is_topology

std.topology.is_topology · Level L3

Whether a finite family of subsets is a topology, as 1 or 0: all four axioms of topology_axioms hold.

[all topology axioms]

Signature

is_topology(tau: f64[m, n]) → 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 all four axioms 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

topology_axioms

Called by

—

sha256:9a5cda3e8922ff9b850b0db8a20e9054b74684caa307ca6adf9285cf40bf4952

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.is_topology · Ω:is_topology
Pins: sha256:90c81d6d145fd7bae50b9cf49e3150bb54a8747aacb8928934fd069980a431ecthis graph and the 1 it reaches through calls
Evidence: sha256:6f0a26f486e1cc45e0fea309896050947ad0cc5f61d39d8d76d84c1f67db6b92the 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.