Chapter 2, Problem 3E

Explanation of Solution

Explanation of regular expression for all sequences of letters other than the keywords:

• The programmer assumes for notational convenience that the expression not (a₁, a₂, …, a_n) is shorthand for (b₁ | b₂ | … | b_m), where the “b_js” are all letters other than the “a_is²”.
• The programmer also assume that letter stands for any letter.
• One way to create a word other than “file”, “for”, or “from” is to start with something other than “f”:

$\text{non-keyword }\to \text{ not (f) letter*}$

Another possibility is to follow “f” with something other than “i”, “o”, or “r”:

$\text{non-keyword }\to \text{ f not (i, o, r) letter*}$

Then another is to follow “fi” with something other than an “l”:

$\text{non-keyword }\to \text{ fi not (l) letter*}$

All the possibilities that the programmer contains,

$\begin{array}{l}\text{non-keyword }\to \text{ not (f) letter* | f not (i, o, r) letter* |\&\#}\end{array}$