function_graph

std.sets.function_graph · Level L3

The graph G_f = {(a, f(a))} of a function f from A = 0 … n − 1 to B = 0 … k − 1 (B given by a carrier vector of length k, only its length read), as an n × k relation: (u, v) ∈ G_f exactly when v = f(u).

G_f = {(a, f(a)) : a ∈ A}

Signature

function_graph(f: i64[n], cod: f64[k]) → f64[n, k]

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 row a has its 1 at f(a) in exact rational arithmetic, on all 40 test cases.
All 525 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

—

sha256:051d07b40b8e95c31e9c36c81b6797d8d86d06af389c61084a9ee78da88018b1

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

Control handle

Symbol: Ω:std.sets.function_graph · Ω:function_graph
Pins: sha256:b8bffc6b54856610b6ba21a03f263538727eec5650e3a9e761f40bf9f18cf5bathis graph alone
Evidence: sha256:b212cb0fdaebb2f30a2790e5d7707da9618c9e0f3d05644fcf4dae5a0b2a5df7the 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.