regex_match

std.seq.regex_match · Level L3

Whether a word is in the language of a regular expression, as 1 or 0, decided exactly: the syntax tree is listed node by node, children first (kind 0 empty, 1 ε, 2 symbol, 3 union, 4 concatenation, 5 star), the last node the root, and each node's span matrix over the word's fenceposts comes from its children's by regex_node_step. Star is the full closure, not a bounded unrolling, so membership is decided rather than searched. Two expressions agreeing on all words up to some length are not shown equal.

w ∈ L(r) ⇔ M_root[0, |w|] = 1

Signature

regex_match(kind: i64[K], sym: i64[K], left: i64[K], right: i64[K], word: i64[L]) → 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 each node's spans as Python sets, star by a fixed point in exact rational arithmetic, on all 40 test cases.
All 40 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

regex_node_step

Called by

—

sha256:538375e3c5c3b720d319b9e4f4e6aca485c74de6383472e4f34a9b26f7761943

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_match · Ω:regex_match
Pins: sha256:be42355b1b76010b03cf9bf34fe2fcc69af5d560d7e74fde65e0ded022fa3eb7this graph and the 3 it reaches through calls
Evidence: sha256:92babee3c87f47ef5130f754e2f02dd02a3610e454a607b2258ddbad3ec7630dthe 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.