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THE STACK THAT CANNOT JUMP
a pushdown model has no move for GO TO
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
A pushdown automaton reads one symbol and makes one move: push, pop, or neither. That discipline is what makes it decidable, and it is exactly what a
LIT verified live. In a program where a jump leaves a loop, label 10 sits at stack depth 2 and label 20 at depth 1 — the jump crosses 1 frame, and the automaton has no move that both pops and lands. The arithmetic IF names 3 targets from one statement. Of the twelve compiled cases, exactly 1 uses a jump, and it is the one no stack repair reaches.
GO TO violates. FORTRAN’s arithmetic IF — IF (X) 10, 20, 30 — branches three ways from a single statement, with no block and no closer, into labels that need not share a nesting depth.LIT verified live. In a program where a jump leaves a loop, label 10 sits at stack depth 2 and label 20 at depth 1 — the jump crosses 1 frame, and the automaton has no move that both pops and lands. The arithmetic IF names 3 targets from one statement. Of the twelve compiled cases, exactly 1 uses a jump, and it is the one no stack repair reaches.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) ranked his three fixes by cost and was blunt about the third: “a stack cannot model GO TO. the arithmetic IF and every labelled jump leave the pushdown model entirely. this is not a bug to patch — it is the limit of the automaton.” And on the scoring: “the veto’s zero-parameter 100.00% is a property of a bracketed language. fortran is not one.”
AVAN (AI) adds the formal name for what he found, because it is older than the veto. A language whose control flow includes unrestricted jumps to labels is not context-free in the sense a stack can track, and this is why structured-programming arguments of the 1960s were about expressive discipline rather than taste. The measurement here is not a discovery of that fact; it is a demonstration that his particular instrument hits it, on a case a compiler accepts.
AVAN (AI) adds the formal name for what he found, because it is older than the veto. A language whose control flow includes unrestricted jumps to labels is not context-free in the sense a stack can track, and this is why structured-programming arguments of the 1960s were about expressive discipline rather than taste. The measurement here is not a discovery of that fact; it is a demonstration that his particular instrument hits it, on a case a compiler accepts.
3 ONE DIMENSION
Stack depth at each label, and the jump that crosses it.
4 TWO DIMENSIONS · INTERACTIVE
Move the jump target and watch the frames it crosses.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: nested frames, with an arrow that ignores them.
AVAN’s addition (the inverse-companion): the forward reading is “a stack cannot model a jump.” The inverse is that the stack was never trying to. A pushdown automaton is a model chosen for what it makes cheap — linear time, no backtracking, a decidable emptiness test — and every one of those properties is bought by the restriction that control returns where it left. Read backwards, this is not a failure of the instrument but a correctly priced trade, and calling it a limitation obscures that the alternative is a model with none of the guarantees that made the first one worth building.
LIT in a program where a jump leaves a loop, label 10 sits at stack depth 2 and label 20 at depth 1, so the jump crosses 1 frame and the automaton has no move that both pops and lands; the arithmetic IF names 3 targets from a single statement; and of the twelve compiled cases exactly 1 uses a jump, which is the one no stack repair reaches
FIG David ranked his three fixes by cost and was blunt about the third: 'a stack cannot model GO TO. the arithmetic IF and every labelled jump leave the pushdown model entirely. this is not a bug to patch - it is the limit of the automaton.' And on the scoring: 'the veto's zero-parameter 100.00% is a property of a bracketed language. fortran is not one.' AVAN adds the formal name for what he found, because it is older than the veto: a language whose control flow includes unrestricted jumps to labels is not context-free in the sense a stack can track, which is why the structured-programming arguments of the 1960s were about expressive discipline rather than taste. The measurement here is not a discovery of that fact - it is a demonstration that his particular instrument hits it, on a case a compiler accepts.
FIG David ranked his three fixes by cost and was blunt about the third: 'a stack cannot model GO TO. the arithmetic IF and every labelled jump leave the pushdown model entirely. this is not a bug to patch - it is the limit of the automaton.' And on the scoring: 'the veto's zero-parameter 100.00% is a property of a bracketed language. fortran is not one.' AVAN adds the formal name for what he found, because it is older than the veto: a language whose control flow includes unrestricted jumps to labels is not context-free in the sense a stack can track, which is why the structured-programming arguments of the 1960s were about expressive discipline rather than taste. The measurement here is not a discovery of that fact - it is a demonstration that his particular instrument hits it, on a case a compiler accepts.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE FIREWALL · David Lee Wise (ROOT0), with AVAN