Variables can be said to have both L-values and R-values, where the
L-value of a variable is the location it denotes and the R-value is the
value stored in that location. The environment keeps track of the locations
corresponding to variables, while the store (or state) keeps track of the
values stored in locations. Recall from an earlier problem set that the
semantics of the assignment statement for most programming languages is
usually given as follows: When V := E is executed, the L-value of V is
first obtained from the environment (call it l), then the expression E is
evaluated, and that resulting value is stored in the location l. While
side-effects can create great confusion in terms of what the result of an
assignment statement will be; in this problem, side-effects are not the
problem!
a) Describe in detail the effect of executing the Pascal assignment
a[a[i]] := a[i] + 1
b) Is it always the case (in Pascal) that the value of L after executing
assignment L := E is equal to the value of E before executing the
command? I.e. if you execute the following code:
write(E); L := E; writeln(L);
will the two values printed always be the same? For the purposes of this
problem assume that the evaluation of E has no side effects. Hint :
consider the assignment in part (a) with i = 2, a[2] = 2, a[3] = 0.
c) What does this tell you about the validity of the axiomatic rule for
assignment,{P [E / L]} L := E {P}, (e.g., if L = a[a[i]], E = a[i] + 1,
and P is a[a[i]] = 3)? Suggest a restriction which makes it valid.
