The default if statement is a special form which means that even when an interpreter follows applicative substitution, it only evaluates one of it's parameters- not both. However, the newly created new-if doesn't has this property and hence, it never stops calling itself due to the third parameter passed to it in sqrt-iter.

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I agree with jsdalton. The reason why new-if runs out of memory is applicative order evaluation, so if the plain-old `if` uses applicative order evaluation, it should not work either.

And I guess for a certain interpreter, maybe it should use a consistent way for all processes?

I believe the above two posters are right and the given answer is wrong.

It's stated clearly in the text that:

"Lisp uses applicative-order evaluation, partly because of the additional efficiency obtained from avoiding multiple evaluations of expressions such as those illustrated with (+ 5 1) and (* 5 2) above and, more significantly, because normal-order evaluation becomes much more complicated to deal with when we leave the realm of procedures that can be modeled by substitution."

So I don't see a reason why MIT-Scheme (which is supposedly what readers of the book use) would be any different. Plus, as andersc wrote, an interpreter would have to be consistent about the evaluation strategy it uses.

As jsdalton said. `new-if` is a procedure, not a special-form, which means that all sub-expressions are evaluated before `new-if` is applied to the values of the operands. That includes `sqrt-iter` which is extended to `new-if` which again leads to the evaluation of all the sub-expressions including `sqrt-iter` etc. Instead, in `if` only one of the consequent expressions is evaluated each time.

`new-if` works on my machine.

Here's my code:

2013-12-05 21:15:18 dpchrist@desktop ~/sandbox/mit-scheme/sicp2 $ cat ex-1.6.scm | grep -v ';' (define (average x y) (/ (+ x y) 2)) (define (square x) (* x x)) (define (improve guess x) (average guess (/ x guess))) (define (good-enough? guess x) (< (abs (- (square guess) x)) 0.001)) (define (sqrt-iter guess x) (if (good-enough? guess x) guess (sqrt-iter (improve guess x) x))) (define (sqrt x) (sqrt-iter 1.0 x)) (sqrt 9) (sqrt (+ 100 37)) (sqrt (+ (sqrt 2) (sqrt 3))) (square (sqrt 1000)) (define (new-if predicate then-clause else-clause) (cond (predicate then-clause) (else else-clause))) (new-if (= 2 3) 0 5) (new-if (= 1 1) 0 5) (define (new-sqrt-iter guess x) (new-if (good-enough? guess x) guess (sqrt-iter (improve guess x) x))) (define (new-sqrt x) (new-sqrt-iter 1.0 x)) (if (= ( sqrt 9) (new-sqrt 9)) 1 0) (if (= ( sqrt (+ 100 37)) (new-sqrt (+ 100 37))) 1 0) (if (= ( sqrt (+ ( sqrt 2) ( sqrt 3))) (new-sqrt (+ (new-sqrt 2) (new-sqrt 3)))) 1 0) (if (= (square ( sqrt 1000)) (square (new-sqrt 1000))) 1 0)

Here's a sample run on Debian 7.2:

2013-12-05 21:17:24 dpchrist@desktop ~/sandbox/mit-scheme/sicp2 $ cat ex-1.6.scm | grep -v ';' | mit-scheme -eval MIT/GNU Scheme running under GNU/Linux Type `^C' (control-C) followed by `H' to obtain information about interrupts. Copyright (C) 2011 Massachusetts Institute of Technology This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. Image saved on Saturday October 15, 2011 at 10:11:41 PM Release 9.1 || Microcode 15.3 || Runtime 15.7 || SF 4.41 || LIAR/i386 4.118 Edwin 3.116 1 ]=> ;Value: average 1 ]=> ;Value: square 1 ]=> ;Value: improve 1 ]=> ;Value: good-enough? 1 ]=> ;Value: sqrt-iter 1 ]=> ;Value: sqrt 1 ]=> ;Value: 3.00009155413138 1 ]=> ;Value: 11.704699917758145 1 ]=> ;Value: 1.7739279023207892 1 ]=> ;Value: 1000.000369924366 1 ]=> ;Value: new-if 1 ]=> ;Value: 5 1 ]=> ;Value: 0 1 ]=> ;Value: new-sqrt-iter 1 ]=> ;Value: new-sqrt 1 ]=> ;Value: 1 1 ]=> ;Value: 1 1 ]=> ;Value: 1 1 ]=> ;Value: 1 1 ]=> End of input stream reached. Moriturus te saluto.

The poster above does not define `new-sqrt-iter` as recursive, as it calls the original `sqrt-iter` instead of itself.

I believe this solution is incorrect.

new-ifdoes not use normal order evaluation, it uses applicative order evaluation. That is, the interpreter first evaluates the operator and operands and then applies the resulting procedure to the resulting arguments. As with Excercise 1.5, this results in an infinite recursion because theelse-clauseis always evaluated, thus calling the procedure again ad infinitum.The

ifstatement is a special form and behaves differently.iffirst evalutes the predictate, andthenevaluates either the consequent (if the predicate evalutes to#t)orthe alternative (if the predicate evalues to#f). This is key difference fromnew-if-- onlyoneof the two consequent expressions get evaluated when usingif, whilebothof the consequent expressions get evaluated withnew-if.wjm

A lenghtier explanation of Applicative Order and Normal Order is here: http://mitpress.mit.edu/sicp/full-text/sicp/book/node85.html