Reduce the first statement, “a ':=' '2' '+' '3';”:
<a ':=' '2' '+' '3' | Env0>
⇒ <a ':=' 2 '+' 3 | Env0> (Rules 1, 7, and 10)
⇒ <a ':=' 5 | Env0> (Rules 3 and 17)
⇒ Env0 & {a=5} = {a=5} (Rule 16)
Update the environment from Env0 to {a=5}:
<a ':=' '2' '+' '3'; b ':=' a '*' '4';
a ':=' b '-' '5' | Env0>
⇒ <b ':=' a '*' '4'; a ':=' b '-' '5' | {a=5}> (Rule 18)
Reduce the second statement, “b ':=' a '*' '4';”:
<b ':=' a '*' '4' | {a=5}>
⇒ <b ':=' 5 '*' '4' | {a=5}> (Rules 15 and 9)
⇒ <b ':=' 5 '*' 4 | {a=5}> (Rules 1 and 12)
⇒ <b ':=' 20 | {a=5}> (Rules 5 and 17)
⇒ {a=5} & {b=20} = {a=5, b=20} (Rule 16)
Update the environment from {a=5} to {a=5, b=20}:
<b ':=' a '*' '4'; a ':=' b '–' '5' | {a=5}>
⇒ <a ':=' b '–' '5' | {a=5, b=20}> (Rule 18)
Reduce the third statement, “a ':=' b '–' '5';”:
<a ':=' b '–' '5' | {a=5, b=20}>
⇒ <a ':=' 20 '–' '5' | {a=5, b=20}> (Rules 15 and 8)
⇒ <a ':=' 20 '–' 5 | {a=5, b=20}> (Rules 1 and 11)
⇒ <a ':=' 15 | {a=5, b=20}> (Rules 4 and 17)
⇒ {a=5, b=20} & {a=15} = {a=15, b=20} (Rule 16)
The program reduces to the environment {a=15, b=20}, which is the semantics of the program.
Note that these reductions are incomplete because we have skipped the reductions of identifiers.