The positive rational numbers, which are ratios of two positive
integers, a/b, can be enumerated by listing them in order of
increasing sums a+b, with those numbers having the same sum
listed in order of increasing numerator a. Those fractions that
are not in lowest terms are omitted from the enumeration. Thus, the
enumeration begins with 1/1, 1/2, 2/1, 1/3, 3/1,... Define a
stream, positive-rationals, that contains all of the positive
rational numbers with numerator and denominator having no common
divisor greater than one. Represent the rational number a/b as
a list (a b) and use the Scheme procedure gcd to test
whether a/b is in lowest terms. Test your program by listing
the first twenty elements of the stream.
Give a definition for Scheme's equal? written in
continuation passing style. Call your function equal-cps?.
Define equal-cps? so that it takes a success continuation
succ and a failure continuation fail. The failure
continuation is applied if any two atoms are not eq?.
Using either define-macro or define-syntax, define a macro,
string-case, which is similar to Scheme's case macro but
works with strings. For example,
> (string-case "dog" (("dove" "turkey") "bird") (("cat" "dog") "mammal") (else "reptile"))
Using the stream file interface given here write a Scheme program which reads a file
containing DNA base pairs (represented by the letters A, G, C, and T)
and translates the file into the twenty amino acids (represented by
the letters F, L, I, M, V, S, P, T, A, etc.) and one stop symbol
(represented by $) using the following genetic
code. Test your program on the chromosomal DNA for the bacterium,
buchnera, which can be downloaded here.