regex_node_step

std.seq.regex_node_step · Level L3

One node of a regular expression's syntax tree, evaluated on the word's parts: the node's 0/1 span matrix over the fenceposts, from its children's matrices: ε the identity, a symbol the single steps that read it, union the elementwise or, concatenation the boolean product, star the reflexive transitive closure (reachability), the empty language 0. The body regex_match scans.

M_ε = I, M_a = [w_i = a, j = i + 1], M_∪ = M_l ∨ M_r, M_· = M_l M_r, M_* = M_l*

Signature

regex_node_step(Ms: f64[K, n, n], k: f64[], kind: i64[K], sym: i64[K], left: i64[K], right: i64[K], W: f64[n]) → f64[K, n, n]

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 node rule on Python lists in exact rational arithmetic, on all 40 test cases.
All 1,571 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

reachability

Called by

regex_match

sha256:b9636ad85f1dfc9ed234995d5b83185a3780867ab138bf2cf4e65bc05304350f

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.regex_node_step · Ω:regex_node_step
Pins: sha256:829345490f7a449a347e9108d3cfa31cc962e600be9542a2e75d901be23ff1efthis graph and the 2 it reaches through calls
Evidence: sha256:784bb072a8671ff72618fb2a3060e110a7021b3ec3f747dc7e12003c71d6c956the 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.