Question

How would I go about writing my own eqv? or equal? in scheme? Would I just do a cond and look for symbol?, number?, etc and return the appropriate #t or #f?

Answer 1

As per R5RS, the minimum specifications for an implementation of eqv? (when passed two arguments obj1 and obj2) to evaluate to #tare:

• obj1 and obj2 are both #t or both #f. (how two boolean literals evaluate to the same value is implementation dependent).
• obj1 and obj2 are both symbols and

(string=?
(symbol->string obj1)
(symbol->string obj2)) =)
=> #t

• obj1 and obj2 are both numbers, are numerically equal (=), and are either both exact or both inexact.
• obj1 and obj2 are both characters and are the same character according to the char=? procedure.
• both obj1 and obj2 are the empty list.
• obj1 and obj2 are pairs, vectors, or strings that denote the same locations in the store (See section 3.4 of R5RS).
• obj1 and obj2 are procedures whose location tags are equal (A lambda
  expression is conceptually tagged with a storage location. What that means varies between Scheme implementations. Also see section 4.1.4 of R5RS).

equal? could be implemented in terms of eqv? as it recursively compares the contents of pairs, vectors, and strings, applying eqv? on other objects such as numbers and symbols.