# Is it possible to generate an equality function based on the data to be compared? [closed]

Two Booleans are equal if the’re the same value, two numbers similarly. Two sets are equal if they have the same elements. In case of checking two sets for equality we can use the following scheme/racket function:

``(define (same-set? l1 l2)   (and (subset? l1 l2) (subset? l2 l1))) ``

How would such a function be generated automatically?

The basic properties of an equivalence relation are:

Substitution property: For any quantities a and b and any expression F(x), if a = b, then F(a) = F(b) (if both sides make sense, i.e. are well-formed). Some specific examples of this are:

For any real numbers a, b, and c, if a = b, then a + c = b + c (here F(x) is x + c);

For any real numbers a, b, and c, if a = b, then a − c = b − c (here F(x) is x − c);

For any real numbers a, b, and c, if a = b, then ac = bc (here F(x) is xc);

For any real numbers a, b, and c, if a = b and c is not zero, then a/c = b/c (here F(x) is x/c).

Reflexive property: For any quantity a, a = a. Symmetric property: For any quantities a and b, if a = b, then b = a. Transitive property: For any quantities a, b, and c, if a = b and b = c, then a = c.

Is it possible to generate a function that obeys the above properties? Would that be enough? Could knowing the type of data help?

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