closure

std.topology.closure · Level L1

The closure of a subset A in a finite topology, as a 0/1 mask: the intersection of all the closed sets containing A, the smallest closed superset of A, computed as X \ int(X \ A).

cl A = X \ int(X \ A)

Signature

closure(tau: f64[m, n], A: f64[n]) → f64[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 complement of the interior of the complement in exact rational arithmetic, on all 40 test cases.
All 141 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

interior

Called by

boundary

sha256:b8be6456dd89c40cd4a5cdaff579a7a6f80fabc9f6a5f72c940b26c9c2c20ecc

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

Control handle

Symbol: Ω:std.topology.closure · Ω:closure
Pins: sha256:e13d5905618251781a8448b814157b357edec88b1608983cbe2cf56280fe77f3this graph and the 1 it reaches through calls
Evidence: sha256:bc29ef48c22bd0b7702c818648269fb9d82c8ce745b6e5a162e7c1fd61390aa7the 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.