 4 5 6 7 8 9

lev tallies the numbers of insertions, deletions, and substitutions; a value of zero indicates an exact match.

> (map (lambda (x) (lev "head" x)) '("head" "read" "load" "list-head"))
(0 1 2 5)

Exact Substring Matching

doc uses assoc to find any exact matches of the full string in the list of procedures. After working with the Levenshtein distance, I realized that exact matching of substrings would generally be more useful than fuzzy matching. I wrote the string-match procedure to test if a search string is present in the target string.

(define (string-match s t)
  (let* ([s-list (string->list s)]
         [t-list (string->list t)])
    (if (char=? (car s-list) #\^)
        (string-match-helper (cdr s-list) t-list)
        (not (for-all (lambda (x) (equal? x #f))
                      (map (lambda (t-sub) (string-match-helper s-list t-sub))
                           (potential-matches (car s-list) t-list)))))))

;; loop through characters in search string
;; to check if search string is found in target string
(define (string-match-helper s-list t-list)
  (cond [(not t-list) #f] 
        [(null? s-list) #t]
        [(< (length t-list) (length s-list)) #f]
        [(char=? (car s-list) (car t-list))
         (string-match-helper (cdr s-list) (cdr t-list))]
        [else #f]))

;; loop through target string
;; to find all potential substring matches
(define (potential-matches char t-list)
  (let loop ([t-list t-list]
             [results '()])
    (if (null? t-list)
        (remove-duplicates (reverse results))
        (loop (cdr t-list) (cons (member char t-list) results)))))
(define (remove-duplicates ls)
  (cond [(null? ls)
        [(member (car ls) (cdr ls))
         (remove-duplicates (cdr ls))]
         (cons (car ls) (remove-duplicates (cdr ls)))]))

member is the workhorse of string-match (via potential-matches). It's an interesting turn for me because when I first started using member in my Scheme code I was puzzled by why it didn't work like %in% in R. For example, (member 2 '(1 2 3)) returns (2 3), but 2 %in% c(1, 2, 3) returns TRUE. Because all values other than #f count as #t in Scheme, member can be used as a predicate, e.g., (if (member 2 '(1 2 3)) 1 0) returns 1. Nonetheless, it wasn't obvious to me how member's behavior was useful...until I started writing string-match. Those experiences make programming fun.

string-match returns a boolean value.

> (map (lambda (x) (string-match "head" x)) '("head" "read" "load" "list-head"))
(#t #f #f #t)

Procedure Discovery

find-proc takes a search-string and two optional arguments, search-type and max-results, which default to 'exact and 10, respectively.

(define find-proc
    [(search-string) (find-proc-helper search-string 'exact 10)]
    [(search-string search-type) (find-proc-helper search-string search-type 10)]
    [(search-string search-type max-results) (find-proc-helper search-string search-type max-results)]))

find-proc-helper maps either lev or string-match to the full list of procedures, proc-list, and then sorts or filters the results, respectively.

(define (find-proc-helper search-string search-type max-results)
  (unless (string? search-string)
    (assertion-violation "(find-proc search-string)" "search-string is not a string"))
  (cond [(symbol=? search-type 'fuzzy)
         (let* ([dist-list (map (lambda (x) (lev search-string x)) proc-list)]
                [dist-proc (map (lambda (dist proc) (cons dist proc)) dist-list proc-list)]
                [dist-proc-sort (sort (lambda (x y) (< (car x) (car y))) dist-proc)])
           (prepare-results dist-proc-sort max-results))]
        [(symbol=? search-type 'exact)
         (let* ([bool-list (map (lambda (x) (string-match search-string x)) proc-list)]
                [bool-proc (map (lambda (bool proc) (cons bool proc)) bool-list proc-list)]
                [bool-proc-filter (filter (lambda (x) (car x)) bool-proc)])
           (prepare-results bool-proc-filter max-results))]
         (assertion-violation "(find-proc search-string search-type)"
                              "search-type must be either 'exact or 'fuzzy")]))

(define (prepare-results ls max-results)
  (let* ([len (length ls)]
         [max-n (if (> max-results len) len max-results)])
    (map cdr (list-head ls max-n))))

I first realized that Levenshtein distance might not be very useful for find-proc when searching for head, a commonly used procedure in R.

> (find-proc "head" 'fuzzy 5)
("read" "and" "cadr" "car" "cd")

However, substring matching points us to the relevant function, list-head, in Chez Scheme.

> (find-proc "head" 'exact 5)
("list-head" "lookahead-char" "lookahead-u8" "make-boot-header")

Fuzzy matching is useful, though, for discovery when there are options with similar forms, e.g., hash-table? and hashtable?.

> (find-proc "hash-table?" 'exact 3)
> (find-proc "hash-table?" 'fuzzy 3)
("hash-table?" "hashtable?" "eq-hashtable?")

The ^ indicates that only search strings found at the start of the procedure should be returned.

> (find-proc "map")
("andmap" "hash-table-map" "map" "ormap" "vector-map")
> (find-proc "^map")

> (find-proc "file" 'exact 3)
("&i/o-file-already-exists" "&i/o-file-does-not-exist" "&i/o-file-is-read-only")
> (find-proc "^file" 'exact 3)
("file-access-time" "file-buffer-size" "file-change-time")

> (find-proc "let" 'exact 5)
("delete-directory" "delete-file" "eq-hashtable-delete!" "fluid-let" "fluid-let-syntax")
> (find-proc "^let" 'exact)
("let*" "let*-values" "let-syntax" "let-values" "letrec" "letrec*" "letrec-syntax")

Under fuzzy matching, the ^ is included as part of the Levenshtein distance calculation and, thus, should not be included in search strings when using fuzzy matching.

> (find-proc "map" 'fuzzy 5)
("map" "max" "*" "+" "-")
> (find-proc "^map" 'fuzzy 5)
("map" "max" "car" "exp" "memp")

[1] proc is shorthand for procedure, but not all of the items in chez-docs are procedures, e.g., &assertion.

[2] The MATLAB post linked to implementations of Levenshtein distance in other languages, including Scheme, but the Scheme example was hard for me to follow so I set it aside.

[3] After translating the MATLAB version of the recursive algorithm to Chez Scheme, I realized that a recursive example was available for Scheme on Rosetta Code.