Question

Write a segment code in any language you prefer that behaves differently if the language used

1. structural equivalence  two types as the same if they consist of the same components.

2. name equivalence  each type declaration introduces a new type, distinct from all others.

3. declaration equivalence  two types are equivalent if they lead back to the same type.

Answer 1

1.Structural Equivalence
An alternative notion of type
equivalence is structural equivalence
(denoted ≡S). Roughly, two types are
structurally equivalent if the two
types have the same definition,
independent of where the definitions
are located. That is, the two types
have the same definitional structure.

Formally,
(a) T ≡S T
(b) Given the declaration
Type T = Q;
T ≡S Q
(c) If T and Q are defined using the
same type constructor and
corresponding parameters in the two
definitions are equal or structurally
equivalent
then T ≡S Q

2.Name equivalence

Code in Java:
public class T1 {
int a;
String s;
char ch;
}
public class T2 {
int a;
String s;
char ch;
}
Here, the two types T1 and T2 are not the same as the names of the data types are different (though inherently they are the same).
i.e.
T1 t1 = new T1();
T2 t2 = new T2();
( t1 == t2 ) will return false.
This is name equivalence in Java.

3. Declaration Equivalence:

• two types are equivalent if they lead back to the same type.
• Example:

  TYPE T1 = ARRAY [0..10] OF CHAR; TYPE T2 = T1; TYPE T3 = T2; TYPE T4 = ARRAY [0..10] OF CHAR; 

  Types T1, T2, T3 are equivalent.

Hope this may help you

Thank you ?