General Computer Science; Problems and Solutions for ... - Kwarc

Problem 1.32 (Nested lists)
In class, we have defined an abstract data type for lists of natural numbers. Using this intuition,
construct an abstract data type for lists that contain natural numbers or lists (nested up to
arbitrary depth). Give the constructor term (the trace of the construction rules) for the list
[3, 4, [7, [8, 2], 9], 122, [2, 2]].
Solution: We choose the abstract data type
〈{N, L}, {[cl : L × L → L], [cn : N × L → L], [nil : L], [o: N], [s: N → N]}〉
The constructors cl and cl construct lists by adding a list or a number at the front of the list. With this,
the list above has the constructor term.
cn(3, cn(4, cl(cn(7, cl(cn(8, cn(2, nil)), cn(9, nil)), cn(122), cl(cn(2, cn(2, nil)))nil))))
where n is the s, o-constructor term of the number n.
33
20pt