is_subset
std.sets.is_subset · Level L1Whether A ⊆ B for subsets of one finite universe, as 1 or 0: every element of A is in B. Also whether A is a proper subset (A ⊆ B, A ≠ B) and whether A = B (sets with the same elements are equal).
A ⊆ B ⇔ ∀x (x ∈ A ⇒ x ∈ B)
Signature
is_subset(A: f64[n], B: f64[n]) → f64[], 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
no element of A outside Bin exact rational arithmetic, on all 40 test cases. - All 120 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:e4fcebf85798125047fcb4fb8df732a5b6caaebf2c1859bb5268c84800ddf134The 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_subset · Ω:is_subset
- Pins
sha256:73ac4ebeb43dfda6b6dc3f36f606a4d7c74730c8ad7bc4d7a8d09b29ff5242b6this graph alone- Evidence
sha256:104f07f15b717055ba4c7cfa02043bbe238e4664571d03b041bea854099c79dbthe 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.