Exercise 2.2. A Radix 8 Numeral Number System (). Based on the idea of the informal Example 2.1, devise a grammar for a radix 8 natural number system, and an informal meaning function that converts radix 8 numerals into radix 10 numbers

Exercise 2.3. A Radix 8 Numeral Number System (). Given a radix 10 number, convert it to a radix 8 numeral. That is : Define, informally, a function which takes a natural number and yields a radix 8 numeral. Assume a function modulo which takes two argument, m, n, both natural number, both larger than 0, and yields a pair w, r such that w x n + r = m

Exercise 4.3. Further Operations on Cartesian Lists. We refer to Example 4.2 on page 67. Define the following operations on Cartesian lists: (L = A*) (token, token) ((a), token) a ((a), ((b), token)) a,b ((a), ((b), ((c), token))) a,b,c ::= (token, token) | (, ) ::= a | b | c |

1. len: The length of a list: The number of (zero, one or more) elements that it contains. 2. inds: The index set of a list: The set of indices, from 1 to and including the length of the list. If the list is empty then the index set is the empty set. 3. elems: The element set of a list: The set of distinct elements of the list. If the list is empty then the element set is the empty set.