Concepts and Semantics of Programming Languages 1

AppendixSolutions to the Exercises

A.1. Introduction to language semantics

Solution to exercise 2.1

1)

2) The evaluation of the sequence of definitions d =[var z = 2;let x =8; var y = 5;let x =3;] leads to the state etat₀ as follows:

There are several sequences of definitions, which leadto state etat₀ . For example, in the sequence d, the definition let x =8may be replaced by let x =!z +6 since, in state ([(z, r_z)], [(r_z, 2)]), the expression !z +6 is evaluated as 8.

3) Let us develop this expression as follows:

4) In state etat0, the evaluation of the expression !x triggers an error, as x is not a mutable variable in Env₀; the evaluation of y + x triggers an error, as y is evaluated as a reference to which addition cannot be applied, and the evaluation of the identifier w triggers an error, as it is unbound in Env₀.

5) By applying the rules given in the statement, we obtain the following states and environments:

6) Applying the rules in the statement, we obtain the following results:

Solution to exercise 2.2

1) Depending on the order in which expressions e₁ and e₂ are evaluated ...