Unformatted text preview: t, or
2. it is a pair whose car is a integer and whose cdr is a list of integers.
We use Int to denote the set of all integers, and List-of-Int to denote the set of
lists of integers.
Deﬁnition 5 (list of integers, bottom-up) The set List-of-Int is the smallest set
of Scheme lists satisfying the following two properties: ¢ ¢ ¢ l List-of-Int. The phrase n List-of-Int, then n Int and l 2. if n List-of-Int, and ¢ 1. l denotes a Scheme list whose car is n and whose cdr is l . Deﬁnition 6 (list of integers, rules of inference) ¢ Int
(n l ) List-of-Int ¢ ¡ ¢ n ¢ () l List-of-Int
List-of-Int 7 1. is a list of integers, because of property 1 of deﬁnition 5 or the ﬁrst rule
of deﬁnition 6. 2. is a list of integers, because of property 2 of deﬁnition 5, since
is a integer and
is a list of integers. We can also write this as an
instance of the second rule for List-of-Int .
¢ A is a list of integers, because of property 2, since is a
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- Fall '09
- Data Structures, eopl, ¡§ £¡, Dr. Wand