THE FOLD / SPAWN / COLD BOOT / THE GRAMMAR THAT CANNOT
THE GRAMMAR THAT CANNOT
make the ambiguity unwriteable
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
A parser could not see an ambiguity, so the grammar was changed until the ambiguity could not be written. Not a smarter checker — a narrower language. The shape that broke the veto is not detected in the suit; it is simply not expressible, because there is no shared label for two constructs to end on.
LIT verified live by enumerating every short program in both grammars. Of 1,364 labelled programs up to length 5, 664 can share a terminator — 48.7%. Of 62 suit programs of the same lengths, 0 can. And the cost is exact and unflattering: the suit expresses 4.55% as many programs, because you cannot remove a shape without removing everything that used it.
LIT verified live by enumerating every short program in both grammars. Of 1,364 labelled programs up to length 5, 664 can share a terminator — 48.7%. Of 62 suit programs of the same lengths, 0 can. And the cost is exact and unflattering: the suit expresses 4.55% as many programs, because you cannot remove a shape without removing everything that used it.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) wrote the conclusion as a general rule rather than a local fix: “the fix for a parser that cannot see an ambiguity is not always a smarter parser. sometimes it is a grammar that cannot express the ambiguity.” The specific target was F2 in his tower — a veto with no braces, for a language whose loops end on labels.
AVAN (AI) enumerated both grammars to put a number on the trade, because the rule is stated as a win and it is really an exchange. Removing the ambiguity removed 95% of the expressible programs at these lengths. Most of those programs were nonsense, and the ratio is sensitive to how each grammar is encoded — but the direction is not in doubt, and a restriction that costs nothing is usually a restriction that removes nothing.
AVAN (AI) enumerated both grammars to put a number on the trade, because the rule is stated as a win and it is really an exchange. Removing the ambiguity removed 95% of the expressible programs at these lengths. Most of those programs were nonsense, and the ratio is sensitive to how each grammar is encoded — but the direction is not in doubt, and a restriction that costs nothing is usually a restriction that removes nothing.
3 ONE DIMENSION
Two grammars, every short program, counted.
4 TWO DIMENSIONS · INTERACTIVE
Grow the program length and watch both counts move.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the expressible space, with the ambiguous region cut out.
AVAN’s addition (the inverse-companion): the forward reading is “make the bad shape unwriteable.” The inverse is that a grammar cannot tell a bad shape from an unforeseen one. The restriction removes the shared terminator and everything isomorphic to it, including uses nobody has thought of yet, and the language has no way to distinguish the ambiguity it was aimed at from a legitimate construction with the same skeleton. Read backwards, this is prohibition rather than detection — it is more reliable precisely because it is less discriminating, and every future need that happens to have that shape is now a language change rather than a bug report.
LIT enumerating every short program in both grammars, of 1,364 labelled programs up to length 5 some 664 can share a terminator - 48.7% - while of 62 suit programs of the same lengths 0 can; and the cost is exact and unflattering, the suit expressing 4.55% as many programs, because you cannot remove a shape without removing everything that used it
FIG David wrote the conclusion as a general rule rather than a local fix: 'the fix for a parser that cannot see an ambiguity is not always a smarter parser. sometimes it is a grammar that cannot express the ambiguity.' The specific target was F2 in his tower - a veto with no braces, for a language whose loops end on labels. AVAN enumerated both grammars to put a number on the trade, because the rule is stated as a win and is really an exchange: removing the ambiguity removed 95% of the expressible programs at these lengths. Most of those were nonsense and the ratio is sensitive to how each grammar is encoded, but the direction is not in doubt - a restriction that costs nothing is usually a restriction that removes nothing.
FIG David wrote the conclusion as a general rule rather than a local fix: 'the fix for a parser that cannot see an ambiguity is not always a smarter parser. sometimes it is a grammar that cannot express the ambiguity.' The specific target was F2 in his tower - a veto with no braces, for a language whose loops end on labels. AVAN enumerated both grammars to put a number on the trade, because the rule is stated as a win and is really an exchange: removing the ambiguity removed 95% of the expressible programs at these lengths. Most of those were nonsense and the ratio is sensitive to how each grammar is encoded, but the direction is not in doubt - a restriction that costs nothing is usually a restriction that removes nothing.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of COLD BOOT · David Lee Wise (ROOT0), with AVAN