Recursion bug in Mosh Scheme
Oh, great. In my first day of working with Mosh Scheme, on pretty elementary stuff, I find a bug.
Here's the simplified example that I sent in as part of the bug report. I want to write a procedure that tests whether a given binary tree of integers contains only even integers. I'm using the empty list to model the empty binary tree, and three-elements lists (root, left subtree, right subtree) to model non-empty ones. So here's the definition:
(define (buggy tree)
(letrec ((recurrer
(lambda (subtree)
(or (null? subtree)
(and (even? (car subtree))
(recurrer (cadr subtree))
(recurrer (caddr subtree)))))))
(recurrer tree)))
And here's a simple test case, giving the wrong answer.
> (buggy '(92 () (103 () ()))) #t
I was particularly puzzled to discover that the error disappears if you use any of the following three variations instead:
(define (ok0 tree)
(or (null? tree)
(and (even? (car tree))
(ok0 (cadr tree))
(ok0 (caddr tree)))))
(define ok1
(letrec ((recurrer (lambda (tree)
(or (null? tree)
(and (even? (car tree))
(recurrer (cadr tree))
(recurrer (caddr tree)))))))
recurrer))
(define (ok2 tree)
(letrec ((recurrer
(lambda (subtree)
(let ((result (or (null? subtree)
(and (even? (car subtree))
(recurrer (cadr subtree))
(recurrer (caddr subtree))))))
result))))
(recurrer tree)))
The explanation should be interesting.
Another bug in Ikarus Scheme?
I've run into another problem that seems to be a bug in Ikarus Scheme, this
one in the processing of syntax definitions. This is supposed to be one of
Ikarus's strong points -- the implementer published a paper on the portable
syntax-case system that he developed for Ikarus -- so I was
surprised to encounter this difficulty.
I'm using syntax-case to automate the implementation of
"tuple" data types -- fixed-length lists in which each position is supposed
to hold values of a specified type. The idea is that I want to be able to
write something like
(define-tuple star (name string? string=?)
(magnitude number? =)
(distance number? =)
(spectral-class symbol? symbol=?))
and have it expand into a sequence of definitions: a constructor, a selector for each field, a "disaggregator" that returns the components as separate values, a classification predicate, and an equality predicate, thus:
(begin
(define (make-star name magnitude distance spectral-class)
(list name magnitude distance spectral-class))
(define (star-name star)
(list-ref star 0))
(define (star-magnitude star)
(list-ref star 1))
(define (star-distance star)
(list-ref star 2))
(define (star-spectral-class star)
(list-ref star 3))
(define (destar star)
(apply values star))
(define (star? something)
(and (list? something)
(= (length something) 4)
(string? (list-ref star 0))
(number? (list-ref star 1))
(number? (list-ref star 2))
(symbol? (list-ref star 3))))
(define (star=? left right)
(and (string=? (list-ref left 0) (list-ref right 0))
(= (list-ref left 1) (list-ref right 1))
(= (list-ref left 2) (list-ref right 2))
(symbol=? (list-ref left 3) (list-ref right 3)))))
Here's my definition of the define-tuple syntax:
(define-syntax define-tuple
(letrec ((as-string
(lambda (x)
(cond ((identifier? x)
(as-string (syntax->datum x)))
((symbol? x)
(symbol->string x))
((string? x) x))))
(construct-id
(lambda (context . parts)
(datum->syntax context
(string->symbol
(apply string-append
(map as-string parts))))))
(iota
(lambda (n)
(let loop ((count n) (so-far '()))
(if (zero? count)
so-far
(let ((next (- count 1)))
(loop next (cons next so-far))))))))
(lambda (input-form)
(syntax-case input-form ()
((_ type-name (field-name classification equality) ...)
(with-syntax ((constructor-name
(construct-id #'type-name "make-" #'type-name))
((selector-name ...)
(map (lambda (fn)
(construct-id #'type-name
#'type-name
"-"
fn))
#'(field-name ...)))
(field-count
(datum->syntax #'type-name
(length #'(field-name ...))))
((field-index ...)
(iota (length #'(field-name ...))))
(disaggregator-name
(construct-id #'type-name "de" #'type-name))
(classification-predicate-name
(construct-id #'type-name #'type-name "?"))
(equality-predicate-name
(construct-id #'type-name #'type-name "=?")))
#'(begin
(define (constructor-name field-name ...)
(list field-name ...))
(define (selector-name type-name)
(list-ref type-name field-index)) ...
(define (disaggregator-name type-name)
(apply values type-name))
(define (classification-predicate-name something)
(and (list? something)
(= (length something) field-count)
(classification
(list-ref something field-index)) ...))
(define (equality-predicate-name left right)
(and (equality (list-ref left field-index)
(list-ref right field-index))
...)))))))))
Ikarus accepts this syntax definition without complaining, but hangs
when it encounters any use of define-tuple, as if it can't
complete the expansion process. Neither PLT Racket nor Larceny has this
problem.
Multiplicative-inverse bug in Ikarus Scheme
In testing the examples from chapter 1 of AFP, I turned up a bug in
the Ikarus Scheme processor (version 0.0.3). One of my examples computes
the multiplicative inverse of -3/8, using the expression
(/ -3/8). The test code, then, was essentially
(= (/ -3/8) -8/3)
The test failed -- Ikarus Scheme returns #f as the value of
the equality test. I tried a few interactions to try to get some idea
of what was going on, but I found the results mystifying:
> (/ -3/8) 8/-3
This isn't exactly wrong, but the form of the number is not what I expecteed, since 8/-3 is not a valid R6RS literal. Ikarus Scheme accepts such literals as input, but appears to normalize them:
> 8/-3 -8/3
It looks like the one-argument / procedure is internally
generating a rational value with a negative denominator and not normalizing
the result:
> (rational? (/ -3/8)) #t > (numerator (/ -3/8)) 8 > (denominator (/ -3/8)) -3
Then the = predicate gets the wrong answer because it
somehow relies the precondition that denominators are positive. It's not
that the = predicate can't deal with signed values:
> (= -8/3 8/-3) #t > (= -8/-3 16/6) #t
Other procedures deal correctly with the negative-denominator rational:
> (< 8/-3 (/ -3/8)) #f > (> 8/-3 (/ -3/8)) #f > (<= 8/-3 (/ -3/8)) #t > (>= 8/-3 (/ -3/8)) #t > (- 8/-3 (/ -3/8)) 0
The two-argument form of the / procedure gives the correct
answer:
> (/ 1 -3/8) -8/3 > (= (/ -3/8) (/ 1 -3/8)) #f > (- (/ -3/8) (/ 1 -3/8)) 0
I looked over the list of bugs fixed in version 0.0.4 and didn't find this one, so I filed a bug report on the LaunchPad site for Ikarus Scheme.
Testing equality for exact rationals seems pretty straightforward -- you multiply the numerator of each one by the denominator of the other and determine whether the resulting integers are equal. But this should work even without the precondition that denominators be positive. I wonder what alternative approach the author of Ikarus Scheme used -- I must be missing something.