pda_step

std.seq.pda_step · Level L3

One step of checking a pushdown automaton's run: apply transition x if it fits the configuration (its from-state is the current state, it reads the next input symbol or ε, and the stack top is the symbol it needs): pop that top, push its replacement bottom to top, and move to its to-state. A transition that does not fit, or would overflow the listed stack, makes the run invalid and leaves the configuration as it was. The body pda_run_check scans.

(q, i, γA) ⊢ (q′, i + [σ ≠ ε], γβ)

Signature

pda_step(state: f64[], pos: f64[], stack: f64[H], h: f64[], valid: f64[], x: f64[], Tfrom: i64[t], Tin: i64[t], Ttop: i64[t], Tto: i64[t], Tlen: i64[t], Tpush: i64[t, 2], wordf: f64[L]) → f64[], f64[], f64[H], f64[], f64[]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference the same move on Python lists in exact rational arithmetic, on all 40 test cases.
All 301 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

—

Called by

pda_run_check

sha256:929e7a27ba767c1a06e13ba1fe32eda014c1c4d604f2e2a277247e3a256e4c8c

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.seq.pda_step · Ω:pda_step
Pins: sha256:b2b3e4cb1ee69d686344b9418d353fd60f81464ad289fbfe1093c36294d08dcathis graph alone
Evidence: sha256:83fbc3075f53ce5d5189fa1a7c95e96f1c1c2d4127a03686a9ae072773a0e12cthe hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.