How detect grammar not derive nonterminals ?

[Andy]

The simplest this case is grammar :
A -> A

but I have

A -> B
A -> b B
B -> A
B -> a A

it is trap for sequence generator. A->B->A->B->A....
How detect similar cases, especially without computing First and Follow sets ?

[gah4]

On Tuesday, September 12, 2023 at 10:42:28 AM UTC-7, Andy wrote:

(the subject not included in the message)

How detect grammar not derive nonterminals ?

Ethernet uses the spanning tree protocol to detect loops in a switched network.

I think the same idea works here, but didn't try it.

[Kaz Kylheku]

Post by gah4
(the subject not included in the message)

How detect grammar not derive nonterminals ?

Ethernet uses the spanning tree protocol to detect loops in a switched network.
I think the same idea works here, but didn't try it.

Loops are allowed in a grammar, and are the essence of expressive
languages that can generate sentences of arbitrary length/depth.

The situation is similar to recursion: recursion can terminate
or run away.

This has a loop, but is okay, because it has a terminating case:

A := A b | b

This isn't okay; and note that all we did was take *away* the b case:

A := A b

--
TXR Programming Language: http://nongnu.org/txr
Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal
Mastodon: @***@mstdn.ca
[At the very least, you'd need some rules that don't have nonterminals
on the right side to make it possible to break loops. -John]

[gah4]

(our moderator wrote)

Post by Kaz Kylheku
[At the very least, you'd need some rules that don't have nonterminals
on the right side to make it possible to break loops. -John]

So do it by back propagation.

Mark all rules that have a terminal on the right side.

Mark all rules that have a rule that has a terminal on the right side.

Repeat until there aren't any more to mark.

Any unmarked rules don't ever reach a terminal.
[It's not quite that, it's rules that have no nonterminals, that
is, either just terminals or empty. This will recognize a
possibly empty sequence of x's:

A: /* nothing */
A: x A

-John]

[Andy]

Post by Andy
it is trap for sequence generator. A->B->A->B->A....
How detect similar cases, especially without computing First and Follow sets ?

I test my grammars:
above
;A->B->A->B....
A -> B
A -> b B
B -> A
B -> a A

;L grows up infinitely
G -> S
G -> L
G -> s
S -> i b t G
L -> i b t L e G
; if will exists L-: some_terminals it will ok, but not exists

E -> E + i
E -> E * i

S -> i S

S -> S i

I found solution: all w these cases handle computing minimal length of nonterminal and rules.
How correct compute it:
```
Rule {
boolean computeMinLen() {
int old = minLen;
minLen = 0;
for (Symbol symbol : this)
if (!symbol.terminal && grammar.getNT(symbol.index).minLen<0) {
minLen = -1;
return minLen != old;
}
for (Symbol symbol : this)
if (symbol.terminal)
minLen++;
else
minLen += grammar.getNT(symbol.index).minLen;
return minLen != old;
}
}

Nonterminal {
boolean computeMinLen() {
int old = minLen;
boolean changed = false;
for (Rule rule : rules) {
if (rule.computeMinLen())
changed = true;
}
for (Rule rule : rules) {
if (rule.minLen >= 0) {
if (minLen<0)
minLen = rule.minLen;
else
minLen = Math.min(minLen, rule.minLen);
}
}
return minLen != old || changed;
}
}

and loop if not change:
boolean changed = true;
while (changed) {
changed = false;
for (Nonterminal nt : nonterminals) {
if (nt.computeMinLen())
changed = true;
}
}

and check:
int index = 0;
for (Nonterminal nt : nonterminals) {
if (nt.minLen < 0)
throw new NoMinLenGrammarException("not computed minLen for " + getNonTerminalName(index));
for (Rule ruleInfo: nt.rules)
if (ruleInfo.minLen < 0)
throw new NoMinLenGrammarException("not computed minLen for " + ruleInfo.toString());
index++;
}

```
-----------------
But what doing if grammar is correct but has generator trap :
A->A
A->a
generates "a" but generator , which I write, calls A->A->...
should be transformed by eliminate A->A

A->B
A->a
B->A
B->b

is cycle A->B->A...
should be transformed by eliminate A->B or B->A

how detect all similar cases and how transform it in general case?