tm_step

std.seq.tm_step · Level L3

One step of a deterministic Turing machine on a tape of T listed cells (unlisted cells are blank and never needed while fell stays 0): in state q reading σ, write Write[q, σ], move by Move[q, σ] ∈ {−1, 0, +1}, and enter Next[q, σ]; a halting state (accept or reject) has no transitions and stays put. fell becomes 1 if the head would leave the listed tape. The body tm_run scans.

(q, h, τ) ↦ (Next[q, τ_h], h + Move[q, τ_h], τ[h ← Write[q, τ_h]])

Signature

tm_step(state: f64[], head: f64[], tape: f64[T], fell: f64[], t: f64[], Next: i64[g, c], Write: i64[g, c], Move: i64[g, c], halting: f64[g]) → f64[], f64[], f64[T], 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 265 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

tm_run

sha256:dc61a202513533018b4ab0e9b3a5b4476b3fc5ce158e6b7a9e50d3a57da71470

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.tm_step · Ω:tm_step
Pins: sha256:abc4533b01e9bdab1a7b203cede1a3fed92b5552f3d71d4ac4f4ef7e62515166this graph alone
Evidence: sha256:c4ae57b7b867efc8cd7223d2354db4dca376e22540768f1fc082b524b04cb65ethe 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.