Denotational Semantic Mapping

Question

Which of the following shows a denotational semantic mapping for evaluating a Boolean expression?

Ma(x=E,s) ≜

  if Me(E, s) == error

then error

else s' = {<i1,v1'>,<i2,v2'>,...,<in,vn'>}, where

for j = 1,2,...,n

if ij == x

then vj' = Me(E,s)

else vj = VARMAP(ij,s)

Mpf(for var in init_expr .. final_expr loop L end loop, s)  ≜

     if VARMAP(i, s) == undef for var or some i in init_expr or final_expr

          then error

          else if Me(init_expr, s) > Me(final_expr, s)

              then s

              else Ml(while init_expr - 1 <= final_expr do L, Ma(var := init_expr + 1, s))

Mb(B, s) ≜

if VARMAP(i, s) == undef for some i in B

          then error

          else B', where B' is the result of

              evaluating B after setting each

                variable i in B to VARMAP(i, s)

Answer 1

The denotational semantic mapping for evaluating a Boolean expression is represented by the function Mb(B, s). The function takes a Boolean expression B and a state s as input and returns the result of evaluating the expression.

Here is the denotational semantic mapping for evaluating a Boolean expression:

Mb(B, s) ≜

if VARMAP(i, s) == undef for some i in B

then error

else B', where B' is the result of

evaluating B after setting each

variable i in B to VARMAP(i, s)

In this mapping, VARMAP(i, s) represents the value of the variable i in the state s. The mapping checks if any variable in the Boolean expression B is undefined in the state s. If so, it returns an error. Otherwise, it evaluates the Boolean expression B by substituting each variable i with its corresponding value VARMAP(i, s) and returns the result B'.