is_reduction

std.sets.is_reduction · Level L3

Whether a total map f from a finite input set of problem A to one of problem B is a many-one reduction A ≤ₘ B, as 1 or 0: x ∈ A exactly when f(x) ∈ B, both directions checked for every x (yes-instances alone are not enough); and the first x where it fails. If A ≤ₘ B and B is decidable, computing f and then B's decider decides A; the converse does not hold. A finite table proves the reduction on that finite domain only.

x ∈ A ⇔ f(x) ∈ B ∀x

Signature

is_reduction(A: f64[n], B: f64[k], f: i64[n]) → f64[], 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 A[x] against B[f(x)] for every x in exact rational arithmetic, on all 40 test cases.
All 80 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

—

sha256:2a68118223dd32ca73a4e51ce744e5744cb644197a9590cc94638e568627f4c5

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.is_reduction · Ω:is_reduction
Pins: sha256:bbb29f35659207ec1aad609cbcfae27807866d05afdecb1030d23c5056a61a29this graph alone
Evidence: sha256:78bdcf021c39988295f9b69c31985821c3c8cef04f0b253755d900d0a1e6858bthe 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.