🚀 go-pugleaf

In article <6224@paris.ics.uci.edu> Doug Schmidt <schmidt@blanche.ics.uci.edu> writes:
> ... can't both a while loop and a for loop be replaced by an if statement
> and a goto?

Yes.  But a more appropriate means to define the while loop is via an equational
specification:

     The while loop 
    
		     WHILE B DO S END

     is the fixed point solution, x, to the equation:

	           x = IF B THEN S; x END

Therefore, the loop is a special form of recursion, known as tail-recursion.
It can be simulated by a parameterless recursively-called procedure (with
equal efficiency when compiled by a self-respecting compiler).  The same goes
for C's for loop (in terms of which its while loop can be reduced):

	    while (B) S; = for (; B; ) S; = for (; B; S) ;

with suitable optimizations for initializations and increments.  Incidentally, 
nearly every while loop I've ever seen in a C program can be more suitably 
represented as a for loop with at least one of the optimizations taking effect,
so it's actually the while loop (and do-while loop) that should be regarded as
superfluous.

For the for-loop:

	 for (Init; Cond; Incr) Body; = Init; x

where x is the fixed point solution to the equation:

	      x = if (Cond) {Body; Incr; x}

Note that all of these equivalences remains so, even taking into account the
effects of evaluating expressions (Cond) with side-effects.

       Just as an added note, C's for loop is formally defined in terms of
its while loop.

>   
>In fact, aren't all high-level control constructs superfluous?

They're supposed to be.  In fact, a well designed language should have most of
its constructs defined in terms of its more basic "core" entities.

The goto is also superfluous once you realise that every goto is a parameterless
procedure call whose return address is the end of the block from which the goto
issued (or some variant of that depending on which language one is talking 
about).