Understanding conditional scheme formatting? SICP exercise 1.6

Question

I understand the big picture applicative vs normal order lesson here I think, but I'm struggling with:

(define (new-if predicate then-clause else-clause) (cond (predicate then-clause) (else else-clause)))

Eva demonstrates the program for Alyssa:

(new-if (= 2 3) 0 5) 5

(new-if (= 1 1) 0 5) 0

And for that matter:

(cond (= 2 3) 0 5) 3

(cond (= 1 1) 0 5) 1

Could you walk me through like a child why these return these values? They are all just predicates with no consequent expressions, right?

Answer 1

(define (new-if predicate then-clause else-clause)
    (cond (predicate then-clause)
    (else else-clause)))

(new-if (= 2 3) 0 5)
5
(new-if (= 1 1) 0 5)
0

when you call first new-if procedure as you can see you test predicate (= 2 3) if it is true it returns then-clause which is 0 and if it is not true then it returns else-clause which is 5. For second new-if procedure predicate is (= 1 1) which is true so it returns then-clause which is 0.

Actually I don't know why these cond expressions returns these values but you should normally use cond like this after cond every parenthesis includes a clause

(cond (<p1><e1>)
      (<p2><e2>)
      ...
      (<pn><en>))

for your example

(cond ((= 2 3) 0)
       (5))

if there is no expression after test in the clause it returns test value as the result which is 5 here or you can call with else either

(cond ((= 2 3) 0)
       (else 5))

Answer 2

Use the substitution method, as explained in the previous chapter.

   (new-if (= 2 3) 0 5)
—> (new-if #f 0 5)
—> (cond (#f 0)
         (else 5))
—> 5

and

   (new-if (= 1 1) 0 5)
—> (new-if #t 0 5)
—> (cond (#t 0)
         (else 5))
—> 0

Your cond examples have bad syntax, but if you have a clause like

(cond
   (= 2 3)
   ...

it is equivalent to

(cond
   (= (begin 2 3))
   ...

that is, the condition is =, and 2 3 is a sequence of expressions that constitute the body.
The value of such a sequence of expressions is the value of the last expression.
(The book will not use such sequences until side effects are introduced, around half way through the book.)