is_function
std.sets.is_function · Level L1Whether a finite relation R from A to B is a (total) function, as 1 or 0: every a relates to exactly one b. The codomain B need not be the range.
∀a ∃! b: aRb
Signature
is_function(R: f64[a, b]) → 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
every row has exactly one 1in 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
—
Called by
—
sha256:a955be4bdd96b1a0b590fb3d368822805d8e4deb8b213ba832e5189afea2245cThe 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_function · Ω:is_function
- Pins
sha256:2a4375cf977404fb1881b0bdfbf1db11ed5e7429e11a6343535695ea69da532athis graph alone- Evidence
sha256:4bf5bf2a45cf5c7556f03ae08f2ebc86458411c06377005db4064f1bd1b3e513the 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.