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 (sort of) equivalent syntax in R is `for (i in 0:9) print(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)
(define (loop s-list t-sub)
(cond [(null? s-list) #t]
[(< (length t-sub) (length s-list)) #f]
[(char=? (car s-list) (car t-sub))
(loop (cdr s-list) (cdr t-sub))]
[else #f]))
(let* ([s-list-temp (string->list s)]
[starts-with? (char=? (car s-list-temp) #\^)]
[s-list (if starts-with? (cdr s-list-temp) s-list-temp)]
[t-list (string->list t)])
(cond [(and starts-with? (not (char=? (car s-list) (car t-list)))) #f]
[(not (for-all (lambda (x) (member x t-list)) s-list)) #f]
[else (loop s-list (member (car s-list) t-list))])))
```

`member`

is the workhorse of `string-match`

. 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, `max-results`

and `fuzzy?`

, which default to `10`

and `#f`

, respectively.

```
(define find-proc
(case-lambda
[(search-string) (find-proc-helper search-string 10 #f)]
[(search-string max-results) (find-proc-helper search-string max-results #f)]
[(search-string max-results fuzzy?) (find-proc-helper search-string max-results fuzzy?)]))
```

`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 max-results fuzzy?)
(unless (string? search-string)
(assertion-violation "(find-proc search-string)" "search-string is not a string"))
(cond [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))]
[else
(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))]))
(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" 5 #t)
("read" "and" "cadr" "car" "cd")
```

However, substring matching points us to the relevant function, `list-head`

, in Chez Scheme.

```
> (find-proc "head" 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?" 3)
("hash-table?")
> (find-proc "hash-table?" 3 #t)
("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")
("map")
> (find-proc "file" 3)
("&i/o-file-already-exists" "&i/o-file-does-not-exist" "&i/o-file-is-read-only")
> (find-proc "^file" 3)
("file-access-time" "file-buffer-size" "file-change-time")
> (find-proc "let" 5)
("delete-directory" "delete-file" "let*" "let*-values" "let-syntax")
> (find-proc "^let")
("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" 5 #t)
("map" "max" "*" "+" "-")
> (find-proc "^map" 5 #t)
("map" "max" "car" "exp" "memp")
```

`proc`

is shorthand for procedure, but not all of the items in`chez-docs`

are procedures, e.g.,`&assertion`

.↩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.↩

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