connectives

std.sets.connectives · Level L1

The truth values of the classical connectives, elementwise on truth values 0 and 1: ¬P, P ∧ Q, P ∨ Q, P → Q (false only when P is true and Q false) and P ↔ Q.

¬P, P ∧ Q, P ∨ Q, ¬P ∨ Q, [P = Q]

Signature

connectives(p: f64[n], q: f64[n]) → f64[n], f64[n], f64[n], 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 truth tables in exact rational arithmetic, on all 40 test cases.
All 805 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

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Called by

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sha256:67bef7713d4aa67c5cfa11b9803c817c601ed0e52f98ad7c9df6a750b9143f22

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.connectives · Ω:connectives
Pins: sha256:459e0b16505f3cd14fcd96a10a0d3fe3f469a703177517ac8e83fdda7d1b9117this graph alone
Evidence: sha256:c620f819a17c264d3d9c5b683fd36758fc91cb2e96142f76474e8c390a21cf24the 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.