Question

Please answer the questions below:

7. Rewrite the following BNF grammar using the form of EBNF described on the bottom
half of page 127 in Sebesta.
<import_decl> → import <import_list> ;
<import_list> → <package_list>
| <package_list> . *
<package_list> → <identifier>
| <package_list> . <identifier>
<identifier> → a | b | c
Make the resulting grammar as simple as possible, but keep all four of the original
nonterminals, which will now be named ImportDecl, ImportList, PackageList, and
Identifier. (Note: There are some typographical errors on page 127. See page 3-21 of the
course notes for a better description of this form of EBNF.)

8. (a) What is the weakest precondition needed to prove the correctness of the following
loop?
while i < j do
i = i + 1;
j = j - 1;
end
{i = j or i = j + 1}
(b) Give an invariant that is strong enough to prove the correctness of the loop.

Answer 1

Rewriting Bnf grammor using the form of · EBNF as follows: <assign) + impost = < import_list) < import_list> < <package_list> {(+1*);". <package_list) →<identifier> $(+) <package_ list> <identifier) (albic) The same gramar is shown on ebne import_list> <package_listy Kpackage_list> is converted to import to <import - list) → <package_list{[+]*)??' and Lidentifiery alblc is converted to Kidentifier> + (alblc) with paranthesis

a The weakest precondition needed is 3/i. b) The invariant strong enough will be througout the 100p is j+j=n (some number) a6"rabe increases and jº valve clecreases. maintaining the value constant to "n